Assertion
Zinc but not copper is used for the recovery of silver from the complex
\( \left[\boldsymbol{A} \boldsymbol{g}(\boldsymbol{C} \boldsymbol{N})_{2}\right] \)
Reason
Zinc is cheaper as well as a strong reducing agent than Cu and replaces Ag from the complex.
Read the above assertion and reason
and choose the correct option regarding
¡t.
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


When we inflate cycle tubes, the volume
of tube as well as the pressure of air inside tube increases
A. It is an exceptional case of Boyle's Las
B. It happens because air is not ideal gas
c. It happens because mass of air is not constant
D. It happens because external force is applied in inflating the tubes


A particle starting with certain initial velocity and uniform acceleration covers a distance of \( 12 \mathrm{m} \) in first 3 s and
a distance of \( 30 \mathrm{m} \) in next 3 s. The initial velocity of the particle is
\( \mathbf{A} \cdot 3 m s^{-1} \)
B . \( 2.5 \mathrm{ms}^{-1} \)
\( \mathbf{c} \cdot 2 m s^{-1} \)
D. \( 1.5 \mathrm{ms}^{-1} \)
E \( \cdot 1 \mathrm{ms}^{-1} \)


A circular road of radius 1000 m has
banking angle \( 45^{0} . \) The maximum safe speed \( \left(\text { in } m s^{\wedge}\{-1\} \$ \$\right) \) of a car having a mass \( 2000 \mathrm{kg} \) will be (if the coefficient of friction between tyre and road is 0.5 )
A . 172
B. 124
c. 99
D. 86


Chloragogen cells of earthworm are similar to the organ of
vertebrates
A . Liver
B. Lung
c. Kidney
D. Spleen


A charge ' \( Q \) ' is placed at each corner of a cube of side 'a'. The potential at the
centre of the cube is :
A \( \cdot \frac{8 Q}{\pi \varepsilon_{0} a} \)
в. \( \frac{4 Q}{4 \pi \varepsilon_{0} a} \)
c. \( \frac{4 Q}{\sqrt{3} \pi \varepsilon_{0} a} \)
D. \( \frac{2 Q}{\pi \varepsilon_{0} a} \)


One side of a parallelogram is \( 8 \mathrm{cm} . \) If the corresponding altitude is \( 6 \mathrm{cm}, \) then its area is given by
A \( .24 \mathrm{cm}^{2} \)
B. 36 \( c m^{2} \)
\( c \cdot 40 c m^{2} \)
D. \( 48 \mathrm{cm}^{2} \)


In the given figure pulleys are massless and frictionless and string A are light
and inextensible. A force is applied on pulley A vertically upward. At any time
acceleration of \( 5 \mathrm{kg} \) is \( a_{1} \) (upward) and
\( 10 \mathrm{kg} \) is \( a_{2}(\text { upward }) \) then \( \left(g=10 m / s^{2}\right) \)
A \( \cdot a_{1}=0, a_{2}=0 \) if \( F=100 N \)
B . \( a_{1}=5 m / s^{2}, a_{2}=0 \) if \( F=300 N \)
C \( \cdot a_{1}=15 m / s^{2}, a_{2}=2.5 m / s^{2} \) if \( F=500 N \)
D. All option is correct


What principle law explains the working of the hydraulic brakes in automobiles?
A. Bernoulli's Law
B. Posieulles principle
c. Pascal's law
D. Archimedes principle


The naming of living organisms is called
A. Classification
B. Taxonomy
c. Nomenclature
D. systematics


SI units of \( b \) is
\( 4 \cdot m^{-2} s^{2} \)
3. \( m^{2} s^{2} \)
c. \( m^{2} s^{-2} \)
D. \( m s^{-} \)


How will you convert ethanal into the following compounds?
But-2-enoic acid


In figure \( \angle \mathbf{1}=\angle \mathbf{2} \) and \( \triangle \boldsymbol{N} \boldsymbol{S} \boldsymbol{Q} \cong \)
\( \triangle M T R, \) then prove that \( \triangle P T S \sim \)
\( \triangle \boldsymbol{P R Q} \)


Which of the following gasses contribute to greenhouse effect?
A. \( C O_{2} \)
в. \( C H_{4} \)
c. \( C F C \) s
D. All of the above


Write the resonating structures for \( \boldsymbol{S O}_{3} \)
\& \( N O_{2} \)


A (trolley+child) of total mass \( 200 k g \) is moving at a uniform speed of \( 36 k m / h \) on a frictionless track. The child of
mass \( 20 k g \) starts running on the trolley from one end to the other \( (10 m \) away)
with a speed of \( 10 m s^{-1} \) relative to the
trolley in the direction of the trolley's motion and jumps out of the trolley with the same relative velocity. What is the final speed of the trolley? How much has the trolley moved from the time the
child begins to run and just before
jump?


\( \frac{Y}{L} \)


For a reaction \( \boldsymbol{P} \rightarrow \boldsymbol{Q} \), the half-life of the
reaction was \( 3 h, \) when the initial
concentration of \( P \) was 0.5 M. As the
concentration of \( P \) was increased to
1.0 \( \mathrm{M} \), half life changes to \( 6 \mathrm{h} \). The order of reaction with respect to P is:
A . zero
B. one
c. two
D. three


If \( f(x) \) and \( g(x) \) are differentiable
functions for \( 0 \leq x \leq 1 \) such that
\( \boldsymbol{f}(\mathbf{0})=\mathbf{2}, \boldsymbol{g}(\mathbf{0})=\mathbf{0}, \boldsymbol{f}(\mathbf{1})=\mathbf{6}, \boldsymbol{g}(\mathbf{1})=\mathbf{2} \)
then in the interval \( (\mathbf{0}, \mathbf{1}) \)
\( \mathbf{A} \cdot f^{\prime}(x)=0 \) for all \( x \)
B . \( f^{\prime}(x)=2 g^{\prime}(x) \) for at least one \( x \)
\( \mathbf{C} \cdot f^{\prime}(x)=2 g^{\prime}(x) \) for at most one \( x \)
D. None of these


Which physical quantity cannot be determined with the help of
potentiometer?
\( A \)
B.
\( c \cdot L \)
D. R


Aerosols inhibits photosynthesis by
A. consuming \( O_{2} \) from air
B. Competing with \( C O_{2} \)
c. Blocking stomata by enhancing particulate matter settlement on the leaves.
D. Decreasing air pollution and reducing \( C O_{2} \)


Which product is formed?


Which substance would dissolve
fastest in water?
A \( .1 g \) granulated sugar
B. \( 1 ~ g \) powdered sugar
C. \( 1 ~ g \) sugar cube
D. \( 1 g \) piece of crystallized sugar


Results of calculations for four different
designs of a fusion reactor using D-D reaction are given below. Which of these is most promising based on Lawson criterion?
A. Deuteron density =2.0 \( \times 10^{12} \mathrm{cm}^{-3} \), confinement \( \operatorname{tim} e=5.0 \times 10^{-3} \mathrm{s} \)
B. Deuteron density=8.0 \( \times 10^{14} \mathrm{cm}^{-3} \), confinement \( \operatorname{time}=9.0 \times 10^{-1} \mathrm{s} \)
c. Deuteron density \( =4.0 \times 10^{23} \mathrm{cm}^{-3} \), confinement \( \operatorname{time}=1.0 \times 10^{-11} \mathrm{s} \)
D. Deuteron density=1.0 \( \times 10^{24} \mathrm{cm}^{-3} \), confinement \( \operatorname{time}=4.0 \times 10^{-12} \mathrm{s} \)


Evaluate \( \int \frac{(x-1)^{2}}{x^{4}+2 x^{2}+1} d x \)
A \( \cdot \frac{x^{3}}{3}+x+\frac{x}{x^{2}+1}+c \)
\( ^{\text {В } \cdot \frac{x^{5}+x^{3}+x+3}{3\left(x^{2}+1\right)}+c} \)
c. \( \frac{x^{5}+4 x^{3}+3 x+3}{3\left(x^{2}+1\right)}+c \)
D. None of these


Solve: \( \frac{4+2 x}{3} \geq \frac{x}{2}-3 \)


The mass of non-volatile, non-elctrolyte solute (molar mass \( 50 g \) mol \( ^{-1} \) ) needed
to be dissolved in \( 114 g \) octane to reduce
its vapour pressure to \( 75 \% \), is
A . \( 150 g \)
в. \( 75 g \)
c. \( 37.5 g \)
D. \( 50 g \)


Let \( S \) be the set of all points in a plane. Let \( R \) be a relation on \( S \) such that for any
two points a and \( b, \) aRb iff b is within 1 \( \mathrm{cm} \) from a. Then R is
A. Equivalence relation
B. Reflexive and symmetric not transitive
C. Reflexive and transitive not symmetric
D. Symmetric and transitive not reflexive


Equal weights of mercury and \( l_{2} \) are allowed to react completely to form a mixture of mercurous and mercuric
iodide leaving none of the reactants. Calculate the ratio of the weights of
\( H g_{2} l_{2} \) and \( H g l_{2} \) formed
A . 1: 0653
B . 0.732: 1
c. 1: 0.523
D. 0.532: 1


A bullet of mass \( 0.012 k g \) and
horizontal speed \( 70 m s^{-1} \) strikes a
block of wood of mass \( 0.4 k g \) and
instantly comes to rest with respect to the block. The block is suspended from the ceiling by means of thin wires. Calculate the height to which the block rises. Also, estimate the amount of heat produced in the block.


Two cars started moving with initial velocities \( v \) and \( 2 v . \) For the same
deceleration, their respective stopping
distances are in the ratio
A . 1: 1
B. 1: 2
\( c \cdot 1: 4 \)
D. 2 : 1
E . 4: 1


If \( S_{n}=n^{2} p \) and \( S_{m}=m^{2} p, m \neq n, \) in
an A.P, prove that \( \boldsymbol{S}_{\boldsymbol{p}}=\boldsymbol{p}^{\boldsymbol{3}} \)


Sulphuryl chloride \( \left(\boldsymbol{S} \boldsymbol{O}_{2} \boldsymbol{C l}_{2}\right) \) reacts
with white phosphorus \( \left(P_{4}\right) \) to give:
A. \( P C l_{5}, S O_{2} \)
в. \( O P C l_{3}, S O C l_{2} \)
c. \( P C l_{5}, S O_{2}, S_{2} C l_{2} \)
D. \( O P C l_{3}, S O_{2}, S_{2} C l_{2} \)


Which one of the following sets forms
the biodegradable polymer?
\( \mathbf{A} \cdot H_{2} N-C H_{2}-C O O H \) and \( H_{2} N-\left(C H_{2}\right)_{5}-C O O H \)
B \( \cdot H O-C H_{2}-C H_{2}-O H \) and \( C O O H-C_{6} H_{4}- \)
\( \mathrm{COOH} \)
\( \mathbf{c} \cdot C_{6} H_{5}-C H=C H_{2} \) and \( C H_{2}=C H-C H=C H_{2} \)
\( \mathbf{D} \cdot C H_{2}=C H-C N \) and \( C H_{2}=C H-C H=C H_{2} \)


State the cause of accelerated
eutrophication


Assertion
One will need a very powerful crane to lift a nuclear mass of even microscopic
size.
Reason
The density of nucleus is very high.
Read the above assertion and reason
and choose the correct option regarding
¡t.
A. The Assertion is correct but Reason is wrong
B. The Assertion is wrong but Reason is correct
c. Both Assertion and Reason are correct and Reason is the correct explanation of Assertion
D. Both Assertion and Reason are correct but Reason is not the correct explanation of Assertion


Which term of the A.P.
\( \mathbf{2 1}, \mathbf{4 2}, \mathbf{6 3}, \mathbf{8 4}, \dots \dots \dots \mathbf{~ i s} \mathbf{2 1 0} \)
\( \mathbf{A} \cdot 9^{t h} \)
B. \( 10^{\text {th }} \)
c. \( 11^{\text {th }} \)
D. \( 12^{\text {th }} \)


Which of the following is used as desiccant for absorbing water in Leibigs method for estimation of \( \mathrm{C} \) and \( \mathrm{H} \) ?
\( \mathbf{A} \cdot M g S O_{4} \cdot 7 H_{2} O \)
в. \( C u S O_{4} .5 H_{2} O \)
c. Anhydrous \( \mathrm{CaCl}_{2} \)
D. КОН


A boat in a circular lake lies at its
centre. The perpendicular distance of the boat is \( 10 \mathrm{m} \) from a bridge lying in
\( 40 \mathrm{m} \) distance across the circular lake.
Find the distance that the boat will have
to travel to reach to the extreme point of left side of bridge is \( m \sqrt{5} \mathrm{m} \). Then, \( m \) is
A . \( 20 \mathrm{m} \)
в. \( 10 \mathrm{m} \)
\( c .-10 m \)
D. both B \&


\( N_{2}+3 H_{2} \rightleftharpoons 2 N H_{3} \)
Which of the followings the correct statement if \( N_{2} \) is added at equilibrium
condition?
A. The equilibrium will shift to the forward direction because according to the second law of thermodynamics, the entropy must increase in the direction of spontaneous reaction
B. The condition for the equilibrium is \( G\left(N_{2}\right)+ \) \( 3 G\left(H_{2}\right)=2 G\left(N H_{3}\right) \) where, G is the Gibbs free energy per mole of the gaseous species measured at that partial pressure. The condition of equilibrium is unaffected by the use of catalyst,which increases the rate of both the forward and backward reactions to the same extent.
c. The catalyst will increase the rate of forward reaction by \( \alpha \) and the backward reaction by \( \beta \)
D. Catalysts will not alter the rate of either of the reactions


Evaluate: \( \lim _{x \rightarrow 0} \frac{\sin 3 x^{2}}{\cos \left(2 x^{2}-x\right)} \)
\( \mathbf{A} \cdot \mathbf{0} \)
B. -
\( c \cdot 4 \)
\( D \)


Fill in the blanks:
is geometric centre of spherical mirror.
A. Principal force (F)
B. Centre of curvature (C)
c. Pole (P)
D. Secondary focus \( \left(F_{2}\right) \)


If \( ^{\prime} 1^{\prime} \) represents the extracellular
digestion, '2' represent the intracellular
digestion and \( ^{\prime} 3^{\prime} \) represent both type
then for coelentrata, ctenophore and
porifera, select the correct option.
A. 1,2,3 respectively
B. 3,3,2 respectively
c. 3,2,1 respectively
D. 3,2,2 respectively


A uniform cylindrical wire of length \( 4 m \)
and diameter \( 0.6 m m \) is stretched by a
certain force such that its length is
increased by \( 4 m m . \) If the Poisson's ratio
of the material is 0.3 then, calculate the
change in diameter of the wire.


