A massive ball moving with speed \( \mathbf{v} \)
collides head-on with a tiny ball at rest having a very small mass as compared to the first ball. If the collision is elastic,
then immediately after the impact, the second ball will move with a speed approximately equal to
\( A \)
B. 2v
\( c \cdot v / 2 \)
D. \( \infty \)


Solve :
\( \frac{d y}{d x}=x(2 \log x+1), \operatorname{given} y=0 \) where
\( \boldsymbol{x}=\mathbf{2} \)


Which one of the following is a free living nitrogen-fixing bacterium?
A. Rhizobium
B. Azotobacter
c. Nitrococcus
D. Both A and E


Let \( \boldsymbol{A}=\{1,2,3,4\} \) and \( B=\{2,4,5,6\} \)
Find \( \boldsymbol{A} \cap \boldsymbol{B} \)


A number of thin prism of prism angle \( A \) and refractive index \( \mu \) are arranged
on periphery of circle such that any light ray entering from one prism move along a regular polygon
A. number of prism used will be \( \frac{4 \pi}{(\mu-1) A} \)
B. If \( A \) is rational, \( \mu \) must be rational
c. if \( A \) is rational, \( \mu \) must be irrational
D. If \( A \) is irrational, \( \mu \) must be irrational


\( \cos A=a \cos B, \sin A=b \sin B \Rightarrow \)
\( \left(b^{2}-a^{2}\right) \sin ^{2} B= \)
A \( \cdot 1+a^{2} \)
B \( \cdot 2+a^{2} \)
c. \( 1-a^{2} \)
D. \( 2-a^{2} \)


Two parallel metal plates having charges \( +Q \) and \( -Q \) face each other at a certain distance between them. If the
plates are now dipped in kerosene oil tank, the electric field between the
plates will :
A. become zero
B. increase
c. decrease
D. remains same


If \( \alpha, \beta \) are solutions of \( \sin ^{2} x+ \) \( a \sin x+b=0 \) and \( \cos ^{2} x+c \cos x+ \)
\( \boldsymbol{d}=\mathbf{0}, \) then \( \sin (\boldsymbol{\alpha}+\boldsymbol{\beta}) \) equals
A \( \cdot \frac{2 a c}{a^{2}+c^{2}} \)
B. \( \frac{a^{2}+c^{2}}{2 a c} \)
c. \( \frac{2 b d}{b^{2}+d^{2}} \)
D. \( \frac{b^{2}+d^{2}}{2 b d} \)


If \( 4 \sin ^{-1} x+\cos ^{-1} x=\pi, \) then \( x \) is
equal to:
A \( \cdot \frac{1}{2} \)
B. 2
c. 1
D.


Write \( T \) against true and \( F \) against false in the following statements:
(a) Like charges attract each other (T/F)
(b) A charged glass rod attract a charged plastic straw (T/F)
(c) Lightning conductor cannot protect a building from lightning (T/F)
(d) Earthquakes can be predicted in advance (T/F)


\( \{a, b\} \) is a subset of \( \{b, c, a\} \).If true
enter 1 else 0


Find the values of a and b so that the
function \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{ccc}x^{2}+3 x+a, & \text { if } & x \leq 1 \\ b x+2, & \text { if } & x>1\end{array} \) is \right.
differentiable at each \( \boldsymbol{x} \in \boldsymbol{R} \)
\( \mathbf{A} \cdot a=1, b=3 \)
В. \( a=5, b=3 \)
c. \( a=3, b=5 \)
D. \( a=3, b=1 \)
1


A manufacturing firm produces steel pipes in three planet with daily production daily production of 500 1000 and 2000 units reespectively. According to past experience, it is known that the fraction of defective
output produced by the three planets are respectively \( 0.005,0.008,0.010 . \) if \( a \) pipe is selected from a day's total production and faund to be defective,
find the probability that is has come
from the first plant


Who used the word 'catalyst' for the first
time?


The radius of \( L a^{3+}(\text { At.No. of } L a=57) \) is
1.06A. Which one of the following given
values will be closest to the radius of
\( L u^{3+}(\text { At.No. of } L u=71) \)
A . \( 1.40 A \)
B. \( 1.06 \mathrm{A} \)
c. \( 0.85 A \)
D. 1.60A


The moon is observed from two
diametrically opposite points \( A \) and \( B \) on earth. The angle subtended at the moon by two directions of observation
is \( 1^{\circ} 54^{\prime} . \) The diameter of the earth is
\( 1.276 \times 10^{7} m . \) Calculate the distance
of moon from earth.


Bacteria are thought to be primitive
organisms because they
A. Are small, microscopic plants, which cannot be seen by naked eye
B. Cause serious diseases in human beings, domesticated animals and crop plants
C. Produce endospores which are very resistant to adverse conditions
D. Possess incipient nucleus and show division similar to amitosis


An \( A C \) source rated \( 100 \vee(r m s) \)
supplies a current of \( 10 \mathrm{A}(\mathrm{rm} s) \) to a circiut. The average power delivered by the source. This question has multiple correct options
A. must be \( 1000 \mathrm{w} \)
B. may be \( 1000 \mathrm{w} \)
c. may be greater than 1000 w
D. may be less than 1000 w


Write IUPAC names of the following compound and classify it into primary, secondary, and tertiary amines.
\( \boldsymbol{C H}_{3} \boldsymbol{N H C H}\left(\boldsymbol{C H}_{3}\right)_{2} \)
A. N-Methylpropan-2-amine \( \left(3^{\circ}\right) \)
B. 3-Methylpropan-2-amine (3^)
c. 2-Methylpropan-2-amine ( 2 \( ^{\circ} \)
D. N-Methylpropan-2-amine (2^)


Heat which can also get transferred is-
A. thermal heat
B. mechanical heat
c. radiant heat
D. none of these


The acceleration experienced by a moving boat after its engine is cut-off, of given by: \( a=-k v^{3} \) where \( k \) is a
constant. If \( v_{0} \) is the magnitude of
velocity at cut-off, then the magnitude
of the velocity at time \( t \) after the cut-off is :-
A \( \cdot \frac{v_{0}}{2 k t v_{0}^{2}} \)
В. \( \frac{v_{0}}{1+2 k t v_{0}^{2}} \)
c. \( \frac{v_{0}}{\sqrt{1-2 k t v_{0}^{2}}} \)
D. \( \frac{v_{0}}{\sqrt{1+2 k t v_{0}^{2}}} \)


Assertion
The universal gravitational constant is same as acceleration due to gravity.
Reason
Gravitational constant and acceleration
due to gravity have same units.
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 solid insulating sphere of radius a
carries a net positive charge \( 3 Q \)
uniformly distributed throughout its volume. Concentric with this sphere is a
conducting spherical shell with inner radius \( n \) and outer radius \( c \) and having
a net charge \( -Q \), as shown
in figure. The electric field in the region
\( b>r>a \) is


Chose the correct alternative from the
given below questions:
The sequency -25,-23,-21,-19
A. is an \( A \).P. Reason \( d=3 \)
B. is an A.P. Reason \( d=2 \)
c. is an A.P. Reason \( d=4 \)
D. is not an \( A . P \)


Degeneration of genetic code is due to
A. First member of codons
B. Second member of codons
c. Third member of codons
D. Entire codons


An aqueous solution of \( Z n S O_{4}, C u S O_{4} \)
and \( F e S O_{4} \) are taken in three test
tubes marked \( A, B \) and \( C \) respectively. Aluminum powder is added to all the
three test tubes. Do all the test tubes
show color change?
[Give your answer in terms of Yes or No]


Given \( \boldsymbol{A}=\{\boldsymbol{x} \in \boldsymbol{W}: \mathbf{7} \leq \boldsymbol{x} \leq \mathbf{1 0}\}, \) find
\( \boldsymbol{A} \times \boldsymbol{A} \)


Show that (-3,2),(-5,-5),(2,-3)
and (4,4) are the vertices of a rhombus.


Factorise the expressions and divide
them as directed.5pq \( \left(p^{2}-q^{2}\right) \div \)
\( \mathbf{2} p(\boldsymbol{p}+\boldsymbol{q}) \)
A \( \cdot \frac{5}{2} q(p-q) \)
в. \( \frac{3}{2} p q \)
c. \( \frac{5}{2} q(p+q) \)
D \( \cdot \frac{2}{5} q(p q) \)


The incorrect IUPAC name is:
\( A \)
в.
2, 3-Dimethylpentane
\( c \)
\( \mathrm{CH}_{3}-\mathrm{C} \equiv \mathrm{CCH}\left(\mathrm{CH}_{3}\right)_{2} \)
4-Methylpent-2-yne
D.
2-Bromo-3-chlorobutane


Which of the following is produced during the light phase of photosynthesis?
\( \mathbf{A} \cdot A T P \)
в. \( N A D P H_{2} \)
c. Both \( A T P \) AND \( N A D P H_{2} \)
D. Carbohydrates


How many \( \boldsymbol{P}-\boldsymbol{O}-\boldsymbol{P} \) linkage(s) is/are
present in tetrapolyphosphoric acid?


The standard hydrogen electrode
potential is zero, because
A. There is no potential difference between the electrode and the solution
B. Hydrogen ions acquire electrons from a platinum electrode
C. It has been measured accurately
D. It has been defined that way


A photon of energy \( 10.2 e V \) collides inelastically with \( H- \) atom in ground state. After a certain time interval of few
\( \mu s \) another photon of energy \( 15 e V \)
collides inelastically with the same \( \boldsymbol{H} \) atom, the observation made by a suitable detector is
A. 1 photon with energy \( 10.2 e V \) and an electron with 1.4 \( e V \)
B. Two photons with \( 10.2 e V \)
C. Two photons with 1.4 eV
D. one photon with 3.4 eV and 1 electron with 1.4 eV


From the given figure it is stated that
\( \boldsymbol{A B}=\boldsymbol{A C} \)
State true or false.
4 . True
B. False


The equilibrium constant \( \boldsymbol{K}_{\boldsymbol{p}} \) for the
following reaction at \( 191^{\circ} \mathrm{C} \) is 1.24
What is \( \boldsymbol{K}_{c} \) ? \( B(s)+\frac{3}{2} F_{2}(g) \rightleftharpoons B F_{3}(g) \)
A . 6.7
B. 0.61
c. 8.30
D. 7.6


If for three non-zero vectors \( \vec{a}, \vec{b} \) and \( \vec{c}, \vec{a} \cdot \vec{b}=\vec{a} \cdot \vec{c} \) and \( \vec{a} \times \vec{b}=\vec{a} \times \vec{c}, \) then
show that \( \vec{b}=\vec{c} \)


Among the following molecules in
increasing order of \( \sigma \) to \( \pi \) bond ratio.
(1)
(2)
(3)
(4)
\( \mathbf{A} \cdot 2<3<4<1 \)
B . \( 2<4<3<1 \)
c. \( 3<2<1<4 \)
D. \( 2<3<1<4 \)


Identify which of the following is/are
a quadratic polynomial function:
This question has multiple correct options
\( \mathbf{A} \cdot f(x)=(x+1)^{3}-(x+2)^{3} \)
\( g(x)=\left\{\begin{array}{cc}\frac{x^{4}}{x^{2}} & \text { if } x \neq 0 \\ 0 & \text { if } x=0\end{array}\right. \)
C \( \cdot h(x)=(x+1)^{2}-(x+2)^{2} \)
D. All of these


Manufacture of nylon- 6,6 uses:
A. hexanoic acid
B. pentanoic acid
c. hexanedioic acid
D. acetic acid


Why are the contact points of an
electric bell made from silver-cadmium
alloy?


Explain the refraction at a spherical surface using a schematic diagram.


Select the correct option.
A. Locomotion is shown by multi cellular organisms
B. Paramecium uses tentacles for locomotion
C. Hydra uses cilia for locomotion
D. Kangroo cannot walk backward


Estimate the number of electrons in 100
g of water. How much is the total
negative charge on these electron?


In the given figure, if 0 is the centre of a
circle, \( P Q \) is a chord and the tangent
\( P R \) at \( P \) makes an angle of \( 50^{\circ} \) with \( P Q \)
find \( \angle P O Q \)
\( A \cdot 40 \)
в. 80
\( c \cdot 100 \)
D. 120


\( \Delta T_{f} / K_{f} \) is expressed in the unit of
A. Degree
B. Degree.mol-^ kg
c. Degree.mol.kg \( ^{-1} \)
D. mol.kg \( ^{-1} \)


\( 8 g O_{2} \) has same number of molecules as that in:
This question has multiple correct options
A. \( 14 g \) CO
в. \( 7 g \) СО
\( \mathrm{c} \cdot 11 g C O_{2} \)
D. \( 22 g C O_{2} \)


How do infra-red waves differ from
ultraviolet waves?
A. Infra-red waves are longitudinal
B. Infra-red waves have a lower speed in vacuo (in a vacuum)
C. Infra-red waves have lower frequencies
D. Infra-red waves have smaller wavelengths


Find the value of \( c \) in the triangle using
Pythagoras theorem.
A .24
B. 25
\( c .26 \)
0.2


Obtain the relation between linear
velocity and angular velocity


Two supplementary angles are in the ratio 7: 11 , then the angles are
A. \( 70^{\circ}, 120^{\circ} \)
В. \( 60^{\circ}, 120^{\circ} \)
\( \mathbf{c} \cdot 70^{\circ}, 110^{\circ} \)
D. \( 50^{\circ}, 130^{\circ} \)


According to the rules of addition of significant numbers, the addition product of 118.017 and 11.0 will be:
A . 129.017
B. 129.0
\( c \cdot 129 \)
D. none of these


The differential equation representing the SHM of a particuleis \( \frac{\mathbf{9 d}^{2} \boldsymbol{y}}{\boldsymbol{d t}^{2}}+\mathbf{4} \boldsymbol{y}=\mathbf{0} \)
The time period of the particle is given by
A \( \cdot \frac{\pi}{3} \sec \)
в. \( \pi \) sec
\( ^{\mathrm{c}} \cdot \frac{2}{\pi} 3 s e c \)
D. \( 3 \pi s e c \)


\( f(x)=\left\{\begin{array}{ll}1 & x>0 \\ 0 & x=0 \text { and } \\ -1 & x<0\end{array}\right. \)
\( \boldsymbol{g}: \boldsymbol{R} \rightarrow \boldsymbol{R}, \boldsymbol{g}(\boldsymbol{x})=[\boldsymbol{x}], \) then \( (\boldsymbol{f} \circ \boldsymbol{g})(\boldsymbol{\pi}) \)
is:
\( A \)
B.
\( c \)
D. -


There are \( _{--}-_{--} \) isotopes of Carbon
A. 0
B.
\( c \cdot 2 \)
D.


