Given below are four statements (i)-(iv).
Which two of the following statements
are correct?
(i) It is estimated that more than 70
percent of the world livestock
population is in India and China.
(ii) Stringent cleanliness and hygiene (both of the cattle and the handlers) are
of paramount importance while milking, storage and transport of the milk and its products.
(iii) Out-breeding is the breeding between animals of the same breed
only.
(iv) Crosses between different breeds is
called inbreeding.
A \( \cdot \) (i) and (ii)
B. (iii) and (iv)
c. (i) and (iv)
D. (ii) and (iii)


A substance that changes color in response to a chemical change is called
as indicator.and Name of the indicator
used when sodium hydroxide is titrated against sulphuric acid is phenolpthalein. For true add 0 and for false add 1


A survey was conducted in a small industrial plant having 50 workers to find the number of \( k m \) each person
commuted to work and the details are
given below. Represent it by a histogram and frequency polygon.
commuted Distance
\[
\begin{array}{lll}
50- & 40- & 30- \\
59 & 49 & 39
\end{array}
\]
\( (k m) \)
No. of workers


The value of \( \sin h^{-1}(3) \)
\( A \cdot \log (1+\sqrt{2}) \)
B \( \cdot \log (2+\sqrt{3}) \)
\( \mathbf{c} \cdot \log (3+\sqrt{5}) \)
D \( \cdot \log (3+\sqrt{10}) \)


Non-metals are less dense and have low
melting and boiling points as compared to metals.
A. True
B. False


The amount of volume of air that can be
inspired / expired normally is called
A. Tidal volume
B. Vital capacity
c. Residual volume
D. Normal volume


Construct a triangle of sides
\( 4.2 c m, 5.1 c m \) and \( 6 c m . \) Then construct
a triangle similar to it, whose sides are
\( \frac{2}{3} \) of corresponding sides of the first triangle.


Complete the following reaction, \( P_{4}+ \)
\( N a O H+H_{2} O \rightarrow ? \)
A. \( P H_{3}+N a_{2} H P O_{2} \)
в. \( P H_{3}+N a H_{2} P O_{2} \)
c. \( H_{3} P O_{4}+N a O \)
D. \( P H_{3}+N a_{2} P O_{4} \)


Anabaena azollae is present in the roots of Azolla.


Baeyer's reagent is:
A. aqueous bromine solution
B. neutral permanganate solution
C . acidified permanganate solution
D. alkaline potassium permanganate solution


Calculate the median for the following
\[
\begin{array}{lcccc}
\begin{array}{l}
\text { Weight } \\
\text { in kg. }
\end{array} & 20 & 22 & 24 & 27 \\
\begin{array}{l}
\text { No. of } \\
\text { boys }
\end{array} & 8 & 10 & 11 & 9
\end{array}
\]
A . 23
B . 26
c. 23.5
D . 24


Myogenic heart is not present in which of the following?
A. Man
B. limulus
c. Frog
D. Musse


The phenomenon in which an emf is induced in a conductor kept just by the side of another conductor through which varying current is passed is called
A. Magnetic effect
B. Electromagnetic induction
c. Photoelectric effect
D. Mechanical effect


Assertion
Li and \( M g \) shows diagonal relationship.
Reason
Li and \( M g \) are diagonal to each other in the Periodic table.
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. Assertion is incorrect but Reason is correct


If two litres of air is passed repeatedly
over heated copper and heated \( M g \) till no further reduction in volume takes
place the volume finally obtained will be approximate:
A. 200 mL
B. 20 mL
c. zero
D. 10 mL


In a certain region of space, the
potential is given by \( \boldsymbol{V}=\boldsymbol{k}\left[\mathbf{2} \boldsymbol{x}^{2}-\boldsymbol{y}^{2}+\boldsymbol{z}^{2}\right] . \) The electric field
at the point (1,1,1) has magnitude \( = \)
A \( . k \sqrt{6} \)
в. \( 2 k \sqrt{6} \)
c. \( 2 \sqrt{3} k \)
D. \( 4 k \sqrt{3} \)
is


Which is the best conductor of
electricity?
A. Iron
B. Silver
c. copper
D. Carbon


Kepler's first law provides information about
A. areal velocity of a planet
B. Shape of the orbit of the planettet
c. Mass of the planet
D. Distance of the planet from the sun


Write the degree of the differential
equation \( x^{3}\left(\frac{d^{2} y}{d x^{2}}\right)^{2}+\left(\frac{d y}{d x}\right)^{4}=0 \)


In the given figure, \( \angle P R Q=\angle P Q R \)
then prove that \( \angle P Q S=\angle P R T \)


\( \operatorname{Let} a_{1}, a_{2}, \dots \dots a_{50} \) are non constant
terms of an A.P. and sum of n terms is
given by \( \boldsymbol{S}_{\boldsymbol{n}}=\mathbf{5 0 n}+(\boldsymbol{n})(\boldsymbol{n}-\boldsymbol{7}) \frac{\boldsymbol{A}}{\mathbf{2}} \)
then ordered pair \( \left(d, a_{50}\right) \) is? (where dis the common difference
A. \( (A, 45 A) \)
B. \( (46 A+50) \)
c. \( (2 A, 46 A) \)
D. \( (2 A, 50+49 A) \)


The decreasing basic order of the following is:
\( \boldsymbol{i} . \boldsymbol{C H}_{3} \quad \boldsymbol{i} \boldsymbol{i} . \boldsymbol{O H} \)
iii.C \( H_{3} \) COO \( ^{\ominus} \) iv. \( H_{2} \) O
A \( \cdot(i)>(i i)>(i i i)>(i v) \)
B. \( (i v)>(i i i)>(i i)>(i) \)
C. \( (i i i)>(i)>(i i)>(i v) \)
D. \( (i v)>(i i)>(i)>(i i i) \)


Nitrogen show pentavalency
A. True
B. False


What is the name of \( \varepsilon_{0} \) ? what is the
value


The total mass of reactants and
products in a reaction will always be the same Thus law is known as?


Which of the following is a natural source of light?
A. Electric lamp
B. Electric filament
c. Torch light
D. Sunlight


The number-of line symmetries that the
given square have:
\( A \)
\( B \)
\( c \)
\( D \)


A point on the parabola \( y^{2}=18 x \) at
which the ordinate increases at twice
the rate of the abscissa is
A \( \cdot(2,4) \)
В \( \cdot(2,-4) \)
\( ^{\mathrm{c}} \cdot\left(-\frac{9}{8}, \frac{9}{2}\right) \)
D. \( \left(\frac{9}{8}, \frac{9}{2}\right) \)


Solve:- \( 2 x^{2}-18=0 \)


The natural frequency of the circuit
shown in adjoining figure is
A \( \cdot \frac{1}{2 \pi \sqrt{L C}} \)
в. \( \frac{1}{2 \pi \sqrt{2 L C}} \)
c. \( \frac{2}{2 \pi \sqrt{L C}} \)
D. zero


Farmers utilized large amount of groundwater by:
A. wells
B. over pumping of groundwater
c. both A and B
D. none of the above


Evaluate: \( \int_{-\pi / 3}^{\pi / 3} \cos ^{2} x d x \)
A. \( \sqrt{3} / 4 \)
в. \( \pi / 3 \)
\( ^{C} \cdot \frac{\pi}{3}+\frac{\sqrt{3}}{4} \)
D. \( \frac{\pi}{3}-\frac{\sqrt{3}}{4} \)


\( \left|\begin{array}{ccc}\mathbf{1} & \boldsymbol{a} & \boldsymbol{a}^{2} \\ \mathbf{1} & \boldsymbol{b} & \boldsymbol{b}^{2} \\ \mathbf{1} & \boldsymbol{c} & \boldsymbol{c}^{2}\end{array}\right|=(\boldsymbol{a}-\boldsymbol{b})(\boldsymbol{b}-\boldsymbol{c})(\boldsymbol{c}-\boldsymbol{a}) \)


ions are absorbed from the soil by
A. Passive transport
B. Active transportt
\( c . \) Both (1) \& (2)
D. Imbibition


Collecting the information about female festicide is the abortion at a female
foetus outside of legal methods.


The component of vector \( \vec{a}=2 \hat{i}+3 \widehat{j} \)
along the vector \( \hat{\boldsymbol{i}}+\widehat{\boldsymbol{j}} \) is:
A \( \cdot \frac{5}{\sqrt{2}} \)
в. \( 10 \sqrt{2} \)
c. \( 5 \sqrt{2} \)
D.


What is the approximate lightning frequency?
A. 1.4 billion flashes per year
B. 1.4 billion flashes per month
c. 1.5 billion flashes per year
D. 1.6 billion flashes per yea


By expressing the following in the form
\( \frac{p}{q}, \) where \( p \) and \( q \) are integers and \( q \neq \)
\( \mathbf{0} \)
0.2 is equal to \( \frac{1}{m}, \) Find the value of \( m \)


Silica gel is used for keeping away the moisture because it?
A. Adsorbs water molecul
B. Absorbs water molecule
c. Reacts with water
D. None of the above


Define a) Dalapon b) Metolachlor


What is displacement?


toppr
Q Type your question
of the electric filed \( |\bar{E}(r)| \) and the
electric potential \( V(r) \) with the
distance \( r \) from the centre, is best
represented by which graph ?
4
3
\( c \)
\( D \)


A synthetic rubber which is resistant to
the action of oils, gasoline and other solvents is:
A. buna-s
B. polyisoprene
c. neoprene
D. polystyrene


What is likely to be orbit number for a
circular orbit of diameter 20 nm of the hydrogen atom?
A . 10
B. 14
c. 12
D. 16


Vascular bundles are scattered in
A. Bryophytes
B. Dicot root
c. Dicot stem
D. Monocot stem


\( 0.3780 \mathrm{gm} \) of an organic chloro compound gave 0.5740 gm of silver chloride in Carius estimation. Calculate
the percentage of chlorine present in the compound (in nearest integer).(If answer is \( X \), then enter \( \frac{X}{6} \) )


What are secondary consumers?


Which of the following is not a disaccharide?
A. Cane sugar
B. Raffinose
c. Lactose
D. Maltose


The magnetic field of an electromagnetic wave is given by \( : \vec{B}= \)
\( \mathbf{1 . 6} \times \mathbf{1 0}^{-\mathbf{6}} \cos \left(\mathbf{2} \times \mathbf{1 0}^{\mathbf{7}} \boldsymbol{z}+\mathbf{6} \times\right. \)
\( \left.10^{15} t\right)(2 \hat{i}+\hat{j}) \frac{W b}{m^{2}} \) The associated
electric field will be :-
A \( \cdot \vec{E}=4.8 \times 10^{2} \cos \left(2 \times 10^{7} z+6 \times 10^{15} t\right)(\hat{i}-2 \hat{j}) \frac{V}{m} \)
B \( \cdot \vec{E}=4.8 \times 10^{2} \cos \left(2 \times 10^{7} z-6 \times 10^{15} t\right)(2 \hat{i}+\hat{j}) \frac{V}{m} \)
C・ \( \vec{E}=4.8 \times 10^{2} \cos \left(2 \times 10^{7} z-6 \times 10^{15} t\right)(-2 \hat{j}+\hat{i}) \frac{V}{m} \)
D・ \( \vec{E}=4.8 \times 10^{2} \cos \left(2 \times 10^{7} z+6 \times 10^{15} t\right)(-\hat{i}+2 \hat{j}) \frac{V}{m} \)


Which of the following statements is not correctly showing the trend of the properties mentioned?
A. \( C H_{3} C H_{2} O H>C H_{3} C H_{2} C H_{2} O H> \)
\( C H_{3} C H_{2} C H_{2} C H_{2} O H \)
B . \( C H_{3} C H_{2} O H>C H_{3} C H_{2} C H_{2} O H> \)
\( C H_{3} C H_{2} C H_{2} C H_{2} O H \)
(Boilingpoint)
c. \( C H_{3} C H_{2} C H_{2} O H>C H_{3} C H-C H_{2} O H> \)
\( C H_{3} \)
\( C H_{3} \)
\( C H_{3}-C_{I}^{\prime}-O H \)
Boiling point
D. \( \quad C H_{3} \)
\[
C H_{3}-C_{C H_{3}}^{L}-O H<C H_{3} C H-C H_{2} O H
\]
\( C H_{3} C H_{2} C H_{C} H_{2} O H \)


Calculate the angles marked with small etters in the following diagram.
(iii) Rhombus


Atomic number of Radon is:
A . 54
B. 86
c. 72
D. 68


What is diffraction of light?
A. The process where the incident light on a surface is bounced back into the same medium
B. Splitting of a ray of light into its 7 constituent colours is known as diffraction
C. The process by which a beam of light is spread out as a result of passing through a narrow aperture or across an edge,is known as diffraction
D. None of these


How many moles of \( O_{2} \) required for complete combustion of one mole of
propane?
A. 7
B. 5
c. 16
D. 10


If \( A \) and \( B \) are two events such that
\( \boldsymbol{P}(\boldsymbol{A})=\mathbf{1} / 2 \) and \( \boldsymbol{P}(\boldsymbol{B})=2 / 3, \) then
This question has multiple correct options
A. \( P(A \cup B) \geq 2 / 3 \)
B . \( P\left(A \cap B^{\prime}\right) \leq 2 / 3 \)
c. \( 1 / 6 \leq P(A \cap B) \leq 1 / 2 \)
D. \( 1 / 6 \leq P\left(A^{\prime} \cap B\right) \leq 1 / 2 \)


Element Electronegative \begin{tabular}{ccc}
\( P \) & 2.1 \\
\( H \) & 2.2 \\
\( B r \) & 2.8 \\
\hline
\end{tabular} \( B^{r} \) 1
\( O \) 3.5 If What is and
On the basis of the electronegativity values given above, in which of the following are the bonds most polar?
\( \mathbf{A} \cdot P H_{3} \)
B. \( H_{2} O \)
\( \mathbf{c} \cdot H B r \)
D. \( P_{4} \)
E \( . P B r_{3} \)


Prove that:
\( \int_{0}^{\pi} \frac{x d x}{1+\sin x}=\pi \)


The globe of Saturn can contain about
A. 150 Earths
B. 472Earths
c. 355 Earths
D. 729 Earths


Choose the correct one from the given
four options. \( \mathrm{pH} \) of bleach powder has an approximate
value of
5
8
11
14


Calculate sum of eleventh term of the
geometric sequence \( 3,6,12,24, \dots \)
A . 3141
B. 6141
\( c .2141 \)
D. 514


Read the bar graph given in above fig.
and answer the following questions:
What was the expenditure on health
and family planning in the year 1982
\( 83 ?(\text { in crores }) \)
Bar graph of the ex health and family planning during the Sixth Five Year Plan in India


Axillary buds are used to raise crop of
A. Wheat
B. Rice
c. Groundnut
D. Sugarcane


A mercury thermometer is placed in a gravity free half without touching. As temperature rises mercury expands and ascend in thermometer. If height
ascend by mercury in thermometer is \( h \) then by what height centre of mass of mercury and thermometer system descend?