The carbon cycle is the movement of carbon on Earth by the processes of
and \( -\cdots \)
A. Plants and animalss
B. Respiration and photosynthesis
c. Breathing in and breathing out
D. Oxygen and carbon dioxide


Which of the following group show \( +M \) effect ?
\( \mathbf{A} \cdot-C N \)
в. \( N O \)
c. \( -C C l_{3} \)
D. - \( C H O \)


State whether the following statements
are true or false.

Heterospory refers to the production of two different kinds of spores, one of which gives rise to male gametophyte and the other-female gametophyte
A. True
B. False


There exists a positive real number \( x \)
satisfying \( \cos \left(\tan ^{-1} x\right)=x \). The value of \( \cos ^{-1}\left(\frac{x^{2}}{2}\right) \) is
A \( \cdot \frac{\pi}{10} \)
в.
c. \( \frac{2 \pi}{5} \)
D. \( \frac{4 \pi}{5} \)


Show that the middle term in the
expansion of \( (1+x)^{2 n} \) is
\( \frac{1.3 .5 \ldots(2 n-1)}{n !} 2^{n} x^{n}, \) where \( n \) is a
positive integer.


Construct a quadrilateral ABCD with Four sides \( : A B=3 \mathrm{cm}, \mathrm{BC}=4 \mathrm{cm}, \mathrm{CD} \)
\( =4.5 \mathrm{cm} \) and \( \mathrm{AD}=3.8 \mathrm{cm} ; \angle A B C=90^{0} \)


If \( y=x^{-\frac{1}{2}}+\log _{5} x+\frac{\sin x}{\cos x}+2^{x} \), then
find \( \frac{d y}{d x} \)
A. \( -\frac{1}{2} x^{-3 / 2}+\frac{1}{x \log _{e} 5}+\sec ^{2} x+2^{x} \log 2 \)
B. \( \frac{1}{2} x^{-3 / 2}+\frac{1}{x \log _{e} 5}+\sec ^{2} x+2^{x} \log 2 \)
c. \( -\frac{3}{2} x^{-3 / 2}+\frac{1}{x \log _{e} 5}+\sec ^{2} x+2^{x} \log 2 \)
D. \( -\frac{1}{2} x^{-3 / 2}+\frac{1}{x \log _{e} 5}+\cos ^{2} x+2^{x} \log 2 \)


What effect will it have on the motion of
the body if it is made to move on a
sandy surface?


An electric charge \( 10^{-3} \mu C \) is placed at the origin (0,0) of \( (x, y) \) co-ordinate
system. Two points \( A \) and \( B \) are situated at \( (\sqrt{2}, \sqrt{2}) \) and (2,0) respectively. The potential difference between the points \( A \) and \( B \) will be:
A \( .4 .5 V \)
B. \( 9 V \)
c. zero
D. \( 2 V \)


\( \ln \mu_{e} \) and \( \mu_{h} \) are electron and hole
mobility. E be the applied electric field, the current density \( J \) for intristic semiconductor is equal to
\( \mathbf{A} \cdot n_{i} e\left(\mu_{e}+\mu_{h}\right) E \)
B \( \cdot n_{i} e\left(\mu_{e}-\mu_{h}\right) E \)
c. \( \frac{n_{i} e\left(\mu_{e}+\mu_{h}\right)}{E} \)
D. \( \frac{E}{n_{i} e\left(\mu_{e}+\mu_{n}\right)} \)


What will happen after action of dilute hydrochloric acid on sodium sulphide?


Calculate the number of electrons in
sulphur atom having \( \boldsymbol{n}+\boldsymbol{l}=\mathbf{3} \)
\( A \cdot 2 \)
B. 4
\( c .6 \)
D.


Henry's law constant for the molality of
methane in benzene at \( 298 \mathrm{K} \) is \( 4.27 \times \)
\( 10^{5} \mathrm{mm} H g \). Calculate the solubility of
methane in benzene at \( 298 \mathrm{K} \) under 760
\( \operatorname{mm} \boldsymbol{H} \boldsymbol{g} \)
A . \( 1.78 \times 10^{-4} \)
В. \( 1.78 \times 10^{-3} \)
c. \( 1.78 \times 10^{4} \)
D. \( 1.78 \times 10^{-6} \)


An ice of mass \( 0.1 \mathrm{kg} \) at \( 0^{0} \mathrm{C} \) is placed in an isolated container which is at
\( 227^{0} C . \) The specific heat \( S \) of the container varies with temperature \( T \) according to the empirical relation \( \boldsymbol{S}= \) \( A+B T, \) where \( A=100 c a l / k g \) K and
\( B=2 \times 10^{-2} c a l / k g K^{2} . \) If the final
temperature of the container is \( 27^{0} C \) the mass of the container is (Latent heat of fusion of water \( =8 \times 10^{4} \mathrm{cal} / \mathrm{kg} \)
the specific heat of water \( =10^{3} \mathrm{cal} / \mathrm{kg} \mathrm{K} \)
A. \( 0.495 \mathrm{kg} \)
в. \( 0.595 \mathrm{kg} \)
c. \( 0.695 \mathrm{s} \) g
D. \( 0.795 k g \)


Sodium fusion extract, obtained from
aniline, on treatment with iron (II)
sulphate and \( H_{2} S O_{4} \) in presence of air
gives a prussian blue precipitate. The blue colour is due to the formation of:
\( \mathbf{A} \cdot F e_{4}\left[F e(C N)_{6}\right]_{3} \)
B. \( F e_{3}\left[F e(C N)_{6}\right]_{2} \)
\( \mathbf{c} \cdot F e_{4}\left[F e(C N)_{6}\right]_{2} \)
D. \( F e_{3}\left[F e(C N)_{6}\right]_{3} \)


A metre bridge is balanced with known
resistance in the right gap and a metal
wire in the left gap. If the metal wire is heated the balance point
A. shifts towards left
B. shifts towards right
c. does not change
D. may shift towards left or right depending on the nature of the metal


\( 1 \mathrm{kg} \mathrm{fcm}^{-2} \)
\( \mathrm{Nm}^{-2} \)
A \( \cdot 10^{3} \)
B . \( 10^{5} \)
\( c \cdot 10^{4} \)
\( D \cdot 10^{6} \)


The IUPAC name of the coordination
compound \( K_{3}\left[F e(C N)_{6}\right] \) is
A. potassium hexacyanoferrate(II)
B. potassium hexacyanoferrate(III)
C. potassium hexacyanoiron(II)
D. tripotassium hexacyanoiron(II)


A mass of \( M \) at rest is broken into two
pieces having masses \( m \) and \( (M-m) \)
The two masses are then separated by a distance. The gravitational force between them will be the maximum
when the ratio of the masses \( [m: \)
\( (M-m)] \) of the two parts is:
A . 1: 1
B. 1: 2
\( c \cdot 1: 3 \)
D. 1: 4


From the following sequence calculate the lattice energy of \( A B(s) \) \( \boldsymbol{A}(\boldsymbol{s}) \rightarrow \boldsymbol{A}(\boldsymbol{g})+\boldsymbol{e} ; \quad \boldsymbol{6} 1 \boldsymbol{0} \boldsymbol{k} \boldsymbol{J} \boldsymbol{m o l}^{-1} \)
\( \boldsymbol{B}(\boldsymbol{g})+\boldsymbol{e} \rightarrow \boldsymbol{B}(\boldsymbol{g}) ; \quad-\boldsymbol{2 6 0} \boldsymbol{k} \boldsymbol{J} \boldsymbol{m o l}^{-1} \)
\( \boldsymbol{A}(s)+\boldsymbol{B}(\boldsymbol{g}) \rightarrow \boldsymbol{A} \boldsymbol{B}(s) \)
\( -569 k J m o l^{-1} \)
\( \mathbf{A} \cdot-219 \)
в. -919
\( \mathbf{c} \cdot+1539 \)
D. +301


Polymer obtained by condensation polymerization is :
A. polythene
B. teflon
c. PVC
D. bakelite


Most characteristic feature of diatoms
is
A. Pigments
B. Stored food
c. Cell wall
D. Non-oxygenic photosynthesis


Vasoconstriction causes
A. Increase in heart beat
B. Decrease in heart beat
C. Increase in blood pressure
D. Decrease in blood pressure


How will our image be in concave and convex mirrors? Collect photographs and display in your class room.


Biogas is a mixture of:
\( \mathbf{A} \cdot S O_{2}+H_{2} S \)
B \( \cdot O_{2}+C O_{2}+O_{3} \)
\( \mathbf{c} \cdot C O_{2}+C H_{4}+N_{2}+H_{2} S \)
D. \( N O_{2}+H_{2}+C O_{2} \)


Fire is extinguished by:
A. removing all combustible substance
B. cutting off supply of air
C . cooling the burning substance
D. all of these


Which of the following hormone contain lodine?
A. Adrenaline
B. Testosterone
c. Thyroxin
D. Insulin


In a uniform electric field, equipotential
surfaces must:
This question has multiple correct options
A. be plane surfaces
B. be normal to the direction of the field
C. be placed such that surfaces having equal differences in potential are separated by equal distances
D. have decreasing potentials in the direction of the field


Let \( \boldsymbol{R}=(\boldsymbol{a}, \boldsymbol{a}),(\boldsymbol{b}, \boldsymbol{c}),(\boldsymbol{a}, \boldsymbol{b}) \) be a relation
on a set \( A=a, b, c . \) Then the minimum
number of ordered pairs which when added to make it an equivalence
relation are


Equivalent of \( \frac{\mathbf{6}}{\mathbf{2 0}} \) is:
A . \( 6 \% \)
B. 20\%
c. \( 26 \% \)
D. 30\%


From 2 moles of \( K C l O_{3} \) by
decomposition of all the \( K C l O_{3}, \) how
many liters of \( \boldsymbol{O}_{2} \) can be produced at
STP?
A . 11.2
в. 22.4
c. 33.6
D. 44.8
E . 67.2


Diuresis is the condition in which
A. The excretion of volume of urine increases
B. The excretion of volume of urine decreases
C. They kidneys fail to excrete urine
D. The water balance of the body is disturbed


Using the Remainder and Factor Theorem, factorise the following polynomial: \( x^{3}+10 x^{2}-37 x+26 \)


If \( f^{1}(x)=\sin (\log x) \) and \( y= \)
\( f\left(\frac{2 x+3}{3-2 x}\right), \) then \( \frac{d y}{d x} \) equals
A. \( \frac{12}{(3-2 x)^{2}} \)
B. \( \sin \left[\log \left(\frac{2 x+3}{3-2 x}\right)\right] \)
c. \( \frac{12}{(3-2 x)^{2}} \sin \left[\log \left(\frac{2 x+3}{3-2 x}\right)\right] \)
D. \( \frac{12}{(3-2 x)^{2}} \cos \left[\log \left(\frac{2 x+3}{3-2 x}\right)\right] \)


Which of the following is a formula of
methanides : \( (a) B e_{2} C(b) C a C_{2}(c) \)
\( \boldsymbol{M} \boldsymbol{g}_{2} \boldsymbol{C}_{3}(\mathrm{d}) \boldsymbol{A} \boldsymbol{l}_{4} \boldsymbol{C}_{3} \)
A. Only \( a, d \)
B. Only \( a, b \)
c. only \( c, d \)
D. only \( b, d \)


Reaction \( \boldsymbol{A}+\boldsymbol{B} \longrightarrow \boldsymbol{C}+\boldsymbol{D} \) follow's
following rate law rate \( =\boldsymbol{k}=[\boldsymbol{A}]^{\frac{1}{2}}[\boldsymbol{B}]^{\frac{1}{2}} \)
Starting with initial conc. of one mole of
\( A \) and \( B \) each, what is the time taken for
amount of A of become 0.25 mole. Given
\( k=2.31 \times 10^{-3} s e c^{-1} . \) (in sec). (Answer
in the form of \( 100 x \) )


In case of formation of ionic
compounds, the electronegativity difference between atom should be
greater than 1.7 Enter 1 if the statement is True or 0 if
the statement is False.


A current carrying wire in the
neighbourhood produces -
A. No field
B. Electric field only
c. Magnetic field only
D. Electric and magnetic fields


A horizontal beam of vertically polarized light of intensity \( 43 \mathrm{w} / \mathrm{m}^{2} \) is sent
through two polarizing sheets. The
polarizing direction of the first is \( 60^{0} \) to the vertical, and that of the second is
horizontal. The intensity of the light transmitted by the pair of sheets is (nearly)
A. \( 8.1 \mathrm{W} / \mathrm{m}^{2} \)
B. 7.3 \( \mathrm{W} / \mathrm{m}^{2} \)
c. \( 6.4 \mathrm{w} / \mathrm{m}^{2} \)
D. 3.8 \( \mathrm{W} / \mathrm{m}^{2} \)


Maximum number of electrons in a
subshell with \( I=3 \) and \( n=4 \) is :
A . 14
B. 16
c. 10
D. 12


What percentage is equivalent to \( \frac{5}{8} \)
\( \mathbf{A} \cdot 62.5 \% \)
B. \( 60.5 \% \)
c. \( 625 \% \)
D. \( 60 \% \)


The \( 4 n+2 \) radioactive series is also
called Uranium series.
A . True
B. False


The tallest moss in the world is
A. Funaria
B. Pogonatum
c. Buxbaumia
D. Dawsonia


\( \left(\frac{\pi}{3}-\sin ^{-1}\left(-\frac{1}{2}\right)\right) \) is equal


The ratio of \( y z \) -plane divide the line
joining the points \( A(3,1,-5), B(1,4,-6) \) is
A . 3: 1
B. -1: 3
c. 1: 3
D \( .-3: 1 \)


Why is it important to study about
reproductive health?


A radioactive element X decays to give two inert gases. X is :
\( A \cdot \frac{238}{92} \mathrm{U} \)
B \( \cdot \frac{286}{88} \) Rа
\( \mathbf{C} \cdot_{84}^{20 \mathrm{p}} \mathrm{o} \)
D. \( \frac{223}{87} \) Fr


Let \( f(x)=\sqrt{5 x-1} \) and let \( c \) be the number that satisfies the Mean value
theorem for \( f \) on the interval [1,10]
Find the value of \( c \)
A . 2.25
B. 3.25 5
c. 4.25
D. None of the above


A catalyst increases the rate of forward
reaction without influencing that of reverse reactions.
A. True
B. False


A persons image appears on the far side of an optical instrument, upside down.
What is the optical instrument?
A. Concave mirror
B. Convex mirror
c. Plane mirror
D. Concave lens
E. Convex lens


\( C r^{2+} \) is unstable in water.


