Which characteristics the weak inter
molecular forces of attraction in a
liquid?
A. High boiling point
B. High vapour pressure
c. High critical temperature
D. High heat of vapourisation


Study the bar graph representing the
number of persons in various age
groups in a town shown in Fig.23.9.
Observe the bar graph and answer the
following questions:
What is the total population of the
town?


\( \frac{\mathbf{3}}{\mathbf{1}+\boldsymbol{i}}-\frac{\mathbf{2}}{\mathbf{2}-\boldsymbol{i}}+\frac{\mathbf{2}}{\mathbf{1}-\boldsymbol{i}} \)
A \( \cdot \frac{1}{10}(17+9 i) \)
в \( \cdot \frac{1}{5}(17-9 i) \)
c \( \cdot \frac{1}{10}(17-9 i) \)
D \( \cdot \frac{1}{5}(17+9 i) \)


A circular coil of 20 turns and \( 10 \mathrm{cm} \)
radius is placed in a uniform magnetic
field of \( 0.10 T \) normal to the plane of the
coil. If the current in the coil is \( 5 A \)
cross-sectional area is \( 10^{-5} m^{2} \) and coil
is made up of copper wire having free
electron density about \( 10^{29} m^{-3}, \) then the average force on each electron in
the coil due to magnetic field is.
\( \mathbf{A} \cdot 2.5 \times 10^{25} N \)
B . \( 5 \times 10^{25} N \)
C \( .4 \times 10^{25} N \)
D. \( 3 \times 10^{25} N \)


For the myopic eye, the far point is farther away than the normal.
A. True
B. False


A ball of mass \( M \) falls from a height \( h \) on a floor which the coefficient of
restitution is \( e . \) The height attained by the ball after two rebounds is:
\( \mathbf{A} \cdot e^{2} h \)
B \( \cdot e h^{2} \)
\( \mathbf{c} \cdot e^{4} h \)
D. \( \frac{h}{e^{4}} \)


The value of
\( \sum_{n=1}^{9999} \frac{1}{(\sqrt{n}+\sqrt{n+1})(\sqrt[4]{n}+\sqrt[4]{n+1})} \)
is
\( \mathbf{A} \cdot \mathbf{9} \)
B. 99
\( c .999 \)
D. 9999


The most widely used commercial chemical as a paint pigment is:
A \( \cdot \) Ti \( O_{2} \)
в. \( \operatorname{si} 0_{2} \)
c. \( M g O \)
D. \( A l_{2} O_{3} \)


A planet is observed by an astronomical reflecting telescope having an objective of focal length \( 16 m \) and an eye-piece of
focal length 2cm. Then:
This question has multiple correct options
A. the distance between the objective and the eye - piece is \( 16.02 m \)
B. the angular magnification of the planet is 800
c. the image of planet is erect
D. the objective is larger than eye - piece


An object of mass \( 2 \mathrm{kg} \) is moving with a velocity of \( 3 \mathrm{m} / \mathrm{s} \) and collide headon with an object B of mass 1 kg moving in the opposite direction with a velocity of \( 4 \mathrm{m} / \mathrm{s} \). after the collision, both objects coalesce so that they move with a common velocity v equal to
\( \mathbf{A} \cdot \frac{2}{3} m / s \)
B. \( 1 \mathrm{m} / \mathrm{s} \)
c. \( 2 \mathrm{m} / \mathrm{s} \)
D. 3 \( \mathrm{m} / \mathrm{s} \)


If area of a long solenoid is doubled,length is trippled and no. of turns are remained contant.Then its
self-inductance will be changed how many times-
A \( \cdot 1 / 3 \)
в. \( 2 / 3 \)
\( c \cdot 1 / 9 \)
D. \( 4 / 3 \)


Who demonstrated the role of light in plant nutrition?
A. Von Helmont
B. Stephen Hales
c. Priestley
D. None of the above


Evaluate :
\( \frac{2 \cos 67^{\circ}}{\sin 23^{\circ}}-\frac{\tan 20^{\circ}}{\cot 50^{\circ}}-\cos 0^{\circ} \)


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


The instantaneous values of alternating
current and voltages in a circuit are
given as
\( i=\frac{1}{\sqrt{2}} \sin (100 \pi t) \) ampere
\( e=\frac{1}{\sqrt{2}} \sin (100 \pi t+\pi / 3) \) volt
The average power in Watts consumed in the circuit is -
A. \( \frac{\sqrt{3}}{4} \)
в.
\( c \cdot \frac{1}{8} \)
D.


In a simple harmonic motion
A. the maximum potential energy equals the maximum kinetic energy
B. the minimum potential energy equals the minimum kinetic energy
C. the minimum potential energy equals the maximum kinetic energy
D. the maximum potential energy equals the minimum kinetic energy


Three charges \( +4 q,-q \) and \( +4 q \) are kept on
a straight line at position \( (0,0,0),(a, 0,0) \) and \( (2 a, 0,0) \) respectively. Considering that they are free to move along the \( x \) -
axis only
A. All the charges are in stable equilibrium
B. All the charges are in unstable equilibrium.
C. Only the middle charge is in stable equilibrium.
D. Only middle charge is in unstable equilibrium.


If length of a rectangle is \( 5 \mathrm{cm} \) and
breadth of the rectangle is \( 12 \mathrm{cm} . \) Find the area of the rectangle.
\( \mathbf{A} \cdot 25 c m^{2} \)
В. \( 60 \mathrm{cm}^{2} \)
\( \mathbf{c} \cdot 31 c m^{2} \)
D. \( 12 \mathrm{cm}^{2} \)


What is motional emf? State any two
factors on which it depends.


What is the similarity between gymnosperms and angiosperms?
A. Phloem of both have companion cells.
B. Endosperm is formed before fertilization in both
c. origin of ovule and seed is similarin both.
D. Both have leaves, stem and roots


The displacement of particle moving
along x-axis versus time is given in the
figure below

The average velocity, \( V_{a v} \) of the particle
in the first four seconds and the velocity
V of it at \( t=4 \) s are
\( (\mathbf{m}) \)
\( (\mathbf{m}) \)
A \( \cdot V_{a v}=-1 m / s, V=-1 m / s \)
В. \( V_{a v}=1 m / s, V=1 m / s \)
C \( \cdot V_{a v}=1 m / s, V=0 m / s \)
D. \( V_{a v}=-1 m / s, V=0 m / s \)


In cell cycle, during which phase, chromosomes are arranged in equatorial plate?
A. Metaphase
B. Anaphase
c. Telophase
D. Prophase


In a triangle, the Sum of two angles is 118 and their difference is \( 32 . \) find each
angle of the triangle.
A. 75,43 and 62
B. 85,33 and 62
c. 65,53 and 62
D. none of the above


Prove the following by using the principle of mathematical induction for
all \( \boldsymbol{n} \in \boldsymbol{N}: \frac{\mathbf{1}}{\mathbf{2 . 5}}+\frac{\mathbf{1}}{\mathbf{5 . 8}}+\frac{\mathbf{1}}{\mathbf{8 . 1 1}}+\dots \dots+ \)
\( \frac{1}{(3 n-1)(3 n+2)}=\frac{n}{(6 n+4)} \)


Which of the following planets can be seen with the naked eye?
A. Mercury, Venus, Mars and Jupiter
B. Mars, Jupiter, Uranus and Neptune
c. Mercury, Venus, Uranus and Neptune
D. Mercury, Mars, Jupiter and Neptune


An object is dropped at the surface of
the earth from the height of \( 3600 \mathrm{km} \) Calculate the ratio of the weight of the body at that height and on the surface of the earth.
A .1 .34
B . 2.44
\( c .6 .25 \)
D. 12.32


The points \( A, B \) and \( C \) on the given
number line represents
A \( \cdot \frac{-3}{10}, \frac{-1}{10}, \frac{3}{4} \)
B. \( \frac{-3}{10}, \frac{1}{10}, \frac{3}{4} \)
c. \( \frac{3}{10}, \frac{-1}{10}, \frac{-3}{4} \)
D. 4,-1,3


Coenzymes NAD and NADP contain the vitamins
A. Niacin
B. Biotin
c. Thiamine
D. Vitamin \( B_{12} \)


Find the resistance of the voltmeter
A. \( 400 \Omega \)
B. 200 \( \Omega \)
c. \( 300 \Omega \)
D. 500 \( \Omega \)


Find out the total current flowing in the circuit as shown in above figure?
\( A \cdot 4 A \)
B. 3A
c. \( 2 A \)
D. \( \frac{4}{3} \)
\( E \)


What coefficient of \( A g N O_{3} \) is required to
balance the following equation?
\( C u+A g N O_{3} \rightarrow C u\left(N O_{3}\right)_{2}+A g \)
\( \mathbf{A} \cdot \mathbf{0} \)
B. 1
c. 2
D. 3


An alpha particle of \( 5 \mathrm{MeV} \) at a large
distance proceeds towards a gold nucleus \( (Z=79) \) to make a head on
collision. The closest distance of
approach from the centre of gold nucleus
is:
A. \( 20 f m \)
B. 15 fm
c. \( 10 f m \)
D. 45 fm


\( \frac{\tan 5 \Theta+\tan 3 \Theta}{\tan 5 \Theta-\tan 3 \Theta}=4 \cos 2 \Theta \cos 4 \Theta \)


Which two metals react with
concentrated alkalis?
A. \( A l, M g \)
в. \( A l, Z n \)
c. \( N a, K \)
D. \( K, A l \)


The audible range in humans is
\( \mathbf{A} \cdot 20 H z \) to \( 2000 H z \)
B. \( 200 H z \) to \( 20,000 H z \)
c. \( 20 H z \) to \( 20,000 H z \)
D. \( 200 H z \) to \( 20 k H z \)


A man 'A' moves in the north direction
with a speed \( 10 \mathrm{m} / \mathrm{s} \) and man 'B' moves
in \( 30^{0} \) North of East with \( 10 \mathrm{m} / \mathrm{s} \). Find
the relative velocity of B w.r.t. A.


