Dry cell is a source of
A. Direct current
B. Alternating current
C. Can be used as direct current source or alternating current source
D. Cant say


The increasing order of the strength of hydrogen bond in the following mentioned linkages is:
(i) \( \boldsymbol{O} \boldsymbol{H}-\boldsymbol{S} \)
(II) \( \boldsymbol{S} \boldsymbol{H}-\boldsymbol{O} \)
(iii) \( \boldsymbol{F} \boldsymbol{H}-\boldsymbol{F} \)
(iv) \( \boldsymbol{F H}-\boldsymbol{O} \)
\( A \cdot(\text { i) }<(\text { ii })<(\text { iv })<(\text { iii }) \)
B. (ii) < (i) < (iv) < (iii)
c. (i) \( < \) (ii) \( < \) (iii) \( < \) (iv)
D. (ii) < (i) < (iii) < (iv)


Refraction index of water is \( 4 / 3 \)
Calculate speed of light in water.
A \( \cdot 3 \times 10^{8} m / s \)
В. \( 62 m / s \)
C \( .2 .25 \times 10^{8} \mathrm{m} / \mathrm{s} \)
D. 1.25


Solve \( \left[-\int_{0}^{\pi / 2} \cos \left(\frac{\pi}{4}+\frac{x}{2}\right) e^{x}\right] d x \)


Find the values of polynomial \( 3 x^{3}- \) \( 4 x^{2}+7 x-5 \) when \( x=3 \) \& \( x=-3 \)
A. 61,-143
В. -61,142
c. 61,142
D. -61,-142


Write the following decimals in the place value table.
\( \mathbf{2 0 0 . 8 1 2} \)


If a curve \( y=f(x) \) passes through the
point (1,-1) and satisfies the differential equation, \( \boldsymbol{y}(\mathbf{1}+\boldsymbol{x} \boldsymbol{y}) \boldsymbol{d} \boldsymbol{x}= \)
\( x d y, \) then \( f\left(-\frac{1}{2}\right) \) is equal to


Which of the following has seven
valence electrons?
A \( . N a^{+} \)
в. \( A l \)
\( c . F \)
D. \( T i \)
E. \( B \)


How many faradays are released when \( 12.7 g \) of copper metal is changed into copper ions?


A circular disc of radius \( 7 \mathrm{cm} \) has a
sector of angle 45 degrees cut out. The area of the remaining part of the disc is
A \( \cdot \) 134.75 \( c m^{2} \)
B . \( 144.75 \mathrm{cm}^{2} \)
c. \( 269.5 \mathrm{cm}^{2} \)
D. None of these


Assertion
A particle is projected upwards with
speed \( v \) and it goes to a height \( h . \) If we double the speed then it will move to height \( 4 h \)
Reason
In case of earth, acceleration due to gravity \( g \) varies as \( g \propto \frac{1}{r^{2}} r \geq R \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The laws of thermodynamics speak
about
A. rates of chemical changes
B. feasibility and energy transformations of a
process
C. Both the rate and energy changes of a process
D. Energy changes in chemical reactions only


Which of the following compounds have zero oxidation state at carbon?
This question has multiple correct options
A. \( C_{6} H_{12} O_{6} \)
в. нсоон
c. нсно
D. \( C H_{4} \)


Cessation of menstrual cycle in human
female is called as
A. Parturition
B. Sterility
c. Menopause
D. Lactation


A body,thrown vertically upwards with an initial velocity \( u, \) reaches maximum
height in 6 seconds. The ratio of the
distance travelled by body in the first second and the eleventh second is:
A . 1: 1
B. 11: 9
c. 1: 2
D. 9: 11


Prove that \( 3+\sqrt{7} \) is irrational number.


A metal sphere weighing \( 60 g m \) in the air is suspended by a thread in oil of
specific gravity \( 0.6 . \) If the tension in the thread is \( 55 g \) mwt, the specific gravity of the metal sphere is
A . 9.4
в. 4.5
\( c .6 .3 \)
D. 7.2


Assertion
A galvanometer can be used as a voltmeter to measure the voltage
across a given section of the circuit.
Reason
For this it must be connected in parallel
with that section of the circuit.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Assertion
Vitamin D cannot be stored in our body.
Reason

Vitamin D is fat soluble vitamin and is
excreted out of the body with urine.
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


Work done by the gravitational force on
a body of mass \( m \) moving on a smooth
horizontal surface through a distance
is: (Given acceleration due to gravity =
\( \boldsymbol{g}) \)
A . \( m g s \)
B. \( -m g s \)
c. 0
D. \( 2 m g s \)


An electron of charge \( e \) and mass \( m \) is
moving in a circular loop of radius \( \boldsymbol{r} \)
with a uniform angular speed \( \omega . \) Then
which of the following statements are
correct?
This question has multiple correct options
A. The equivalent current flowing in the circular path is proportional to \( r^{2} \)
B. The magnetic moment due to circular current loop is independent of \( m \)
C. The magnetic moment due to circular loop is equal to \( 2 e / m \) times the angular momentum of the electron
D. The angular momentum of the particle is proportional to the areal velocity of electron


Relative molecular mass is the ratio of
A. the average mass of one molecule of an element or compound to of the mass of an atom of carbon-12
B. the average mass of one molecule of an element or compound to one twelfth of the mass of an atom of carbon-12
C. the average mass of one molecule of an element or compound to one fifth of the mass of an atom of carbon-12
D. the average mass of one molecule of an element or compound to one twelfth of the mass of an atom of carbon-16


Atropa belladonna, an important medicinal plant is of the family
A . Liliaceae
B. Cucurbitaceae
c. cruciferae
D. Solanceae


Number of nodal planes in \( 4 p \) suborbit
will be:
A .
B.
\( c \cdot 2 \)
D.


Find the value of
\( \cos 1^{0} \cos 2^{0} \cos 3^{0} \ldots . . \cos 89^{0} \ldots . . \cos 179 \)


Chlorine reacts with saturated
hydrocarbons at room temperature in
the :
A. absence of sunlight
B. presence of sunlight
c. presence of water
D. presence of hydrochloric acid


For a fast chain reaction, the size of
\( U^{235} \) block, as compared to its critical size, must be
A. greater
B. smaller
c. same
D. anything


\( \int \tan ^{-1} \sqrt{\frac{1-\cos 2 x}{1+\cos 2 x}} d x, \) where \( 0< \)
\( x<\frac{\pi}{2} \) is equal to
A. \( 2 x^{2}+C \)
B. \( x^{2}+C \)
c. \( \frac{x^{2}}{2}+C \)
D. \( \frac{x^{3}}{3}+C \)


Which of the following is a physical change ?
A. solubility in water
B. combustibility
c. aerial oxidation
D. reaction with water


\( \boldsymbol{x}^{2}-(\boldsymbol{m}-\boldsymbol{3}) \boldsymbol{x}+\boldsymbol{m}=\mathbf{0}(\boldsymbol{m} \in \boldsymbol{R}) \) be a
quadratic equation. Find the value of \( m \)
for which, both roots are smaller than 2
\( ^{\mathrm{A}} \cdot\left(-\frac{3}{2}, 3\right) \)
в. \( (-\infty, 1] \)
c. (0,4]
D. \( (1, \infty) \)


Chordotonal organs are connected with sense of
A. Hearing
B. Smell
c. taste
D. Thermoreceptor


Which of the following pairs represent the same rational number? \( \frac{-7}{21} \) and \( \frac{3}{9} \)


Compute the geometric mean of 2,4,8
A .4
B. 6
\( c .8 \)
D. 2


\[
\text { If } \boldsymbol{A}=\left[\begin{array}{cc}
\mathbf{2} & \mathbf{2} \\
\mathbf{- 3} & \mathbf{1} \\
\mathbf{4} & \mathbf{0}
\end{array}\right], \boldsymbol{B}=\left[\begin{array}{cc}
\mathbf{6} & \mathbf{2} \\
\mathbf{1} & \mathbf{3} \\
\mathbf{0} & \mathbf{4}
\end{array}\right], \text { find }
\]
matrix \( C \) such that \( A+B+C=0 \)
where \( \boldsymbol{O} \) is the zero matrix.


\( 5-8 \)
\( 6-8 \)
-6


The IUPAC name of the complex
\( \left[\boldsymbol{C r} \boldsymbol{C l}_{2}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{4}\right] \boldsymbol{N} \boldsymbol{O}_{3} \) is :
A. Dichlorotetraaquachromium(III) nitrate
B. Tetraaquadichlorochromium(III) nitrate
c. chromiumtetraaquadichloro nitrate
D. Dichlorotetraaquadnromium nitrate


A cylindrical bucket, \( 32 \mathrm{cm} \) high and with radius of base \( 18 \mathrm{cm} \), is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is \( 24 \mathrm{cm} . \) Find the radius and slant
height of the heap.


Solve the following inequalities graphically in two-dimensional plane:
\( x>-3 \)


Identify the portion corresponding to
negative resistance.
\( A \cdot A B \)
B. BC
\( c \cdot c D \)
\( D \)


Define Ozone layer.


Convert into improper fraction:
\( 3 \frac{2}{5} \)


A mass \( m \) is placed on an inclined
plane. If the mass is in equilibrium, the maximum inclination of the plane with
horizontal would be
\( A \cdot \tan ^{-1} \mu \)
B. \( \tan ^{-1} \mu / 2 \)
\( \mathbf{c} \cdot \tan ^{-1} 2 / \mu \)
\( \mathbf{D} \cdot \cot ^{-1} \mu \)


Witches Broom of Potato Tree is caused
by
A. Mycoplasma
B. Bacteria
c. Viruses
D. All the above


Hydrogenation reaction:
\( \mathbf{A} \cdot R_{2} C=C R_{2}+H_{2} \stackrel{N i}{\rightarrow} R_{2} C H-C H R_{2} \)
B \( \cdot R_{2} C=C R_{2}+H_{2} \stackrel{N i}{\rightarrow} R_{2} C H-C H_{2} R \)
\( \mathbf{c} \cdot R_{2} C=C R_{2}+H_{2} \stackrel{N i}{\rightarrow} H_{2} C H-C H R_{2} \)
D. \( R_{2} C=C R_{2}+H_{2} \stackrel{N i}{\rightarrow} R_{2} C H-C H_{3} \)


A barometer is constructed with its
tube having radius \( 1.0 \mathrm{mm} \). Assume
that the surface of mercury in the tube is spherical in shape. If the atmospheric pressure is equal to \( 76 \mathrm{cm} \) of mercury, what will be the height raised in the barometer tube? The contact angle of
mercury with glass \( =135^{\circ} \) and surface
tension of mercury \( =0.465 \mathrm{N} m^{-1} \)
Density of mercury \( =13600 \mathrm{kg} m^{-3} \)


If \( f(x)=\left[\cos x \cos (x+2)-\cos ^{2}(x+\right. \)
1) \( ] \) where \( [.] \) denotes the greatest integer function \( \leq x \). Then solution of
the equation \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x} \) is :
\( \mathbf{A} \cdot \mathbf{1} \)
B. -
\( c \cdot 0 \)
D. none of these


Two moles of \( P C l_{5} \) were heated to
\( 327^{\circ} \mathrm{C} \) in a closed two litre vessel and
when equilibrium was achieved, \( \boldsymbol{P C l}_{5} \)
was found to be \( 40 \% \) disociated into
\( P C l_{3} \) and \( C l_{2} . \) Calcutta the equilibrium
constant \( \left(\boldsymbol{K}_{c}\right) \) for the reaction.


If \( A \& B \) are two given events, then
\( \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B}) \) is
A. Not less than \( P(A)+P(B)-1 \)
B. Not greater than \( P(A)+P(B)-P(A \cup B) \)
C . Equal to \( P(A)+P(B)+P(A \cap B) \)
D. Equal to \( P(A)+P(B)+P(A \cup B) \)


In the redox reaction: \( \boldsymbol{x} \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}+ \)
\( \boldsymbol{y} \boldsymbol{P} \boldsymbol{b} \boldsymbol{O}_{2}+\boldsymbol{z} \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \rightarrow \boldsymbol{H} \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{4}+ \)
\( \boldsymbol{P b}\left(\boldsymbol{N} \boldsymbol{O}_{3}\right)_{2}+\boldsymbol{H}_{2} \boldsymbol{O} \)
A. \( x=2, y=5, z=10 \)
в. \( x=2, y=7, z=8 \)
c. \( x=2, y=5, z=8 \)
D. \( x=2, y=5, z=5 \)


A.


Three prisms 1,2 and 3 have \( A=6^{\circ} \)
but refractive indices are 1.4,1.5,1.6
and their angles of deviation are
\( \boldsymbol{\delta}_{1}, \boldsymbol{\delta}_{2}, \boldsymbol{\delta}_{3} \) respectively. Then
\( \mathbf{A} \cdot \delta_{3}>\delta_{2}>\delta_{1} \)
В \( \cdot \delta_{1}>\delta_{2}>\delta_{3} \)
\( \mathbf{c} \cdot \delta_{2}>\delta_{1}>\delta_{3} \)
D. \( \delta_{1}=\delta_{2}=\delta_{3} \)


Velocity at the top of vertical journey under gravity when a body is projected upward with velocity \( 1000 m / s \) is
A. zero
в. \( 10 \mathrm{m} / \mathrm{s} \)
c. \( 100 m / s \)
D. \( 1000 \mathrm{m} / \mathrm{s} \)


The concentration of \( K^{+} \) in interior and
exterior of a Nerve cell are \( 500 \mathrm{mM} \) and
\( 25 \mathrm{mM} \) respectively. The electrical potential (in volt) that exists across the
membrane is : \( \left[\log _{10} 2=\right. \) \( \mathbf{0 . 3}, \mathbf{2 . 3 0 3} \boldsymbol{R} \boldsymbol{T} / \boldsymbol{F}=\mathbf{0 . 0 6}] \) (Given answer
be multiplying with 1000)


Monochromatic radiations of
wavelength \( \lambda \) are incident on a
hydrogen sample in the ground state. Hydrogen atom absorbs the light and subsequently emits radiations of 10 different wavelengths. The value of \( \lambda \) is
nearly
A . 203 nm
B. 95 nm
c. \( 80 n m \)
D. 73 nm


The variance of first \( n \) natural numbers
is
A \( \cdot \frac{n(n+1)}{12} \)
B. \( \frac{(n+1)(n+5)}{12} \)
c. \( \frac{(n+1)(n-1)}{12} \)
D. \( \frac{n(n-5)}{12} \)


If a wooden cylinder of radius 'r' and height 'h' is peeled to produce a perfect cone of same radius and height, then find the volume of the peels.


f \( \tan x=-\frac{3}{4}, \frac{3 \pi}{2}<x<2 \pi, \) then find
\( \sin 2 x \)


The separation of an emulsion into its constituent liquids is known as:
A. emulsification
B. protection of colloid
c. coagulation
D. demulsification


Complete the following sentence.
Sound can not travel through but it requires a
A. air, medium
B. water, medium
c. solids, medium
D. vacuum, medium


Describe the methods by which the presence of complex ions may be detected in solution.