Three infinitely charged sheets are kept parallel to \( x-y \) plane having charge
densities as shown. Then the value of
electric field at \( ^{\prime} \boldsymbol{P}^{\prime} \) is:
A \( \frac{-4 \sigma}{\epsilon_{0}} \)
в. \( \frac{4 \sigma}{\epsilon_{0}} \)
c. \( \frac{-2 \sigma}{\epsilon_{0}} \)
\( D \cdot \frac{2 \sigma}{\epsilon_{0}} \)


The mass of proton is 1836 times that of an electron. An electron and a proton are
projected into a uniform electric field in a direction perpendicular to the field with equal initial kinetic energies, then:
A. the electron trajectory is less curved than the proton trajectory
B. the proton trajectory is less curved than the electron trajectory
c. both trajectories are equally curved
D. both trajectories will be straight


A string vibrates in its first normal mode with a frequency of 220 vibrations/s. The vibrating segment is \( 70.0 \mathrm{cm} \) long and has a mass of \( 1.20 \mathrm{g} \) Find the tension in the string.


\( \boldsymbol{g}(\boldsymbol{x}+\boldsymbol{y})=\boldsymbol{g}(\boldsymbol{x})+\boldsymbol{g}(\boldsymbol{y})+\mathbf{3} \boldsymbol{x} \boldsymbol{y}(\boldsymbol{x}+ \)
\( \boldsymbol{y}) \forall \boldsymbol{x}, \boldsymbol{y} \boldsymbol{\epsilon} \boldsymbol{R} \) and \( \boldsymbol{g}^{\prime}(\mathbf{0})=-4 . \) For which of
the following values of \( x \) is \( \sqrt{g(x)} \) not
defined?
A \( \cdot[-2,0] \)
в. \( [-2, \infty] \)
c. [-1,1]
D. none of these


The force of friction is
normal reaction between the surfaces.


Solve: \( \int_{0}^{\pi} \sqrt{1-\sin x} d x \)


Two statements are provided. Choose
which is true and which is false.

Statement I: Image formed by half cut mirror has just half the intensity as that of the intensity of image formed by
complete mirror
Statement II: More the lateral
separation between the two halves of the mirror, less will be separation
between the two images, as show in the
given situation
A . \( T, T \)
в. \( T, F \)


Submarine uses ..................................... for
navigation which works on principle of
A. Radar, Reflection of ultrasonic waves
B. Sonar, Reflection of ultrasonic waves.
c. Radar, Detection of cosmic radio waves.
D. Periscope, bending of light.


Silk produced by Antheraea mylitta is also called?
A. Muga silk
B. Tussar silk
c. Eri silk
D. Mysore silk


Q Type your question_
Scheme -1
Scheme -2
\( \mathbf{A} \)
\( B \)
\( C \)
D.


If the arithmetic mean of n numbers of
a series is \( \bar{x} \) and the sum of the first \( (n- \)
1) numbers is \( k \), then the nth number is
\( A \cdot n+k \)
B . \( n \bar{x}+k \)
c. \( n \bar{x}-k \)
D. n-k


Two containers of equal volume
containing the same gas at pressure \( P_{1} \)
and \( P_{2} \) and absolute temperature \( T_{1} \) and
\( T_{2} \) respectively were connected with
narrow capillary tube. The gas reaches a
common pressure \( \mathrm{P} \) and a common
temperature T. The ratio P/T is equal to :
A \( \cdot \frac{P_{1}}{T_{1}}+\frac{P_{2}}{T_{2}} \)
B \( \cdot \frac{1}{2}\left(\frac{P_{1}}{T_{1}}+\frac{P_{2}}{T_{2}}\right) \)
c. \( \frac{P_{1} T_{2}+P_{2} T_{1}}{T_{1}+T_{2}} \)
D. \( \frac{P_{1} T_{2}-P_{2} T_{1}}{T_{1}-T_{2}} \)


A light year is the unit of :
A. time
B. distance
c. intensity of light
D. frequency


A right triangular plate \( A B C \) of mass \( m \)
is free to rotate in the vertical plane about a fixed horizontal axis through \( \mathbf{A} \) It is supported by a string such that the side \( A B \) is horizontal. The reaction at the
support \( A \) is :
\( A \cdot \frac{m}{3} \)
B. \( \frac{2 m g}{3} \)
\( c \cdot \frac{m g}{2} \)
D. \( m g \)


Which of the following is not a celestial body of the universe?
A. Earth
B. Star
c. Planet
D. Aeroplane


A drilling machine of power \( \boldsymbol{P} \) watt is used to drill a hole in copper block of mass \( M \) kg. If the specific heat of copper is \( s J k g^{-1} o C^{-1} \) and \( 40 \% \) of the power is lost due to heating of the machine, the rise in the temperature of
the block in \( T \) seconds will be (in \( ^{o} C \) )
A \( \cdot \frac{0.6 P T}{M s} \)
в. \( \frac{0.6 P}{M s T} \)
c. \( \frac{0.4 P T}{M s} \)
D. \( \frac{0.4 P}{M s T} \)


The molecule having zero dipole
moment is:
A \( . C H_{3} C l \)
в. \( C H_{2} C l_{2} \)
c. \( C H C l_{3} \)
D. \( C C l_{4} \)


The angular momentum of the electron in hydrogen atom in the ground state is
\( \mathbf{A} \cdot 2 h \)
в. \( \frac{h}{2} \)
c. \( \frac{h}{2 \pi} \)
D. \( \frac{h}{4 \pi} \)


Munnabhai had 4 crates, with 24 eggs
in each crate costing \( R s .4 .50 \) per egg. On his bicycle. while cycling to his shop with three crates he went over a big pothole. On reaching his shop he found
that 33 eggs were broken. If he sold the remaining eggs at 6.00 per each, What loss per cent did he suffer?


Evaluate \( \int \frac{\cos x+x \sin x}{x^{2}+\cos ^{2} x} d x \)
A \( \cdot-\tan ^{-1}\left(\frac{\cos x}{x}\right)+c \)
в. \( \ln \left(\frac{x+\cos x}{x}\right)+c \)
c. \( \tan ^{-1}\left(\frac{x}{x+\cos x}\right)+c \)
D. None


Which one of the following acids undergoes decarboxylation on strong heating:
This question has multiple correct options
A. Adipic acid
B. 3 - butenoic acid
c. Formic acid
D. Salicylic acid


A truck of mass \( 5 \times 10^{3} k g \) starting
from rest travels a distance of \( 0.5 \mathrm{km} \) in
\( 10 s \) when a force is applied on ¡t. Calculate the acceleration acquired by the truck
A \( \cdot 25 m s^{-2} \)
B. \( 1 m s^{-2} \)
c. \( 10 \mathrm{cms}^{-2} \)
D. \( 10 m s^{-2} \)


Lightning conductor is made up of conducting materials.
A. True
B. False


If the mean of \( 20,14,16,19, p \) and 21
is 27 then find the value of \( ^{\prime} p^{\prime} \)


The first important biological investigation, which led to the conclusion that plant makes its
substance from water and not from soil
carried out by
A. Lamarck
B. De Vries
c. van Helmont
D. Darwin


In dimer of phosphorus pentaoxide, in what order number of PP, P=0 \& POP
bonds are there?
A \( . P O P>P=O>P P \)
в. \( P=O>P O P>P P \)
c. \( P O P>P P>P=O \)
\( D, P=O>P P>P O P \)


\( \boldsymbol{N} \boldsymbol{i}\left|\boldsymbol{N} \boldsymbol{i}^{2+}(\boldsymbol{1} . \boldsymbol{0} \boldsymbol{M}) \| \boldsymbol{A} \boldsymbol{u}^{3+}(\mathbf{1} . \boldsymbol{0} \boldsymbol{M})\right| \boldsymbol{A} \boldsymbol{u} \)
(where \( \boldsymbol{E}^{o} \) for \( \boldsymbol{N} \boldsymbol{i}^{2+} / \boldsymbol{N} \boldsymbol{i} \) is \( -\mathbf{0 . 2 5} \) and \( \boldsymbol{V} \)
and \( E^{o} \) for \( A u^{3+} / A u \) is \( 0.150 V \) ). What
is the emf of the cell?
A \( .+0.4 V \)
в. \( -1.75 V \)
\( \mathrm{c} .+1.25 \mathrm{V} \)
D. \( +1.75 V \)


The \( 4^{t h} \) term of an AP is zero.Prove that
the \( 25^{t h} \) term is thrice its \( 11 t h \) term


Threshold wavelength depends on
A. Frequency of incident radiation
B. Work function of the substance
C. Velocity of electrons
D. Energy of electrons


Which element show more pronounced inert pair effect?
A .
B. Sn
\( c \cdot c \)
D. Pb


If the position vector of a point \( \boldsymbol{A} \) is \( \vec{a}+\overrightarrow{2 b} \) and \( \vec{a} \) divides \( \overrightarrow{A B} \) in the ratio
\( 2: 3, \) then the position vector of \( B \) is
A \( \cdot \overrightarrow{2 a}-\vec{b} \)
B . \( \vec{b}-\overrightarrow{2 a} \)
c. \( \vec{a}-\overrightarrow{3 b} \)
D. \( \vec{b} \)


Three identical bulbs are connected as
shown in figure. When switch \( S \) is
closed, the power consumed in bulb \( B \)
is \( P . \) What will be the power consumed by the same bulb when switch \( S \) is
opened?
\( ^{A} \cdot \frac{9 P}{4} \)
в. \( \frac{16 P}{9} \)
c. \( \frac{9 P}{16} \)
D. \( \frac{4 P}{9} \)


If two systems are in thermal equilibrium, then they should have
same temperature
A. True
B. False


During respiration, pyruvic acid is formed by
A. Glycolysis
B. Krebs cycle
c. HMP pathway
D. None of the above


\( \mathbf{H}_{2} \mathrm{O}_{2} \) is sold as a solution of
approximately \( 5.0 \mathrm{g} \mathrm{H}_{2} \mathrm{O}_{2} \) per \( 100 \mathrm{ml} \) of the solution the molecular mass of
\( \mathbf{H}_{2} \mathbf{O}_{2} \) is \( \mathbf{3 4} . \) The molarity of this solution is approximately:
A . \( 1.15 \mathrm{M} \)
в. 1.5 М.
c . \( 3.0 \mathrm{M} \)
D. 3.4M


toppr
Q Type your question
and chemical processes are measured with an instrument called Calorimeter.
Heat change in the process is calculated as :
\( \boldsymbol{q}=\boldsymbol{m} \boldsymbol{s} \boldsymbol{\Delta} \boldsymbol{T}_{\ldots} \ldots . . \boldsymbol{s}=\boldsymbol{s} \boldsymbol{p} e c i f i c \quad \boldsymbol{h} e a \boldsymbol{t} \)
\( =c \Delta T_{\ldots \ldots . . c}=h e a t \quad \) capacity
Heat of reaction at constant volume is
measured using bomb Calorimeter.
\( \boldsymbol{q}_{V}=\boldsymbol{\Delta} \boldsymbol{U}= \) internal energy change
Heat of reaction at constant pressure is measured using bomb Calorimeter.
\( \boldsymbol{q}_{\boldsymbol{P}}=\boldsymbol{\Delta} \boldsymbol{H} \)
\( \boldsymbol{q}_{\boldsymbol{P}}=\boldsymbol{q}_{\boldsymbol{V}}+\boldsymbol{P} \boldsymbol{\Delta} \boldsymbol{V} \)
\( \boldsymbol{\Delta} \boldsymbol{H}=\boldsymbol{\Delta} \boldsymbol{U}+\boldsymbol{\Delta} \boldsymbol{n} \boldsymbol{R} \boldsymbol{T} \)
The heat capacity of a bomb calorimeter is \( 500 J K^{-1} . \) When \( 0.1 g \) of
Methane was burnt in this calorimeter,
the temperature rose by \( 2^{\circ} \mathrm{C} \). The value
of \( \Delta U \) per mole will be :
в. \( +260 k J \)
\( c .-2 k J \)
D. \( +2 k J \)


Myopia occurs due to:
A. Increase in the focal length of eye lens
B. Decrease in the distance between retina and lens
C. Decrease in the focal length of the eye lens
D. Increase in the distance between retina and lens


One and only one out of \( \boldsymbol{n}, \boldsymbol{n}+\mathbf{4}, \boldsymbol{n}+ \)
\( 8, n+12 \) and \( n+16 \) is \( \dots \dots \) (where n is
any positive integer)
A. Divisible by 5
B. Divisible by 4
c. Divisible by 10
D. Divisible by 12


Write the product of this reaction:
\[
\left.\left.\left.\right|_{\mathrm{OH}} ^{\mathrm{CH}_{2}} \frac{\mathrm{CH}}{\mathrm{OH}} \frac{\mathrm{CH}-\mathrm{CH}_{2}}{\mathrm{OH}}\right|_{\mathrm{OH}} ^{\mathrm{HIO}_{4}}\right)
\]


\( \boldsymbol{I f} \mathbf{A}=\left[\begin{array}{ll}\mathbf{1} & \mathbf{3} \\ \mathbf{2} & \mathbf{1}\end{array}\right], \) then the determinant
\( \mathbf{A}^{2}-2 \mathbf{A}: \)
A . 5
B . 25
\( c .-5 \)
D. -25


The strength of the magnetic field
around a straight conductor:
A. is same everywhere around the conductor
B. obeys inverse square law
C. is directly proportional to the square of the distance from the conductor
D. none of these


Integrate following with respect to \( x \)
(i) \( \sqrt{x^{2}+4} \)
(ii) \( \sqrt{x^{2}+2 x+5} \)


The position vector of three particles of
masses \( \boldsymbol{m}_{1}=\mathbf{1} \boldsymbol{k} \boldsymbol{g}, \boldsymbol{m}_{2}=\boldsymbol{2} \boldsymbol{k} \boldsymbol{g} \) and
\( \boldsymbol{m}_{3}=\mathbf{3} \boldsymbol{k} \boldsymbol{g} \operatorname{are} \overrightarrow{\boldsymbol{r}}_{1}=(\hat{\boldsymbol{i}}+\boldsymbol{4} \hat{\boldsymbol{j}}+ \)
\( \hat{\boldsymbol{k}}) \boldsymbol{m}, \overrightarrow{\boldsymbol{r}}_{2}=(\hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}}) \boldsymbol{m} \) and \( \overrightarrow{\boldsymbol{r}}_{3}= \)
\( (2 \hat{i}-\hat{j}-2 \hat{k}) \mathrm{m} \) respectively. Find the position vector of their center of mass.
A \( \cdot \frac{1}{2}(\hat{i}+\hat{j}-\hat{k}) m \)
B \( \cdot \frac{1}{2}(\hat{i}+3 \hat{j}-\hat{k}) m \)
c \( \cdot \frac{1}{2}(\hat{i}+\hat{j}-3 \hat{k}) m \)
D \( \cdot \frac{1}{2}(3 \hat{i}+\hat{j}-\hat{k}) m \)


A sample of pure calcium weighing 1.35
g was quantitatively converted to 1.88 g of pure calcium oxide.

