In the following reaction, trace the
position of isotopic \( ^{18} \boldsymbol{O}: \)
\[
\begin{array}{c}
\mathbf{0} \\
\mathbf{c H}_{3}-\mathbf{C}-\mathbf{0}-\mathbf{H}+\mathbf{C H}_{3} \mathbf{C H}_{2}-\mathbf{0}-\mathbf{H}
\end{array} \longrightarrow \mathbf{C H}_{3}-\mathbf{I}-\mathbf{O}-\mathbf{C H}_{2} \mathbf{C H}_{3}+\mathbf{H}_{2} \mathbf{O}
\]
\( \mathbf{A} \cdot H_{2} O^{18} \)
B.
\[
\begin{array}{c}
C H_{3}-C_{\|}-O C H_{2} C H_{3} \\
^{18} O
\end{array}
\]
\( \mathbf{c} \)
\[
\begin{array}{c}
C H_{3}-\underset{\| \atop D}{C}-^{18} O C H_{2} C H_{3} \\
O
\end{array}
\]
D. can be in all three above


On the basis of Rutherford's model of an
atom, which subatomic particle is present it the nucleus of an atom?


Let \( \overrightarrow{\boldsymbol{a}}=\boldsymbol{a}_{1} \hat{\boldsymbol{i}}+\boldsymbol{a}_{2} \hat{\boldsymbol{j}}+\boldsymbol{a}_{3} \hat{\boldsymbol{k}}, \overrightarrow{\boldsymbol{b}}=\boldsymbol{b}_{1} \hat{\boldsymbol{i}}+ \)
\( \boldsymbol{b}_{2} \hat{\boldsymbol{j}}+\boldsymbol{b}_{3} \hat{\boldsymbol{k}}, \overrightarrow{\boldsymbol{c}}=\boldsymbol{c}_{1} \hat{\boldsymbol{i}}+\boldsymbol{c}_{2} \hat{\boldsymbol{j}}+\boldsymbol{c}_{3} \hat{\boldsymbol{k}} . \).If \( |\overrightarrow{\boldsymbol{c}}|= \)
1 and \( (\vec{a} \times \vec{b}) \times \vec{c}=0 \) then
\( \left|\begin{array}{lll}\boldsymbol{a}_{1} & \boldsymbol{a}_{2} & \boldsymbol{a}_{3} \\ \boldsymbol{b}_{1} & \boldsymbol{b}_{2} & \boldsymbol{b}_{3} \\ \boldsymbol{c}_{1} & \boldsymbol{c}_{2} & \boldsymbol{c}_{3}\end{array}\right|^{2}= \)
A . 0
в.
c. \( |\vec{a}|^{2}|\vec{b}|^{2} \)
D. \( |\vec{a} \times \vec{b}|^{2} \)


Which of the following can possibly be used as analgesic without causing addiction or any modification?
A. Morphine
B. Acetylsalicylic acid
c. Daizepam
D. Tetra hydrocatenol


Find out the current through \( 2 \Omega \) resistor
in the circuit shown in figure.
\( A, 2,5 A \)
B. 5 A
c. 1.25 A
D. 2 A


Solve :-
\( \left(3 x^{2}+5 x-9\right) \times(3 x-5) \)


Transporting pull arise mainly from
A. Roots
B. Leaves
c. Stems
D. All


Simplify by combining like terms:
\( -5 t^{2}-3 t^{2} \)


If a transversal intersects a pair of lines
in such a way that a pair of alternate angles are equal, then the lines are
A. parallel
B. perpendicular
c. transversal
D. none of these


The dissociation constant of a
substituted benzoic acid at \( 25^{\circ} C \) is
\( 1 \times 10^{-4} . \) The \( p H \) of a \( 0.01 M \) solution
of its sodium salt is:


Prove that \( ,(\vec{a} \cdot \vec{b})^{2} \leqslant|\vec{a}|^{2} \cdot|\vec{b}|^{2} \)


For the gas phase exothermic reaction,
\( A_{2}+B_{2} \rightleftharpoons C_{2} \) carried out in a closed
vessel, the equilibrium moles of \( A_{2} \) can be increased by:
This question has multiple correct options
A. increasing the temperature
B. decreasing the pressure
c. adding inertgas at constant pressure
D. removing some \( C_{2} \)


In the circuit shown in the figure, \( \boldsymbol{R}_{1}> \)
\( R_{2} . \) In which resistance the power
dissipated is greater?
\( A \cdot \ln R_{1} \)
\( \mathbf{B} \cdot \ln R_{2} \)
C. Equal in both
D. Uncertain


A constant torque of \( 25 \mathrm{N} \mathrm{m} \) is needed
to keep a wheel make 10 revolutions in 20 secs. The average power exerted by
this torque is
A . 19.6 watts
B. 62.8 Watts
c. 35 watts
D. 70 Watts


Find the real number \( \boldsymbol{x} \) if \( (\boldsymbol{x}-\mathbf{2} \boldsymbol{i})(\mathbf{1}+ \)
\( i) \) is purely imaginary.
\( A \cdot 2 \)
B. -2
\( c \cdot 4 \)
D. -4


The release of the energy stored in ATP
molecule takes place when it
A. Passes electrons to NADH.
B. Splits into a phosphate ion and ADP
c. Loses electrons and becomes ADP.
D. Breaks its bonds and loses all its phosphate ions
E. Breaks the bonds within one of its phosphate groups


The process involved in the RNA
formation on the DNA template is called
as
A. Translation
B. Transduction
c. Transcription
D. Transformaion


The inhibitory effect of malonic acid on succinic dehydrogenase enzyme is
A. Competitive inhibition
B. Non-competitive inhibition
c. Feedback inhibition
D. Inhibition due to end product


A spherical ball of lead \( 5 \mathrm{cm} \) in diameter
is melted and recast into three
spherical balls. The diameters of two of these balls are \( 2 \mathrm{cm} \) and \( 2(14.5)^{1 / 3} \mathrm{cm} \) Find the diameter of the third ball.
A. \( 8 \mathrm{cm} \)
B. \( 5 \mathrm{cm} \)
\( c .4 \mathrm{cm} \)
D. \( 1 \mathrm{cm} \)


Applications of \( \boldsymbol{O}_{3} \) are:
(a) It absorbs UV light. It is used as a disinfectant to purify drinking water,
since it destroys bacteria and viruses.
(b) Its advantage over \( C l_{2} \) for this purpose is that it avoids the unpleasant smell and taste of chlorine since any
excess \( 0_{3} \) soon decompose to \( O_{2} \)
A. Both are true.
B. (a) is true \& (b) is false.
c. (a) is false \( \& \) (b) is true.
D. None of these


Choose the correct statements among
the following:
This question has multiple correct options
A. Heat flow between two bodies is due to difference in
their temperatures.
B. The change in temperature in celsius and Kelvin scale are same.
C. Kelvin is the standard temperature scale.
D. Heat is cause while temperature is the effect.


Which of the following ray is not electromagnetic wave?
A. X-rays
B. \( \gamma \) -rays
c. \( \beta \) -rays
D. Heat rays


A car running with a velocity \( 72 \mathrm{kmph} \) on a level road, is stopped after travelling a distance of \( 30 \mathrm{m} \) after
disengaging its engine \( \left(g=10 m s^{-2}\right) \)
The coefficient of friction between the
road and the tyres is.
A. 0.33
B. 4.
c. 0.67
D. 0.8


A solid metal sphere of radius \( \boldsymbol{R} \) has a
charge \( +2 Q . \) A hollow spherical shell of
radius \( 3 R \) placed concentric with the
first sphere has net charge - \( \boldsymbol{Q} \)
A. The electric field between the spheres at a distance \( r \) from the centre of the inner sphere at \( R<r<2 R \) is
\( \frac{Q}{2 \pi \epsilon_{0} r^{2}} \)
3. The potential difference between the spheres is \( \frac{Q}{3 \pi \epsilon_{0} R} \)
c. The final distribution of charges if the spheres are joined by a conducting wire is zero on both inner and outer surfaces of the outer sphere
\( D \)
If the inner sphere is earthed, the charge on it is


A girl weighing 50 kg makes a high jump of \( 1.2 \mathrm{m} . \mathrm{What} \) is her kinetic energy at the highest point? \( \left(\boldsymbol{g}=\mathbf{1 0 m s}^{-\mathbf{2}}\right) \)
A. 6000
B. 600 J
c. 60 J
D. zero


Amy is 5 years older than her sister Julie. If the product of their ages is 6 Find the age of Julie.
A. 1 year
B. 2 years
c. 3 years
D. 4 years


Which of the following process does not involve heating?
A. Calcination
B. Smelting
c. Roasting
D. Levigation


\( \int_{-1}^{1} x|x| d x \) is equal to
A \( \cdot \frac{2}{3} \)
B. \( -\frac{2}{3} \)
c. 0
D. None of these


Figure shows a small loop carrying
current \( I . \) The curved portion is an arc of
a circle of radius \( R \) and the straight portion is a chord to the same circle subtending at an angle \( \theta . \) The magnetic
induction at center \( O \) is :
A . zero
B. always inward irrespective of the value of \( \theta \)
c. inward as long as \( \theta \) is less than \( \pi \)
D. always outward irrespective of the value of \( \theta \)


The sum of the first five terms an AP
and the sum of the first seven terms of
the same \( A P \) is 167 . If the sum of the first
ten terms of this \( A P \) is 235 , find the sum
of its first twenty terms.
A . -4230
в. 4230
c. -2430
D. -3240


The complex \( \left[\boldsymbol{P t}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4}\right]^{2+} \) has
. whrure :
A. square planer
B. tetrahedral
c. pyramidal
D. pentagonal


ff \( x^{18}=y^{21}=z^{28}, \) prove that 3
\( \mathbf{3} \log _{y} \boldsymbol{x}, \mathbf{3} \log _{z} \boldsymbol{y}, \mathbf{7} \log _{\boldsymbol{x}} \boldsymbol{z} \) form an A.P.


How will the image formed by a convex lens be affected if the upper half of the lens is wrapped with a black paper?
A. the size of the image is reduced to one-half
B. the upper half of the image will be absent
c. the brightness of the image is reduced.
D. there will be no effect.


For a gas deviation from ideal behaviour is maximum at:
\( \mathbf{A} \cdot 0^{0} C \) and \( 1.0 a t m \)
B. \( 100^{\circ} \mathrm{C} \) and 2.0 atm
c. \( -13^{0} \mathrm{C} \) and 1.0 atm
D. \( -13^{0} C \) and 2.0 atm


Consider the given reaction.
This question has multiple correct options
A. It is disproportionation reaction.
B. It is intramolecular redox reaction
C. \( O H^{-} \) is a reducing as well as oxidising agent
D. \( C H O-C H O \) is a reducing as well as oxidising agentt


Give an example of fibrous and globular
protein.


A person on a high protein diet is interested in the random variable \( X \), the
gain in weight in a week. Then the random variable is
A. not continuous
B. Not discrete
c. continuous
D. discrete


If the standard deviation is small, we
define a new variable known as
A. student's F-distribution
B. student's T-variable
c. chi-square distribution
D. student's G-variable


Name the Fungi


The area of cross-section of the wider
tube shown in figure is \( 800 \mathrm{cm}^{2} \). if mass of \( 12 k g \) is placed on the massless piston, the difference in heights h in the level of water in the two tubes is:
\( \mathbf{A} \cdot 10 \mathrm{cm} \)
B. \( 6 \mathrm{cm} \)
\( \mathrm{c} \cdot 15 \mathrm{cm} \)
D. \( 2 c m \)


The amplitude and the periodic time of a SHM are \( 5 c m \) and \( 6 s \) respectively. At a
distance of \( 2.5 \mathrm{cm} \) away from the mean position, the phase will be
\( ^{A} \cdot \frac{\pi}{3} \)
в.
c.
D. \( \frac{5 \pi}{12} \)


If \( K . E . \) body is increased by \( 100 \% . \) Then
\( \% \) change \( ^{\prime} \boldsymbol{P}^{\prime} \)
A . \( 50 \% \)
B. \( 41 \% \)
c. \( 10 \% \)
D. 20\%


A compound \( M X_{2} \) has observed
and normal molar masses 65.6 and 164
respectively. The apparent degree of
ionization of \( M X_{2} \) is:
A . \( 75 \% \)
B. \( 85 \% \)
c. \( 65 \% \)
D. \( 25 \% \)


Three resistor of \( 10 \Omega, 20 \Omega, \) and \( 30 \Omega \) are
connected in parallel in a circuit. Calculate the equivalent resistance.
A. \( 6000 \Omega \)
в. \( 0.017 \Omega \)
\( c \cdot 1 \Omega \)
D. \( 60 \Omega \)
E. \( 5.45 \Omega \)


Assertion
Decrease in the vapour pressure of
water by adding 1 mol of sucrose to one jg of water is higher to that produced by
adding 1 mol of urea to the same quantity of water at the same temperature.
Reason
Molecular mass of sugar is less than
that of urea.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Which of the following statements are
incorrect:
This question has multiple correct options
A. Molar volume of every gas at STP is \( 22.4 \mathrm{L} \)
B. Under critical states compressibility factor is 1
C. All gases will have equal value of average \( \mathrm{KE} \) at a given temperature
D. At absolute zero, KE is 3/2 R


When an article is bleached by \( S O_{2} \) it
loses its colour. The colour can be
restored by:
A. Exposure to air.
B. Heating.
c. Dilution.
D. None of these.


Answer the following questions:
1. Derive the mathematical expression
between molar mass of a non-volatile
solute and elevation of boiling point
2. State and explain van't Hoff-
Avogadro's law.