If \( \mathbf{A} \) is non-singular matrix such that \( A^{2}=A^{-1} \) then \( a d j A= \)
A.
B. \( A^{-1} \)
c. \( A^{3} \)
D. \( \left(\mathrm{A}^{-1}\right)^{2} \)


Describe an experiment in detail to prepare 1 molar \( N a O H \) solution.


What type of isomers are the following?
\( \left[(\boldsymbol{C O})_{5} \boldsymbol{M} \boldsymbol{n} \boldsymbol{S} \boldsymbol{C} \boldsymbol{N}\right] \boldsymbol{a} \boldsymbol{n} \boldsymbol{d}\left[(\boldsymbol{C} \boldsymbol{O})_{5} \boldsymbol{M} \boldsymbol{n} \boldsymbol{N} \boldsymbol{C} \boldsymbol{S}\right] \)
A. coordination
B. Linkage
c. solvate
D. lonization


If \( a, b, c \) are in A.P., then the following are also in A.P. \( \frac{1}{b c}, \frac{1}{c a}, \frac{1}{a b} \)
A . True
B. False


Which of the following group of elements belong to the representative
group?
A. \( L i, M g, N, Z n \)
в. \( A g, A u, Z n \)
c. \( N a, K, B e \)
D. \( F e, C u, M n \)


Which of the following compounds can be detected by Molisch's test??
A. Nitro compounds
B. Sugars
c. Amines
D. Primary alcohols


An organic compound of molecular
formula \( C_{4} H_{10} O \) does not react with
sodium. With excess of HI, it gives only one type of alkyl iodide. The compound is :
A. unsymmetrical ether
B. symmetrical ether
c. alcohol
D. none of these


The principle of superposition of waves can not be used to explain wave phenomenalike
A. Interference
B. Diffraction
c. stationary Waves and beats
D. Dispersion


The minimum value of \( \boldsymbol{f}(\boldsymbol{x})= \)
\( |\boldsymbol{x}-\mathbf{1}|+|\boldsymbol{x}-\mathbf{2}|+|\boldsymbol{x}-\mathbf{3}| \) is:
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot 3 \)
D. None of the above


Chemosynthetic pathway of photosynthesis occur in :-
A. cytosol
B. Stroma
c. Membrane of thylakoid
D. Lumen


The equilibrium constant \( K_{p}(\text { in atm }) \)
for the reaction is 9 at 7 at \( m \) and \( 300 K \)
\( \boldsymbol{A}_{2}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{B}_{2}(\boldsymbol{g})+\boldsymbol{C}_{2}(\boldsymbol{g}) \)
Calculate the average molar mass (in \( \mathrm{gm} / \mathrm{mol} \) ) of an equilibrium mixture:
Given Molar of \( A_{2}, B_{2} \) and \( C_{2} \) are 70,49
\& 21 gm/ mol respectively.
A . 50
B. 45
c. 40
D. 37.5


The sum of two numbers is 9 and their
product is 20. Find the sum of their
cubes
A . 189
в. 130
c. 76
D. 39 9


Write the approximate wavelengths for blue light?
\( \mathbf{A} \cdot 800 A^{\circ} \)
B . \( 1600 A^{\circ} \)
c. \( 3200 A^{\circ} \)
D. \( 4800 A^{\circ} \)


Which of the following statements is
not true about Gauss's law?
A. Gauss's law is true for any closed surface
B. The term \( q \) on the right side of Gauss's law includes the sum of all charges enclosed by the surface
C. Gauss's law is not much useful in calculating electrostatic field when the system has some symmetry
D. Guss's law is based on the inverse square dependence on distance contained in the coulomb's law


The pressure inside a tyre is 4 times that of atmosphere. If the tyre burst suddenly at temperature \( 300 K, \) what will be the new temperature?
\( \mathbf{A} \cdot 300(4)^{7 / 2} \)
В. \( 300(4)^{2 / 7} \)
\( \mathbf{C} \cdot 300(2)^{7 / 2} \)
D. \( 300(4)^{-2 / 7} \)


Which of the following plays important role in controlling movement, motivation and cognition?
A. Noradrenaline
B. Dopamine
c. Amphetamine
D. Adrenaline


The radius of the earth is \( R \) and
acceleration due to gravity at its surface is 'g'. If a body of mass ' \( m \) ' is
sent to a height of \( \boldsymbol{R} / \mathbf{4} \) from the earth's surface, the potential energy is:
\( A \cdot m g R / 3 \)
в. \( m g R / 4 \)
c. \( m g R / 5 \)
D. \( m g R / 16 \)


Difference between mass and weight.


A neutron breaks into a proton and an electron. This decay of neutron is
accompanied by the release of energy. Assuming that \( 50 \% \) of the energy is produced in the form of electromagnetic radiation, what will be the frequency of radiation produced. Will this photon be sufficient to cause ionization of aluminum? In case it is
able to do so what will be the energy of the electron ejected from the aluminum
atom
\( \boldsymbol{I} \boldsymbol{E}_{1} \) of \( \boldsymbol{A l}=\mathbf{5 7 7} \mathrm{KJ} / \mathrm{mol} \)


Balance the following equations by
oxidation number method.
\( \boldsymbol{H}_{2} \boldsymbol{O}_{2}+\boldsymbol{C l} \boldsymbol{O}_{2}+\boldsymbol{O} \boldsymbol{H}^{-} \rightarrow \boldsymbol{C l}^{-}+\boldsymbol{O}_{2}+ \)
\( \boldsymbol{H}_{2} \boldsymbol{O} \)


For the reaction \( \mathbf{N H}_{4}^{+}+\mathbf{S}^{-2} \rightleftharpoons \)
\( \mathbf{N H}_{3}+\mathbf{H S}^{-}, \mathbf{N H}_{3} \) and \( \mathbf{S}^{-2} \) are a group
of :-
A. Acids
B. Bases
c. Acid-base pair
D. None of these


Ducts of Bellini are found in.
A . Liver
B. Intestine
c. Medulla oblongata
D. Kidney


Let \( h \) be a twice continuously differentiable positive function on an open interval \( J . \) Let \( g(x)=n(h(x)) \) for
\( \operatorname{each} x \epsilon J \)
\( A \cdot g \) is increasing on \( J \)
B. \( g \) is decreasing on \( J \)
c. \( g \) is concave up on \( J \)
D. \( g \) is concave down on \( J \)


A system can be taken from the initial
state \( p_{1}, V_{1} \) to final state \( p_{2}, V_{2} \) by two
different methods. Let \( \Delta Q \) and \( \Delta W \)
represent the heat given to the system and the work done by the system. Which of the following must be the same in both the methods.?
\( A \cdot \Delta Q \)
в. \( \Delta W \)
c. \( \Delta Q+\Delta W \)
D. \( \Delta Q-\Delta W \)


Bisecting means dividing into two
parts.
A. Unequal
B. Equal
c. Triangular
D. None of these


Find the oxidation number of nitrogen in each case:
\( N \) in \( N H_{3}, N H_{2} O H, N a N_{3} \) and
\( N H_{4} N O_{2} \)
\( \mathbf{A} \cdot_{-3,-1,-\frac{1}{3},+3 \&-3} \)
B. \( _{-3,-2,-\frac{1}{3},+1} \)
D. None of the above


Obtain a differential equation from the
following equation:
\( \sin ^{-1} x+\sin ^{-1} y=\sin ^{-1} c \)


Match the rate law given in column I with the dimensions of rate constant
given in column II and mark the
appropriate choice.
Column I Column I
(A) Rate\( =k\left[N H_{3}\right]^{0} \)
(i) \( \operatorname{mol} L^{-1} s^{-1} \)
(B) \( R a t e=k\left[H_{2} O_{2}\right]\left[I^{-}\right] \)
(ii) \( L m o l^{-1} s^{-1} \)
(C) \( \operatorname{Rate}=k\left[C H_{3} C H O\right]^{3 / 2} \)
\( s^{-1} \)
(D) \( \operatorname{Rate}=k\left[C_{2} H_{5} C l\right] \)
(iv) \( L^{1 / 2} m o l^{-1 / 2} s^{-1} \)
\( \mathbf{A} \cdot(A) \rightarrow(i v),(B) \rightarrow(i i i),(C) \rightarrow(i i),(D) \rightarrow(i) \)
B. \( (A) \rightarrow(i),(B) \rightarrow(i i),(C) \rightarrow(i i i),(D) \rightarrow(i v) \)
c. \( (A) \rightarrow(i i),(B) \rightarrow(i),(C) \rightarrow(i v),(D) \rightarrow(i i i) \)
D. \( (A) \rightarrow(i),(B) \rightarrow(i i),(C) \rightarrow(i v),(D) \rightarrow(i i i) \)


\( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{r}\frac{\boldsymbol{K} \cos \boldsymbol{x}}{\boldsymbol{\pi}-\mathbf{2} \boldsymbol{x}} ; \boldsymbol{x} \neq \frac{\boldsymbol{\pi}}{\mathbf{2}} \\ \boldsymbol{5} ; \boldsymbol{x}=\frac{\boldsymbol{\pi}}{2}\end{array}\right. \)
Find the value of \( K \) so that the function is continuous at the point \( \boldsymbol{x}=\frac{\boldsymbol{\pi}}{\mathbf{2}} \)


The term used to describe a fracture
along the earth's crust is
A. aftershock
B. fault
c. focus
D. tremor


Assertion
Air is a bad conductor of heat.
Reason
It's molecules are in continuous contact
with each other.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Find the electric potential at an
arbitrary point on the \( x \) axis? \( \left(V_{o}=\frac{\boldsymbol{q}}{4 \pi \epsilon_{o} a}\right) \)
\( ^{\mathrm{A}} \cdot V(x)=V_{o}\left(\frac{1}{\left|\frac{x}{a}-1\right|}-\frac{1}{\left|\frac{x}{a}+1\right|}\right) \)
B. \( V(x)=V_{o}\left(\frac{1}{\left|\frac{x}{a}+1\right|}-\frac{1}{\left|\frac{x}{a}-1\right|}\right) \)
c. \( V(x)=\left(\frac{1}{\left|\frac{x}{a}-1\right|}-\frac{1}{\left|\frac{x}{a}+1\right|}\right) \)
D. \( V(x)=\left(\frac{1}{\left|\frac{x}{a}+1\right|}-\frac{1}{\left|\frac{x}{a}-1\right|}\right) \)