\( C r-C \) bond in the compound
\( \left[\boldsymbol{C r}(\boldsymbol{C O})_{6}\right] \) shows \( \boldsymbol{\pi} \) - character due to
A. covalent bonding
B. coordinate bonding
c. synergic bonding
D. ionic bonding


We harm Earth with various activities
such as unorganised disposal of waste. Which of the following kinds of wastes lasts longest in the environment?
A. Kitchen waste
B. Chemical waste from factories
c. Agricultural waste
D. Nuclear waste


In the figure, the two triangles are
congruent. The corresponding parts are
marked. We can write \( \Delta \) RAT \( \equiv ? \)


If \( f(x) \) and \( g(x) \) are two polynomials with integral coefficients which vanish at \( x=\frac{1}{2}, \) then what is the factor of HCF
of \( \boldsymbol{f}(\boldsymbol{x}) \) and \( \boldsymbol{g}(\boldsymbol{x}) ? \)
\( \mathbf{A} \cdot x-1 \)
B. \( x-2 \)
c. \( 2 x-1 \)
D. \( 2 x+1 \)


\( \int \frac{(\boldsymbol{x}+\mathbf{1})}{\boldsymbol{x}\left(\mathbf{1}+\boldsymbol{x} \boldsymbol{e}^{\boldsymbol{x}}\right)} \boldsymbol{d} \boldsymbol{x}= \)
\( \mathbf{A} \cdot \log \left|\frac{e^{x}}{1+x e^{x}}\right|+c \)
в. \( -\log \left|\frac{e^{x}}{1+x e^{x}}\right|+c \)
c. \( \log \left|\frac{x e^{x}}{1+x e^{x}}\right|+c \)
D. \( -\log \left|\frac{e^{x}}{1-x e^{x}}\right|+c \)


Terms apoplast and symplast were first
used by
A. Clark
B. Munch
c. Dixon
D. Lundegardh


A ladder \( A B \) is supported by a smooth
vertical wall and rough horizontal floor
as shown. A boy starts moving from \( A \) to
\( B \) slowly. The ladder remains at rest, then pick the correct statement(s) from
the following:
This question has multiple correct options
A. Magnitude of normal reaction by wall on ladder at point B will increase
B. Magnitude of normal reaction by wall on ladder at point B will decrease
c. Magnitude of normal reaction by floor on ladder at point A will remain unchanged
D. Magnitude of friction force by floor on ladder at point A will increase


From group 6 only one metal forms hydride. This metal is:
A. Mo
в.
\( c \cdot c r \)
D. \( c o \)


f \( a_{i j}=0(i \neq j) \) and \( a_{i j}=2(i=j) \)
then the matrix \( A=\left[a_{i j}\right]_{n \times n} \) is a
matrix
A . unit
B. null
c. scalar
D. skew symmetric


Two progressive waves each of
frequency \( 10 H z \) travelling at \( 20 \mathrm{cm} s^{-1} \) are superposed. In the resulting stationary wave, the distance between the successive nodes is
A \( .1 \mathrm{cm} \)
B. \( 2 \mathrm{cm} \)
c. \( 0.5 \mathrm{cm} \)
D. 0


The susceptibility of a diamagnetic substance is
\( A \cdot \infty \)
B. zero
c. small but negative
D. small but positive


Plants do not have glands, then how do
they secrete hormones?
A. Each cell is capable of producing hormones
B. One cell produces hormone and then is transferred to others
C. Hormones are produced by soil and taken up by the roots
D. None of these


The synthesis of proteins for formation of spindle fibres takes place in
A. Gi phase
B. s phase
c. \( \mathrm{G}_{2} \) phase
D. M phase


\( K_{c} \) for the synthesis of \( \mathrm{Hl}(\mathrm{g}) \) from \( \boldsymbol{H}_{2}(\boldsymbol{g}) \)
and \( I_{2}(g) \) is \( 50 . \) The degree of dissociation of HI is:
A . 0.10
B. 0.14
c. 0.22
D. 0.93


Find the number of solutions of the
equations;
\( \mathbf{2}^{\cos x}=|\sin x| \) when \( \boldsymbol{x} \epsilon[-2 \pi, 2 \pi] \)


State the reasons for the deforestation
and it's consequences.


Explain why the given names in the following are wrong.

Give the correct name in each case:
3-bromo-2-methylpropane


A car moves on a horizontal track of
radius \( r, \) the speed increasing constantly at rate \( \frac{\boldsymbol{d} \boldsymbol{v}}{\boldsymbol{d} \boldsymbol{t}}=\boldsymbol{a} . \) The
coefficient of friction between road and
tyre is \( \mu . \) Find the speed at which the car
will skid.
A \( \cdot\left[\left(\mu^{2} g^{2}+a^{2}\right) r^{2}\right]^{1 / 4} \)
B . \( \sqrt{\mu g r} \)
\( ^{\mathrm{C}} \cdot\left[\left(\mu^{2} g^{2}-a^{2}\right) r^{2}\right]^{1 / 4} \)
D. \( \sqrt{a r} \)


The volume of a colloidal particle, \( V_{c} \) as
compared to volume of solute particle
\( V_{s}, \) in a true solution could be
A \( \cdot \frac{V_{c}}{V_{s}}=10^{-3} \)
в. \( \frac{V_{c}}{V_{s}}=10^{3} \)
c. \( \frac{V_{c}}{V_{s}}=10 \)
D. \( \frac{V_{C}}{V_{s}}=10^{22} \)


If \( A, B \) and \( C \) are interior angles of a
triangle \( A B C, \) then show that tan \( \left(\frac{\boldsymbol{A}+\boldsymbol{B}}{\mathbf{2}}\right)=\cot \frac{\boldsymbol{C}}{2} \)


Which one of the following statement is meaningless?
\( ^{\mathbf{A}} \cdot \cos ^{-1}\left(\ln \left(\frac{2 e+4}{3}\right)\right) \)
B. \( \operatorname{cosec}^{-1}\left(\frac{\pi}{3}\right) \)
c. \( \cot ^{-1}\left(\frac{\pi}{2}\right) \)
D \( \cdot \sec ^{-1}(\pi) \)


If \( \boldsymbol{A}=\{1,2,3\} \) and \( B=\{3,8\}, \) then
\( (A \cup B) \times(A \cap B) \) is equal to
A \( \cdot\{(8,3),(8,2),(8,1),(8,8)\} \)
B - \{(1,2),(2,2),(3,3),(8,8)\}
c. \{(3,1),(3,2),(3,3),(3,8)\}
D・ \{(1,3),(2,3),(3,3),(8,3)\}


A charge \( q_{1}=2 \mu C \) is located at the
origin and a charge \( \boldsymbol{q}_{2}=-\boldsymbol{6} \boldsymbol{\mu} \boldsymbol{C} \) is
located at \( (0,3 m) . \) Find the total
electric potential due to the charges at point \( (4 m, 0) \)
\( \mathbf{A} \cdot-6.29 e V \)
В. \( -6.29 m V \)
\( \mathbf{c} .-6.29 M V \)
D. - \( 6.29 V \)


whose hemispherical base is of
diameter \( 0.20 \mathrm{m} . \) The height of the flask
is \( 0.25 \mathrm{m} \). The flask is filled to the brim
with 2.5 litres \( \left(1 \text { litre }=10^{-3} m^{3}\right) \) of
water and sealed with a glass lid.
What is the approximate magnitude of
the total vertical force exerted by the
water on the curved surface of the
flask? (Take the acceleration due to
gravity, \( g, \) to be \( 10 m s^{-2} \) ).
\( A \cdot O N \)
B. 78.5
c. 53.5 N
D. 25.0


Clean water should have BOD value:
A. \( <5 \) ppm
B. > 5 ppm
c. \( <10 \) ppm
D. \( <2 \) ppm


Area of a parallelogram, whose diagonals are \( 3 \hat{i}+\hat{j}-2 \hat{k} \) and \( \hat{i}-3 \hat{j}+ \) \( 4 \hat{k} \) will be
A . \( 14 u n i t \)
B. \( 5 \sqrt{3} \) unit
c. \( 10 \sqrt{3} \) unit
D. \( 20 \sqrt{3} u \) unit.


The following bar graph shows the
results of an annual examination in a
secondary school. Read the bar graph
and choose the alternative in each of
the following:
The pair of classes in which the results
of boys and girls are inversely
proportional are:
A. VI, vIII
B. VI, IX
c. VIII, IX
D. VIII. \( x \)


The area of cross section of a steel wire
\( \left(y=2 \times 10^{11} N / m^{2}\right) \) is \( 0.1 c m^{2} . \) The
force required to double its length will
be:
A \( \cdot 2 \times 10^{12} N \)
В. \( 2 \times 10^{11} N \)
C . \( 2 \times 10^{10} N \)
D. \( 2 \times 10^{6} N \)


Energy gap of conductor is
A. 0 eV
в. 1 eV
\( c \cdot 2 e V \)
D. 3 eV


In forward bias, the depletion layer behaves like
A . an insulator
B. a conductor
c. a semiconductor
D. a capacitor


Bulbs in street lightning are all connected in
A. parallel
B. series
c. series-parallel
D. end-to-end


When current flows in a wire, it creates field around it. Fill in the
blank:
A . gravitational
B. magnetic
c. repulsive
D. attractive


The length of a simple pendulum is determined by measuring the length of thread / by meter scale and radius of bob r by Vernier callipers. The effective length \( L \) is obtained by adding the two i.e., \( \boldsymbol{L}=\boldsymbol{l}+\boldsymbol{r} . \) If \( \boldsymbol{l}=\mathbf{1 0 2 . 4} \mathrm{cm} \) and \( \boldsymbol{r}= \)
\( 2.24 \mathrm{cm}, \) how would you use quote \( L \) in proper significant figures?
\( A \cdot 104.64 \mathrm{cm} \)
B. 104.6 cm
\( c .105 \mathrm{cm} \)
D. \( 1.0464 \mathrm{cm} \)


Assertion : 'Chipko Andolan' was done by women of Reni village.

Reason : 'Chipko Andolan' was done to protect wildlife.
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. Both the assertion and reason are false.
E. If the assertion is false but reason is true.


\( A B=x c m, B C=(4 x+4) \mathrm{cm} \) and \( A C=(4 x) \)
+5) \( \mathrm{cm} . \) Find \( \mathrm{AC} \)


A satellite in geostationary orbit is used for:
A. weather monitoring
B. astronomical research
c. TV broadcasting
D. all of the above


In an examination, Kavita scored 120 out of 150 in maths, 136 out of 200 in English and 180 out of 150 in Science.
Find her percentage score in each subject and also on the whole
(aggregate).


The number of straight line that are
equally inclined to the three dimensional co- ordinate axes, is


A ball of mass \( m \) is thrown vertically up
with an initial velocity so as to reach a
height \( h . \) The correct statement is:
A. potential energy of the ball at the ground is \( m g h \)
B. kinetic energy imparted to the ball at the ground is zero
c. kinetic energy of the ball at the highest point is \( m g h \)
D. potential energy of the ball at the highest point is \( m g h \)


For the reaction \( 2 N H_{3(g)} \frac{1130 K}{M o} \)
\( N_{2(g)}+3 H_{2(g)}, \) the order is:


What change occur among boys and
girls during adolescence?


While doing an experiment with potentiometer (figure) it was found that the deflection is one sided and (i) the
deflection decreased while moving from
one end \( A \) of the wire, to the end \( R ;(\text { ii }) \)
the deflation increased, while the jockey
was removed towards the end D.

Which terminal positive or negative of
the cell \( E_{1} \) is connected at \( X \) in case
(i) and how is \( E_{1} \) related to E?
(ii) Which terminal of the cell \( E_{1} \) is
connected at \( X \) in case (ii)?


A conductor A with a cavity as shown in the figure is given a charge \( Q . \) Find net charge appear on the inner surface of
the cavity.
\( \mathbf{A} \cdot+Q \)
B. - \( Q \)
c. \( -Q / 2 \)
D. zero


If \( A \) and \( B \) are events having probabilities, \( \boldsymbol{P}(\boldsymbol{A})=\mathbf{0 . 6 , P}(\boldsymbol{B})= \)
\( \mathbf{0 . 4}, \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B})=\mathbf{0}, \) then the probability
that neither \( A \) nor \( B \) occurs is
A \( \cdot \frac{1}{4} \)
B. 1
\( c \cdot \frac{1}{2} \)
\( D \)


\( \ln \) a certain G.P. if \( S_{6}=126 \) and \( S_{3}=14 \)
then find \( a \) and \( r \)


For a given circuit, it is observed that
the current \( I \) is independent of the
value of the resistance \( R_{6} \). Then, the
resistance values must satisfy
A \( \cdot R_{2} R_{3}=R_{1} R_{4} \)
в. \( R_{3} R_{4} R_{6}=R_{2} R_{1} R_{5} \)
c. \( \frac{1}{R_{3}+R_{4}}=\frac{1}{R_{5}}+\frac{1}{R_{6}}-\frac{1}{R_{1}+R_{2}} \)
D. \( R_{3} R_{1}=R_{2} R_{4}=R_{5} R_{6} \)


The points where the function \( f(x)= \)
\( [\boldsymbol{x}]+|\mathbf{1}-\boldsymbol{x}|,-\mathbf{1} \leq \boldsymbol{x} \leq \mathbf{3}, \) where [
denotes the greatest integer function, is not differentiable are
A. \( x=-1,0,1,2,3 \)
B. \( x=-1,0,2 \)
c. \( x=0,1,2,3 \)
D. \( x=-1,0,1,2 \)


A tuning fork produces 8 beats /s with a sonometer wire. When tension in the
wire is increased by \( 21 \% \) again 8 beats/s produced with the same tuning fork, the frequency of the tuning fork is
\( \mathbf{A} \cdot 168 H z \)
в. \( 176 H z \)
\( \mathrm{c} .328 \mathrm{Hz} \)
D. \( 336 H z \)


State one advantage of disposable paper cups over disposable plastic
cups?


Though the statement quoted above may be disputed, most physicists do have a feeling that the great laws of physics are at once simple and beautiful. Some of the
notable physicists, besides Dirac, who have articulated this feeling, are:
Einstein, Bohr, Heisenberg, Chandrasekhar and Feynman. You are urged to make special efforts to
get access to the general books and writings by these and other great masters of physics. (See the Bibliography at the end of this book.) Their writings are truly inspiring!


Transition metals show paramagnetism
due to
A. Characteristic configuration
B. high lattice energy
c. variable oxidation states
D. unpaired electrons


A hammer exerts a force of 1.5 N on each
of the two nails \( A \) and \( B \). The area of
cross section of tip of nail is \( 2 m m^{2} \)
while that of nail \( \mathrm{B} \) is \( 6 \mathrm{mm}^{2} \). Calculate
pressure on each nail in pascal.