A paramagnet magnet behaves like a solenoid because both contain currents
in the form of
A. Circles
B. Parabola
c. Straight line
D. Ellipse


What types of isomer are
\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{5} \boldsymbol{B r}\right] \boldsymbol{S} \boldsymbol{O}_{4} \) and
\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{5} \boldsymbol{S O}_{4}\right] \boldsymbol{B r} ? \)


The number of \( \boldsymbol{P}-\boldsymbol{H} \) bond(s) in
\( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{2}, \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{3} \) and \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4} \)
respectively, is:
\( \mathbf{A} \cdot 2,0,1 \)
B. 1,1,1
c. 2,0,0
D. 2,1,0


In acid rain, pH of rain water is:
A. 7
в. 9.
c. more than 9.6
D. below 5.6


If \( \operatorname{cosec} x-c o t x=\frac{1}{3}, \) where \( x \neq 0 \)
then the value of \( \cos ^{2} x-\sin ^{2} x \) is
A \( \cdot \frac{16}{25} \)
в. \( \frac{9}{25} \)
\( c \cdot \frac{8}{25} \)
D. \( \frac{7}{25} \)


Two charged balls of the same radius and weight suspended on threads of equal length are immersed into a liquid having density of \( d_{1} \) and a dielectric constant \( K \)
The density \( d \) of the material of the balls for the angles of divergence of the
threads in the air and in the dielectric to
be the same is:
A \( \cdot \frac{K d}{K-1} \)
B. \( \frac{K-1}{K d} \)
C. \( \frac{d}{K-1} \)
D. \( \frac{K-1}{d} \)


If \( 0.01 M \) solution of an electrolyte has a
resistance of 40 ohms in a cell having a cell constant \( 0.4 \mathrm{cm}^{-1} \) then its molar
conductance would be:
A \( \cdot 10^{4} \)
B . \( 10^{3} \)
\( c \cdot 10^{2} \)
D. 10


Find the values of \( x \) and \( y, \) if \( \left[\begin{array}{cc}\boldsymbol{x}+\mathbf{1 0} & \boldsymbol{y}^{2}+\mathbf{2} \boldsymbol{y} \\ \mathbf{0} & -\mathbf{4} \\ \mathbf{3} \boldsymbol{x}+\mathbf{4} & \mathbf{3} \\ \mathbf{0} & \boldsymbol{y}^{\mathbf{2}}-\mathbf{5} \boldsymbol{y}\end{array}\right]= \)


Identical springs of steel and copper
\( \left(\boldsymbol{Y}_{\text {steel}}>\boldsymbol{Y}_{\text {copper}}\right) \) are equally stretched
then:
A. Less work is done on copper spring
B. Less work is done on steel spring
c. Equal work is done on both the springs
D. Data is incomplete


Give Reason: Racemic mixture is
optically inactive.


If for two events \( A \) and \( B, P(A \cup B)= \) \( \frac{1}{2}, P(A \cap B)=\frac{2}{5} \) and \( \operatorname{then} P\left(A^{c}\right)+ \)
\( \boldsymbol{P}\left(\boldsymbol{B}^{c}\right) \) equals
A \( \cdot \frac{4}{5} \)
в.
c. \( \frac{11}{10} \)
D. None of these


The characters of gymnosperms are
A. Seeds are naked
B. Fruits are absent
c. True carpel absent
D. All of the above


Which of the following is an incorrect
statements?
A. Blood group 'O' person have A and B antibodies in plasma.
B. Eosinophilia is associated with allergic infection.
C. RBCs contain carbonic anhydrase.
D. T wave of normal ECG represent of depolarization of ventricle.


(a) How does use of fuse wire protect electrical appliances?
(b) Name factors on which resistance depend?


The flow of electric pulse from one
neuron to another takes place from
A. Cell body to the dendrite through synapse
B. Axonal end to the dendrite through synapse
C. Dendrite to the other dendrite through synapse
D. None of the above


A conducting loop is placed in a uniform magnetic field with its plane perpendicular to the field. An emf is induced in the loop if
\( A \). it is translated
B. it is rotated about its axis
c. it is kept untouched for several minutes
D. it is cut into two pieces


Evaluate \( \int_{1}^{3}\left(x^{2}+3 x+e^{x}\right) d x \)


In a
multiplying the previous term by a constant.
A . arithmetic sequence
B. geometric series
c. arithmetic series
D. harmonic progression


A light ray travels at some angle (not head on) from water in a rectangular aquarium, through the glass side, and out into air. The indices if refraction for
water, glass, and air are \( 1.33, \) about 1.6 and \( 1.0, \) respectively.

Rank the material;s according to the angles of refraction made by the light ray with the normal in each, greatest
first.
A. air, water, glass.
B. air, glass, water.
C. water, air, glass.
D. water, glass, air
E. glass, water, air


One Newton is the force which produces an acceleration of -
A \( \cdot 1 m \cdot s^{-2} \) on a body of mass \( 1 \mathrm{gm} \)
B. \( 1 \mathrm{cm} . s^{-2} \) on a body of mass \( 1 \mathrm{kg} \)
c. \( 1 \mathrm{cm} . \mathrm{s}^{-2} \) on a body of mass \( 1 \mathrm{gm} \)
D. \( 1 m . s^{-2} \) on a body of mass \( 1 \mathrm{kg} \)


Human dentition is described as
A. Heterodont, diphyodont and thecodont
B. Heterodont, monophyodont and thecodont
C. Heterodont, diphyodont, thecodont and bundodont
D. Heterodont, polyphyodont and pleurodont


\( \int \frac{1}{\sqrt{1+x}} d x \)


The line \( 0 Q \) is called the :
A. reflected ray
B. incident ray
C . normal
D. refracted ray


A bar magnet has coercivity \( 4 \times \)
\( 10^{3} A m^{-1} . \) It is desired to demagnetize
it by inserting it inside a solenoid \( 12 \mathrm{cm} \) long and has 60 turns. The current that
should be sent through the solenoid is:
\( A \cdot 8 A \)
в. \( 10 A \)
\( c .12 A \)
D. \( 14 A \)


\( \theta \) toppr
Q Type your question
was isolated from the intestinal lining of a calf. Assays were undertaken to evaluate the activity of the enzyme sample. The substrate of lactase is the
disaccharide lactose. Lactase breaks a
lactose molecule in two, producing a glucose molecule and a galactose molecule. Two assays were carried out.
Assay
Lactose \( \begin{array}{llll}\text { concentration } & 15 & 15 & 15\end{array} \)
(\% w/v)
concentration of enzyme \( \operatorname{sample(s一u/v)} \)
Reaction rate u moleglucose \( \quad \) o \( \quad \) 25 \( \quad \) 50 \( s e c^{-1} m L^{-1} \)
Assay 2
Lactose \( \begin{array}{llll}\text { concentration } & \text { o } & \text { 5 } & \text { 15 }\end{array} \) (\% w/v)
concentra of enzyme \( \operatorname{sample}(\% v / v v \)
Reaction rate \mu mole glucose \( \quad \) o \( \quad 15 \quad \) 25 \( \sec ^{-1} m L^{-1} \)
What are the variables in each of the
two assays?
A. Assay1- Lactose concentration Assay 2 - concentration of enzyme sample
B. Assay 1- concentration of enzyme sample Assay 2 - Lactose concentration
c. Assay 1 - Lactose concentration Assay 2 - Lactose concentration
D. Assay 1- concentration of enzyme sample Assay 2- -concentration of enzyme sample


Commutative law states that
\( \mathbf{A} \cdot \vec{a}-\vec{b}=\vec{b} \vec{a} \)
В . \( \vec{a}+\vec{b}=\vec{b}-\vec{a} \)
c. \( \vec{a}+\vec{b}=\vec{b}+\vec{a} \)
D. None of the above


Which of the following quantities is zero on an average for the molecules of an ideal gas in equilibrium?
A. Kinetic energy
B. Momentum
c. Density
D. speedd


Which of the following is a sink for CO?
A. Haemoglobin
B. Microorganism presence in the soil
c. Ocean
D. Plant


Match the terms to these definitions.
gastrovascular cavity, coelom, tubewithin-a-tube body plan, pseudocoelom, sac body plan schizocoelom, metamorphosis, segmentation, aemocoel, homeothermic, poikilotherm
al, notochord, deuterostome, vertebral column,
protostome

Body cavity lying between the digestive tract and body wall that is completely lined by mesoderm.


\( \lim _{\boldsymbol{x} \rightarrow \mathbf{5}}\left(\frac{\sqrt{1-\cos (2 \boldsymbol{x}-\mathbf{1 0})}}{\sin (\boldsymbol{x}-\mathbf{5})}\right) \)
\( A \cdot-\sqrt{2} \)
B. \( \sqrt{2} \)
c. does not exist
D. none of these


In an interference pattern of two waves fringe width is \( \beta . \) If the frequency of source is doubled then fringe width will become:-
A \( \cdot \frac{1}{2} \beta \)
B. \( \beta \)
\( c \cdot 2 \beta \)
D. \( \frac{3}{2} \)


Protists having transverse and longitudinal groove in their theca are
A. Foraminiferans
B. Radiolarians
c. Diatoms
D. Dinoflagellates


Particles used in the Rutherford's
scattering experiment to deduce the
structure of atoms.
A. Had atomic number 2 and were fully ionised
B. Had atomic number 2 and were neutral
c. Had atomic number 4 and were fully ionised
D. Had atomic number 4 and were neutral


According to the assumption of Newlands, what is the total number of
elements in nature?


If \( \boldsymbol{H}_{2} \) He, \( \boldsymbol{O}_{2} \boldsymbol{N}_{2} \) travel with the same
velocity then the longest de-broglie wavelength should be associated with


Although \( \left[N i(C O)_{4}\right] \) has tetrahedral geometry, it is diamagnetic. Explain.


A ball is thrown vertically upwards with
a velocity of \( 10 m s^{-1} . \).IT returns to the
ground with a velocity of9 \( m s^{-1} \) 1. If \( g= \)
\( 9.8 m s^{-} 2, \) then the maximum height
attained by the ball is nearly ( assume a resistance to be uniform)
A . \( 5.1 \mathrm{m} \)
B. 4.1 \( m \)
c. \( 4.61 \mathrm{m} \)
D. \( 5 \mathrm{m} \)


Our eye lens is held in position by :
A. Rods and cones
B. Iris and pupil
c. ciliary muscles
D. None of these


Choose the correct answers from the
alternatives given

The term taxon refers to a taxonomic
group of:
A. family rank
B. order rank
c. class rank
D. any rank


State and explain the laws of limits friction.


For points \( \boldsymbol{A}(\mathbf{1},-\mathbf{1}, \mathbf{1}), \boldsymbol{B}(\mathbf{1}, \boldsymbol{3}, \mathbf{1}), \boldsymbol{C}(\mathbf{4}, \boldsymbol{3}, \mathbf{1}) \) and
\( D(4,-1,1) \) taken in order are the
vertices of
A. a parallelogram which is neither a square nor a rhombus
B. rhombus
c. as isosceles trapezium
D. a cyclic quadrilateral


Out of \( 1.0 \mathrm{g} \) dioxygen, \( 1.0 \mathrm{g} \) atomic oxygen and \( 1.0 \mathrm{g} \) ozone, the maximum number of oxygen atoms are contained
in
A. \( 1.0 g \) of atomic oxygen
B. 1.0 g of ozone
c. \( 1.0 g \) of oxygen gas
D. All contain the same number of atoms


Find the value of \( x \) in each of the
following figures?


The enthalpy of combustion of \( \mathrm{C}_{6} \mathrm{H}_{6}(l) \) is \( -3250 \mathrm{kJ} . \) When \( 0.39 \mathrm{g} \) of benzene is burnt in excess of oxygen in an open vessel, the amount of heat liberated is:
A. \( 16.25 \mathrm{KJ} \)
B. 33.50 KJ
c. 32.5 K
D. 65 K J


ffigure \( \square A B C D A B C D \) is a
parallelogram, what is the \( x \) -coordinate
of point B?
4
B.
\( c \)
\( D \)


What are the products when ethyl isopropyl ether is cleaved with
concentrated \( H I ? \)
A. Ethanol and 2-iodo-2-methylpropane
B. Ethanol and 2-methylpropane
c. lodoethane and isopropyl alcohol
D. lodoethane and 2-methylpropane


Pelvic girdle of rabbit consists of
A. llium, ischium and pubiss
B. llium, ischium and coracoid
c. coracoid, scapula and clavicle
D. Ilium, coracoid and scapula


\( \mathbf{P} \mathrm{Cl}_{3} \) on hydrolysis gives:
\( A \cdot H_{3} P O_{4} \)
в. \( \mathrm{H}_{3} \mathrm{PO}_{3} \)
c. \( P O C \)
D. \( \mathrm{H}_{3} \mathrm{PO}_{2} \)


Find \( (f . g)(2) \) when \( f(x)=x-1 \) and
\( \boldsymbol{g}(\boldsymbol{x})=-\mathbf{5} \boldsymbol{x}^{2}+\mathbf{1 4} \boldsymbol{x}+\mathbf{7} \)
A . 45
B. -39
c. 39
D. 15


For common emitter configuration of a
transistor, the collector voltage \( V_{c}= \)
\( 2 V \) and, base current changes from
\( 100 \mu A t o 200 \mu A, \) and collector
current changes from \( 5 \mathrm{mA} \) to \( 10 \mathrm{mA} \) The current gain is
A . 100
B. 25
\( c \cdot 125 \)
D. 50


Is the following equation quadratic? \( \mathbf{1 3}=-\mathbf{5} \boldsymbol{y}^{2}-\boldsymbol{y}^{\boldsymbol{3}} \)
A. Yes
B. No
c. Ambiguous
D. Data insufficient


Net magnetic field at the centre ofthe
circle 0 due to a current carrying
loop as shown in figure is \( \left(\boldsymbol{\theta}<\mathbf{1 8 0}^{\circ}\right) \)
A. zero
B. perpendicular to paper inwards
C. perpendicular to paper outwards
D. is perpendicular to paper inwards if \( \theta \leq 90^{\circ} \) and
perpendicular to paper outwards if \( 90^{0} \leq \theta<180^{\circ} \)


These are the organisms which are called prokaryotes.
A. Green algae, brown algae and red algae
B. Yeasts and other fungi
c. Mycoplasmas, bacteria, cyanobacteria
D. None of the above groups


At a rate of 10 p.c.p.a, what would be the interest for one year on \( \boldsymbol{R} \boldsymbol{s} . \boldsymbol{6} \boldsymbol{0} \boldsymbol{0} \boldsymbol{0} ? \)


n tne Tlgure (IIVIAGE
(a) \( \operatorname{Is} \angle 1 \)
adjacent to \( \angle 2 ? \)
(b) \( \operatorname{ls} \angle A O C \)
adjacent to \( \angle A O E \) ?
(c) Do \( \angle C O E \) and \( \angle E O D \) from linear
pair?
(d) Are \( \angle B O D \) and \( \angle D O A \)
supplementary?
(e) is \( \angle 1 \) vertically opposite to \( \angle 4 ? \)
(f) What is the vertically opposite angle
of \( \angle 5 ? \)


Name the following alkyl groups:
\( \left(\boldsymbol{C} \boldsymbol{H}_{3}\right)_{2} \boldsymbol{C H} \)


A thin uniform tube is bent into a circle
of radius \( r \) in the vertical plane. Equal volumes of two immiscible liquids,
whose densities are \( \rho_{1} \) and \( \rho_{2}\left(\rho_{1}>\rho_{2}\right) \)
fill half the circle. The angle \( \theta \) between
the radius vector passing through the common interface and the vertical is:
\( \boldsymbol{\theta}=\tan ^{-1}\left[\frac{\pi}{2}\left(\frac{\rho_{1}-\rho_{2}}{\rho_{1}+\rho_{2}}\right)\right] \)
B. \( \quad \theta=\tan ^{-1} \frac{\pi}{2}\left(\frac{\rho_{1}-\rho_{2}}{\rho_{1}+\rho_{2}}\right) \)
\( ^{\mathrm{C}} \theta=\tan ^{-1} \pi\left(\frac{\rho_{1}}{\rho_{2}}\right) \)
D. None of above


On dissolving smaller (less than 3M) amount of sodium metal in liquid ammonia at low temperature, which
one of the following does not occur?
A. Blue coloured solution is obtained
B. Ammoniated \( N a^{+} \) ions are formed in the solution.
c. Liquid ammonia becomes good conductor of electricity
D. Liquid ammonia remains diamagnetic.