Which acid is used in medicine for the
treatment of gout?
A. Hydrochloric acid
B. Methanoic acid
c. Ethanoic acid
D. None of these


Four cards are drawn from a deck of 52
cards, the probability of all being spade ¡s
\( ^{A} \cdot \frac{1}{256} \)
в. \( \frac{1}{56} \)
c. \( \frac{1}{64} \)
D. \( \frac{31}{256} \)


A horse tied to a cart is standing stationary on road. Which of the following statement is CORRECT?
A. Horse is applying force on the carttt
B. Cart is applying force on the horse
c. Force applied by the horse is balanced by the force applied by the cart
D. No forward force is being applied by the horse or the cart


Major chemical species present in stratosphere is:
A. \( N_{2}, O_{2} \)
в. \( O_{3}, H_{2} O \)
c. Both A and B
D. None of these


Complete the following sentence by selecting the correct option. The breathing rhythm is generated in the \( _{--}(i)_{--} \) and is influenced by variation in levels of \( _{--}\left(\text {ii) }_{---} \) in the \right.
blood.
A. (i)medulla \( \left(\text { ii) } C O_{2}\right. \)
B . (i)medulla \( \left(\text { ii) } O_{2}\right. \)
c. (i)frontal lobe
(ii) \( C O_{2} \) and \( O_{2} \)
D. (i)frontal lobe
(ii) \( C O_{2} \)


If same potential difference is applied across two resistances, more heat will
be produced in the large value of resistance.


What is the half-life of a Radium-226 if
its decay rate is \( 0.000436 ? \)
A \( . t=1237 \)
B . \( t=1365 \)
c. \( t=1440 \)
D. \( t=1590 \)


f cross section area and length of a long solenoid are increased 3 times then its
self-inductance will be changed how
many times-
A.
B. 2
\( c \cdot 3 \)
\( D \)


In an aqueous solution at \( 25^{\circ} \mathrm{C} \) has
twice as many \( O H^{-} \) as pure water its
\( p O H \) will be:
\( \mathbf{A} \cdot 6.699 \)
B. 7.307
\( c \cdot 7 \)
D. 6.98


Which of the following is not correctly matched?
\( A \)
\[
\text { Neoprene }\left[\begin{array}{c}
-\mathrm{CH}_{2}-\mathrm{C}=\mathrm{CH}-\mathrm{CH}_{2}- \\
\mathrm{Cl}
\end{array}\right]
\]
B.
Nylon \( -6,6-[\ln ] \)
\( r \)
Terylene \( \left.\left[-\mathrm{OCH}_{2}-\mathrm{CH}_{2}-\mathrm{C}-\langle\bigcirc\rangle^{\mathrm{I}}\right]_{\mathrm{n}}^{\mathrm{II}}\right] \)
\( D \)
\[
\left.\operatorname{PMMA}\left[-\mathrm{CH}_{2} \frac{\mathrm{CH}_{3}}{\mathrm{C}}\right]_{\mathrm{COOH}_{3}}\right|_{\mathrm{n}_{\mathrm{n}}}
\]


Find the roots using factorisation
\( 9 x-x^{2}=0 \)
A . 1,9
B. 0,9
\( c .9,9 \)
D.


Which element reacts most explosively in water?
\( \mathbf{A} \cdot K \)
в. \( C a \)
\( c \cdot B r \)
D. \( K r \)
E. \( Z n \)


\( A \cdot A-4, B-3, C-1, D-2 \)
B. \( A-3, B-1, C-4, D-3 \)
C. \( A-3, B-2, C-3, D-1 \)
D. \( A-1, B-2, C-4, D-3 \)


For the reaction \( 2 H I(g) \Leftrightarrow H_{2}(g)+ \)
\( I_{2}(g), \) the degree of dissociation \( (\alpha) \) of
\( H I(g) \) is related to the equilibrium
constant, \( \boldsymbol{K}_{\boldsymbol{p}} \) by the expression:
\( ^{\mathrm{A}} \cdot \frac{1+2 \sqrt{K_{p}}}{2 \sqrt{K_{p}}} \)
B. \( \sqrt{\frac{1+2 K_{p}}{2}} \)
\( ^{\mathrm{c}} \cdot \sqrt{\frac{2 K_{p}}{1+2 K_{p}}} \)
D. \( \frac{2 \sqrt{K_{p}}}{1+2 \sqrt{K_{p}}} \)


can imagine 2 similar objects rotating around a sphere at the same velocity but at different orbits. One object would
rotate around the sphere faster than the other, right? What is puzzling to me is that if I think of both objects going now in a straight line one could not say that one object was going faster than the other. Can someone help me through this? Is there a subtlety here?


What will be the atomic number of an
atom with an electron dot arrangement
similar to : \( I: ? \)
\( \mathbf{A} \cdot \mathbf{1} \)
B. 6
\( c \cdot 9 \)
D. 10
E . 14


Assertion
Force experienced by moving charge
will be maximum if direction of velocity of charge is perpendicular to applied magnetic field.
Reason
Force on moving charge is independent of direction of applied magnetic field.
A. Both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
B. Both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
C. Assertion is correct but Reason is incorrect.
D. Assertion is incorrect but Reason is correct.


In which of the following reactions, \( \boldsymbol{K}_{\boldsymbol{p}} \)
is less than \( K_{C} ? \)
A \( \cdot N_{2} O_{4(g)} \rightleftharpoons 2 N O_{2(g)} \)
B. \( 2 H I_{(g)} \rightleftharpoons H_{2(g)}+I_{2(g)} \)
\( \mathrm{c} \cdot 2 S O_{2(g)}+O_{2(g)} \rightleftharpoons 2 S O_{3(g)} \)
D. \( N_{2(g)}+O_{2(g)} \rightleftharpoons 2 N O_{(g)} \)


Which of the following statements is
not correct for Braille system?
A. Transcription method for preparing Braille includes slates and stylus
B. Character represents a letter, a combination of letters, a common word or a grammatical sign
C. Each character in Braille system need to be recognised
D. For some languages, Braille is read from right to left


Find if limit of function exists as \( x \)
tends to zero
\( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{lr}\frac{\mathbf{1}}{\boldsymbol{x}}-\mathbf{1} & \boldsymbol{x} \neq \mathbf{0} \\ \boldsymbol{e} \boldsymbol{x}+\mathbf{1} \\ \mathbf{0} & \boldsymbol{x}=\mathbf{0}\end{array}\right. \)


When equal volumes of nitrogen gas and oxygen gas at low pressure are
sparked, they react at \( 3000^{\circ} C \) to form:
A. nitrogen dioxide
B. dinitrogen pentoxide
c. nitrogen (II) oxide
D. none of the above


Plastic sulphur has an octahedral
shape
A . True
B. False


A lens forms a real image of an object
on a screen placed at a distance of 100
\( \mathrm{cm} \) from the screen. If the lens is moved
by \( 20 \mathrm{cm} \) towards the screen, another image of the object is formed on the screen. The focal length of the lens is:
\( A \cdot 12 \mathrm{cm} \)
B. 24 \( \mathrm{cm} \)
\( c \cdot 36 \mathrm{cm} \)
D. \( 48 \mathrm{cm} \)


The idea of froth floatation method
came from a person \( X \) and this method is related to the process \( Y \) of ores. \( X \) and
Y, respectively, are:
A. fisher woman and concentration
B. washer man and reduction
c. washer woman and concentration
D. fisher man and reduction


Which is the main causative factor of
desertification
A. Developmental activities
B. Tourism
c. overgrazing
D. Irrigated agriculture


Show that function \( f: N \rightarrow N \) given by
\( f(x)=3 x \) is one-one but not onto.


How are the following compounds
related to each other?
A. Enantiomer
B. Diastereomers
c. Meso
D. Identical


By what number 4320 must be multiplied to obtain a number which is a perfect cube?
\( \mathbf{A} \cdot 60 \)
B . 45
c. 50
D. 55


Gibbs-Helmholtz equation relates the free energy change to the enthalpy and entropy changes of the process as \( (\Delta G)_{P T}=\Delta H-T \Delta S \)
The magnitude of \( \Delta H \) does not change
much with the change in temperature
but the entropy factor \( \boldsymbol{T} \boldsymbol{\Delta} \boldsymbol{S} \) changes
appreciably.
Thus, spontaneity of a process depends
very much on temperature.
For the reaction at \( 25^{\circ} C, X_{2} O_{4}(l) \longrightarrow \)
\( 2 X O_{2} \)
\( \Delta H=2.0 K c a l \) and \( \Delta S=20 c a l K^{-1} \)
the reaction would be:
A. spontaneous
B. at equilibrium
C. unpredictable
D. non-spontaneous


A spinning ball is moving in a direction opposite to the direction of the wind. The ball moves in a curved path as:
A. the pressure at the top and the bottom of the ball are equal
B. the pressure at the top \( > \) the pressure at the bottom
c. the pressure at the top \( < \) the pressure at the bottom
D. there is no relation between the pressures


Evaluate \( \int \frac{e^{-x}}{1+e^{x}} d x \)


India has had a long and unbroken tradition of great scholarship - in mathematics, astronomy, linguistics, logic and ethics. Yet, in parallel with this, several superstitious and obscurantistic attitudes and practices flourished in our society and unfortunately continue even today among many educated people too. How will you use your knowledge of science to develop strategies to counter these attitudes?


Match the catalysts to the correct
processes:
Catalyst \( \quad \) Process
A. \( T i C l_{3} \) ¡. Wacker process
ii. Ziegler - Natta
B. \( P d C l_{2} \quad \) polymerization
С. \( C u C l_{2} \)
iii. Contact process
D. \( V_{2} O_{5} \)
¡v. Deacon's process
\( A \cdot(A)-(i i i),(B)-(i i),(C)-(i v),(D)-(i) \)
B. (A) - (ii), (B) - (i), (C) - (iv), (D) - (iii)
C. \( (A)-(\text { ii) },(B)-(\text { iii) },(C)-(i v),(D)-(i) \)
D. (A) - (iii), (B) - (i), (C) - (ii), (D) - (iv)


In which of the following, there is intermolecular hydrogen bonding? This question has multiple correct options
A . water
в. \( C_{2} H_{5} O H \)
c. \( C H_{3} \) СООН
D. \( H-F \)


Integrate \( \int_{0}^{2}\left(x^{2}+x\right) d x \)


In a group 14 males and 6 females, 8
and 3 of the males and females
respectively are aged above 40 years. The probability that a person selected at random from the group is aged above
40 years, given that the selected person is female, is
A \( \cdot \frac{2}{7} \)
B. \( \frac{1}{2} \)
\( c \cdot \frac{1}{4} \)
D.


Which is not a compound of aluminium
A. Corundum
B. Ruby
c. Diaspore
D. Dolomite


The distribution below gives the
weights of 30 students of a class. Find
the median weight of the students.
\( \begin{array}{ll}\text { Weight (in kg) } & \text { No. of students } \\ 40-45 & 2 \\ 45-50 & 3 \\ 50-55 & 8 \\ 55-60 & 6 \\ 60-65 & 6 \\ 65-70 & 3 \\ 70-75 & 2\end{array} \)
A . 56.67kg
B. 66.06kg
c. \( 56.00 \mathrm{kg} \)
D. 46.89kg


Let \( A \) being a square matrix, then prove that \( \boldsymbol{A}+\boldsymbol{A}^{T} \) is symmetric.


If in a G.P., 5th term and the 12th term are 9 and \( \frac{1}{243} \) respectively, find the 9 th term of G.P.
A \( \cdot \frac{1}{7} \)
B. \( \frac{1}{8} \)
\( c \cdot \frac{1}{9} \)
D. \( \frac{1}{81} \)


Hybridization state of beryllium atom in
\( B e C l_{2} \) molecule is \( x . \) The type of
hybridization changes to \( y \) when \( B e C l_{2} \) transforms to the solid state. Then \( \boldsymbol{x}, \boldsymbol{y} \)
are respectively:
A \( . s p, s p^{2} \)
B . \( s p, s p^{3} \)
c. \( s p^{2}, s p^{3} \)
D. \( s p, s p \)


Calculate the wave number and
frequency of radiation having wavelength \( 5800 \lambda \)
\( \left(172400 c m^{-1}, 5.172 \times 10^{14} c y \operatorname{cles} s^{-1}\right) \)


Let z satisfy \( |z-3|=4, \) then find max
and min. value of \( |z-5-7 i| \)


of the resistors in the circuit pictured
below?
A \( \cdot R_{1} \rightarrow 10 V ; R_{2} \rightarrow 4 V ; R_{3} \rightarrow 2 V ; R_{4} \rightarrow 4 V \)
B . \( R_{1} \rightarrow 1 V ; R_{2} \rightarrow 3 V ; R_{3} \rightarrow 2 V ; R_{4} \rightarrow 4 V \)
c. \( R_{1} \rightarrow 10 V ; R_{2} \rightarrow 2 V ; R_{3} \rightarrow 4 V ; R_{4} \rightarrow 4 V \)
D. \( R_{1} \rightarrow 1 V ; R_{2} \rightarrow 4 V ; R_{3} \rightarrow 4 V ; R_{4} \rightarrow 2 V \)


Electron accelerated by potential \( V \) are
diffracted from a crystal. If \( \boldsymbol{d}=\mathbf{1} \boldsymbol{A} \) and
\( \boldsymbol{i}=\mathbf{3 0}^{\circ} . \boldsymbol{V} \) should be about \( \boldsymbol{h}=\mathbf{6 . 6} \times \)
\( \mathbf{1 0}^{-\mathbf{2 4}} \mathbf{J s m}_{e}=\mathbf{9 . 1} \times \mathbf{1 0}^{-\mathbf{3 3} \mathbf{k g} . \boldsymbol{e}}= \)
\( \mathbf{1} . \mathbf{6} \times \mathbf{1 0}^{-\mathbf{1 9}} \mathbf{C} \)
A . \( 2000 V \)
в. \( 50 V \)
\( \mathbf{c} .500 V \)
D. \( 1000 V \)


Resolving power of a telescope
increases with
A. increase in focal length of eye-piece
B. increase in focal length of objective
C. increase in aperture of eye piece
D. increase in aperture of objective


In Ramsay - Rayleighs first method from
air, the correct statement is :
\( A \cdot O_{2} \) is removed as \( \mathrm{CO}_{2} \)
B. \( \mathrm{N}_{2} \) is removed as its oxide
c. oxygen is removed as \( \mathrm{CuO} \) and nitrogen is removed as \( \mathrm{Mg}_{3} \mathrm{N}_{2} \)
D. \( \mathrm{O}_{2} \) and \( \mathrm{N}_{2} \) are simultaneously removed as oxides of nitrogen


A delta is formed at the meeting point of sea water and river water. Why?