\( a, b, c \) are three positive numbers and
\( a b c^{2} \) has greatest value \( \frac{1}{64} . \) Then
A \( \cdot a=b=\frac{1}{2}, c=\frac{1}{4} \)
В \( \cdot a=b=\frac{1}{4}, c=\frac{1}{2} \)
c. \( a=b=c=\frac{1}{3} \)
D. none of these


Preparation of Bakelite proceeds via
reactions :
A. Electrophilic substitution and dehydration
B. Electrophilic addition and dehydration
C. Nucleophilic addition and dehydration
D. Condensation and elimination


Which of the following correctly
represents Dalton's symbols?
1
2
3
4
0
0
A. 1: oxygen, 2: hydrogen, 3 : nitrogen, 4: carbon and 5 sulphur
B. 1: hydrogen, 2: nitrogen, 3 : oxygen, 4: carbon and 5 sulphur
C. 1: hydrogen, 2 : nitrogen, 3: oxygen, 4 : sulphur and 5 carbon
D. 1: hydrogen, 2: carbon, 3 : oxygen, 4 : sulphur and 5 nitrogen


HA is a weak electrolyte. At \( 25^{0} C \), the degree of dissociation of 0.5 mol \( L^{-1} \) HA is 0.1. What is its molar conductivity ( in \( \left.\boldsymbol{S} \boldsymbol{c m}^{2} \boldsymbol{m o l}^{-1}\right) ? \)
(The limiting molar conductivity of HA is \( 390 S c m^{2} m o l^{-1} \) )
A . 39
в. 195
\( c \cdot 3.9 \)
D. 390


Assertion
\( A l(O H)_{3} \) is amphoteric in nature.
Reason
It cannot be used as an antacid.
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 ladder of length 17 meters rests with one end against a vertical wall and the other on the level ground. if the lower end slipes away at the rate of \( 1 \mathrm{m} / \mathrm{sec} \)
then, when it is \( 8 m \) away from the well, its upper end is coming down at the rate of
\( ^{\mathrm{A}} \cdot \frac{5}{8}^{m / s e c} \)
в. \( \frac{8}{15} m / \)sec.
c. \( \frac{5 \pi}{8} m / \) sec.
D. \( \frac{15}{8} m / \) sec.


In a hydraulic machine, a force of \( 2 N \) is
applied on the piston of area of cross
section \( 10 \mathrm{cm}^{2} \). What force is obtained
on its piston of area of cross section
\( 100 \mathrm{cm}^{2} ? \)
A. 20 N
B. 10 N
\( c \cdot 5 N \)
D. 40 N


Factory waste is neutralized before
disposing it off into the water bodies. Explain why?


The distribution of Abhishek's high
school grades by percentage of course credits is given in the circle graph.

What is Abhishek's grade point average
if each \( A \) is worth 4 points; each \( B, 3 \)
points; and each \( C, 2 \) points?
A . 3.0
B. 3.4
\( c .3 .6 \)
D. 3.7
E. Cannot be determined from the given information


The haemoglobin like pigment is found
in
A. Seeds of legumes
B. Clostridium
c. Rhizobium
D. Leguminous root nodules


In the electrolysis of \( A g N O_{3} \) solution
\( 0.7 \mathrm{g} \) of \( \mathrm{Ag} \) is deposited after a certain period of time. Calculate the quantity of electricity required in coulomb. Molar mass of \( \mathrm{Ag} \) is \( 107.9 \mathrm{gmol}^{-1} \)
A \( \cdot 426^{\circ} \mathrm{C} \)
B. \( 536^{\circ} \mathrm{C} \)
c. \( 626^{\circ} \mathrm{C} \)
D. \( 736^{\circ} \mathrm{C} \)


\( \operatorname{Let} f(x)=\frac{1}{a x+b} \) then \( f^{\prime \prime}(0)= \)
A \( \cdot \frac{2 a^{3}}{b^{2}} \)
в. \( \frac{2 a^{2}}{b^{3}} \)
c. \( \frac{2 a^{3}}{b^{3}} \)
D. none of these


The formula of ethyne is:
A. \( C_{2} H_{2} \)
в. \( C_{6} H_{6} \)
\( \mathbf{c} \cdot C_{2} H_{4} \)
D. \( C_{2} H_{6} \)


The diagram shows the energy levels for an electron in a certain atom. Which
transition shown represents the
emission of a photon with the most energy?
\( A \cdot I \)
в. \( I I \)
c. \( I I I \)
D. \( I V \)


The radius of a semi-circular plot is 21
m. Find its area and perimeter.


Show that:
\( \sin ^{-1}\left(\frac{12}{13}\right)+\cos ^{-1}\left(\frac{4}{5}\right)+ \)
\( \tan ^{-1}\left(\frac{63}{16}\right)=\pi \)


A complex involving \( d^{2} s p^{3} \) hybridization
is :
A. a square planargeometry
B. a tetrahedral geometry
C. an octahedral geometry
D. trigonal planar geometry


What is geothermal energy?
A. Ocean thermal energy
B. Interior heat of the earth.
C. Energy obtained from the heat of hot dry rocks
D. None of these


Among the elements \( B, M g, A l \) and \( K \) the correct order of increasing metallic
character is:
A. \( B<A l<M g<K \)
в. \( B<M g<A l<K \)
c. \( M g<B<A l<K \)
D. \( M g<A l<B<K \)
Е. \( K<M g<A l<B \)


The moments of inertia of a non-
uniform circular disc (of mass \( \mathrm{M} \) and
radius \( R \) ) about four mutually perpendicular tangents \( A B, B C C D, D A \)
\( \operatorname{are} I_{1}, I_{2}, I_{3} \) and \( I_{4} \) respectively (the
square ABCD circumscribes the circle.)
The distance of the center of mass of
the disc from its geometrical center is
given by
A \( \cdot \frac{1}{4 M R} \sqrt{\left(I_{3}-I_{3}\right)^{2}+\left(I_{2}-I_{4}\right)^{2}} \)
B \( \cdot \frac{1}{12 M R} \sqrt{\left(I_{3}-I_{3}\right)^{2}+\left(I_{2}-I_{4}\right)^{2}} \)
C \( \cdot \frac{1}{3 M R} \sqrt{\left(I_{1}-I_{2}\right)^{2}+\left(I_{3}-I_{4}\right)^{2}} \)
D. \( \frac{1}{2 M R} \sqrt{\left(I_{1}-I_{2}\right)^{2}+\left(I_{3}-I_{4}\right)^{2}} \)


\( \cos 45^{\circ} \cdot \tan (-495)^{\circ}- \)
\( \tan 585^{\circ} \cdot \cot \left(-495^{\circ}\right)=0 \)


The value of the derivative of \( |\boldsymbol{x}-\mathbf{1}|+ \)
\( |x-3| \) at \( x=2 \) is:
\( A \cdot 2 \)
B.
\( c .0 \)
D. - 2


Most realistic growth curve is
A. J-shaped
B. Sigmoid
c. Parabolic
D. Both (A) \& (B)


The \( 4 t h \) term from the end of the \( A P \)
\( -11,-8,-5, \dots \dots \dots \dots \)
A . 37
B . 40
\( c .43 \)
D. 58


The acceleration due to gravity at a
place is \( 0.2 m / s 2 . \) Find its height above
the earth's surface.


Which of the following is the property of cardiac muscle?
A. It is involuntary muscles.
B. It is resistant to fatigue
c. It is striated muscle.
D. All of the above


Wobble hypothesis deals with
A. Phenomena of multiple codons coding for the code for a single amino acid
B. Phenomena of multiple codons coding for the code for a different amino acid
C. Phenomena of anticodon coding for the code for a different amino acid
D. None of the above


In figure, \( A B C D \) is a trapezoid in which
\( A B \) is parallel to \( \overline{C D}, \overline{A D} \) is perpendicular to \( \overline{D C} \), and \( \overline{A D} \) is
perpendicular to \( \overline{A B} \). Calculate the length of \( B C \).
4
3.
\( c \)
\( D \)
\( E \)


The degree and order of \( (2 x+ \)
\( \mathbf{3} \boldsymbol{y})\left(\frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}\right)^{3}+\mathbf{7} \boldsymbol{x} \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}}+\boldsymbol{y}=\boldsymbol{e}^{2 \boldsymbol{x}} \) are:
A .2,2
B. 1,3
\( c \cdot 1,2 \)
D. 2,


If the equivalence point is at a pH of 8.4 in an acid-base titration, then
indicator should be used
A. methyl violetttet met
B. alizarin yellow
c. phenolphthalein
D. methyl red


Which of the following statements is/are incorrect?
. Amylose does not give blue colour with
\( I_{2} \) solution.
II. Amylopectin gives blue colour with \( I_{2} \) solution.
III. Amylum is present in wheat, maize, rice, potatoes, barley, sorghum etc.
IV. Amylose is linear polymer of \( D \) glucose units.
A. I and II only
B. III and IV only
c. I and III only
D. II and III only


What is the activation energy of a
reaction if its rate doubles when
temperatures is raised from \( 20^{\circ} \mathrm{C} \) to \( 35^{\circ} \)
\( \mathrm{C} ?\left(\mathrm{R}=8.314 \mathrm{JK}^{-1} \mathrm{mol}^{-1}\right) \)
A. 34.7 k) \( m o l^{-1} \)
-
B. \( 15.1 \mathrm{kJ} \mathrm{mol}^{-1} \)
c. 342 k) \( m o l^{-1} \)
D. 269 ks \( m o l^{-1} \)


A beam of unpolarised light having flux \( 10^{-3} \) watt falls normally on a polarizer
of cross sectional area \( 3 \times 10^{-4} m^{2} \)
The polarizer rotates with an angular frequency of 31.4 rad/s. The energy of light passing through the polarizer per revolution will be:
\( \mathbf{A} \cdot 10^{-4} \) joule
B . \( 10^{-3} \) joule
C \( \cdot 10^{-2} \) joule
D. \( 10^{-1} \) joule


Absolute zero is:
This question has multiple correct options
A. the temperature at which all particles stop moving.
B. at -273 kelvins.
C . at 0 degrees Celsius.
D. the temperature at which water freezes.
E. the temperature at which all gases turn into liquids.