Explain budding in hydra with the help of labelled diagrams.


Assertion: Diamagnetism is universal, it is present in all materials.

Reason: Field due to induced magnetic
moment is opposite to the magnetising
field
A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true and reason is not the correct explanation of assertion
c. If assertion is true but reason is false.
D. If both assertion and reason are false


The circuit shown below contains two
diodes each with a forward resistance
of \( 50 \Omega \) and
with infinite backward resistance. Find
the current through \( 150 \Omega \) resistor.
A. zero
B. \( 0.01 A \)
c. \( 0.02 A \)
D. 0.03 A


In a bag there are 6 white and 4 black
balls. Two balls are drawn one after
another without replacement.ff the 1 st ball is known to be white, the probability that the 2 nd ball drawn is also white is
\( A \cdot \frac{2}{9} \)
в. \( \frac{5}{9} \)
\( c \cdot \frac{8}{9} \)
D. \( \frac{8}{13} \)


When a potential difference \( \boldsymbol{V} \) is
applied across a conductor at a temperature \( \boldsymbol{T}, \) the drift velocity of electrons is proportional to
\( \mathbf{A} \cdot \sqrt{V} \)
в. \( V \)
c. \( \sqrt{T} \)
D. \( T \)


Find the mode of the following data in
each case:
14,25,14,28,18,17,18,14,23,22,14,18


Photooxidation of water results in the
formation of
\( \mathbf{A} \cdot \mathbf{H}^{+}, \mathbf{O}_{2}, \) ATP
B . H \( ^{+}, \mathrm{O}_{2}, \mathrm{e}^{-}, \) ATP
c. н \( ^{+}, 0_{2}, \) e \( ^{-} \)
D. None of the above


What is the feature found in all ortho-
para directing groups?
A. An oxygen is directly attached to the aromatic ring
B. The atom attached to the aromatic ring possess an unshared pair of electrons
C. The group has ability to delocalize the positive charge of the arenium ions
D. The atom directly attached to the aromatic ring is more electromagentic than carbon


Some salts, although containing two different metallic elements, give test for one of them in solution. Such salts are:
A. complex salt
B. double salt
c. normal salt
D. none of these


The difference between amylose and
amylopectin is
A. Amlyopetin have \( 1 \rightarrow 4 \alpha \) -linkage and \( 1 \rightarrow 6 \beta \) - linkage
B. Amlyopetin have \( 1 \rightarrow 4 \alpha \) -linkage and \( 1 \rightarrow 6 \alpha \) - linkage
C. Amylose is made up of glucose and galactose
D. Amylose have \( 1 \rightarrow 4 \alpha \) -linkage and \( 1 \rightarrow 6 \beta \) - linkage


State the principle of working of a moving coil galvanometer giving its labelled diagram. Increasing the current sensitivity of a galvanometer may not necessarily increase its voltage sensitivity. Justify this statement.


The turn ratio of transformers is given as \( 2: 3 . \) If the current through the
primary coil is \( 3 A \), thus calculate the
current through load resistance.
A . \( 1 A \)
в. \( 4.5 A \)
\( c .2 A \)
D. \( 1.5 A \)


Choose the correct statement(s).
This question has multiple correct options
A. Aldrin is used as a pesticide.
B. The maximum permissible limit of nitrate in water is 50 ppm.
C. The maximum permissible limit of fluoride is 6 ppm.
D. All of the above


Water drops fall from a tap on to the floor \( 5.0 \mathrm{m} \) below at regular intervals of time. The first drop strikes the floor
when the fifth drop beings to fall. The height at which the third drop will be from ground, at the instant when the first drop strikes the ground is (Take \( \boldsymbol{g}=\mathbf{1 0 m s}^{-2} \mathbf{j} \)
A . \( 1.25 m \)
B. \( 2.15 m \)
c. \( 2.75 m \)
D. \( 3.75 m \)


If object having total energy \( \boldsymbol{E}_{1} \) is
having the same \( P E \) curve as shown in
the figure, then
\( \mathbf{A} \cdot r_{0} \) is the maximum distance of the object from the
earth's centre
B. the object and the earth system is bounded one
C. the \( K E \) of the object is zero when \( r=r_{0} \)
D. all the above


Which of the following sometimes requires initiation from a neutron?
A. nuclear fission
B. radiation therapy
c. radioactive tracer
D. radioactive carbon dating


A mixture of 3.8 moles of \( \mathrm{NO} \) and 0.924
moles of \( C O_{2} \) was allowed to react in a \( 1.0 \mathrm{L} \) container.The equilibrium mixture
contains 0.124 mole of \( C O_{2} . \) Calculate
\( K_{c} \) for the reaction.
\( N O_{(g)}+C O_{2(g)} \rightleftharpoons N O_{2(g)}+C O_{(g)} \)


Which of the following molecules
possess same shape as \( \boldsymbol{H}_{3} \boldsymbol{O}^{+} \) ? This question has multiple correct options
\( \mathbf{A} \cdot N H_{4}^{+} \)
в. \( N H_{3} \)
\( \mathrm{c} . P H_{3} \)
D. \( C H_{4} \)


The angular frequency for which he detects maximum current in the circuit
is
\( \mathbf{A} \cdot 10^{5} / 7 r a d / s \)
B . \( 10^{4} r a d / s \)
c. \( 10^{5} r a d / s \)
D. \( 10^{4} / 7 r a d / s \)


Give \( I U P A C \) name of following
compound.
\( \boldsymbol{C H}_{3}-\boldsymbol{C H}=\boldsymbol{C H}-\boldsymbol{C} \equiv \boldsymbol{C H} \)


The reactions of Kreb's/citric acid cycle
take place
A. In the cytoplasm
B. In ER
c. In matrix of mitochondria
D. on the surface of mitochondria


\( P(-2,3), Q(3,7) . \) The point \( A \) on the \( x \) axis for which \( \mathbf{P A}+\mathbf{A Q} \) is least is
\( ^{\mathrm{A}} \cdot\left(\frac{-1}{2}, 0\right) \)
в. \( \left(\frac{1}{2}, 0\right) \)
c. \( \left(0, \frac{-1}{2}\right) \)
D. \( \left(0, \frac{1}{2}\right) \)


Knot like bodies known as 'nodules'
found in the root of groundnut plant are produced by
A. Azospirillum
B. Azotobacter
c. Pseudomonas
D. Rhizobium


Which of the following causes decrease in blood pressure?
A. Renin
B. Angiotensin
c. ANF
D. None of the above


The table below
shows the daily expenditure on food of 30 households in a locality
Daily expenditure
\[
\begin{array}{lll}
100- & 150- & 200- \\
150 & 200 & 250
\end{array}
\]
(in Rs.)
No. of households
6
Find the mean and the median daily
expenditure on food.


Which of the following is correct
statement?
A. Conductivity \& molar conductivity of solution increase on dilution
B. Voltage of button cell remain unchanged through out its life time
C. On electrolysis of aqueous \( C u S O_{4} \) using platinum
electrode its concentration \( \left[C u^{2+}\right] \) remain constant
D. On electrolysis of aqueous \( N a C l \), solution becomes acidic


A coil of one turn is made of a wire of
certain length and then from the same length a coil of two turns is made. If the same current is passed in both the cases, then the ratio of the magnetic inductions at their centres will be:
A .2:
B. 1: 4
\( c \cdot 4: \)
D. 1: 2


The plots of \( \frac{1}{X_{A}} v s \cdot \frac{1}{Y_{A}}\left(\text { where }, X_{A} \text { and } Y_{A}\right. \) are the mole fraction of liquid \( A \) in liquid and vapour phase respectively) is linear with slope and intercepts respectively
\( ^{\mathbf{A}} \cdot p_{A}^{0} / P_{B}^{0} \) and \( \frac{\left(P_{A}^{0}-P_{B}^{0}\right)}{P_{B}^{0}} \)
в. \( \quad P_{A}^{0} / P_{B}^{0} \) and \( \frac{\left(P_{B}^{0}-P_{A}^{0}\right)}{P_{B}^{0}} \)
\( ^{\mathbf{c}} P_{B}^{0} / P_{A}^{0} \) and \( \frac{\left(P_{A}^{0}-P_{B}^{0}\right)}{P_{B}^{0}} \)
\( P_{B}^{0} / P_{A}^{0} \) and \( \frac{\left(P_{B}^{0}-P_{A}^{0}\right)}{P_{B}^{0}} \)


Which element is largest in size?
A . \( C o \)
в. \( N i \)
c. \( C u \)
D. \( Z n \)


The molal lowering of vapour pressure( in cm to nearest integer) for \( \boldsymbol{H}_{2} \boldsymbol{O} \) at
\( 100^{\circ} \mathrm{C} \) is


Which of the following elements is added to turn artificial diamond into
semi conductors?
A. Beryllium
B. Boron
c. Magnesium
D. Calcium


Derive \( v^{2}-u^{2}=2 a s ? \)


The \( E_{\text {cell }}^{o} \) for \( \boldsymbol{C u}\left|\boldsymbol{C} \boldsymbol{u}^{2+} \| \boldsymbol{A} \boldsymbol{g}^{+}\right| \boldsymbol{A} \boldsymbol{g} \) is:
A . \( 0.415 V \)
в. \( 0.374 V \)
c. \( -0.415 V \)
D. \( -0.374 V \)


Consider the function \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \sin \left(\sin ^{-1} 2 x\right)+\sec \left(\sec ^{-1} 3 x\right)+ \)
\( \tan \left(\tan ^{-1} 4 x\right) \) and \( g(x)=9 x, \) then
which of the following is correct? This question has multiple correct options
A \( \cdot \) fog \( (x) \) and \( g o f(x) \) are equal function
B . \( f(x) \) is an odd function
C. Number of integers in range of \( f(x) \) are 4
D. Number of integers in domain of \( f(x) \) are 2


Which one of the following does not exist?
A. \( X e O F_{4} \)
в. \( N e F_{2} \)
c. \( X e F_{2} \)
D. \( X e F_{6} \)


Among the following which one has largest atomic radius?
A \( . C l \)
в. \( F \)
c. \( L i \)
D. Ne
E . \( N a \)


An AP consists of 50 terms of which \( 3^{r d} \)
term is 12 and the last term is \( 106 . \) Find
the \( 29^{t h} \) term.


State whether true or false:
The deviation produced by a prism is independent of the angle of incidence and is same for all the colours of light.
A . True
B. False


Tuning fork causes them to vibrate and produce sound. This is due to
A. the two metal prongs of that tuning fork
B. the length of the prongs of that tuning fork
c. the speed of the molecules hit the tuning fork
D. both A and


Mention catalyst in the following reaction:
\( \boldsymbol{K} \boldsymbol{C l} \boldsymbol{O}_{3} \rightarrow \boldsymbol{K} \boldsymbol{C l}+\boldsymbol{O}_{2} \)
A. \( M n O_{2} \)
в. \( F e C l_{3} \)
c. \( P d C l_{2} \)
D. \( Z n O / C u O \)


Comment on the above reaction.


Find \( \overrightarrow{\boldsymbol{P}} \cdot \overrightarrow{\boldsymbol{Q}} \)
where \( \overrightarrow{\boldsymbol{P}}=2 \hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} \) and \( \overrightarrow{\boldsymbol{Q}}=\hat{\boldsymbol{i}}-\hat{\boldsymbol{j}}+ \)
\( \boldsymbol{2} \hat{\boldsymbol{k}} \)


When did a major Tsunami occur in the
Indian ocean?
A \( \cdot \) on \( 26^{t h} \) December, 2004
B. On \( 26^{\text {th }} \) July, 2004 .
c. on \( 26^{\text {th }} \) December, 2001
D. on \( 26^{t h} \) July, 2001


A drop of oil of mass 2 ng is kept stationary in between two plates \( 2 \mathrm{cm} \) apart. A potential difference is 2 kV is applied. The number of electrons it gained is
A . 16
B. 160
\( c \cdot 4 \)
D. 1600


The number of lines which are equally
inclined to the axes is
\( A \cdot 2 \)
B. 4
\( c \cdot 6 \)
D. 8


Which option is correct for the region labelled as \( A \) and \( B \) in the given diagram of transverse section of gut?
A. A-Mucosa B-Submucosa
B. A-Nerve B-Circulatory muscle
c. A-Villi B-Mucosal gland
D. A-Longitudinal muscle B-Muscularis mucosa


Which is NOT a commercial method for
preparation of Dihydrogen?
A. Lane's Process
B. Thermal cracking of natural gas
c. Reacting metals with dilute mineral acids
D. syngas-Bosch Process


Which of the following statements is/are wrong about pericyclic reaction?
This question has multiple correct options
A. It is intramolecular cyclisation of acyclic compound.
B. It is intermolecular cyclisation of acyclic compound.
C . It proceeds via concerted mechanism in which breaking and formation of bonds take place simulataneusly.
D. It Proceeds via free-radical mechanism.