The atomic mass of calcium would be:
A . 20
B. 40
c. 80
D. 10


Solve \( : 3^{4 x+1}-2 \times 3^{2 x+2}-81=0 \)
A. \( x=-3 \)
B. \( x=9 \)
c. \( x=-1 \)
D. \( x=1 \)


Phenolphthalein gives a pink colour in alkalinate medium due to the fact that:
A. It is coloured compound
B. It ionises to give coloured ions
c. It is decomposed by alkali
D. It forms a complex compound with alkal


\( \ln \) a circuit \( L, C, R \) are connected in
series with an alternating voltage source of frequency \( f \). The current lags
the voltage by \( 45^{0} . \) The value of \( C \) is:
A \( \cdot \frac{1}{\pi f(2 \pi f L+R)} \)
B・ \( \frac{1}{2 \pi f(2 \pi f L-R)} \)
c. \( \frac{1}{2 \pi f(2 \pi f L+R)} \)
D. \( \frac{1}{\pi f(2 \pi f L-R)} \)


The complexes
\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{6}\right]\left[\boldsymbol{C r}(\boldsymbol{C} \boldsymbol{N})_{6}\right] \boldsymbol{a} \boldsymbol{n} \boldsymbol{d}\left[\boldsymbol{C r}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{6}\right. \)
are the examples of which type of isomerism?
A. Linkage isomerism
B. lonization isomerism
c. coordination isomerism
D. Geometrical isomerism


Experts have warned about Taj Mahal
that:
A. pollutants in air are discolouring its white marble
B. pollutants in water are discolouring its white marble
C . pollutants in land are discolouring its white marble
D. all of the above


How does \( H_{2} O_{2} \) behave as a bleaching
agent


In a set of the given reactions, acetic acid yields a product \( C . \) Product \( C \) would be:
\( \boldsymbol{C H}_{3} \boldsymbol{C O O H}+\boldsymbol{P C l}_{5} \rightarrow \)
\( \boldsymbol{A} \frac{C_{6} \boldsymbol{H}_{6}}{\text {Anhy.AlCl}_{3}} \boldsymbol{B} \frac{C_{2} \boldsymbol{H}_{5} M \boldsymbol{g} \boldsymbol{B r} / \text {ether}}{(i i) \boldsymbol{H}^{+}} \boldsymbol{C} \)
A \( \cdot C H_{3} C H(O H) C_{2} H_{5} \)
в. \( C H_{3} C O C_{6} H_{5} \)
c. \( C H_{3} C H(O H) C_{6} H_{5} \)
D. \( \quad c_{2} \), и\( _{5} \)
\[
C H_{3}-C-(O H) C_{6} H_{5}
\]


Solubility of which among the following substances in water increases slightly with rise in temperature?
A. Potassium bromide
B. Potassium chlorid
c. Potassium nitrate
D. Sodium nitrate


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


Find the total surface area of the
following cylinders


One litre of a buffer solution containig
\( 0.01 M N H_{4} C l \) and \( 0.1 M N H_{4} O H \)
having \( \boldsymbol{p} \boldsymbol{K}_{\boldsymbol{b}} \) of \( \boldsymbol{5} \) has pH of:
A . 10
B. 9
\( c \cdot 4 \)
D. 6


Write the structures of the following organic halogen compounds.
(i) 2-Chloro-3-methylpentane
(ii) p-Bromochlorobenzene
(iii) 1 -Chloro-4-ethylcyclohexane
(iv) 2 -(2-Chlorophenyl)-1-iodooctane
(v) 2 -Bromobutane
(vi) 4-tert-Butyl-3-iodoheptane
(vii) \( 1- \) Bromo- 4 -sec-butyl-2methylbenzene (viii) 1,4-Dibromobut2-ene


Let \( A, B \) and \( C \) be sets such that \( \phi= \)
\( \boldsymbol{A} \cap \boldsymbol{B} \subseteq \boldsymbol{C} . \) Then which of the following
statements is not true?
\( \mathbf{A} \cdot \) If \( (A-C) \subseteq B, \) then \( A \subseteq B \)
в. \( (C \cup A) \cap(C \cup B)=C \)
c. If \( (A-B) \subseteq C \), then \( A \subseteq C \)
D. \( B \cap C \neq \phi \)


The eccentricity of the conic \( 9 x^{2}+ \)
\( 25 y^{2}=225 \) is
A \( \cdot \frac{2}{5} \)
B. \( \frac{4}{5} \)
\( c \cdot \frac{1}{3} \)
D.
E.


Three cuboids of width \( 8 \mathrm{m} \) and joined along its width. Find surface area of resulting cuboid. \( (l=1 \mathbf{m}, h=1 \mathbf{m}) \)
\( \mathbf{A} \cdot 34 m^{2} \)
B. \( 64 m^{2} \)
\( \mathbf{c} \cdot 98 m^{2} \)
D. None of the above


A ball collides with a fixed inclined
plane of inclination \( \boldsymbol{\theta} \) after falling
through a distance h. If it moves horizontallyjust after the impact, the coefficient of restitution is :
A \( \cdot \tan \theta \)
B \( \cdot \tan ^{2} \theta \)
c. \( \cot \theta \)
D. \( \cot ^{2} \theta \)


The curved surface of a shining spoon could be considered as a
A. Curved mirror
B. Plane mirror
c. concave mirror only
D. None


Near the earth's surface time period of a satellite is 1.4 hrs. Find its time period
if it is at the distance \( ^{\prime} 4 R^{\prime} \) from the
centre of the earth.
A . 32 hrs
B. \( \left(\frac{1}{8 \sqrt{2}}\right) \) hrs
c. \( 8 \sqrt{2} \hbar r s \)
D. 16 hrs


Can nucleic acids, proteins and starch be considered as step growth polymers?


Cells in Go phase of cell cycle
A. Exit cell cycle
B. Enter cell cycle
c. suspend cell cycle
D. Terminate cell cycle


Which of the following metals occur in
the native form?
This question has multiple correct options
A. Lithium
B. Silver
c. Gold
D. Sodium


Identify the terms related to proteins:
This question has multiple correct options
A. zwitter ions
B. peptide bond
c. saccharides
D. fermentation


Absorption of water in DCT is controlled
by
\( \mathbf{A} \cdot \) АСТН
в. АDН
c. LH
D. Oxytocin


An example of a salt that will not
hydrolyse is :
A \( . N H_{4} C l \)
в. КСl
\( \mathbf{c} \cdot C H_{3} C O O N H_{4} \)
D. \( C H_{3} \) СООК


In a hostel, \( 60 \% \) of the students read Hindi news paper, \( 40 \% \) read English
news paper and \( 20 \% \) read both Hindi
and English news papers. A student is selected at random.
(a) Find the probability that she reads neither Hindi nor English news papers.
(b) If she reads Hindi news paper, find the probability that she reads English
news paper
(c) If she reads English news paper, find the probability that she reads Hindi
news paper.
A \( .0 .56,0.78,0.76 \)
в. 0.20,0.33,0.50
\( c .0 .65,0.45,0.34 \)
D. 0.56,0.56,0.65


Three concentric metallic shells \( A, B \)
and \( C \) of radii \( a, b \) and \( c(a<b<c) \)
have surface charge densities, \( \sigma,-\sigma \)
and \( \sigma \) respectively. Find the potentials
of three shells \( A, B \) and \( C \).


Which of these can absorb visible light
\( ? \)
A \( \cdot\left[\operatorname{Sc}\left(H_{2} O\right)_{6}\right] C l_{3} \)
В \( \cdot\left[T i(e n)_{3}\right]\left(S o_{4}\right)_{2} \)
\( \mathbf{c} \cdot\left[Z n\left(N H_{3}\right)_{6}\right] S O_{4} \)
D \( \cdot\left[\operatorname{Cr}\left(N H_{3}\right)_{6}\right] C l_{3} \)


Statistical method is used in
type of classification.
A. Phenetic
B. Numerical
c. Adansonian
D. All of the above


The equivalent capacitance \( C_{A B} \) of the
circuit shown in the figure is:
\( A \cdot \frac{5}{1} \)
\( B \cdot \frac{4}{E} C \)
\( c \cdot 2 C \)
D. \( C \)


Clitellar segments in earthworm are
A. 13-17
B. \( 14-16 \)
c. \( 15-19 \)
D. 14-18


Find the principal value of \( \cos ^{-1}\left(\cos \frac{7 \pi}{6}\right) \)


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


\( H_{2} O_{2} \) decolourises \( K M n O_{4} \) in acid medium.
A. True
B. False


One mole of calcium phosphide on
reaction with excess of water
gives
A. One mole of phosphine
B. Two moles of phosphoric acid
c. Two moles of phosphine
D. One mole of phosphorous penta-oxide


Which salt will give basic solution on
hydrolysis?
\( \mathbf{A} \cdot K C N \)
в. \( K C l \)
c. \( N H_{4} C l \)
D. \( C H_{3} C O O N H_{4} \)


Hormone involved in phototropism is
\( A \cdot \) IAA
B. gibberellin
c. kinetin
D. 2, 4-D.


What are dimensional constant?


The chemical differences between DNA
and RNA are
A. DNA has deoxyribose sugar and RNA has ribose sugar
B. DNA is double stranded and RNA is single stranded
C. Nitrogenous bases are only present in DNA.
D. Both A and B


\( \boldsymbol{A}(\boldsymbol{a} \boldsymbol{q}) \longrightarrow \boldsymbol{B}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{C}(\boldsymbol{a} \boldsymbol{q}) \) is a first
order reaction.
Time
moles of reagent
Reaction progress is measure with help of titration ' \( R \) '. If all \( A, B \) and \( C \) reacted
with reagent and have 'n' factors \( [n \)
factor; \( \left.e q . w t=\frac{\text { mol.wt. }}{n}\right] \) in the ratio of
1: 2: 3 with the reagent. The \( k \) in terms
of \( t, n_{1} \) and \( n_{2} \) is :
A \( \cdot k=\frac{1}{t} \ln \left(\frac{n_{2}}{n_{2}-n_{1}}\right) \)
в. \( \quad k=\frac{1}{t} \ln \left(\frac{2 n_{2}}{n_{2}-n_{1}}\right) \)
c. \( _{k}=\frac{1}{t} \ln \left(\frac{4 n_{2}}{n_{2}-n_{1}}\right) \)
D.
\[
k=\frac{1}{t} \ln \left(\frac{4 n_{2}}{5\left(n_{2}-n_{1}\right)}\right)
\]


A concave lens is used in:
A. a simple camera
B. spectacles for the correction of short sightedness
C . a magnifying glass
D. vehicles to see objects on rear side


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\hline \\
\hline \\
\hline \\
\hline \\
\hline
\end{tabular}


A tangent galvanometer has 80 turns of wire. The internal and external
diameters of the coil are \( 19 \mathrm{cm} \) and
\( 21 \mathrm{cm} \) respectively. The reduction factor
of the galvanometer at a place where \( \boldsymbol{H}=\mathbf{0 . 3 2} \) oersted will be (1 oersted \( = \)
\( \mathbf{8 0} \boldsymbol{A} / \boldsymbol{m}) \)
A .0 .0064
B. 0.64
\( c \cdot 0.064 \)
D. None of these


What are food preservatives?


Write the chemical reaction involved in
the extraction of copper from copper
pyrites using a limited supply of air in a reverberatory furnace.


Which of the following refers to particularly stable arrangements of amino acid residues in a protein that give rise to recurring patterns?
A. Primary structure
B. Secondary structure
c. Tertiary structure
D. Quaternary structure


Nitrogen reacts with a metal \( M \) to
produce a compound \( X . \) This compound
\( X, \) when dissolved in water forms
pungent gas \( Y \) which can be identified easily by the formation of white fumes in the presence of \( \boldsymbol{H} \boldsymbol{C l} \)
Identify the metal \( M \)
A. Calcium
B. Sodium
c. cobalt
D. Iron


Find the sum of all odd natural numbers
less than 50 .


For a non-volatile solute:
A. vapour pressure of solution is more than vapour pressure of solvent
B. vapour pressure of solvent is zero
C. vapour pressure of solute is zero
D. all of the above


A metal 'M' which is one of the best
conductor of heat and electricity is used in making electric wires is found
in nature as sulphide ore \( M_{2} S ? \)
(i) Name the metal 'M'.
(ii) Which process will be suitable for extraction of this metal M from its ore
\( M_{2} S ? \) Write the balanced chemical
reactions involving in the process of extraction. With the help of a labelled diagram, explain the process of electrolytic refining of the metal.


The lanthanide contraction is
responsible for the fact that
A. zn and Y have about the same radii
B. zrand Nb have similar oxidation state
c. zrand Hf have about the same radii
D. zrand zn have the same oxidation state


When an electric current passes
through a solenoid, the distance between any two adjacent rings of the solenoid
A . decreases
B. increases
c. does not change
D. first increases and then decreases


In the presence of a catalyst, the heat evolved or absorbed during the reaction:
A. increases
B. decreases
c. remains unchanged
D. may increase or decrease


\( \lim _{x \rightarrow 2}\left[\frac{1}{x-2}-\frac{2}{x(x-1)(x-2)}\right]= \)
\( A \)
2
B. \( \frac{2}{3} \)
\( c \cdot \alpha \)
D.


the same park. The tables show the
weight of each person, along with the
distance between their centers of mass.
Which pair has the strongest attraction for each other (gravitationally)?
\( \mathbf{A} \)
\begin{tabular}{|l|l|}
\hline \multicolumn{1}{|c|} { Weight of Person 1 } & \multicolumn{1}{|c|} {100 pounds } \\
\hline Weight of Person 2 & 100 pounds \\
Distance between Them & 5 feet \\
\hline
\end{tabular}
B. \begin{tabular}{|l|l|}
\hline \multicolumn{1}{|c|} { Weight of Person 3 } & \multicolumn{1}{|c|} {50 pounds } \\
\hline Weight of Person 4 Distance between Them & 100 pounds 5 feet \\
\hline
\end{tabular}
\( c \)
\begin{tabular}{|l|l|}
\hline \multicolumn{1}{|c|} { Weight of Person 5 } & \multicolumn{1}{|c|} {300 pounds } \\
\hline Weight of Person 6 & 100 pounds \\
Distance between Them & 15 feet \\
\hline
\end{tabular}
D. \begin{tabular}{|l|l|}
\hline \multicolumn{1}{|c|} { Weight of Person 7 } & 300 pounds \\
\hline Weight of Person 8 & 200 pounds \\
Distance between Them & 30 feet \\
\hline
\end{tabular}
E. Some pairs tie for the greatest attraction


Increase in temperature favors the
forward reaction in:
A \( \cdot 2 S O_{2}(g)+O_{2}(g) \leftrightharpoons 2 S O_{3}(g) \)
в. \( 203 \leftrightharpoons 302(g) \)
c. \( C(\text { graphite }) \leftrightharpoons C(\text { diamond }) \)
D \( \cdot H_{2}(g)+\frac{1}{2} O_{2}(g) \leftrightharpoons H_{2} O(g) \)


What is the effective mass of photon
having wavelength \( \lambda ? \)


The period of oscillation of a simple pendulum is \( T=2 \pi \sqrt{L / g} . \) Measured
value of \( L \) is \( 20.0 \mathrm{cm} \) known to \( 1 \mathrm{mm} \)
accuracy and time for 100 oscillations of
the pendulum is found to be 90 s using a wrist watch of 1 sec resolution. What is
the accuracy in the determination of


Solar energy transducer is
A. Agaricus
B. Rhizobium
c. Orobanche
D. chlorella


Ozone exists in earth stratosphere and is responsible for protecting humans from harmful
A . clouds
B. rains
c. ultraviolet rays
D. all of the above


Which of the one is copolymer?
A. Styrene butadiene rubber
B. Polythene
c. Nylon
D. None of the above


Which of the following statements is
not correct?
\( \mathbf{A} \cdot L a(O H)_{3} \) is less basic than \( L u(O H)_{3} \)
B. In lanthanide series, radii of elements decreases with an increase in atomic number
C . \( L a \) is actually an element of transition series rather than lanthanides
D. Atomic radii of \( Z r \) and \( H f \) are same because of lanthanide contraction


Lack of oxygen in body fluids is known
as
A. Hyperpnoea.
B. Anoxemia.
c. Anoxia.
D. Hypoxia.