Point charges \( q_{1} \) and \( q_{2} \) lie on the \( x- \)
axis at points \( \boldsymbol{x}=-\boldsymbol{a} \) and \( \boldsymbol{x}=+\boldsymbol{a} \)
respectively. Given the net electrostatic force on point charge \( +\boldsymbol{Q} \) placed at \( \boldsymbol{x}= \)
\( +a / 2 \) to be zero and \( q_{1}=n q_{2} . \) Find \( n \)


Evaluate
\( \sin 1^{0} \sin 2^{0} \sin 3^{0} \ldots \sin 179^{0} \sin 180^{0} \)


All the students of a batch opted
Psychology, Business, or both. \( 73 \% \) of
the students opted Psychology and \( 62 \% \) opted Business. If there are 220
students, how many of them opted for both Psychology and business?
\( \mathbf{A} \cdot 60 \)
в. 100
c. 77
D. 35


The intensity of gamma radiation from
a given source is \( I . \) On passing through
\( 36 m m \) of lead, intensity is reduced to \( \frac{I}{8} . \) The thickness of lead which reduces the intensity to \( \frac{I}{2} \) is
\( \mathbf{A} \cdot 6 m m \)
B. \( 9 m m \)
\( c .18 m m \)
D. \( 12 \mathrm{mm} \)


Euclids division lemma, the general
equation can be represented as
A. \( a=b \times q+r \)
B. \( a=b \div q+r \)
c. \( a=b-q-r \)
D. \( a=b+q-r \)


Which compound acts as oxidising as well as reducing agent?
\( A \cdot S O_{2} \)
в. \( M n O_{2} \)
c. \( A l_{2} O_{3} \)
D. \( C r O_{3} \)


Assertion
A bell ringing in an evacuated jar
cannot be heard.
Reason
Sound waves in a gas are longitudinal.
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


Cleansing action of soap occurs
because:
A. oil and grease can be absorbed into the hydrophobic centres of soap micelles and washed away
B. oil and grease can be absorbed into hydrophilic centres of soap micelles and washed away
C. oil and grease can be absorbed into both hydrophilic and hydrophobic centres but cannot be washed away
D. cleansing action is not related to micelles


The kinetic energy needed to project a body of mass \( m \) from earth's surface
radius \( R \) ) to infinity is
A \( \cdot \frac{m g R}{2} \)
в. \( 2 m g R \)
c. \( m g R \)
D. \( \frac{m g R}{4} \)


Water is flowing continuously from a
tap having an internal diameter \( 8 \times 10^{-3} \)
m. The water velocity as it leaves the tap is \( 0.4 \mathrm{m} \mathrm{s}^{-1} \). The diameter of the water
stream at a distance \( 2 \times 10^{-1} \mathrm{m} \) below
the tap is close to
\( A \cdot 5.0 \times 10^{-3} \mathrm{m} \)
B. 7.5 \( \times 10^{-3} \mathrm{m} \)
c. \( 9.6 \times 10^{-3} \mathrm{m} \)
D. 3.6 \( \times 10^{-3} \mathrm{m} \)


A community, which starts succession in a habitat is
A. Pioneer community
B. Seral community
c. Biotic community
D. Ecosere


Show that the Signum Function \( \boldsymbol{f} \)
\( R \rightarrow R, \) is neither one one nor onto?
\[
f(x)=\left\{\begin{array}{l}
1, \text { if } x>0 \\
0, \text { if } x=0 \\
-1, \text { if } x<0
\end{array}\right.
\]


A wheel of radius \( r \) rolling on a straight
line, the velocity of its centre being \( \boldsymbol{v} \). At
a certain instant the point of contact of
the wheel with the grounds is \( M \) and \( N \)
is the highest point on the wheel
(diametrically opposite to \( M \) ). The
incorrect statement is:
A. The velocity of any point \( P \) of the wheel is proportional to MP.
B. Points of the wheel moving with velocity greater than v form a larger area of the wheel than points moving with velocity less than v.
C. The point of contact M is instantaneously at rest.
D. The velocities of any two parts of the wheel which are equidistant from centre are equal


What is the role of a catalyst in a reaction ?
A. Lowers the activation energy
B. Increase the activation energy
c. Affects the free energy change
D. Affects the enthalpy change


When \( 400 g \) of a \( 20 \% \) Solution was
cooled \( 50 g \) of the solute precipitated. What is the percent concentration of the
remaining solution.


Which of the following molecules represents the order of hybridisation
\( s p^{2}, s p^{2}, s p, s p \) from left to right carbon
atoms?
A \( \cdot C H_{2}=C H-C H=C H_{2} \)
в. \( H C=C-C \equiv C H \)
c. \( C H_{3}-C H=C H-C H_{3} \)
D. \( C H_{2}=C H-C \equiv C H \)


Which of the following statements
relationships is correct?
\( \mathbf{A} \cdot K_{P}=K_{C} \) for \( N_{2}+O_{2} \rightleftharpoons 2 N O \)
B. \( Q_{P}>K_{C} \) corresponds to backward reaction
C \( . K_{P} \) is not defined for \( C H_{3} C O O C H_{3}+H_{2} O \rightleftharpoons \)
\( C H_{3} C O O H+C H_{3} O H \)
D. \( K_{s p}=4 s^{-1} \) (for salt like \( C a F_{2} \) ) is applicable even in an \( H F \) solution


Number of spectral lines that are emitted by atomic hydrogen excited to
the \( n t h \) energy level is:
A \( \cdot \frac{1}{2} n(n-1) \)
B . \( \frac{1}{4} n(n-1) \)
c. \( \frac{1}{2} n(n+1) \)
D \( \cdot \frac{1}{2} n(n-2) \)


An object is placed on the principal axis of a concave mirror at a distance of 60
\( \mathrm{cm} . \) If the focal length of the concave mirror is \( 40 \mathrm{cm} \) then determine the magnification of the obtained image.
\( A \cdot 4 \)
B. - -
\( c \cdot-4 \)
\( D \cdot+2 \)


Calcium phosphate used in the production of :
A. phosphoric acid
B. fertilizers
c. both a and \( b \)
D. none of the above


Write difference between pioneer community and climax community


Solve graphically the following pairs of
equations. \( \boldsymbol{y}-\mathbf{2} \boldsymbol{x}+\mathbf{2}=\mathbf{0} ; \boldsymbol{y}=\mathbf{4} \boldsymbol{x}-\mathbf{4} \)
\( \mathbf{A} \cdot(1,0) \)
B \( \cdot(2,0) \)
\( \mathbf{c} \cdot(3,0) \)
D. None of these


Name the sulpha drug which is used for
the treatment of pneumonia?
A. Sulphapyridine
B. Sulphadiazine
c. sulphaguanidine
D. none of these


The four wire loops shown in figure have
vertical edge lengths of either \( L, 2 L \) or
3 \( L \). They will move with the same speed
into a region of uniform magnetic field \( \vec{B} \) directed out of the page. Rank them according to the maximum magnitude of the induced emf greatest to least.
A. 1 and 2 tie, then 3 and 4 tie
B. 3 and 4 tie, then 1 and 2 tie
c. 4,2,3,1
D. 4 then 2 and 3 tie, and then 1
E. answer required


Assertion
STATEMENT-1: An alcohol does not react
with \( C l^{-} \) ion in aqueous medium, but
reacts with concentrated \( H C I \) solution
to form alkyl chloride.
Reason
STATEMENT-2: The strong acid \( (\boldsymbol{H} \boldsymbol{C} \boldsymbol{I}) \) accelerates the removal of proton from
\( -O H \) group of alcohol
A. STATEMENT-1 is True, STATEMENT-2 is True STATEMENT-2 is a correct explanation for STATEMENT-
B. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1
C. STATEMENT-1 is True, STATEMENT-2 is False
D. STATEMENT-1 is False, STATEMENT-2 is True


Which of the following statement is
correct?
A. Alpha particles are singly ionised helium atoms
B. Protons and neutrons have exactly the same mass
C. Beta rays are same as cathode rays
D. Gamma rays are high energy neutrons


Mark the incorrect statement
A. During motion of waves, energy is transferred from one point to another
B. All vibrating bodies produce sound
C. A transverse wave consists of crests and troughs
D. Transverse wave can propagate through any medium


If \( \boldsymbol{A} \) is a square matrix such that \( \boldsymbol{A}^{2}= \)
\( I, \) then find the simplified value of \( (A- \)
\( \boldsymbol{I})^{3}+(\boldsymbol{A}+\boldsymbol{I})^{3}-\mathbf{7} \boldsymbol{A} \)


Which element among those listed below, has the lowest electronegativity?
A \( . M g \)
в. \( C a \)
\( c . B a \)
D. \( S r \)
E . \( B e \)


Compare LPG and wood as fuels.


How do you verify the 1st law of reflection of light with an experiment??