Laborer's working with phosphorus suffer from a disease in which bones
decay. It is known as:
A. arthritis.
B. phossy jaw.
c. rickets
D. cancer


Identify the postulate, based on which the given pair of triangle can be said
similar?
A. SAS similarity postulate
B. AAA similarity postulate
c. sss similarity postulate
D. AAS similarity postulate


Suppose that \( f(x)=x^{3}-3 x^{2}-4 x+12 \)
\( \operatorname{and} h(x)=\left\{\begin{array}{ll}\frac{f(x)}{x-3} & x \neq 3 \\ K & x=3\end{array}, \) then \right.
find the value of \( \mathrm{K} \) that makes
h' continuous at \( x=3 \)


Which of the following statements is
incorrect?
A. Friction acts on a ball rolling along the ground.
B. Friction acts on a boat moving on water.
C. Friction acts on a bicycle moving on a road.
D. Friction does not act on a ball moving through air


\( P C l_{3} \) on hydrolysis gives fumes of:
A. \( H_{3} P O_{3}+H C l \)
в. \( H_{3} P O_{4}+H C l \)
c. \( H_{3} P O_{2} \) and \( H_{3} P O_{3} \)
D. \( H_{3} P O_{2}+H C l \)


In a moderately skewed distribution the values of mean and median are 5 and 6
respectively. The value of mode in such a situation is approximately equal to
\( A \cdot 8 \)
B. 11
c. 16
D. none of these


A cylinder contained \( 10 \mathrm{kg} \) of gas at
pressure \( 10^{7} \mathrm{N} / \mathrm{m}^{2} . \) The quantity of gas
taken out of cylinder if final pressure is \( 2.5 \times 10^{6} \mathrm{N} / \mathrm{m}^{2} \) is (Assume temperature of gas is
onstant
A. zero
B. 7.5 \( \mathrm{Kg} \)
c. \( 2.5 \mathrm{Kg} \)
\( D .5 \mathrm{kg} \)


Find the acute angles \( A \) and \( B \) satisfying \( \sec A \cot B-\sec A-2 \cot B+2=0 \)


\( F(n) \) be a polynomial function
satisfying \( \boldsymbol{f}(\boldsymbol{x}) \cdot \boldsymbol{f}\left(\frac{1}{x}\right)=\boldsymbol{f}(\boldsymbol{x})+ \)
\( f\left(\frac{1}{x}\right) \forall x \in R-\{0\} \) and \( f(3)=-26 \)
Determine \( \boldsymbol{f}(\mathbf{1}) \)


Gravitational force between two bodies
is 1 newton.If the distance between them
twice, what will be the force?


State whether true or false.
A couple tends to produce motion in a straight line.
A. True
B. False


What happens to the half life period for a first order reaction, if the intial concentration of the reactants is
increased?


The movement of dispersion medium
under the influence of an electric field
is called:
A. Electro-osmosis
B. Diffusion
c. Sublimation
D. Enthalpy gain


Three particles of masses \( 50 g, 100 g \)
and \( 150 g \) are placed at the vertices of
an equilateral triangle of side \( 1 m \) (as
shown in the figure). The \( (x, y) \) coordinates of the centre of mass will
be :
\( ^{\mathbf{A}} \cdot\left(\frac{7}{12} m, \frac{\sqrt{3}}{8} m\right) \)
B \( \cdot\left(\frac{\sqrt{3}}{4} m, \frac{5}{12} m\right) \)
\( ^{\mathbf{c}} \cdot\left(\frac{7}{12} m, \frac{\sqrt{3}}{4} m\right) \)
D. \( \left(\frac{\sqrt{3}}{8} m, \frac{7}{12} m\right) \)


Motion of the aeroplane is an example
of motion.
A. zero dimensional
B. one dimensional
c. two dimensional
D. three dimensional


A boy of mass \( 40 \mathrm{kg} \) is climbing a vertical pole at a constant speed. If the coefficient of friction between his
palms and the pole is 0.8 and \( g=10 m s^{-2} \) the horizontal force that he is applying on the pole is:
A. 300 N
B. 400 N
c. \( 500 \mathrm{N} \)
D. 600 N


Assertion
If we apply force to a lump of putty or mud, they have no gross tendency to regain their previous shape.
Reason
This type of substances are called
plastic substances.
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


Two point charges \( +3 \mu C \) and \( +8 \mu C \) repel each other with a force of \( 40 N . \) If a
charge of \( -5 \mu C \) is added to each of them, the force between them will become:
A \( .-10 N \)
B. \( 10 N \)
\( c .20 N \)
D. \( -20 N \)


\( \boldsymbol{P b S}+\boldsymbol{H}_{2} \boldsymbol{O}_{2} \rightarrow \boldsymbol{H}_{2} \boldsymbol{O}+\ldots \ldots \)
A \( . P b S O_{3} \)
в. \( P b S O_{4} \)
c. \( P b\left(S O_{4}\right)_{2} \)
D. \( P b\left(S O_{4}\right)_{3} \)


Convert the following Celsius temperature to kelvin scale
(i) \( -273^{0} C \)
(ii) \( 30^{0} C \)
\( (\text { iii })-100^{0} C \)
\( (i v)-40^{0} C \)


Would you expect the equilibrium constant for the reaction \( \boldsymbol{I}_{2}(\boldsymbol{g}) \rightleftharpoons \mathbf{2} \boldsymbol{I}(\boldsymbol{g}) \)
to increase or decrease as temperature increases? Why?


If \( S_{n}=n^{2} p \) and \( S_{m}=m^{2} p, m \neq n, \) in
an A.P., then \( S_{p}=p^{3} \)
A. True
B. False


In the figure if \( B D \| E F \), then \( \angle C E F \) is:
\( A \cdot 100^{\circ} \)
B. 120
\( c \cdot 140 \)
D. 160


Alkenes are characterised by presence
of
A. single bond
B. double bond
c. triple bond
D. -OH group


Solve the problem:\( \left(\frac{1}{5}+i \frac{2}{5}\right)-\left(4+i \frac{5}{2}\right) \)


Two particles projected from the same point with same speed \( u \) at angles of
projection \( \alpha \) and \( \beta \) strike the horizontal
ground at the same point. If \( \boldsymbol{h}_{1} \) and \( \boldsymbol{h}_{\mathbf{2}} \) are the maximum heights attained by
the projectile, \( \boldsymbol{R} \) is the range for both \( \boldsymbol{t}_{1} \)
and \( t_{2} \) are their times of flights,
respectively, then This question has multiple correct options
\( \mathbf{A} \cdot \alpha+\beta=\frac{\pi}{2} \)
B . \( R=4 \sqrt{h_{1} h_{2}} \)
c. \( \frac{t_{1}}{t_{2}}=\tan \alpha \)
D \( \cdot \tan \alpha=\sqrt{\frac{h_{1}}{h_{2}}} \)


Hormone responsible for ageing is
A . GA
B. IAA
c. Ethylene
D. Cytokinin


Assertion
The ratio weights of carbon and oxygen
in \( C O_{2} \) is 3: 8 and it is a constant.
Reason

The atomic weights of carbon and
oxygen are constant.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
B. Both Assertion and Reason are correct, but Reason is not the correct explanation for Assertion
c. Assertion is correct, but Reason is incorrect
D. Assertion is incorrect, but Reason is correct.


A quantity of electrical charge that brings about the deposition of \( 4.5 g A l \)
from \( A l^{3+} \) at the cathode will also
produce the following volume at \( (\boldsymbol{S T P}) \)
of \( \boldsymbol{H}_{2}(\boldsymbol{g}) \) from \( \boldsymbol{H}^{+} \) at the cathode
A . \( 44.8 L \)
B. 22.4 L
c. \( 11.2 L \)
D. \( 5.6 L \)


Solve:
Add \( 3 a(a-b+c), 2 b(a-b+c) \)


On which continent Homo sapiens arose?


Equal volumes of \( 1 \mathrm{M} K_{2} S O_{4} \) and \( 1 \mathrm{M} \)
\( A l_{2}\left(S O_{4}\right)_{3} \) solutions are mixed. Which
of the following is incorrect?
A. The concentration of \( K^{+} \) is 1 M
B. The concentration of \( A l^{3+} \) is 1M
C. The concentration of \( S O_{4}^{2-} \) is 2 M
D. The concentration of all the three ions is 1 M


Which of the following forms cationic micelles above certain concentrations?
A. Sodium dodecyl sulphate
B. Urea
c. Sodium acetate
D. Cetyl trimethyl ammonium bromide


Which one of the following statement is correct about the given compound?
A. An anionic surfactant
B. A soap
c. A non-ionic surfactant
D. A cationic surfactant


In which of the following process the system and surrounding does not comes back to original state after
the process is complete?
A. Reversible process
B. Adiabatic process
c. Quasi-static process
D. Spontaneous process


In \( \Delta A B C, \) D and \( E \) are two mid points of
sides \( A B \) and \( A C \) respectively. If
\( \angle B A C=40^{\circ} \) and \( \angle A B C=65^{\circ}, \) then
\( \angle C E D \) is
A . 75
B. 125
\( c \cdot 130 \)
D. 105


A steady current is passing through a
linear conductor of non uniform cross-
section. The net quantity of charge crossing any cross section per second
is
A. Independent of area of cross-section
B. Directly proportional to the length of the conductor
C. Directly proportional to the area of cross section.
D. Inversely proportional to the length of the conductor


In Millikan's oil drop experiment an oil drop of radius \( r \) and charge \( Q \) is held in equilibrium between the plates of a charged parallel plate 'capacitor when
the potential difference is \( V . \) To keep a
drop of radius \( 2 r \) and with a charge \( 2 Q \)
in equilibrium between the plates, the potential difference required will be :
A . \( 8 V \)
в. \( 4 V \)
\( c .2 V \)
D. \( 1 V \)


A \( 4 \mathrm{cm} \) tall object is placed on the
principal axis of a convex lens. The distance of the object from the optical
centre of the lens is \( 12 \mathrm{cm} \) and its sharp image is formed at a distance of \( 24 \mathrm{cm} \) from it on a screen on the other side of
the lens. If the object is now moved a
little away from the lens, in which way (towards the lens or away from the lens) will he have to move the screen to get a
sharp image of the object on it again? How will the magnification of the image be affected?


The set of all \( x \) in \( (-\pi, \pi) \) satisfying \( |4 \sin x-1|<\sqrt{5} \) is
\( \boldsymbol{x} \boldsymbol{\epsilon}\left(-\boldsymbol{\pi},-\frac{\boldsymbol{k} \boldsymbol{\pi}}{\mathbf{1 0}}\right) \cup\left(-\frac{\boldsymbol{\pi}}{\mathbf{1 0}}, \frac{\boldsymbol{\pi}}{\mathbf{1 0}}\right) \cup \)
\( \left(\frac{k \pi}{10}, \pi\right) . \) Find the value of \( k \)


Two spheres \( A \) and \( B \) moving in opposite
directions have velocities of \( 10 m s^{-1} \)
and \( 20 m s^{-1} . \) The two spheres collide
with each other elastically. If \( A \) continues to move in the same
direction at \( 4 m s^{-1}, \) the velocity of
sphere B just after the collision is
A. \( 34 m / s \) in the same direction
B. \( 34 m / s \) in the opposite direction
c. \( 26 m / s \) in the same direction
D. \( 34 m / s \) in the opposit direction


What will be the molality of the solution containing 18.25 g of \( H C l \) gas in 500 g of water?
\( \mathbf{A} \cdot 0.1 \mathrm{m} \)
B. \( 1 \mathrm{m} \)
c. \( 0.5 \mathrm{m} \)
D. 2 \( m \)


Let \( \mathrm{p}, \mathrm{q}, \mathrm{r} \in \boldsymbol{R}^{+} \) and \( 27 p q r \geq(p+q+ \)
\( r)^{3} \) and \( 3 p+4 q+5 r=12 \) then \( p^{3}+ \)
\( \boldsymbol{q}^{4}+\boldsymbol{r}^{\boldsymbol{5}} \) is equal to
\( A \cdot 2 \)
B. 6
\( c \cdot 3 \)
D. None of these


Why do coastal areas experience less contrasts in temparature conditions?
A. Due to moderating effect of the seas
B. Due to land mass
c. Due to heat conditions
D. Due to rotation of the earth


\( \boldsymbol{f}(\boldsymbol{x})=\mathbf{2} \boldsymbol{x}+\mathbf{1}, \boldsymbol{a}=\mathbf{1}, \boldsymbol{l}=\mathbf{3} \) and \( \boldsymbol{\epsilon}= \)
\( 0.001, \) then \( \delta>0 \) satisfying \( 0<\mid x- \)
\( \boldsymbol{a} \mid<\boldsymbol{\delta} \) such that \( |\boldsymbol{f}(\boldsymbol{x})-\boldsymbol{l}|<\boldsymbol{\epsilon}, \) is
A . 0.0005
B. 0.005
c. 0.001
D. 0.0001


Two whistles \( A \) and \( B \) produces notes of frequencies \( 600 \mathrm{Hz} \) and \( 596 \mathrm{Hz} \) respectively. There is a listener at the midpoint of the line joining them. Both
the whistles \( A, B \) and the listener start moving with speed \( 30 \mathrm{m} / \mathrm{s} \) in the same direction. If the speed of the sound is \( 330 \mathrm{m} / \mathrm{s} \), the number of beats that
will be heard by the listener are:
\( A \cdot 2 \)
B. 4
\( c \cdot 6 \)
D.