A galvanometer coil has a resistance of
\( 50 \Omega \) and the meter shows full scale
deflection for a current of \( 5 m A \). This
galvanometer is converted into
voltmeter of range \( 0-20 V \) by
connecting
A. \( 3950 \Omega \) in series with galvanometer
B. \( 4050 \Omega \) in series with galvanometer
c. \( 3950 \Omega \) in parallel with galvanometer
D. \( 4050 \Omega \) in parallel with galvanometer


Ground state electronic configuration of nitrogen atom can be represented by :
This question has multiple correct options
\( A \)
\( \uparrow \downarrow \)
в. \( \uparrow \downarrow \)
\( c \)
\( \uparrow \downarrow \) \( \uparrow \quad \downarrow \quad \downarrow \)
D. \( \uparrow \downarrow \) \( \downarrow \downarrow \downarrow \downarrow \downarrow \)


According to the definition of oblique collision in the paragraph, which of the following collisions cannot be oblique?
A. Collision between two point masses
B. Collision between two rings of same radius
c. collision between two rings of different radius
D. collision between a particle and a ring of finite radius


A solid sphere is rotating freely about
its symmetry axis in free space. The radius of the sphere is increased keeping its mass same. Which of the following physical quantities would remain constant for the sphere?
A. Rotational kinetic energy
B. Angular velocity
c. Angular momentum
D. Moment of inertia


\( 26 z^{3}\left(32 z^{2}-18\right) \div 13 z^{2}(4 z-3) \)
A \( \cdot z(4 z+3) \)
в. \( (4 z+3) \)
c. \( 4 z(4 z+3) \)
D. None


Which of the following is NOT a chemical change?
A. Digestion of food
B. Precipitation of rain and snow
c. Rusting of iron
D. Burning of paper


If \( x^{2}+2 x y+y^{3}=42, \) find \( \frac{d y}{d x} \)


In which of the following reactions product will be aldehyde? This question has multiple correct options
\( A \)
\[
\mathrm{CH}_{3}-\mathrm{C}=\mathrm{C}-\left.\mathrm{C}_{2} \mathrm{H}_{5} \frac{(\mathrm{i}) \mathrm{O}_{3}}{\mathrm{CH}_{3}}\right|_{\mathrm{CH}_{3}}
\]
в. \( C H_{3}-C H=C H_{2} \frac{C O / H_{2} / C O_{2}(C O)_{8}}{\Delta} \)
c. \( C H_{3}-C \equiv C H \frac{B_{2} H_{6}}{N a O H, H_{2} O_{2}} \)
D. \( C H_{3}-C \equiv C H \stackrel{H O H / H g S O_{4} / H_{2} S O_{4}}{\longrightarrow} \)


Find the smallest no. by which each of the following no. must be divided to
obtain a perfect cube.
(i) 81
(ii) 128
(iii) 135
(iv) 192
(v) 704


11 oranges are bought for Rs 10 and 10 oranges are sold for Rs. 11. The gain 1 loss percent is
A \( .21 \% \) loss
B. \( 11 \% \) gain
c. \( 21 \% \) gain
D. \( 11 \% \) loss


The efficiency of a heat engine:
A. is independent of the temperature of the source and the sink
B. is independent of the working substance
c. can be \( 100 \% \)
D. is not affected by the thermal capacity of the source or the sink


Fresh milk has a pH of 6. On changing into curd, its pH becomes:
A. more than 6
B. less than 6
c. does not change
\( D \)


An electron is removed from sodium,
this is an \( _{---}- \) process and removing an electron from fluorine is an
process.
A. endothermic, exothermic
B. exothermic, endothermic
C. endothermic, endothermic
D. exothermic, exothermic
E. more information is needed


Members of which of the following have similar chemical properties?
A. Isotope
B. Isobars
c. Allotropes
D. Both isotopes and allotropes


All of the following are good laboratory
practices except
A. Wait for a hot object to cool before weighing it.
B. Rinse a burette with the solution that will be used to fill the times
C. Wear goggles at all times
D. Return unused chemicals to the reagent bottles
E . To dilute \( H_{2} S O_{4} \), pour it into water slowly.


One of the two equal angles of an
isosceles triangle measures \( 55^{\circ} \) determine the other angles.


The osmotic pressure of equimolar
solutions of \( \mathrm{BaCl}_{2}, \) NaCl and glucose will
be in the order:
A \( . \) glucose \( >N a C l>B a C l_{2} \)
в. \( B a C l_{2}>N a C l> \) glucose
c. \( N a C l>B a C l_{2}>g l u \operatorname{cose} \)
D. \( N a C l>g l u c o s e>B a C l_{2} \)


Thread is massless. On applying force \( F \)
KE increases by \( 20 \mathrm{J} \) in \( 1 \mathrm{s} \)
A. tension in the string is \( \mathrm{Mg} \)
B. the tension in the string is \( F \)
c. work done by the tension in 1 s is 20 J
D. the work done by the force of gravity is 20 Jin


Solve the following equations.
\( \cos 9 x-2 \cos 6 x=2 \)


To treat myasthenia gravis,
A. Acetylcholine esterase activity is inhibited
B. Receptors on motor end plate are reduced
C. Secretion from nerve terminals is reduced
D. Secretion from nerve terminals is enhanced


A rod of mass \( \mathrm{M} \) kg and length \( \mathrm{L} \mathrm{m} \) is bent in the form of an equilateral
triangle as shown in figure. The moment of inertia of the triangle about a vertical axis perpendicular to the plane of the
triangle and passing through the centre (in units of \( \mathrm{kg} \boldsymbol{m}^{2} \) ) is?
A \( \cdot \frac{M L^{2}}{12} \)
B. \( \frac{M L^{2}}{54} \)
c. \( \frac{M L^{2}}{162} \)
D. \( \frac{M L^{2}}{108} \)


The freezing point on a thermometer is
marked as \( 20^{\circ} \) and the boiling point as
\( 150^{\circ} . A \) temperature of \( \left(60^{\circ} C\right) \) on this thermometer will be read as:
A \( \cdot 40^{\circ} \)
B . \( 65^{\circ} \)
\( \mathrm{c} \cdot 98^{\circ} \)
D. None of these


A varying current in the transformer's
primary winding creates a varying
magnetic flux in the core and a varying
magnetic field impinging on the
A. iron core
B. electromagnetic field
C. secondary windings
D. none of the above


Which process is not involved in the
reaction?
\( \boldsymbol{K} \boldsymbol{O}_{2}+\boldsymbol{H}_{2} \boldsymbol{O}+\boldsymbol{C} \boldsymbol{O}_{2} \rightarrow \boldsymbol{K} \boldsymbol{H} \boldsymbol{C} \boldsymbol{O}_{3}+\boldsymbol{O}_{2} \)
A. Hydrolysis
B. Auto-redox
c. Acid-base reaction
D. Non redox change


Find the oxidation number of \( N \& C l \) in
\( N O C l_{4} \) respectively is:
\( A \cdot+3,+6 \)
B. +2,+6
\( \mathrm{c} \cdot+3,+7 \)
\( \mathrm{D} \cdot+2,+7 \)


If \( P=\cos \frac{\pi}{20} \cdot \cos \frac{3 \pi}{20} \cdot \cos \frac{7 \pi}{20} \cdot \cos \frac{9 \pi}{20} \& Q \)
\( =\cos \)
\( \frac{\pi}{11} \cdot \cos \frac{2 \pi}{11} \cdot \cos \frac{4 \pi}{11} \cdot \cos \frac{8 \pi}{11} \cdot \cos \frac{16 \pi}{11}, \) ther
is
A. not defined
B. 1
\( c \cdot 2 \)
D. none of these


Write a short note on the hip bone.


Conjugate base of \( H C l \) in the following reaction is:
\( \boldsymbol{H} \boldsymbol{C l}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \boldsymbol{C l}^{-}(\boldsymbol{a q})+\boldsymbol{H}_{3} \boldsymbol{O}^{+} \)
A \( \cdot H_{3} O^{+} \)
в. \( H_{2} O \)
c. \( C l^{-} \)
D. нс


n triangle \( A B C, \angle B A C=90^{\circ}, \) and
\( A D \) is its bisector. If \( D E \) is drawn
\( \perp A C, \) prove that \( D E \times(A B+A C)= \)
\( \boldsymbol{A B} \times \boldsymbol{A C} \)


Find the antiderivative of the function
\( \left(\sin \frac{x}{2}+\cos \frac{x}{2}\right)^{2} \)


Which of the following has lowest pH?
A \( . . M g S O_{4} \)
B \( . M g C O_{3} \)
c. \( N a C l \)
D. \( N a_{2} C_{2} O_{4} \)


Assertion
Optical fibres are used to transmit light
without any appreciable loss in its intensity over distance of several
kilometers.
Reason
Optical fibres are very thick and all the
light is passed through it without any
loss.
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


In the given figure, \( \angle A=\angle C E D \). Prove
that \( \triangle \mathrm{CAB} \sim \triangle \mathrm{CED} \). Also, find the
value of \( \boldsymbol{x} \)


appeared in a test of 100 marks in the subject of social
studies and the data about the marks
secured is as below:
\begin{tabular}{cc}
Marks secured & Number of Students \\
\hline \( 0-25 \) & 50 \\
\( 26-50 \) & 220 \\
\hline \( 51-75 \) & 100 \\
Above 75 & 30 \\
Total number of students & 400 \\
\hline
\end{tabular} If the result card of a student he picked
up at random, what is the probability
that the student has secured more than
50 marks.
A. 0.586
B. 0.75
c. 0.325
D. 0.1


Potential difference across each
capacitor at that instant.


The maximum energy is stored at following trophical level in any
ecosystem
A. Producers
B. Herbivores
c. Carnivores
D. Top carnivores


The wavelength of light wave of wave
number \( 4000 \mathrm{cm}^{-1} \) is:


Suppose you are standing on a boat in the middle of a swimming pool. The boat is loaded with a bag of stones. Can you get to the shore using the stones? If
yes, explain the concept behind it.


The integral \( \int_{\frac{\pi}{4}}^{\frac{3 \pi}{4}} \frac{d x}{1+\cos x} \)
A .2
B. 4
\( c \cdot-1 \)
D. -


It takes ten minutes to increase the
temperature of a body from \( 70^{\circ} \mathrm{C} \) to \( 80^{\circ} \)
c. Time required to increase the
temperature of the body from \( 60^{\circ} \) to \( 70^{\circ} \)
would be.
A. More than 10 minutes
B. Less than 10 minutes
c. 10 minutes
D. Data is inadequate so can't be determined


Draw the necessary table to find the
Standard Deviation for the data
\( \mathbf{2 0}, \mathbf{1 4}, \mathbf{1 6}, \mathbf{3 0}, \mathbf{2 1}, \mathbf{a n d} \mathbf{2 5} \)


Which of the following reagents are used as primary standard?
\( \boldsymbol{I}: \boldsymbol{K} \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{4} ; \boldsymbol{I} \boldsymbol{I}: \boldsymbol{N} \boldsymbol{a} \boldsymbol{O} \boldsymbol{H} ; \boldsymbol{I} \boldsymbol{I} \boldsymbol{I} \)
\( \boldsymbol{K}_{2} \boldsymbol{C r}_{2} \boldsymbol{O}_{7} \)
\( \boldsymbol{I} \boldsymbol{V}: \boldsymbol{F} \boldsymbol{e} \boldsymbol{S} \boldsymbol{O}_{4}\left(\boldsymbol{N} \boldsymbol{H}_{4}\right)_{2} \boldsymbol{S} \boldsymbol{O}_{4} \cdot \boldsymbol{6} \boldsymbol{H}_{2} \boldsymbol{O} ; \boldsymbol{V} \)
\( \boldsymbol{H}_{2} \boldsymbol{C}_{2} \boldsymbol{O}_{4} \cdot \boldsymbol{2} \boldsymbol{H}_{2} \boldsymbol{O} \)
A. All except II, \( I V \)
B. All except I, II
C. All except \( I \), II, III
D. only \( I V \)


The arrangement of following
compounds:
i. Bromomethane
ii. Bromoform
iii. Chloromethane
iv. Dibromomethane
In the increasing order of their boiling point is :
A . \( i i i<i<i v<i i \)
в. \( i v<i i i<i<i i \)
c. \( i i<i i i<i<i v \)
D. \( i<i i<i i i<i v \)


The number of arbitrary constants in the particular solution of the differential equation of order 3 is
\( A \cdot 0 \)
B.
\( c \cdot 2 \)
\( D \)


Sequence of events in kreb's cycle is


A salt associated with water of
crystallization is known as a:
A . acid
B. buffer
c. hydrate
D. anion


The density of water is 1 g/ml. The number of molecules present in 1 litre of
water is:
A \( \cdot 18 \times 6.023 \times 10^{23} \)
В. \( 1.8 \times 6.023 \times 10^{23} \)
c. \( 6.023 \times 10^{23} \)
D . \( 55.55 \times 6.023 \times 10^{23} \)


f the volume of each cube is 1 cubic \( \mathrm{cm} \)
then the volume of the cuboid given in the following figure is
A. 12 cubic cm
B. 24 cubic cm
\( c .36 \) cubic cm
D. 26 cubic cm


Prove the following:
\( \left|\begin{array}{llll}\boldsymbol{x} & \boldsymbol{a} & \boldsymbol{a} & \boldsymbol{a} \\ \boldsymbol{a} & \boldsymbol{x} & \boldsymbol{a} & \boldsymbol{a} \\ \boldsymbol{a} & \boldsymbol{a} & \boldsymbol{x} & \boldsymbol{a} \\ \boldsymbol{a} & \boldsymbol{a} & \boldsymbol{a} & \boldsymbol{x}\end{array}\right|=(\boldsymbol{x}+\boldsymbol{3} \boldsymbol{a})(\boldsymbol{x}-\boldsymbol{a})^{3} \)


A body of mass \( 0.1 k g \) is executing simple harmonic motion according to the equation \( \boldsymbol{x}=\mathbf{0 . 5} \cos \left(\mathbf{1 0 0} \boldsymbol{t}+\frac{\mathbf{3} \boldsymbol{\pi}}{\mathbf{4}}\right) \) metre. Find:
(i) the frequency of oscillation, (ii)
initial phase, (iii) maximum velocity,
(iv) maximum acceleration,
(v) total
energy.