Which sugar does not increases the calorific value?
A. sucrose
B. Glucose
c. Aspartame
D. Fructose


A body dropped from a height \( h \) with initial velocity zero, strikes the ground with velocity \( 3 \mathrm{m} / \mathrm{s} \). Another body of the same mass is dropped from the height \( \boldsymbol{h} \) with an initial velocity of \( \mathbf{4} \mathrm{m} / \mathrm{s} \). Find the velocity with which it strikes the
ground.
\( A \cdot 3 m / s \)
B. \( 4 \mathrm{m} / \mathrm{s} \)
\( c \cdot 5 m / s \)
D. \( 12 \mathrm{m} / \mathrm{s} \)


If \( \alpha \neq \beta \) and \( |\beta|=1 \) then \( \left|\frac{\alpha-\beta}{1-\alpha \beta}\right| \)
equals
A . -
B. 0
\( c \)
D. None of these


Two thin lenses of focal lengths \( 20 \mathrm{cm} \)
and \( 25 c m \) are placed in contact. The effective power of the combination is
A. \( 9 D \)
в. \( 2 D \)
\( c .3 D \)
D. \( 7 D \)


Assertion
\( C_{p}-C_{V}=R \) for an ideal gas.
Reason \( \left[\frac{\partial \boldsymbol{E}}{\partial \boldsymbol{V}}\right]_{T}=\mathbf{0} \) for an ideal gas.
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


Nucleic acids are constituents of:
A. haemoglobin
B. nucleoproteins
c. all proteins
D. only lipid proteins


It is dangerous to leave the engine of a car running in a closed garage as it may lead to poisoning by:
A. carbon
B. petrol vapour
c. carbon dioxide
D. carbon monoxide


Which term of the arithmetic
progression \( 8,14,20,26 \dots \dots \dots \) will be 144 more than \( 23^{r d} \) term?


Determine the amount of \( C a C l_{2}(i= \) 2.47) dissolved in 2.5 litre of water such
that its osmotic pressure is 0.75 atm at
\( 27^{\circ} C \)


In which stage do chromosomes appear as thin long threads?
A. Zygotene
B. Pachytene
C. Leptotene
D. Prophose


Anthracene present in coal tar is
in nature.
A. neutral
B. acidic
c. basic
D. amphoteric


Which of the following is an indicator of water pollution?
A. Salmonella
B. Psedomonas
c. coliform bacteria
D. Yeast


\( \int \frac{7^{2 x+3} \sin ^{2} 2 x+\cos ^{2} 2 x}{\sin ^{2} 2 x}=\frac{7^{2 x+3}}{2 \log 7}- \)
\( \frac{(\cot x+x)}{b} \cdot \) Find \( b \)


Arrange the following in increasing value of magnetic moments.
(i) \( \left[\boldsymbol{F e}(\boldsymbol{C N})_{\mathbf{6}}\right]^{4-} \)
(ii) \( \left.\boldsymbol{F e}(\boldsymbol{C N})_{6}\right]^{3-} \)
(iii) \( \boldsymbol{C r}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{6}^{3+} \)
\( \left.(\text { iv }) N i\left(H_{2} O\right)^{4}\right]^{2+} \)
A \( \cdot(I)<(I I)<(I I I)<(I V) \)
в. \( (I)<(I I)<(I V)<(I I I) \)
c. \( (I I)<(I I I)<(I)<(I V) \)
D. \( (I V)<(I I I)<(I I)<(I) \)


Write the formula of the following complexes. Bis (ethnylene diammine) dichloro iridium
(III) ion


The number of oxygen atoms in 6.4 g of
oxygen are :
A. \( 6.023 \times 10^{23} \)
3 \( 3.02 \times 10^{3} \times 10^{-63} \)
В. \( 6.023 \times 10^{22} \)
c. \( 1.2046 \times 10^{23} \)
D. \( 1.2046 \times 10^{22} \)


What is the chemical formula of 2,4
dibromopentane?


Find the \( x \) coordinate of the particle at
the moment of time \( t=6 s \)
\( \mathbf{A} \cdot x=0.4 m \)
B. \( x=0.24 m \)
c. \( x=0.42 \mathrm{m} \)
D. \( x=0.44 \mathrm{m} \)


\( A=\cos ^{2} \theta+\sin ^{4} \theta, \) find range of \( A \)


The price of a garment has been reduced by \( 15 \% \) in a sale to \( R s 306 \) Find its original price.


A massless rope is wrapped several
times on a disc of mass \( \mathrm{M} \) and radius \( \mathrm{R} \).
The other end is tied to a mass \( \mathrm{m}, \) which
at the beginning is at a height of h above
the ground shown in the figure.

When released the velocity of the mass
as it touches the ground is
A \( \cdot \frac{m M I}{2(M+m)} \)
B. \( \frac{m l}{M+m} \)
\( c \)
\( \mathbf{D} \cdot_{v}=\sqrt{\frac{4 m g h}{2 m+M}} \)


Refer to the given figure. Select the
correct statement regarding the
labelled parts A-C.
A. The inner wall of B towards C is thick and elastic
B. The opening and closing of the stomata is due to change in the turgidity of B
C. The opening of the stoma is aided due to the orientation of A in the cell walls of B
D. All of these


Let \( A B C D E F \) be a convex hexagon in which the diagonals \( A D, B E, C F \) are
concurrent at \( O . \) Suppose the area of
triangle \( O A F \) is the geometric mean of
those of \( O A B \) and \( O E F ; \) and the area
of triangle \( O B C \) is the geometric mean
of those of \( \boldsymbol{O} \boldsymbol{A} \boldsymbol{B} \) and \( \boldsymbol{O} \boldsymbol{C} \boldsymbol{D} \). Prove that
the area of triangle \( O E D \) is the
geometric mean of those of \( O C D \) and
OEF.


The area bounded by the parabolas \( y^{2}=4 a(x+a) \) and \( y^{2}=-4 a(x-a) \)
is
A \( \cdot \frac{16}{3} a^{2} \) sq units
B. \( \frac{8}{3} \) sq units
c. \( \frac{4}{3} a^{2} \) sq units
D. None of these


Positive and negative point charges of equal magnitude are kept at \( \left(0,0, \frac{a}{2}\right) \) and \( \left(0,0, \frac{-a}{2}\right), \) respectively. The work done by the electric field when another
positive point charge is moved from \( (-a, 0,0) \) to \( (0, a, 0) \) is:
A. positive
B. negative
c. zero
D. depends on the path connecting the initial and final positions


Define Semipermeable membrane.


Assertion
NAND is a universal gate.
Reason
It can be used to describe all other logic
gates.
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


When ammonium chloride is dissolved
in water the solution becomes cold
because
A. Heat of solution of ammonium chloride is positive
B. Heat of solution of ammonium chloride is negative
c. Heat of dilution of ammonium chloride is positive
D. Heat of formation of ammonium chloride is positive


Evaluate the following question. \( \lim _{x \rightarrow 0} \sin x \)


State the following statement is True or
False

The zero of the polynomial \( x^{3}-27 \) is 3
A. True
B. False


Define specific latent heat of fusion, \( L_{f} \)
A. The specific heat of fusion of a substance is the quantity of heat required to convert a unit mass of the substance from liquid to gaseous state at its boiling point.
B. The specific heat of fusion of a substance is the quantity of heat required to convert a unit mass of the substance from solid to liquid state at its melting point.
C. The specific heat of fusion of a substance is the quantity of heat required to raise the temperature of unit mass of the substance by \( 1^{\circ} \mathrm{C} \)
D. The specific heat of fusion of a substance is the quantity of heat required to lower the temperature of unit mass of the substance by \( 1^{\circ} \mathrm{C} \)


\( \mathbf{A} \)
0.1 M solution of a monobasic acid
has a specific resistance of 'r' ohm-cm. Its molar conductivity is:
A \( \cdot \frac{10}{r} \)
в. \( 10 r \)
c. \( \frac{10^{4}}{r} \)
D. \( \frac{10^{4}}{2 r} \)


Define the following term. Surface charge density.


The replacement of diazonium group by fluorine is known as:
A . Gattermann reaction
B. Sandmeyer reaction
c. Balz-Schiemann reaction
D. Etard reaction


The value of the determinant
\( \left|\begin{array}{c}b^{2}-a b b-c b c-a c \\ a b-a^{2} a-b b^{2}-a b \\ b c-a c c-a a b-a^{2}\end{array}\right|= \)
A \( . a b c \)
B. \( a+b+c \)
c. 0
\( \mathbf{D} \cdot a b+b c+c a \)


What is the frequency of a wave if 3
waves are produced in half second?
\( \mathbf{A} .8 H z \)
в. \( 9 H z \)
\( \mathrm{c} .5 \mathrm{Hz} \)
D. \( 6 H z \)


Darwin correlated variations observed
in nature to variations found in
A. Human society
B. Breeding domesticated animals
c. Breeding crop plants
D. caged animals


Heisenberg uncertainty principle is not valid for :
This question has multiple correct options
A. moving electrons
B. motor car
c. stationary particles
D. all of the above


Explain two properties of carbon:
(i) Catenation
(ii) Tetravalency


Which of the following is true for indefinite integral?

This question has multiple correct options
A. An indefinite integral of a function fis a differentiable function F whose derivative is equal to the original function f.
B. This can be stated symbolically as \( F=f \)
c. without upper and lower limits, also called an antiderivative
D. None of the above


A.M. and H.M. between two quantities are 27 and 12 respectively, find their G.M


A man crosses the river, perpendicular
to river flow in time \( t \) seconds and
travels an equal distance down the stream in \( T \) second. The ratio of man's
speed in still water to the speed of river
water will be:
\( ^{A} \cdot \frac{t^{2}-T^{2}}{t^{2}+T^{2}} \)
в. \( \frac{T^{2}-t^{2}}{T^{2}+t^{2}} \)
c. \( \frac{t^{2}+T^{2}}{t^{2}-T^{2}} \)
D. \( \frac{T^{2}+t^{2}}{T^{2}-t^{2}} \)


Two simple harmonic motions are given
by
\( \boldsymbol{x}_{1}=\boldsymbol{a} \sin \omega \boldsymbol{t}+\boldsymbol{a} \cos \omega t \) and
\( \boldsymbol{x}_{2}=\boldsymbol{a} \sin \omega \boldsymbol{t}+\frac{\boldsymbol{a}}{\sqrt{\mathbf{3}}} \cos \boldsymbol{\omega} \boldsymbol{t} \)
The ratio of the amplitudes of first and
second motion and the phase difference between them are respectively
A \( \cdot \sqrt{\frac{3}{2}} \) and \( \frac{\pi}{12} \)
B. \( \frac{\sqrt{3}}{2} \) and \( \frac{\pi}{12} \)
c. \( \frac{3}{\sqrt{2}} \) and \( \frac{\pi}{12} \)
D. \( \sqrt{\frac{3}{2}} \) and \( \frac{\pi}{6} \)