Cinnabar \( (H g S) \) is heated in air, it is
first converted into which
is then reduced to on further
heating
A. \( H g O, H g \)
в. \( H g O, H g_{2} O \)
\( \mathbf{c} \cdot H g_{2} O, H g \)
D. \( H g_{2} O, H g O \)


By which of the following processes ATP
is produced?
I. Photosynthesis
Il. Aerobic respiration
III. Anaerobic respiration
A. I only
B. II only
C. I and III only
D. II and III only
E . I, II, and III


One fermi is?
A \( \cdot 10^{-15} \mathrm{cm} \)
B. \( 10^{-13} \mathrm{cm} \)
\( \mathbf{c} \cdot 10^{-10} \mathrm{cm} \)
D. \( 10^{-12} \mathrm{cm} \)


The amplitude of a damped oscillator becomes \( \left(\frac{1}{3}\right) r d \) in \( 2 s . \) If its amplitude \( \operatorname{after} 6 s \operatorname{in} \frac{1}{n} \) times the original
amplitude, the value of \( n \) is
\( A \cdot 3^{2} \)
B. \( 3 \sqrt{2} \)
\( c \cdot 3^{3} \)
D. \( 2^{3} \)


Which equation has an enthalpy change of reaction which corresponds to the standard enthalpy change of atomisation of chlorine?
\( ^{\mathbf{A}} \cdot \frac{1}{2} C l_{2}(g) \rightarrow C l(g) \)
в. \( \frac{1}{2} C l_{2}(l) \rightarrow C l(g) \)
c. \( C l_{2}(g) \rightarrow 2 C l(g) \)
D. \( C l_{2}(l) \rightarrow 2 C l(g) \)


The brightest star in the night sky as seen from earth is
A. sun
B. Alpha centime
c. sirius
D. Pleides


Which of the following gas mixture is used by the divers inside the sea?
A. \( O_{2}+H e+N_{2} \)
B. \( O_{2}+X e \)
\( \mathbf{c} \cdot O_{2}+A r+N_{2} \)
D. \( O_{2}+N_{2} \)


(i) When water is poured on an icy surface, some ice melts.
(ii) When an ice block is added to water
in a drum, some ice melts.
So in which case is more ice melted.
When water is added to ice, or ice to
water?


The centre of mass of two particles lies
on the line
A. joining the particles
B. perpendicular to the line joining the particles
c. at any angle to this line
D. None of these


If \( \sec ^{2} \theta=\frac{4}{3}, \) then the general solution
of \( \boldsymbol{\theta} \) is
\( \mathbf{A} \cdot 2 n \pi \pm \pi / 6 \)
в. \( 2 n \pi \pm \pi / 3 \)
c. \( n \pi \pm \pi / 6 \)
D. \( n \pi \pm \pi / 3 \)


The hydraulic press shown in the figure is used to raise the mass \( M \) through a height of \( 0.5 \mathrm{cm} \) by performing \( 500 \mathrm{J} \) of work at the small piston. The diameter
of the large piston is \( 10 \mathrm{cm} \), while that of
the smaller one is \( 2 c m \). The mass \( M \) is
A. \( 100 k g \)
В. \( 10^{6} k g \)
\( \mathbf{c} \cdot 10^{3} k g \)
D. None of these


A silver atom in a solid oscillates in
simple harmonic motion in some
direction with a frequency of \( 10^{12} / \) sec.
What is the force constant of the bonds
connecting one atom with the other? (Mole wt. of silver \( =108 \) and Avagadro
number \( =\mathbf{6 . 0 2} \times \mathbf{1 0}^{\mathbf{2 3}} \mathbf{g} \mathbf{m} \mathbf{m o l}^{-\mathbf{1}} \) ).
A. \( 2.2 \mathrm{N} / \mathrm{m} \)
в. \( 5.5 \mathrm{N} / \mathrm{m} \)
c. \( 6.4 \mathrm{N} . \mathrm{m} \)
D. \( 7.1 \mathrm{N} / \mathrm{m} \)


A beam of unpolarized light is passed first through a tourmaline crystal \( \boldsymbol{A} \) and then through another tourmaline
crystal \( B \) oriented so that its principal
plane is parallel to that of \( A \). The
intensity of final emergent light is \( I \)
The value of the \( I \) is
A \( \cdot \frac{I_{o}}{2} \)
в. \( \frac{I_{o}}{4} \)
c. \( \frac{I_{o}}{8} \)
D. none of these


Which of the following statement is not
true?
A. Electrostatic force is a conservative force.
B. Potential at a point is the work done per unit charge in bringing a charge from infinity to that point in an electric field.
C. Electrostatic force is non-conservative.
D. Potential is the ratio of work to charge.


A block of mass 2 kg slides on a rough surface at \( t=0, \) if speed is \( 2 \mathrm{m} / \mathrm{s} \). It stops after covering a distance of \( 20 \mathrm{cm} \) because of friction. Find work done by
the friction.


When \( A g N O_{3} \) is heated strongly, the
products formed are :
A \( \cdot N O \) and \( N O_{2} \)
B. \( N O_{2} \) and \( N_{2} O \)
c. \( N O_{2} \) and \( O_{2} \)
D. \( N O \) and \( O_{2} \)


The distance between the plates of a
condenser is reduced to \( \frac{1}{4} t h \) and the
space between the plates is filled up by a medium of dielectric constant \( \mathrm{K}(2.8) \). The
capacity is increased by :
A. 5.6times
B. 11.2times
c. 22.4 times
D. 44.8 times


The first order differential equation of
the family of circles with fixed radius \( \mathbf{r} \)
and with centre on \( x \) -axis is:
A \( \cdot y^{2}\left(\frac{d y}{d x}\right)^{2}+y^{2}=r^{2} \)
B・ \( x^{2}\left(\frac{d y}{d x}\right)^{2}+y^{2}=r^{2} \)
c. \( \left(\frac{d y}{d x}\right)^{2}+y^{2}=r^{2} \)
D. \( y^{2}-\left(\frac{d y}{d x}\right)^{2}=r^{2} \)


Describe the process of nutrition in
amoeba.Draw labelled diagram to show
that various steps of nutritions in
amoeba.


Find the equations of the lines for which \( \tan \theta=\frac{1}{\sqrt{2}}, \) where \( \theta \) is the angle of
inclination of the line and \( y- \) intercept
is 1


Let \( S(\alpha)=\left\{(x, y): y^{2} \leq x, 0 \leq x \leq \alpha\right\} \)
and \( A(\alpha) \) is area of the region \( S(\alpha) . \) If
for a \( \lambda, 0<\lambda<4, A(\lambda): A(4)=2: 5 \)
then \( \lambda \) equals
\( ^{\mathrm{A}} \cdot\left(\frac{4}{25}\right)^{\frac{1}{3}} \)
\( ^{\mathrm{B}} 4\left(\frac{4}{25}\right)^{\frac{1}{3}} \)
\( ^{c} \cdot\left(\frac{2}{5}\right)^{\frac{1}{3}} \)
\( ^{\mathrm{D}} 4\left(\frac{2}{5}\right)^{\frac{1}{3}} \)


An athlete completes one round of a circular track of radius \( \boldsymbol{R} \) in \( \mathbf{4 0} \boldsymbol{s} \). His
displacement at the end of 2 minutes will be
A \( .2 \pi R \)
в. \( 6 \pi R \)
\( c .2 R \)
D. Zero


\( 25 \% \) of a number is less than \( 18 \% \) of 650
by \( 19 . \) The number is
\( \mathbf{A} \cdot 380.8 \)
в. 392
c. 450
D. 544


How much pressure will a girl of \( 50 \mathrm{kg} \)
wearing heels with an area of cross
section \( 1 c m^{2} \) exert on the ground?
A \( .150 \times 10^{4} P a \)
В. \( 250 \times 10^{4} P a \)
\( \mathbf{c} .350 \times 10^{4} P a \)
D. \( 450 \times 10^{4} P a \)


If \( A \) is a skew-symmetric matrix of
order 3 then find \( |A| \)


Show budding in hydra diagrammatically


Figure shown a spherical concave
mirror with its pole at (0,0) and
principal axis along x axis. There is a
point object at \( (-40 \mathrm{cm}, 1 \mathrm{cm}), \) find the
position of image.


Which of the following ray diagram is
correct?
\( A \)
B.
\( c \)
\( D \)


If specific heat of 1 g of coal is \( S \) then the specific heat of 10 g of coal is


The order of \( \left(\frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}}\right)^{2}+\left(\frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}\right)^{3}+\boldsymbol{3} \boldsymbol{y}= \)
\( x^{4} \) is:
\( \mathbf{A} \cdot \mathbf{3} \)
B.
\( c \cdot 2 \)
D.


Assertion
Orbit and orbital are synonymous.
Reason
A circular path around the nucleus in
which an electron moves is called orbit
or orbital.
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


(a) Write the Haworth structure of
sucrose.
(b) Sucrose is a non-reducing sugar. Why?


A body is projected vertically up with u. Its velocity at half its maximum height is?
A \( \cdot \frac{u}{2} \)
в. \( \frac{u^{2}}{2} \)
c. \( \sqrt{2} u \)
D. \( \frac{u}{\sqrt{2}} \)


The main axis forms a cup-shaped receptacle with a narrow terminal opening. Flowers are arranged in cymose within the cup. The description refers to
A. Syconus
B. Cyathium
c. Hypanthodium
D. Verticillaster


In a transverse wave, the distance
between a crest and the immediate
trough is \( \lambda / 2 ? \)


The layer containing petroleum oil and gas is:
A. below water
B. between water and sand
c. below sand
D. above the water


A box starts at rest at the top of a 30.0
degree incline as shown and slides
down a diagonal distance of \( 4.00 m \). If
the box weighs \( 2.00 k g \) and there is no
friction, the speed of the box at the bottom of the incline is most nearly:
A. \( 4.43 \mathrm{m} / \mathrm{s} \)
B. \( 6.26 \mathrm{m} / \mathrm{s} \)
c. \( 8.24 \mathrm{m} / \mathrm{s} \)
D. \( 8.86 m / s \)
E. Not enough information


In a rectangle \( A B C D, A B=12 \mathrm{cm} \)
and \( \angle B A C=30^{\circ} . \) Calculate the length
of side \( B C \) and diagonal \( A C \)


A gun fires a bullet of mass 50 g with a velocity of mass \( 130 \mathrm{ms}^{-1} \). Because of
this, the gun is pushed back with a velocity of \( 1 \mathrm{ms}^{-1} \). The mass of the gun
is :
\( \mathbf{A} \cdot 15 \mathrm{kg} \)
B. 30 kg
c. \( 6.5 \mathrm{kg} \)
D. 20 kg


If \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{S} \) defined by \( \boldsymbol{f}(\boldsymbol{x})=\sin \boldsymbol{x}- \)
\( \sqrt{3} \cos x+1 \) is onto, then the interval of
\( \boldsymbol{S} \) is
A \( \cdot[-1,3] \)
в. [1,1]
c. [0,1]
D. [0,-1]


The displacement - time graph is shown in the figure above. What does this
graph represent? Find velocity at point
\( \mathbf{A} \)


Which of the following statements are
correct?
\( \mathbf{A} \cdot \beta-\mathrm{D}(+) \) glucopyranose is more stable than \( \alpha-\mathrm{D}(+) \) glucopyranose
B. Invert sugar is laevorotatory
C. Dextrose is \( D(+) \) glucose
D. Levulose is D(-) fructose


Two symmetrical double convex lenses A and B have same focal length,but the radii of curvature differ so that \( \boldsymbol{R}= \)
\( 0.9 R . \) If \( \mu=1.63 \) find the \( \mu_{B} \)


A parallel plate condenser has circular plates, each of radius \( 5 \mathrm{cm} \). It is being charged so that electric field in the gap between its plates rises steadily at the rate of \( 10^{12} V / m s . \) What is the
displacement current?
\( \mathbf{A} \cdot 0.07 A \)
B . \( 1.39 A \)
c. \( 13.9 A \)
D. \( 139 A \)


Rate at which electric work is done is
called as ?
A. electric power
B. electric energy
c. electric force
D. voltage.


Show that the function \( f(x)=\frac{x-2}{x+1} \)
for \( \boldsymbol{x} \neq \mathbf{0} \) is increasing.


Phase difference \( (\phi) \) and path
difference \( (\delta) \) are related by :
A \( \cdot \frac{2 \pi}{\lambda} \delta \)
в. \( \frac{\pi}{2 \lambda} \delta \)
\( c \cdot \frac{\lambda}{2 \pi} \delta \)
D. \( \frac{2 \lambda}{\pi} \)


Evaluate.
\( \mid \begin{array}{ccc}\frac{1}{z} & \frac{1}{z} & -\frac{(x+y)}{z^{2}} \\ -\frac{(y+z)}{x^{2}} & \frac{1}{x} & \frac{1}{x} \\ -\frac{y(y+z)}{x^{2} z} & \frac{x+2 y+z}{x z} & -\frac{y(x+y)}{x z^{2}}\end{array} \)


Assertion
Statement \( -1 f(x)=|x| \cos x \) is not
differentiable at \( \mathbf{x}=\mathbf{0} \)
Reason
Statement - 2 Every absolute value functions are not differentiable.
A. Statement-1 is True, Statement-2 is True
Statement- 2 is a correct explanation for
Statement-1.
B. Statement-1 is True, Statement-2 is True
Statement-2 is NOT a correct explanation
for Statement-
c. Statement-1 is True, Statement-2 is False
D. Statement-1 is False, Statement-2 is True


Let \( \boldsymbol{z}=\frac{\cos \boldsymbol{\theta}+\boldsymbol{i} \sin \boldsymbol{\theta}}{\cos \boldsymbol{\theta}-\boldsymbol{i} \sin \boldsymbol{\theta}}, \frac{\boldsymbol{\pi}}{\boldsymbol{4}}<\mathbf{0}<\frac{\boldsymbol{\pi}}{\boldsymbol{2}} \)
Then arg z is
\( A \cdot 2 \theta \)
в. \( 2 \theta-\pi \)
\( c . \pi+2 \theta \)
D. None of these


\( N m^{-1} \) is the Sl unit of:
A. viscosity
B. spring constant
c. surface tension
D. both B and C


Weightlessness experienced in a spaceship is due to
A. absence of of inertia.
B. absence of gravity
c. absence of accelerating force.
D. free fall of the spaceship


Which of the following is an intensive property?
A. Surface tension and density
B. Surface tension and volume
c. Enthalpy mass and density
D. None of these