Where are the field lines most
concentrated around a bar magnet?
A. At the North Pole.
B. At the centre.
c. At both poles
D. At the South Pole


The animal which lives in polar regions
is
A. Nightingale
B. Frog
c. Polar bear
D. Fish


Ultramicroscope works on the principle
of:
A . light reflection
B. light absorption
c. light scattering
D. light polarization


Match the column.


lonic radius in a group while moving down?
A. remains same from top to bottom
B. decreases from top to bottom
c. increases from top to bottom
D. first increases and then decreases


Two circular coils can be arranged in
any of three situations as shown in the
figure. Their mutual inductance will be:
A. maximum in situation (i)
B. maximum in situation (ii)
c. maximum in situation (iii)
D. same in all situation


Which of the following compounds is
expected to be optically active?
\( \mathbf{A} \cdot\left(C H_{3}\right)_{2} C H C H O \)
в. \( C H_{3} C H_{2} C H_{2} C H O \)
c. \( C H_{3} C H_{2} C H(B r) C H O \)
D. \( C H_{3} C H_{2} C B r_{2} C H O \)


The correct order of stability of the halous acids in aqueous solution is:
A. \( \mathrm{HClO}<\mathrm{HBrO}<\mathrm{HlO} \)
B. \( \mathrm{HClO}>\mathrm{HBrO}<\mathrm{HlO} \)
c. \( \mathrm{HClO}>\mathrm{HBrO}> \) HlO
D. HClO < HBrO > HlO


Matter is
A. everything around you
B. anything that has mass and takes up space
C . anything that has mass
D. none of the above


The time in which activity of an element reduces to \( 90 \% \) of its original value is:
The half-life period of element is \( 1.4 \times \)
\( 10^{10} \) years.
A \( \cdot 2.128 \times 10^{9} \) years
B . \( 1.578 \times 10^{7} \) years
c. \( 6.954 \times 10^{7} \) years
D. none of these


Fill in the blank:
Earth's plates are in motion.
A . circular
B. vibrational
c. rotational
D. continual


An ordinary die has four blank faces.
One face marked \( 2, \) an other marked 3
Then the probability of obtaining a total of exactly 12 in 5 throws is
A \( \cdot \frac{15}{6^{4}} \)
в. \( \frac{10}{6^{4}} \)
c. \( \frac{5}{6^{4}} \)
D. \( \frac{6}{6^{4}} \)


\( \Delta A B C \) is a right angled at \( A, \) the value
of \( \tan B \times \tan C \) is:
\( A \cdot O \)
B.
\( c \cdot-1 \)
D. None of the above


Q Type your question
over a trictionless light tixed pulley by an inextensible string of negligible
mass. The other end of the string is
pulled by a constant force \( \boldsymbol{F} \) in the
vertically downward direction. The
linear momentum of the block
increases by \( 2 k g m s^{-1} \) in \( 1 s \) after the
block starts from rest. Then:
\( \left(\text { Given } g=10 m s^{-2}\right) \)
This question has multiple correct options
A. The tension in the string is \( F \)
B. The tension in the string is \( 3 N \)
c. The work done by the tension on the block is \( 20 \mathrm{J} \) during this \( 1 s \)
D. The work done against the force of gravity is 10


Which of the following represent \( s p- \)
\( s p-s p^{2}-s p-s p^{2}-s p^{3} \)
hybridization from left to right order?
\( A \)
\( C H_{2}=C H-C=C-C \equiv N \)
B. \( C H \equiv C-C H=C=C H-C H_{3} \)
c.
\( N \equiv C-C-C-C H-C H_{3} \)
\( D \)


If \( A B C D \) is a parallelogram and \( E, F \)
are the centroids of \( \triangle A B D \) and \( B C D \)
respectively, then \( \boldsymbol{E} \boldsymbol{F} \) equals
\( \mathbf{A} \cdot A E \)
в. \( B E \)
c. \( C E \)
D. \( D E \)


Oxidation number of iodine in
\( I O_{3}^{-}, I O_{4}^{-}, K I \) and \( I_{2} \) respectively
are
A. -1,-1,0,+1
B. +3,+5,+7,0
\( \mathbf{c} .+5,+7,-1,0 \)
D. -1,-5,-1,0
E. -2,-5,-1,0


Evaluate \( \int_{0}^{\pi / 2} \frac{\cos ^{2} x}{1+3 \sin ^{2} x} d x \)


Two sound sources of sound are placed
along the diameter of a circle of radius
\( \boldsymbol{R}(\boldsymbol{R}>>\mathbf{4} \boldsymbol{\lambda}) \) How many minima will be
heard as one moves along the perimeter
of circle?
\( A \cdot 16 \)
В. 12
\( c \cdot 4 \)
\( D \)


A balloon initially at rest, starts rising from the ground with an acceleration of
\( 2 m / s^{2} . \) After \( 4 s, \) a stone is dropped
from a balloon. In one second of time
after the drop, the stone will cover a
distance of \( \left(\boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{2}\right) \)
A. \( 3.0 \mathrm{m} \)
в. 3.4 m
\( \mathbf{c} .3 .8 \mathrm{m} \)
D. \( 2.6 \mathrm{m} \)


Boiling point of water at normal atmospheric pressure is
\( \mathbf{A} \cdot 0^{\circ} C \)
B. \( 100^{\circ} \mathrm{C} \)
c. \( 110^{\circ} \mathrm{C} \)
D. \( -4^{\circ} \mathrm{C} \)


The half life of Uranium - 233 is 160000
years i.e., Uranium 233 decays at a
constant rate in such a way that it reduces to \( 50 \% \) in 160000 years. in how
many years will it reduce to \( 25 \% ? \)
A. 80000 years
B. 240000 years
c. 320000 years
D. 40000 years


Write the main product formed when propanal reacts with the following
reagents:
(i) 2 moles of \( C H_{3} O H \) in presence of
dry \( \boldsymbol{H} \boldsymbol{C l} \)
(ii) Dilute \( N a O H \)
(iii) \( H_{2} N-N H_{2} \) followed by heating
with \( K O H \) in ethylene glycol


The number of elements present in fourth period is:
A . 32
B. 8
\( c \cdot 18 \)
\( D \)


To use Charles' Law, which of the
following needs to remain constant?
A. Pressure and the number of moles of a gas
B. Pressure and temperature
C. Temperature and the number of moles of a gas
D. Pressure and volume
E. Temperature and volume


Give four examples of heterogeneous catalysis.


When \( 1 k g \) of ice at \( 0^{\circ} C \) melts to water
at \( 0^{\circ} \mathrm{C}, \) the resulting change in its entropy, taking the latent heat of ice to
be \( 80 c a l / C^{o} ? \)
A. 273 cal / \( K \)
B . \( 8 \times 10^{4} c a l / K \)
c. 80 cal \( K \)
D. \( 293 c a l / K \)


Figure depicts the charge in conc. of species \( x \& y \) for reaction \( 2 x \rightarrow y, \) as a
function of time the point of inter
section of two curves represents?
\( A \cdot t_{1 / 2} \)
В \( \cdot t_{1 / 3} \)
\( c \cdot t_{1 / 4} \)
\( \mathbf{D} \cdot t_{2} \)


If \( \sin ^{-1}(1-x)-2 \sin ^{-1} x=\pi / 2, \) then
\( x \) equals-
в. \( _{0, \frac{1}{2}} \)
c. 0
D. None of these


If each side of an equilateral triangle is doubled then its angle will
A. become half
B. be doubled
c. be tripled
D. remain same


An element 'X' with atomic number 114
has recently been discovered. Its IUPAC name is:
A. Eka-lead
B. Ununfortium
c. Ununquadium
D. Bohrium


Two identical conductors \( P \) and \( Q \) are
placed on two frictionless rails \( R \) and \( S \)
in a uniform magnetic field directed
into the plane. If \( P \) is moved in the
direction shown in figure with a
constant speed, then rod \( Q \)
\begin{tabular}{c|c|c}
& \( P \) & \( Q \) \\
& & \\
\( \times \) & \( \times \) & \( \times \) \\
\hline\( \times \) & \( \widehat{V} \) & \( \times \) & \( \times \) \\
\hline\( s \) & & & \\
\hline\( \times \) & \( \times \) & \( \times \) \\
\hline
\end{tabular}
A. will be attracted toward \( P \)
B. will be repelled away from \( P \)
c. will remain stationary
D. may be repelled away or attracted toward \( P \)
E. answer required


Two painters are working from a wooden board \( 5 \mathrm{m} \) long suspended from the top of a building by two ropes attached to the ends of the plank. Either rope can withstand a maximum tension of 1040
N. Painter A of mass \( 80 \mathrm{kg} \) is working at
a distance of \( 1 \mathrm{m} \) from one end. Painter
B of mass \( 60 \mathrm{kg} \) is working at a
distance of \( x \) m from the centre of mass
of the board on the other side. Take
mass of the board as \( 20 \mathrm{kg} \) and \( g= \)
\( 10 m s^{-2} . \) The range of \( x \) so that both the
painters can work safely is :
A \( \cdot \frac{1}{3}<x<\frac{11}{6} \)
в. \( 0<x<\frac{11}{6} \)
c. \( _{0<x}<\frac{10}{3} \)
D. \( \frac{1}{3}<x<2 \)


Which of the following provides shelter for many living organisms?
A. A-Horizon
B. B-Horizon
c. C-Horizon
D. None of the above


Spontaneous reactions are:
A. Endergonic
B. Exergonic
C . Energy neutral
D. Exer-endergonic reactions


Predict product(s) in the following reaction:
\( \boldsymbol{C l}_{2}+\boldsymbol{O} \boldsymbol{H}^{-} \stackrel{\boldsymbol{h} o t}{\rightarrow} \)
This question has multiple correct options
A \( \cdot C l \)
в. \( C l O_{2} \)
c. \( O C l^{-} \)
D. \( C l O_{3}^{-} \)


Assertion
Anhydrous \( H_{2} S O_{4} \) undergoes
autoprotolysis \( \quad H_{2} S O_{4}+H_{2} S O_{4} \rightleftharpoons \)
\( \boldsymbol{H}_{3} \boldsymbol{S} \boldsymbol{O}_{4}^{+}+\boldsymbol{H} \boldsymbol{S} \boldsymbol{O}_{4}^{-} \)
Reason
Anhydrous \( H_{2} S O_{4} \) has very high electrical conductivity
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect.


The wave number of first line of Balmer
series of hydrogen atom is \( 15200 \mathrm{cm}^{-1} \) What is the wave number of first line of
Balmer series of \( L i^{2+} \) ion.
A. \( 15200 \mathrm{cm}^{-1} \)
В. \( 136800 m^{-1} \)
c. \( 76000 \mathrm{cm}^{-1} \)
D. \( 13680 \mathrm{cm}^{-1} \)


Explain how the use of CNG in automobiles has reduced pollution in our cities.


Divide the given polynomial by the given monomial.
\( \left(p^{3} q^{6}-p^{6} q^{3}\right) \div p^{3} q^{3} \)


Name the plant hormone that inhibits plant growth and metabolism. What is
the role of this hormone in seed
development


If the denominator of a fraction has only
factors of 2 and factors of 5 , the decimal
expression
A. has equal numerator and denominator
B. becomes a whole number
c. does not terminate
D. terminates


Q Type your question
indices of refraction are given for water
and for air. The angle the light ray makes with the normal in air is shown.
What angle does the light ray make with the normal as it approaches the
boundary from the water?
The angles in the drawing are not
necessarily drawn with accurate
measurements.
\( A \cdot 30.0^{\circ} \)
B \( \cdot 29.7^{\circ} \)
c. \( 33.1^{\circ} \)
D \( .58 .5^{\circ} \)
\( E \)


Bud dormancy is induced by
\( A \cdot \) IAA
B. GAA
c. ABA
D. ethylene.


Which one is not an excretory organ?
A. skin
B. Kidneys
c. Intestine
D. Liver


The force of interaction between two
atoms is given by \( \boldsymbol{F}=\boldsymbol{\alpha} \boldsymbol{\beta} \exp \left(-\frac{\boldsymbol{x}^{2}}{\boldsymbol{\alpha k t}}\right) \)
where \( x \) is the distance, \( k \) is the
Boltzman constant and \( \boldsymbol{T} \) is
temperature and \( \alpha \) and \( \beta \) are two
constants. The dimension of \( \beta \) is
A \( \cdot M^{2} L^{2} T^{-2} \)
B. \( M^{2} L T^{-4} \)
c. \( M^{0} L^{2} T^{-4} \)
D. \( M L T^{-2} \)


Vegetative propagation refers to formation of new plants from
A. Stem, roots and leaves
B. Leaves, flowers and seeds
c. stem, roots and seeds
D. Fruits, seeds and spores


All waves can be classified into two
categories which are
A. Sound waves and electromagnetic waves
B. Transverse waves and electromagnetic waves
C. Longitudinal waves and electromagnetic waves
D. Transverse waves and longitudinal waves


Let tangents at \( A\left(z_{1}\right) \) and \( B\left(z_{1}\right) \) are drawn to the circle \( |z|=2 . \) Then which of the following is/are CORRECT ?
A \( \cdot \) The equation of tangent at \( A \) is given by \( \frac{z}{z_{1}}+\frac{\bar{z}}{\overline{z_{1}}}=2 \)
B. If tangents at \( A\left(z_{1}\right) \) and \( B\left(z_{2}\right) \) intersect at \( P\left(z_{p}\right) \), then \( z_{p}=\frac{2 z_{1} z_{2}}{z_{1}+z_{2}} \)
c. slope of tangent at \( A\left(z_{1}\right) \) is \( \frac{1}{i}\left(\frac{z_{1}+\bar{z}_{1}}{z_{1}-\bar{z}_{1}}\right) \)
D. If points \( A\left(z_{1}\right) \) and \( B\left(z_{2}\right) \) on the circle \( |z|=2 \) are such that \( z_{1}+z_{2}=0, \) then tangents intersect at \( \frac{\pi}{2} \)


At the magnetic north pole of the earth,
the value of the horizontal component of earth's magnetic field and angle of dip are respectively.
A. zero, maximum
B. maximum,minimum
c. maximum,maximum
D. minimum,minimum


In a group of 15 women, 7 have nose studs, 8 have ear rings and 3 have neither. How many of these have both
nose studs and ear rings?
A . 0
B . 2
\( c .3 \)
\( D \)


A metre scale weighs 50 grams and carries 20 grams at one end, the scale balances when it is suspended at a
distance \( x \) from other endpoints. Then \( x \)
is equal to?
A . \( 35.7 \mathrm{cm} \)
в. 64.3 ст
c. \( 14.3 \mathrm{cm} \)
D. \( 50 \mathrm{cm} \)


The part of the ear that transmits sound vibrations to the brain is the
A. cochlea
B. Stirrup
c. Eardrum
D. Auditory nerve


Which of the following is diamagnetic?
A . \( N O \)
в. \( N O \)
c. \( N O^{+} \)
D. \( N O^{-2} \)


Which of the following constitutes a group of isoelectronic species?
A \( \cdot C O, N_{2}, O_{2}^{-} \)
в. \( N_{2}, C N^{-}, N O^{+} \)
\( \mathrm{c} \cdot O_{2}^{-}, N O, C_{2}^{2} \)
D. \( C l^{-}, A r, N A^{+} \)
E \( \cdot S^{2-}, C a^{2+}, C N^{-} \)


The table below shows the melting point of three liquids.
\( \begin{array}{lll}\text { Melting point } & \text { Boiling point } \\ \text { Alcohol } & -115^{\circ} \mathrm{C} & 78^{\circ} \mathrm{C} \\ \text { Mercury } & -39^{\circ} \mathrm{C} & 357^{\circ} \mathrm{C} \\ \text { Water } & 0^{\circ} \mathrm{C} & 100^{\circ} \mathrm{C}\end{array} \)
Which liquid is most suitable to be
used in a thermometer for measuring a
temperature range of \( -10^{\circ} \mathrm{C} \) to \( 95^{\circ} \mathrm{C} \)


Amino acid sequence, in protein synthesis is decided by the sequence of which one of the following?
\( A \cdot \) cDNA
B. rRNA
\( c \cdot \operatorname{tRNA} \)
D. mRNA


Establish the relation between moment
of inertia and angular momentum. Define moment of inertia on the basis of
this relation.