During electrolysis bonds in \( \boldsymbol{H}_{2} \boldsymbol{O} \) are
broken 18 times faster than \( D_{2} O \)
A. True
B. False


What would happen when a solution of potassium chromate is treated with an excess of dilute nitric acid?
This question has multiple correct options
A \( \cdot C r_{2} O_{7}^{2-} \) and \( H_{2} O \) are formed
B . \( C r O_{7}^{2-} \) is reduced to +3 state of \( C r \)
\( \mathrm{c} \cdot \mathrm{Cr} \mathrm{O}_{7}^{2-} \) is oxidized to +7 state of \( \mathrm{Cr} \)
D. \( C r^{3+} \) and \( C r_{2} O_{7}^{2-} \) are formed


If we strike a water-filled bowl with
spoon, then why there is variation in the sound produced due to change in water
level of the bowl?
A. due to change in pitch
B. due to change in amplitude
c. both A and B
D. None of the above


\( \int_{-\pi / 2}^{\pi / 2} \log \left(\frac{2-\sin \theta}{2+\sin \theta}\right) d \theta=? \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D. -


\( \boldsymbol{P} \boldsymbol{Q} \boldsymbol{R} \boldsymbol{C} \) parallelogram, \( \boldsymbol{Q} \boldsymbol{M} \) is the height
form \( Q \) to \( R C \) and \( Q N \) is the height from \( Q \) to \( P S . \) If \( R C=12 \mathrm{cm} \) and
\( Q M=7.6 \mathrm{cm} . \) Find
(a) the area of the parallegram \( P Q R C \)
\( (b) Q N \) if \( P S=8 c m \)


The complex formed by a pair of synapsed chromosomes is called as
A. Kinetochore
B. Bivalent
c. Axoneme
D. Equatorial plate


If the number of moles of adenine in
DNA of E.coli sample is \( 4,65,000, \) the number of moles of guanine present in its DNA is:
\( \left[\text { Given: } \frac{\boldsymbol{A}+\boldsymbol{T}}{\boldsymbol{G}+\boldsymbol{C}}=\mathbf{0 . 9 3}\right] \)
A. 5,00,000
B. 4,65,000
c. 3,65,000
D. 9,30,000


Eutrophication may be due to
A. Runoff from agriculture
B. Pollution from septic systems
C . Sewage sludge spreading
D. All of the above


Find the remainder
\( \left(x^{2}+3 x+9\right) \div(x-3) \)


In following pairs of triangles, find the
pairs which are congruent? Also, write
the criterion of congruence


Determine whether \( (x+1) \) is a factor of
the polynomial:
\( \boldsymbol{x}^{3}-\mathbf{1 4 x}^{\mathbf{2}}+\mathbf{3 x + 1 2} \)


Find the respective terms for the
following APs
\( a_{1} 2 ; a_{3}=26 \) find \( a_{2} \)


\( A B C D \) is a square, \( X \) and \( Y \) are points
on sides \( A D \) and \( B C \) respectively, such that \( A Y=B X . \) Prove that.
\( \angle B A Y=\angle A B Y \)


A milkman adds a very small amount of baking soda to fresh milk.
(a) Why does he shift the \( p H \) of the
fresh milk from 6 to slightly alkaline?
(b) Why does this milk take a long time
to set as curd?


Alcohols are isomeric with:
\( A \). acids
B. ethers
c. esters
D. aldehydes


From the following figure find value of
\( \boldsymbol{X} \boldsymbol{Y} \) if \( \angle \boldsymbol{A} \boldsymbol{O} \boldsymbol{B}=\angle \boldsymbol{X} \boldsymbol{O} \boldsymbol{Y} \)
3. 11
\( r \)
2


A hammer weighing of \( 1 \mathrm{kg} \) moving with the speed of \( 10 \mathrm{m} \mathrm{s}^{-1} \) strikes the head
of a nail driving it \( 10 \mathrm{cm} \) into a wall.
Neglecting the mass of the nail, calculate the acceleration during the
impact
A. \( 400 \mathrm{m} \mathrm{s}^{-2} \)
B. \( 500 \mathrm{m} \mathrm{s}^{-2} \)
c. \( 600 \mathrm{m} \mathrm{s}^{-2} \)
D. \( 700 \mathrm{m} \mathrm{s}^{-2} \)


Find the principal value of:
\( \operatorname{cosec}^{-1}\left(2 \tan \frac{11 \pi}{6}\right) \)


The value of \( \tan \left[\frac{1}{2} \cos ^{-1}\left(\frac{2}{3}\right)\right] \) is
A \( \cdot \frac{1}{\sqrt{5}} \)
B. \( \sqrt{\frac{3}{10}} \)
c. \( \sqrt{\frac{5}{2}} \)
D. \( 1-\sqrt{\frac{5}{2}} \)


A 20 m deep well with diameter 7 m is dug up and the earth from digging is evenly spread out to form a platform 22 \( m \times 14 m \) The height of the platform is
\( \mathbf{A} \cdot 2.5 \mathrm{m} \)
B. \( 1.5 \mathrm{m} \)
c. \( 1 \mathrm{m} \)
D. 2 m


The equilibrium concentration of \( \boldsymbol{X}, \boldsymbol{Y} \)
and \( Y X_{2} \) are 4,2 and 2 moles respectively for the equilibrium \( 2 X+ \)
\( \boldsymbol{Y} \rightleftharpoons \boldsymbol{Y} \boldsymbol{X}_{2} . \) The value of \( \boldsymbol{K}_{c} \) is:
A. 0.625
B. 0.0625
c. 6.25
D. 0.00625


The mechanism of the reaction
\( \mathbf{2} N \boldsymbol{O}+\boldsymbol{O}_{2} \rightarrow \mathbf{2} \boldsymbol{N} \boldsymbol{O}_{2} \) is:
\( N O+N O \underset{k_{-1}}{\Gamma} N_{2} O_{2}(\text { fast }) ; N_{2} O_{2}+ \)
\( O_{2} \stackrel{k_{2}}{\longrightarrow} 2 N O_{2}(s l o w) \)
The rate constant of the reaction is:
\( \mathbf{A} \cdot k_{2} \)
B. \( k_{2} k_{1}\left(k_{-1}\right) \)
\( \mathbf{c} . k_{2} k_{1} \)
D \( \quad k_{2}\left(\frac{k_{1}}{k_{-1}}\right) \)


Which of the following statement(s) is/are true or false?
\( S_{1}: \) In organometallic compounds, carbon is bonded to metals directly.
\( S_{2}: \) Complexes having \( d^{0} \) or \( d^{10} \) configuration of metal ions are always diamagnetic.
\( \boldsymbol{S}_{3}: \) Extra stability of metal carbonyls is
explained by synergic bonding.
\( S_{4}: \ln F e(C O)_{5}, \) the Fe-C bond
possesses both \( \sigma \) and \( \pi \) characteristics.
A. TTTT
B. TTFF
c. FTFT
D. FTTT


Mark the correct statement(s) w.r.t. a
concave spherical mirror
This question has multiple correct options
A. For real extended object, it can form a diminished virtual image
B. For real extended object, it can form a magnified virtual image
C. For virtual extended object, it can form a diminished real image
D. For virtual extended object, it can form a magnified real image


Major product contains how many ester
groups?


The rational number of the form \( \frac{p}{q}, q \neq \) \( 0, p \) and \( q \) are positive integers, which represents \( 0.1 \overline{34} \) i.e., \( (0.1343434 \ldots . .) \) is
A \( \cdot \frac{134}{999} \)
в. \( \frac{134}{990} \)
c. \( \frac{133}{999} \)
D. \( \frac{133}{990} \)


How was the of cloning sheep Dolly achieved? What was the purpose of cloning this sheep?


The force required to just move a body up the inclined plane is double the force required to just prevent the body from sliding down the plane. The coefficient of friction is \( \mu . \) The inclination \( \theta \) of the
plane is:
\( A \cdot \tan ^{-1} \mu \)
B. \( \tan ^{-1} \mu / 2 \)
\( \mathbf{c} \cdot \tan ^{-1} 2 \mu \)
D. \( \tan ^{-1} 3 \mu \)


Factorize \( 4 x^{2}-3 x-7 \)


While digging if fossils are found at deeper layers of the earth, we can conclude that
A. Fossil is the most recent
B. Fossil is very old may be more than thousand years
c. Fossil age cannot be computed
D. None of the above


For what value of \( k,(4-k) x^{2}+ \)
\( (2 k+4) x+(8 k+1)=0 \) is a perfect
square:


Which occurs to minimum extent in
nature?
\( \mathbf{A} \cdot H g S \)
в. \( H_{2} \).
\( \mathrm{c} \cdot B i_{2} S_{3} \)
\( \mathrm{D} \cdot \mathrm{CS}_{2} \)


What do you understand by
Reverberations in relation to sound
waves?


Which of the following is an organic polymer?
A . Glass
B. Rayon
c. silicone rubbers
D. All


Which of the following is a nuclear process that results in no change in the
mass number and atomic number of a
nuclide?
A. Gamma decay
B. Nuclear fusion
c. Alpha decay
D. Positron emission
E. Nuclear fission


A sum \( R s .1000 \) is invested at \( 8 \% \) per
annum simple interest. Calculate the
interest at the end of each year. Show that these interest form an AP. Using this fact, find the interest at the end of
30 years


A current-carrying circular coil of magnetic moment \( M \) is situated in a
magnetic field \( B \). The work done in
deflecting it from an angle \( 0^{\circ} \) to \( \theta^{\circ} \) will
be :
\( A . M B \)
В. \( M B(1-\cos \theta) \)
\( \mathrm{c} \cdot-M B \)
D. \( M B(1-\sin \theta) \)


What is cellulose diacetate?
A. Semisynthetic polymer
B. Plasticizer
c. Natural polymer
D. synthetic polymer


If the egg of an organism has 40 pg of DNA in its nucleus, how much DNA
would a diploid cell of same organism have in pachytene(X), diakinesis(Y) and anaphase-I(Z)?
A. \( x=160 \) pg, \( Y=160 \) pg, \( z=160 p g \)
B. \( \mathrm{x}=80 \mathrm{pg}, \mathrm{Y}=80 \mathrm{pg}, \mathrm{Z}=160 \mathrm{pg} \)
c. \( x=160 p g, Y=80 \) pg, \( z=160 p g \)
D. \( x=80 \) pg, \( Y=160 p g, z=80 \) pg


Withdrawal of which of the following
hormones is the immediate cause of
menstruation?
A. Estrogen
B. FSH
c. FSH-RH
D. Progesterone


Given balanced equations for the
following:
Preparation of ethanol from monochloroethane and aq. sodium
hydroxide.


Find the value of \( p \) if the points
\( (2,1),(p,-1) \) and (-1,3) are collinear.


The given figure shows a parallelogram
ABCD.E is a point in \( A D \) and \( C E \)
produced meets BA produced at point \( F \)
If \( A E=4 c m, A F=8 \mathrm{cm} \) and \( A B=12 \)
cm. find the perimeter of the parallelogram ABCD.
\( A \cdot 48 \mathrm{cm} \)
B. \( 44 \mathrm{cm} \)
\( c .60 \mathrm{cm} \)
D. \( 50 \mathrm{cm} \)
E . \( 45 \mathrm{cm} \)
\( F .54 \mathrm{cm} \)
G. none of the above


Which of the following reactions do not
involve oxidation or reduction:
A \( \cdot 2 R b+2 H_{2} O \rightarrow 2 R b O H+H_{2} \)
в. \( 2 C u I_{2} \rightarrow 2 C u+I_{2} \)
c. \( N H_{4} C l+N a O H \rightarrow N a C l+N H_{3}+H_{2} O \)
D. None of these.


The finches that populate the
Galapagos islands are genetically much more closely related to a species of ground finch found on the mainland in
South America than they are to a species of finch found on the mainland
in North America. This observation
suggests that
A. The finches on the Galapagos islands have descended directly from the finches in South America.
B. The climatic environment on the Galapagos islands is more similar to the climatic environment in South America than North America
C. The Galapagos islands were once physically connected to the continent of South America
D. The finches on the Galapagos islands and the finches on the mainland of South America are experiencing convergent evolution


If \( \boldsymbol{y}=\boldsymbol{a}+\frac{\boldsymbol{b}}{\boldsymbol{x}}, \) where \( \boldsymbol{a} \) and \( \boldsymbol{b} \) are
constants, and if \( \boldsymbol{y}=\mathbf{1} \) when \( \boldsymbol{x}=-\mathbf{1} \)
and \( y=5 \) when \( x=-5, \) then \( a+b \)
equals.
A . -1
B.
c.
D. 10
E. 11


A physical quantity \( A \) is related to four observable \( a, b, c \) and \( d \) as follows, \( A= \) \( \frac{a^{2} b^{3}}{c \sqrt{d}}, \) the percentage errors of
measurement in \( a, b, c \) and \( d \) are \( 1 \%, 3 \% \) \( 2 \% \) and \( 2 \% \) respectively. What is the percentage error in the quantity \( \boldsymbol{A} \) ?
A . \( 12 \% \)
B . \( 7 \% \)
c. \( 5 \% \)
D. 14\%


If \( f(x)=\left|\begin{array}{ccc}\cos x & x & 1 \\ 2 \sin x & x^{2} & 2 x \\ \tan x & x & 1\end{array}\right|, \) then
\( \lim _{x \rightarrow 0} \frac{f^{\prime}(x)}{x} \)
A. Exists and is equal to -2
B. Does not exist
C. Exist and is equal to 0
D. Exists and is equal to 2


If the length of a rectangle is two times its breadth and area is \( 228 \mathrm{cm}^{2} \), then
length and breadth are respectively
A \( .20 \mathrm{cm}, 10 \mathrm{cm} \)
в. \( 12 \mathrm{cm}, 24 \mathrm{cm} \)
c. \( 24 c m, 12 c m \)
D. \( 16 \mathrm{cm}, 18 \mathrm{cm} \)


Calculate the overall complex dissociation equilibrium constant for the \( C u\left(N H_{3}\right)_{4}^{2+} \) ion, given that \( \beta_{4} \) for
this complex is \( 2.1 \times 10^{3} \)


The melting point of ice when pressure increases.
A. increases
B. decreases
c. remains same
D. none of these


\( \mathbf{n}\left[\boldsymbol{A} \boldsymbol{g}\left(\boldsymbol{C} \boldsymbol{N}_{2}\right)\right]^{-}, \) the number of \( \boldsymbol{\pi} \) bonds
is :
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. 6


State true or false:
Every rational number is a whole
number.
A. True
B. False


Which of the following statement about Mendeleev's periodic table is incorrect?
A. He leftgaps for some elements which were discovered later and correctly predicted the properties of them
B. Inert gases could be placed in a new group without disturbing the existing order
C. He arranged the elements according to the properties of elements
D. The properties of the elements are the periodic function of their atomic numbers


Q Type your question.
\( B \)
\( \mathbf{C} \)
\( D \)


Dispersion medium in which dispersed
phase is present. This consists of continuously interlinked molecules.
A. True
B. False


Let \( a, b \) be non-zero real numbers. The
equation
\( \left(a x^{2}+b y^{2}+c\right)\left(x^{2}-5 x y+6 y^{2}\right) \)
represents
A. four straight lines, when \( c=0 \) and \( a, b \) are of the same \( \operatorname{sign} \)
B. two straight lines and a circle, when \( a=b \) and \( c \) is of sign opposite to that of \( a \)
C. two straight lines and a hyperbola, when \( a \) and \( b \) are of the same sign and \( c \) is of sign opposite to that of \( a \)
D. a circle and an ellipse, when \( a \) and \( b \) are of the same
\( \operatorname{sign} \)


Which experiment has equally likely outcomes?
A. Choose a number at random from 1 to 7
B. Toss a coin
c. Roll a die
D. All the above


Raw materials used for the
manufacture of Portland cement are:
A. gypsum and limestone
B. limestone and clay
c. alumina, clay and gypsum
D. gypsum and clay


The greatest number that can be
formed by the digits 7,0,9,8,6,3
A. 9,87,360
В. 9,87,063
c. 9,87,630
D. 9,87,603


The phenomena during arising due to the superstition of waves is/are:
A. Beats
B. Stationary waves
c. Lissajous figures
D. All of these


If \( \frac{m}{10} \) is a rational numbers between 3
and \( 4 . \) How many integer value can \( m \)
take?