\( U^{235} \) and \( U^{238} \) are separated by:
A. sublimation
B. gaseous diffusion
c. electrolysis
D. precipitation


Consider the following statements A and \( \mathrm{B} \) and identify the correct answer
A) The speed acquired by a body when falling in a vacuum for a given time is dependent on the mass of the falling body
B) A stone falls freely from rest and the total distance covered by it in the last
second of its motion equals the distance covered by it in the first three seconds of its motion. The stone
remains in the air for \( 5 s .\left[g=10 m s^{-2}\right] \)
A. Both A \& B are true
B. A is true but B is false
c. B is true but A is false
D. Both A \& B are false


Dalton's atomic theory was not
accepted fully:
A. when atoms combine It must be presumed to be a binary one, unless some cause appear to the contrary.
B. when elements react, their atoms sometimes combine in more than one simple, whole-number ratio.
C. elements are characterized by the mass of their atoms.
D. None of the above


Resultant force acting on a diamagnetic material in a magnetic field is in direction.
A. From stronger to the weaker part of the magnetic field
B. From weaker to the stronger part of the magnetic field
c. Perpendicular to the magnetic field
D. In the direction making \( 60^{\circ} \) to the magnetic field


If \( \alpha+\beta=\frac{\pi}{2} \) and \( \sin \alpha=\frac{1}{3}, \) then \( \sin \beta \)
is equal to
A. \( \frac{\sqrt{2}}{3} \)
B. \( \frac{2 \sqrt{2}}{3} \)
\( c \cdot \frac{2}{3} \)
D. 3


Find the value of \( x \)
A \( \cdot 50^{\circ} \)
B \( .60^{\circ} \)
\( c \cdot 70^{\circ} \)
D. \( 80^{\circ} \)


The most probable radius (in pm) for
finding the electron in \( \boldsymbol{H} \boldsymbol{e}^{+} \) is:
A . \( 0 . \)
в. 52.9
c. 26.45
D. 105.8


Name one metal in each part fitting the given description:
A metal that reacts with oxygen without burning. This question has multiple correct options
A. aluminium
B. chromium
c. iron
D. None of the above


The heat of formation \( \left(\Delta H_{f}^{o}\right) \) of \( H_{2} O(l) \) is equal to:
A. zero
B. molar heat of combustion of \( H_{2}(l) \)
c. molar heat of combustion of \( H_{2}(g) \)
D. sum of heat of formation of \( H_{2} O(g) \) and \( O_{2}(g) \)


Which of the following is correct for
cathode rays in discharge tube?
A. Independent of the nature of the cathode
B. Independent of the nature of the gas
C. Is observed in presence of electric and magnetic field
D. All of the above


What are viruses? How do they differ
from other microbes?


The shape of the wave diverging from a point of source is


A long string under tension of \( 100 N \)
has one end at \( x=0 . \) A sinusoidal
wave is generated at \( x=0 \) whose
equation is given by
\( \boldsymbol{y}= \)
\( (0.01 c m) \sin \left[\left(\frac{\pi x}{10} m\right)-50 \pi t(s e c)\right] \)
Draw velocity time graph of particle at
\( \boldsymbol{x}=\mathbf{5} \boldsymbol{m} \)


Male \( X X \) and female \( X Y \) sometime such
conditions occur due to
A. Deletion
B. Transfer of segments in \( x \) and \( Y \) chromosomes
c. Aneuploidy
D. Hormonal imbalance


A short solenoid of length \( 4 c m, \) radius
\( 2 c m \) and 100 turns is placed inside and
on the axis of a long solenoid of length
\( 80 c m \) and 1500 turns. A current of \( 3 A \)
flows through the short solenoid. The mutual inductance of two solenoids is
A. \( 0.012 H \)
H
в. \( 5.3 \times 10^{-5} H \)
\( \mathbf{c} \cdot 5.91 \times 10^{-3} \mathrm{H} \)
D. \( 8.3 \times 10^{-5} H \)


\( A=12 B=15 \) find \( 5 A-3 B \)


Define S phase and related events.


A \( 500 W \) heating unit is designed to operate on a \( 115 \mathrm{V} \) line. If line voltage
drops to \( 110 V \) line, the percentage drop in heat output will be:
A. \( 7.6 \% \)
B. \( 8.5 \% \)
c. \( 8.1 \% \)
D. 10.2 \%


In a triangle \( A B C, \) it is given that \( \angle B= \)
\( \mathbf{1 0 5}^{\circ} \) and \( \angle C=\mathbf{5 0}^{\circ} \). Find \( \angle \boldsymbol{A} \)


Glucose is stored as glycogen in
A. Pancreas
B. Bone
c. Kidney
D. Liver


If \( A B C D \) is a rhombus such that
\( \angle A C B=40^{\circ}, \) then \( \angle A D B \) is
A \( \cdot 40^{\circ} \)
B . \( 45^{\circ} \)
\( c .50^{\circ} \)
D. \( 60^{\circ} \)


Evaluate : \( \int \frac{1}{2 x^{2}+x+1} d x \)


In reverse bias, pn-junction diode
depletion layer width:
A. decreases
B. increases
c. remains same
D. can't predict


Isotopes are those atoms which have
same :
A. atomic number
B. atomic mass
C. atomic charge
D. all


Represent the structure of dichromate
ion.


In mechanism of hormone action, which
of the following is not a second
messenger?
A. Cyclic AMP
в. \( I P_{3} \)
\( \mathbf{c} \cdot C a^{++} \)
D. \( M g^{+} \)


Find \( \int \frac{d x}{x\left(x^{3}+1\right)^{2}} \)


In which of the following compounds the carbon marked with asterisk is most
electronegative?
\( \mathbf{A} \cdot C H_{3}-C H_{2}-\dot{C} H_{2}-C H_{3} \)
в. \( C H_{3}-\dot{C H}=C H-C H_{3} \)
c. \( C H_{3}-C H_{2}-C \equiv \dot{C} H \)
D. \( C H_{3}-C H_{2}-C H=\dot{C} H_{2} \)


Iris : controls the size of the pupil ::
: regulates the amount of light entering the eye
A. Pupil
B. Lens
c. Retina
D. cornea


From which of the following, methanol is not used?
A. For making dyes, phenol and polymer
B. Used as raw material in plastic industry
c. To preserve residues of dead animals
D. In production of ammonia


A barometer is faulty. When the true barometer reading are 73 and \( 75 \mathrm{cm} \) of \( \mathrm{Hg}, \) the faulty barometer reads \( 69 \mathrm{cm} \) and \( 70 \mathrm{cm} \) respectively. What is the true reading when the faulty barometer reads \( 69.5 \mathrm{cm} ? \)


The chlorination of methane is an
example of :
A. Addition
B. Elimination
c. substitution
D. Chain reaction


The inverse of the statement \( (p \wedge \sim \)
\( \boldsymbol{q}) \rightarrow \boldsymbol{r} \) is
A. \( (p \vee \sim q) \rightarrow \sim r \)
в. \( (\sim p \wedge \sim q) \rightarrow \sim r \)
c. \( (\sim p \vee q) \rightarrow \sim r \)
D. None of these.


The order and degree of the differential equation of all circles in the first quadratic which touch the co-ordinate axis is:
A .1,2
в. 2,1
\( c .3,2 \)
D. 4,3


Compared to a burn due to water at \( 100^{\circ} \)
C, a burn due to steam at \( 100^{\circ} \mathrm{C} \) is
A. more dangerous
B. less dangeour
c. equally dangerous
D. none of these


In what form fuels store their energy?
A. Chemical
B. Nuclear
c. Both A and B
D. Thermal


At room temperature, copper has free electron density of \( 8.4 \times 10^{28} m^{-3} . \) The
electron drift velocity in a copper conductor of cross-sectional area of
\( 10^{-6} m^{2} \) and carrying a current of \( 5.4 A \) will be
A \( \cdot 4 m s^{-1} \)
B. \( 0.4 \mathrm{ms}^{-1} \)
\( \mathrm{c} \cdot 4 \mathrm{cms}^{-1} \)
D. \( 0.4 \mathrm{mms}^{-1} \)


An object of mass \( 1 \mathrm{kg} \) has a PE of 1 relative to the ground when it is at a height of:
A. \( 0.102 \mathrm{m} \)
B. \( 1 \mathrm{m} \)
c. \( 9.8 \mathrm{m} \)
D. 32 \( m \)


Surface charge density of a sphare of a radius \( 10 \mathrm{cm} \) is \( 8.85 \times 10^{-8} c / m^{2} \)
Potential at the centre of the sphare is
A . \( 1000 V \)
B. \( 885 V \)
\( c \cdot 10^{-3} \)
D. \( 442.5 V \)


The following table gives the
distribution of expenditures of different
families on education. Find the mean
expenditure on education of a family.
\( \begin{array}{ll}\text { Expenditure (in. Rs.) } & \text { No. of families } \\ 1000-1500 & 24 \\ 1500-2000 & 10 \\ 2000-2500 & 33 \\ 2500-3000 & 28 \\ 3000-3500 & 30 \\ 3500-4000 & 22 \\ 4000-4500 & 16 \\ 4500-5000 & 7\end{array} \) mean is 2823.53
If true then enter 1 and if false then
enter 0


If BOD value is greater than 17 ppm, then water belongs which of the following to category?
A. Normal water
B. Highly polluted water
c. Usable water
D. Slightly polluted water


A prothallus is
A. A structure in pteridophytes formed before the thallus develops
B. A sporophytic free living structure formed in pteridophytes
C. A gametophyte free living structure formed, in pteridophytes
D. A primitive structure formed after fertilisation in pteridophytes


The reaction \( \frac{1}{2} \times H_{2}(g)+A g C l(a q) \rightarrow \)
\( H^{+}(a q)+A g(s) \)
can be represented in the galvanic cell
as:
\( \mathbf{A} \cdot \operatorname{Ag} / \mathrm{AgCl}(\mathrm{s})\left|\mathrm{KCl}(\mathrm{sol}) \| \mathrm{AgNO}_{3}(\mathrm{sol})\right| \mathrm{Ag} \)
B. PtH \( _{2} \) (g) I HCI(sol) II AgNO \( _{3} \) (sol) \( \mid \) Ag
C. \( P t, H_{2}(g) \mid \) HCI \( (\text { sol }) \| \) AgCI \( (s) \mid A g \)
D. \( \mathrm{H}_{2}(\mathrm{g}) \) | HCI(sol) \( \| \) AgCI(s) \( \mid \) Ag


Greatest extent of adaptation to various
environments is found in
A. Gymnosperms.
B. Bryophytes.
c. Ferns
D. Angiosperms


Gene is composed of which of the following?
A. Amino acids
B. Polynucleotide
c. Fatty acid
D. Nitrogen bases


For which of the following dependence of
drift velocity \( v_{d} \) on electric field \( \mathrm{E} \), is
Ohm's law obeyed?
A \( \cdot v_{d} \propto E^{2} \)
B. \( v_{d}=E^{1 / 2} \)
\( \mathbf{c} \cdot v_{d}= \) constant
D. \( v_{d} \propto E \)


If \( z_{1}, z_{2} \) are roots of equation \( z^{2}-a z+ \)
\( a^{2}=0, \) then \( \left|\frac{z_{1}}{z_{2}}\right|= \)


If \( ^{n-1} C_{r}=\left(K^{2}-3\right)^{n} C_{r+1^{\prime}}, \) then \( k \)
belongs to
\( \mathbf{A} \cdot[-\sqrt{3}, \sqrt{3}] \)
В \( \cdot(-\infty,-2) \)
\( \mathbf{c} \cdot(2, \infty) \)
D. \( [-2,-\sqrt{3}] \cup[\sqrt{3}, 2] \)


A road roller is cylindrical in shape . Its circular end has a diameter \( 200 \mathrm{cm} \) and
its width it \( 1.4 \mathrm{m} \). Find the least number
of revolutions that the roller must make
in order to level a playground of
dimensions \( 125 m \times 20 m \)


Let \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) be defined as \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{ll}0, & x \text { is Irrational } \\ \sin |x|, & x \text { is Rational }\end{array} . \) Then, which of \right.
the following is true?
A. \( f \) is discontinuous for all \( x \)
B. \( f \) is continuous for all \( x \)
c. \( f \) is discontinuous at \( x=k \pi \), where \( k \) is an interger
D. \( f \) is continuous at \( x=k \pi, \) where \( k \) is an integer


The coefficient of \( x^{4} \) in the expansion of
\( \left(\frac{x}{2}-\frac{3}{x^{2}}\right)^{10} \) is equal to:


A string of length \( 2 \mathrm{L} \), obeying Hooke's Law, is stretched so that its extension is
L. The speed of the transverse was traveling on the string is v. If the string is further stretched so that the extension in the string becomes 4L. The speed transverse wave traveling on the string will be.
A \( \cdot \sqrt{2} v \)
B.
c. \( 2 \sqrt{2} v \)
D. \( 2 v \)


What is the new quantum number proposed by Sommerfeld?
A. Principal
B. spin
c. Azimuthal
D. Magnetic


Solar cells are made up of:
A. conductors
B. insulators
c. semiconductors
D. superconductors


toppr 'OGIN
Q Type your question
A, D, , anu
A. A-Fructose-6-phosphate; B-Fructose-1,6-biphosphate;
C- 3-PGAL; D-1,3-biphosphoglyceric acid
B. A- Fructose -1,6-biphosphate ; B- 3-PGAL ; C-1,3biphosphoglyceric acid ; D-3 PGAL
C. A- 3PGAL; B-1,3 biophosphoglyceric acid ; C-3PGAL; Dse-1,6-biphosphate
D \( \quad \) uctose -1,6 -biophosphate ; B-Fructose - \( 6- \) phosphate ; C-PGAL ; D-1,3- biphosphoglyceric acid


Find a vector of magnitude 5 units which is coplanar with vectors \( 3 \hat{i}-\hat{j}- \) \( \hat{\boldsymbol{k}} \) and \( \hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}-2 \hat{\boldsymbol{k}} \) and is perpendicular
to the vector \( 2 \hat{i}+2 \hat{j}+\hat{k} \)


A converging lens is used to form an image on a screen. When the upper half of the lens is covered by an opaque
screen.
a) Half of the image will disappear
b) No part of image will disappear
c) Intensity of the image will increase
d. Intensity of the image will decrease
\( A \cdot \) a and \( c \) are true
B. a and d are true
c. b and c are true
D. b and d are true


Find the principal value the following
expression:
\( \sin ^{-1}\left(-\frac{\sqrt{3}}{2}\right) \)


Which of the following statements are
correct?
A. The second ionization enthalpy of oxygen element is greater than that of the fluorine element.
B. The first ionization enthalpy of phosphorus is greater than that of aluminium.
C. The first ionization enthalpy of aluminum is slightly greater than that of gallium.
D. The first ionization enthalpy of \( B \) is less than that of Be.