\( \cos ^{-1}(\sqrt{\frac{\boldsymbol{a}-\boldsymbol{x}}{\boldsymbol{a}-\boldsymbol{b}}})=\sin ^{-1}(\sqrt{\frac{\boldsymbol{x}-\boldsymbol{b}}{\boldsymbol{a}-\boldsymbol{b}}}) \)
possible if
A \( . a>x>b \) or \( a<x<b \)
В. \( a=x=b \)
C. \( a>b \) and \( x \) takes any value
D. \( a<b \) and \( x \) takes any value


Benzene is converted to benzene
sulfonate using sulphuric acid and eventually through the
benzene sulfonate is gradually transformed to phenol
A. neutralization
B. fusion
c. acidification
D. All of the above


Mathematical expression for \( t_{1 / 4} \) i.e.
when \( (1 / 4)^{t h} \) reaction is over following
first order kinetics can be given by:
A \( \cdot t_{1 / 4}=\frac{2.303}{K} \log 4 \)
B \cdot \( t_{1 / 4}=\frac{2.303}{K} \log 1 / 4 \)
C \( \cdot t_{1 / 4}=\frac{2.303}{K} \log 2 \)
D \( \cdot t_{1 / 4}=\frac{2.303}{K} \log \frac{4}{3} \)


The excess of fertilizers not consumed
by crops are washed away from land by rain and pollute
A. water
B. air
c. noise
D. soil


If a live Earthworm is pricked with needle on its outer surface without damaging its gut, the fluid that comes out is
A. Coelomic fluid
B. Excretory fluid
c. slimy mucus
D. Haemolymph


HIV has a protein coat and genetic material, which is
A. ssRNA
B. dsRNA
c. ssDNA
D. dsDNA


The parameters for a particle that describe a uniform circular motion and
a uniform velocity motion in a straight line are given below. Which one of them will you use to distinguish their motions
A. Speed of both the particles
B. Distance traveled by both the particles
C. Average velocity of both the particles
D. None of these


'Tornaria' was first described by
A. J. Muller in 1850
B. Delle Chiaea in 1829
c. Eschscholtz in 1850
D. None of the above


What criteria do we use to decide
whether something is alive?


A liquid has a volume \( V_{1} \) at
temperature \( \theta_{1} \). The temperature is
increased to \( \theta_{2} \). If \( \gamma \) is the coefficient of
cubic expansion, the increase in
volume is given by
A \( \cdot V_{1} \gamma\left(\theta_{2}-\theta_{1}\right) \)
в. \( V_{1} \gamma \theta_{2} \)
c. \( V_{1}+V_{1} \gamma \theta_{2} \)
D. \( V_{1}\left[1+\gamma\left(\theta_{2}-\theta_{1}\right]\right. \)


If \( z \) satisfies \( |z+1|<|z-2|, \) and \( \omega= \)
\( \mathbf{3} z+\mathbf{2}+\mathbf{i}, \) then
\( \mathbf{A} \cdot|\omega+1|<|\omega-8| \)
B . \( |\omega+1|<|\omega-7| \)
c. \( \omega+\bar{\omega}>7 \)
D \( \cdot|\omega+5|<\mid \omega-4 \)


For filtering low frequency noise out of a signal the circuit can be built by just putting resistor and capacitor in
A. Series
B. Parallel
c. Perpendicular
D. Bipolar


The Earth's crust is fragmented and each fragment is known as:
A. a spott
B. a plate
c. a valley
D. none of the above


The order of rotational symmetry of a ceiling fan with 3 blades is
A . 2
B. 3
\( c \cdot 4 \)
\( D \cdot 6 \)


How sexual reproduction gives rise to more viable variations than asexual
reproduction?
A. Separation of homologous chromosomes (by chance only) during gamete formation
B. Crossing over (recombination) of homologous chromosomes
C. Fertilisation of gametes to form zygote
D. All of the above


Assertion
EDTA is a hexadentate ligand.
Reason
Denticity of a ligand is given by number
of lone pairs donated to central atom by
a ligand.
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 sum of the products of the corresponding terms of the sequences 2,4,8,16,32 and \( 128,32,8,2, \frac{1}{2} \)


A point \( P(2,-1) \) is equidistant from the points \( (a, 7) \) and \( (-3, a) . \) Find 'a'


Find the roots
\( 4 x^{2}+4 \sqrt{3 x}+3=0 \)


The reaction of \( N a C l \) and \( C a C O_{3} \) gives sodium carbonate. But this reaction
cannot be used for the manufacture of
washing soda since it is a reversible reaction.
A. True
B. False


P-protein occurs in
A. Sieve tube elements
B. Tracheids
c. Vessels
D. Phloem parenchyma


Write the IUPAC name of the compound


Three observers \( A, B \) and \( C \) measure the speed of light coming from a source
as \( v_{A}, v_{B} \) and \( v_{C} . \) Observer \( A \) moves
towards the source, \( C \) moves away from source and \( B \) stays stationary. The surrounding medium is water. If \( A \) and C are moving at the same speed, then This question has multiple correct options
A \( \cdot v_{A}>v_{B}>v_{C} \)
в. \( v_{A}<v_{B}<v_{C} \)
c. \( v_{A}=v_{B}=v_{C} \)
D. \( v_{B}=\frac{1}{2}\left(v_{C}+v_{A}\right) \)


Which of the following statements is
not correct?
A. All halogens except flourine from 0XO-acids
B. Hypohalous acids HOCI,HOBr and HOI are all strong acids
C. Hypochlorous acid is the most stable among hypohalous acids
D. Chlorous acid is the only halous acid known


Low level of noradrenaline is the cause
of depression. What type of drugs are needed to cure this problem? Name two drugs.


The cube root of \( x \) varies inversely as the square of y. If \( x=8 \) when \( y=3 \), then find \( \mathbf{x} \) when \( \boldsymbol{y}=\mathbf{1} \frac{\mathbf{1}}{\mathbf{2}} \)


What is a Reflex Arc? Draw a flowchart
showing of events which occur during sneezing.


What is the role of aspartame in the food industry?


Find the values of \( c \) that satisfy the MVT for integrals on \( [\mathbf{0}, \mathbf{1}] \) \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}(\mathbf{1}-\boldsymbol{x}) \)
A \( c_{c}=\frac{1}{2} \)
B. \( c=-\frac{1}{2} \)
c. \( _{c=\frac{2}{3}} \)
D. \( c=-\frac{1}{3} \)


The displacement of a body which starts from rest, and moving with an
acceleration of \( 1 \mathrm{ms}^{-2} \) at the end of \( 5 s \)
in \( \mathrm{m} \) is:
A . 12.5
B. 25
\( c .7 .5 \)
D. 15


A class of spermicides (used for contraception) inhibits the flagellar motion of the sperm thereby preventing it from swimming towards the egg. This is achieved by
A. Inhibiting the motor protein dynein
B. Inhibiting the motor protein kinesin
c. Disrupting the microflaments
D. Depolymerizing microtubules


Heat travels through vacuum by:
A. convection
B. radiation
c. conduction
D. of all these


Let \( \boldsymbol{A}=\{\mathbf{1}, \mathbf{2}, \mathbf{3}, \mathbf{4}, \mathbf{5}\}, \boldsymbol{B}= \)
\{1,3,5,7,9,10,17,26,30\} Which of the
following sets of ordered pairs are (i) relations (ii) functions (iii) neither,from
\( A \) to \( B \)
\( (a) R_{1}=\{(1,3),(3,3),(5,17),(1,2)\} \)
(b) \( R_{2}=\{(3,7),(4,5),(5,30)\} \)
(c) \( R_{3}=\{(x, y): x \epsilon A, y \epsilon B, x+y=8\} \)
(d) \( R_{4}= \)
\( \left\{(x, y): x \epsilon A, y \epsilon B, y=x^{2}+1\right\}(e) \)
\( \boldsymbol{R}_{5}=\{(\boldsymbol{x}, \boldsymbol{y}): \boldsymbol{x} \boldsymbol{\epsilon} \boldsymbol{A}, \boldsymbol{y} \boldsymbol{\epsilon} \boldsymbol{B}, \boldsymbol{y}=\boldsymbol{2} \boldsymbol{x}-\mathbf{1}\} \)


Express each of the following exponential expressions as a rational number. \( \left(\frac{2}{5}\right)^{(-3)} \)


A line charge \( \lambda \) per unit length is lodged uniformly onto the rim of a wheel of
mass \( M \) and radius \( R \). The wheel has
light non-conducting spokes and is free
to rotate without friction about its axis
as shown in above figure. A uniform
magnetic field extends over a circular
region within the rim. It is given by,
\( \boldsymbol{B}=-\boldsymbol{B}_{0} \boldsymbol{k} \quad(\boldsymbol{r} \leq \boldsymbol{a} ; \boldsymbol{a}<\boldsymbol{R}), \) or
\( B=0 \) (otherwise)
What is the angular velocity of the wheel after the field is
suddenly switched off?


Assertion
Tin is refined by liquation method.
Reason
Tin has low melting point as compared to impurities.
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


Eutrophication can be observed in
A. Saline soil
B. Desert
c. Fresh water lakes
D. Agricultural fields


"Sodium metal when dissolved in
ammonia conducts electricity because of solvated electrons."

Answer whether the above statement is
true or false.
If true enter 1 , else enter 0 .


In the reaction \( \boldsymbol{I}^{\oplus}+\boldsymbol{I}_{2} \rightarrow \boldsymbol{I}_{3}^{\ominus}, \) the lewis
acid is:
\( \mathbf{A} \cdot I_{2} \)
B . \( I^{\oplus} \)
\( c \cdot I_{3}^{0} \)
D. \( I_{3}^{\text {o }} \) and \( I_{2} \)


A spy report about a suspected car reads as follows. "The car moved
\( 2.00 k m \) towards east, made a
perpendicular left turn, ran for \( 500 m \) made a perpendicular right turn, ran for \( 4.00 \mathrm{km} \) and stopped". Find the
displacement of the car.


The specific conductance of a saturated solution of \( A g C l \) at \( 298 \mathrm{K} \) is found to be
\( 1.386 \times 10^{-6} \mathrm{Scm}^{-1} . \) Calculate its
solubility. \( \left(\lambda_{A g^{+}}^{\circ}=62.0 S c m^{2} m o l^{-1} \text {and } \lambda_{C l^{-}}^{\circ}=7\right. \)


Which of the following is not a coenzyme?
A. NAD
B. NADP
c. FAD
D. ATP


How many \( \sigma- \) and \( \pi- \) bonds are there
\( \mathbf{n} \)
\( \mathbf{A} \cdot 14 \sigma, 8 \pi \)
B. \( 18 \sigma, 8 \pi \)
\( \mathbf{c} \cdot 19 \sigma, 4 \pi \)
D. \( 14 \sigma, 2 \pi \)


If \( \int\left(x^{3}-2 x^{2}+3 x-1\right) \cos 2 x d x \)
\( =\frac{\sin 2 x}{4} u(x)+\frac{\cos 2 x}{8} v(x)+C \) then
\( \mathbf{A} \cdot u(x)=x^{3}-4 x^{2}+3 x \)
B . \( u(x)=2 x^{3}-4 x^{2}+3 x \)
C \( \cdot u(x)=3 x^{3}-4 x+3 \)
D \( \cdot v(x)=6 x^{2}-8 x \)


A ball of mass 100 g is moving with a velocity of \( 10 . \) The ball is stopped by the boy in \( 0.2 m s . \) Find the force of the ball?


The formula for \( \% \) composition of \( a \)
compound is:
A. molar mass of a compound/mass due to specific component \( \times 100 \)
B. mass due to specific component \( \times 100 \)
C. mass due to specific component/molar mass of a compound \( \times 100 \)
D. molar mass of a specific component/temperature \( x \) 100


The acid used in the making of vinegar
is:
A. formic acid
B. acetic acid
c. sulphuric acid
D. nitric acid


Assertion
Boron forms only covalent compounds.
Reason

Due to small size of boron, sum of its
first three ionization enthalpies are very
high.
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


Active hydrogen is:
A. hydrogen with unit positive charge
B. hydrogen with unit negative charge
C . a atomic hydrogen
D. a molecular hydrogen


Why the applications of permanent magnet in the field of engineering are quite limited?
A. The field of these magnets are not everlasting.
B. They also lose their magnetism, if they get subjected to physical shock or vibration.
c. Their magnetic field is normally weaker.
D. All


The molecule that deviates from octet
rule is:
A . \( N a C l \)
в. \( B e C l_{2} \)
\( \mathbf{c} \cdot B H_{4}^{-} \)
D. \( N H_{3} \)


For real values of \( x, \) the range of \( \frac{x^{2}+2 x+1}{x^{2}+2 x-1} \) is
B \( \cdot\left[\frac{1}{2}, 2\right] \)
c. \( \left(-\infty, \frac{-2}{9}\right] \cup(1, \infty) \)
D \( \cdot(-\infty,-6] \cup(-2, \infty) \)


In parallelogram \( A B C D \) the length \( A B \)
and \( C D \) are both 4 , the length of
diagonal \( A C=4 \) and the length of
diagonal \( B D=6 . \) The length \( A D \) equal
to
A. \( \sqrt{10} \)
B. \( \sqrt{12} \)
\( c \cdot \sqrt{15} \)
D. \( \sqrt{20} \)


The eighth term of an AP is half its
second term and the eleventh term
exceeds one third of its fourth term by 1 Find the 15 th term.