What are the draw backs of Bohrs
atomic model? Show that the
circumference of the Bohr orbit for the
hydrogen atom is an integral multiple of the de Broglie wavelength associated with the electron revolving around the
orbit.


What is the value of acceleration, if \( \mathbf{v}-\mathbf{t} \)
graph is a straight line parallel to the
time axis?
A. Non zero finite value
B. 0
c. Infinite
D. Can not be determined


Gauss's law is true only if force due to a
charge varies as
A \( \cdot r^{-1} \)
B . \( r^{-2} \)
\( c \cdot r^{-3} \)
D. \( r^{-4} \)


\( \sqrt[3]{\frac{54}{250}} \) equals:
A \( \cdot \frac{9}{25} \)
B. \( \frac{3}{5} \)
c. \( \frac{27}{125} \)
D. \( \frac{\sqrt[3]{2}}{5} \)


Find the dimensions of capacitance :
\( \mathbf{A} \cdot=\left[M^{-1} L^{2} T^{4} A^{-2}\right] \)
B . \( =\left[M^{-1} L^{-2} T^{-4} A^{2}\right] \)
\( \mathbf{c} \cdot=\left[M^{-1} L^{-1} T^{4} A^{2}\right] \)
D. \( =\left[M^{-1} L^{-2} T^{4} A^{2}\right. \)


A heterosporous plant is one that
A. Produces a gametophyte that bears both sex organs
B. Produces microspores and megaspores giving rise to separate male and female gametophytes
C. Is a seedless vascular plant
D. Produces two kinds of spores, one asexually by mitosis and one by meiosis


If \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \lim _{p \rightarrow \infty} \frac{\boldsymbol{x}^{p} \boldsymbol{g}(\boldsymbol{x})+\boldsymbol{h}(\boldsymbol{x})+\mathbf{7}}{\mathbf{7} \boldsymbol{x}^{\boldsymbol{p}}+\mathbf{3} \boldsymbol{x}+\mathbf{1}} ; \boldsymbol{x} \neq \mathbf{1} \) and
\( \boldsymbol{f}(\mathbf{1})=\mathbf{7}, \boldsymbol{f}(\boldsymbol{x}), \boldsymbol{g}(\boldsymbol{x}) \) and \( \boldsymbol{h}(\boldsymbol{x}) \) are all
continuous functions at \( x=1 . \) Then
which of the following statement(s) is/are correct
This question has multiple correct options
A. \( g(1)+h(1)=70 \)
B. \( g(1)-h(1)=28 \)
D. \( g(1)-h(1)=-28 \)


\( ^{23} N a \) is the more stable isotope of \( N a \)
By which process \( _{11}^{24} N a \) can undergo radioactive decay?
\( \mathbf{A} \cdot \beta^{-}-e m i s s i o n \)
B. \( \alpha \) - emission
c. \( \beta^{+}- \) emission
D. None of these


Draw an angle of measure \( 147^{\circ} \) and
construct its bisector.


The resistance between \( A \) and \( B \) in the
given figure will be(in ohm):
A. 20
B. 30
c. 90
D. more than 10 but less than 20


Assertion (A): Internal energy is a state
function and extensive property.
Reason ( \( \mathrm{R} \) ): Internal energy of a
substance depends on gravitational force of attraction.
A. A and R are true and \( \mathrm{R} \) is correct explanation of
B. A and R are true and R is not correct explanation of A
c. A is true, R is false
D. A is false, R is true


If \( \boldsymbol{A}=\left[\begin{array}{ccc}1 & 2 & -3 \\ 5 & 0 & 2 \\ 1-1 & 1\end{array}\right], B=\left[\begin{array}{ccc}3 & -12 \\ 4 & 2 & 5 \\ 2 & 0 & 3\end{array}\right] \) and
\( \boldsymbol{C}=\left[\begin{array}{ccc}\mathbf{4} & \mathbf{1} & \mathbf{2} \\ \mathbf{0} & \mathbf{3} & \mathbf{2} \\ \mathbf{1}-\mathbf{2 3}\end{array}\right], \) then compute \( (\boldsymbol{A}+\boldsymbol{B}) \)
and \( (B-C) \)
Also, verify that \( \boldsymbol{A}+(\boldsymbol{B}-\boldsymbol{C})= \)
\( (\boldsymbol{A}+\boldsymbol{B})-\boldsymbol{C} \)


The Earth's radius is \( 6371 k m \). The
order magnitude of the Earth's radius is
A \( \cdot 10^{3} \)
B. \( 10^{2} \)
\( c \cdot 10^{7} \)
D. \( 10^{5} \)


A gas is kept at \( 13^{\circ} \mathrm{C} \) in a vessel. If the
volume of the gas is kept constant and is heated, the pressure will be doubled to its initial pressure at a temperature
\( \mathbf{A} \cdot 576 \mathrm{K} \)
B. 286 K
c. \( 143 \mathrm{k} \)
D. 73


Find the probability distribution of number of doublets in three throws of a
pair of dice.


A function \( R \) on the set \( N \) of natural
numbers is defined as \( R=\{(2 n, 2 n+ \)
\( \mathbf{1}): \boldsymbol{n} \in \boldsymbol{N}\} \)
The domain of \( R=\{2,4,6,8, \ldots, \ldots, \ldots\} \)
A. True
B. False


\( \sin 1^{\circ} \sin 2^{\circ} \sin 3^{\circ} \dots \dots \sin 180^{\circ} \) is equal
to
\( \mathbf{A} \cdot \mathbf{1} \)
B. -
c. 0
D. \( \frac{1}{2} \)


Assertion
\( 35 C l \) and \( 37 C l \) do not differ in their \( 17^{17} \) chemical reactions.
Reason
Isotopes contain identical numbers of electrons, equal to the atomic number of the atom.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Assertion
Ball and socket joints are the most mobile joints.
Reason
Synovial fluid is, present here.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Maximum value of \( g(x) \) in \( x \in[0,7] \) is.
\( A \cdot 3 \)
B. \( 9 / 2 \)
\( c .3 / 2 \)
\( D \)


The fraction occupied by nucleus in an
atom is


What type of bond is formed if an atom captures an electron lost by another atom?
A. Hydrogen bonding
B. Covalent
c. lonic
D. Metallic
E. Polar covalent


Speed of sound waves in fluid is
A. directly proportional to the square root of bulk modulus of the medium.
B. inversely proportional to the bulk modulus of the medium
C. directly proportional to the density of the medium.
D. inversely proportional to the density of the medium.


Assertion: A tennis ball bounces higher on hills than in plains.

Reason: Acceleration due to gravity on
the hill is greater than that on the
surface offearth.
A. If both Assertion and Reason are true and the Reason is the correct explanation of the Assertion
B. If both Assertion and Reason are true but the Reason is not the correct explanation of the Assertion.
c. If Assertion is true statement but Reason is false
D. If both Assertion and Reason are false


Pauling scale Linus Pauling: Phenomenon of electronegativity Relative electronegativities of two atoms in a molecule
\( \boldsymbol{E} \boldsymbol{N}(\boldsymbol{X})-\boldsymbol{E} \boldsymbol{N}(\boldsymbol{Y})=\mathbf{0 . 1 0 2}(\triangle \mathbf{1} / 2) . \mathbf{1} \)
0.02 is conversion factor between \( k J \)
and eV is:


\( A \) and \( B \) are events such that \( p(A \cup \)
\( \boldsymbol{B})=\mathbf{3} / \mathbf{4}, \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B})=\frac{\mathbf{1}}{\mathbf{4}}, \boldsymbol{P}(\overline{\boldsymbol{A}})=\frac{\mathbf{2}}{\mathbf{3}} \)
\( \operatorname{then} P((\bar{A} \cap B) \) equals
A \( \cdot \frac{5}{12} \)
B. \( \frac{3}{8} \)
\( c \cdot \frac{4}{5} \)
\( D \cdot \frac{5}{4} \)


Ten different letter of an alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have at least
one letter repeated is:
A . 19670
B. 39758
c. 69760
D. 99748


Find the principal value of \( \tan ^{-1}(-\sqrt{3}) \)


What is the transition period from childhood to adulthood?


Find the degree of the polynomial:
\( \mathbf{7} \boldsymbol{x}^{\mathbf{3}}+\mathbf{2} \boldsymbol{x}^{\mathbf{2}}+\boldsymbol{x} \)


The maximum value of function \( \boldsymbol{f}(\boldsymbol{x})= \) \( 3 x^{3}-18 x^{2}+27 x-40 \) on the \( \operatorname{set} S= \)
\( \left\{\boldsymbol{x} \in \boldsymbol{R}: \boldsymbol{x}^{2}+\mathbf{3 0} \leq \mathbf{1 1} \boldsymbol{x}\right\} \) is:
A . 122
B . -222
c. -122
D. 222


State true or false:
If \( a^{x}=b, b^{y}=c \) and \( c^{z}=a, \) then \( x y z= \)
1
A. True
B. False


In the figure shown below the maximum
possible unknown resistance \( (X) \) that can be measured by the post office box
\( \operatorname{are} X_{\max } \) is given by \( R \times 10^{5} \Omega \) then \( \mathrm{R} \) is
(given that in this experiment we can
take out only one plug from arm \( A B \) and
only one plug from arm BC but from arm AD we can take out many plugs)


Subtract the sum of \( \left(5 x^{2}-7 x+4\right) \)
and \( \left(2 x-5 x^{3}+1\right) \) from
\( \left(3 x^{2}-1+5 x\right) \)
B. \( 5 x^{3}-2 x^{2}+10 x-6 \)
\( c \cdot 3 x^{3}+11 x^{2}+3 x+5 \)
5
D. \( 11 x^{3}+3 x^{2}+5 x-3 \)


Adsorption of gas follows Freundlich
adsorption isotherm. In the given plot, \( x \)
is the mass of the gas absorbed on
mass \( m \) of the adsorbent at pressure \( p \)
is proportional to:
\( \mathbf{A} \cdot P^{\frac{1}{4}} \)
B. \( P^{2} \)
\( c \cdot P \)
\( D \cdot P^{\frac{1}{2}} \)


Selection of temperature to carry out a reduction process depends so as to
make :
A. \( \Delta G \) negative
B. \( \Delta G \) positive
c. \( \Delta H \) negative
D. \( \Delta H \) positive


The vertical component of earth's magnetic field at a place is \( \sqrt{3} \) times the horizontal component the value of angle of dip at this place is?
A \( .30^{\circ} \)
B . \( 45^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 90^{\circ} \)


A molecule in a gas container hits a
horizontal wall with speed \( 200 \mathrm{m} s^{-1} \)
and angle \( 30^{0} \) with the normal, and
rebounds with the same speed. Is momentum conserved in the collision?
Is the collision elastic or inelastic?


Consider two curves \( C_{1}: y=\frac{1}{x} \) and
\( C_{2}: y=\ln x \) on the \( x y \) plane. Let \( D_{1} \)
denotes the region surrounded by
\( C_{1}, C_{2} \) and the line \( x=1 \) and \( D_{2} \)
denotes the region surrounded by
\( C_{1}, C_{2} \) and the line \( x=a . \) If \( D_{1}=D_{2} \)
then the sum of logarithm of possible values of \( a \) is:


Number of neutrons in heavy hydrogen
atom is :
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
\( D \)


Which of the following products are formed when ethyl alcohol is heated
with \( \boldsymbol{H}_{2} \boldsymbol{S O}_{4} ? \)
This question has multiple correct options
A. Ethene
B. Diethyl ether
c. Dimethyl ether
D. Ethane


Solve:
\( \lim _{\boldsymbol{y} \rightarrow \mathbf{7}} \frac{\boldsymbol{y}^{2}-\boldsymbol{4} \boldsymbol{y}-\boldsymbol{2} \mathbf{1}}{3 \boldsymbol{y}^{2}-17 \boldsymbol{y}-\mathbf{2 8}} \)


The rate of reaction \( A+B \rightarrow \) Products is given by the equation \( r=k[A][B] . \) If \( B \) is taken in large excess the order of the reaction would be :


Express in the simplest form. \( \sqrt{\frac{\mathbf{1 7 5}}{\mathbf{2 7}}} \)
A. \( -\frac{5}{3} \sqrt{\frac{7}{3}} \)
в. \( \frac{5}{3} \sqrt{\frac{7}{3}} \)
c. \( \frac{5}{3} \sqrt{\frac{1}{3}} \)
D. Not possible


Two stretched membranes of area
\( 2 \mathrm{cm}^{2} \) and \( 3 \mathrm{cm}^{3} \) are placed in a liquid at the same depth. The ratio of the
pressure on them is
A . 1: 1
B. 2: 3
c. 3: 2
\( D \cdot 2^{2}: 3^{2} \)


The value of a car depreciates \( 20 \% \) every
year. If after two years the price of a car is Rs.208000,find the original price of
the car.


Which of the following species has the maximum number of lone pair of
electrons on the central atom?
A. \( C l O_{3} \)
в. \( X e F_{4} \)
\( \mathrm{c} \cdot S F_{4} \)
D. \( I_{3} \)


Which of the following is a free-living nitrogen fixing bacterium present in the soil?
A . Azotobacter
B. Nitrosomonas
c. Rhizobium
D. Pseudomonas


If sum to infinity of series \( 3-5 r+ \)
\( 7 r^{2}-9 r 3+. \) is \( 14 / 9, \) find \( r \)


Consider two identical charges placed at a distance \( 2 \mathrm{d} \) apart as shown in the
figure. The equilibrium of a positive test
charge placed at point 0 midway
between them may be:

This question has multiple correct options
A. Neutral
B. Stable for displacement along the X-axis
C. Stable for displacement along the \( y \) -axis
D. Unstable for displacement along the x-axis


Butane has a \( _{--}-_{-}--_{-} \) boiling point to that of propanol.
A. higher
B. similar
c. lower
D. none of these


Which one is the base: \( C s O H \) or \( H B r \) ?
A. \( C s O H \)
в. НВт
c. Both \( A \) and \( B \)
D. None of the above


A massless spring balance is attached to 2 kg trolley and is used to pull the trolley along a flat surface as shown in
the fig. The reading on the spring balance remains at \( 10 \mathrm{kg} \) during the motion. The acceleration of the trolley
is: (Use \( \boldsymbol{g}=\mathbf{9 . 8} \boldsymbol{m s}^{-2} \) )
\( \mathbf{A} \cdot 4.9 \mathrm{ms}^{-2} \)
B. \( 9.8 m s^{-2} \)
\( \mathrm{c} \cdot 49 \mathrm{ms}^{-2} \)
D. \( 98 m s^{-2} \)


\( C_{n} H_{2 n+1}(O H)_{3} \) is a general formula for trihydric alcohols.
A. True
B. False


Find \( n(B-C)^{c} \)


A definite amount of solid \( N H_{4} H S \) is placed in a flask already containing gas at a certain temperature and 0.50 atm
pressure. \( N H_{4} H S \) decomposes to give
\( N H_{3} \) and \( H_{2} S \) and at equilibrium total
pressure in flask is 0.84 atm. The
equilibrium constant for the reaction is:
A . 0.30
B. 0.18
c. 0.17
D. 0.11


The current which does not contribute
to the power consumed in an AC circuit is called:
A. Non-ideal current
B. Wattless current
c. convectional current
D. Inductance current


Assertion
Echo is produced only when sound is incident on hard and polished surface
Reason

Sound energy can be totally reflected by objects with soft and loose texture
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Length of the latusrectum of the
hyperbola \( \boldsymbol{x} \boldsymbol{y}-\boldsymbol{3} \boldsymbol{x}-\boldsymbol{4} \boldsymbol{y}+\boldsymbol{8}=\boldsymbol{0} \) is
A .4
B. \( 4 \sqrt{2} \)
\( c \cdot 8 \)
D. None of these


All successions proceed to a similar climax community-the mesic Explain.