If the sum of the mean and variance of a
binomial distribution for 6 trials be
\( 10 / 3, \) find the distribution.


The dissociation constant of acetic acid
at a given temperature is \( 1.69 \times 10^{-5} \)
The degree of dissociation of \( 0.01 M \)
acetic acid in the presence of \( 0.01 M \)
HCl is equal to:
A . 0.41
в. 0.13
c. \( 1.69 \times 10^{-3} \)
D. 0.013


Choose the correct answers from the
alternatives given :

Which of the following does not form during glycolysis?
A. NADH
в. Атр
c. Pyruvate
D. \( F A D H_{2} \)


In every radioactive series, the final element formed is lead (Pb)
A. True
B. False


Assertion
Monocot stem has collateral open
vascular bundle.
Reason
Open vascular bundle is without
vascular cambium.
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.


If the line joining the points
\( \left(a t_{1}^{2}, 2 a t_{1}\right),\left(a t_{2}^{2}, 2 a t_{2}\right) \) is parallel to \( \mathbf{y}= \)
\( \mathbf{x}, \) then \( \mathbf{t}_{\mathbf{1}}+\mathbf{t}_{\mathbf{2}}= \)
A \( \cdot \frac{1}{2} \)
B. 4
\( c \cdot \frac{1}{4} \)
D. 2


By selling an article for \( R s .225 \), the shopkeeper losses \( 25 \% \). Find the \( \% \) gain or loss, if be article be sold for \( \boldsymbol{R} \boldsymbol{s} \). \( \boldsymbol{3} \boldsymbol{6} \boldsymbol{0} \)
A. \( 20 \% \) gain
B. \( 20 \% \) loss
c. \( 10 \% \) loss
D. \( 10 \% \) gain


\( \sqrt{V} \) on two particles \( A \) and \( B \) are plotted against de-broglie wavelengths. Where V is the potential on the particles. Which of the following relation is correct about the mass of particles?
A \( \cdot m_{A}=m_{B} \)
в. \( m_{A}>m_{B} \)
\( \mathbf{c} \cdot m_{A}<m_{B} \)
D \( . m_{A} \leq m_{B} \)


Lower is the critical micelle
concentration of surfactant, \( \ldots \) is the
detergency
1. lower
2. higher
3. indeterminate
4. none of the above
Fill in the blank with the correct answer
number.


The unit of Respiratory System is


If the area enclosed by the curves \( y^{2}= \)
\( 4 \lambda x \) and \( y=\lambda x \) is \( \frac{1}{9} \) square units then
value of \( \lambda \) is
A .24
B. 37
c. 48
D. 38


\( \left(\frac{-9}{13} \times \frac{5}{6}\right)-\left(\frac{-9}{13} \times \frac{4}{6}\right)=\frac{-9}{13} \times \)
\( \left(\frac{5}{6}-\frac{4}{6}\right) \)
If true then enter 1 and if false then
enter 0


A homogeneous bar, as shown in the figure, has mass \( m \) and length L. The bar which is free to rotate in the vertical
plane about a pin at \( 0, \) is released from
rest in the position \( \theta=0 . \) The angular
acceleration, when \( \theta=60^{0} \) is:
A \( \cdot \frac{g}{2 L} \)
в. \( \frac{0.25 g}{L} \)
c. \( \frac{g}{L} \)
D. \( \frac{0.75 g}{L} \)


Find the value of the determinant:
\[
\left|\begin{array}{ccc}
\cos (\theta+\phi) & -\sin (\theta+\phi) & \cos 2 \phi \\
\sin \theta & \cos \theta & \sin \phi \\
-\cos \theta & \sin \theta & \cos \phi
\end{array}\right|
\]


What is the main reason for using a
solenoid instead of a straight wire to produce magnetic field?


A resistance and inductance are
connected in series with a source of
alternating e.m.f. Derive an expression for resultant voltage impedance and phase difference between current and
voltage in alternating circuit.


\( 3 \frac{2}{5}=3+---- \)
\( A \cdot \frac{3}{5} \)
B.
\( c \cdot \frac{2}{5} \)
D. \( _{3} \frac{2}{5} \)


If. \( x=2-2^{1 / 3}+2^{2 / 3}, \) then value of \( x^{3}- \)
\( 6 x^{2}+18 x+18 \) is
A . 22
B. 33
\( c \cdot 45 \)
D. 40


The first artificial transmutation was
observed by Rutherford. If true enter 1 else enter 0


If 3 coins are tossed simultaneously, the probability of 1 head and 2 tails is:
A \( \cdot \frac{1}{8} \)
в. \( \frac{3}{8} \)
\( c \cdot \frac{5}{8} \)
D. \( \frac{7}{8} \)


Very Short Answer Type:
Define wall pressure.


Digestion in amoeba mainly takes place in
A. Food vacuole
B. Cytoplasm
c. water vacuole
D. None of the above


toppr
Q Type your question
Why
acceleration of block \( \boldsymbol{A} \) and \( \boldsymbol{B} \). Which
graph best represents acceleration \( a_{1} \)
and \( a_{2} \) of block \( A \) and \( B \) respectively
with time?
\( A \)
B.
\( c \)
D.


is an obsolete
scientific model of the atom proposed by J. J. Thomson in 1904.
A. Musk melon model
B. Plum pudding model
c. Christmas melon model
D. Pudding model


What is the highest generated power?
\( ^{\mathbf{A}} \cdot P_{\max }=\frac{v^{2} B^{2} d}{4 \rho S} \)
B. \( \quad P_{\max }=\frac{v^{2} B^{2} S d}{4 \rho} \)
\( ^{\mathrm{C}} P_{\max }=\frac{v^{2} B^{2} S d}{\rho} \)
D \( \quad P_{\max }=\frac{v^{2} B^{2} S d}{2 \rho} \)


At \( 25^{\circ} \mathrm{C} \) molar conductance of 0.1 molar
aqueous solution of an ammonium
hydroxide is 9.54 oh \( m^{-1} c m^{2} \) mol \( ^{-1} \) and
at infinite dilution its molar
conductance is 238 oh \( m^{-1} c m^{2} m o l^{-1} \)
The degree of ionization of ammonium hydroxide at the same concentration
and temperature is?


Pancreatic juice contains
A. Trypsin, lipase and maltase
B. Pepsin, trypsin and maltase
C. Trypsin, chymotrypsin, amylase and lipase
D. Trypsin, pepsin and amylase


A stone is tied to the middle of a string
and suspended from one end as shown
in the figure. Here \( \mathrm{S} \) is the stone and 0 is the pint of suspension
(ii) if we increase the pull at \( \mathrm{P} \)
gradually, the string will break
A. Below the stone
B. At the point P itself
c. Above the stone
D. Nothing can be decided


What number of chromosomes are
present in a gamete as compared to the parent cell after meiosis?
A. Twice
B. Three times
c. same
D. half
E. One quarter


The metallic character of the element of
IV A group
A. Decreases from top to bottom
B. Has no significance
c. Does not change
D. Increase from top to bottom


: The area bounded by \( x=2 \cos \theta, y= \)
\( 3 \sin \theta \) is \( 36 \pi \) sq. units.
II: The area bounded by \( x=2 \cos \theta, y= \)
\( 2 \sin \theta \) is \( 4 \pi \) sq.units.
Which of the above statement is
correct?
A. Onlyı
B. Only II
c. Both I and II
D. Neither I nor II.


What change in colour is observed when white silver chloride is left exposed in
sunlight? State the type of chemical reaction and also write its chemical
equation.


A point charge of \( +6 \mu C \) is placed at a distance \( 20 \mathrm{cm} \) directly above the centre of a square of side \( 40 \mathrm{cm} . \) The magnitude of the flux through the
square is
\( A \cdot \epsilon_{0} \)
в. \( \frac{1}{\epsilon_{0}} \)
c. \( \epsilon_{0} \times 10^{-6} \)
D. \( \frac{1}{\epsilon_{0}} \times 10^{-6} \)


What is the value of
\( \cos \left\{\cos ^{-1} \frac{4}{5}+\cos ^{-1} \frac{12}{13}\right\} ? \)
A . \( 63 / 65 \)
B. 33/65
c. 22/65
D. \( 11 / 65 \)


When copper rod donates electrons to
hydrogen ions, it gains charge.
A. positive
B. negative
c. no charge
D. can't say


Find unit vector in the direction of vector \( \vec{a}=2 \hat{i}+3 \widehat{j}+\widehat{k} \)


Let \( S \) and \( S^{\prime} \) be two foci of the ellipse \( \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 . \) If a circle described on
\( S S^{\prime} \) as diameter intersects the ellipse
in real and distinct points, then the eccentricity \( e \) of the ellipse satisfies
\( ^{A} \cdot e=\frac{1}{\sqrt{2}} \)
в. \( _{e} \in\left(\frac{1}{\sqrt{2}}, 1\right) \)
\( ^{\mathrm{c}} \cdot_{e} \in\left(0, \frac{1}{\sqrt{2}}\right) \)
D. None of these


Which describes a nonspontaneous reaction?
A. Positive \( \Delta H \)
B. Negative \( \Delta H \)
c. Positive \( \Delta G \)
D. Positive \( \Delta S \)
E. None of these


Action and reaction forces never
balance out. Because,
A. they are equal but not opposite always
B. they are unequal in magnitude even though opposite in direction
C. they act on different bodies
D. they are unequal in magnitudes


A double slit is illuminated by light of wave length \( 6000 A^{0} \). The slits are \( 0.1 \mathrm{cm} \)
apart and the screen is placed 1 m away Then the angular position of 10 th maxima is
A . \( 6 \times 10^{-3} r a d \)
B. 6 rad
c. \( 0.006^{\circ} \)
D. \( 6^{\circ} \)


Define e.m.f. of a cell. How can you compare the emf of two cells using potentiometer?


The diagram, given below, shows two paths drawn inside a rectangular field \( 80 \mathrm{m} \) long and \( 45 \mathrm{m} \) wide. The widths of
the two paths are \( 8 \mathrm{m} \) and \( 15 \mathrm{m} \) as shown. Find the area of the shaded portion


In a particular isomer of
\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4} \boldsymbol{C l}_{2}\right], \) the \( \boldsymbol{C l}-\boldsymbol{C o}-\boldsymbol{C l} \)
angle is \( 90^{\circ}, \) the isomer is known as:
A. Linkage isomer
B. Optical isomer
c. Cis-isomer
D. Position isomer


Two coils \( P \) and \( Q \) are lying parallels and very close to each other. Coil P is
connected to an AC source whereas Q is
connected to a sensitive galvanometer. On pressing key \( \mathrm{K} \)
A. small variations are observed in the galvanometer for applied 50 Hz voltage
B. deflections in the galvanometer can be observed for applied voltage of 1 Hz to 2 Hz.
c. no deflection in the galvanometer will be observed
D. constant deflection will be observed in the galvanometer for 50 Hz supply voltage


What is \( \int_{0}^{2 \pi} \sqrt{1+\sin \frac{x}{2}} d x \) equal to?
\( A \cdot 8 \)
B. 4
\( c \cdot 2 \)
D.


Which one of the following is a base analogue?
A. Nitrous acid
B. Colchicine
c. 5 - bromouracil
D. Caffeine


A man stands in front of a hill rock and
fires a gun. He hears an echo after 1.5 sec. The distance of the hill rock from
the man is (velocity of sound in
air=330m/s)
A . 220m
B. 247.5m
\( c .268 .5 \mathrm{m} \)
D. 292.5m


What is the primary characteristic on which the broad division is made?


Eighty-nine students of class VIII appeared for a combined test in Maths and Physics. If 62 students passed in
both \( ; 4 \) failed in Maths and Physics and
7 failed only in Maths. How many passed in Physics. (Use a Venndiagram)


Pressure of an ideal gas is increased by keeping temperature constant. The kinetic energy of molecules.
A . Decreases
B. Increases
c. Remains same
D. Increases or decreases depending on the nature of gas


The fission of a heavy nucleus gives, in
general, two smaller nuclei, two or three neutrons, some \( \beta- \) particles, and
some \( \gamma- \) radiation. It is always true
that the nuclei produced
A. have a total rest-mass that is greater than that of the original nucleus
B. have large kinetic energies that carry off the greater part of the energy released
c. travel in exactly opposite directions
D. have neutron-to-proton ratios that are too low for stability
E. have identical neutron-to


Botanical name of tomato is
A . Allium cepa
B. Solanum tuberosum
c. saccharum officinarum
D. Lycopersicon esculentum


\( \sin \theta=\cos \theta \) for all values of \( \theta \)
Enter 1 for true and 0 for false


f the given figure ,if \( X Y=Y Z \) then
\( \angle X Y T=? \)
\( A \cdot 35^{\circ} \)
B . \( 100^{\circ} \)
\( c \cdot 110^{\circ} \)
0.70


A box of mass \( \mathrm{m} \) slides down a
frictionless inclined plane of Iength L and vertical height h. Calculate the kinetic energy at the bottom of plane.
A . mgl
в. mghh
c. \( \mathrm{mgL} / \mathrm{h} \)
D. \( \operatorname{mgh} / \mathrm{L} \)
E. mghL


Solve the following system of inequalities graphically:
\( \mathbf{3} \boldsymbol{x}+\mathbf{4} \boldsymbol{y} \leq \mathbf{6 0}, \quad \boldsymbol{x}+\mathbf{3} \boldsymbol{y} \leq \mathbf{3 0}, \quad \boldsymbol{x} \geq \)
\( 0 . y \geq 0 \)


Most abundant metal in earth crust
is
\( A \cdot A \)
B.
c. \( \mathrm{Fe} \)
\( D \cdot s i \)


What are the two properties of carbon which lead to the huge number of carbon compounds we see around us?