In an experiment on the specific heat of a metal a \( 0.20 \mathrm{kg} \) block of the metal at
\( 150^{\circ} \mathrm{C} \) is dropped in a copper calorimeter (of water equivalent 0.025
kg) containing \( 150 \mathrm{cm}^{3} \) of water at
\( 27^{\circ} \mathrm{C} . \) The final temperature is \( 40^{\circ} \mathrm{C} \)
Compute the specific heat of the metal. If heat losses to the surroundings are not negligible, is your answer greater or smaller than the actual value for
specific heat of the metal?


Which of the following taxonomical ranks contain organisms least similar to the other similar taxon?
A. Class
B. Genus
c. Family
D. species


For \( \boldsymbol{n} \in \boldsymbol{N}, \boldsymbol{x}^{n+1}+(\boldsymbol{x}+\mathbf{1})^{2 n-1} \) is
divisible by
\( A \)
B. \( x+1 \)
c. \( x^{2}+x+1 \)
D. \( x^{2}-x+1 \)


The vertical displacement traveled by
the proton as it exits the region between
the plates is (mass of proton is \( 1.67 \times \)
\( \left.10^{-27} k g .\right) \)
A \( \cdot 1.6 \times 10^{-8} \mathrm{m} \)
B . \( 3.25 \times 10^{-8} \mathrm{m} \)
\( c \cdot 5.25 \times 10^{-6} m \)
D. \( 2.73 \times 10^{-6} \mathrm{m} \)


In \( _{-}-_{-}-_{-} \) bonding, the valence
electrons are shared among all the
atoms of the metallic elements.


Kepler's second law states that the radius vector to a planet from the sun sweeps out equal areas in equal intervals of time.This law is a
consequence of the conservation of
A . Time
B. Mass
c. Angular momentum
D. Linaer momentum


A solid sphere of radius \( R \) made of a
material of bulk modulus \( K \) is
surrounded by a liquid in cylindrical
container. A massless piston of area \( \boldsymbol{A} \) floats on the surface of the liquid. When
a mass \( M \) is placed on the piston to compress the liquid, the fractional change in the radius of the sphere,
\( \delta R / R, \) is


Two identical balls \( A \& 13 \) of mass \( m \)
each are placed on a fixed wedge as shown in figure Ball B is kept at rest and it is released just before two balls
collides. Bali A roll down without
slipping on inclined plane \( \& \) collide elastically with ball B. The kinetic energy of ball A just after the collision with ball B is:
A \( \cdot \frac{m g h}{7} \)
B. \( \frac{m g h}{2} \)
c. \( \frac{2 m g h}{5} \)
D. \( \frac{7 m g h}{5} \)


Match the columns and choose the
correct combination.
Growth
Regulator Action
\( (a) \)
Abscisic
acid
(1)
Delays leaf
abscission
\( (b) \)
Ethylene \( \quad(2) \quad \begin{array}{l}\text { Inhibits seed } \\ \text { germination }\end{array} \)
\( (c) \)
cytokinin
(3)\( \quad \) Herbicide
\( (d) \)
Auxin \( \quad(4) \quad \begin{array}{l}\text { Hastens fruit } \\ \text { ripening }\end{array} \)
A \( . a-2, b-4, c-1, d-3 \)
в. \( a-1, b-2, c-3, d-4 \)
c. \( a-2, b-3, c-4, d-1 \)
D. \( a-2, b-1, c-3, d-4 \)
E . \( a-3, b-4, c-1, d-2 \)


A galvanometer (coil resistance \( 99 \Omega) \)
is converted into a ammeter using a
shunt of \( 1 \Omega \) and connected as shown in
the figure ( \( i \) ). The ammeter reads \( 3 A \)
The same galvanometer is converted
into a voltmeter by connecting a
resistance of \( 101 \Omega \) in series. This
voltmeter is connected as shown in
figure ( \( i i \) ). Its reading is found to be \( 4 / 5 \)
of the full scale reading. Find the internal resistance \( r \) of the cell (in
ohms)


Inside the sun, four nuclei of hydrogen
combine to form:
A. two nuclei of helium
B. four nuclei of helium
c. one nucleus of helium
D. deuterium


A planet of mass \( m \) is in an elliptical
orbit about the sun \( \left(\boldsymbol{m}<<\boldsymbol{M}_{\text {sun }}\right) \) with
an orbital period. If \( A \) be the area of orbit, then its angular momentum would be:
\( ^{\mathrm{A}} \cdot \frac{2 m A}{T} \)
в. \( m A T \)
c. \( \frac{m A}{2 T} \)
D. \( 2 \mathrm{mAT} \)


Alpha-rays are fast moving helium
nuclei.
If true enter 1 , else enter 0 .


The function \( f(x)=\int_{-1}^{x} t\left(e^{t}-1\right)(t- \)
1) \( (t-2)^{3}(t-3)^{5} d t \) has a local
\( \operatorname{maximum} \operatorname{at} x= \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D. 3


Reactions having molecularity \( \geq 2 \) and order of reaction \( =_{-1-} \) are known as pseudo unimolecular reactions.


A sulfide ore is first converted into its
oxide before reduction. This is done
because
A. A sulphide ore cannot be reduced to metal at all
B. No reducing agent is found suitable for reducing a sulphide ore
c. The enthalpy of formation of \( C O_{2} \) is more than that of \( C S_{2} \)
D. A metal oxide is generally less stable than the metal sulphide


Two equal spheres of mass \( m \) are in
contact on a smooth horizontal table. A
third identical sphere impinges symmetrically on them and is reduced to rest. Prove that \( e=2 / 3 \) and find the
loss in KE.


Write two properties of a material suitable for making (a) a permanent magnet, and
(b) an electromagnet.


Why Vitamin C can't be stored in our
body?


What happens when the sodium metal
is dropped in the ethanol?


In the given figure, ABCD is a trapezium
of area \( 24.5 c m^{2} . \) If \( A D \| \)
\( \boldsymbol{B C}, \angle \boldsymbol{D A B}=\mathbf{9 0}^{0}, \boldsymbol{A D}= \)
\( 10 c m, B C=4 c m \) and \( A B E \) is
quadrant of circle then find the area of
the shaded region.


Two uncharged bodies when rubbed
against each other get charged. This is known as
A. Charging by conduction
B. Charging by friction
c. charging by induction
D. Charging by convection


Which Bryophyte indicates algal ancestory of Bryophytes?
A . Riccio
B. Riella
c. Anthoceros
D. Marchantia


The monthly incomes of Aryan and
Babban are in the ratio 3: 4 and their
monthly expenditures are in the ratio \( 5: 7 . \) If each saves Rs. 15000 per month, find their monthly incomes using matrix method. This problem reflects which value?


Evaluate the integral \( \int_{0}^{2 \pi} \frac{1}{1+\tan ^{4} x} d x \)
A.
в.
c. \( \frac{3 \pi}{4} \)
D. \( \pi \)


Average power developed in time \( t \) due to the decay of the radionuclide is
A \( \cdot\left(\frac{q_{0} t}{2}-\frac{q_{0}}{\lambda}+\frac{q_{0}}{\lambda^{2} t}-\frac{q_{0}}{\lambda^{2} t} e^{-\lambda t}\right) E_{0} \)
B. \( \left(\frac{q_{0} t}{2}+\frac{q_{0}}{\lambda}+\frac{q_{0}}{\lambda^{2} t}-\frac{q_{0}}{\lambda^{2} t} e^{-\lambda t}\right) E_{0} \)
c. \( \left(\frac{q_{0} t}{2}-\frac{q_{0}}{\lambda}+\frac{q_{0}}{\lambda^{2} t}+\frac{q_{0}}{\lambda^{2} t} e^{-\lambda t}\right) E_{0} \)
D. \( \left(\frac{q_{0} t}{2}+\frac{q_{0}}{\lambda}+\frac{q_{0}}{\lambda^{2} t}+\frac{q_{0}}{\lambda^{2} t} e^{-\lambda t}\right) E_{0} \)


An electric circuit contains an
operating heating element and a lit lamp. Which statement best explains why the lamp remains lit when the heating element is removed from the circuit?
A. The lamp and heating element were connected in parallel
B. The lamp has less resistance than the heating element
C. The lamp has more resistance than the heating element
D. The lamp and heating element were connected in series


Explain why:
ICl is more reactive than \( \boldsymbol{I}_{2} \)


Find the volume of a sphere whose
surface area is \( 55.44 \mathrm{cm}^{2} . \) (Take \( \pi=\frac{22}{7} \)
\( \mathbf{A} \cdot 38.808 \mathrm{cm}^{3} \)
B. \( 38.008 \mathrm{cm}^{3} \)
c. \( 32.808 \mathrm{cm}^{3} \)
D. \( 28.808 \mathrm{cm}^{3} \)


Liquid brakes in automobiles follow
principle of bramha press (Pascal's principle). What about air brakes? Collect the information about the
working process of air brakes.


When coal is mixed with a hot solvent
and heated with hydrogen, it forms:
A. Ammonia
B. Liquid hydrocarbon
c. synthetic rubber
D. Plastic


Evaluate the value of \( \sin \frac{\pi}{6}+\cos \frac{\pi}{6} \)


If wavelength of photon and electron is same then ratio of total energy of electron to total energy of photon would be:
A. \( \frac{\text { Velocity of electron }}{\text { Light's speed }} \)
B. \( \frac{\text { Light's speed }}{\text { Electon's speed }} \)
c. \( \frac{\text { Light's speed }}{\text { Velocity of electron }} \)
D. \( \frac{\text { Electron's speed }}{\text { Light's speed }} \)


Two glass tumblers have been stuck together (one into the other). They can
be seperated by
A. Placing hot water in the inner tumbler
B. Placing the tumblers in cold water
c. Placing the outer tumbler in hot water
D. Hamming them vigorously


Octet rule is not valid for the which of
the following molecule?
A \( \cdot C O_{2} \)
B. \( N O \)
\( c \cdot O_{2} \)
D. \( P C l_{3} \)


Which of the following metals forms amphoteric oxide when it reacts with oxygen?
A. Sodium
B. Magnesium
c. Aluminium
D. Potassium


Which of the following statement(s) is/are correct?
I. Starch is almost insoluble in cold
water but relatively more soluble in boiling water.
II. Starch solution gives blue colour with
\( I_{2} \) solution in cold.
III. Starch is a reducing sugar.
IV. Starch forms osazone.
A. III and IV
B. I and II
c. ॥ and III
D. I and IV


Find the number of arrangements of the
letters of the word INDEPENDENCE. In
how many of these arrangements do all
vowels occur together.


In a streamline flow.
This question has multiple correct options
A. The speed of the particle always remains same
B. The velocity of the particle always remains same
C. The kinetic energies of all the particles arriving at a given point are same
D. The momenta of all the particles arriving at the given point are same


The outer most shell of a representative
element contains 'a' electrons and
penultimate shell contains 'b' electrons. The valency of the element will be:
A \( \cdot a+b \)
в. \( b-a \)
\( c \cdot b \)
D. \( a \) or \( 8-a \)


In the Argand plane, the vector \( O P \)
where \( O \) is the origin and \( P \) represents
the complex number \( z=4-3 i, \) is
turned in the clockwise sense through
\( 180^{\circ} \) and streched 3 times. the complex
number represented by the new vector is


A pair of fair dice is rolled together till a sum a either 5 or 7 is obtained. If \( p \)
denoted the probability that 7 comes before \( 5, \) find \( 15 p \)


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


\( P R \) and \( Q S \) are two diameters of a
circle with center \( O \) such that
\( \angle P O Q=90 . \) Then the quadrilateral
PQRS is a
A. rectangle
\( c . \) rhombus
D. square


Which of the following changes occurs
when excess of \( C O_{2} \) gas is passed into
a clear solution of lime water?
A . A white precipitate containing both \( C a C O_{3} \) and \( C a\left(H C O_{3}\right)_{2} \) is formed
B . Initially a white precipitate of \( C a C O_{3} \) is formed which changes into soluble \( C a\left(H C O_{3}\right)_{2} \) on passing excess \( C O_{2} \) gas
C. A white precipitate of \( C a\left(H C O_{3}\right)_{2} \) is formed
D. A white precipitate of \( C a C O_{3} \) is formed


The value of \( \left|\begin{array}{ccc}(\boldsymbol{a}+\boldsymbol{d})(\boldsymbol{a}+\mathbf{2} \boldsymbol{d}) & \boldsymbol{a}+\mathbf{2} \boldsymbol{d} & \boldsymbol{a} \\ \mathbf{2} \boldsymbol{d}(\boldsymbol{a}+\mathbf{2} \boldsymbol{d}) & \boldsymbol{d} & \boldsymbol{d} \\ \mathbf{2} \boldsymbol{d}(\boldsymbol{a}+\mathbf{3} \boldsymbol{d}) & \boldsymbol{d} & \boldsymbol{d}\end{array}\right| \)
A . \( 4 d \)
B \( .4 d^{2} \)
\( c \cdot 4 d^{3} \)
D. \( 4 d^{4} \)


Number of covalent bonds present in
\( \boldsymbol{C} \boldsymbol{a}(\boldsymbol{O} \boldsymbol{C l})_{2} \)


The difference between the angular momentum of two orbits of \( H e^{+2} \) is \( \frac{2 h}{\pi} \)
The energy of an electron present in the higher orbit is -1.51 eV. Indentify the lower orbit.
A
B. 2
\( c \cdot 3 \)
D. 4


A rectangle with sides \( 2 m-1 \) and \( 2 n-1 \)
is divided into square of unit length by drawing parallel lines as shown in
diagram, then the number of rectangles possible with odd side length is
A \( \cdot(m+n-1)^{2} \)
B. \( 4^{m+n-1} \)
\( \mathbf{c} \cdot m^{2}-n^{2} \)
D. \( m(m+1) n(n+1) \)


The most primitive of the bilaterally symmetrical organisms is
A. Fluke
B. Earthworm
c. Rotifera
D. crayfish


Number of sigma and pi bonds in \( \mathrm{ClO}_{4}^{-} \)
ion are:
\( \mathbf{A} \cdot 4 \sigma \) and \( 4 \pi \)
B. \( 4 \sigma \) and \( 2 \pi \)
\( \mathbf{c} \cdot 4 \sigma \) and \( 3 \pi \)
D. \( 3 \sigma \) and \( 2 \pi \)