The earth's magnetic field at a given point is \( 0.5 \times 10^{-5} W b m^{-2} . \) This field is
to be annulled by magnetic induction at the centre of a circular conducting loop
of radius \( 5.0 \mathrm{cm} . \) The current required to
be flown in the loop is nearly
в. \( 0.4 A \)
\( c .4 A \)
D. \( 40 A \)


To a germanium sample, traces of gallium are added as an impurity. The resultant sample would behave like:
A. a conductor
B. a p-type semi-conductor
c. an n-type semi-conductor
D. an insulator


Which one is more effective greenhouse
\( \operatorname{gas}, C O \) or \( H_{2} O ? \)
If the answer is \( H_{2} O \) then enter 1 , else
enter 0


The true statement is
A. Sound waves in air are transverse waves
B. Sound wave does not required a material medium for its propagation
C. Sound travels faster in gas than in solid
D. Sound travels faster in solid than in gas


The earliest human has been named as
A. Australopithecus
B. Homo erectus
c. Homo habilis
D. Homo sapiens


Mark the correct alternative of the
following.
In figure, \( A B|| C D \) and \( E F \) is a transversal
intersecting \( A B \) and \( C D \) at \( P \) and \( Q \)
respectively. The measure of \( \angle D P Q \) is
\( \mathbf{A} \cdot 100^{\circ} \)
B . \( 80^{\circ} \)
\( \mathbf{c} \cdot 110^{\circ} \)
D. \( 70^{\circ} \)


Area bounded by \( y=2 x-x^{2} \&(x- \)
1) \( ^{2}+y^{2}=1 \) in first quadrant, is:
A \( \cdot \frac{\pi}{2}-\frac{4}{3} \)
B \( \cdot \frac{\pi}{2}-\frac{2}{3} \)
c. \( \frac{\pi}{2}+\frac{4}{3} \)
D. \( \frac{\pi}{2}+\frac{2}{3} \)


Which measure of dispersion has a
different unit other than the unit of
measurement of values?
A . Range
B. Mean deviation
c. standard deviation
D. Variance


Define heat capacity and state its \( \mathrm{S} \) I unit.


Which of the following are the observations of the experiment
conducted to determine whether a given compound is acid, base or salt?
A. Glowing of the bulb indicates conduction of electricity through the electrolyte
B. If a solution is a strong electrolyte the bulb glows brightly when the current is switched on
c. If a solution is a weak electrolyte the bulb glows dimly when the current is switched on
D. All of the above


Molecules which rotate plane of polarised light in either of direction are:
A. optically active
B. optically inactive
c. meso compound
D. none of these


Which is found as both straightchained and branched polymers?
A. Nucleic acids
B. Carbohydrates
c. Proteins
D. Electrolytes
E. Lipids


The equation of a wave propagating along a stretched string is given by \( \boldsymbol{Y}=\boldsymbol{4} \sin 2 \boldsymbol{\pi}[(\boldsymbol{t} / \mathbf{0} . \mathbf{0} \mathbf{2})-(\boldsymbol{x} / \mathbf{1 0 0})] \)
where \( Y \) and \( x \) are in \( \mathrm{cm} \) and \( t \) in
second. Determine wavelength.


For the reaction given below,
\( \mathbf{2} \mathbf{O}_{\mathbf{3}}(\mathbf{g}) \rightarrow \mathbf{3} \mathbf{O}_{\mathbf{2}}(\mathbf{g}) \)
\( \operatorname{Step} \mid: \mathbf{O}_{3}(\mathbf{g}) \rightarrow \mathbf{O}_{2}(\mathbf{g})+\mathbf{O}(\mathbf{g}) \)
Step \( 2: \mathrm{O}_{3}(\mathrm{g})+\mathrm{O} \rightarrow^{\text {slow }} 2 \mathrm{O}_{2}(\mathrm{g}) \)
Statement I: The molecularity of the first step is 1 and of the second step is 2
Statement-II: \( O(g) \) is an intermediate
and rate of reaction is \( \mathbf{K}\left[\mathbf{O}_{3}\right]^{2}\left[\mathbf{O}_{2}\right]^{-1} \) and
order of reaction is 1
A. Both statements are true Statement - - ll is correct explanation of Statement- -
B. Both statements are true but Statement- -II is not correct explanation of Statement- -
c. Statement - - lis true but Statement - II is false
D. Statement-lis false but Statement- 11 is true


The rate of elementary reaction, \( \boldsymbol{A} \rightarrow \boldsymbol{B} \)
increases by 100 times when the concentration of \( A \) is increased ten
folds. The order of the reaction with
respect to A is:
\( A \)
B. 2
\( c \cdot 10 \)
D. 100


For the reaction \( \boldsymbol{P} \boldsymbol{C l} \boldsymbol{l}_{5}(\boldsymbol{g}) \rightarrow \boldsymbol{P} \boldsymbol{C l}_{3}(\boldsymbol{g})+ \)
\( \boldsymbol{C l}_{2}(\boldsymbol{g}) \)
\( \mathbf{A} \cdot \Delta H=\triangle E \)
B . \( \triangle H>\triangle E \)
c. \( \triangle H<\triangle E \)
D. None of these


Shamrao's income in \( 2015-16 \) after
paying all taxes is \( R s .6,40,000 . \) He pays \( R s .2000 \) per month for insurance
and \( 20 \% \) of his annual income into his
provident fund. He puts aside \( \boldsymbol{R} \boldsymbol{s} . \mathbf{5 0 0} \) per month for emergencies. How much
money does he have form yearly spending?


Given standard electrode potentials:
\( \boldsymbol{F} \boldsymbol{e}^{\boldsymbol{3}+}+\boldsymbol{3} \boldsymbol{e}^{-} \longrightarrow \boldsymbol{F} \boldsymbol{e} ; \boldsymbol{E}^{\boldsymbol{o}}=-\mathbf{0 . 0 3 6} \boldsymbol{v o l} \boldsymbol{t} \)
\( \boldsymbol{F} \boldsymbol{e}^{2+}+\boldsymbol{2} \boldsymbol{e}^{-} \longrightarrow \boldsymbol{F} \boldsymbol{e} ; \boldsymbol{E}^{o}=-\mathbf{0 . 4 4 0} \boldsymbol{v o l t} \)
The standard electrode potential \( E^{o} \) for \( \boldsymbol{F} \boldsymbol{e}^{\boldsymbol{3}+}+\boldsymbol{e}^{-} \longrightarrow \boldsymbol{F} \boldsymbol{e}^{\boldsymbol{2}+} \) is:
A. 0.476 volt
B. 0.404 volt
c. 0.440 volt
D. 0.772 volt


What is meant by scattering of light? Use this phenomenon to explain why the clear sky appears blue or the Sun appears reddish at sunrise.


State radioactive decay law. Prove that radioactive decay is exponential in
nature


Assertion
Let \( \bar{a}, \bar{b}, \bar{r} \) be the vectors such that \( \bar{r}+ \) \( \overline{\boldsymbol{r}} \times \overline{\boldsymbol{a}}=\overline{\boldsymbol{b}} \operatorname{then}|\overline{\boldsymbol{r}}|^{2}=\frac{(\overline{\boldsymbol{a}} \cdot \overline{\boldsymbol{b}})^{2}+|\overline{\boldsymbol{b}}|^{2}}{\mathbf{1}+|\overline{\boldsymbol{a}}|^{2}} \)
Reason
\( \overline{\boldsymbol{r}}=\frac{(\overline{\boldsymbol{a}} \cdot \overline{\boldsymbol{b}}) \overline{\boldsymbol{a}}+\overline{\boldsymbol{b}}+\overline{\boldsymbol{a}} \times \overline{\boldsymbol{b}}}{\mathbf{1}+|\overline{\boldsymbol{a}}|^{2}} \)
A. Both Assertion \& Reason are individually true \& Reason is correct explanation of Assertion
B. Both Assertion \& Reason are individually true but Reason is not the correct (proper) explanation of Assertion
C. Assertion is true but Reason is false
D. Assertion is false but Reason is true


The valency of element with atomic
number 10 is:
A . 0
B.
\( c \cdot 2 \)
\( D \)


Filter circuit
A. eliminates a.c. component
B. eliminates d.c. component
c. does not eliminate a.c. component
D. None of these


Q Type your question
\( A \)
\( B \)
\( c \)
\( D \)


On a rainy day, a raindrop falls from very high clouds and faces retardation due to air. This retardation is directly proportional to the instantaneous speed of the drop and proportionality constant is given as \( \alpha . \) An expression for the
distance travelled \( s \) by the drop in time \( t \)
is: (given acceleration due to gravity \( = \)
\( \boldsymbol{g} \)
A. \( s=\frac{g}{\alpha^{2}}\left(e^{-\alpha t}-1\right)+\frac{g}{\alpha} t \)
в. \( _{s}=\frac{g t}{\alpha} \)
c. \( _{s}=\frac{g}{\alpha^{2}}\left(e^{-\alpha t}-1\right) \)
D. \( _{s}=\frac{g t}{\alpha^{2}}+\frac{g}{\alpha}\left(e^{-\alpha t}-1\right) \)


Which source of energy uses the
production of steam to generate electrical energy?
A. Hydroelectric
B. Nuclear
c. Tides
D. waves


No. of permutations of 25 dissimilar things taken more than 15 at a time when repetitions are allowed is
A \( \cdot \frac{25}{24}\left(25^{25}-25^{15}\right) \)
В \( \cdot \frac{25}{24}\left(25^{25}-25^{10}\right) \)
c. \( \frac{25}{24}\left(25^{25}+25^{15}\right) \)
D. \( \frac{25}{24}\left(25^{25}+25^{10}\right) \)


A body of mass \( m \) is moving in a circular orbit of radius \( \boldsymbol{R} \) about a planet
of mass \( M . \) At some instant, it splits into two equal masses. The first mass moves in a circular orbit of radius \( \frac{\boldsymbol{R}}{\longrightarrow} \) \( \overline{2} \)
and the other mass, in a circular orbit of radius \( \frac{3 R}{2} . \) The difference between the final and initial total energies is:
A. \( -\frac{G M m}{2 R} \)
в. \( +\frac{G M m}{6 R} \)
c. \( \frac{G M m}{2 R} \)
D. \( -\frac{G M m}{6 R} \)


Read the following statements which are taken as axioms:
(i) If a transversal intersects two
parallel lines, then corresponding angles are not necessarily equal.
(ii) If a transversal intersect two parallel lines, then alternate interior angles are
equal

Is this system of axioms consistent?


The difference of two numbers is 72 and
the quotient obtained by dividing the one by the other is 3 . Find the numbers.
\( \mathbf{A} \cdot 60 \) and 132
B. 42 and 114
c. 36 and 108
D. 30 and 102


A block of a mass of \( 10 \mathrm{kg} \) rests on a horizontal table. The coefficient of
friction between the block and the table
is \( 0.05 . \) When hit by a bullet of mass 50 g moving with speed \( v \), that gets embedded in it, the block moves and
comes to rest after moving a distance of
\( 2 \mathrm{m} \) on the table. If a freely falling object were to acquire speed \( \frac{v}{10} \) after being dropped from height H, then neglecting energy losses and taking \( g=10 m s^{-2} \)
the value of \( \mathrm{H} \) is close to:
B. \( 0.05 k m \)
\( c .0 .02 k m \)
D. \( 0.03 k m \)


Consider the structure pictured above,
including the accompanying ligand.
Which of the following CORRECTLY
identifies the pictured compound by
name, and identifies the bonding
involved in its structure?
A. The compound is ammonium dichromate. It contains both ionic and covalent bonds.
B. The compound in diammonium chromate. It contains both ionic and covalent bonds.
C. The compound is ammonium dichromate. It contains only ionic bonds.
D. The compound is ammonium chromate. It contains ionic bond.


Hydrogen bomb is based on the
principle of:
A. Nuclear fission
B. Nuclear fusion
c. Nuclear explosion
D. Chemical reaction


Evaluate: \( \int_{0}^{1} \frac{\sqrt{\tan ^{-1} x}}{1+x^{2}} d x \)


From the given figure, find :
\( \angle A C B \)
\( \mathbf{A} \cdot 70^{\circ} \)
B. \( 80^{\circ} \)
\( c \cdot 75^{\circ} \)
D. none of the above


Two solvent \( A \) and \( B \) have \( K_{f} \) values 1.86
and \( 2.79 \mathrm{K} \) mol\( ^{-1} \) kg respectively.
given amount of substance when
dissolved in 500 g of \( A, \) it completely dimerizes and when same mass of
substance is dissolved in 500 g of \( \mathrm{B} \), the solute undergoes trimerization.
The ratio of observed lowering of freezing points in two cases is \( 1:(?) \)


In a purely resistive \( \boldsymbol{A C} \) circuit
A. voltage leads current
B. voltage lags current
C . voltage and current are in same phase
D. nothing can be said


Which of the following statements is
not correct regarding conservation laws?
A. A conservation law is a hypothesis based on observations and experiments
B. Conservation laws do not have a deep connection with symmetries of nature.
c. A conservation law cannot be proved
D. Conservation of energy, linear momentum, angular momentum are considered to be fundamental laws of physics


In the radioactive change, \( \stackrel{A}{Z} \boldsymbol{P} \longrightarrow_{Z+1}^{A} \boldsymbol{Q} \longrightarrow_{Z-1}^{A-4} \boldsymbol{R} \longrightarrow_{Z-1}^{A-4} \boldsymbol{S} \)
the radiations emitted in sequence are:
\( \mathbf{A} \cdot \alpha, \beta, \gamma \)
в. \( \beta, \alpha, \gamma \)
c. \( \gamma, \alpha, \beta \)
D. \( \beta, \gamma, \alpha \)


For the shown graph the slope of graph
from point \( A \) to point \( B: \)
A. continuously decreases
B. Continuously increases
c. First increases then decreases
D. First decreases then increases


Rate of evaporation increases
A. with the rise in temperature
B. with the fall in temperature
C. irrespective of temperature
D. only beyond room temperature


An example of solid sol is :
A. butter
B. gem stones
c. paint
D. hair cream


What is the frequency of light emitted when an electron in a hydrogen atom jumps from 2nd orbit to 1st orbit?