A long straight wire of radius R carries a current distributed uniformly over its cross-section. The magnitude of the magnetic field is This question has multiple correct options
A. maximum at the axis of the wire
B. minimum at the axis of the wire
c. maximum at the surface of the wire
D. minimum at the surface of the wire


Calculate the rate at which the tank is
filled in gallons per second. (in gal/s)
A .0 .0729
B. 0.07
c. 0.072
D. 0.029


If \( \boldsymbol{A}=\left[\boldsymbol{a}_{i j}\right] \) is a \( \mathbf{4} \times \mathbf{4} \) matrix and \( \boldsymbol{c}_{i j} \) is
the co-factor of the element \( \boldsymbol{a}_{\boldsymbol{i} j} \) in \( |\boldsymbol{A}| \)
then the expression \( a_{11} c_{11}+a_{12} c_{12}+ \)
\( \boldsymbol{a}_{13} \boldsymbol{c}_{13}+\boldsymbol{a}_{14} \boldsymbol{c}_{14} \) equals
\( \mathbf{A} \cdot \mathbf{0} \)
B. -
c. 1
D. \( |A| \)


A particle moves from \( \boldsymbol{A} \) to \( \boldsymbol{B} \) diametrically opposite in a circle of
radius \( 5 m \) with a velocity \( 10 m s^{-1} . \) Find
the average acceleration.
A . zero
в. \( \frac{40}{\pi} m s^{-2} \)
c. \( \frac{20}{\pi} m s^{-2} \)
D. none


An aeroplane with wing span \( 50 m \) is flying horizontally with a speed of \( 360 k m / h r \) over a place where the
vertical component of the earth's magnetic field is \( 2 \times 10^{-4} W b / m^{2} . \) The
potential difference between the tips of the wings would be
A . \( 0.1 V \)
в. \( 1.0 V \)
\( c .0 .2 V \)
D. \( 0.01 V \)


Integrate \( \int e^{\log (\sec x+\tan x)} \sqrt{1+\tan ^{2} x} d x \)


Select the group that shares maximum number of common characteristics.
A. 2 individuals of species
B. 2 species of genus
c. 2 genera of a family
D. 2 genera of 2 families


Mammalian lungs have an enormous number of minute aiveoli (air sacs)
This is to allow
A. more surface area for diffusion of gases
B. more nerve supply to keep the the lungs working
c. more space for increasing the volume of inspired air
D. more spongy texture for keeping lung in proper shape


Arrange the following in order of decreasing \( N-O \) bond length :
\( N O_{2}^{+}, N O_{2}^{-}, N O_{3}^{-} \)
A \( \cdot N O_{3}^{-}>N O_{2}^{+}>N O_{2} \)
в. \( N O_{3}^{-}>N O_{2}^{-}>N O_{2}^{+} \)
c. \( N O_{2}^{+}>N O_{3}^{-}>N O_{2} \)
D. \( N O_{2}^{-}>N O_{3}^{-}>N O_{2} \)


Which is used in extraction of metals?
A. Coal gas
B. Coal tar
c. coke
D. Petrol


toppr
Q Type your question
\( \begin{array}{llllll}\text { Life } \bmod e & 0- & 20- & 40- & 60- & 80 \\ \text { Hrs.) } & 20 & 40 & 60 & 80 & 100\end{array} \)
No. of
electric
bulbs
\[
82
\]
\begin{tabular}{lll}
31 & 36 & 38 & 42 \\
\hline
\end{tabular} Find the modal life of the electric bulbs.


Tangent law is applicable only when
A. applied field is parallel to the earth's horizontal component
B. applied field is antiparallel to the earth's horizontal component
C . applied field is perpendicular the earth's horizontal component in horizontal plane
D. applied field is inclined to the earth's horizontal component


If \( f^{\prime \prime}(x)<0 \) for all \( x \in(a, b), \) then
\( \boldsymbol{f}^{\prime}(\boldsymbol{x})=\mathbf{0} \)
A. exactly once in \( (a, b) \)
B. at most once in \( (a, b) \)
c. at least once in \( (a, b) \)
D. none of these


lodine reacts with alcohols to give alkyl iodine only in presence of phosphorus. Why?


If the straight line, \( 2 x-3 y+17=0 \) is
perpendicular to the line passing through the points (7,17) and \( (15, \beta) \)
then equals:
A . -5
B. \( -\frac{35}{3} \)
c. \( \frac{35}{3} \)
D. 5


From the given v-t graph, it can be inferred that the object is
A. in uniform motion
B. at rest
c. in non-uniform motion
D. moving with uniform acceleration


\( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) turns acidified \( \boldsymbol{T} \boldsymbol{i} \boldsymbol{O}_{2} \) solution to
orange coloured pertitanic acid \( \left[\boldsymbol{H}_{2} \boldsymbol{T} \boldsymbol{i} \boldsymbol{O}_{4}\right] \)
A. True
B. False


Balanced equation for the reaction of conc. sulphuric acid with Sucrose is \( 2 C_{12} H_{22} O_{11}+H_{2} S O_{4}(\text { conc }) \rightarrow \)
\( 12 C+5 H_{2} O+H_{2} S O_{4}(d i l) \)
A. True
B. False


The temperature coefficient resistivity of a material is \( 0.0004 / K . \) When the
temperature of the material is
increased by \( 50^{\circ} C, \) its resistivity increases by \( 2 \times 10^{-8} \) ohm - meter
The initial resistivity of the material of the resistance
A . \( 50 \times 10^{-8} \)
B. \( 90 \times 10^{-8} \)
c. \( 100 \times 10^{-8} \)
D. \( 200 \times 10^{-8} \)


A solution containing \( 10 g d m^{-3} \) of urea
(molecular mass \( =60 g m o l^{-1} \) ) is
isotonic with a \( 5 \% \) solution of a
nonvolatile solute. The molecular mass
of this is nonvolatile solute is:
A \( \cdot 250 g m o l^{-1} \)
в. 300 gmol-\( ^{-1} \)
c. 350 gmol-\( ^{-1} \)
D. \( 200 g \) mol \( ^{-1} \)


If \( d \) is the \( H C F \) of 45 and \( 27, \) then \( x, y \)
satisfying \( \boldsymbol{d}=\mathbf{2 7} \boldsymbol{x}+\mathbf{4 5} \boldsymbol{y} \) are :
A \( . x=2, y=1 \)
в. \( x=2, y=-1 \)
c. \( x=-1, y=2 \)
D. \( x=-1, y=-2 \)


If true enter 1 , else enter 0 . Atomic mass
unit is also called Dalton(Da).


Which of the following electrical devices works on the principle of electromagnetic induction?
A. Electric fan
B. Electric bulb
C. Electric cooker
D. L.E.D.


A reaction in equilibrium is represented by the following equation.
\( \mathbf{2} \boldsymbol{A}_{(s)}+\mathbf{3} \boldsymbol{B}_{(g)} \rightleftharpoons \mathbf{3} \boldsymbol{C}_{(\boldsymbol{g})}+\boldsymbol{D}_{(\boldsymbol{g})}+\boldsymbol{Q} \)
If the pressure on the system is reduced to half of its original value:
A. The amounts of \( c \) and D decreases
B. The amounts of C and D increases
c. The amount of D decreases
D. All the amounts remain constant


In an oscillating LC circuit the maximum charge on the capacitor is \( Q \)
The charge on capacitor when the energy is stored equally between electric and magnetic field is :
\( \mathbf{A} \cdot Q / 2 \)
в. \( Q / \sqrt{3} \)
c. \( Q / \sqrt{2} \)
D. \( Q \)


Which of the following correctly represents the heat of formation of
methane?
A \( \cdot \mathrm{c} \) (diamond) \( +2 \mathrm{H}_{2(g)} \rightarrow \mathrm{CH}_{4(9)} \)
B. \( c \) (diamond) \( +2 H_{2(g)} \rightarrow C H_{4(l)} \)
c. c (graphite) \( +2 H_{2(g)} \rightarrow C H_{4(g)} \)
D. c (graphite) \( +4 H_{(g)} \rightarrow C H_{4(g)} \)


The most primitive tracheary elements
are
A. Tracheids with annular thickenings
B. Tracheids with scalariform thickenings
c. Pitted tracheids
D. Pitted tracheids and vessels


Two particles are shown in figure. At
\( t=0, \) a constant force \( F=6 N \) starts
acting on the 3 kg mass. Find the velocity of the centre of mass of these
particles at \( t=5 s \)
\( \mathbf{A} \cdot 5 m / s \)
B. \( 4 m / s \)
\( \mathrm{c} .6 \mathrm{m} / \mathrm{s} \)
D. \( 3 m / s \)


Name the three metals which react with
cold water to form hydrogen gas. Support your answer with equally balanced chemical equations.


To get from one office to another, one travels as follows (with all angles
measured clockwise from the West) \( 2 m \)
at \( 180^{\circ}, 0.5 m \) at \( 150^{\circ}, \) and \( 1 m \) at \( 30^{\circ} \) How far will a person be from his starting point? \( (\text { in } m) \)
A . 1.5
B. 1.43
\( c .1 \)
D. 1.96


An electron completes \( 6 \times 10^{15} \)
revolutions per second in a circular orbit. Current in the loop will be:
\( \mathbf{A} \cdot 0.96 m A \)
в. \( 0.96 \mu A \)
c. \( 28.8 A \)
D. none of the above


A hollow cylinder has a charge \( q \) coulomb within it. If \( f \) the electric flux in
units of volmeter associated with the
curved surface \( \mathrm{B} \), the fl乂 linked with the
plane surface A in units of V-m will be:
A \( \cdot \frac{q}{2 \varepsilon_{0}} \)
в. \( \frac{\Phi}{3} \)
c. \( \frac{q}{\varepsilon_{0}} \)
D. \( \frac{4 q}{\varepsilon_{0}} \)


The magnetic susceptibility is negative
for:
A. diamagnetic material only
B. paramagnetic material only
C . ferromagnetic material only
D. paramagnetic and ferromagnetic materials


For the complex number \( \sqrt{37}+\sqrt{-19} \)
Real part is \( \sqrt{3} 7 \) and imaginary is \( \sqrt{19} \)
Enter 1 if true or 0 for false


Shape of \( O_{2} F_{2} \) is similar to:
A \( \cdot C_{2} F_{2} \)
в. \( H_{2} O_{2} \)
c. \( H_{2} F_{2} \)
D. \( C_{2} H_{2} \)


It is possible to project a particle with a given speed in two possible ways so
that it has the same horizontal range \( \boldsymbol{R} \) The product of the times taken by it in the two possible ways is
A \( \cdot \frac{R}{g} \)
в. \( \frac{2 R}{g} \)
c. \( \frac{3 R}{g} \)
D. \( \frac{4 R}{g} \)


Solve the differential equation:
\( \left(1+e^{2 x}\right) d y+\left(1+y^{2}\right) e^{x} d x=0 \)


In the shown figure, length of the rod is
\( L, \) area of cross-section \( A, \) Young's
modulus of the material of the rod is \( Y \).
Then, \( B \) and \( A \) is subjected to a tensile
force \( \boldsymbol{F}_{A} \) while force applied at end
\( B, F_{B} \) is lesser than \( F_{A} \). Total change in length of the rod will be
\( A \)
\[
F_{A} \times \frac{L}{2 A Y}
\]
B.
\[
F_{B} \times \frac{L}{2 A Y}
\]
\( c \)
\[
\frac{\left(F_{A}+F_{B}\right) L}{2 A Y}
\]
\( D \)
\[
\frac{\left(F_{A}-F_{B}\right) L}{2 A Y}
\]


The product of \( n \) positive numbers is 1
Their sum is
A. a positive integer
B. divisible by \( n \)
c. equal to \( n+\frac{1}{n} \)
D. greater than or equal to \( n \)


For equilibrium, \( 2 N O_{2}(g) \rightleftharpoons \)
\( N_{2} O_{4}(g)+14.6 k \) cal increases of
temperature would
A. Favour the formation of \( N_{2} O_{4} \)
B. Not after the equilibrium
C. Favour the decomposition of \( N_{2} O_{4} \)
D. Stop the reaction


Which term best describes a solution
with a \( p H \) of \( 8 ? \)
A. Very basic
B. Slightly acidic
c. Neutral


If the strain in wire is not more than
\( 10^{-3} \) and \( Y=4 \times 10^{11} N / m^{2}, \) diameter of
wire is \( 1 \mathrm{mm} \), then the maximum weight that can be hanged from wire is then:-
\( \mathbf{A} \cdot 157 N \)
в. \( 314 N \)
c. \( 120 N \)
D. \( 160 N \)


Acid present in honey bee sting is:
A. formic acid
B. propanoic acid
c. butanoic acid
D. none of these


Subtract (-5) from (-9)
\( A \cdot 4 \)
B. -4
c. -14
D. 14


A car headlamp of \( 48 \mathrm{W} \) works on the car battery of \( 12 \mathrm{V} \). The correct fuse for the circuit is
A . 5A
B. 2A
\( c \cdot 3 A \)
D. 15A


The above conversion can proceed throuought is
A. carbocation intermediate
B. transition state
c. free radical intermediate
D. carbanion intermediate


Let \( X \) and \( Y \) be two related variables.
The two regression lines are given by \( \boldsymbol{x}-\boldsymbol{y}+\mathbf{1}=\mathbf{0} \) and \( \mathbf{2} \boldsymbol{x}-\boldsymbol{y}+\mathbf{4}=\mathbf{0} . \) The
two regression lines pass through the point:
A \( \cdot(-4,-3) \)
в. (-6,-5)
c. (3,-2)
D. (-3,-2)


\( \lim _{x \rightarrow \frac{\pi}{2}} \frac{\cot x-\cos x}{(\pi-2 x)^{3}} \) equals:
A \( \cdot \frac{1}{24} \)
B. \( \frac{1}{16} \)
c. \( \frac{1}{2} \)
D.