\( \boldsymbol{A} \boldsymbol{g}_{2} \boldsymbol{S}+\boldsymbol{N} \boldsymbol{a} \boldsymbol{C} \boldsymbol{N} \rightarrow \boldsymbol{A} \)
\( \boldsymbol{A}+\boldsymbol{Z} \boldsymbol{n} \rightarrow \boldsymbol{B} \)
B is a metal. Hence \( A \) and \( B \) :
\( \mathbf{A} \cdot \operatorname{Na}_{2}\left[\operatorname{Zn}(C N)_{4}\right], Z n \)
в. \( \operatorname{Na}\left[\operatorname{Ag}(C N)_{2}\right] \) ], \( A g \)
c. \( \operatorname{Na}\left[\operatorname{Ag}(C N)_{4}\right] \) ], \( A g \)
D・ \( \left.\operatorname{Na}_{3}\left[\operatorname{Ag}(C N)_{4}\right)\right], A g \)


Which of the following is correct match of genetic name with it's common name?
A. Exocoetus - flying frog
B. Betta - Fighting fish
c. Toad - Tree frog
D. Pristis - Electric fish


The speed of an electromagnetic wave in a material medium of permeability \( \mu \)
and permittivity \( \varepsilon \) is
A \( \cdot \frac{1}{\mu \varepsilon} \)
в. \( \frac{1}{2 \mu \varepsilon} \)
c. \( \frac{1}{\sqrt{\mu \varepsilon}} \)
D. \( \frac{1}{\sqrt{2 \mu \varepsilon}} \)
E \( \cdot \frac{2}{\mu \varepsilon} \)


If \( \Delta A B C \cong \Delta D E F, \angle A=47^{\circ}, \angle E= \)
\( 83^{\circ}, \) then the value of \( \angle C \) is:
A \( \cdot 47^{\circ} \)
B. 30
c. 40
\( D \cdot 50^{\circ} \)


single Correct Answer Type
f a stone has to hit at a point which is
at a distance \( d \) away and at a height \( h \)
above the point from where the stone starts, then what is the value of initial
speed \( u \) if the stone is thrown at an
angle \( \theta ? \)
A \( \cdot \frac{g}{\cos \theta} \sqrt{\frac{d}{(2(d \tan \theta-h)}} \)
в. \( \frac{d}{\cos \theta} \sqrt{\frac{g}{(2(d \tan \theta-h)}} \)
c. \( \sqrt{\frac{g d^{2}}{h \cos ^{2} \theta}} \)
D. \( \sqrt{\frac{g d^{2}}{(d-h)}} \)


The molecules of which of the following gas have higher speed?
A . Hydrogen at \( -50^{\circ} \mathrm{C} \)
B. Methane at \( 298 K \)
c. Nitrogen at \( 1000^{\circ} \mathrm{C} \)
D. Oxygen at \( 0^{\circ} \mathrm{C} \)


The velocity of air over the upper surface of the wing of an aerplane is \( 40 m / s \) and that on the lower surface is
\( 30 m / s . \) If the area of the wing is \( 5 m^{2} \)
and the mass of the wing is \( 300 k g \), the
net force acting on the wing is then (Density of air \( =1.3 k g / m^{3} \) and \( g= \)
\( \left.10 m / s^{2}\right) \)
A . 725 N upward
B. 725 N downward
c. \( 2275 N \) upward
D. \( 2275 N \) downward


Classify the following as a constant, linear, quadratic and cubic polynomials
\( \sqrt{2} x-1 \)
A. Linear
B. Quadratic
c. cubic
D. None of these


A non-conducting wall is given a
negative net charge. Next, a sheet of
very flexible rubber with zero net charge
is suspended from the ceiling near the charged wall as shown below. The
rubber sheet will:
flexible
net zero
A. not be affected by the charges on the wall since rubber is an insulator.
B. not be affected by the charged wall because the rubber sheet has zero net charge.
C. bend away from the wall due to the electrical repulsion between the electrons in the rubber and the charges on
the wall
D. bend away from the wall due to the polarization of the rubber molecules by the charged wall.
E. bend towards the wall due to the polarization of the rubber molecules by the charged wall.


since it is the sino-auricular node,
which initiates the impulses in the heart of mammal, it is known as
A. Cholinergic
B. Adrenergic
c. Neurogenic
D. Myogenic


A sample of an ideal gas occupies a volume \( V \) at pressure \( P \) and absolute temperature T. The mass of each molecule is m. The equation for density is
\( \mathbf{A} \cdot m K T \)
в. \( \frac{P}{K T} \)
c. \( \frac{P}{K T V} \)
D. \( \frac{P m}{K T} \)


The area of a coil is \( 500 c m^{2} \) and the
number of turns in it is \( 2000 . \) It is kept
perpendicular to a magnetic field of induction \( 4 \times 10^{-5} W b / m^{2} . \) The coil is
rotated through 180 in 0.1 second. If
the resistance of the total circuit is \( 20 \Omega \)
then the value of the induced charge
flowing in the circuit will be :
A \( \cdot 1 \times 10^{-4} C \)
В. \( 2 \times 10^{-4} \mathrm{C} \)
c. \( 3 \times 10^{-4} C \)
D. \( 4 \times 10^{-4} C \)


The forbidden gap for a pure silicon at the room temperature is eV.
A. Less than one
B. 1.1
\( c \cdot 3 \)
D.


At \( 800 K \) hydrogen and bromine react to form hydrogen bromide. The value of equilibrium constant for this reaction is \( 5 \times 10^{8} \). Calculate the amount of
\( \boldsymbol{H}_{2}, \boldsymbol{B} \boldsymbol{r}_{2} \) and \( \boldsymbol{H} \boldsymbol{B} \boldsymbol{r} \) at equilibrium if \( \mathbf{a} \)
mixture of 0.6 mol of \( H_{2} \) and 0.2 mol of
bromine is heated to \( 700 K \)


Consider the following statements:
Statement I
\( x>\sin x \) for all \( x>0 \)
Statement II:
\( f(x)=x-\sin x \) is an increasing
function for all \( x>0 \)
Which one of the following is correct in respect of the above statements?
A. Both Statements I and II are true and Statement II is the correct explanation of statement
B. Both Statements I and II are true and Statement II is the not correct explanation of Statement
c. statement lis true but Statement II is false
D. Statement I is true but Statement II is true


Write chemical reactions taking place
in the extraction of zinc from zinc
blende.


The derivative of \( \ln (x+\sin x) \) with
respect to \( (x+\cos x) \) is
A \( \cdot \frac{1+\cos x}{(x+\sin x)(1-\sin x)} \)
B. \( \frac{1-\cos x}{(x+\sin x)(1+\sin x)} \)
c. \( \frac{1-\cos x}{(x-\sin x)(1+\cos x)} \)
D. \( \frac{1+\cos x}{(x-\sin x)(1-\cos x)} \)


Acetic acid dimerises in vapour phase
at \( 437 K \) as \( 2 C H_{3} C O O H(g) \rightleftharpoons \)
\( \left(C H_{3} C O O H\right)_{2}(g) . A \) mass of \( 0.0519 g \)
of acetic acid was found to have
764.3 \( m m \) pressure at \( 437 K \) in a container of \( 21.45 \mathrm{cm}^{3} . \) Calculate degree
of dimerisation for acetic acid
dimerisation.


Block A weight 4N and block weight 8N The coefficient of kinetic friction is 0.25
for all surfaces. Find the force \( F \) to slide
\( \mathrm{B} \) at a constant speed when \( (\mathrm{a} 0 \mathrm{A} \) rests on B and moves with it, (b) A is held at
rest, and (c) A and B are connected by a light cord passing over a smooth pulley as shown in Fig., respectively.


A car accelerates from rest at \( 5 m / s^{2} \) and then retards to rest at \( 3 m / s^{2} . \) The
maximum velocity of the car is \( 30 m / s \)
The distance covered by the car is
A . \( 150 \mathrm{m} \)
B. 240 m
c. \( 300 \mathrm{m} \)
D. 360 \( m \)


Which of the following compounds take
part in exchange reaction with \( D_{2} O ? \)
A . \( N a O H \)
в. \( H_{3} P O_{2} \)
c. \( H_{3} P O_{3} \)
D. All the above


A charged particle moves in a circular path in a uniform magnetic field.If the speed is reduced then its time period will
A. increase
B. decrease
c. remain same
D. None of these


The order of the differential equation \( \left(\frac{d y}{d x}\right)^{2}+\left(\frac{d y}{d x}\right)-\sin ^{2} y=0 \)


\( J(4,-5), L(-6,7), m: n=3: 5 \) is (19,-23)
If true then enter 1 and if false then
enter \( \mathbf{0} \)


The unit of ebullioscopic constant is:
A \( \cdot K \) Kg mol\( ^{-1} \) or \( K(\text { molality })^{-1} \)
B . mol Kg \( K^{-1} \) or \( K^{-1} \) (molality)
C \( \cdot k g \) mol \( ^{-1} K^{-1} \) or \( K^{-1}(\text {molality })^{-1} \)
D \cdot K mol kg \( ^{-1} \) or \( K(\text { molality }) \)


Which statement is true according to
Ohm's law?
A. Current will increase by increasing voltage in circuit
B. Resistance will increase by increasing voltage in circuit
C. Resistance will increase by increasing current in circuit
D. Resistance and current both will increase by increasing voltage.


If order of \( A, B, C \) are \( 3 \times 4,5 \times 4,5 \times 8 \)
then if the order of \( \left(A B^{T} C\right) \) is \( m \times \) \( \boldsymbol{n} \) then find \( \boldsymbol{m}+\boldsymbol{n} \)


Draw a labelled diagram of a simple a.c.
generator.


The chemical formula of marsh gas
(methane) is:
A \( \cdot C_{2} H_{6} \)
в. \( C H_{4} \)
\( \mathbf{c} \cdot C_{3} H_{8} \)
D. \( C_{4} H_{10} \)


Crystalline fullerene has properties.
A. semiconducting
B. insulating
c. both \( A \) and \( B \)
D. none of these


A point traversed half the distance with
a velocity \( v_{0} . \) The remaining part of the
distance was covered with velocity \( \boldsymbol{v}_{1} \)
for half the time, and with velocity \( v_{2} \) for the other half of the time. If the mean
velocity of the point averaged over the
whole time of motion is \( \langle\boldsymbol{v}\rangle= \)
\( \frac{\boldsymbol{x} \boldsymbol{v}_{0}\left(\boldsymbol{v}_{1}+\boldsymbol{v}_{2}\right)}{\mathbf{2} \boldsymbol{v}_{0}+\boldsymbol{v}_{1}+\boldsymbol{v}_{2}} . \) Find \( \boldsymbol{x} \)


Which one of the following is the chief ore of copper?
A . galena
B. copper pyrite
c. siderite
D. All of the above.


Assertion
Puccinia can infect wheat only if Berberis vulgaris is growing near wheat.
Reason
Black rust is heteroecious.
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.


Under what condition does a biconvex
lens of glass having a certain refractive
index act as a plane glass sheet when immersed in a liquid?


Show that the rate of change of the speed is \( \frac{\boldsymbol{d} \boldsymbol{v}}{\boldsymbol{d} \boldsymbol{t}}=\frac{\left(\boldsymbol{v}_{\boldsymbol{x}} \boldsymbol{a}_{\boldsymbol{x}}+\boldsymbol{v}_{\boldsymbol{y}} \boldsymbol{a}_{\boldsymbol{y}}\right)}{\sqrt{\boldsymbol{v}_{\boldsymbol{x}}^{2}+\boldsymbol{v}_{\boldsymbol{y}}^{2}}} \)


State the type of Bonding in the
following molecules:
Calcium oxide.


Assertion
The ability of carbon to form chains gives rise to a homologous series of
compounds.
Reason
Homologous series is a series of
compounds with the same general formula, usually varying by a single
parametersuch as the length of a
carbon chain
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 class consists of 100 students, 25 of
them are girls and 75 boys, 20 of them are rich and remaining poor, 40 of them are fair complexioned. The Probability of selecting a fair complexioned rich girl is


Which of the following is covalent?
A . \( N a C l \)
в. \( K C l \)
c. \( B e C l_{2} \)
D. \( M g C l_{2} \)
E \( \cdot C a C l_{2} \)


Scala vestibuli is connected with
A. Fenestra rotundus
B. Fenestra ovalis
c. Scala tympani
D. Scala media


What is the use of colloidal copper?
\( \mathbf{A} \cdot \) In treatment of cancer
B. In treatment of syphilis
C. Diagnostic agent for paresis
D. None of these


An elevator in which a man is standing
is moving upwards with a constant speed of \( 10 \mathrm{m} / \mathrm{sec} \). If the man drops a
coin a from a height \( 2.45 m \), it reaches the floor of the elevator after a time
\( \left(g=9.8 m / s^{2}\right) \)
A \( \cdot \sqrt{2} s \)
B. \( \frac{1}{\sqrt{2}} \)
c. \( 2 s \)
D. \( \frac{1}{2} s \)


\( \int \sec x d x \)


Bond energy is highest for :
A. \( S n-S n \)
в. \( G e-G e \)
c. \( C-C \)
D. \( s i-s i \)


Answer true or false. 'Faster the
movement of the air greater is the drop
in pressure'.
A. True
B. False


Suppose you are given a circle. Give a construction to find its centre.


In a hostel of 50 girls, there are food provisions for 40 days. If 30 more girls join the hostel, how long will these provisions last ? (in days)


A \( 100 \% \) efficiency transformer has 100
turns in the primary and 25 turm coil. If the current in the secondary coil is \( 4 A \) then the current in the primary coil is
\( A \cdot 1 A \)
B. 4 A
\( c \cdot 8 A \)
D. 16 A


In the reaction,
\( \mathbf{2} \boldsymbol{H}_{2} \boldsymbol{S}+\boldsymbol{S} \boldsymbol{O}_{2} \rightarrow \mathbf{2} \boldsymbol{H}_{2} \boldsymbol{O}+\boldsymbol{3} \boldsymbol{S} \)
mol each of \( S O_{2} \) and \( H_{2} S \) will give how much sulphur?
A. 1 mol
B. 3 mol
c. 1.5 mol
D. 2 mol


The capacitance of a capacitor becomes \( \frac{7}{6} \) times its original value if a dielectric slab of thickness, \( t=\frac{2}{3} d \) is introduced in
between the plates. \( d \) is the separation
between the plates. The dielectric
constant of the dielectric slab is:
\( \mathbf{A} \cdot \frac{14}{11} \)
B. \( \frac{11}{14} \)
\( c \cdot \frac{7}{11} \)
D. \( \frac{11}{7} \)


\( \boldsymbol{C H}_{3}-\boldsymbol{N H}-\boldsymbol{C}_{2} \boldsymbol{H}_{5} \) and \( \left(\boldsymbol{C H}_{3}\right)_{3} \boldsymbol{N} \)
show which type of isomerism?
A. Position
B. Functional
c. chain
D. None of the above


Which of the following is true about
given compound?
A. It is aromatic.
B. It is non aromatic
C. It is anti aromatic.
D. Its aromatic behavior cannot be predicted.