In alkyl halides, the homologous series of alkyl halide is represented as:
A. \( C_{n} H_{2 n+1} X \)
в. \( C_{n} H_{2 n+4} X \)
c. \( C_{n} H_{2 n+3} X \)
D. \( C_{n} H_{Z n+2} X \)


Solar energy stored in material such as wood, grain, sugar, and municipal waste is called:
A . fossil fuels
B. biomass
c. geothermal energy
D. natural gas


How will you obtain the following (Give only chemical equations)?
(i) \( N_{2} \) from \( N H_{3} \)
(ii) \( N H_{3} \) from \( N H_{4} C l \)


Non-relativistic protons move
reactilinearly in the region of space where there are uniform mutually perpendicular electric and magnetic fields with E and B. The trajectory of the
protons lie in the plane \( X \) -Y as shown in
fig. and forms an angle \( \phi \phi \) with \( X \) -axis. If the pitch of the helical trajectory
along which the protons will move after
the electric field is switched off is
Pitch \( =\frac{\boldsymbol{x} \boldsymbol{\pi} \boldsymbol{m} \boldsymbol{E}}{\boldsymbol{q} \boldsymbol{B}^{2}} \boldsymbol{t a n} \boldsymbol{\phi} \). Find \( \boldsymbol{x} \)


Select the incorrect statement
regarding medical termination of
pregnancy.
A. It is legal up to \( 12^{t h} \) week of pregnancy.
B. It cannot be done without surgery.
C. It is consider to be safe during first trimester.
D. It needs the assistance of qualified medical practitioners.


A raw egg and hard boiled egg are made
to spin on a table with the same angular momentum about the same axis. The
ratio of the time taken by the two to stop is
\( A \cdot=1 \)
в. \( <1 \)
\( c \cdot>1 \)
D. None of these


If \( \tan \alpha=2 \sqrt{2}, \) then the value of
\( \frac{\tan \alpha}{\frac{\sin ^{3} \alpha}{\cos \alpha}+\sin \alpha \cdot \cos \alpha} \)
\( \mathbf{A} \cdot \mathbf{0} \)
B. 2
c. \( 2 \sqrt{2} \)
\( D \)


The oxoanion which contains all
equivalent \( M-O \) bond is:
\( (I) C r O_{4}^{2-} \)
\( (I I) M n O_{4}^{-} \)
\( (I I I) C r_{2} O_{7}^{2-} \)
A. III only
В. \( I, I I, I I I \)
c. \( I, I I \)
D. I only


A chord of a circle is \( 12 \mathrm{cm} \) in length and its distance from the centre is 8 cm. The length of the chord of the same
circle which is at a distance of \( 6 \mathrm{cm} \)
from the centre is
\( A .30 \mathrm{cm} \)
B. \( 24 \mathrm{cm} \)
\( c .16 \mathrm{cm} \)
D. \( 18 \mathrm{cm} \)


Which of the following statements are true (T) and which are false (F)?

In any quadrilateral, if a pair of opposite sides is equal, it is a parallelogram.
A . True
B. False


Subtraction of +43 from -26 gives
A . -17
B. +17
\( c .-69 \)
D. +69


What are natural fibres? Explain with examples.


If \( \boldsymbol{A} \) is symmetric matrix and \( \boldsymbol{n} \in \boldsymbol{N} \)
write whether \( A^{n} \) is symmetric or skewsymmetric or neither of these two


The distance between 50 consecutive
crests is \( 10 \mathrm{cms} \). Find the wavenumber
A. \( 50 / \mathrm{m} \)
B. 500 / m
c. \( 250 / \mathrm{m} \)
D. 25/ \( m \)


Prove that for spherical mirrors the products of the distance of the object and the image to the principles focus is
always equal to the square of the principles focal length.


Evaluate \( \lim _{x \rightarrow 0} \frac{\sin x}{|x|} \)
A .
B. 0
c. -1
D. does not exist


The latus rectum of the hyperbola \( 16 x^{2}-9 y^{2}=144 \) is
A \( \cdot \frac{13}{6} \)
в. \( \frac{32}{3} \)
\( c \cdot \frac{8}{3} \)
D. \( \frac{4}{3} \)


Electron vacancy in PSI in ETS is replaced by
A. PSII
B. Plastocyanin
c. Photolysis of water
D. None of these


Bacteria, fungi and lower plants survive during adverse conditions by
A. Suspended growth
B. Migration
c. Diapause
D. Formation of thick-walled spores


Find \( |\vec{a}| \) and \( |\vec{b}|, \) if \( (\vec{a}-\vec{b}) \cdot(\vec{a}+\vec{b})= \)
\( \mathbf{2 7} \) and \( |\overrightarrow{\boldsymbol{a}}|=\mathbf{2}|\overrightarrow{\boldsymbol{b}}| \)


Anti-ageing hormone is
A. Thyroxine
B. Melatonin
C. Estrogen
D. Testosterone


In which of the following cases entropy decreases?
A. Solid changing to liquid
B. Expansion of a gas
c. crystals dissolve
D. Polymerisation


Pancreatic juice is released into
A. Duodenum
B. Ileum
c. Stomach
D. Jeiunum


\( \lim _{x \rightarrow 0} \frac{(1+x)^{5}-1}{(1+x)^{3}-1}= \)
A . 0
B.
\( c \cdot \frac{5}{3} \)
D. 3


An image which can be only seen by the eye but cannot be taken on a screen is called a
A. virtual image
B. real image
c. artificial image
D. shadow


Which of the the following is correct representation of the complex number:
\( (a, b) \)
в. \( (a, 0) \times(0, b) \)
c. \( (a, 0)+(0, b) \)
D. None of these


Match the following with correct
combination
\begin{tabular}{lll|l}
& Column-I & & Column-II \\
a. & Anthoceros & 1. & Walkin fern \\
b. & Asplenium & 2. & Alga \\
c. & Sargassum & 3. & Inferae \\
d. & Prothallus & 4. & Gametophyte \\
e. & Asterales & 5. & Hornwort \\
& 6. & Livewort
\end{tabular}
\( A \)
\( a-6, b-5, c-1, d-3, e-4 \)
\( B \cdot a-5, b-4, c-3, d-2, e-1 \)
\( C \cdot a-5, b-1, c-2, d-4, e-3 \)
D. \( a-3, b-2, c-1, d-5, e-4 \)
\( E \cdot a-1, b-4, c-3, d-5, e-2 \)


Similar charges each other
whereas opposite charges each
other.
A. repel, attract
B. attract, repel
c. repel, repel
D. attract, attract


Find the compound interest on
\( R s .1000 \) at the rate of \( 8 \% \) per annum
for one year, When interest is compounded yearly.


What is the temperature of Fahrenheit
scale corresponding to \( -10^{\circ} \mathrm{C} \) ?
\( \mathbf{A} \cdot 14^{\circ} F \)
B. \( -14^{\circ} F \)
\( \mathbf{c} \cdot 22^{\circ} F \)
D . \( 24^{\circ} F \)


Assertion
\( N C l_{3} \) undergoes hydrolysis.
Reason
Chlorine possesses vacant d-orbitals.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is
not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Which of the following is used in cancer treatment?
\( \mathbf{A} \cdot \frac{1331}{51} \)
B . \( _{15}^{22} P \)
\( \mathrm{c} \cdot_{27}^{60} \mathrm{Co} \)
\( \mathrm{D} \cdot_{1}^{2} \mathrm{H} \)


A sum of \( R s .10,000 \) is borrowed at a rate of interest \( 15 \% \) per annum for 2 years. Find the simple interest on this sum and the amount to be paid at the
end of 2 years.


On treating bleaching powder with ethyl alcohol it gives chloroform.
A. True
B. False


Which of the sport is most affected by variation of 'g'?
A. swimming
B. jump
c. horse riding
D. shooting
E. all are equally affected


If \( \sin x=\frac{2 t}{1+t^{2}}, \) tany \( =\frac{2 t}{1-t^{2}}, \) then
\( d y \) is equal to \( A_{n} \)
A . -
B. 2
\( c \cdot 0 \)
D.


The number of \( C l^{-} \) and \( C a^{2+} \) ions in
\( 222 g \) of \( C a C l_{2} \) is:
A \( \cdot 4 N_{A}, 2 N_{A} \)
в. \( 2 N_{A}, 4 N_{A} \)
C \( .1 N_{A}, 2 N_{A} \)
D. \( 2 N_{A}, 1 N_{A} \)


Hydrocarbon PCB is called
\( a s \)
A. polychlorinated biphenyls
B. polycalcium biphenyls
C . polychlorinated bicarbonate
D. none of the above


If \( \boldsymbol{A}=\{1,2\}, \boldsymbol{B}=\{\mathbf{2}, \boldsymbol{3}\} \) and \( \boldsymbol{C}= \)
\( \{3,4\}, \) then what is the cardinality of
\( (\boldsymbol{A} \times \boldsymbol{B}) \cap(\boldsymbol{A} \times \boldsymbol{C}) \)
\( \mathbf{A} \cdot \mathbf{8} \)
B. 6
\( c \cdot 2 \)
D.


As per Braun's principle, yield of Ammonia will be more in Haber's
process under conditions
\( \boldsymbol{L}=\operatorname{Low} ; \boldsymbol{H}=\operatorname{high} ; \boldsymbol{T}=\operatorname{Temp} ; \boldsymbol{P}= \)
Pressure)
A. \( L T ; L P \)
B. \( L T ; H P \)
c. \( H T ; H P \)
D. \( H T ; L P \)


The position vector of the vertices of a triangle \( A B C \) are \( \hat{i}, \hat{j}, \hat{k} \) then the
position vector of its orthocentre is
\( \mathbf{A} \cdot \hat{i}+\hat{j}+\hat{k} \)
B . \( 2(\hat{i}+\hat{j}+\hat{k}) \)
c \( \cdot \frac{1}{3}(\hat{i}+\hat{j}+\hat{k}) \)
D \( \cdot \frac{1}{\sqrt{3}}(\hat{\imath}+\hat{j}+\hat{k}) \)


The specific conductance of a
\( N / 10 K C I \) at \( 25^{0} C \) is
0.0112 oh \( m^{-1} c m^{-1} . \) The resistance of
cell containing solution at the same temperature was found to be 55ohms.
The cell constant will be:
A \( \cdot 6.16 \mathrm{cm}^{-1} \)
B. \( 0.616 c m^{-1} \)
c. \( 0.0616 \mathrm{cm}^{-1} \)
D. \( 616 \mathrm{cm}^{-1} \)


If the reactance of a choke coil is \( X_{L} \)
and its resistance is \( R \) then
A. \( X_{L}=R \)
в. \( X_{L}>>R \)
c. \( x_{L}<<R \)
D. \( X_{L}=\alpha \)


Two long thin parallel conductor are
kept very close to each other without
touching. One carries a current \( i \) and
the other has charge \( \lambda \) per unit length. An electron moving parallel to the
conductor is undeflected. If \( c \) is the
velocity of light. then :
This question has multiple correct options
A \( \cdot v=\frac{\lambda c^{2}}{i} \)
B. \( v=\frac{i}{\lambda} \)
c. \( c=\frac{i}{\lambda} \)
D. the electron may be at any distance from the conductor


toppr LoGin Jolv now
Q Type your question reacivul with
Phenolphthalien
solution Solution \( \begin{array}{ll}\text { pH } & \text { ne } \\ \text { Vlaue } & \begin{array}{l}\text { Phe } \\ \text { so }\end{array}\end{array} \)
1 нС।
A 7 Distilled
water No colour
change.
13 Naoн Turns into pink
colour.
Lemon
juice \( 2.5 \quad \) No colour
change. .
Nacı 7 \( c \) No colour
change.
Baking
Soda Tu Turns into pink
colour. into
yell
colo
(a) List out the acids in the above table.
(b) What is the nature of the solution
which gives pink colour with Phenolphthalein solution?
(c) List out the neutral solutions in the
above table.
(d) Name the strongest acid and the
strongest base among the given
solutions.


The specific heat capacities of two
bodies \( A \) and \( B \) is 1: 2 and masses in the
ratio 3: 4 respectively. The ratio of their heat capacities is :
A .3: 2
B. 2:3
\( c \cdot 7: 16 \)
D. 3:8


If
\( \boldsymbol{a}_{1} \boldsymbol{a}_{2} \ldots \ldots \ldots \ldots \boldsymbol{a}_{\boldsymbol{n}} \boldsymbol{\epsilon} \boldsymbol{R}^{+} \boldsymbol{a} \boldsymbol{n} \boldsymbol{d} \boldsymbol{a}_{1} \boldsymbol{a}_{2} \ldots \ldots \boldsymbol{a}_{n}= \)
1 then the least value of \( \left(1+a_{1}+\right. \)
\( \left.\boldsymbol{a}_{1}^{2}\right)\left(\mathbf{1}+\mathbf{1}_{2}+\boldsymbol{a}_{2}^{2}\right) \ldots \ldots \ldots\left(1+\boldsymbol{a}_{n}+\boldsymbol{a}_{n}^{2}\right) \)
is
\( \mathbf{A} \cdot 3^{n} \)
В . \( n 3^{n} \)
\( c \cdot 3^{3 n} \)
D. Data inadequate


Friction is needed to produce motion or
prevent motion. Which of the following
statements suits for each application shown in fig (i) and fig (ii)? why?


f the magnetic induction at the center of the rotating sphere is \( \vec{B}= \) \( \frac{2}{X} \mu_{0} \omega \sigma R(\hat{k})\left[\quad \sin ^{3} \theta=\frac{1}{4}(3 \sin \theta\right. \)
Find \( X ? \)


The thermal decomposition of a compound is of first order. If \( 50 \% \) of a sample of the compound is decomposed in 120 min how long will it
take for \( 90 \% \) of the compound to decompose?
A. 412 min
B. 399 min
c. \( 450 \mathrm{min} \)
D. 499 min


Which one of following pairs of gases is the major cause of greenhouse effect?
A. \( C O_{2} \) and \( O_{3} \)
в. \( C O_{2} \) and \( C O \)
c. \( C F C \) and \( S O_{2} \)
D. \( C O_{2} \) and \( N_{2} O \)


A steel wire if \( 1 ~ m \) long and \( 1 m m^{2} \)
cross section area is hanged from rigid end when weight of \( 1 k g \) is hang from it, then change in length will be (Young's coefficient for wire \( \boldsymbol{Y}=\mathbf{2} \times \)
\( \left.\mathbf{1 0}^{\mathbf{1 1}} \mathbf{N} / \boldsymbol{m}^{2}\right) \)
A. \( 0.5 \mathrm{mm} \)
B. \( 0.25 \mathrm{mm} \)
c. \( 0.05 \mathrm{mm} \)
D. \( 5 m m \)


Which of the following is correct?
A \( . A \cup B=\phi \)
B. \( A \cap B=\phi \)
c. \( A+B= \)
D. None of the above