What is the effect of \( p C O_{2} \) on oxygen
transport?


To parallel rail track an north south.
Train \( A \) moves north with a speed of
\( \mathbf{5 4} k \boldsymbol{m} / \boldsymbol{h} \) and train \( \boldsymbol{B} \) moves south with
a speed of \( 90 \mathrm{km} / \mathrm{h} \). What is the Velocity of \( B \) with respect to capital \( A ? \)
Velocity of ground with respect to \( B \) ?
Velocity of monkey running on the roof
of train \( A \) against its motion with a velocity of \( 18 \mathrm{km} / \mathrm{h} \) with respect to the \( \operatorname{train} A \) as observe by man standing on
the ground?


Reflected ray is the ray of light reflected from a surface.
A . True
B. False


\( \int \frac{\boldsymbol{d} \boldsymbol{x}}{\boldsymbol{x}\left(\boldsymbol{x}^{5}+\boldsymbol{3}\right)} \)


If the thio-cyanide ion is added to potash-ferric alum then red colour appears. This colour is due to the
formation of:
A. \( K S C N \)
в. \( F e(S C N)_{3} \)
\( \mathbf{c} \cdot \operatorname{Fe}(S C N)_{2} \)
D. \( F e(S C N) \)


Which of the following is a source of magnetic field?
A. isolated Magnetic pole
B. static electric charge
c. current loop
D. moving light source


An electrical device draws \( 2 \mathrm{kW} \) power from ac mains voltage \( 223 \mathrm{V}(\mathrm{rms}) . \) The current differs lags in phase by \( \phi= \)
\( \tan ^{-1}[]-\frac{3}{4}[\mathbb{1}] \) as compared to voltage. The
resistance \( R \) in the circuit is
A . \( 15 \Omega \)
в. 20 \( \Omega \)
\( c .25 \Omega \)
D. 30 \( \Omega \)


What is the name given to a pure substance with only one kind of atoms?
A. Element
B. Compound
c. Mixture
D. Suspension


\( \lim _{x \rightarrow 0} \frac{\sin ^{-1} x-\tan ^{-1} x}{x^{3}}= \)
\( A \cdot 2 \)
B.
\( c \cdot-1 \)
D.


\( N a O H+P_{4}+H_{2} O \rightarrow \)
\( \mathbf{A} \cdot P H_{3}+N a H_{2} P O_{2} \)
в. \( P H_{3}+N a_{2} P O_{4} \)
c. \( P H_{3}+N a_{2} H P O \)
D. \( H_{3} P O_{4}+N a O \)


Formula of soap is:
A. \( C_{16} H_{32} \) COONa
в. \( C_{17} \mathrm{H}_{35} \mathrm{COONa} \)
c. \( C_{17} H_{33} \)COONa
D. \( C_{17} H_{36} \)COONa


All allotropes of carbon exist in
state at room
temperature
A. liquid
B. solid
c. gas
D. plasma


I : Length of the perpendicular from \( \left(x_{1}, y_{1}\right) \) to the line \( a x+b y+c=0 \) is \( \left|\frac{\boldsymbol{a} \boldsymbol{x}_{1}+\boldsymbol{b} \boldsymbol{y}_{1}+\boldsymbol{c}}{\sqrt{\boldsymbol{a}^{2}+\boldsymbol{b}^{2}}}\right| \)
II : The equation of the line passing through (0,0) and perpendicular to \( a x+b y+c=0 \) is
\( b x-a y=0 . \) Then which of the
following is true?
A. only I
B. only II
c. both 18 ॥
D. neither I nor II


The colour code of a resistor is brown, black and brown. Then the value of
resistance is
A. \( 10 \Omega \)
в. 100 тл
c. \( 0.1 k \Omega \)
D. 1000 \( \Omega \)


Few quantities with their units are listed below. Mark the units which are
not correctly matched.
(i) Density \( : \operatorname{kg} m^{-3} \)
(ii) Velocity of light \( : \mathrm{m} s^{-1} \)
(iii) Planck's constant \( : \boldsymbol{J}^{-1} \boldsymbol{s}^{-1} \)
(iv) Acceleration : \( \mathrm{m} \boldsymbol{s}^{-2} \)
(v) Force : \( \mathrm{kg} \) m
A. (ii) and (iv)
B. (i) and (iii)
c. (iii) and (v)
D. (iv) and (v)


Two wires each of radius of cross
section \( r \) but of different materials are
connected together end to end (i.e., in series). If the densities of charge carriers in the two wires are in the ratio
\( 2: 3, \) the drift velocity of electrons in the
two wires will be in the ratio of
A .2: 3
B. 3: 2
c. 4: 9
D. 9: 4


If \( \frac{x}{2}-\frac{x}{3}=\frac{x}{4}+\frac{1}{2}, \) then the value of \( x \) is
\( A \cdot 6 \)
B . 24
\( c .-6 \)
\( D \)


Which one of the following statement is
not correct?
During protein synthesis,
A. UAA codon codes for lysine.
B. UGG codon codes for tryptophan.
c. cysteine is coded by UGU and UGC codons.
D. Tyrosine is coded by UAU and UAC


The \( _{-}-_{-}-_{-}-_{-}-_{-} \) of an object does
not change from place to place.
A. weight
B. Velocity
c. Mass
D. Pressure


Venaparthy has increased groundwater
level by adopting
A. Percolation tank
B. Cropping pattern
c. Biofertilizers
D. Rainwater harvesting system


15.Match the terms given under column 'A' with their functions given under
column 'B' and select the answer from
the options given below:


Displacement current is
A. continuous when electric field is changing in the circuit
B. continuous when magnetic field is changing in the circuit
C . continuous in both types of fields
D. continuous through wires and resistance only


In the following figure the bulb will start
lighting suddenly if :
A. Key is closed
B. Key is opened
C. Key is either closed or opened
D. Nothing is done


An aeroplane starting from a point travels towards north-east with a
velocity of 400 kmph. Another aeroplane starting from the same point travels towards north west with a velocity of
\( 300 \mathrm{kmph} . \) The relative velocity of one aeroplane w.r.t. other is
A. \( 350 \mathrm{kmph} \)
в. \( 500 \mathrm{kmph} \)
c. \( 100 \mathrm{kmph} \)
D. \( 200 \mathrm{kmph} \)


The number of electrons in \( 3 d \) orbitals
for element with Atomic number 26 is:
A . 4
B. 6
\( c \cdot 8 \)
D. 10


Prove that \( \sin \cot ^{-1} \tan \cos ^{-1} x= \)
\( \sin \operatorname{cosec}^{-1} \cot \tan ^{-1} x=x \) where
\( x \in(0,1] \)


\( \int_{0}^{a} \frac{x-a}{x+a} d x= \)
\( \mathbf{A} \cdot a+2 a \log 2 \)
B. \( a-2 a \log 2 \)
c. \( 2 a \log -a \)
D. \( 2 a \log 2 \)


Which of the following has allotropes?
A. Aluminium
B. Boron
c. indium
D. Thallium


Which nutrient is produced when large amount of energy breaks the atom bonds of nitrogen?
A. Protein
B. Mineral
c. Iron
D. Calcium


The number of time a person breathes
in a minute is known as
This question has multiple correct options
A. Respiration rate
B. Breathing rate
c. combustion rate
D. None of the above


An electrical device draws 2 kW power
from ac mains voltage \( 223 V(r m s) \) The current differs lags in phase by \( \phi=\tan ^{-1}\left(-\frac{3}{4}\right) \) as compared to
voltage. The resistance \( R \) in the circuit
is:
A . \( 15 \Omega \)
B. 20\Omega
c. \( 25 \Omega \)
D. 30\Omega


When benzaldehyde is oxidised to give benzoic acid then the oxidation state of
carbon of aldehydic group is changed from:
\( \mathbf{A} \cdot+2 \) to +3
B. +1 to +3
c. zero to +2
D. No change


Answer the following with reference to
the anatomy of dicot root. Which type of cells constitute the
cortex?


The D.E whose solution is \( \boldsymbol{y}= \)
\( a \cos (3 x+b) \) is?
A \( \cdot y_{2}+3 y=0 \)
В. \( y_{2}+y=0 \)
c. \( y_{2}+9 y=0 \)
D. \( y_{2}+6 y=0 \)


The direction of energy flow is
A. Producers \( \rightarrow \) Herbivores \( \rightarrow \) Decomposers \( \rightarrow \) Omnivores
B. Producers \( \rightarrow \) Carnivore \( \rightarrow \) Herbivores \( \rightarrow \) Decomposes
C. Decomposers \( \rightarrow \) Carnivores \( \rightarrow \) Herbivores \( \rightarrow \) Producers
D. Producers \( \rightarrow \) Herbivores \( \rightarrow \) Carnivores \( \rightarrow \)
Decomposers


When two unknown resistors are
connected in series with a battery, \( 225 W \) power is delivered to the
combination with a total current \( 5 A \). For
the same total current \( 50 W \) is delivered
when the resistors are connected in
parallel. Find the ratio of the two resistances
\( A \cdot 2 \)
B. 5
\( c \cdot 4 \)
D. 10


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Q Type your question
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Which of the following diagrams would properly describe this observation?
\( A \)
B.
\( c \)
\( D \)


Coulomb's law for electrostatic force
between two point charges and Newton's law for gravitational force
between two stationary point masses, both have inverse-square dependence on the distance between the
charges/masses.
(a) Compare the strength of these forces by determining the ratio of their magnitudes (i) for an electron and a proton and (ii) for two protons.
(b) Estimate the accelerations of electron and proton due to the
electrical force of their mutual
attraction when they are \( 1 A \)
\( \left.\mathbf{1 0}^{-\mathbf{1 0}} \boldsymbol{m}\right) \) apart? \( \left(\boldsymbol{m}_{\boldsymbol{p}}=\mathbf{1 . 6 7} \times\right. \)
\( \left.\mathbf{1 0}^{-\mathbf{2 7}} \mathbf{k g}, \boldsymbol{m}_{e}=\mathbf{9 . 1 1} \times \mathbf{1 0}^{-\mathbf{3 1}} \mathbf{k g}\right) \)


\( \mathrm{XeF}_{2} \) molecule is
A. Trigonal planar
B. Square planar
C. Linear
D. Pyramidal


Q Type your question
acceleration due to gravity (g) using a simple pendulum. They use different lengths of the pendulum and/or record time for different number of
oscillations. The observations are
shown in the following table. Least count for length \( =0.1 \mathrm{cm}, \) Least count for
time \( =0.1 s \)
Length of \( \quad \) Number of Student Pendulum \( \quad \) oscillations \( (n) \)
\[
\begin{array}{l}
(\mathrm{cm}) \\
64.0
\end{array}
\]
\[
64.0
\]
\[
20.0
\]
If \( \boldsymbol{E}_{\boldsymbol{I}}, \boldsymbol{E}_{\boldsymbol{I I}}, \boldsymbol{E}_{\boldsymbol{I I I}} \) are the percentage errors
in \( g, \) i.e., \( \left(\frac{\Delta g}{g} \times 100\right) \) for students I, II and
III, respectively, then
A \( \cdot E_{I}=0 \)
B. \( E_{I} \) is minimum
\( \mathbf{c} \cdot E_{I}=E_{I I} \)
D. \( E_{I I} \) is maximum


Mark the correct statement.
A. Time taken by two consecutive compressions or one rarefaction is called the time period of the wave.
B. Sound of a vollin and a flue are different due to the difference in the medium through which they travel.
C. How the brain interpnetes the frequency of an emmitted sound is called pitch.
D. All true


What is the electronic configuration of the ground state of the magnesium
cation, \( M g^{2+} ? \)
A \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} \)
B \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s \)
C \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} \)
D. \( 1 s^{2} 2 s^{2} 2 p^{4} 3 s^{2} \)


What specifications would you select
for the material to make a fuse wire?
A. Greater specific heat, less melting point
B. Greater specific heat, greater melting point
C. Less specific heat, greater melting point
D. Less specific heat, less melting point


The white solid compound \( A \) decomposes quite rapidly on heating in the presence of a black substance \( X \) to form a solid compound \( \mathrm{B} \) and a gas \( \mathrm{C} \) When an aqueous solution of compound \( \mathrm{B} \) is reacted with silver nitrate solution,
then a white precipitate of silver chloride is obtained along with potassium nitrate solution. Gas C does not burn itself but helps to burn other things.
What is compound A?


\( \left|\begin{array}{ccc}\boldsymbol{x}^{\boldsymbol{n}} & \boldsymbol{x}^{\boldsymbol{n}+\mathbf{2}} & \boldsymbol{x}^{\boldsymbol{n}+\mathbf{3}} \\ \boldsymbol{y}^{\boldsymbol{n}} & \boldsymbol{y}^{\boldsymbol{n}+\mathbf{2}} & \boldsymbol{y}^{\boldsymbol{n}+\boldsymbol{3}} \\ \boldsymbol{z}^{\boldsymbol{n}} & \boldsymbol{z}^{\boldsymbol{n}+\mathbf{2}} & \boldsymbol{z}^{\boldsymbol{n}+\mathbf{3}}\end{array}\right|=(\boldsymbol{x}-\boldsymbol{y})(\boldsymbol{y}- \)
\( (z-x)\left(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}\right), \) then the value
of \( n \) is
\( A \)
B. -
\( c \cdot 1 \)
\( D \)


The number of values of \( n \), for which
\( \boldsymbol{p}(\boldsymbol{n})=\mathbf{1} !+\mathbf{2 !}+\mathbf{3 !}+\mathbf{4} !+\cdots+\boldsymbol{n} ! \) is
the square of a natural number, is equal
to
\( A \cdot 0 \)
B. 1
\( c \cdot 2 \)
D. 3


Match the columns:
\( \begin{array}{llll} & \text { Column I } & & \text { Column II } \\ \text { a. } & \text { Thymus gland } & \text { p. } & \text { Epinephrine } \\ \text { b. } & \begin{array}{l}\text { Adrenal } \\ \text { medulla }\end{array} & \text { q. } & \text { Thymosin } \\ \text { c. } & \begin{array}{l}\text { Parathyroid } \\ \text { gland }\end{array} & \text { r. } & \text { Calcitonin } \\ \text { d. } & \text { Thyroid gland } & \text { s. } & \begin{array}{l}\text { Bone } \\ \text { desorption }\end{array}\end{array} \)
\( A \cdot a-q, b-p, c-s, d-r \)
\( B \cdot a-s, b-r, c-q, d-p \)
\( \mathrm{C} \cdot \mathrm{a}-\mathrm{r}, \mathrm{b}-\mathrm{p}, \mathrm{c}-\mathrm{s}, \mathrm{d}-\mathrm{q} \)
D. \( a-p, b-q, c-q, d-s \)