Lines \( m \) and \( n \) are cut by a transversal
so that \( \angle 1 \) and \( \angle 5 \) are corresponding
angles. If \( \angle \mathbf{1}=\mathbf{2 6} \boldsymbol{x}-\mathbf{7}^{o} \) and \( \angle \mathbf{5}= \)
\( 20 x+17^{\circ} . \) What value of \( x \) makes the
lines \( m \) and \( n \) parallel?
A . 5
B. 4
c. \( _{4} \frac{1}{2} \)
D. \( _{3} \frac{1}{4} \)


The thickness of a newspaper sheet is of the order of
\( A \cdot 0.1 \mathrm{m} \)
B. \( 0.1 \mathrm{cm} \)
\( c .0 .1 \mathrm{mm} \)
D. 1 micrometre


The current density (number of free
electrons per \( m^{3} \) ) in metallic conductor
is of the order of
A \( \cdot 10^{2} \)
2
B. \( 10^{24} \)
\( c \cdot 10^{26} \)
D. \( 10^{2} \)


A series RLC circuit is made as shown
in the figure with an \( A C \) source of \( 60 \vee \)
20 Hz. Then
This question has multiple correct options
A. the rms current through the resistor R is 4.2 A
B. the effective potential difference between P and should be \( 42 \mathrm{v} \)
c. the instantaneous current leads the source voltage by 45
D. the instantaneous current lags behind the applied voltage by \( 45^{\circ} \)


Find the root of \( x^{2}-20 x+100 \)


\( \triangle A B C \) is similar to \( \triangle X Y Z \) by \( S A S \) similarity. If in \( \triangle A B C A B= \)
\( \mathbf{1 2}, \boldsymbol{B C}=\mathbf{8}, \angle \boldsymbol{B}=\mathbf{6 0} \)
and in \( \triangle \boldsymbol{X} \boldsymbol{Y} \boldsymbol{Z} \boldsymbol{X} \boldsymbol{Y}=\mathbf{3}, \angle \boldsymbol{Y}=\mathbf{6 0} . \) Find
the value of \( Y Z \)
A . 15
B . 20
\( c \cdot 4 \)
D. 2


Calculate the internal energy at \( 298 \mathrm{K} \)
for the formation of one mole of
ammonia, if the enthalpy change at
constant pressure is \( -42.0 \mathrm{kJ} \) mol\( ^{-1} \)
\( \left[\text { Given: } \boldsymbol{R}=\mathbf{8 . 3 1 4} \mathbf{J} \boldsymbol{K}^{-\mathbf{1}} \boldsymbol{m o l}^{-1}\right] \)


Electrical work done per unit time is
A. electrical energy
B. electrical current
c. electrical power
D. electrical circuit


Fuse wire is made up of
A. Alloy
B. Mixture
c. Metals
D. Non metals


The resistance of hot tungesten filament is about 10 times the cold resistance. The resistance of \( 100 \mathrm{W} \) and
\( 200 \mathrm{V} \) lamp, when not in use is
A . \( 40 \Omega \)
B. 20\Omega
c. \( 400 \Omega \)
D. 200\Omega


Two forces of \( 1 \mathrm{N} \) each act on the
smallest and the largest sides of a
rectangular box. Which side experiences greater pressure?


What used to be described as Nissi
granules in a nerve cell are now identified as?
A. Cell metabolites
B. Fat granules
c. Ribosomes
D. Mitochondria


Rainbow appears due to dispersion of sunlight by
A. Water droplets
B. Prism
c. Glass block
D. All


Write Ampere's circuital law. Obtain an expression for magnetic field on the axis of current carrying very long solenoid. Draw necessary diagram.


Sudoriferous glands are present in
A. Lung.
B. Kidney.
\( c . \) skin
D. Alimentary canal.


The composition in brown ring test is :
\( \mathbf{A} \cdot\left[F e\left(H_{2} O\right)_{6} N O\right] S O_{4} \)
\( \mathbf{B} \cdot\left[F e\left(H_{2} O\right)_{5} N O\right] S O_{4} \)
\( \mathbf{c} \cdot\left[F e\left(H_{2} O\right)_{4}(N O)_{2}\right] S O_{4} \)
\( \mathbf{D} \cdot\left[F e\left(H_{2} O\right)_{3} N O\right] S O_{4} \)


How are interhalogen compounds formed? What general compositions can be assigned to them?


The maximum and minimum resultant
capacity that can be obtained with \( 2 \mu F, 3 \mu F \) and \( 6 \mu F \) are respectively:
A. \( 11 \mu F, 1 \mu F \)
в. \( 11 \mu F, 6 \mu F \)
c. \( 11 \mu F, 2 \mu F \)
D. \( 11 \mu F, 4 \mu F \)


Sound of frequency below \( 20 H z \) is
called
A. audio sounds
B. infrasonic
c. ultrasonic
D. supersonics


Carbon present in the compounds is oxidised to carbon dioxide which:
A. turns blue litmus redd
B. turns lime water milky
c. turns solution to green
D. has no effect on solution


Calculate the escape velocity of a body from the surface of the earth. [Average
density of earth \( =5.5 \times \)
\( \mathbf{1 0}^{\mathbf{3}} \mathbf{k g} / \boldsymbol{m}^{\mathbf{3}}, \boldsymbol{G}=\mathbf{6 . 6 7} \times \)
\( 10^{-11} N m^{2} / k g^{2}, \) radius of earth \( R= \)
\( \left.\mathbf{6 . 4} \times \mathbf{1 0}^{\mathbf{6}} \mathbf{m}\right] \)


Find the valueof \( c \) if the point (4,5)
pases through \( \boldsymbol{y}=\mathbf{5} \boldsymbol{x}+\boldsymbol{c} \)
A . -15
B. 15
\( c .5 \)
\( D \cdot-5 \)


An ant moves along a circle 5 times in 1
minute with a uniform speed and a
lizard moves in a straight line to and fro
5 times in 5 minutes. Then
A. The motion of the ant is uniformly accelerated but non periodic
B. The motion of the lizard is uniformly accelerated but non periodic
C. Both ant and lizard are periodic
D. Both ant and lizard are accelerated and their direction
is along the direction of velocity


For the manufacture of ammonia by the
reaction \( \boldsymbol{N}_{2}+\boldsymbol{3} \boldsymbol{H}_{2} \rightleftharpoons \mathbf{2} \boldsymbol{N} \boldsymbol{H}_{3}+ \)
21.9 \( K c a l \), the favorable conditions are:
A. low temperature, , low pressure \& catalyst
B. low temperature, high pressure \& catalyst
c. high temperature, low pressure \( \& \) catalyst
D. low temperature, high pressure


Find the discriminant of the equation
and the nature of roots. Also find the
roots, if they are real:
\( 3 x^{2}-2 x+\frac{1}{3}=0 \)
A. Roots are imaginary
B. \( \mathrm{D}=0, \) Roots are real and equal \( \frac{1}{3}, \frac{1}{3} \)
\( \mathrm{c} \cdot_{\mathrm{D}=} \frac{2}{5}, \) Roots are real and unequal \( \frac{1}{5}, \frac{1}{2} \)
D. Cannot be determined


If the displacement-time graph of an object is a curve, the object
A. is stationary
B. moves with uniform velocity
c. moves with non-uniform velocity
D. moves with infinite velocity


Kingdom Animalia is also known as
A. Metazoa
B. Protozoa
c. Both A and B
D. None of the above


Bouncing of light into the same medium, from which the light ray is incident, is termed as
A. Refraction
B. Diffraction
c. Reflection
D. Scattering


Reaction, \( \boldsymbol{C l}_{2}+\mathbf{2} \boldsymbol{N} \boldsymbol{a} \boldsymbol{O} \boldsymbol{H} \rightarrow \boldsymbol{P} \)
What are the products?
A. \( N a C l+N a O C l+H_{2} \)
в. \( N a C l+N a O C l+H_{2} O_{2} \)
c. \( N a C l+N a O C l+H_{2} O \)
D. \( N a C l+N a O C l+O_{2} \)


Two particles of masses \( m_{1}, m_{2} \) movie
with initial velocities \( u_{1} \) and \( u_{2} . \) On
collision, one of the particles get excited to higher level, after absorbing energy If final velocities of particles be
\( v_{1} \) and \( v_{2} \) then we must have :
A \( \cdot \frac{1}{2} m_{1} u_{1}^{2}+\frac{1}{2} m_{2} u_{2}^{2}=\frac{1}{2} m_{1} v_{1}^{2}+\frac{1}{2} m_{2} v_{2}^{2}-\varepsilon \)
B. \( \frac{1}{2} m_{1} u_{1}^{2}+\frac{1}{2} m_{2} u_{2}^{2}+\varepsilon=\frac{1}{2} m_{1} v_{1}^{2}+\frac{1}{2} m_{2} v_{2}^{2} \)
c. \( \frac{1}{2} m_{1}^{2} u_{1}^{2}+\frac{1}{2} m_{2}^{2} u_{2}^{2}-\varepsilon=\frac{1}{2} m_{1}^{2} v_{1}^{2}+\frac{1}{2} m_{2}^{2} v_{2}^{2} \)
D. \( m_{1}^{2} u_{1}+m_{2}^{2} u_{2}-\varepsilon=m_{1}^{2} v_{1}+m_{2}^{2} v_{2} \)


If \( c \) is 6 less than thrice of \( b \), which of
the following represents the relation between b and c?
A \( \cdot c=\frac{b-2}{3} \)
B. \( c=\frac{b+2}{3} \)
c. \( c=3 b-2 \)
\( \mathbf{D} \cdot c=3 b-6 \)


Select the correct statement(s):
This question has multiple correct options
\( \mathbf{A} \cdot P b I_{4}, F e I_{3} \) do not exist while \( P b C l_{4}, F e C l_{3} \) exist.
B \( \cdot P b C l_{4}, F e C l_{3} \) do not exist while \( P b I_{4}, F e I_{3} \) exist.
\( \mathrm{C} \cdot \mathrm{CO}_{2} \) is gaseous while \( \mathrm{SiO}_{2} \) is solid.
D. \( C O_{2} \) is solid while \( S i O_{2} \) is gaseous.