The hysteresis cycle for the material of a transformer core is?
A. Short and wide
B. Tall and narrow
c. Tall and wide
D. short and narrow


If a simple pendulum has significant amplitude (up to a factor of \( 1 / \) e of original) only in the period between \( t= \) \( 0 s \) to \( t=\tau s, \) then \( \tau \) may be called the
average life of the pendulum. When the spherical bob of the pendulum suffers a retardation (due to viscous drag) proportional to its velocity, with b' as the constant proportionality, the average life time of the pendulum in seconds (assuming damping is small) in second :-
A. \( \frac{0.693}{b} \)
B. \( b \)
c. \( \frac{1}{b} \)
D. \( \frac{2}{b} \)


When \( C l_{2} \) water is added to an aqueous solution of potassium halide in the presence of chloroform, a violet color is
obtained. On adding more of \( C l_{2} \) water, the violet color disappears and a colorless solution is obtained. This test
confirms the presence of the following in aqueous solution:
A . iodide
B. bromide.
c. chloride.
D. iodide and bromide


A hydrogen atom is in the excited state
of the principal quantum number \( n . \) It
emits a photon of wavelength \( ^{\prime} \lambda^{\prime} \) when
returns to ground state. The value of \( n \)
is
\( \mathbf{A} \cdot \sqrt{\lambda R(\lambda R-1)} \)
B. \( \sqrt{\frac{\lambda R-1}{\lambda R}} \)
\( \mathbf{c} \cdot \sqrt{\frac{\lambda R}{\lambda R-1}} \)
D. \( \sqrt{\lambda(R-1)} \)


In pyrrole
The electron density is maximum on


is most commonly used to refer to the amount borrowed or the
amount still owed on a loan, separate
from interest.
A. Interest
B. Rate
c. Principle
D. Amount


Which of the following organizations developed 'Saheli', an oral contraceptive drug for females?
A. National Institute of Pharmaceutical Education And Research (NIPER)
B. Central Drug Research Institute(CDRI)
c. International Centre for Genetic Engineering and Biotechnology (ICGEB)
D. Indian Institutes of Science Education \& Research Bhopal


Formation of benzene from acetylene is :
A. Trimerisation
B. Tetramerisation
c. Dimerisation
D. condensation


Evaluate
\( \lim _{x \rightarrow \infty} 2^{-x} \sin \left(2^{x}\right) \)


Hybridization and structure of \( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{4} \) is:
A \( \cdot s p^{3} d \), triogonal bipyramidal
B \( \cdot s p^{3} \), tetrahedral
c. \( s p^{3} d^{2} \), square planar
D. \( s p^{3} d^{2} \), hexagonal


A \( _{-1-}- \) experiment is a process
whose outcome is undetermined.
A. variable
B. random
c. event
D. sample


Choose the wrong statement when we
measure the temperature of a water
kept in a beaker:
A. Thermometer should be kept vertical so that the bulb does not touch sides or bottom of the beaker
B. Thermometer should be kept vertical so that the bulb touches the bottom of the beaker
C. Thermometer should not be kept tilted so that the bulb touches sides or bottom of the beaker
D. Thermometer should be kept tilted without touching bottom or sides of the beaker


A man walks in a horizontal circle round
the foot of a pole which is inclined to the
vertical. The foot of the pole is at the
centre of the circle. The greatest and least angles which the pole subtends at his eye are \( \tan ^{-1}\left(\frac{9}{5}\right) \) and \( \tan ^{-1}\left(\frac{6}{5}\right) \)
respectively and when he is midway between the corresponding positions, the angle is \( \theta \). If the man's height be neglected, find the length of the pole.


Assertion
If the distance traveled by body is directly proportional to the square of
time taken, then its speed is increasing
with time.
Reason
The speed is equal to the time rate of change of distance.
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


\( \boldsymbol{F}_{1} \) particle of oxysome
A. Releases proton energy
B. Utilises proton energy
C. Has no role in energy consumption
D. Lies in outer chamber


Why is the metre bridge suitable for
resistances of moderate values only?


In human sex determination, the key factor is
A. Y chromosome
B. X chromosome
c. Both A and B
D. None of the above


Two wires of the same material and
length but diameters in ratio 1: 2 are
stretched by the same force. The potential energy per unit volume for the two wires when stretched will be in
the ratio :-
\( \mathbf{A} \cdot 16: 1 \)
B . 4: 1
c. 2: 1
D. 1: 1


Midrib is observed in which part of leaf?
A. Leaf base
B. Lamina
c. Petiole
D. stipule


Reaction at \( 0-5^{0} C \) between aniline,
\( N a N O_{2} \) and HCl is known
as
A. Suphonation of benzene
B. Acylation of aniline
C . Alkylation of aniline
D. Diazotisation


The diagram given shows the internal structure of a spinal cord depicting a phenomenon. Study the diagram and answer the question. Name the parts numbered 1,2 and 3


The common ratio for the term \( \boldsymbol{a}_{n}= \)
\( 2 \times\left(\frac{1}{4}\right)^{n-1} \) is
A \( \cdot \frac{1}{2} \)
в. \( \frac{1}{3} \)
\( c \cdot \frac{1}{4} \)
D.


An a.c of \( 50 H z \) and \( 1 A \) peak value flow
in the primary coil of a transformer. The mutual inductance between primary
and secondary coils is \( 1.5 H . \) Then peak value of induced emf across secondary coil is
A. \( 75 \pi \) volt
B . \( 150 \pi \) volt
c. 225 volt
D. 300volt


\( H_{2} S O_{4} \) can not be used to prepare HI
from KI as
A. its reaction with KI is very slow.
B. it oxidises HI to iodine
c. it disproportionates HI,
D. it reduces HI


NaOCl is used as a bleaching agent
and sterilising agent. It can be prepared by the action of:
A. \( N a C l \) with \( H_{2} O \)
B. \( N H_{4} C l \) with \( N a O H \)
C. \( C l_{2} \) with cold and dil. \( N a O H \)
D. \( C l_{2} \) with hot and conc. \( N a O H \)


The function/s of the renin produced by kidney is/are
A. Stimulate hematopoiesiss
B. Change angiotensinogen into angiotensin
c. Influence ultrafiltration
D. All of the above


A radioactive element decays by \( \beta \)
emission. If the mass of parent and
daughter nuclide are \( m_{1} \) and \( m_{2} \)
respectively, the energy liberated during the emission is :
A. \( \left[m_{1}-m_{2}-2 m_{e}\right] c^{2} \)
в. \( \left[m_{1}-m_{4}-2 m_{e}\right] c^{1} \)
c. \( \left[m_{1}-m_{1}-3 m_{e}\right] c^{3} \)
D. None of these


If (5,12) and (24,7) are the foci of an
ellipse passing through the origin, then the eccentricity of the conic is
A \( \cdot \frac{\sqrt{386}}{12} \)
B. \( \frac{\sqrt{386}}{13} \)
c. \( \frac{\sqrt{386}}{25} \)
D. \( \frac{\sqrt{386}}{38} \)


How many organisms in the list given are autotrophs Lactobacillus, Nostoc, Chara, Nitrosomonas, Nitrobacter
Streptomyces, Trypanosoma, Porphyra, Wolffia
A. Four
B. Five
\( c . \) six
D. Three


Arrange the following compounds in decreasing order of basic strength \( ( \) In gaseous phase):
\( N H_{3},\left(C_{2} H_{5}\right)_{2} N H,\left(C H_{3}\right)_{3} N \)


The cost of levelling a square lawn at Rs.15 per square meter is \( R s .19,935 \)
Find the cost of fencing the lawn at
Rs.22 per meter.


\( \int_{1}^{e} \log x d x=_{-} \)
A \( \cdot e+1 \)
в. \( e-1 \)
\( \mathbf{c} \cdot e+2 \)
\( D \)


A point charge \( \boldsymbol{q}=\mathbf{1 0 0} \mu \boldsymbol{C} \) is located in
the \( x \) -y plane at the point with position vector \( \vec{r}_{0}=2 \hat{i}+3 \hat{j}+\hat{k} . \) What is the
electric field vector(in \( \mathrm{kV} / \mathrm{m} \) ) at the
point with position vector \( \vec{r}=8 \hat{i}- \) \( \mathbf{5} \hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} ? \)
\( \mathbf{A} \cdot 4 \cdot 2 \hat{i}-5.6 \hat{j} \)
в. \( 6 \hat{i}-8 \hat{j} \)
c. \( 54 \hat{i}-72 \hat{j} \)
D. \( 5.4 \hat{i}-7.2 \hat{j} \)


A circle of radius \( 10 \mathrm{cm} \) has its centre at the vertex \( C \) of an equilateral triangle ABC and passes through the other two vertices. The side AC extended through C intersects the circle at D. The number
of degrees of angle ADB is:
A \( \cdot 15^{\circ} \)
B . \( 30^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 90^{\circ} \)
E \( .120^{\circ} \)


In the triangle \( A B C, P Q \) is parallel to
\( B C . \) Find the length of \( x \) and \( y \)
A. \( x=26.25, y=17.1 \)
B. \( x=17.1, y=26.25 \)
c. \( x=17.34, y=26.57 \)
D. \( x=26.45, y=17.33 \)


Two coins are available, one fair and the
other two-headed. Choose a coin and
toss it once; assume that the unbiased coin is chosen with probability \( \frac{3}{4} . \) Given that the outcome is head the probability that the two-headed coin was chosen, is
A.
в. \( \frac{2}{5} \)
\( c \cdot \frac{1}{5} \)
D.


During a nuclear fission reaction:
This question has multiple correct options
A. a heavy nucleus breaks in two or more fragment by itself
B. a light nucleus bombarded by thermal neutrons breaks up
C. a heavy nucleus bombarded by thermal neutrons breaks up
D. two light nuclei combine to give a heavier nucleus and possibly other products


Find the surface area of a sphere of
radius:
\( \mathbf{1 4} c \boldsymbol{m} \)


Quicklime is a chemical compound
known as calcium oxide \( \boldsymbol{C a}(\boldsymbol{O} \boldsymbol{H})_{2} \)
If true enter 1 ,if false enter 0
\( A \cdot O \)


A needle of length \( 5 \mathrm{cm}, \) placed \( 45 \mathrm{cm} \) from a lens form an image on a screen placed \( 90 \mathrm{cm} \) on the other side of the
lens. The type of lens and its focal length
are :
A. convex, 30 cm
B. concave, 30 cm
c. convex, \( 60 \mathrm{cm} \)
D. concave, 60 cm


Predict whether the following statement
is true or false.

The most abundant metal in the earth's
crust is Al.
If true enter \( 1, \) else enter 0


When white light is passed through an upside down (inverted) prism then
A. White light is obtained
B. Spectrum is obtained with violet colour undergoing maximum and red colour undergoing minimum deviation
c. spectrum is obtained with red colour undergoing maximum deviation and violet colour undergoing minimum deviation
D. Light gets blocked


A graph between \( \log t_{1 / 2} \) and \( (\log \mathrm{a}) \)
(abscissa) a being the initial
concentration of \( A \) in the reaction. For
reaction \( A \rightarrow \) product, the rate law is:
A \( \cdot \frac{-d(A)}{d t}=k \)
B. \( \frac{-d(A)}{d t}=k[A] \)
\( \mathbf{c} \cdot \frac{-d(A)}{d t}=k[A]^{2} \)
D. \( \frac{-d(A)}{d t}=k[A]^{3} \)


If the bisector of an angle of a triangle bisects the opposite side, then prove that the triangle is isosceles.


If \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{cc}\frac{x\left(3 e^{1 / x}+4\right)}{2-e^{1 / x}}, & x \neq 0 \text { then } f(x) \\ 0 & , x=0\end{array}\right. \)
A. \( f \) is not continuous
B. \( f \) is continuous but not differentiable at \( x=0 \)
C \( \cdot f^{\prime \prime}(0) \) exist
\( \mathbf{D} \cdot f^{\prime}(0+)=2 \)


Gelly is a colloidal solution of :
A. solid in liquid
B. liquid in solid
c. liquid in liquid
D. solid in solid


A ship moves along the equator to the
east with velocity \( v_{0}=30 k m / h . \) The
southeastern wind blows at an angle
\( \varphi=60^{\circ} \) to the equator with velocity
\( \boldsymbol{v}=\mathbf{1 5} \boldsymbol{k m} / \boldsymbol{h} . \) The angle \( \boldsymbol{\varphi}^{\prime} \) between the
equator and the wind direction in the
reference frame fixed to the ship is (in degrees)


The minimum number of \( C \) atoms an
alkyne must have to show
diasteromerism is:
\( A \cdot 4 \)
B. 5
\( c \cdot 6 \)
D.


State one relevant observation for each
of the following reactions:
Burning of ammonia in air.


The equivalent weight of \( M n O_{2} \) is equal to its molecular weight when it is converted to:
\( \mathbf{A} \cdot M n_{2} O_{3} \)
B. \( M n O \)
c. \( M n O_{4}^{2} \)
D. \( M n O_{4}^{-} \)


The decreasing order of acidic character of the following is:
(I) \( E t O H \)
(II) \( M e- \) COOH
(III) \( M e O O C-C H_{2}-C O O M e \)
A \( . I>I I I>I V>I \)
B. \( I I>I I I>I>I V \)
c. \( I>I V>I I I>I I \)
D. \( I V>I>I I I>I I \)


The length of a tangent from a point \( \boldsymbol{A} \)
at distance \( 5 \mathrm{cm} \) from the centre of the
circle is \( 4 \mathrm{cm} \).Find the radius of the
circle.


Of the 1000 inhabitants of a town, \( 60 \% \)
are males of whom \( 20 \% \) are literate. If of
all the inhabitants \( 25 \% \) are literate, then
what per cent of the females of the town are literate?
A . \( 22.5 \% \)
B . \( 27.5 \% \)
c. \( 32.5 \% \)
D. 37.5\%


Find the odd one form the brackets and
give reason behind your selection. [Blur, Yellow ,Red,Green]


A cubical block of side a is moving with velocity v on a horizontal smooth plane
as shown in figure. It hits a ridge at point \( 0 . \) The angular speed of the block after it hits 0 is:
\( \mathbf{A} \cdot \frac{3 v}{4 a} \)
B. \( \frac{3 v}{2 a} \)
c. \( \sqrt{\frac{3}{2} c} \)
D. zero


How many \( P-O H \) bonds in
pyrophosphoric acid are?
A. Two
B. Three
c. Four
D. one


Study the graph. Explain how is oxygen concentration affected in the river when
sewage is discharged in it.