Which one of the following organisms is
correctly matched with its three
characteristics?
A. Pea- \( C_{3} \) -pathway, endospermic seed, vexillary aestivation
B. Tomato- twisted aestivation, axile placentation, berry
C. Onion- Bulb, Imbricate aestivation, axile placentation
D. Maize- \( C_{3} \) -pathWay, closed vascular bundle, scutellum


Presence of RBC in urine is called
A. Anuria
B. Haematuria
c. Glycosuria
D. Ketonuria


\( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{l}2 \boldsymbol{a}-\boldsymbol{x}, \text { for }-\boldsymbol{a}<\boldsymbol{x}<\boldsymbol{a} \\ \mathbf{3} \boldsymbol{x}-\mathbf{2} \boldsymbol{a}, \text { for } \boldsymbol{x} \geq \boldsymbol{a}\end{array}\right. \)
Then which of the following is true?
A. \( f(x) \) is discontinuous at \( x=a \)
B. \( f(x) \) is not differentiable at \( x=a \)
C. \( f(x) \) is differentiable at all \( x \geq a \)
D. \( f(x) \) is continuous at all \( x<a \)


The vapour pressure of a pure liquid \( \boldsymbol{A} \)
is 70 torr at \( 27^{\circ} \mathrm{C} \). It forms an ideal
solution with another liquid \( B \). The mole
fraction of \( B \) is 0.2 and total vapour
pressure of the solution is 84 torr at
\( 27^{\circ} \mathrm{C} . \) The vapour pressure of pure
liquid \( B \) at \( 27^{\circ} \mathrm{C} \) is:
A . 14
B. 56
\( c .140 \)
D. 70


When \( _{3} L i^{7} \) nuclei are bombarded by
protons and the resultant nuclei are
\( 4 B e^{8}, \) the emitted particles will be?
A. Alpha particles
B. Beta particles
c. Gamma photons
D. Neutrons


Which of the following reactions is endergonic?
\( \mathbf{A} \cdot A T P \rightarrow A D P+P_{i} \)
B \( \cdot N A D H \rightarrow N A D^{+}+H^{+} \)
\( \mathbf{c} \cdot\left(C H_{2} O\right)_{n}+O_{2} \rightarrow C O_{2}+H_{2} O \)
D. None of the above


When bauxite is boiled with aqueous
NaOH solution, sodium metal aluminate solution is formed. This part
in the metallurgy of aluminium is called:
A. liquation
B. amalgamation
c. leaching
D. calcination


Two moles of helium gas undergo a
cyclic process as shown in figure.
Assuming the gs to be ideal, calculate the following quantities in this
process. The net change in internal
energy.


The following reaction that has reached equilibrium:
\( N a C l(s) \longleftarrow \rightarrow N a C l(a q) \)
What should be the nature of the
solution of \( N a C l \) for the phase
equilibrium to exist?
A. concentrated
B. Saturated
c. Dilute
D. Heated
E. Unsaturated


Find the cube root of :
\( \mathbf{1} \)
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
c. Does not exist
D. None of these


The capacitance between adjacent plates shown in Fig \( 20.95(a) \) is 50 nF. \( A 1 \mu C \) charge is placed on the middle
plate. Find the charge on the outer surface of upper plate and the potential difference between upper and middle plates:
A. \( 0.5 \mu C, 10 V \)
B. \( 1 \mu C, 20 V \)
c. \( 0.5 \mu C, 20 V \)
D. \( 1.0 \mu, 40 V \)


A person has deposited Rs. 25,000 in an investment which yields \( 14 \% \) simple
interest annually. Do these amounts (principal \( +\text { interest }) \) form an A.P.? If so
determine the amount of investment
after 20 years


A current of \( 5 A \) is flowing at \( 220 V \) in the primary coil of a transformer. If the voltage produced in the secondary coil
is \( 2200 V \) and \( 50 \% \) of power is lost, then
the current in the secondary will be
A . \( 2.5 A \)
в. \( 0.5 A \)
c. \( 0.25 A \)
D. \( 5 A \)


In the following network, potential at 0
is
\( 4.4 v \)
\( 3.3 v \)
\( c \cdot 6 v \)
\( D \cdot 4.8 v \)


If \( \boldsymbol{A}-\boldsymbol{B}=\boldsymbol{C} \) and \( \boldsymbol{A}+\boldsymbol{B}=\frac{\pi}{2} \) then
\( \tan A=\tan B+2 \tan C \)


Find any two rational numbers between \( \frac{-1}{2} \) and \( \frac{-2}{3} \)


Find the value of \( i^{i} \)


Construct a quadrilateral \( P Q R S \) in
which \( P Q=3.8 \mathrm{cm}, Q R=3.4 \mathrm{cm} \)
\( \boldsymbol{R} \boldsymbol{S}=\mathbf{4 . 5} \mathrm{cm}, \boldsymbol{S} \boldsymbol{P}=\mathbf{5} \mathrm{cm} \) and \( \angle \boldsymbol{Q}= \)
\( 80^{\circ} . \) State which of these is the first
step.
A. From \( Q \), set \( Q R=3.4 \mathrm{cm} \)
B. With \( P \) as center and radius equal to \( 5 \mathrm{cm} \), draw an arc
c. Join \( P S \) and \( R S \)
D. Make \( \angle P Q X=80^{\circ} \)


The outer region of secondary wood is lighter in colour, known as
A. Autumn wood
B. Alburnum
c. sap wood
D. Both B and C


There are 4 letter boxes in a post office.
In how many ways can a man post 8 distinct letters?
\( \mathbf{A} \cdot 4 \times 8 \)
B . \( 8^{4} \)
\( c \cdot 4^{8} \)
D \( \cdot P(8,4) \)


Identify product \( \mathrm{D} \) in the following
reaction sequence:
\[
\begin{array}{l}
\boldsymbol{C H}_{\boldsymbol{3}}- \\
\boldsymbol{C H}_{3} \\
\dot{\boldsymbol{C}}-\boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{O} \boldsymbol{H} \frac{\boldsymbol{K}_{2} \boldsymbol{C r}_{2} \boldsymbol{O}_{7} ; \boldsymbol{H}_{2} \boldsymbol{S O}_{4}}{\boldsymbol{H}_{2} \boldsymbol{O} \text { heat }}
\end{array}
\]
\( \boldsymbol{A} \stackrel{\boldsymbol{S O C l}_{2}}{\longrightarrow} \boldsymbol{B} \frac{\left(\boldsymbol{C H}_{3}\right)_{2} \boldsymbol{N} \boldsymbol{H}}{(\boldsymbol{2} \boldsymbol{m o l e})} \)
\[
C \frac{1 . \text { LiAl } H_{4} \text { diethyl ether }}{2 . H_{2} O} D
\]
A. \( \quad C H_{3} \)
\[
C H_{3} C C H_{2} C \equiv N
\]
\[
\begin{array}{c}C C \\ C H_{3}\end{array}
\]
B.
\[
\begin{array}{c}
C H_{3} \\
C H_{3} C C H_{2} C H_{2} N\left(C H_{3}\right)_{2} \\
C H_{3}
\end{array}
\]
\( c \)
\[
\begin{array}{c}
C H_{3} \quad N\left(C H_{3}\right)_{2} \\
C H_{3} C C H_{2} C H N\left(C H_{3}\right)_{2} \\
C H_{3}
\end{array}
\]


A gas in a flexible container initially has volume of 320 L. If we decrease the
pressure of the gas from 4.0 atm to 1.0 atm and decrease the temperature form 273 degrees Celsius to 0 degrees Celsius, what is the new volume of the
gas?
A. \( 0 L \)
B. 320 L
\( c \cdot 160 L \)
D. 640 L
E. 80


According to the third law of motion,
action and reaction
A. always act on the same body
B. always act on different bodies in opposite directions
C. have same magnitude and direction
D. act on either body at normal to each other


If the maximum angle rotated by the
rod after the collision is \( 60^{\circ}-\cos ^{-1} \frac{z}{8} \)
find the value of \( z \)


A radioactive isotope \( \boldsymbol{X} \) with half life of \( 1.37 \times 10^{9} \) years decays to \( Y, \) which is
stable. A sample of rock from moon was found to contain both the elements \( \boldsymbol{X} \)
and \( Y \) in the ratio \( 1: 7 . \) What is the age
of the rock?


Which of the following applications is not based on use of ICs?
A. Microprocessor chip.
B. Laptops and personal computers.
c. Mobile phones.
D. Transformers


The value of \( \sum_{i=1}^{n} \sum_{j=1}^{i} \sum_{k=1}^{j} 1= \)


Number of permutation of 10 different objects taken all at a time in which particular 4 never comes together
A. \( 10 ! \times 4 \)
B. \( 10 !-4 \)
c. \( \frac{7 ! 6 !}{4 !} \)
D. \( 10 !-7 ! 4 ! \)


Lead chloride has a solubility product of
\( 1.7 \times 10^{-5} . \) What is its solubility in
moles / L?


A simple telescope used to view distant objects has eyepiece and objective lens
of focal lengths \( \mathrm{f}_{\mathrm{e}} \) and \( \mathrm{f}_{0}, \) respectively.
Then


Evaluate \( : \lim _{x \rightarrow 3} \frac{\sqrt[4]{x}-\sqrt[4]{3}}{\sqrt[3]{x}-\sqrt[3]{3}} \)


Assertion
The outer electronic configurations of Cr and Cu are \( 3 d^{5} 4 s^{1} \) and \( 3 d^{10} 4 s^{1} \)
respectively.
Reason
Electrons are filled in orbitals in order of
their increasing energies given by \( (n+1) \)
rule
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


Three point charges \( +\boldsymbol{q},-\boldsymbol{2} \boldsymbol{q} \) and \( +\boldsymbol{q} \)
are placed at points \( (\boldsymbol{x}=\mathbf{0}, \boldsymbol{y}=\boldsymbol{a}, \boldsymbol{z}= \)
\( \mathbf{0}),(\boldsymbol{x}=\mathbf{0}, \boldsymbol{y}=\mathbf{0}, \boldsymbol{z}=\mathbf{0}) \) and \( (\boldsymbol{x}= \)
\( \boldsymbol{a}, \boldsymbol{y}=\mathbf{0}, \boldsymbol{z}=\mathbf{0}) \) respectively. The
magnitude and direction of the electric
dipole moment vector of this charge assembly are :
A . \( \sqrt{2 q a} \) along \( +y \) direction
B. \( \sqrt{2} q a \) along the line joining points \( (x=0, y=0, z= \)
0) and \( (x=a, y=a, z=0) \)
c. \( q a \) along the line joining points \( (x=0, y=0, z= \)
0) and \( (x=a, y=a, z=0) \)
D. \( \sqrt{q} a \) along \( +x \) direction


If \( X \) follows a binomial distribution
with parameters \( n=8 \) and \( p=\frac{1}{2}, \) then
\( \boldsymbol{P}(|\boldsymbol{X}-\mathbf{4}| \leq \mathbf{2}) \) is
A \( \cdot \frac{119}{128} \)
в. \( \frac{119}{228} \)
c. \( \frac{19}{128} \)
D. \( \frac{18}{28} \)


What is the degree of the polynomial
\( (x+1)\left(x^{2}-x-x^{4}+1\right) ? \)


Which of the following is not a
quadratic equation?
A \( \cdot 2(x-1)^{2}=4 x^{2}-2 x+1 \)
B. \( \left(x^{2}+1\right)^{2}=x^{2}+3 x+9 \)
\( \mathbf{C} \cdot\left(x^{2}+2 x\right)^{2}=x^{4}+3+4 x^{3} \)
D \( \cdot x^{2}+9=3 x^{2}-5 x \)


If \( |\vec{A}+\vec{B}|=|\vec{A}-\vec{B}|, \) then the angle between \( \vec{A} \) and \( \vec{B} \) will be
\( A \cdot 30^{\circ} \)
B . 45
\( c \cdot 60 \)
D. 90


Which is the most primitive ancestor of
man?
A. Ramapithecus
B. Australopithecus
c. Homo habilis
D. Homo neanderthalensis


A place where a signal passes from one nerve cell to next is described as
A. Synaptic cleft
B. Synapsis
c. synapse
D. Symport movement


Find the expansion of \( (3 x+1)(3 x+2)(3 x+5) \)
A \( \cdot 27 x^{3}+72 x^{2}+51 x+10 \)
B. \( 27 x^{3}-72 x^{2}+51 x+10 \)
c. \( 27 x^{3}+72 x^{2}-51 x+10 \)
D. None of these


Find the square root of 27225 using
repeated subtraction.


Which statement explains why elements in Group VIII of the Periodic Table are unreactive?
A. They are monatomic gases
B. They form stable diatomic molecules
c. They have a full outer shell of electrons
D. They share electrons with each other


Find the left hand and right hand limits of the greatest integer function \( f(x)= \) \( [x]= \) greatest integer less than or equal
to \( x, \) at \( x=k, \) where \( k \) is an integer.
Also, show that \( \lim _{x \rightarrow k} f(x) \) does not exist.


A particle of mass \( \mathrm{m} \) is projected from
ground with velocity u making angle \( \theta \) with the vertical. The de Broglie wavelength of the particle at the highest point is
\( A \cdot \infty \)
B. \( h / m u \) sin \( \theta \)
c. \( h / m u \cos \theta \)
\( \mathbf{D} \cdot h / m u \)


Which of the following are correct?
This question has multiple correct options
\( \mathbf{A} \cdot \) If \( R \) is the radius of a planet, \( g \) is the acceleration due to gravity, the mean density of the planet is \( 3 g / 4 \pi G R \)
B. Acceleration due to gravity is a universal constant.
C. The escape velocity of a body from earth is \( 11.2 \mathrm{km} \mathrm{s}^{-1} \) The escape velocity from a planet which has double the mass of earth and half its radius is \( 22.4 \mathrm{km} \mathrm{s}^{-1} \)
D. The ratio of gravitational mass and inertial mass of a body at the surface of earth is 1


There are 6 multiple choice questions on an examination. How many
sequences of answers are possible, if
the first three questions have 4 choices
each and the next three have 5 each?


A copper wire of diameter \( 1.6 m m \)
carries a current \( i . \) The maximum
magnetic field due to this wire is \( 5 x \)
\( 10^{-3} T . \) The value of \( i \) is
A \( .40 A \)
в. \( 5 A \)
\( c \cdot 20 A \)
D. 2A


How many independent cells are produced by meiosis cell division?
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot 3 \)
D. 4
\( E .5 \)


The acceleration due to gravity \( g \) and mean density of earth \( \rho \) are related by
which of the following relations? \( [G= \) gravitational constant and \( \mathrm{R}= \) radius of earth].
A \( \cdot \rho=\frac{4 \pi g R^{2}}{3 G} \)
В \( \cdot \rho=\frac{4 \pi g R^{3}}{3 G} \)
\( \mathbf{c} \cdot \rho=\frac{3 G}{4 \pi g R} \)
D. \( \rho=\frac{3 G}{4 \pi g R^{3}} \)


In which of the following layers of the atmosphere most of the ozone is present?
A. Troposphere
B. Exosphere
c. Mesosphere
D. Stratosphere
E. None of these


The number of cytosine bases in a DNA molecule is equal to the number of
bases.