A stream of water flowing horizontally with a speed of \( 15 m s^{-1} \) gushes out of a
tube of cross-sectional area \( 10^{-2} m^{2} \)
and hits a vertical wall normally. Assuming that it does not rebound from the wall, the force exerted on the wall by the impact of water is:
A \( \cdot 1.25 \times 10^{3} N \)
В. \( 2.25 \times 10^{3} N \)
c. \( 3.25 \times 10^{3} N \)
D. \( 4.25 \times 10^{3} N \)


Cells of Grass leaves which help in minimising cuticular transpiration are
A. Bulliform cells
B. Guard cells
c. subsidiary cells
D. Endodermal cells


Convection occurs usually in
A. Solids
B. Fluids
\( c . \) Both
D. None


Which element has neither definite
shape nor volume?
A. Sodium
B. Hydrogen
c. lodine
D. Lithium


Number of electrons involved in the
electrodeposition of \( 63.5 g \) of \( C u \) from a
solution of \( C u S O_{4} \) is?
A \( \cdot 6.022 \times 10^{23} \)
3 \( 3.02 \times 10^{2}+0.62^{23} \)
B. \( 3.011 \times 10^{23} \)
c. \( 12.044 \times 10^{23} \)
D. \( 6.022 \times 10^{22} \)


Assertion
Spontaneous process is an irreversible process and may be reversed by some
external agency.
Reason
Decrease in enthalpy is a contributory
factor for spontaneity.
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


If \( I_{n}=\int(\log x)^{n} d x, \) then \( I_{6}+6 I_{5}= \)
\( \mathbf{A} \cdot x(\log x)^{5} \)
B. \( -x(\log x)^{5} \)
\( \mathbf{c} \cdot x(\log x)^{6} \)
\( \mathbf{D} \cdot-x(\log x)^{6} \)


The correct formula of critical velocity
\( \left(V_{c}\right) \) is :
A \( \cdot V_{c}=\frac{k \eta d}{r} \)
B. \( v_{c}=\frac{k \eta}{d r} \)
\( ^{\mathrm{C}} \cdot_{V_{c}}=\frac{d r}{k \eta} \)
D. \( V_{c}=\frac{r \eta}{d k} \)


The length of a rectangle is increased by
\( 60 \% \). By what percent would the width be decreased so as to maintain the
same area?
A \( \cdot 37 \frac{1}{2} \% \)
B. 60\%
c. \( 75 \% \)
D. 120\%


Chlorofluorocarbons (CFCs) are widely used in air conditioners, refrigerators etc, because of being:
A. highly reactive
B. flammable
c. non-reactive
D. all of these


Find the distance of the point \( \boldsymbol{P}(\boldsymbol{3}, \boldsymbol{4}, \boldsymbol{4},) \)
from the point, where the line joining
the points \( \boldsymbol{A}(\boldsymbol{3},-\boldsymbol{4},-\boldsymbol{5}) \) and \( \boldsymbol{B}(\boldsymbol{2},-\boldsymbol{3}, \boldsymbol{1}) \)
intersected the plane \( 2 x+y+z=7 \)


For a thin convex lens when the height of the object is doubled than its image, its object distance is equal to
\( A \cdot f \)
B . \( 2 f \)
\( c \cdot 3 f \)
D. \( 4 f \)


A die has 6 faces marked by the given numbers as shown below:
The die is thrown once. What is the
probability of getting the smallest integer?
\( 1 3 \longdiv { 2 3 } \)


Assertion: The strength of an oxy acid increases when the choice of the central
atom is made from down a group.
Reason: The strength of an oxy acid increases with EN value of the central
atom
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
E. Both Assertion and Reason are false


Energy liberated in the de-excitation of hydrogen atom from the third level to the first level falls on a photo-cathode. Later when the same photo-cathode is exposed to a spectrum of some unknown hydrogen-like gas, excited to the second energy level, it is found that the de Broglie wavelength of the fastest photoelectrons now ejected has
decreased by factor of \( 3 . \) For this new gas, difference of energies of the second Lyman line and the first Balmer line is
found to be 3 times the ionization
potential of the hydrogen atom. Select
the correct answers.
This question has multiple correct options
A. The gas is lithium
B. The gas is helium
c. The work function of photo-cathode is 8.5 eV
D. The work function of photo-cathode is 5.5 eV


Fill in the blanks:
A push or a pull on an object are types of
A. pressure
B. attraction
c. repulsion
D. force


In which stage of its life cycle, the silk moth begins to produce silk fibre?
A. 3rd instar larva
B. 4th instar larva
c. 5 th instar larva
D. Pupa


At a curved path of the road, the road bed is raised a little on the side away
from the centre of the curved path. The slope of the road bed is given by
A \( \cdot \tan \theta=r g / v^{2} \)
B . \( \tan \theta=r / g v^{2} \)
C. \( \tan \theta=v^{2} / r g \)
D. \( \tan \theta=v^{2} g / r \)


Consider the following statements
about sucrose and choose the wrong
statement.
A. Hydrolysis of sucrose with dilute acid yields an equimolar mixture of D-glucose and D-fructose
B. Acid hydrolysis of sucrose is accompanied by a change in optical rotation
C. In sucrose, the glycosidic linkage is between \( C-1 \) of glucose and \( \mathrm{C}-2 \) of fructose
D. Aqueous solution of sucrose exhibits mutarotation


From the \( \alpha \) -particle scattering
experiment, Rutherford concluded that:
This question has multiple correct options
A. \( \alpha \) -particles can approach within a distance of the order of \( 10^{-14} \mathrm{m} \) of the nucleus
B. the radius of the nucleus is less than \( 10^{-14} m \)
C . scattering follows Coulomb's law
D. the positively charged parts of the atom move with extremely high velocities


In distance-time graph, which of the following is plotted on the x-axis?
A. speed
B. distance
\( c . \) time
D. none of the above


Factorise:
\( \mathbf{2} \sqrt{\mathbf{2}} \boldsymbol{a}^{\mathbf{3}}+\mathbf{1 6} \sqrt{\mathbf{2}} \boldsymbol{b}^{\mathbf{3}}+\boldsymbol{c}^{\mathbf{3}}-\mathbf{1 2 a b} \boldsymbol{c} \)


Arrange the following in the increasing order of their basic strength in aqueous solution:
\( \boldsymbol{C H}_{3} \boldsymbol{N} \boldsymbol{H}_{2},\left(\boldsymbol{C H}_{3}\right)_{3} \boldsymbol{N},\left(\boldsymbol{C H}_{3}\right)_{2} \boldsymbol{N} \boldsymbol{H} \)


Write the difference between potential
difference and emf.


Which of the following statements regarding motion of particle is true?
A. The motion between \( A \) and \( B \) is known
B. The motion between \( A \) and \( B \) is erratic
c. The motion between \( A \) and \( B \) may have been steady o erratic
D. The motion between \( A \) and \( B \) is steady


A substance has a half-life of 5 years Find out how much of the initial sample remains after 10 years?
A. one-fourth (1/4)
B. one-sixteenth (1/16)
c. one-half \( (1 / 2) \)
D. one-fifth (1/5)
E . one-eighth (1/8)


The reagent(s) for the following conversion,
is/are
A. alcoholic KOH
B. alcoholic KOH followed by NaNHa
c. aqueous KOH followed by \( \mathrm{NaNH}_{2} \)
D. \( \mathrm{Zn} / \mathrm{CH}_{3} \mathrm{OH} \)


\( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{l}a \tan ^{-1}\left(\frac{1}{x-4}\right) \text { if } 0 \leq x<4 \\ b \tan ^{-1}\left(\frac{2}{x-4}\right) \text { if } 4<x<6 \\ \sin ^{-1}(7-x)+a \frac{\pi}{4} \quad \text { if } \sin ^{-1}(7-2)\end{array}\right. \)
and \( f(4)=\pi / 2 \) is continuous on (0,8)
then
A . (1,1)
B. (1,-1)
c. (-1,1)
D. (-1,-1)


A store has in stock 1230 pairs of socks and the price is 50 per pair of socks, then the total amount the store owner
gets after selling all the items in the stock. Ans in Rs \( k 00 . \) Find the value of \( k \)


rooe vaurauestion
a, which of the following graph is


A small bead of mass m moving with
velocity v gets threaded on a stationary semicircular ring of mass \( \mathrm{m} \) and radius R kept on a horizontal table. The ring can freely rotate about its centre. The bead comes to rest relative to the ring. What will be the final angular velocity of
the system?
A. \$\$displaystyle \{vyl《R\$\$
B. \$\$|displaystyle(2v)|(R)\$\$
c. \$\$ ldisplaystyle \{v)|(2R) \$\$
D. \$\$ldisplaystyle \{3v)|(R)\$\$


Find the value of \( s: \)
\( s(3 s-7)-3 s(s-8)=9 \)
A \( \cdot \frac{17}{9} \)
в. \( \frac{9}{17} \)
\( c \cdot \frac{-9}{17} \)
D. \( \frac{-17}{9} \)


For the gas phase reaction,
\[
\boldsymbol{P} \boldsymbol{C l}_{5(g)} \rightleftharpoons \boldsymbol{P} \boldsymbol{C l}_{3(g)}+\boldsymbol{C l}_{2(g)}
\]
Which of the following conditions are
correct?
\( \begin{array}{lll}\text { A. } \triangle H<0 & \text { and } & \Delta S<0\end{array} \)
B. \( \triangle H>0 \) and \( \Delta S<0 \)
c. \( \Delta H=0 \) and \( \Delta S<0 \)
\( \begin{array}{lll}\text { D. } \triangle H>0 & \text { and } & \Delta S>0\end{array} \)


Barometer is used for measuring:
A. Liquid pressure
B. Thrust
c. Atmospheric pressure
D. Air temp


Predict hybridization and shape of \( \boldsymbol{S} \boldsymbol{F}_{4} \)
molecule.
A \( \cdot s p^{3} d \) and see saw
B . sp \( ^{3} \) and tetrahedral
c. sp and T-shape
D. \( s p^{3} d^{2} \) and octahedral


Assertion
Amoebiasis is caused by Amoeba
Reason
The protist feeds on red blood
corpuscles
A. If both the assertion and the reason are true and the
reason is a correct explanation of the assertion
B. If both the assertion and reason are true but the
reason is not a correct explanation of the assertion
C. If the assertion is true but the reason is false
D. If both the assertion and reason are false


The isotopes of carbon is used as radiocarbon dating.
A. \( C-12 \)
в. \( C-13 \)
c. \( C-14 \)
D. \( C-11 \)


When domestic sewage mixes with
river water
A. Small animals like rats will die after drinking river water
B. The increased microbial. activity releases micronutrients such as iron
C. The increased microbial activity uses up dissolved oxygen
D. The river water is still suitable for drinking as impurities are only about \( 0.1 \% \)


Two balls are dropped from different heights at different instants. Second
ball is dropped 2 sec after the first ball. If both balls reach the ground simutlanously after 5 sec of dropping the first ball, the difference of initial
heights of the two balls will be: \( (g= \)
\( 9.8 m / s^{2} \)
\( \mathbf{A} \cdot 58.8 m \)
B. \( 78.4 m \)
c. \( 98.0 m \)
D. \( 117.6 m \)


\( \int \frac{1+2 x^{2}}{x^{2}\left(1+x^{2}\right)} d x= \)
A. \( \quad \tan ^{-1} x+\frac{1}{x}+c \)
B. \( \tan ^{-1} x-\frac{1}{x}+c \)
c. \( \frac{\tan ^{-1} x}{x}+c \)
D. \( \frac{\tan ^{-1} x}{x^{2}}+c \)


Let \( A=\{1,2,3\} . \) Then number of
equivalence relations containing (1,2) is:
\( A \)
B. 2
\( c \cdot 3 \)
D. 4


Power dissipated in the resistor is \( \boldsymbol{P}= \)
A. \( V I \)
B . \( I^{2} R \)
\( ^{\mathrm{C}} \cdot \frac{V^{2}}{R} \)
D. Any of these


The chloro-bis (ethylenediamine)
nitrocobalt(III) ion is -
\( \mathbf{A} \cdot\left[\operatorname{Co}\left(N O_{2}\right)_{2}(e n)_{2} C l_{2}\right]^{+} \)
B. \( \left[\operatorname{CoCl}\left(N O_{2}\right)_{2}(e n)_{2}\right]^{+} \)
c. \( \left[\operatorname{Co}\left(N O_{2}\right) C l(e n)_{2}\right] \)
D. \( \left.[\operatorname{Co(en}) C l_{2}\left(N O_{2}\right)_{2}\right] \)


In the following reaction
\[
\begin{array}{c}
\boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{2}+\boldsymbol{B} \boldsymbol{r} \boldsymbol{O}_{3}^{-}+\boldsymbol{H}_{2} \boldsymbol{O} \longrightarrow \boldsymbol{X} \boldsymbol{e}+ \\
\boldsymbol{B r} \boldsymbol{O}_{4}^{-}+\mathbf{2} \boldsymbol{H} \boldsymbol{F}
\end{array}
\]
equivalent mass of \( B r O_{3}^{-}= \)
molar mass


Suppose the triangle \( A B C \) has an obtuse angle at \( C \) and let \( D \) be the midpoint of side AC Suppose E is on BC such that the segment DE is parallel to AB. Consider the following three statements
i) E is the midpoint of BC
ii) The length of DE is half the length of
\( A B \)
iii) DE bisects the altitude from \( C \) to \( A B \)
A. only (i) is true
B. only (i) and (ii) are true
c. only (i) and (iii) are true
D. all three are true


Equal amounts of \( (e, e) \) and \( (a, a) \) conformers of trans - 1, 2 - dichloro
cyclohexane exist in non-polar solvents but the (e, e) conformer exists in polar solvents. Explains.