Fill in the blank:
Ursa Major :: Orion:
Hunter
A. Big Dipper
B. Leo Major
c. Great Bear
D. Saptarshi


If the sum of two unit vectors is a unit
vector, then the magnitude of their difference is:
A \( \cdot \sqrt{2} \)
B. \( \sqrt{3} \)
c. \( 1 / \sqrt{2} \)
D. \( \sqrt{5} \)


In mammals, the urinary bladder opens
into
A. Uterus
B. Urethra
c. vestibule
D. Ureter


In an ideal parallel LC circuit, the capacitor is charged by connecting it to a DC source which is then disconnected
The current in the circuit
A. becomes zero instantaneously
B. grows monotonically.
c. decays monotonically.
D. oscillates instantaneously


Light travels faster in air than that in glass. This is accordance with
A. wave theory of light
B. corpuscular theory of light
c. neither (a) nor (b)
D. Both (a) and (b)


A non-malleable and non-ductile metal
is \( ------ \) at room temperature
A . iron
B. silver
c. gold
D. zinç


Which type of ore is concentrated by froth floatation process?


Human shows
A. Radial symmetry
B. Asymmetry
C. Bilateral symmetry
D. All of the above


Answer the following:
(1) What is the effect of temperature on
ionic product of water \( (\boldsymbol{K} \boldsymbol{w}) \) ?
(2) What happen to the ionic product of
water \( (K w) \) if some acid is added to it?


When \( \overrightarrow{\boldsymbol{A}} \cdot \overrightarrow{\boldsymbol{B}}=-|\boldsymbol{A}||\boldsymbol{B}|, \) then
\( \mathbf{A} \cdot \vec{A} \) and \( \vec{B} \) are perpendicular to each other
B. \( \vec{A} \) and \( \vec{B} \) Act in the same direction
C . \( \vec{A} \) and \( \vec{B} \) Act in the opposite direction
D. \( \vec{A} \) and \( \vec{B} \) can act in any direction


Calculate the concentration of nitric
acid in moles per litre in a sample which has a density, \( 1.41 g m L^{-1} \) and
the mass per cent of nitric acid in it
being \( 69 \% \)


The magnitude of focal length of a concave mirror is \( f . A n \) object is placed at a distance \( x \) from the focus and
forms a real image. The magnification is :
A. \( -f / x \)
в. \( -x / f \)
c. \( -f /(f-x) \)
D. \( x /(x-f) \)


In an orbital, the signs of lobes indicate
the:
A. sign of the wave function
B. sign of the probability distribution
c. presence or absence or electron
D. sign of charge


A diatomic ideal gas is heated at constant volume until its pressure
becomes three times. It is again heated
at constant pressure until its volume is doubled. Find the molar heat capacity
for the whole process.


Ethanol has a higher boiling point than dimethyl ether though they have the same molecular weight. This is due to:
A. resonance
B. coordinate bonding
c. Hydrogen Bonding
D. ionic bonding


The Van't Hoff factor (i) for \( K_{2} S O_{4} \) is
\( A \)
B. 2
\( c \cdot 0 \)
D. 3


Which of the following occur with zinc in sulfides?
A. Boron
B. Aluminium
c. Thallium
D. Indium


Q Type your ques
\( 20^{\circ} \mathrm{C}:(1) 1 \) mole of solid
\( \left(C O O N H_{4}\right)_{2} H_{2} O \) is burned in oxygen
(2) 1 mole of solid \( (C O O H)_{2}\left(H_{2} O\right)_{2} \) is
burned in oxygen,
(3) 1 mole of solid
\( \left(C O O N H_{4}\right)_{2} H_{2} O \) is dissolved in a large excess of water, (4) 1 mole of solid
\( (C O O H)_{2}\left(H_{2} O\right)_{2} \) is dissolved in a
large excess of water, (5) 1 mole of oxalic acid in dilute solution is
neutralized with gaseous ammonia.
They found
(1) \( 189.86 k c a l,(2) \)
53.10kcal, (3) - 11.47kcal, (4)
\( -8.62 k c a l \)
(5) \( 43.13 k c a l ;(1) \) and were measured at constant volume, the
others at constant pressure. The end products of (1) and (2) were nitrogen, carbon-di-oxide and water. The heat of
formation for 1 mole of water from the
elements had previously been
determined as \( 68.35 k \) cal at constant
pressure and \( 20^{\circ} \mathrm{C} \). Find the change in
enthalpy when 1 mole of \( N H_{3} \) is formed
from the elements at \( 20^{\circ} \mathrm{C} \) (only
magnitude in nearest integer in kcal)


A wire of \( 1 \mathrm{m} \) long has an area of cross section of \( 2 \times 10^{-3} \mathrm{cm}^{2} \) and has a
resistance of 10 ohm. The resistivity of
the material of the wire is:
A \( \cdot 2 \times 10^{-6} \Omega c m \)
В. \( 2 \times 10^{-4} \Omega c m \)
c. \( 2 \times 10^{-2} \Omega c m \)
D. \( 2 \times 10^{-8} \Omega c m \)


Select the incorrect reaction from the
following.
\( \mathbf{A} \cdot 2 N a_{2} C r O_{4}+H^{+} \rightarrow N a_{2} C r_{2} O_{7}+2 N a^{+}+H_{2} O \)
B. \( 4 M n O_{2}+4 K O H+O_{2} \rightarrow 4 K M n O_{4}+2 H_{2} O \)
\( \mathbf{c} \cdot 2 M n O_{4}^{-}+5 C_{2} O_{4}^{2}+16 H^{+} \rightarrow 2 M n^{2+}+10 C O_{2}+8 H_{2} O \)
D. \( M n O_{4}^{-}+8 H^{+}+5 F e^{2+} \rightarrow 5 F e^{3+}+M n^{2+}+4 H_{2} O \)


f we plot volume of a certain mass of a
gas against temperature at constant
pressure, we get a straight line intersecting on the negative side at
\( -273^{\circ} C \) which explains about absolute
zero. This graph is known as:
A. isochor
B. isotherm
\( c . \) isotone
D. isobar


The length and breadth of a rectangular
field is \( 110 \mathrm{m} \) and \( 30 \mathrm{m} \) respectively. Calculate the length of the longest rod
which can measure the length and
breath of the field exactly.


The middle term of \( \left(\boldsymbol{x}-\frac{1}{\boldsymbol{x}}\right)^{2 n+1} \) is
\( \mathbf{A} \cdot^{2 n+1} C_{n} \cdot x \)
B. \( 2 n+1 C_{n} \)
C \( \cdot(-1)^{n} \cdot 2^{2+1} C_{n} \)
D \( \cdot(-1)^{n} \cdot^{2 n+1} C_{n} \cdot x \)


A red coloured mixed oxide \( (X) \) on
treatment with concentrate \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \)
gives a compound (Y). (Y) with HCI, produces a chloride compound (z) which can also be produced by treating
(X) with concentrate HCl. Compounds \( (X),(Y) \) and \( (Z) \) will be :
A. \( M n_{3} O_{4}, M n O_{2}, M n C l_{2} \)
в. \( P b_{3} O_{4}, P b O_{2}, P b C l_{2} \)
\( \mathrm{c} \cdot \mathrm{Fe}_{3} \mathrm{O}_{4}, \mathrm{Fe}_{2} \mathrm{O}_{3}, \mathrm{FeCl}_{2} \)
D. \( F e_{3} O_{4}, F e_{2} O_{3}, F e C l_{3} \)


Above the resonant frequency,
A. the frequency of the body is less than the frequency of the external periodic force.
B. the frequency of the body is greater than the frequency of the external periodic force.
C. the frequency of the body is exactly equal to the frequency of the external periodic force.
D. both (A) and (B)


A point 0 is placed midway between the
two converging mirror of focal length \( \boldsymbol{f} \)
each. find \( d \) so that object and image
coincide:
A \( .2 f, 4 f \)
B. \( 2 f, 3 f \)
\( c \cdot 4 f \)
D. \( 2 f, f \)


Differentiate w.r.t. \( x \)
\( \boldsymbol{y}=\sin \left(5 x^{3}+2 x\right) \)


An unknown compound \( A \) dissociates
at \( 500^{\circ} \mathrm{C} \) to give products as follows\( \boldsymbol{A}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{B}(\boldsymbol{g})+\boldsymbol{C}(\boldsymbol{g})+\boldsymbol{D}(\boldsymbol{g}) \)
Vapour density of the equilibrium mixture is 50 when it dissociates to the
extent to \( 10 \% \). What will be the
molecular weight of compound \( \boldsymbol{A} \) ?
A. 120
в. 130
\( c \cdot 134 \)
D. 140


Find the number of total possible
ionization isomers in \( \left[\mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}\right] \mathrm{Br}_{2} \)


At what phase of meiosis are homologous chromosomes separated?
A. At prophase II
B. At prophase
c. At anaphase
D. At anaphase II


Write the electronic configurations of the elements with the atomic numbers
\( 61,91,101, \) and 109


Find: \( \int \frac{\left(x^{4}-x\right)^{\frac{1}{4}}}{x^{5}} d x \)


When diamond is heated to 1500 , in the
absence of air, it forms:
A. graphite
B. carbon black
\( c . \) soot
D. coke


Best method to increase the sensitivity of the moving coil galvanometer is to decrease
A. radius of the coil
B. number of turns of the coil
c. external magnetic field
D. couple per unit twist


\( \ln (25)^{15} \) unit digit is 5


Bicarpellary, sycarpous gynoecium with bilocular ovary axile swollen placenta and oblique septum occurs in
A . Cruciferae
B. Solanaceae
c. cucurbitaceae
D. Liliaceae


Aqueous solution of a mixture contains
LiCl, NaCl and KCl. LiCl is
separated using ether as ether extracts LiCl (covalent) from mixture.
A. True
B. False
c. Ambiguous
D. None of these


Emulsifiers prevent the generation of free radicals which damage the food. If this is true enter 1 , if false enter 0 .


Chlorine solution can be used as an
antiseptic If this is true enter 1 , if false enter 0 .


Among the following, which one acts as a food preservative?
A. Aspartame
B. Aspirin
c. Sodium Benzoate
D. Paracetamol


The polynomial having atmost 3 zero
A. constant polynomial
B. linear polynomial
C. quadratic polynomial
D. cubic polynomial


During acute myocardial infarction which of the following changes occurs in the ECG.
A. Flattened T wave
B. Depressed ST segment
c. Elevated ST segment
D. Increased length of PQ interval


Which of the following compounds contains \( \mathrm{S}=0 \) as well as \( \mathrm{S}=\mathrm{S} \) bonds?
A. Sulphuric acid
B. Thiosulphuric acid
c. sulphurous acid
D. Thiosulphurous acid


The figure shows the position -time \( \left(x^{-}\right. \)
t) graph of one-dimensional motion of a
body of mass 0.4 kg. The magnitude of
each impulse is :
\( \mathbf{t}(\mathrm{s}) \)
A . \( 0.4 \mathrm{Ns} \)
B. 0.8 Ns
c. 1.6 Ns
D. 0.2 Ns


Which of the following is the correct
order for strength of \( C-X \) bond?
A. \( C H_{3} F<C H_{3} C l<C H_{3} B r<C H_{3} I \)
B. \( C H_{3} F>C H_{3} C l>C H_{3} B r>C H_{3} \)
c. \( C H_{3} I>C H_{3} F>C H_{3} C l>C H_{3} B r \)
D. \( C H_{3} C l>C H_{3} B r>C H_{3} F>C H_{3} \)


The volume of gases obtained at the
anode at STP (1 bar and 298 \( K \) ) when 2
faraday of electricity is passed is
A. 67.2 litres
B. 68.1 litres
c. 73.2 litres
D. 74.1 litres


The probability of an \( _{-----} \) is greater
than or equal to 0 and less than or equal
to 1.
A. space
B. experiment
c. sample
D. event


If \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) is defined by \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2}- \)
\( 3 x+2, \) then \( f\left(x^{2}-3 x-2\right)= \)
A \( \cdot x^{4}+1 \)
B. \( x^{4}-3 x+2 \)
c. \( x^{4}-6 x^{3}+2 x^{2}+21 x+12 \)
D. \( x^{4}+2 x+2 \)


\( \frac{(\mathbf{1}) \boldsymbol{H} \boldsymbol{C I}}{(\mathbf{2}) \boldsymbol{C H}_{2} \boldsymbol{O} \boldsymbol{H}} \times \frac{(\mathbf{1}) \boldsymbol{L} \boldsymbol{i} A \boldsymbol{I} \boldsymbol{H}_{4} / \boldsymbol{E} \boldsymbol{t}_{2} \boldsymbol{O}}{(\mathbf{2}) \boldsymbol{H}_{2} \boldsymbol{O}} \boldsymbol{Y} \stackrel{\boldsymbol{H}_{O}^{+}}{\longrightarrow} \boldsymbol{Z} \) ldentify \( X, Y \) and \( Z \)
(according to the image shown, the
correct ans is)


In Young's double slit experiment, first slit has width four times the width of
the second slit. The ratio of the
maximum intensity to the minimum intensity in the interference
fringe system is:
A . 2: 1
B . 4: 1
c. 9: 1
D. 8: 1


An athelete diving off a high spring board can perform a variety of physical moments in the air before entering the water below. Which one of the following parameters will remain constant during the fall? The athelete's:
A. linear velocity
B. linear momentum
c. moment of inertia
D. angular momentum


Assertion
Heater wire must have high resistance than connecting wires and high metallic point.
Reason
If resistance is high, the electrical
conductivity will be less.
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 center of an equilateral triangle is
0. Three forces \( F_{1}, F_{2} \) and \( F_{3} \) are applied along \( A B, B C \) and \( A C \) respectively. The
magnitude of \( F_{3} \) so that the total torque
about 0 should be zero is:
A \( \cdot\left(F_{1}+F_{2}\right) \)
в. \( \left(F_{1}-F_{2}\right) \)
c. \( \frac{F_{1}+F_{2}}{2} \)
D. \( 2\left(F_{1}+F_{2}\right) \)


Match the column.


If \( \boldsymbol{A}=\left\{(\boldsymbol{x}, \boldsymbol{y}) \mid \boldsymbol{x}^{2}+\boldsymbol{y}^{2} \leq \mathbf{4}\right\} \) and \( \boldsymbol{B}= \)
\( \left\{(x, y) \mid(x-3)^{2}+y^{2} \leq 4\right\} \) and the
point \( P\left(a, a-\frac{1}{2}\right) \) belongs to the set \( B-A, \) then the set of possible real
values of \( a \) is
\( ^{\mathrm{A}} \cdot\left(\frac{1+\sqrt{31}}{4}, \frac{7+\sqrt{7}}{4}\right] \)
в. \( \left[\frac{7-\sqrt{7}}{4}, \frac{1+\sqrt{31}}{4}\right) \)
\( ^{c} \cdot\left(\frac{1-\sqrt{31}}{4}, \frac{7-\sqrt{7}}{4}\right] \)
D. None of the above


Column-I contains four entries and
Column-II contains four entries. Entries
of Column-I are to be matched with
some entries of Column-II. One or more
than one entries of Column-I may have
matching with the same entries of
Column-II.