All the products formed in the oxidation
of \( N a B H_{4} \) by \( I_{2}, \) are:
A. \( B_{2} H_{6} \) and \( N a I \)
B. \( B_{2} H_{6}, H_{2} \) and \( N a I \)
\( \mathrm{c} . B I_{3} \) and \( N a H \)
D. \( N a B I_{4} \) and \( H I \)


A body at \( 50^{0} \) cools in a surrounding
maintained at \( 30^{0} \) C. The temperature
at which the area of cooling is half that
of the begining is
A \( \cdot 16.3^{0} \mathrm{C} \)
в. 26.3 \( ^{0} \) С
\( c \cdot 40^{0} c \)
D. \( 46.3^{0} \mathrm{C} \)


Find the area of a rhombus whose
perimeter is \( 80 \mathrm{m} \) and one of whose diagonal is \( 24 \mathrm{m} \)
A. 324 sq. \( \mathrm{m} \)
B. 384 sq.m
c. 184 sq.m
D. 326 sq.m


In one average life:
A. half the radioactive nuclei decay
B. less than half the radioactive nuclei decay
C. more than half the radioactive nuclei decay
D. all the nuclei decay


Assertion
The configuration of \( B \) -atom cannot be
\( 1 s^{2} 2 s^{2} \)
Reason
Hund's rule demands that the
configuration should display maximum multiplicity.
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


Let \( f(x) \) be a continuous function which satisfies \( \boldsymbol{f}\left(\boldsymbol{x}^{2}+\mathbf{1}\right)=\frac{\mathbf{2}}{\boldsymbol{f}\left(\mathbf{2}^{x}\right)-\mathbf{1}} \boldsymbol{\&} \)
\( \boldsymbol{f}(\boldsymbol{x})>\mathbf{0} \forall \boldsymbol{x} \varepsilon \boldsymbol{R} \) Then \( \lim _{\boldsymbol{x} \rightarrow \mathbf{1}} \boldsymbol{f}(\boldsymbol{x}) \) is
\( A \cdot 4 \)
B. 2
\( c \)
D. does not exist


The sum of number of neutrons and
protons in all the isotopes of hydrogen is :
\( A \cdot 2 \)
B. 4
\( c \cdot 5 \)
D. 6


Pyrolysis of benzene sulphonic acid to form phenol is by:
A. combustion
B. double displacement
c. addition-elimination
D. both A and B


Derive the formula for the ionization
constant \( \left(K_{b}\right) \) for weak bases.


If \( a_{1}=a_{2}=2, a_{n}=a_{n-1}-1(n>2) \)
then \( a_{5} \) is ?
\( \mathbf{A} \cdot \mathbf{1} \)
B. - -
\( c .0 \)
D. -


Many elements have non integral atomic masses because:

This question has multiple correct options
A. they have isotopes
B. their isotopes have non-integral masses
C. their isotopes have different masses
D. the constituents, neutrons, protons and electrons combine to give fractional masses


10 g of cane sugar (molecular mass =
342) in \( 1 \times 10^{-3} m^{3} \) of solution
produces an osmotic pressure of \( 6.68 \times 10^{4} N m^{-2} \) at \( 273 \mathrm{K} . \) Calculate
the value of \( \mathrm{R} \) in SI units.
A. \( 8.3684 J K^{-1} \mathrm{mol}^{-1} \)
B . \( 9.3684 J K^{-1} \) mol \( ^{-1} \)
c. \( 7.3684 J K^{-1} \) mol \( ^{-1} \)
D. \( 5.3684 J K^{-1} \) mol \( ^{-1} \)


The angle between particle velocity and wave velocity in transverse waves is
A . \( \pi \)
в. \( \pi / 2 \)
c. \( \pi / 4 \)
D. zero


The conductor AD moves to the right in a uniform magnetic field directed into
the paper:
\( (x) \)
This question has multiple correct options
A. The free electrons in AD will move towards A
B. D will acquire a positive potential with respect to A
C. If \( D \) and \( A \) are joined by a conductor externally, a current will flow from A to D in AD
D. The current in AD flows from lower to higher potential


A lake near a village suffered heavy mortally of fishes within a few days. Consider the following reasons for this.
(A) Lots of urea and phosphate fertilizers were used in the crops in the vicinity.
(B) The area was sprayed with DDT by an aircraft.
(C) The lake water turned green and stinky
(D) Phytoplankton populations in the lake declined initially thereby greatly reducing photosynthesis. Which two of the above were the main
causes of fish mortality in the lake?
\( A \cdot(A),(C) \)
B. (A), (B)
\( c \cdot(B),(C) \)
D. (c), (D)


Which one of the following is a tertiary alcohol?
A. \( C H_{3} C H_{2} C H_{2} O H \)
в. \( C H_{3} C H(O H) C H_{3} \)
c. \( \left(C H_{3}\right)_{2} \) СНСН\( _{2} \) ОН
D. \( \left(C H_{3}\right)_{3} C O H \)


From a point within a triangle segments are drawn to the vertices A necessary
and sufficient condition that the three
triangles formed have equal areas is that the point be
A. such that the three angles formed each have a measure of 120
B. the centre of the inscribed circle
c. the centre of the circumscribed circle
D. the intersection of the medians


Aluminium oxide is not reduced by
chemical reaction since
A. reducing agent contaminates
B. the process pollutes the environment
c. aluminium oxide is highly stable
D. aluminium oxide is reactive


Formation of nitric oxide is a highly
exothermic reaction.
A. True
B. False


How many times a \( 0.1 M \) strong monobasic acid solution should be
diluted so that \( p H \) of the resulting solution is tripled?
\( \mathbf{A} \cdot 50 \)
в. 10
c. 25
D. 100
E. 1000


Which of the following reptile is warm blooded?
A. chelone
B. Heloderma
c. crocodilus
D. None of the above


If \( f_{1}(x) \) and \( f_{2}(x) \) are defined on
domains \( D_{1} \) and \( D_{2} \) respectively, then
\( f_{1}(x)+f_{2}(x) \) is defined on \( D_{1} \cap D_{2} \)
A. True
B. False


KCN forms soluble complex with silver
If true enter 1 , else enter 0


nanometer is \( _{--} \) femtometer.
A \( \cdot 10^{5} \)
B. \( 10^{\text {6 }} \)
\( c \cdot 10^{7} \)
D. \( 10^{4} \)


Autumnal leaf colour is due to
A. chlorophyll a
B. Carotenoids
c. Anthocyanins
D. Betacyanin


The outer electronic configuration of transitional elements is:
A \( \cdot(n-1) s^{2} n d^{1-2} \)
B \( \cdot(n+1) s^{2} n d^{1-5} \)
C \( \cdot(n-1) s^{2} n p^{6}(n-1) d^{1-10} n s^{1,2} \)
D \( \cdot n s^{2}(n-1) d^{1-10} \)


How many electrons constitute a
current of one microampere?
\( \mathbf{A} \cdot 6.25 \times 10^{6} \)
B. \( 6.25 \times 10^{12} \)
\( \mathbf{C} \cdot 6.25 \times 10^{9} \)
D. \( 6.25 \times 10^{15} \)


The field normal to the plane of wire of \( n \) turns and radius r which carries i is
measured on the axis at a small
distance h from the centre of the coil
The is smaller than field at the center by
the fraction
\( ^{A} \cdot \frac{2 h^{2}}{13 r^{2}} \)
в. \( \frac{3 r^{2}}{2 h^{2}} \)
c. \( \frac{3 h^{2}}{2 r^{2}} \)
D. \( \frac{2 h^{2}}{3 r^{2}} \)


Find the perimeter of each of the following closed figures:
(ii)


In the reaction \( \boldsymbol{H}_{2} \boldsymbol{S}+\boldsymbol{C l}_{2} \rightarrow \boldsymbol{2} \boldsymbol{H} \boldsymbol{C l}+ \)
\( S, \) the oxidizing agent is :
A \( . H_{2} \)
в. \( C l_{2} \)
c. \( H C l \)
D. \( S \)


Let \( a, b, c \) be the sides of a triangle. No
two of them are equal and \( \lambda \epsilon R \) If the
roots of the equation \( x^{2}+2(a+b+ \)
\( c) x+3 \lambda(a b+b c+c a)=0 \) are real
then.


Subtract the first rational number from
the second in each of the following:
\( \frac{11}{13}, \frac{-4}{13} \)


Assertion
If a positively charged particle is placed in front of a spherical uncharged conductor. The number of lines of forces
terminating on the sphere will be more than those emerging from it.
Reason
The surface charge density at a point on the sphere nearest to the point charge will be negative and maximum in magnitude compared to other points on the sphere
A. If both Assertion and Reason are correct and Reason is the correct explanation of Assertion
B. If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion
c. If Assertion is correct but Reason is incorrect
D. If Assertion is incorrect but Reason is correct


The electronic configuration of two elements \( X \) and \( Y \) are given below:
\( \boldsymbol{X}=\mathbf{2}, \mathbf{8}, \mathbf{2} \)
\( \boldsymbol{Y}=\mathbf{2}, \mathbf{8}, \mathbf{7} \)
The formula of a compound that can be formed between these two elements is:
A . \( X Y \)
в. \( X Y_{2} \)
c. \( X_{2} Y \)
D. \( X Y_{3} \)


Find the sum to infinite terms of the
series \( \frac{7}{5}\left(1+\frac{1}{10^{2}}+\frac{1.3}{1.2} \cdot \frac{1}{10^{4}}+\frac{1.3 .5}{1.2 .3} \cdot \frac{1}{10^{6}}+\right. \)


Investigate for what values of \( \lambda, \mu \) the
simultaneous equation \( \boldsymbol{x}+\boldsymbol{y}+\boldsymbol{z}= \)
\( \mathbf{6} ; \boldsymbol{x}+\mathbf{2} \boldsymbol{y}+\mathbf{3} \boldsymbol{z}=\mathbf{1 0} \& \boldsymbol{x}+\mathbf{2} \boldsymbol{y}+\boldsymbol{\lambda} \boldsymbol{z}= \)
\( \mu \) have a unique solution
A. \( \lambda \neq 3 \)
в. \( \lambda \neq 5 \)
c. \( \lambda \neq 1 \)
D. \( \lambda \neq 2 \)


A stretched spring possesses
energy.
A. kinetic
B. elastic potential
c. electric
D. magnetic


Unsaturated solvents are
filled with solutes.
A. completely
B. not completely
c. Both a and
D. None of the above


In mosses, asexual reproduction is also known as
A. Alternation of generations
B. Sporophyte generation
c. Vegetative reproduction
D. Gametophyte reproduction
E. Binary fission


In a class of 60 boys and 20 girls, half of the boys and half of the girls know cricket. Find the probability of the event that a person selected from the class is
either a boy or a girl who knows cricket.