A diverging lens of focal length \( f_{1} \) is placed in front of and coaxially with a
concave mirror of focal length \( f_{2} \). Their
separation is d. A parallel beam of light incident on the lens returns as a
parallel beam from the arrangement. Then
This question has multiple correct options
A. the beam diameters of the incident and reflected beams must be the same
в. \( d=2\left|f_{2}\right|-\left|f_{1}\right| \)
c \( \cdot d=\left|f_{2}\right|-\left|f_{1}\right| \)
D. if the entire arrangement is immersed in water, the conditions will remain unaltered


Momentum measures the amount of:
A. Inertia in a body
B. Acceleration of a body
C. Velocity of a body
D. Motion of a body


Pure water has a pleasant taste.
A. True
B. False


Solve the following equations:
\( \frac{x}{2}-\frac{1}{4}=\frac{x}{3}+\frac{1}{2} \)


What is the difference between
organism on the basis of coelom? Give examples for each.


Let \( C(\theta)=\sum_{n=0}^{\infty} \frac{\cos (n \theta)}{n !} \)
Which of the following statements is
FALSE?
B. \( C(0) . C(\pi)>2 \)
c. \( C(\theta)>0 \) for all \( \theta \in R \)
D. \( C(\theta) \neq 0 \) for all \( \theta \in R \)


The following data gives the information on the life - time (in hours) of 75
electrical instruments.
\( \begin{array}{ll}\text { Lifetime } & \text { o- } \\ \text { (in } & \text { 20 } \\ \text { hours) }\end{array} \)
46
\( 20- \)
40 60
Frequency 10
15
find the mean lifetime of the
instruments.


An ideal solenoid having 5000 turns \( / m \)
has an aluminium core and carries a
current of \( 5 A . \) If \( \chi_{A l}=2.3 \times 10^{-5}, \) then
the magnetic field developed at center will be
A. \( 0.031 T \)
\( T \)
в. \( 0.048 T \)
c. 0.0277
D. \( 0.050 T \)


Water is flowing through a very narrow tube. The velocity of water below which the flow remains a streamline flow is
known as:
A. relative velocity
B. terminal velocity
c. critical velocity
D. particle velocity


In a fermentation tank,
molasses solution is mixed with
yeast enzymes. After three days alcohol was observed. The speed of the reaction
in this case is:
A. slow
B. medium
\( c . \) fast
D. very fast


A particle is thrown up inside a stationary lift of sufficient height. The
time of flight is \( T . \) Now it is thrown
again with same initial speed \( v_{0} \) with
respect to lift. At the time of second
throw, lift is moving up with speed \( v_{0} \) and uniform acceleration \( g \) upward (the
acceleration due to gravity). The new
time of flight is :
A \( \cdot \frac{T}{4} \)
в. \( \frac{T}{2} \)
c. \( T \)
D. \( 2 T \)


The equilibrium constant for the
reaction \( \boldsymbol{H}_{2}\left(\boldsymbol{g}()+\boldsymbol{I}_{2}(\boldsymbol{g}) \rightleftharpoons 2 \boldsymbol{H} \boldsymbol{I}(\boldsymbol{g}) \) is \right.
50 at \( 500 \mathrm{K} . \) In presence of suitable catalyst, equilibrium is attained four times faster. The equilibrium constant of the reaction at \( 500 \mathrm{K} \) in the presence
of catalyst should be-
A . 200
в. \( 4 \times 10^{4} \)
\( c \cdot 50 \)
D. 83.6


Explain the beneficial role of the
following.
Nitrogen in air


Biomass is used instead of extensive
use of petroleum. This is an application
of :
A. Green revolution
B. waste management
c. Green chemistry
D. revolution resource recover


Assertion
Van't Hoff factor for solute showing
dissociation is always greater than for solute showing association.
Reason
Dissociation leads to increase in
number of particles whereas,
association leads to a decrease in
number of particles.
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


The main function of frothers is to
A. stick to the ore and take it to the top
B. convert the insoluble ore into soluble part
C. make the ore hydrophobic
D. none of the above


Equipotentials surfaces are shown in
figure a and b. The field is uniform in
A . a only
B. b only
\( c \cdot a \) and \( b \)
D. none


The transcription unit extends from
A. TATA box to start point
B. TATA box to stop codon
C . Start point to stop codon
D. 35 sequence to start point


Measurement of rate of oxygen utilisation by a unit volume of water over a period of time is to measure
A. Biochemical oxygen demand
B. Biosynthetic pathway
c. Biogas generation
D. Fermentation


The number of books bought by 200 students in a book exhibition is given
below.
No. of
\[
\text { books } \quad 0 \quad 1 \quad 2
\]
No. of \( \quad 35 \)
\( 64 \quad 68 \quad 18 \)
uder
Find the variance and standard
variation


A particle is projected with a velocity
making an angle \( \theta \) with the horizontal.
What is the radius of curvature of the
parabola where the particle makes an angle \( \theta \) /2 with the horizontal?


Wavelength of wave is a distance between two particles which are
differing in phase by
\( A \cdot \pi \)
в. \( 2 \pi \)
c. \( \frac{2 \pi}{3} \)
D.


In atoms of nitrogen molecule, which type of bond are present?
A. Hydrogen bond
B. lonic bond
c. Polar covalent bond
D. Nonpolar covalent bond
E. Metallic bond


Which of the following acts only as reducing agent :
\( A \cdot K M n O_{4} \)
в. \( \mathrm{CaOC} 1_{2} \)
c. \( \mathrm{H}_{2} \) s
D. HNO


If \( \Delta A B C \) is an isosceles triangle and
midpoints \( D, E, \) and \( F \) of \( A B, B C, \) and
\( C A \) respectively are joined, then \( \Delta D E F \) is:
A. Equilateral
B. Isosceles
c. Scalene
D. Right-angled


Show that the sum of the three
altitudes of a triangle is less than the sum of its three sides.


Which of the following is the stable
electronic configuration of \( F e^{3+} \) ion?
A \( \cdot 3 d^{6} 6 s^{0} \)
B. \( 3 d^{5} s s^{0} \)
c. \( 3 d^{6} 4 s^{2} \)
D. \( 3 d^{4} 4 s^{2} \)


A white light is passed through the two
narrow slits and produced a pattern of
alternating bright and dark lines on the
screen as shown above. What will
effects on the central bright band, if the
distance between screen and slits are
increased?
A. become wider
B. become narrower
C. remain unchanged
D. disappear completely
E . rotate \( 90^{\circ} \)


If one of the diagonals of a square is
along the line \( x=2 y \) and one of its
vertices is \( (3,0), \) then its sides through
this vertex are given by the equations
A. \( y-3 x+9=0,3 y+x-3=0 \)
в. \( y-3 x-9=0,3 y+x-3=0 \)
c. \( y-3 x+9=0,3 y-x+3=0 \)
D. \( y-3 x+3=0,3 y+x+9=0 \)


The first two terms of an A.P. are 27 and
24 respectively. How many terms of the
progression are to be added to get \( -30 ? \)
A . 15
B. 20
c. 25
D. 18


Assertion
Antheridia of Funaria are sunk in pit.
Reason
Its antheridial cluster is surrounded by
perigoniai leaves
A. If both the assertion and the reason are true and the
reason is a correct explanation of the assertion
B. If both the assertion and reason are true but the
reason is not a correct explanation of the assertion
C. If the assertion is true but the reason is false
D. If both the assertion and reason are false


The electric field in a region of space is
given by \( \boldsymbol{E}=\mathbf{5} \boldsymbol{i}+\mathbf{2} \boldsymbol{j} \boldsymbol{N} / \boldsymbol{C} . \) Determine
the electric flux due to this field
through an area \( 2 m^{2} \) lying in the \( Y Z \) plane:
A . 10
B . 20
c. \( 10 \sqrt{2} \)
(
D. \( 2 \sqrt{29} \)


If \( \tan 22^{\circ}+\tan 38^{\circ}-\sqrt{3}= \)
\( k \tan 22^{\circ} \tan 38^{\circ} \) then find \( k \)
A \( \cdot \sqrt{3} \)
B. \( -\sqrt{3} \)
\( c \cdot \sqrt{7} \)
\( D \cdot 5^{-} \sqrt{5} \)


Arteries are the blood vessels which
have elastic walls and \( -\ldots- \) are the
blood vessels with non-elastic thin
walls.


How may words can be formed using the letter \( A \) thrice, the letter \( B \) twice and
the letter C once?
\( \mathbf{A} \cdot 60 \)
в. 120
c. 90
D. 59


State whether true or false.
The angle of incidence is equal to twice the angle of reflection.
A. True
B. False


What is standard hydrogen electrode?
How is it prepared? Explain with labelled diagram?


The isotope of hydrogen which is/are radioactive in nature:
A. protium and deuterium
B. tritium and deuterium
c. only tritium
D. only deuterium


\( \boldsymbol{L} \boldsymbol{t}_{x \rightarrow 0} \frac{\boldsymbol{x}}{\sqrt{\mathbf{1}+\boldsymbol{x}}-\mathbf{1}} \)


Some meta-directing substituents in aromatic substitution are given. Which one is most deactivating?
A. \( -S O_{3} H \)
B. \( -C N \)
\( \mathrm{c} .-\mathrm{COOH} \)
D. \( -N O_{2} \)


The radius of earth is about \( 6400 \mathrm{km} \)
and that of mars is \( 3200 \mathrm{km} \). Thus
mars of the earth is about 10 times
mass of mars. An object weighs \( 200 \mathrm{N} \) on the surface of earth. Then its weight on the surface of mars will be
A. 80 N
B. 40 N
\( c \cdot 20 N \)
\( D \cdot 8 N \)


The statement "lt is impossible to
construct a heat engine which can convert heat directly to work completely" was given by
A. Clausius
B. Carnot
c. Plank
D. Kelvin \& Plank


Given above is a diagram showing which defect of human eye?


An unbiased coin is tossed. If the result
is a head, a pair of unbiased dice is rolled and the number obtained by
adding the numbers on the two faces is noted. If the result is a tail, a card from
a well shuffled pack of eleven cards numbered \( 2,3,4, \dots . .12 \) is picked and the number on the card is noted. The
probability that the noted number is
either 7 and 8 is \( 1 k 3 / 792 \),where \( k \) is
ten's place of the number \( 1 k 3 . \) F ind the
value of \( k .\{1 k 3=100+10 \times k+3\} \)


A plane wave of wavelength \( 6250 A \) is
incident normally on a slit of width \( 2 x \)
\( 10^{-2} \mathrm{cm} . \) The width of the principal
maximum on a screen distant \( 50 \mathrm{cm} \)
will be
A. 312.5 \( \times 10^{-3} \mathrm{cm} \)
В. 32.5 \( \times 10^{-3} \mathrm{m} \)
c. \( 312.5 \times 10^{-3} \mathrm{m} \)
D. 312 m


Determine the function which has a
domain of \( \boldsymbol{x} \leq \mathbf{3} \)
\( \mathbf{A} \cdot \)
\[
f(x)=(2-x)^{\frac{1}{2}}+\frac{x}{2}
\]
B. \( \quad f(x)=(3-x)^{\frac{1}{2}}+\frac{x}{2} \)
C
\[
f(x)=(x-3)^{\frac{1}{3}}+\frac{x}{4}
\]
D. \( \quad f(x)=(2-x)^{\frac{1}{4}}+\frac{x}{3} \)
E


Find the equation of the line that passes through the points (-1,0) and (-4,12)
A \( . y+4 x=-1 \)
B. \( y+4 x=-4 \)
c. \( -y+4 x=-8 \)
D. \( y-8 x=-12 \)


When the conductivity of a semiconductor is only due to breaking of covalent bonds, the semiconductor is
called
A. n-type
B. p-type
c. intrinsic
D. extrinsic


In the figure the sides \( B C, C A \) and \( A B \)
of a \( \triangle A B C \) have been produced to \( D, E \)
and \( F \) respectively. If \( \angle A C D=105^{\circ} \)
and \( \angle E A F=45^{\circ}, \) find all the angles of
the \( \triangle A B C \)


Neopentyl bromide, undergoes dehydrohalogenaton to give alkenes even though it has no hydrogen. This is due to:
A. \( E_{2} \) mechanism
B. \( E_{1} \) mechanism
C. Rearrangement of carbocations by \( E_{1} \) mechanism
D. \( E_{1} c B \) mechanism
E. \( E_{1} \) mechanism


If a unit charge is taken from one point to another over an equipotential surface, then :
A. Work is done on the charge
B. Work is done by the charge
c. work done on the charge is constant
D. No work is done


Water, milk, fruit juice, cold drinks are examples of which states of matter?
A. Solid
B. Liquid
c. Gas
D. Plasma


Define centripetal acceleration. Derive an expression for the centripetal
acceleration of a particle moving with
uniform speed 'v' along a circular path
of radius 'r'. Give the direction of this
acceleration.


Which of the above compounds would be expected to decarboxylate when
heated?
\( A \)
B. I
c. ॥॥
D. IV


State true or false:
If a number ends with \( 5, \) then its cube
ends with 5
A. True
B. False


The reduction potential of hydrogen electrode when placed in a buffer solution is found to be -0.413 V. The pH
of the buffer is:
A . 10
B. 4
\( c \cdot 7 \)
D. 12


Plants with no roots, but have stems
and leaves are known as


Middle zone is the hottest zone of a
flame.
A . True
B. False


An isosceles triangle is formed with
rods of length \( L_{1} \& L_{2} \) as shown in the figure.The coefficient of linear
expansion \( \alpha_{1}=2 \times 10^{-5} /^{0} C \) and
\( \boldsymbol{\alpha}_{2}=\boldsymbol{8} \times \mathbf{1 0}^{-\mathbf{5}} /^{\mathbf{0}} \boldsymbol{C} \) for the two pieces. If
the distance between apex and the
midpoint of the base remains
unchanged as the temperature is
varied, then \( \frac{L_{1}}{L_{2}} \) is equal to:


The equation of the straight line which passes through the point (2,-3) and makes an angle of \( \frac{\pi}{4} \) with the axis of \( x \)
is
A. \( x-y=1 \)
В. \( x-y=5 \)
c. \( x y=1 \)
D. \( x+y=5 \)


The significance of meiosis is that it
A. Produce four cells having chromosomal number equal to mother cell.
B. Occurs in all types of cells.
c. Maintains the constant chromosomes number of a particular species.
D. Growth of animal body organs.