The change in the value of \( g \) at a height
\( h \) above the surface of earth is the same
as at a depth \( d \) below the earth. When
both \( d \) and \( h \) are much smaller than the
radius of earth, then which one of the
following is correct?
\( ^{A} \cdot_{d}=\frac{h}{2} \)
B. \( d=\frac{3 h}{2} \)
c. \( d=2 h \)
\( \mathbf{D} \cdot d=h \)


Given that \( \boldsymbol{U}= \)
\( \{3,7,9,11,15,17,18\}, M= \)
\{3,7,9,11\} and \( N=\{7,11,15,17\} \)
Find
(i) \( \boldsymbol{M}-\boldsymbol{N} \)
(ii) \( \boldsymbol{N}-\boldsymbol{M} \)
(iii) \( N^{\prime}-M \)
(iv) \( M^{\prime}-N \)
\( (v) M \cap(M-N) \)
\( (v i) N \cup(N-M) \)
(vii) \( \boldsymbol{n}(\boldsymbol{M}-\boldsymbol{N}) \)


In a right - angled triangle, it is given
that \( A \) is an acute angle and \( \tan A= \) \( \frac{5}{12} . \) Find the values of :
\( \sin A \) is \( \frac{5}{m}, \) then \( m \) is


The oxidation state of xenon is +6 in:
A. \( X e O F_{2} \)
в. \( X e F_{6} \)
c. \( X e F_{4} \)
D. \( X e O_{4} \)


A small straight condctor PQ is lying at right angles to an infinite current
carrying conductor \( X Y \). If the conductor PQ is displaced on metallic rails parallel to the conductor \( X Y \), then the
direction of induced emf in PQ will be:
A. from Q to P
B. from P to Q
c. vertically downwards
D. vertically upwards


The gas which contributes maximum to
the heating value of natural gas is:
A. \( C O \)
в. \( C O_{2} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \)
D. \( C H_{4} \)


f \( \boldsymbol{y}=(\mathbf{1}+\boldsymbol{x})\left(\mathbf{1}+\boldsymbol{x}^{2}\right)\left(\mathbf{1}+\boldsymbol{x}^{4}\right) \dots(\mathbf{1}+ \)
\( \left.x^{2^{n}}\right), \) then \( \frac{d y}{d x} \) at \( x=0 \) is
\( \mathbf{A} \cdot \mathbf{1} \)
B. -
\( c \cdot 0 \)
D. none of these


\( \int \frac{x^{3}}{\sqrt{1+x^{2}}} d x \)
A. \( \quad \sqrt{1+x}-\frac{x}{3}\left(1+x^{2}\right)^{3 / 2}+c \)
B \( \cdot \quad x \sqrt{1+x^{2}}+\frac{2}{3}\left(1+x^{2}\right)^{3 / 2}+c \)
C \( \cdot \frac{x^{2} \sqrt{1+x^{2}}}{3}-\frac{2}{3} \sqrt{1+x^{2}}+c \)
D. \( \quad x^{2} \sqrt{1+x^{2}}-\frac{1}{3}\left(1+x^{2}\right)^{3 / 2}+c \)


Evaluate the determinant :
\( \left|\begin{array}{ccc}\mathbf{1}+\boldsymbol{a} & \mathbf{0} & \mathbf{0} \\ \mathbf{0} & \mathbf{1}+\boldsymbol{a} & \mathbf{0} \\ \mathbf{0} & \mathbf{0} & \mathbf{1}+\boldsymbol{a}\end{array}\right| \)


Let \( F \) be the force acting on a particle
having position vector \( r \) and \( \tau \) be the torque of this force about the origin.
Then
A. \( r . \tau=0 \) and \( F . \tau \neq 0 \)
B. \( r . \tau \neq 0 \) and \( F . \tau=0 \)
c. \( r . \tau \neq 0 \) and \( F . \tau \neq 0 \)
D. r. \( \tau= \) O and \( F . \tau=0 \)


The density of nucleus is about times the density of atom.
A \( \cdot 10^{-14} \)
B. \( 10^{12} \)
\( c \cdot 10^{-8} \)
D. \( 10^{10} \)


The magnitude of colligative properties in all colloidal dispersions
is than solution.
A. lower
B. higher
c. Both
D. None of the above


Three charges \( Q,+q \) and \( +q \) are placed
at the vertices of a right-angled isosceles triangle between as shown. The net electrostatic energy of the configuration is zero if \( Q \) is equal to
\( ^{A} \cdot \frac{-2 q}{1+\sqrt{2}} \)
в. \( \frac{2 q}{2+\sqrt{2}} \)
\( c \cdot-2 q \)
D. \( +q \)


Differentiate the following w.r.t. \( x \)
\( \sin x \log x \)
A \( \cdot \frac{\sin x}{x}-\cos x \log x \)
B. \( \frac{\sin x}{x}+\cos x \log x \)
c. \( \frac{\cos x}{x}+\cos x \log x \)
D. \( \frac{\tan x}{x}+\cos x \log x \)


A metal pipe is \( 77 \mathrm{cm} \) long. The inner diameter of a cross section is \( 4 \mathrm{cm} \), the
outer diameter being \( 4.4 \mathrm{cm} . \) Find its
inner curved surface area.


Let \( \boldsymbol{A}=\{\boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c}\} \) and \( \boldsymbol{B}=\{1,2\} \)
Consider a relation \( \boldsymbol{R} \) defined from set
\( A \) to set \( B . \) Then \( R \) is equal to set
A. \( A \)
в. \( B \)
c. \( A \times B \)
D. \( B \times A \)


If \( R \) is radius of the earth and \( W \) is work
done in lifting a body from the ground to an altitude \( R \), the work which should be
done in lifting it further to twice that altitude is:
A \( \cdot \frac{W}{2} \)
B. \( W \)
c. \( \frac{W}{3} \)
D. \( 3 W \)


Construct a \( 2 \times 3 \) matrix \( A=\left[a_{i j}\right] \)
whose elements are given by \( a_{i j}= \)
\( |2 i-3 j| \)


Show that \( 3 \sqrt{2} \) is irrational.


All of the following are the characteristics of the kingdom Protista
except
A. Members can be photosynthetic
B. Members can be free living
c. Some members move via flagella
D. Some members are shaped like rods and termed bacill
E. Some members spend part of their life cycle inside insects


Solve \( n=\frac{3 n}{5}-1+\frac{3 n}{5}-2 \)


Give the names of four reproductive events that occur after puberty in human beings.


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


Blowing air with open mouth is an example of :
A. isobaric process
B. isochoric process
c. isothermal process
D. adiabatic process


The perpendicular drawn at the point of incidence on a mirror is called:
A. incident ray
B. reflected ray
c. normal
D. image


Which of the following is not an ore of
Iron?
A. Magnetite
B. Haematite
c. Dolomite
D. limonite


Among the following, which one option
have both ionic and covalent bonds?
\( \mathbf{A} \cdot N H_{3} \) and \( N_{2} H_{4} \)
B. \( ^{16} O \) and \( ^{17} O \)
C \( . N H_{4} C l \) and \( N H_{4} N O_{3} \)
D. \( C H_{3} O C H_{3} \) and \( C H_{3} C H_{2} O H \)
\( E \cdot O_{2} \) and \( O_{3} \)


Indicate in which case/cases the
spontaneity of a change is favoured when
This question has multiple correct options
\( \mathbf{A} \cdot \Delta G i s+v e \)
B. \( \Delta \)His \( - \)ve
c. \( \Delta \) Sis \( +v e \)
D. \( \Delta \) Sis \( -v e \)
E . \( \Delta \) Gis \( - \) ve


Which of the following pump is preferred for flood control and irrigation applications?
A. Centrifugal pumop
B. Axial Flow pump
C. Mixed flow pump
D. Reciprocating pump


A horizontal straight conductor when placed along south-north direction falls under gravity; there is
A. an induced current from south-to-north direction
B. an induced emf current from north-to-south direction
c. no induced emf along the length of the conductor
D. an induced emf along the length of the conducto


What is the velocity of the ball two seconds after it is dropped?
A . 19.6
B . 25
c. 18.4
D. 23


An element of p-block in which last electron enters into s-orbital of valence
shell instead of p-orbital is:
A . \( A s \)
в. \( G a \)
\( c . T e \)
D. \( H e \)


Velocity-time graph of a body with uniform velocity is a straight line
A. Parallel to x-axis
B. Parallel to y-axis
c. Inclined to x-axis
D. Inclined to y-axis


Which of the following is not a carbonate ore?
A. Dolomite
B. Calamine
c. siderite
D. zincite


Find the area of the region bounded by the curves \( x=\frac{1}{2}, x=2, y=\log x \) and
\( \boldsymbol{y}=\mathbf{2}^{\boldsymbol{x}} \)
\( ^{\mathbf{A}} \cdot \frac{4-\sqrt{2}}{\log 2}-\frac{5}{2} \log 2+\frac{3}{2} s q \cdot u n i t s \)
B. \( \frac{4+\sqrt{2}}{\log 2}-\frac{3}{2} \log 2+\frac{5}{2} \) sq.units
\( ^{\mathrm{c}} \cdot \frac{4-\sqrt{2}}{\log 2}-\frac{3}{2} \log 2+\frac{5}{2} s q \cdot u n i t s \)
D. \( \frac{4+\sqrt{2}}{\log 2}-\frac{5}{2} \log 2+\frac{3}{2} \) sq.units


\( -8 y z \times-2 x y= \)
A . \( 16 x y z \)
B . \( -16 x y^{2} z \)
c. \( 16 x y^{2} z \)
D. \( -16 x^{2} y^{2} z^{2} \)


Which of the following cannot give a precipitate with an aqueous solution of
\( A g N O_{3} ? \)
A. \( K I \)
в. \( K_{2} S O_{4} \)
c. \( C H C l_{3} \)
D. KCl


\( \lim _{x \rightarrow \frac{\pi}{4}} \frac{\sin x}{\cos ^{-1}\left[\frac{1}{4}(3 \sin x-\sin 3 x)\right]} \)
D denotes integer function, is-
A \( \cdot \frac{\sqrt{2}}{\pi} \)
B. 1
\( c \cdot \frac{4}{\pi} \)
D. does not exist


Name the parts of the ovary which give
rise to:
Fruit wall


In aqueous solution, \( \left[\boldsymbol{C o}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{6}\right]^{2+}(\boldsymbol{X}) \)
reacts with molecular oxygen in the
presence of excess liquor \( N H_{3} \) to give
a new complex \( Y \). The number of
unpaired electrons in \( X \) and \( Y \) are,
respectively.
A . 3,1
в. 3,0
c. 3,3
D. 7,0


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


Match the molecules/ions (in Column-I)
with their shapes (in Column-II).


topp
onwo
\( ^{80^{\circ}} \)


Calculate the effective nuclear charge
of the last electron in an atom whose
configuration is \( 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{5} \)


Three electrolytic cells \( A, B \) and \( C \)
containing electrolytes \( Z n S O_{4} \)
\( A g N O_{3} \) and \( C u S O_{4} \) respectively were connected in series. A steady current of
1.50 ampere was passed through them until 1.45 of \( A g \) were deposited at the
cathode of cell \( B \). How long did the current flow? What mass copper and
zinc were deposited? (Atomic weight of \( \boldsymbol{C u}=\mathbf{6 3 . 5}, \boldsymbol{Z n}=\mathbf{6 5 . 3}, \boldsymbol{A} \boldsymbol{g}=\mathbf{1 0 8} \)


Which one of the following features represents a recessive character in
Mendel's pea plants?
A. Round seed
B. Green pod colour
c. Red flower
D. Yellow pod colour


Which of the following is a measurement of water pollution?
A. \( P C S \)
в. \( P C B \)
\( c . B O D \)
D. \( C O D \)


The correct \( I . U . P . A . C \) name for
\( \boldsymbol{H}_{2}\left[\boldsymbol{P t C l}_{6}\right] \) complex:
A. Hexachloridoplatinic (IV) acid
B. Hexachloridoplatinate (IV) acid
c. Hydrogenhexachloridoplatinate (IV) acid
D. Di hydrogenhexachloridoplatinate (IV) acid


A circle passes through the point (2,1) and the line \( x+2 y=1 \) is a tangent to it at the point (3,-1) Determine its equation.


\( \lim _{x \rightarrow \infty} \frac{1}{1+x^{2}}+\frac{2}{4+x^{2}}+\frac{3}{9+x^{2}}+ \)
\( \cdots+\frac{x}{x^{2}+x^{2}} \)


The basic character of the hydrides of
\( V^{t h} \) group elements decreases in the
order:
\( \mathbf{A} \cdot N H_{3}>P H_{3}>A s H_{3}>S b H_{3} \)
\( \mathbf{B} \cdot S b H_{3}>A s H_{3}>P H_{3}>N H_{3} \)
\( \mathbf{C} \cdot N H_{3}>S b H_{3}>P H_{3}>A s H_{3} \)
\( \mathbf{D} \cdot S b H_{3}>P H_{3}>A s H_{3}>N H_{3} \)


State whether the given statement is True or False:
\( 2 \sqrt{3}-1 \) is an irrational number
A . True
B. False


Name any one hormone which increases
femaleness in plants?


The quantity \( \frac{b}{2 \sqrt{m k}} \) is called
A. critical coefficient
B. damping coefficient
C. friction coefficient
D. None of these


Two monatomic ideal gases 1 and 2 of
molecular masses \( m_{1} \) and \( m_{2} \)
respectively are enclosed in separate
containers kept at the same
temperature. The ratio of the speed of
sound in gas 1 to that in \( \operatorname{gas} 2 \) is given
by.
A \( \cdot \sqrt{\frac{m_{1}}{m_{2}}} \)
B. \( \sqrt{\frac{m_{2}}{m_{1}}} \)
\( \mathbf{c} \cdot \frac{m_{1}}{m_{2}} \)
D. \( \frac{m_{2}}{m_{1}} \)


A charge \( Q \) is distributed over two concentric hollow spheres of radii r and \( R(>r) \) such that the surface charge densities are equal. Find the potential
at the common centre,
A \( \cdot \frac{Q}{4 \pi \varepsilon_{0}}\left(\frac{R-r}{R^{2}+r^{2}}\right) \)
в. \( \frac{Q}{4 \pi \varepsilon_{0}}\left(\frac{R+r}{R^{2}+r^{2}}\right) \)
c. \( \frac{Q}{4 \pi \varepsilon_{0}}\left(\frac{-R+r}{R^{2}+r^{2}}\right) \)
D.


is the compound which can remove both oxygen and nitrogen from the air when they are passed over it at \( 1000^{0} \mathrm{C} \)
A \( \cdot \mathrm{CaC}_{2} \)
в. \( \mathrm{CaCl}_{2} \)
c. \( \mathrm{CaCN}_{2} \)
D. \( \mathrm{Ca}(\mathrm{CN})_{2} \)