Let \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{3}-\boldsymbol{x}+\boldsymbol{p}(\boldsymbol{0} \geq \boldsymbol{x} \geq \mathbf{2}) \)
where \( p \) is a constant. The value \( c \) of
mean value theorem is :
A \( \cdot \frac{\sqrt{3}}{2} \)
B. \( \frac{\sqrt{6}}{2} \)
c. \( \frac{\sqrt{3}}{3} \)
D. \( \frac{\sqrt{2}}{3} \)
E \( \cdot \frac{2 \sqrt{3}}{3} \)


Relationship between DO and BOD is
that they
A. Are directly proportional
B. Are inversely proportional
c. Are not related
D. Always remain equal to each other


The molecular weight of acetone is \( \mathrm{M} \) The molecular weight of diacetone alcohol is:
A.
B. M/2
\( c . \) २м
D. 3M


Which of the following is true for diamond?
A. It is a good conductor of electricity
B. It is very soft
c. It is a good conductor of heat
D. It is made up of carbon, hydrogen and oxygen atoms


\( f(x)=\left\{\begin{array}{ll}\frac{1-\cos x}{x^{2}}, & \text { when } x \neq 0 \\ 1, & \text { when } x=0\end{array}\right. \)
then show that \( f(x) \) is discontinuous at
\( \boldsymbol{x}=\mathbf{0} \)


Epiphysis is connected with
A. Brow spot in embryo
B. Hypophysis
c. Optic lobes
D. None of the above


Write the equation for the complete combustion of ethane.


The term 'thio' is used in the names of
all the following compounds except
A. \( N a_{2} S_{2} O_{3} \)
в. \( C_{2} H_{6} S \)
c. \( N a S C N \)
D. \( N a_{2} S O_{3} \)


A mass of \( 5 \mathrm{kg} \) is acted upon by a force of \( 1 N \) Starting from rest, how much is
distance covered by the mass in \( 10 s ? \)


Volkmann's canals are found in
A. Bones of birds
B. Bones of amphilbians
C. Bones of mammals
D. Cartilage of mammals


Figure shows a point \( \mathrm{P} \) near a long
conductor XY carrying a current 1. MN is a short current carrying conductor, kept at the point \( P, \) parallel to the conductor
\( \mathbf{X Y} \)
(i) What is the direction of magnetic
flux density 'B' at the point P due to the current flowing through XY?
(ii) What is the direction of the force
experienced by the conductor MN due to the current flowing through XY?


The pteridophytes are mostly
A. Asporous
B. Homosporous as well as few heterosporous
C . Heterosporous
D. Homosporous in early stage and hetrosporous in the later stage of the life-cycle


The speed of the block when it reaches
the point \( Q \) is
\( \mathbf{A} \cdot 5 m s^{-1} \)
B. \( 10 m s^{-1} \)
c. \( 10 \sqrt{3} \mathrm{ms}^{-1} \)
D. \( 20 \mathrm{ms}^{-1} \)


Comparing real and virtual images, we
may say that
A. real images can not be obtained on a screen and virtual images can be
B. virtual images can not be obtained on a screen and real images can be
C. both real and virtual images can be obtained on a screen
D. neither real nor virtual images can be obtained on a screen


How many five-digit multiples of 11 are there, if the five digits are 3,4,5,6 and
7?
A \( \cdot 12 \)
B. 13
c. 10
D. 16


Assertion
Chemical messengers are received at the binding sites of receptor proteins.
Reason

Chemical messengers gives messages to the cell without entering the cell.
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


Find the product:
\( \left(\frac{1}{2} p^{3} q^{6}\right)\left(-\frac{2}{3} p^{4} q\right)\left(p q^{2}\right) \)


Select the correct statements.
\( \mathbf{x} \)
This question has multiple correct options
\( A \)
\( (\mathbf{Y}) \)
B. \( (Z) \) has three carbonyl groups
\( c \)
D. Formation of \( (X) \) involves equilibrium mixture of the iminium salt and the acylated enamine


Critical temperature and pressure of a
real gas is \( 27^{\circ} C \& 150 \) atm respectively The critical volume of 1 mole of real gas
is :
A . 0.12
B. 0.24
\( c .0 .50 \)
D. None


In honey bee the drones (males) are
produced from
A. Unfertilized eggs
B. Fertilized eggs
C. Larvae from unfertilized eggs, which are fed on royal jelly
D. Larvae from unfertilized eggs, which are not cared by the workers at all


Find: \( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}\left[\frac{\sin (\boldsymbol{x}+\boldsymbol{a})}{\cos \boldsymbol{x}}\right] \)


According to the first law of
thermodynamics, \( \Delta U=q+w . \) In
special cases the statement can be
expressed in different ways. Which of
the following is not a correct
expression?
A. At constant temperature: \( q=-w \)
B. When no work is done: \( \Delta U=q \)
C. In gaseous system: \( \Delta U=q+P \Delta V \)
D. When work is done by the system: \( \Delta U=q+w \)


Which of the following exhibits
tautomerism?
A \( \cdot(C H)_{3} C-C H O \)
в.
\( c \)
D.


The law which states that in a chemical
reaction, the total mass of the products is equal to the total mass of the reactants
A. Law of constant proportions
B. Law of conservation of energy
c. Law of conservation of mass
D. Law of multiple proportions


reaction?
\( A \)
\( B \)
\( c \)
\( D \)


Which type of reaction produces heat and light?
A. Endothermic
B. Phytochemical
c. Reduction
D. Exothermic


An electrical technician requires a
capacitance of \( 2 \mu F \) in a circuit across
a potential difference of \( 1 \mathrm{kV} . \) A large number of \( 1 \mu F \) capacitors are available to him each of which can withstand a potential difference of not more than \( 400 \mathrm{V} . \) Suggest a possible arrangement that requires the minimum number of capacitors.


A particle moves along the \( x \) -axis
according to: \( \boldsymbol{x}=\boldsymbol{A}[\mathbf{1}+\boldsymbol{s} \boldsymbol{i} \boldsymbol{n} \boldsymbol{\omega} \boldsymbol{t}] . \) What
distance does it travel between \( t=0 \) and
\( \boldsymbol{t}=\mathbf{2 . 5} \boldsymbol{\pi} / \boldsymbol{\omega} ? \)
A. \( 4 A \)
B. 6A
\( c \cdot 5 A \)
D. None


Two identical calorimeters \( P \) and \( Q \)
contain an equal quantity of the water
at \( 12^{\circ} \mathrm{C} . \mathrm{A} 5 \mathrm{g} \) piece of metal \( x \) of specific heat 0.2 cal \( g^{-1 o} C^{-1} \) is
dropped into \( P \) and a \( 5 g \) piece of metal \( y \) into Q. The equilibrium temperature in
\( P \) is \( 22^{\circ} C \) and in \( Q 23^{\circ} C . \) If the initial
temperature of both the metals is \( 40^{\circ} \mathrm{C} \) Find the specific heat of metal \( y \)


The equivalent capacitance between
point \( a \) and \( b \) in the combination of
capacity figure is
\( A \cdot 15 \mu F \)
B. \( 10 \mu F \)
с. \( 11.2 \mu F \)
D. \( 7.4 \mu F \)


Free aldehyde group can be produced on hydrolysis of which of the following compound(s)?
This question has multiple correct options
A. Maltose
B. Sucrose
c. \( \alpha \) -D Glucose
D. Lactose


Draw the structure of
(i) \( B e C l_{2} \) (vapour)
(ii) \( B e C l_{2}(\text { solid }) \)


Prove that \( : \sqrt{\left(\sec ^{2} \Theta+\operatorname{cosec}^{2}\right.}= \)
\( \tan \Theta+\cot \Theta \)


Optical activity is expected for:
A. 2 -methyl propanoic acid
B. 2-chloro propanoic aicd
C . methyl-2-methyl proponoate
D. 2-chloro-2-methyl propanoic acid


Find the equation of the line passing through the points \( A(3,2,-1) \) and
\( \boldsymbol{B}(\mathbf{4},-\mathbf{1}, \mathbf{3}) \)


A compound 'X' gives brisk
effervescence of \( C O_{2} \) on treatment with
Na H \( C O_{3} \) and when treated with

Li \( A l H_{4} \) gives ethyl alcohol. Therefore 'X
may be:
A. \( C H_{3} C O C H_{3} \)
в. \( C H_{3} C H_{2} C H O \)
c. \( C H_{3} C H O \)
D. \( C H_{3} C O O H \)


Choose the wrong statement
\( \mathbf{A} \cdot 1 k g w t=9.8 N \)
B. Momentum is a vector quantity
C. Force is always conserved
D. Momentum is conserved in the absence of an external
force


The area of circle if the circumference
is \( 20 \pi \)


Assertion
Replication and transcription occur in the nucleus but translation occurs in
the cytoplasm.
Reason
mRNA is transferred from the nucleus
into the cytoplasm where ribosomes and amino acids are available for
protein synthesis.
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 contact force cannot act through
A. Empty space
B. Touching
C. Touching with a metal rod
D. Touching with a wooden rod


A rectangular pipe of metal \( 16 \mathrm{cm} \times 32 \) \( \mathrm{cm} \) rolled along its length and a cylinder is formed. Find the surface area of the
cylinder. (Use \( \left.\boldsymbol{\pi}=\frac{\mathbf{2 2}}{\mathbf{7}}\right) \)
A \( .532 .13 \mathrm{cm}^{2} \)
B. \( 542.13 \mathrm{cm}^{2} \)
c. \( 552.13 c m^{2} \)
D. \( 562.13 \mathrm{cm}^{2} \)


The area between the curves \( y=\sqrt{x} \)
and \( \boldsymbol{y}=\boldsymbol{x}^{3} \) is
A \( \cdot \frac{1}{12} \) sq. units
в. \( \frac{5}{12} \) sq. units
c. \( \frac{3}{5} \) sq. units
D. \( \frac{4}{5} \) sq. units


Solve \( \int \frac{x^{2} \tan ^{-1} x^{3}}{1+x^{6}} d x \)


Two oxides of metal contain 30.0 and
27.6 per cent of oxygen respectively. If
the formula of the first oxide is \( M_{2} O_{3} \)
then find the formula of the second
oxide.
A. \( M O_{4} \)
в. \( M_{5} O_{4} \)
c. \( M_{3} O \)
D. \( M_{3} O_{4} \)


A fish looks upward at an unobstructed
overcast sky. What total angle does the sky appear to subtend? (Take refractive index of water as \( \sqrt{2} \) ).
\( \mathbf{A} \cdot 180 \)
B. 90
\( c \cdot 75 \)
D. \( 60^{\circ} \)


Which of the following names is correct
for \( \boldsymbol{C H}_{2}-\boldsymbol{C H}-\boldsymbol{C H}_{2} ? \)
\begin{tabular}{lll}
CHO & CHO & CHO \\
\hline
\end{tabular}
A. 3- Formaldehyde-1,3-dial
B. 1,2,3- Triformaylpropane
c. 2-Formylmethylbutane-1,4-dial
D. Propane-1,2,3-tricarbaldehyde


Q Type your question
following statements:
It will be easier to compress this
rubber then expand it
II. Rubber does not return to its
original length after it is stretched
III. The rubber band will get heated if it
is stretched and released.

Which of these can be deduced from the
graph?
A. III only
B. II and III
c. \( I \) and \( I I I \)
D. I only


By mathamatical induction \( n\left(n^{2}-1\right) \) is divisible by
A . 19
B . 23
\( c \cdot 24 \)
D . 29


A gas formed by burning sulphur in air
is
A. sulphur dioxide
B. ammonia
c. hydrogen sulphide
D. chlorine


A count rate-meter is used to measure
the activity of a given sample. At one instant the meter shows 4750 counts
per minute. Five minutes later it shows
2700 counts per minute. The decay constant of the sample is
\( A \cdot 0.565 \min ^{-1} \)
B. \( 0.452 \mathrm{min}^{-1} \)
c. \( 0.226 \min ^{-1} \)
D. \( 0.113 \min ^{-1} \)


Two waves with same amplitude, frequency and phase are travelling along \( X \) and \( Y \) axis to meet at the origin forming stationary waves
A . True
B. False


Use the graphical method to find the
value of \( k, \) if \( (5, k-2) \) lies on the
straight line \( \boldsymbol{x}-\mathbf{2} \boldsymbol{y}+\mathbf{1}=\mathbf{0} \)
A .2
B. 3
\( c \cdot 4 \)
D. 5


An increase in the rate of a reaction for
a rise in temperature is due to:
This question has multiple correct options
A. increase in collision frequency
B. shortening of mean free path
C. increase in the number of activated molecules
D. none of the above


The \( 6563 A \) line emitted by hydrogen atom in a star is found to be red shifted by 5 , is the speed with which the star is receding from the earth is:
A \( \cdot 17.3 \times 10^{3} \mathrm{m} / \mathrm{s} \)
B . \( 4.29 \times 10^{7} \mathrm{m} / \mathrm{s} \)
c. \( 3.39 \times 10^{5} \mathrm{m} / \mathrm{s} \)
D. \( 2.29 \times 10^{5} \mathrm{m} / \mathrm{s} \)


Name two objects other than planets
which are members of the solar
system?


Remedies of which of the following are examples of neutralisation in everyday life?
This question has multiple correct options
A. Ant sting
B. Indigestion
c. Factory wastes
D. None of these


Evaluate \( \int_{0}^{\pi / 2} \cos x d x \)


Construct a scalene triangle \( \boldsymbol{A B C} \)
\( \operatorname{given} A B=3 \mathrm{cm}, A C=5 \mathrm{cm} \) and
\( B C=4 \mathrm{cm} \)


Find the area bounded between the
curves \( \boldsymbol{y}=\boldsymbol{x}^{2}, \boldsymbol{y}=\sqrt{\boldsymbol{x}} \)


A circular racetrack of radius \( 300 m \) is
banked at angle of \( 15^{\circ} \) If the coefficient
of friction between the wheels of a race
car and the road is 0.2 what is the \( (a) \)
optimum speed of the race car to avoid
wear and tear on its tyres and maximum permissible speed to avoid slipping?