On the basis of the following thermochemical data
\( \boldsymbol{H}_{2} \boldsymbol{O}_{(\boldsymbol{g})} \longrightarrow \boldsymbol{H}_{(a q)}^{+}+\boldsymbol{O} \boldsymbol{H}_{(a q)}^{-} ; \boldsymbol{\Delta} \boldsymbol{H}= \)
\( \mathbf{5 7 . 3 2 k J} \)
\( \boldsymbol{H}_{2(g)}+\frac{1}{2} \boldsymbol{O}_{2(g)} \longrightarrow \boldsymbol{H}_{2} \boldsymbol{O}_{(l)} ; \boldsymbol{\Delta} \boldsymbol{H}= \)
\( -286.2 k J \)
The value of enthalpy of formation of
\( O H^{-} \) ion at \( 25^{\circ} C \) is:
\( \mathbf{A} \cdot+288.88 k J \)
в. \( -343.52 k J \)
c. \( -22.88 k J \)
D. \( -228.88 k J \)


A chemical reaction proceeds into the following steps
Step \( \mid: 2 A \rightleftharpoons X \) (fast)
Step II: \( \boldsymbol{X}+\boldsymbol{B} \rightarrow \boldsymbol{Y}(\text { slow }) \)
Step III: \( Y+B \rightarrow \) Product(fast)
The rate low for the overall reaction \( ^{*} \) is:


the radial acceleration:
A \( \cdot 1.65 m s^{-2} \)
B. \( 5.65 \mathrm{ms}^{-2} \)
c. \( 11.65 m s^{-2} \)
D \( .21 .65 \mathrm{ms}^{-2} \)


The value of \( \left(1+\tan ^{2} \theta\right) \sin ^{2} \theta \) is
\( \mathbf{A} \cdot \sin ^{2} \theta \)
B. \( \cos ^{2} \theta \)
\( \mathbf{c} \cdot \tan ^{2} \theta \)
\( D \cdot \cot ^{2} \theta \)


When the temperature of a straight rigid rod increases from \( t \) to \( t+\Delta t \), its
moment of inertia changes from I to
\( I+\Delta I . \) If \( \alpha \) be the coefficient of linear
expansion, then \( 2 \alpha \Delta t \) will be equal to.
\( ^{A} \cdot \frac{I}{\Delta I} \)
B. \( I \times \Delta I \)
c. \( \frac{\Delta I}{I} \)
D. \( 2 I \Delta I \)


One mole of any substance contains
\( 6.022 \times 10^{23} \) atoms/molecules. Number
of molecules of \( H_{2} S O_{4} \) present in 100
\( \mathrm{mL} \) of \( 0.02 \mathrm{M} H_{2} S O_{4} \) solution is
\( -? \)
A . \( 12.044 \times 10^{20} \) molecules
B. \( 6.022 \times 10^{23} \) molecules
C. \( 1 \times 10^{23} \) molecules
D. \( 12.044 \times 10^{23} \) molecules


The \( \overrightarrow{\boldsymbol{s}}-\boldsymbol{t} \) graph of a body is as shown in
the figure. The time for which the body
is in motion is:
\( A \cdot 2 \)
B. 3
\( c .6 \)
\( D \cdot 10 \)


\( \boldsymbol{A}+\boldsymbol{B} \leftrightharpoons \boldsymbol{C}+\boldsymbol{D}, \boldsymbol{K}_{c} \) for this
reaction is \( 10 . \) If 1,2,3,4 mole/litre of \( A, B, C \) and \( D \) respectively are present
in a container at \( 25^{\circ} \mathrm{C} \), the direction of
reaction will be:
A. from left to right
B. from right to left
c. reaction is at equilibrium
D. unpredictable


The anomers of fructofuranose are
called:
A. \( \alpha \) anomers
B. \( \beta \) anomers
c. both \( A \) and \( B \)
D. none of these


Which substance is not present in
nucleic acids?
A. Cytosine
B. Adenine
c. Thymine
D. Guanidine


Two bodies \( A \) and \( B \), moving in the same direction collide and after collision,
move with the common velocity in the direction of \( \mathbf{A} \)
A. The magnitude of force exerted by A on B is greater than the magnitude of force exerted by B on \( A \)
B. Both exertequal but opposite force on each other
c. The change in momentum of A and B are equal but opposite in direction
D. Both (B) and (C)


Predict the structure of the following and indicate whether the bond angles are likely to be dissorted from the
theoretical values:
\( \boldsymbol{P F}_{3} \)


The vagus nerve is the cranial nerve,
numbering
\( \mathbf{A} \cdot 10^{t h} \)
B. \( 9^{\text {th }} \)
c. 5th
D. 8th


Write the function of the following parts of nuclear reactor along with material used in making it.
a. Control rod
b. Moderator


What causes electrification of two
bodies when they are rubbed together?
A. Transfer of atoms from one body to the other body.
B. Transfer of electricity from one body to the other body.
C. Transfer of electrons from one body to the other body.
D. Transfer of heat from one body to the other body.


Phosphorus is present in
A. Protein
B. DNA
\( c . \) RNA
D. Both DNA and RNA


The \( N a^{+} / K^{+} \) pump is present in the plasma membrane of mammalian cells
where it.
A. Expels potassium from the cell
B. Expels sodium and potassium from the cell
c. Pumps sodium into the cell
D. Expels sodium from the cell


Show that the following points form a right angled triangle. (2,-3),(-6,-7) and (-8,-3)


From the following, reverse biased diode
is
\( A \)
в.
c.
D.


A shopkeeper sells sugar in such a way that the selling price of 950 gm is the same as the cost price of one kg. Find his gain \%.
A \( \cdot 3 \frac{7}{12} \% \)
в. \( _{4} \frac{11}{14} \% \)
c. \( _{5} \frac{5}{19} \% \)
D. \( 6 \frac{9}{14} \% \)


Evaluate \( \int_{0}^{200 \pi} \sqrt{1+\cos x} d x \)


The unit of inductance is equivalent to
A. \( \frac{\text { volt } \times \text { ampere }}{\text { second }} \)
в. \( \frac{\text { ampere }}{\text {volt } \times \text { second }} \)
c. \( \frac{v o l t}{\text { Ampere } \times \text { second }} \)
D. \( \frac{\text {volt } \times \text { second }}{\text { ampere }} \)


The cells surrounding the stomata are known as
A . Guard cells
B. Subsidiary cell
c. stoma
D. None of the above


Fill in the blanks:
\( \mathbf{1 0 0} \times(-\mathbf{6})=\dots \dots \dots \)


Statement-1: The angular velocity of all the points on the rigid body as seen
from any other point on it is the same. Statement-2: The distance between any
2 points on the rigid body remains
constant.
A. Statement-1 is true,statement-2 is true and statement 2 is correct explanation for statement- -
B. Statement-1 is true,statement-2 is true and statement 2 is NOT the correct explanation for statement- -
c. Statement-1 is true, statement-2 is false.
D. Statement-1 is false, statement-2 is true


Assertion
Light is not considered as matter.
Reason

Light do not occupy space, have no
mass or volume.
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.


Solve:
\( \lim _{x \rightarrow 0} \frac{3 \sin ^{2} x-2 \sin x^{2}}{3 x^{2}} \)


A small piece of space junk is at rest in outer space. A very small asteroid strikes it, exerting a force on it that is NOT directed through the piece of space junk's center of mass. Which of the following describes the motion of the piece of space junk DURING the asteroid strike?
A. Because the asteroid is small, the space junk remains at rest
B. The piece of space junk spins, but does NOT move linearly
c. The piece of space junk moves at constant velocity linearly, but does NOT spin
D. The piece of space junk accelerates linearly, but does NOT spin
E. The piece of space junk accelerates linearly, AND spins


Which of the following equations is not
shown by the appropriate halogen?
\( \mathbf{A} \cdot F_{2}+2 O H^{-} \)solution\( \rightarrow 2 F^{-}+H_{2} O+O F_{2} \)
B \( \cdot 2 F_{2}+4 O H^{-} \) conc \( \stackrel{\text {hot}}{\longrightarrow} 4 F^{-}+2 H_{2} O+O_{2} \)
\( \mathbf{c} \cdot X_{2}+2 O H^{-} \operatorname{conc} \stackrel{\text {hot}}{\longrightarrow} H_{2} O+X^{-}+X O^{-} \) where \( X \) is \( \mathrm{Cl} \)
Br and
\( \mathbf{D} \cdot X e F_{4} \)


The name of given compound is:
A. malonic acid
B. carbon suboxide
c. tartaric acid
D. acetic acid


Heavy water is a compound of :
A. hydrogen and heavier isotope of oxygen.
B. heavier isotope of hydrogen and heavier isotope of oxygen.
C. oxygen and heavier isotope of hydrogen.
D. none of the above


Gypsum is added to Portland cement to:
A. fasten the process of setting
B. slow down the process of setting
C. improve the colour of the cement
D. increase the melting point of cement


A root parasite is
A. Loranthus
B. Rafflesia
c. viscum
D. cuscuta


Describe the following:
(i) Cross aldol condensation
(ii) Decarboxylation


An element \( X \) combines with oxygen to
form an oxide \( X_{2} O . \) This oxide is
electrically conducting.
(i) How many electrons would be there in the outermost shell of the element \( \boldsymbol{X} \)
(ii) To which group of the periodic table does the element \( X \) belong.
(iii) Write the formula of the compound
which is formed when \( X \) reacts with
chlorine.


Older resin-clogged central secondary xylem and younger outer secondary xylem are respectively known as
A. Alburnum and duramen
B. Duramen and alburnum
c. Autumn wood and springwoodd
D. springwood and autumn wood


Is similarity of triangles different from similarity of polygons?


The mixture of \( C O \) and \( N_{2} \) is called as:
A. Water gas
B. Producergas
c. synthetic gas
D. Marsh gas


Solve: \( \int_{0}^{1} \frac{\boldsymbol{d} \boldsymbol{x}}{\sqrt{\boldsymbol{x}+\mathbf{1}}+\sqrt{\boldsymbol{x}}} \)


The equilibrium constant for the
reaction, \( N_{2}(g)+O_{2}(g)=2 N O(g) \) is
\( 4 \times 10^{-4} \) at \( 2000 \mathrm{k} . \) In the presence of a
catalyst, the equilibrium is attained ten times faster. Therefore, the equilibrium constant in the presence of the catalyst of \( 2000 \mathrm{k} \) is:
A. \( 4 \times 10^{-2} \)
B. \( 40 \times 10^{-4} \)
c. \( 4 \times 10^{-4} \)
D. \( 4 \times 10^{-1} \)


When \( N_{2} O_{5} \) is heated at certain
temperature, it dissociates as \( N_{2} O_{5}(g) \rightleftharpoons N_{2} O_{3}(g)+ \)
\( O_{2}(g) ; \quad K_{c}=2.5 . \) At the same time
\( N_{2} O_{3} \) also decomposes as:
\( N_{2} O_{3}(g) \rightleftharpoons N_{2} O+O_{2}(g) . \) If initially
4.0 moles of \( N_{2} O_{5} \) are taken in 1.0 litre
flask and allowed to dissociation,
concentration of \( O_{2} \) at equilibrium is
\( \mathbf{2 . 5} \boldsymbol{M} \)
Equilibrium concentration of \( N_{2} O_{5} \) is:
A. \( 1.0 M \)
в. 1.5 М
c. \( 2.166 M \)
D. \( 1.834 M \)


What is the other name of \( S H E ? \)
A. Concentration cell
B. Inactive electrode
c. Reference electrode
D. Active electrode


The place value of 2 in the number
\( \mathbf{1 5 . 5 2 6} \) is
A . 20
B. 2
\( c \cdot \frac{2}{10} \)
D. \( \frac{2}{100} \)


When two tuning forks \( A \) and \( B \) are
sounded together, 4 beats per second
are heard. The frequency of the fork \( B \) is
\( 384 H z . \) When one of the prongs of the
fork \( A \) is filed and sounded with \( B \), then
beat frequency increases, then
frequency of the fork \( \boldsymbol{A} \) is
A. \( 380 H z \)
в. 388 Нг
c. 379 Н \( z \)
D. \( 389 ~ H z \)


Let \( \vec{v}(t) \) be the velocity of a particle at
time \( t . \) Then
This question has multiple correct options
\( ^{\mathbf{A}} \cdot\left|\frac{d \vec{v}(t)}{d t}\right| \) and \( \frac{d|\vec{v}(t)|}{d t} \) are always equal
\( ^{\mathbf{B}} \cdot\left|\frac{d \vec{v}(t)}{d t}\right| \) and \( \frac{d|\vec{v}(t)|}{d t} \) may be equal
c. \( \frac{d|\vec{v}(t)|}{d t} \) can be zero while \( \left|\frac{d \vec{v}(t)}{d t}\right| \) is not zero
D \( \cdot \frac{d|\vec{v}(t)|}{d t} \neq 0 \) implies \( \frac{|d \vec{v}(t)|}{d t} \neq 0 \)


In the above figure \( \boldsymbol{A B} \| \boldsymbol{C D} \)
\( \angle A B E=120^{\circ}, \angle D C E=110^{\circ} \) and
\( \angle B E C=x^{\circ} \) then \( x^{\circ} \) will be
\( A \cdot 60 \)
B. 50
\( c \cdot 4 \)
D. 70


A man \( m=80 k g \) is standing on a
trolley of mass \( 320 \mathrm{kg} \) on a smooth surface. If man starts walking on trolley along rails at a speed of \( 1 \boldsymbol{m} / \boldsymbol{s}, \) then
after 4 sec, his displacement relative to
ground is
A . \( 4 m \)
B. \( 4.8 m \)
c. \( 3.2 m \)
D. \( 6 m \)


Consider an aqueous solution, \( 0.1 \mathrm{M} \)
each in \( H O C N, H C O O H,(C O O H)_{2} \)
and \( H_{3} P O_{4}, \) for \( H O C N, \) we can write \( \boldsymbol{K}_{\boldsymbol{a}}(\boldsymbol{H} \boldsymbol{O C N})=\frac{\left[\boldsymbol{H}^{+}\right]\left[\boldsymbol{O C N}^{-}\right]}{[\boldsymbol{H O C N}]} \cdot\left[\boldsymbol{H}^{+}\right] \)
in this expression refers to:
A \( . H^{+} \) ions released by \( H O C N \)
B. sum of \( H^{+} \) ions released by all monoprotic acids
C. sum of \( H^{+} \) ions released only the first dissociation of all the acids
D. overall \( H^{+} \) ion concentration in the solution


In which of the following cases \( C-C \)
bond length will be the longest?
A. \( C H_{3}-C F_{3} \)
В. \( F C H_{2}-C H_{2} F \)
\( \mathbf{c} \cdot F_{2} C H-C H F_{2} \)
D. \( C F_{3}-C F_{3} \)


Distinguish between photosynthesis
and respiration


If \( [x]=4, \) where [.] denotes greatest
integer function, then it lies in the interval
A. (2,3)
(年) (2,3,3)
в. [-1,2]
c. [4,5]
D. [4,5]


A 1 m long rod is half dipped in a swimming pool. The sunlight is incident
at \( 45^{\circ} \) on the rod. Find the length of the shadow on the bed of swimming pool.
\( \mathbf{A} \cdot 73 \mathrm{cm} \)
B. \( 78.25 \mathrm{cm} \)
c. \( 74.17 \mathrm{cm} \)
D. \( 81.5 \mathrm{cm} \)


Le Chatelier's principle is applicable to both homogeneous and heterogeneous equilibria.
If true enter 1 , if false enter 0 .


Which of the following system has maximum number of unpaired electrons?
A \( \cdot d^{4} \) (Octahedral,Low spin)
B . \( d^{6} \) (tetrahedral)
c. \( d^{6} \) (octahedral, low spin)
D. \( d^{9} \) (Octahedral)


Table salt becomes sticky on exposure during the rainy season. Explain.