Two nucleons are at a separation of \( 1 \times \)
\( 10^{-15} \) m. The net force between them is
\( F_{1} \) if both are neutrons, \( F_{2} \) if both are
protons and \( F_{3} \) if one is a proton and
other is a neutron. In such a case
A \( \cdot F_{2}>F_{1}>F_{3} \)
в. \( F_{1}>F_{2}>F_{3} \)
C. \( F_{1}>F_{3}>F_{2} \)
D. \( F_{3}=F_{1}>F_{2} \)


This is known as heavy hydrogen:
A. protium
B. tritium
c. deuterium
D. proton


The action of bacteria on meat and fish
produces a poisonous compound called cadaverine. As its name and origin imply, it stinks. It is \( 58.77 \% C, 13.81 \% \)
\( H \) and \( 27.42 \% N . \) Its molar mass is 102
g/mol. Determine the molecular formula of cadaverine.
A \( \cdot C_{6} H_{16} N \)
в. \( C_{5} H_{16} N_{2} \)
c. \( C_{5} H_{14} N_{2} \)
D. \( C_{4} H_{16} N_{3} \)


An electric generator actually acts as:
A. source of electric charge
B. source of heat energy
c. an electromagnet
D. a converter of energy


The \( 15^{t h} \) terms of the series \( 2 \frac{1}{2}+ \) \( 1 \frac{7}{13}+1 \frac{1}{9}+\frac{20}{23}+_{----} \)
\( A \cdot \frac{5}{12} \)
в. \( \frac{10}{21} \)
c. \( \frac{10}{39} \)
D. None of these


Let \( \boldsymbol{f}: \mathbb{R} \rightarrow \mathbb{R} \) defined by \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \frac{a x^{2}+a x+b}{a x+b} \) then
A. \( f \) is many one
B. \( f \) is one-one
c. \( f \) is onto
D. range of \( f \) is not a single-tone set


The self-inductance of the motor of an
electric fan is \( 10 \mathrm{H} \). In order to impart maximum power at \( 50 \mathrm{Hz} \), it should be
connected to a capacitance of : (Take \( \pi^{2} \) \( =10) \)
A \( .4 \mu F \)
в. \( 8 \mu F \)
c. \( 1 \mu F \)
D. \( 2 \mu F \)


The changes in concentration, pressure, volume, and temperature can change the equilibrium position. Explain.


A light is travelling from air into a medium. Velocity of light in a medium is reduced to 0.75 times the velocity in
air. Assume that angle of incidence 'i' is
very small, the deviation of the ray is
\( \mathbf{A} \cdot i \)
B. \( \frac{i}{3} \)
\( c \cdot \frac{i}{4} \)
D. \( \frac{3 i}{4} \)


The height at which the acceleration due to gravity becomes \( \frac{\mathbf{g}}{\mathbf{g}} \) (where \( \mathbf{g}= \)
the acceleration due to gravity on the surface of the earth) in terms of \( \mathbf{R} \), the
radius of the earth, is:
A . 2 R
B. \( \frac{\mathrm{R}}{\sqrt{2}} \)
c. \( \mathrm{R} / 2 \)
D. \( \sqrt{2} \mathrm{R} \)


Tartaric acid is a colourless, crystalline acid found in fruit juices, like that of grapes. Some of its uses are mentioned
here. Pick the false one:
A. In photography
B. In cosmetics
c. In dyeing of cloth
D. In medicines


If the sum of first \( p \) terms of an A.P.is
equal to the sum of the first \( q \) terms,
then find the sum of the first \( (\boldsymbol{p}+\boldsymbol{q}) \)
terms.


The compounds obtained by heating of orthophosphoric acid are :
This question has multiple correct options
A. metaphosphoric acid
B. pyrophosphoric acid.
\( \mathrm{c} \cdot P_{4} O_{6} \)
D. \( P_{4} O_{10} \)


Which of the following has the highest
electron affinity?
A. \( F \)
в. \( C l \)
\( c . B r \)
D. \( I \)


Calculate the pH of \( 0.1 M \) \( \boldsymbol{C H}_{3} \boldsymbol{C O O H}\left(\boldsymbol{K}_{\boldsymbol{a}}=\mathbf{1 . 8} \times \mathbf{1 0}^{-\mathbf{5}}\right) \)


Heterothallism refers to
A. Fusion is not accompanied with zygote formation
B. Fusion between morphologically similar strain
C. Fusion between the strains that are structurally similar but physiologically different
D. All of the above


0.365 gm of an organic compound containing nitrogen gives \( 56 \mathrm{ml} \) of nitrogen at STP. The percentage of nitrogen in the given compound is:
A . \( 19.18 \% \)
B. \( 38.36 \% \)
c. \( 9.18 \% \)
D. 29.18\%


The oxidation state of nitrogen is a fractional value in:
A. Hydroxyl amine
B. Hydrazoic acid
c. Nitrate ion
D. Hydrazine


Evaluate the following determinant:
\( \left|\begin{array}{ccc}1 & 4 & 9 \\ 4 & 9 & 16 \\ 9 & 16 & 25\end{array}\right| \)


General solution for \( |\sin x|=\cos x \) is
A \( \cdot 2 n \pi+\frac{\pi}{4}, n \in I \)
В \( \cdot 2 n \pi \pm \frac{\pi}{4}, n \in I \)
c. \( n \pi+\frac{\pi}{4}, n \in I \)
D. None of these


Solve \( \int_{0}^{\pi} \frac{1}{3+2 \sin x+\cos x} d x \)
A \( \cdot \frac{5 \pi}{4} \)
в.
\( c \cdot-\frac{\pi}{4} \)
D. None of these


In which of the following isolations no reducing agent is required?
A. Iron from haematite
B. Aluminium from bauxite
c. Mercury from cinnabar
D. zinc from zinc blende


An alpha nucleus of energy \( \frac{1}{2} m v^{2} \) bombards a heavy nuclear target of
charge Ze. Then the distance of closest
approach for the alpha nucleus will be proportional to
A \( \cdot v^{2} \)
в. \( \frac{1}{m} \)
c. \( \frac{1}{v^{4}} \)
D. \( \frac{1}{Z e} \)


Among the following, the highest value of prefix is:
A. yocto
в. deca
c. giga
D. yotta


Sclerides are the sclerenchyma cells with very thick secondary wall deposits and provide mechanical support. In which of the following plant organs one would expect to find abundant sclerides?
A. Underground tuberous roots
B. Leaves of floating hydrophyte
c. Flower petals of mesophytes
D. Petioles of xerophytic plant


A bar magnet is \( 0.10 \mathrm{m} \) long and its
pole strength is \( 120 A \) m. Find magnitude of magnetic field at a point
on the its axis at a distance \( 20 \mathrm{cm} \) from
¡t.


A shopkeeper gives a discount of \( 25 \% \) on the marked price of an article and still earns a profit of \( 20 \% \) on his outlay, If he had not given any discount, then the profit on his outlay would have been
A . \( 45 \% \)
B. \( 50 \% \)
\( c .55 \% \)
D. \( 60 \% \)


Information from the ear first enters the
of the brain
A. Medulla
B. Pons
c. Brain stem
D. Thalamus


If the ratio of distances travelled by
freely falling body in the last and last but one second of its motion is \( 7: 5 . \) The
velocity with which the body strikes the
ground is : (Given \( \boldsymbol{g}=\mathbf{9 . 8} \boldsymbol{m s}^{-2} \) )
\( \mathbf{A} \cdot 29.4 \mathrm{ms}^{-1} \)
B. \( 39.2 \mathrm{ms}^{-1} \)
\( \mathbf{c} \cdot 19.6 \mathrm{ms}^{-1} \)
D. \( 49 \mathrm{ms}^{-1} \)


The scientist who gave me three laws of planetary motion was
A. Newton
B. Kepler
c. Galileo
D. Robert Boyle


The best method to determine the age
of tree is
A. To measure its diameter
B. To count the number of leaves
C. To count the number of annual rings in the main stem at the base
D. To measure its height


Assertion
\( f(x)=\frac{1}{x-7} \) is decreasing \( \forall x \epsilon R \)
\{7\}
Reason
\( \boldsymbol{f}^{\prime}(\boldsymbol{x})<\mathbf{0} \forall \boldsymbol{x} \neq \mathbf{7} \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The ratio of mass densities of nuclei of
\( ^{40} \mathrm{Ca} \) and \( ^{16} \mathrm{O} \) is close to:
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c .0 . \)
D. 5


What are \( N \) and \( M ? \)
products
\( A \cdot 6,6 \)
B. 6,4
\( c \cdot 4,4 \)
\( D \cdot 3,3 \)


Assertion
\( X e F_{4} \) exists while \( X e H_{4} \) does not exist
Reason
\( \ln X e H_{4} \) d-orbital contraction is absent
A. The Assertion is true, the Reason is true and Reason is the correct explanation for Assertion
B. The Assertion is true, Reason is true and Reason is NOT the correct explanation for Assertion
c. Assertion is true, Reason is false.
D. Assertion is false, Reason is true.


A wire has a mass \( 0.3 \pm 0.003 g \) and
length \( 6 \pm 0.06 \) cm. The maximum
percentage error in the measurements
of its linear mass density is:-
A \( . \)
B. 2
\( c \cdot 3 \)
D. 4


At constant temperature and pressure,
the volume of a given gas is related to
mass as
A. Volume is not related to mass
B \( \cdot v \propto \frac{1}{m} \)
c. \( v \propto-\frac{1}{m} \)
D. \( v \propto m \)


In an experiment, 4 g of \( M_{2} O_{x} \) oxide
was reduced to \( 2.8 g \) of the metal. If the
atomic mass of the metal is \( 56 g m o l^{-1} \)
The number of \( O- \) atoms in the oxide is:
A . 1
в. \( \frac{48}{16} \)
c. \( \frac{58}{32} \)
D. 4


Check the validity of the following
statement:
\( \boldsymbol{p}: \mathbf{1 0 0} \) is a multiple of \( \mathbf{4} \) and \( \mathbf{5} \)
A. True
B. False


In each case; given below, find the value of \( x \) in terms of \( a, b \) and \( c \)
A \( . x=180^{\circ}-a-b+c \)
B . \( x=180^{\circ}+b+a+c \)
c. \( x=180^{\circ}+b-a-c \)
D. \( x=180^{\circ}+a+b-c \)


Give an example of a solid solution in which the solute is a gas.


The boiling point of water is inversely proportional to the atmospheric
pressure.
A. True
B. False


If the \( n^{t h} \) term of an A.P. is \( (2 n+1), \) find
the sum of first \( n \) terms of the A.P.


Name the unit of electrical potential:
A. Coulomb
B. Watt
c. Joule
D. volt


A planet of mass \( M=2.4 \times 10^{14} k g \) is
orbiting a star in time \( \boldsymbol{T}=\boldsymbol{3} \times \mathbf{1 0}^{4} \boldsymbol{s} \)
sweeps an area of \( \boldsymbol{A}=\mathbf{6 . 9} \times \mathbf{1 0}^{\mathbf{8}} \boldsymbol{m}^{\mathbf{2}} \)
Calculate Angular Momentum of Planet


A real image of a distant object is formed by a plano-convex lens on its principal axis. Spherical aberration is :
A . absent.
B. smaller, if the curved surfaces of the lens face an object.
c. smaller, if the plane surface of the lens faces the object.
D. same, whichever side of the lens faces the object


A fair coin is tossed at a fixed number
of times. If the probability of getting exactly 3 heads equals the probability
of getting exactly 5 heads, then the probability of getting exactly one head
is
A \( \cdot \frac{1}{64} \)
в. \( \frac{1}{32} \)
c. \( \frac{1}{16} \)
D.


Choose the correct answers from the
alternatives given :
Synapsis is characteristic of
A. leptotene
B. zygotene
c. pachytene
D. diakinesis


Solve the following equation
\( 3 x-4 y=1 \)
\( -2 x+\frac{8}{3} y=5 \)


Let \( A \) be a square matrix of order \( 3 \times 3 \)
then \( |k A| \) is equal to
\( \mathbf{A} \cdot k \mid A \)
в. \( k^{2}|A| \)
c. \( k^{3}|A| \)
D. \( 3 k|A| \)


There are ........ periods in the Modern Periodic Table.
A. 7
B. 18
\( c \cdot 9 \)
\( D \)


To find the equation of tangent and normal to the circle \( x^{2}+y^{2}-3 x+ \)
\( 4 y-31=0 \) at the point (2,3)


A cylinder of radius \( R \) and length \( l \) is placed in a uniform electric field \( \boldsymbol{E} \)
parallel to the axis of the cylinder. The total flux over the curved surface of the
cylinder is :
A. zero
B \( \cdot \pi R^{2} E \)
\( \mathbf{c} \cdot 2 \pi R^{2} E \)
D. \( E / \pi R^{2} \)


One mole of an element contains \( 4.2 \times \)
\( 10^{24} \) electrons. What is the atomic
number of the element??


Which character mostly differentiates
angiosperms from gymnosperms?
A. Triploid endosperm
B. Vessels in xylem
c. Seeds enclosed in fruits
D. Attractive petals


The curve \( a y^{2}=x^{2}(3 a-x) \) cuts the \( y \)
axis at coordinates \( (0, k) . \) Then \( k= \)


n fig-10, \( \triangle \boldsymbol{A B C} \) and \( \triangle \boldsymbol{A D C} \) are two
right triangles with common
hypotenuse AC. Show that, \( \angle C A D= \)
\( \angle C B D \)


Consider the reaction represented by the equation represented by the equation
\[
\begin{array}{l}
\boldsymbol{C H}_{3} \boldsymbol{C l}(\boldsymbol{g})+\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \rightarrow \\
\boldsymbol{C H}_{3} \boldsymbol{O H}(\boldsymbol{g})+\boldsymbol{H C l}(\boldsymbol{g})
\end{array}
\]
These kinetic data were obtained for the
given reaction concentrations
\( \begin{array}{ll}\text { Initial } & \text { Initial } \\ \text { conc (M) } & \text { conc (M) }\end{array} \) Initial rate of
disappearance of
\( \left[C H_{3} C l\right] \quad\left[H_{2} O\right] \) \( C H_{3} C l(M s \)
0.2 0.2
0.4 0.2 2
0.4
If \( H_{2} O \) is taken in large excess, the order of the reaction will be:
\( A \)
B. 2
\( c \cdot 3 \)
D. None of these


If
\( A, B \) and \( C \) are three events such that \( P(B)=\frac{3}{4}, P\left(A \cap B \cap C^{\prime}\right)=\frac{1}{3} \) and
\( P\left(A^{\prime} \cap B \cap C^{\prime}\right)=\frac{1}{3}, \operatorname{then} P(B \cap C) \) is
equal to
A \( \cdot \frac{1}{12} \)
B.
c. \( \frac{1}{15} \)
D.