The bulk modulus of water is \( 2.1 \times \)
\( 10^{9} N / m^{2} . \) The pressure required to
increase the density of water by \( 0.1 \% \)
is:-
A \( \cdot 2.1 \times 10^{5} N / m^{2} \)
B . \( 2.1 \times 10^{3} N / m^{2} \)
C \( \cdot 2.1 \times 10^{6} N / m^{2} \)
D. \( 2.1 \times 10^{7} N / m^{2} \)


Find the equation to the straight line drawn at right angles to the straight line \( \frac{x}{a}-\frac{y}{b}=1 \) through the point where
it meets the axis \( a \) of \( x \)


Two monochromatic coherent point
sources \( S_{1} \) and \( S_{2} \) are separated by a
distance \( L \). Each source emits light of
wavelength \( \lambda \), where \( L>>\lambda \). The line
\( S_{1} S_{2} \) when extended meets a screen
perpendicular to it at a point \( \boldsymbol{A} \)
A. The interference fringes on the screen are circular in shape
B. The interference fringes on the screen are straight lines perpendicular to the line \( S_{1} S_{2} A \)
c. Point \( A \) is an intensity maxima if \( L=n \lambda \)
D. Point \( A \) is always an intensity maxima for any separation \( L \)


The equation of the curve through \( \left(0, \frac{\pi}{4}\right) \) satisfying the differential
equation. \( e^{x} \tan y d x+(1+ \)
\( \left.e^{x}\right) \sec ^{2} y d y=0 \) is given by
A \( \cdot\left(1+e^{x}\right) \tan y=2 \)
B . \( 1+e^{x}=2 \tan y \)
C \( \cdot 1+e^{x}=2 \sec y \)
D・ \( \left(1+e^{x}\right) \tan y=1 \)


The Casparian strips of root endoderm contain a mixture of
A. Cellulose and cutin
B. Cellulose and lignin
c. Lignin and suberin
D. Cellulose and suberin


Two spherical lumps of clay attract each other with some amount of
gravitational force, as explained by Newton's law of universal gravitation. If add clay to one lump and to the other so that the mass of one is 5 times as much
as before and the mass of the other is 3
times as much as before, and I move the lumps (still spherical) so that their centers are now 4 times as far apart as
before, how does the new gravitational force between them compare?
A. The new force is slightly smaller.
B. The new force is slightly greater.
c. The new force is more than 3 times as great
D. The new force is less than one-third as greatt
E. We cannot answer this question without knowing the universal gravitational constant


A charged particle of unit mass and
unit charge moves with velocity \( \vec{v}= \) \( (8 \hat{i}+6 \hat{j}) m s^{-1} \) in a magnetic field of \( \vec{B}=2 \hat{k} T . \) Choose the correct
alternative(s).
This question has multiple correct options
A \( \cdot \) the path of the particle may be \( x^{2}+y^{2}-4 x-21=0 \)
B. the path of the particle may be \( x^{2}+y^{2}=25 \)
c. the path of the particle may be \( y^{2}+z^{2}=25 \)
D. the time period of the particle will be 3.14 s


Factorize the following using appropriate identities:
\( (\mathrm{i}) 9 x^{2}+6 x y+y^{2} \)
\( (\mathrm{ii}) 4 \boldsymbol{y}^{2}-\mathbf{4} \boldsymbol{y}+\mathbf{1} \)
\( (i i i) x^{2}-\frac{y^{2}}{100} \)


Mark the correct statement about given
graph.
A. \( x \) is threshold energy level.
B. \( Y \) and \( z \) are energy of activation for forward and backward reaction respectively
c. \( \mathrm{Q} \) is heart of reaction and reaction is exothermic
D. All of the above


Cerium \( (z=58) \) is an important member of the Lanthanides. Which of
the following statements about cerium is incorrect?
A. The +3 oxidation state of cerium is more stable than the +4 oxidation state
B. The common oxidation states of cerium are +3 and +4
c. Cerium (IV) acts as an oxidizing agent
D. The +4 oxidation state of cerium is not known in solutions


Consider the situation shown in the
figure. Calculate the acceleration of the
\( 1.0 \mathrm{kg} \) blocks


toppr LoGin 5
Q Type your question
\( \begin{array}{llllll} & 0 & 10 & 20 & 30 & 40 \\ \text { Class } & - & - & - & - & - \\ & 10 & 20 & 30 & 40 & 50\end{array} \)
frequency \( 5 \quad 8 \quad \) 7 \( \quad \) 12


When is a body said to be in motion?
A. A body is said to be in motion when its position continuously changes with respect to time.
B. A body is said to be in motion when its position does not change with respect to time.
C. A body is said to be in motion when its average speed is zero.
D. All the above.


For each operation \( * \) defined below, determine whether \( * \) is binary, commutative or associative.
(i) On \( Z, \) define \( a * b=a-b \)
(ii) On \( Q, \) defined \( a * b=a b+1 \)
(iii) On \( Q, \) defined \( a * b=\frac{a b}{2} \)
(iv) \( \operatorname{On} Z^{+}, \) defined \( a * b=2^{a b} \)
(v) \( \operatorname{On} Z^{+}, \) defined \( a * b=a^{b} \)
\( (v i) \) on \( R-\{-1\}, \) defined \( a * b=\frac{a}{b+1} \)


Which of the following is true regarding acidity of phenol?
A . It is a stronger acid than carbonic acid
B. It is a stronger acid than benzoic acid.
c. It is a stronger acid than water
D. It is a stronger acid than benzene sulphonic acid


Repeated application of integration by parts gives us the reduction formula, if the integrand is dependent on a natural
number \( n \)
If \( \int \frac{\cos ^{m} x}{\sin ^{n} x} d x=\frac{\cos ^{m-1} x}{(m-n) \sin ^{n-1} x}+ \)
\( A \int \frac{\cos ^{m-2} x}{\sin ^{n} x} d x+C, \) then \( A \) is equal
to
A \( \cdot \frac{m}{m+n} \)
в. \( \frac{m-1}{m+n} \)
c. \( \frac{m}{m+n-1} \)
D. \( \frac{m-1}{m-n} \)


A hot liquid contained in a container of
negligible heat capacity loses temperature at rate \( 3 K / \)min just before it begins to solidify. The temperature remains constant for 30 min. If the ratio of specific heat capacity of liquid to specific latent heat of fusion is \( \frac{x}{90} K^{-1} . \) Find \( x \). (given that rate of losing heat is constant).


A coil of resistance \( 400 \Omega \) is placed in a magnetic field. If the magnetic flux \( \phi(W b) \) linked with the coil varies with time \( t(\sec ) \) as \( \Phi=50 t^{2}+4 \)
The current in the coil at \( t=2 \sec \) is
A. 2A
B. 1A
\( c .0 .5 A \)
D. 0.1A


Plant that reserves its food in its roots
system is
A. Brinjal
B. Bean
c. carrot
D. Sugarcane


In a full-wave rectifier, the output is
taken across a load resistor of 800 ohm. If the resistance of diode in the forward
biased condition is 200 ohm, the efficiency of rectification of ac
power into dc power is(in percentage)
A . \( 64.96 \% \)
B . \( 40.6 \% \)
c. \( 81.2 \% \)
D. \( 80 \% \)


Sea water is a good conductor of electricity but distilled water is not because:
A. sea water contains mineral salts
B. distilled water contains mineral.
c. both A and B
D. none of the above


The monsoon winds that carry a lot of water to India come from the?
A. South-East
B. North-East
c. North-west
D. None of these


The two functional groups present in a typical carbohydrate are:
A. \( -O H \) and \( -C O O H \)
B. \( -C H O \) and \( -C O O H \)
\( \mathrm{c} .>C=O \) and \( -O H \)
D. \( -O H \) and \( -C H O \)


Find:
\( \frac{d y}{d x}=\sin (x+y)+\cos (x+y) \)


In common systems, the alkynes are named as derivatives of acetylene.
A. True
B. False


A block of mass \( 100 g \) is moved with a speed of \( 5.0 m / s \) at the highest point in a closed circular tube of radius tube of
radius \( 10 \mathrm{cm} \) kept in a vertical plane. The cross-section of the tube is such
that the block just fits in it. The block makes several oscillations inside the
tube and finally stops at the lowest point. Find the work done by the tube on the block during the process.
A. \( -1.45 \mathrm{J} \)
в. +1.45 J
c. \( -2.9 J \)
D. \( +2.9 J \)


Numbers of ways in which 75600 can be
resolved as product of two divisors which are relatively prime?
A .44
B. 8
\( c .9 \)
D. 16


A parallel beam of light is incident normally on a plane surface absorbing \( 40 \% \) of the light and reflecting the rest. If the incident beam carries 60 watt of
power, the force exerted by it on the surface is:
A . \( 3.2 \times 10^{-8} N \)
В. \( 3.2 \times 10^{-7} N \)
c. \( 5.2 \times 10^{-7} N \)
D. \( 5.12 \times 10^{-8} N \)


Which among the following are known as false fishes?
A. Pisces
B. Cyclostomata
c. ostracodermi
D. All of the above


The output Y of the gate circuit shown
in the fig is
\( \mathbf{A} \cdot \bar{A}+\bar{B} \)
B. \( \overline{A+\bar{B}} \)
\( c \cdot \overline{A+B} \)
\( D \cdot A+B \)


Which conserved motifs are found in
E.coli genes?
A. TATA box
B. CAAT box
c. Pribnow box
D. All of the above


\( \int_{2}^{4} \frac{\sqrt{x^{2}-4}}{x^{4}} d x= \)
\( A \cdot \frac{3}{32} \)
B. \( \frac{\sqrt{3}}{32} \)
\( c \cdot 3 \)
8
D. \( \frac{\sqrt{3}}{8} \)


Which of the following is used as a substitute of glass?
A . Glyptal
B. Urea formaldehyde resin
c. РММА
D. All


How will you 'weigh the sun', that is estimate its mass? The mean orbital
radius of the earth around the sun is
\( 1.5 \times 10^{8} k m \)


Give the names of the functional
groups:
(I) \( -\mathbf{C H O} \)


\( f(x)=x^{3}-2 x^{2}+3 \) Find \( f(3) \)


A vehicle is moving with a velocity \( v \) on
a curved road of width \( b \) and radius of
curvature \( R \). For counteracting the centrifugal force on the vehicle, the
difference in elevation required in
between the outer and inner edge of the
road is
A \( \cdot \frac{v^{2} b}{R g} \)
B. \( \frac{v b}{R g} \)
c. \( \frac{v b^{2}}{R g} \)
D. \( \frac{v b}{R^{2} g} \)


Calcium carbonate decomposes on heating according to the following equation.
\( \boldsymbol{C a} \boldsymbol{C O}_{3}(\boldsymbol{s}) \rightleftharpoons \boldsymbol{C a O}(\boldsymbol{s})+\boldsymbol{C O}_{2}(\boldsymbol{g}) \)
How many moles of \( C O_{2} \) will be
obtained by decomposition of 50 g \( \boldsymbol{C a C O}_{3} ? \)
A. \( \frac{3}{2} \)
в. \( \frac{5}{2} \)
\( c \cdot \frac{1}{2} \)
D.


The distillation of rectified spirit gives absolute ethanol.
A . True
B. False


A particle moves in a circle describing equal angle in equal times, its velocity vector
A. remains constant
B. changes in magnitude
c. change in direction
D. changes in magnitude and direction


Evaluate \( \mathbf{7}+\mathbf{7 7}+\mathbf{7 7 7}+\ldots \ldots \ldots \ldots . . \) upto
\( n \) terms.
A \( \cdot \frac{7}{81}\left[10^{n+1}-9 n\right] \)
B. \( \frac{7}{81}\left[10^{n+1}-9 n-10\right] \)
c. \( \frac{7}{81}\left[10^{n}-9 n-10\right] \)
D. \( \frac{7}{81}\left[10^{n+1}-n-10\right] \)


The path with which electron travels
from \( y \) -plate to screen is
A. Parabolic
B. Hyperbolic
C. Circular
D. Straight line
E . Helix


An rms voltage of \( 110 \mathrm{V} \) is applied across a series circuit having a resistance \( 11 \Omega \) and an impedance
\( 22 \Omega . \) The power consumed is
A \( .275 ~ W \)
в. \( 366 \mathrm{W} \)
\( c .550 W \)
D. \( 1100 W \)


The outer electronic configuration of radioactive element present in IA group is :
\( \mathbf{A} \cdot 8 s^{1} \)
B . \( 7 s^{\text {। }} \)
c. \( 5 s^{\text {। }} \)
D. \( 6 s^{\text {th }} \)


A magnetic needle placed near a wire carrying alternating current does not show any deflection.