Let N denote the set of all natural
numbers. Define two binary relations on \( \mathrm{N} \) as \( \boldsymbol{R}_{1}=\{(\boldsymbol{x}, \boldsymbol{y}) \boldsymbol{\epsilon} \boldsymbol{N} \times \boldsymbol{N}: \boldsymbol{2} \boldsymbol{x}+\boldsymbol{y}= \)
\( \mathbf{1 0}\} \) and \( \boldsymbol{R}_{2}=\{(\boldsymbol{x}, \boldsymbol{y}) \boldsymbol{\epsilon} \boldsymbol{N} \times \boldsymbol{N}: \boldsymbol{x}+ \)
\( \mathbf{2} \boldsymbol{y}=\mathbf{1 0}\} . \) Then
\( A \cdot \) Both \( R_{1} \) and \( R_{2} \) are transitive relations
B. Both \( R_{1} \) and \( R_{2} \) are symmetric relations
C. Range of \( R_{2} \) is \{1,2,3,4\}
D. Range of \( R_{1} \) is \{2,4,8\}


Draw the following triangles and construct circumcircles for them.
In \( \triangle A B C, A B=6 c m, B C=7 \mathrm{cm} \)
and \( \angle A=60^{\circ} \)


A purchases an article for Rs. 3,600 and sells it to B for Rs. \( 4,800 . \) B, in turn, sells the article to \( C \) for Rs. \( 5,500 . \) If the sales-
\( \operatorname{tax}(\text { under } V A T) \) is \( 10 \%, \) find the VAT
levied on \( A \) and \( B \).
A. VAT levied A= Rs. 140, VAT levied B= Rs. 50
B. VAT levied A= Rs. 130, VAT levied B= Rs. 60
c. VAT levied A= Rs. 120, VAT levied B= Rs. 70
D. None of these


Non-mineral essential elements are
A. Carbon, Hydrogen and Oxygen
B. Hydrogen, Nitrogen and Sulphur
C. Hydrogen, Nitrogen and Fluorine
D. Chlorine, Fluorine and Nitrogen


The difference between the maximum
and the minimum obervations in data
is called the
A. mean of the data
B. range of the data
c. mode of the data
D. median of the data


3 moles of \( \boldsymbol{P} \) and 2 moles of \( \boldsymbol{Q} \) are
mixed, what will be their total vapour pressure in the solution if their partial
vapour pressures are 80 and 60 torr respectively?
A. 80 torr
B. 140 torr
c. 72 torr
D. 70 torr


State whether true or false.
Newton's second law gives the measure of force.
A. True
B. False


The part which protects the human eye is called:
A. Cornea
B. Choroid
c. Retina
D. Blind spot


Desmosomes are concerned with
A. Cell division
B. Cellular excretion
c. cytolysis
D. Cell adherence


The line \( \frac{\boldsymbol{x}-\mathbf{2}}{\mathbf{3}}=\frac{\boldsymbol{y}-\mathbf{3}}{\mathbf{4}}=\frac{\boldsymbol{z}-\mathbf{4}}{\mathbf{5}} \) is
parallel to the plane.
A. \( 2 x+3 y+4 z=29 \)
B. \( 3 x+4 y-5 z=10 \)
c. \( 3 x+4 y+5 z=38 \)
D. \( x+y+z=0 \)


Two identical inductance carry currents
that vary with time according to linear laws (as shown in figure). In which of
two inductance is the self induction
emf greater?
\( A \)
B. 2
\( c . \) same
D. data are insufficient to decide


The equilibrium position for a static pendulum changes with
A. acceleration of the bob
B. velocity of the bob
c. displacement of the bob
D. none of the above


Name the process:
\( Z r+2 I_{2} \stackrel{600^{\circ} C}{\longrightarrow} Z r I_{4} \stackrel{1800^{\circ} C}{\longrightarrow} Z r+2 I_{2} \)
Options:
1. Monds
2. Van Arkel
3. Hall
4. Bausch
Enter the correct option in the form of
the number


Draw a rough sketch of a quadrilateral
KLMN. State two pairs of opposite sides


Some liquids on mixing form
'azeotropes'. What are 'azeotropes'?


Assertion
\( \sin ^{-1}\left[x-\frac{x^{2}}{2}+\frac{x^{3}}{4} \dots\right]=\pi / 2 \)
\( \cos ^{-1}\left[x^{2}-\frac{x^{4}}{2}+\frac{x^{6}}{4} \ldots .\right] \) for \( 0<|x|< \)
\( \sqrt{2} \) has a unique solution.
Reason
\( \tan ^{-1} \sqrt{x(x+1)}+ \)
\( \sin ^{-1} \sqrt{x^{2}+x+1}=\pi / 2 \) has no
solution for \( -\sqrt{2}<x<0 \)
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. Assertion is incorrect but Reason is correct


Platinum, Palladium and Iridium are
called noble metals because:
A. Alfred Nobel discovered them
B. they are shining lustrous and pleasing to look at
C. they are found in native state
D. they are inert towards many common reagents


Write a short note on ecosystem
services.


Using Euclid's division algorithm find
the HCF of the following numbers.
\( \mathbf{2 0 2 4} \) and \( \mathbf{1 8 7 2} \)


Consider following cases:
I. \( 2 \mathrm{M} C H_{3} \mathrm{COOH} \) solution in benzene at
\( 27^{0} \) where there is dimer formation to
the extent of \( 100 \% \)
Il. \( 0.5 \mathrm{M} \) KCl aq. solution at \( 27^{0}, \) which
ionises \( 100 \% \)
Which is lare true statements(s):
A. both are isotonic
B. I is hypertonic
c. I lis hypertonic
D. none is correct


Write general terms of this
\( 2 x\left[3+2 x^{2}\right]^{20} \)


General formula of saturated
monocarboxylic acid is :
A. \( C_{n} H_{2 n+1} \) COOH
в. \( C_{n} H_{2 n} O_{2} \)
c. Both A and B
D. None of the above


Assuming the earth to be a sphere of uniform density, how much could a body weigh at a height equal to radius of earth when it weighs \( 250 \mathrm{N} \) on the surface of the earth.


Figure below shows two infinitely long
and thin current carrying conductors \( \boldsymbol{X} \)
and \( Y \) kept in vacuum, parallel to each
other, at a distance 'a
Define ampere, in terms of force
between two current carrying
conductors


Fill in the blanks:
Principal axis is also called of the lens.
A. Optical axis
B. x-axis
c. y-axis
D. axis


The hormone that prepares the uterus for the implantation of the embryo is:
A. Estradiol
B. Progesterone
c. Insulin
D. Androgens


To which of the following flowers 'synandrous' condition is found?
A. Sunflower (Helianthus sp.)
B. Gourd (cucurbita sp.)
c. Pea (Pisum sativum)
D. Lemon (Citrus sp.)


Corresponding sides of two similar triangles are in the ratio \( 2: 3 . \) If the area
of the smaller triangle is \( 48 \mathrm{cm}^{2} \) determine the area of the larger triangle.


Evaluate \( ^{20} C_{5}+\sum_{r=2}^{5}^{25-r} C_{4} \)


Assuming that shear stress of base of a mountain is equal to force per unit area to its weight, calculate the maximum possible height of a mountain on the earth if breaking stress of a typical rock
is \( 30 \times 10^{7} N m^{-2} \) and specific gravity
is \( 3 \times 10^{3} k g / m^{3} \)
\( A \cdot 10 \mathrm{km} \)
B. \( 8 \mathrm{km} \)
\( c \cdot 7 k m \)
\( D .6 \mathrm{km} \)


If the acceleration of an object is zero:
A. it must be at rest
B. it may or may not be at rest
c. it must be moving
D. it must be falling freely under gravity


Read the following statements about
the given diagram carefully and state which of them are correct?
(i) A carries urine and sperms.
(ii) \( \mathrm{B} \) secretes a fluid that helps in the lubrication of penis.
(iii) D produces testosterone but not
sperms
(iv) \( \mathrm{C} \) stores sperms.
\( A \cdot \) (i) and (ii)
B. (ii) and (iii)
c. (ii) and (iv)
D. (i) and (iv)


Write the chemical formula of Mustard
gas and Phosgene.


Evaluate the integral \( \int_{2}^{3} \frac{\sqrt{\boldsymbol{x}}}{\sqrt{\mathbf{5}-\boldsymbol{x}}+\sqrt{\boldsymbol{x}}} \boldsymbol{d} \boldsymbol{x} \)
A \( \cdot 1 / 2 \)
B . \( 3 / 2 \)
\( c \cdot 5 / 2 \)
D. 0


A piano-convex lens (refractive index \( \mu_{1} \)
fits exactly into a piano-concave lens (refractive index \( \mu_{2} \) ). Their plane surfaces are parallel to each other. R is the radius of curvature of the curved
surface of the lenses, then focal length of the combination is:
A. \( \frac{R}{\mu_{1}-\mu_{2}} \)
в. \( \frac{2 R}{\mu_{2}-\mu_{1}} \)
c. \( \frac{R}{2\left(\mu_{1}-\mu_{2}\right)} \)
D. none of these


Given set of quantum numbers for a multi-electron atom is:
\( \boldsymbol{n} \)
\( l \) \( m \) \( s \)
2
\( \begin{array}{cc}0 & 0\end{array} \) \( +1 / 2 \)
2
\( -1 / 2 \)
What is the next higher allowed set of ' \( n \)
and 'l' quantum numbers for this atom
in the ground state?
A. \( n=2, l=0 \)
В. \( n=2, l=1 \)
c. \( n=3, l=0 \)
D. \( n=3, l=1 \)


The net magnetic flux through any closed surface, kept in a magnetic field is
A . zero
в. \( \frac{\mu_{0}}{4 \pi} \)
c. \( 4 \pi \mu_{0} \)
D. \( \frac{4 \mu_{0}}{\pi} \)


Mirror formula can also be written as:
A \( \cdot \frac{1}{2 v}+\frac{1}{2 u}=\frac{1}{2 f} \)
B. \( \frac{1}{v}+\frac{1}{u}=\frac{2}{R} \)
c. \( \frac{1}{v}+\frac{2}{u}=\frac{1}{f} \)
D. \( \frac{1}{2 v}+\frac{4}{u}=\frac{3}{R} \)


A piano wire \( 0.5 m \) long and mass \( 5 g m \)
is stretched by a tension of \( 400 N \). The
number of highest overtone that can be heard by a person is
A. 160
B. 99
\( c .140 \)
D. 120


For wave connected with proton, debroglie wavelength change by \( 0.25 \% \) if
its momentum change by \( P_{0} \) initial
momentum =
A. \( 100 P_{0} \)
в. \( \frac{P_{0}}{400} \)
c. \( 401 P_{0} \)
D. \( \frac{P_{0}}{100} \)


Assertion
The de-Broglie wavelength equation has significant for any microscopic and submicroscopic particles.
Reason
de-Broglie wavelength is inversely proportional tot he mass of the object, if its velocity is constant.
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


State whether the following statement is True or False
\( A=\{x \mid x \text { is a negative integer } ; x> \)
-5\} is a finite set.
A. True
B. False


The zero polynomial is the identity of the additive group of polynomials.
A. multiplicative
B. additive
c. multiplicative inverse
D. additive inverse


The reference calomel electrode is
made from which of the following?
A. \( Z n C l_{2} \)
в. \( C u S O_{4} \)
c. \( H g_{2} C l_{2} \)
D. \( H g C l_{2} \)


Explain the working of a half wave diode
rectifier.


The circuit given below is for the operation of an industrial fan. The resistance of the fan is 3 ohm. The
regulator provided with the fan is a
fixed resistor and a variable resistor in
parallel. Under what value of the variable resistance given, power transferred to the fans will be
maximum? The power source of the fan
is a dc source with internal resistance
of 6ohm
A . \( 3 \Omega \)
B.
\( c \cdot \alpha \)
D. 6.9


The potential difference across a \( 2 H \)
inductor as a function of time is shown
in figure. At time \( t=0, \) current is zero
Current at \( t=2 \) second is:
A . \( 1 A \)
в. 3 А
\( c \cdot 4 A \)
D. \( 5 A \)


IUPAC name of alizarin is
A. 2, 3 - dihydroxyphenanthraquinone
B. 1, 4-dihydroxyphenanthraquinone
c. 1,2 - dihydroxyphenanthraquione
D. 1,2- dihydroxyanthraquione


Solution of the equation \( \tan \left(\cos ^{-1} x\right)=\sin \left(\cot ^{-1} \frac{1}{2}\right) \)
A \( \cdot x=\pm \frac{\sqrt{7}}{3} \)
B. \( x=\pm \frac{\sqrt{5}}{3} \)
c. \( x=\pm \frac{3 \sqrt{5}}{2} \)
D. None of these


A particle is located at \( (3 m, 4 m) \) and moving with \( \overrightarrow{\boldsymbol{v}}=(4 \hat{\boldsymbol{i}}-\boldsymbol{3} \hat{\boldsymbol{j}}) \boldsymbol{m} / \boldsymbol{s} . \) Find
its magnitude of angular velocity about origin at this instant in rad/sec


Which of the following is represented by the area enclosed by a hysteresis loop
(B-H curve)?
A. Permeability
B. Retentivity
c. Heat energy lost per unit volume in the sample
D. susceptibility


Crosses represent uniform magnetic
field directed into the paper. A conductor XY moves in the field towards
right side. Find the direction of induced
current in the conductor. Name the rule
you applied. What will be the direction of current if the direction of field and
the direction of motion of the conductor
both are reversed?


Answer the following:
Name two carbon compounds used in day-to-day life.