A jet plane starts from rest at \( S=0 \) and
is subjected to the acceleration shown.
Determine the speed of the plane when
it has traveled \( 60 m \).
A. \( 46.47 \mathrm{m} / \mathrm{s} \)
В. \( 36.47 \mathrm{m} / \mathrm{s} \)
c. \( 26.47 m / s \)
D. \( 16.47 \mathrm{m} / \mathrm{s} \)


At absolute zero, a semiconductor is an
insulator because
A. No electron is present in the conduction band
B. All electrons occupy the valence band
C. The value of \( E_{G} \) is large
D. All of the above


Figures shows a convex lens cut
symmetrically into two equal halves and separated laterally by a distance h.
A point object placed at a distance 30 \( \mathrm{cm}, \) from the lens halves, forms two real
images separated by a distance d. A plot of d versus h is shown in figure. The focal length of the lens is
A. 35 cm
B. \( 40 \mathrm{cm} \)
\( c .45 \mathrm{cm} \)
D. \( 60 \mathrm{cm} \)


Which of the following is most acidic?
A \( . H_{2} O \)
в. \( H_{2} \).
\( \mathbf{c} \cdot H_{2} S e \)
D. \( H_{2} T e \)


Two adjacent angles whose sum is \( 180^{\circ} \) is called
A. complementary angles
B. linear pair
c. vertically opposite angles
D. none


Assertion
Water in liquid state is more stable
than ice at room temperature.
Reason
Water in liquid form has higher entropy
than ice.
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


What do the letters I \( C \) and \( E \) stand for in
a RICE table?
A . Initial, Change, Equilibrium
B. Initial, Concentration, Equilibrium
c. Instant, Change Equilibrium
D. Instant, Concentration, Equilibrium
E. Initial, Change, Exact amounts


The electropositive character is the maximum for which of the following elements in Group 13?
A \( \cdot \) Al
в. T
c. Both of the above
D. None of the above


The tube which connects the cavity of
the middle ear to the throat is known as


The reaction of toluene with chlorine in
the presence of iron and in the absence
of light yields
\( \mathbf{A} \)
B.
\( c \)
D. mixture of (b) and (c)


Enzymes which catalyse reactions involving changes in structure of a molecule are
A . Ligases
B. Isomerases
c. Hydrolases
D. Transferases


The main raw materials required for the manufacture of portland cement are:
A. limestone and clay
B. limestone and gpsum
c. limestone and calcium chloride
D. limestone and silica


Show that \( (x-2) \) is a factor of \( x^{3}- \)
\( 3 x^{2}-10 x+24 \)


For a collection of data, if \( \sum x= \)
\( \mathbf{3 5}, \boldsymbol{n}=\mathbf{5}, \sum(\boldsymbol{x}-\mathbf{9})^{2}=\mathbf{8 2}, \) then find
\( \sum x^{2} \) and \( \sum(x-\bar{x})^{2} \)


How the waves are analysed in water
with the help of computer?
A. Ultrasonic waves return after reflection from anything in the water
B. Infrasonic waves return after reflection from anything in the water
C. Ultrasonic waves never return after reflection from anything in the water
D. Ultrasonic waves return after refraction from anything in the water


An excess of liquid Hg was added to
\( 10^{-3} \mathrm{M} \) acidified solution of \( F e^{3+} \) ions.
was found that only \( 4.6 \% \) of the ions
remained as \( F e^{3+} \) at equilibrium at \( 25^{\circ} \)
C. Calculate \( \boldsymbol{E}^{o} \) for \( \mathbf{2} \boldsymbol{H} \boldsymbol{g} / \boldsymbol{H} \boldsymbol{g}_{2}^{2+} \) at \( \boldsymbol{2} \mathbf{5}^{\boldsymbol{o}} \mathbf{C} \)
for,
\( 2 H g+2 F e^{3+} \rightleftharpoons H g_{2}^{2+}+2 F e^{2+} \) and
\( \boldsymbol{E}_{\boldsymbol{F e}^{2+} / \boldsymbol{F e}^{3+}}^{o}=-\mathbf{0 . 7 7 1 2} \boldsymbol{V} \)
A. - -0.7912 V
в. - 0.7721 V
c. \( -0.9922 \mathrm{v} \)
D. None of these


Find the mean
\begin{tabular}{lccccc}
Age (yrs) & 7 & 8 & 9 & 10 & 11 \\
No. of Students & 5 & 6 & 4 & 12 & 7 \\
\hline
\end{tabular}
\( A \cdot 9.3 \)
B. 8.7
C. 11.9
\( D \cdot 5.2 \)


Out of 64 codons only 61 codes for the 20
different amino acids. This character of genetic code is called as
A. Degeneracy
B. Non ambiguous nature
c. Redundancy
D. Overlapping


Select a ferromagnetic material from the following?
A. Dioxygen
B. Chromium (IV) oxide
c. Benzene
D. Dihydrogen monoxide


Prolonged liberal irrigation of agriculture fields is likely to create the problem of
A . Acidity
B. Aridity
c. salinity
D. Metal toxicity


In order for an electron to move from the
second energy level (n=2) to the fourth energy level \( (n=4) \) the atom needs to:
A. release heat
B. release a photon
C. maintain a constant energy
D. release energy.
E. absorb energy.


Assertion
Let \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2}+\mathbf{7} \boldsymbol{x}+\boldsymbol{4} \) be a polynomial
function, then \( \boldsymbol{f}^{\prime}(\mathbf{2})=\mathbf{1 1} \)
Reason
A polynomial function is differentiable everywhere
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


Find the total flux due to charge \( q \)
associated with the given
hemispherical surface
A \( \cdot(a) \frac{q}{2 \varepsilon_{0}},(b) 0,(c) \frac{q}{\varepsilon_{0}},(d) 0,(e) 0 \)
В \( \cdot(a) 0,(b) \frac{q}{2 \varepsilon_{0}},(c) 0,(d) \frac{q}{\varepsilon_{0}},(e) 0 \)
c. \( (a) \frac{q}{2 \varepsilon_{0}},(b) \frac{q}{\varepsilon_{0}},(c) 0,(d) \frac{q}{\varepsilon_{0}},(e) 0 \)
D. \( (a) 0,(b) \frac{q}{2 \varepsilon_{0}},(c) 0,(d) \frac{q}{\varepsilon_{0}},(e) \frac{q}{\varepsilon_{0}} \)


A water tank of capacity \( 3000 L \) is filled
with \( 1216 L 50 m L \). Find the volume of
water which is required to fill the tank.


For the following reaction
\( \left(\boldsymbol{C} \boldsymbol{H}_{3}\right)_{3} \boldsymbol{C C l}+\boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \)
\( \left(\boldsymbol{C} \boldsymbol{H}_{3}\right)_{3} \boldsymbol{C O H}+\boldsymbol{H} \boldsymbol{C l}\left(\frac{d \boldsymbol{x}}{d t}\right)= \)
\( \boldsymbol{k}\left[\left(\boldsymbol{C} \boldsymbol{H}_{3}\right)_{3} \boldsymbol{C C l}\right] \)
the rate determining step is:
A \( \cdot\left(C H_{3}\right)_{3} C C l \rightarrow\left(C H_{3}\right)_{3} C \oplus+C l \)
B . \( \left(C H_{3}\right)_{3} C C l+H_{2} O \rightarrow\left(C H_{3}\right)_{3} C O H+H C l \)
C. \( \left(C H_{3}\right)_{3} C \oplus+H_{2} O \rightarrow\left(C H_{3}\right)_{3} C O H+H^{+} \)
D. \( H^{+}+C l^{-} \rightarrow H C l \)


\( H_{2} O_{2} \) turns blackened lead paintings to white colour. In this reaction it oxidizes
PbS to \( P b S O_{4} \). The number of moles of
\( H_{2} O_{2} \) needed to oxidize 0.1 moles of
\( P b S \) is:
A . 1 mole
B. 0.1 mole
c. 0.5 mole
D. 0.4 mole


In which of the following, whole leaf is modified into tendril?
A. Pisum sativum
B. Lathyrus aphaca
c. Gloriosa superba
D. None of the above


Bakelite is obtained from phenol by reacting with:
\( \mathbf{A} \cdot\left(C H_{2} O H\right)_{2} \)
в. \( C H_{3} C H O \)
c. \( C H_{3} \) СОСН\( _{3} \)
D. \( H C H O \)


Draw the magnetic field lines due to a current passing through a long solenoid. Use Ampere's circuital law, to obtain the expression for the magnetic field due to the current I in a long solenoid having n number of turns per unit length.


Let \( f \) be a function defined by \( f(x)= \)
\( \mathbf{5} \boldsymbol{x}^{2}+\mathbf{2}, \boldsymbol{x} \in \boldsymbol{R} . \) Find a such that \( \boldsymbol{f}(\boldsymbol{a})= \)
22


topp
Q type your question
difference across the plates with
respect to the charge on the condenser?
\( A \)
B.
\( c \)
\( D \)


Factorize \( : 4 a x+4 a y \)
A. \( 4 a(x+y) \)
в. \( 4(x+y) \)
c. \( 4 a(x-y) \)
D. \( 4(x-y) \)


Which of the following is brittle at low temperature?
A. Lead
B. Tin
c. zinc
D. All of these


Which of the following has highest bond dissociation energy?
\( \mathbf{A} \cdot C H_{3}-F \)
в. \( C H_{3}-C l \)
c. \( C H_{3}-B r \)
\( \mathbf{D} \cdot C H_{3}-I \)


The diagram shows three capacitor with
their capacitances with breakdown
voltages.what should be the maximum
value of external emf of source such
that no capacitor breaks down:-
\( A \cdot \frac{33}{2} v o l t \)
B . \( \frac{11}{3} \) volt
\( c \cdot \frac{13}{3} v o l t \)
D. \( \frac{11}{2} \) volt


Which of the following elements has the hardest allotropic form?
A. Iron
B. Silicon
c. carbon
D. Aluminium


Assertion
The matrix \( \boldsymbol{A}=\left(\begin{array}{ccc}\mathbf{0} & \boldsymbol{a} & \boldsymbol{b} \\ -\boldsymbol{a} & \mathbf{0} & \boldsymbol{c} \\ -\boldsymbol{b} & -\boldsymbol{c} & \mathbf{0}\end{array}\right) \) is a
skew symmetric matrix.
Reason
A square matrix \( \boldsymbol{A}=\left(\boldsymbol{a}_{\boldsymbol{i} j}\right) \) of order \( \mathbf{m} \) is
said to be skew symmetric if \( \boldsymbol{A}^{\boldsymbol{T}}=-\boldsymbol{A} \)
A. Both (A) \& (R) are individually true \& (R) is correct explanation of (A),
B. Both (A) \&
(R) are individually true but (R) is not the correct (proper) explanation of (A).
C. (A)is true but (R) is false,
D. (A)is false but (R) is true.


A person moves \( 30 \mathrm{m} \) North and then \( 20 \mathrm{m} \) towards East and finally \( 30 \sqrt{2} \mathrm{m} \) in South-West direction. The
displacement of the person from the origin will be
A. \( 10 \mathrm{m} \) along North
B. \( 10 \mathrm{m} \) along south
c. \( 10 \mathrm{m} \) along west
D. zero


How many \( \sigma \) and \( \pi- \) bonds are present
in peroxymonosulfuric acid?
If the answer is 2 and \( 4, \) represent as 24]


(A) Mention any two conditions for
liquefying a gas.
(B) What happens to the intermolecular distances during liquefaction of a gas?


Which of the following does not happen during exhalation?
A. The space in chest cavity decreases
B. Diaphragm goes up
c. Air is released
D. Ribs are pushed upward and outward


Probability of any event \( \boldsymbol{x} \) lies
A. \( 0<x<1 \)
в. \( 0 \leq x<1 \)
c. \( 0 \leq x \leq 1 \)
D. \( 1<x<2 \)


will form an ion with a
-3 charge
A. Nitrogen
в. oxygen
c. Chlorine
D. Neon
E. Beryllium


Statements that are true of d-and \( f- \)
block elements are:
1. The colour of \( K_{2} C r_{2} O_{7} \) is due to d-d
transition.
2. Actinides have larger number of oxidation states than lanthanides.
3. Tripositive ions of \( \operatorname{Pr}(\text { At. } N o .=59) \)
and \( T m(A t . N o .=69) \) have the same
(green) colour.
4. Actinides have paramagnetic moments less than theoretically predicted values.
A. 2,3,4
B. 1,2,3
\( c \cdot 2,4 \)
D. 1,2,4


The angle between the original path of the incident ray and the emergent ray coming out of a prism is called angle of
A. incidence
B. reflection
c. prism
D. deviation


In nuclear reactors, heavy water is used
as a:
A . fue
B. projectile
c. moderator
D. arrestor


\( \lim _{x \rightarrow \infty} \cos (\sqrt{x+1})-\cos (\sqrt{x}) \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
c. Do not exist
D. 78


An article is sold at a profit of \( 5 \% \). if it was sold for \( R s 250 \) more, the gain would have been \( 10 \% \). Find \( \mathrm{CP} \) of the
article.


Strongest bond is formed by the headon overlapping of :
A. \( 2 s \) -and \( 2 p \) -orbitals
B. \( 2 p- \) and \( 2 p \) -orbitals
c. \( 2 s- \) and \( 2 s \) -orbitals
D. All of these


A spherical surface of radius of curvature \( 10 \mathrm{cm} \) separates two media \( \mathrm{X} \) and Y of refractive indices \( 3 / 2 \) and \( 4 / 3 \)
respectively. Centre of the spherical surface lies in denser medium. An
object is placed in medium X. For image to be real, the object distance must be
A. greater than \( 90 \mathrm{cm} \)
B. less than \( 90 \mathrm{cm} \)
c. greater than \( 80 \mathrm{cm} \)
D. less than \( 80 \mathrm{cm} \)


\( \angle A D C=\angle B C D \)


The element with lowest
electronegativity in 13th group is:
\( A \cdot B \)
в. А।
\( c \cdot \) Ga
D. In


Which of the following is not a fat soluble vitamin?
\( A \cdot \) Vitamin A
B. Vitamin B complex
c. Vitamin D
D. Vitamin E


Odd sepal is anterior in family
A. Solanaceae
B. Asteraceae
c. Brassicaceae
D. Fabaceae


Find the square of the following binomials by using the identity \( (-z+6) \)


An artificial satellite moving in circular orbit around the earth has a total
kinetic + potential ) energy \( \boldsymbol{E}_{0} \). Its
potential energy and kinetic energy respectively are
A \( \cdot 2 E_{0} \) and \( -2 E_{0} \)
B . \( 2 E_{0} \) and \( 3 E_{0} \)
\( \mathbf{c} \cdot 2 E_{0} \) and \( -E_{0} \)
D. \( -2 E_{0} \) and \( -E_{0} \)


If the angle of incidence is i and that of refraction is \( r \). Then the speed of light in the medium to which the light is
reflected from air is?
A \( \cdot v=C \frac{\sin i}{\cos r} \)
B. \( v=C \frac{\cos r}{\cos i} \)
c. \( v=C \frac{\sin r}{\sin i} \)
D. \( v=C \frac{\sin i}{\sin r} \)


The maximum velocity and the maximum acceleration of a body moving in a simple harmonic oscillator
are \( 2 m / s \) and \( 4 m / s^{2} . \) The angular velocity will be:
A. \( 3 r a d / s \)
B. \( 0.5 r a d / s \)
c. \( 1 r a d / s \)
D. \( 2 r a d / s \)


A boy is cycling such that the wheels of
the cycle are making 140 revolutions per minute. If the diameter of the wheel
is \( 60 \mathrm{cm}, \) then find the speed per hour with which the boy is cycling.


In the diagram, PQ and QR are tangents
to the circle, centre \( 0, \) at \( P \) and \( R \)
respectively. Find the value
\( A \cdot 25 \)
3.35
\( c \cdot 45 \)
55


f \( a, b, c \) are \( p \) th \( , q \) thand \( r \) th terms of a
\( \mathrm{GP}, \) then \( \left|\begin{array}{lll}\log \boldsymbol{a} & \boldsymbol{p} & \mathbf{1} \\ \log \boldsymbol{b} & \boldsymbol{q} & \mathbf{1} \\ \log \boldsymbol{c} & \boldsymbol{r} & \mathbf{1}\end{array}\right| \) is equal to
\( \mathbf{A} \cdot \mathbf{0} \)
B.
c. \( \log a b c \)
D. none of these