Find the area of the triangle whose
vertices are (10,-6),(2,5) and (-1,3)


If given arrangement is moving towards left with speed \( v, \) then potential
difference between \( B \) and \( D \) and current
in the loop are respectively.
A. BvR and non-zero
B. 2BvR and zero
c. 4 Bv \( \operatorname{R} \) and non-zer
D. 4BvR and zero


\( 5 g \) of zinc is treated separately with an excess of
(a) dilute hydrochloric acid and
(b) aqueous sodium hydroxide.
The ratio of the volumes of \( \boldsymbol{H}_{2} \) evolved
in these two reactions is :
A . 1: 1
B . 2: 1
\( c \cdot 1: 4 \)
D. 1: 2


If \( \overrightarrow{\boldsymbol{u}}=\overrightarrow{\boldsymbol{a}}-\overrightarrow{\boldsymbol{b}} ; \overrightarrow{\boldsymbol{v}}=\overrightarrow{\boldsymbol{a}}+\overrightarrow{\boldsymbol{b}} \) and \( |\overrightarrow{\boldsymbol{a}}|=|\overrightarrow{\boldsymbol{b}}|= \)
2 then \( |\vec{u} \times \vec{v}| \) is equal to
\( \sqrt[A \cdot]{2\left(16-(\vec{a} \cdot \vec{b})^{2}\right)} \)
в. \( 2 \sqrt{\left(16-(\vec{a} . \vec{b})^{2}\right)} \)
\( ^{\mathrm{c}} \sqrt[2]{\left(4-(\vec{a} \cdot \vec{b})^{2}\right)} \)
D . \( \left[4-(\vec{a} . \vec{b})^{2}\right] \)


If the total charge stored in the LC
circuit is \( Q_{0}, \) then for \( t \geq 0 \)
A \( \cdot \) the charge on the capacitor is \( \mathrm{Q}=\mathrm{Q}_{0} \cos \left(\frac{\pi}{2}+\frac{\mathrm{t}}{\sqrt{\mathrm{LC}}}\right) \)
B. the charge on the capacitor is \( \mathrm{Q}=\mathrm{Q}_{0} \cos \left(\frac{\pi}{2}-\frac{\mathrm{t}}{\sqrt{\mathrm{LC}}}\right) \)
c. the charge on the capacitor is \( Q=-L C \frac{d^{2} Q}{d t^{2}} \)
D. the charge on the capacitor is \( \mathrm{Q}=-\frac{1 \mathrm{d}^{2} \mathrm{Q}}{\sqrt{\mathrm{LC}} \mathrm{d}^{2}} \)


Find the general solution of the equation \( \tan ^{2} \alpha+2 \sqrt{3} \tan \alpha=1 \)


The ratio in which the joint of
(2,1,5),(3,4,3) is divided by the plane \( 2 x+2 y-2 z-1=0 \)
\( \mathbf{A} \cdot 5: 12 \)
B. 12: 5
\( c .5: 7 \)
D. 7: 5


A fort is provisioned for 42 days. After 10 days, a reinforcement of 200 men
arrives and the food will now last only 24
days. How many men were there in the fort?
A .200
в. 600
\( c .500 \)
D. 300


Which of the following is pyrimidine
base?
A. Adenine
B. Guanine
c. Uracil
D. All the above


If a force of \( 200 N \) acts on a body. The
momentum acquired is \( 100 k g m / s \) What is the period for which force acts on the body?
A . \( 0.2 \sec \)
B. \( 0.5 \mathrm{sec} \)
c. \( 0.4 \mathrm{sec} \)
D. 0.25 sec


If \( A \) is the amplitude of the component waves, the resultant amplitude of two waves that interfere to produce destructive interference is
\( A \cdot 2 A \)
B. A
\( c \cdot 0 \)
D. - -


In a potentiometer experiment of a cell of emf \( 1.25 \mathrm{V} \) gives balancing length of \( 30 \mathrm{cm} . \) If the cell is replaced by another cell, balancing length is found to be 40
cm. What is the emf of second cell?
\( \mathbf{A} \cdot \simeq 1.57 V \)
\( \mathbf{B} \cdot \simeq 1.67 V \)
\( \mathbf{c} . \simeq 1.47 V \)
\( \mathbf{D} \cdot \simeq 1.37 V \)


The element having electronic configuration \( [\boldsymbol{K} \boldsymbol{r}] \boldsymbol{4} \boldsymbol{d}^{10} \boldsymbol{4} \boldsymbol{f}^{14} \boldsymbol{5} \boldsymbol{s}^{2} \boldsymbol{5} \boldsymbol{p}^{6} \boldsymbol{5} \boldsymbol{d}^{1} \boldsymbol{6} \boldsymbol{s}^{2} \) belongs to
A. s-block
B. p-block
c. d-block
D. f-block


Two sound sources produce progressive
waves given by \( y_{1}=12 \cos (100 \pi t) \) and
\( \boldsymbol{y}_{2}=4 \cos (102 \pi t) \) near the ear of an
observer. When sounded together, the observer will hear:
A. 2 beats per second with an intensity ratio of maximun to minimum nearly 4:
B. 1 beat per second with an intensity ratio of maximumm to minimum nearly \( \sqrt{2}: 1 \)
c. 2 beats per second with an intensity ratio of maximun to minimum nearly 9 :
D. 1 beat per second with an intensity ratio of maximumm to minimum nearly 4:


A conducting loop is pulled outward
with a constant speed.

The induced emf between the point \( A \) and B, just after the motion start is


Assertion
All combustion reactions are
exothermic.
Reason
Enthalpies of products are greater than enthalpies of reactants
\( \left(\sum \boldsymbol{v}_{\boldsymbol{p}} \boldsymbol{\Delta}_{f} \boldsymbol{H}(\boldsymbol{P})>\sum \boldsymbol{v}_{\boldsymbol{R}} \boldsymbol{\Delta}_{f} \boldsymbol{H}(\boldsymbol{R})\right) \)
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. Assertion is incorrect but Reason is correct


Density of graphite is:
A \( .0 .5 g / c m^{3} \)
B. \( 2.266 g / c m^{3} \)
\( \mathbf{c} \cdot 1.08 g / \mathrm{cm}^{3} \)
D. none of the above


Bond pair of electrons in \( C-X \) bond is
nearer to:
\( \mathbf{A} \cdot X \)
в. \( C \)
c. equidistant
D. can't be predicted


Which one of the following is not a
correct statement?
A. Physical adsorption is reversible in nature.
B. Physical adsorption involves Van der Waals forces.
C. Rate of chemical adsorption increases with increase of temperature.
D. High activation energy is involved in chemical adsorption.


Proximal and distal convoluted tubules
are parts of a
A. Nephron
B. oviduct
c. vas deferens
D. Caecum


Assertion
The mass spectrometer is used for determination of the atomic mass of
isotopes.
Reason
Isotopes are the atoms of the same element having a same atomic number but different mass numbers
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 incorrect but Reason is correct
D. Both Assertion and Reason are incorrect


How Aniline is obtained from
Nitrobenzene?


If volume ratio of \( 0.02 M H C l \) and
\( 0.02 M B O H \) (a weak base) mixed to
make \( 200 \mathrm{mL} \) of buffer of \( p H=7 \) is
\( 2.23: X . \) The value of \( X \) is:
\( \boldsymbol{K}_{b} \) for \( \boldsymbol{B O H}=\mathbf{8 . 1} \times \mathbf{1 0}^{-\mathbf{8}} \)
\( A \)
B. 5
\( c \cdot 0.2 \)
D. 2.5


In the given figure \( A B C D E, E Y= \)
\( \boldsymbol{C Y}=\boldsymbol{4} \boldsymbol{c m}, \boldsymbol{A} \boldsymbol{X}=\boldsymbol{B} \boldsymbol{X}= \)
\( 6 c m, D E=D C=5 c m, D X=9 \mathrm{cm} \)
\( D X \) is perpendicular to \( E C \) and \( A B \)
Find the area of \( A B C D E \)


Which one of the following is mainly responsible for depletion of ozone layer?
A. Methane
B. Carbon dioxide
c. water
D. chlorofluorocarbon


What is the need for measurement of a
physics quantity?


Benzoylation of phenol in alkaline medium is known as
A. Friedel-craft's reaction
B. Wurtz-Fittig reaction
c. Schotten-Baumann reaction
D. Sabatier Senderens reduction


A cotton sheet is ironed with hot
electricity. How is energy transferred through the metal base of the iron to the
sheet?
A. by conduction only
B. by convection only
c. by radiation only
D. by convection and radiation only


Which of the following is a good sedative but not hypnotic?

This question has multiple correct options
\( A \cdot K B r \)
B. Asprin
c. Formalin
D. Dettol


A neutron, a proton, an electron and an
\( \boldsymbol{\alpha}- \) particle enter a region of uniform
magnetic field with the same velocities.
The magnetic field is perpendicular and
directed into the plane of the paper. The
tracks of the particles are labelled in
the figure. The electron follows the track
Q Magnetic field
\( A . D \)
B. \( B \)
\( c \cdot C \)
\( \mathbf{D} \cdot A \)


Let \( f(x) \) be a continuous function
defined for \( 1 \leq x \leq 3 \). If \( f(x) \) takes
rational values for all \( x \) and \( f(2)=10 \)
then the value of \( \boldsymbol{f}(\mathbf{1} . \mathbf{5}) \) is
A . 7.5
B. 10
\( c .5 \)
D. none of these


If \( f \) is an identity function then \( f(-5)= \)
\( A \cdot-5 \)
B. 1
\( c \cdot-1 \)
D. None of these


A person always prefers to eat parantha and vegetable dish in his meal. How
many ways can he make his plate in a marriage party if there are three types of paranthas, four types of vegetable dishes, three types of salads, and two types of sauces?
A . 3360
в. 4096
c. 3000
D. None of these


The equation of hyperbola whose coordinates of the foci are (±8,0) and
the lenght of latus rectum is 24 units, is
A \( \cdot 3 x^{2}-y^{2}=48 \)
в. \( 4 x^{2}-y^{2}=48 \)
c. \( x^{2}-3 y^{2}=48 \)
D. \( x^{2}-4 y^{2}=48 \)


Which of the following is an example of contact force?
This question has multiple correct options
A . Muscular force
B. Magnetic force
c. Gravitational force
D. Frictional force


A man of height \( \boldsymbol{H} \) is standing in front
of a mirror, which has been fixed on the
ground. What length of his body can the
man see in the mirror? The length of the mirror is \( \frac{\boldsymbol{H}}{\mathbf{2}} . \) (Neglect seperation between eyes and head of men)
\( \mathbf{A} \cdot H \)
B.
c. zero
D. \( \frac{2 H^{2}}{L} \)


How is Chlorine prepared by electrolyt method? Explain its reaction with:
(a) excess \( N H_{3} \)
(b) cold and dil. NaOH
(c) slaked lime


Find the next term of the sequence:
\( 2,5,8,11, \dots \dots \dots \)
A . 14
B . 15
c. 16
D. 18


1 a.m. \( u \) is equivalent to
\( \mathbf{A} \cdot 931 \mathrm{MeV} \)
В. \( 139 \mathrm{MeV} \)
\( \mathbf{c} .93 \mathrm{MeV} \)
D. \( 39 \mathrm{MeV} \)


An ellipse with foci (2,2),(3,-5)
passes through \( (6,-1), \) then its semilatus rectum is:
\( A \cdot \frac{7}{2} \)
в. \( \frac{5}{2} \)
\( c \cdot \frac{9}{2} \)
D. \( \frac{11}{2} \)


A conducting circular loop is placed in a uniform magnetic field \( B=0.020 T \)
with its plane perpendicular to the field. Somehow, the radius of the loop starts
shrinking at a constant rate of \( 1 \mathrm{mm} / \mathrm{s} \) Find the induced current in the loop at
an instant when the radius is \( 2 \mathrm{cm} \)


Two blocks \( A \) and \( B \) are connected by a
light inextensible string passing over a fixed smooth pulley as shown in Fig. The coefficient of friction between the block
A and B the horizontal table is \( \mu=0.5 \)
If the block \( A \) is just to slip, find the ratio of masses of the blocks.


Explain the term, target molecules or drug targets as used in medicinal chemistry.


Marbles, each of mass \( 1 \mathrm{g} \) are dropped from a height of \( 10 \mathrm{m} \) on to a horizontal
smooth metal surface at the rate of 50
per second. Find the force on the surface. If the surface were inclined to
the horizontal at an angle of \( 60^{\circ}, \) what would be force on it be? Assume
collisions to be elastic. \( g=9.8 m / s^{2} \)
A. \( 1.2 N ; 0.7 N \)
в. \( 1.4 N ; 0.5 N \)
c. \( 1.4 N ; 0.7 N \)
D. \( 0.4 N ; 0.4 N \)


gauss is equal to
\( \mathbf{A} \cdot 10^{4} T \)
B \( \cdot 10^{-4} T \)
\( \mathbf{c} \cdot 10^{3} T \)
D. none of these


Compute the area of the region bounded
by the curves \( y=\tan x \) and \( y= \) \( \tan ^{2}\left(\frac{-\pi}{2}<x<\frac{\pi}{2}\right) \)


In the caster-Kleiner cell used for the
manufacture of \( N a O H, \) the cathode in
the central compartment is made up of
A. carbon
B. iron
c. mercury
D. nickel


Which of the following is the most basic?
A \( \cdot C e(O H)_{3} \)
в. \( L u(O H)_{3} \)
\( \mathbf{c} \cdot Y b(O H)_{3} \)
D. \( A l(O H)_{3} \)


Why does the sun appear reddish early in the morning? Will this phenomenon be observed by an astronaut on the Moon? Give reason to justify your
answer


A uniform thin rod of mass \( m \) and
length \( l \) is standing on a smooth horizontal surface. A slight disturbance causes the lower end to slip on the
smooth surface and the rod starts
falling. Find the velocity of centre of mass of the rod at the instant when it
makes and angle \( \theta \) with horizontal.


A broadcasting centre broadcasts at 300 metre band. A capacitor of capacitance \( 2.5 \mu \mathrm{F} \) is available. The value of the inductance required for resonant circuit is nearly
A \( \cdot 1 \times 10^{-4} \mathrm{H} \)
В. \( 1 \times 10^{-8} \mathrm{H} \)
c. \( 1 \times 10^{-6} H \)
D. \( 1 \times 10^{-2} H \)


A pure resistance is connected as
shown in the figure. The phase difference between the voltage applied and the current flowing in it will be
A . zero
в. \( \frac{\pi}{2} \)
\( c \cdot-\frac{\pi}{2} \)
D. \( \frac{\pi}{4} \)


Which of the following is used in optical fibres?
A. Total internal reflection
B. Scattering
c. Diffraction
D. Refraction


Heating together of sodium ethoxide
and ethyl iodide will give:
A. ether
B. ethyl alcohol
c. acetaldehyde
D. acetic acid


Electronic configuration of \( M g^{+2} \) is
identical with?
A . Ne
B. Na a
c.
D.


What is the mistake in computation of \( \mathbf{1}=\sqrt{\mathbf{1}}=\sqrt{(-\mathbf{1})(-\mathbf{1})}=\sqrt{-\mathbf{1}} \times \)
\( \sqrt{-\mathbf{1}}=\boldsymbol{i} \times \boldsymbol{i}=-\mathbf{1} \)


The area enclosed between the curve
\( \boldsymbol{y}^{2}=\boldsymbol{x} \boldsymbol{a} \boldsymbol{n} \boldsymbol{d} \boldsymbol{y}=|\boldsymbol{x}| \) is
A \( \cdot \frac{1}{6} \)
в. \( \frac{1}{3} \)
\( c \cdot \frac{2}{3} \)
D. 1


In photoelectric effect, the momentum
of incident photon of energy \( 3 \times 10^{-19} J \)
is :
\( \mathbf{A} \cdot 9 \times 10^{11} \mathrm{kgms}^{-1} \)
B. zero
c. \( 10^{-27} \mathrm{kgms}^{-1} \)
D. \( 3 \times 10^{-11} \mathrm{kgms}^{-1} \)


The propagation of a sound wave in a gas is given by the equation \( \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{t}^{2}}=\frac{\boldsymbol{k}}{\boldsymbol{l}} \cdot \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}} \)
Then the velocity of sound is given by
A \( \cdot \frac{k}{l} \)
в. \( \frac{l}{k} \)
c. \( \sqrt{\left(\frac{k}{l}\right)} \)
D. \( \sqrt{\left(\frac{l}{k}\right)} \)


The point (0,-2,5) lies on the
\( A \cdot z \) axis
B. x axis
c. xy plane
D. yz plane
E . xz plane