Let \( m \) be a positive integer and \( \Delta_{r}= \) \( \left|\begin{array}{ccc}\mathbf{2 r}-\mathbf{1} & \boldsymbol{m} \boldsymbol{C}_{\boldsymbol{r}} & \mathbf{1} \\ \boldsymbol{m}^{\mathbf{2}}-\mathbf{1} & \mathbf{2}^{\boldsymbol{m}} & \boldsymbol{m}+\mathbf{1} \\ \sin ^{2}\left(\boldsymbol{m}^{2}\right) & \sin ^{2}(\boldsymbol{m}) & \sin ^{2}(\boldsymbol{m}+\mathbf{1})\end{array}\right| \)
\( \boldsymbol{r} \leq \boldsymbol{m}) . \) Then the value of \( \sum_{r=0}^{m} \boldsymbol{\Delta}_{\boldsymbol{r}} \)
\( A . \)
B. \( m^{2}-1 \)
\( c \cdot 2^{m} \)
D \( \cdot 2^{m} \sin ^{2}\left(2^{m}\right) \)


An urn contains 6 white and 4 black
balls. A fair die whose faces are
numbered from 1 to 6 is rolled and
number of balls equal to that of the number appearing on the die is drawn from the urn at random. The probability that all those are white is
A. 1 5
B. \( \frac{2}{5} \)
\( c \cdot \frac{3}{5} \)
\( D \cdot \frac{4}{5} \)


Evaluate \( \int_{0}^{2} 3 x+2 d x \)


The role of metal written on arrows in the given chemical reactions is :
\( \mathrm{cH}_{3} \mathrm{CooH}+\mathrm{cH}_{3} \mathrm{cH}_{2} \mathrm{oH} \frac{\mathrm{Conc.} \mathrm{H}_{2} \mathrm{s} \mathrm{O}_{4}}{\longrightarrow} \mathrm{cH}_{3} \mathrm{cooc}_{2} \mathrm{H}_{5}+\mathrm{H}_{2} \mathrm{O} \)
\( \mathrm{cH}_{3} \mathrm{cH}_{2} \mathrm{o} \) н \( \frac{\mathrm{Alk}_{4} \mathrm{KMn}_{4}}{\mathrm{Heat}} \)
A. catalyst
B. oxidising agent
c. reducing agent
D. dehydrating agent


Monazite is an ore of:
A. titanium
B. throium
c. zirconium
D. iron


Based on equations reducible to linear
equations Solve for \( x \) and \( y \frac{1}{3 x}-\frac{1}{7 y}=\frac{2}{3} ; \frac{1}{2 x}- \)
\( \frac{1}{3 y}=\frac{1}{6} \)
A. \( x=1 / 8, y=1 / 2 \)
в. \( x=1 / 3, y=1 / 6 \)
c. \( x=1 / 7, y=1 / 8 \)
D. \( x=1 / 5, y=1 / 7 \)


An ideal gas is enclosed in a cylinder with a movable piston on top of it. The
piston has a mass of \( 8000 g \) and an
area of \( 5.00 \mathrm{cm}^{2} \) and is free to slide up
and down, keeping the pressure of the gas constant. How much work is done
on the gas as the temperature of 0.200 mol of the gas is raised from
\( \mathbf{2 0 . 0 ^ { \circ }} \boldsymbol{C} \) to \( \mathbf{3 0 0 ^ { \circ }} \boldsymbol{C} \) ?
A. \( -466 J \)
в. -233.5
с. 233 .
D. \( 0 . J \)


The second stage of demographic transition is characterised with
population explosion.
A. True
B. False


Find the slope of the inclination of the
line of the following:
\( \boldsymbol{\theta}=\mathbf{6 0}^{\circ} \)
A \( \cdot \frac{1}{\sqrt{3}} \)
B. \( \sqrt{3} \)
c. \( \frac{2}{\sqrt{3}} \)
D. \( \frac{\sqrt{3}}{2} \)


In how many ways can 5 men can draw water from 5 taps if no tap can be used
more than once?
A. 120
B. 75
\( c .32 \)
D. 62


Hydrolysis of trichloromethane with
aqueous KOH gives?
A . acetic acid
B. methanol
c. formic acid
D. ethanol


If the air pressure of an area decreases suddenly then our blood vessels swells
up and sometimes bursts.
A. True
B. False


Buchner was successful in extracting a respiratory enzyme complex
A. ATP
B. NADH
c. zymase
D. Mitochondria


Zinc, cadmium and mercury are found in nature as sulphides. Values of standard reduction potentials for the half-reactions are :
\( M^{2+}(a q)+2 e^{-} \rightarrow M(s) \)
\( M \quad E^{\circ} \)
\( Z n-0.76 V \)
\( C d \quad-0.40 V \)
\( H g+0.79 V \)
Which sulphides give element not
oxide on roasting?
A. \( Z n S \)
в. \( H g S \)
c. \( C d S \)
D. None of these


Express 0.006006 in scientific notation
with three significant digits.
A. \( 6.01 \times 10^{-3} \)
B. \( 6.006 \times 10^{-3} \)
c. \( 6.00 \times 10^{-3} \)


\( 4 \mu F \) and \( 6 \mu F \) capacitors are joined in series and \( 500 v \) are applied between
the outer plates of the system. What is the charge on each plate?
A \( \cdot 1 \cdot 2 \times 10^{3} C \)
в. \( 6 \cdot 0 \times 10^{3} C \)
\( \mathrm{c} \cdot 5 \cdot 0 \times 10^{-3} \mathrm{C} \)
D. \( 2 \cdot 0 \times 10^{-3} C \)


Which of the following best explains the evolution of sexual reproduction?
A. Chlamydomonas
B. Ulothrix
c. Puccinia
D. Albugo


Maximum work in periodic table related with atomic number was done by:
A. Mendeleev
B. Aston
c. Mosley
D. Newland


The figure represents two bodies of masses \( 10 \mathrm{kg} \) and \( 20 \mathrm{kg} \) and moving with an initial velocity of \( 10 m s^{-1} \) and
\( 5 m s^{-1}, \) respectively. They are colliding with each other, After collision, they are
moving with velocities \( 12 m s^{-1}, 4 m s^{-1} \) respectively. The time of collision is 2 s.
Then calculate \( F_{1} \) and \( F_{2} \)


Mercury is used as a thermometric liquid.
A. True
B. False


Find the eleventh term of the A.P.
\( 7,13,19,25, \dots \dots \)


Match the nuclear processes given in column I with the appropriate option(s) in column II.


\( \int(\sin x)^{99}(\cos x)^{-101} d x=_{-} \ldots-C_{ } \)
A. \( \frac{(\tan x)^{100}}{100} \)
B. \( \frac{(\tan x)^{2}}{2} \)
c. \( \frac{(\tan x)^{98}}{98} \)
D. \( \frac{(\tan x)^{97}}{97} \)


Hemoglobin in the RBCs helps in the
A. Transport of oxygen
B. Transport of nutrients
C. Transport of carbon dioxide
D. Both A and C


What should be the angle of banking of
a circular track of radius \( 600 m \) which
is designed for cars at an average speed
of \( 180 k m / h ? \)


The cyanide ions are toxic because they bind almost irreversibly to the \( \boldsymbol{F e}(\boldsymbol{I} \boldsymbol{I} \boldsymbol{I}) \)
ion in:
A. cytochrome oxidase
B. thyroid
c. haemoglobin.
D. cytochrome C.


pascal is equal to \( \ldots \ldots . N m^{-2} \)
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot 3 \)
D. 4


If the order of a matrix is \( 20 \times 5 \) then
the number of elements in the matrix is
\( \mathbf{A} \cdot \mathbf{5} \)
B. 20
c. 50
D. 100


Find the total current that passes
through the circuit. Find the heat
generated across the each resistor:


What is the common difference of an
A.P., in which \( a_{21}-a_{7}=644 \)


If \( f(x)=\tan x, \) find \( f^{\prime}(x) \) and hence find \( \boldsymbol{f}^{\prime}\left(\frac{\boldsymbol{\pi}}{\boldsymbol{4}}\right) \)


Write the following in the simplest form:
\( \tan ^{-1}\left\{\frac{\sqrt{1+x^{2}}-1}{x}\right\}, x \neq 0 \)


Plants in cold regions shed leaves because of
A. cold weather
B. Water scarcity
c. Longer nights
D. shorter days


Electric intensity due to a charged sphere at a point outside the sphere decreases with
A. increase in charge on sphere
B. increase in dielectric constant
c. decrease in the distance from the centre of sphere
D. decrease in square of distance from the centre of sphere


The specific latent heat of fusion of
water is :
A. 80 cal \( g^{-1} \)
В. \( 2260 \mathrm{J} g^{-1} \)
c. \( 80 J g^{-1} \)
D. \( 3366 J g^{-1} \)


Find the velocity of the disc after the
collision.
A. \( v^{\prime}=\frac{4+\eta}{4+\eta} v \)
B. \( v^{\prime}=\frac{4-\eta}{4-\eta} v \)
\( ^{\mathrm{C}} \cdot v^{\prime}=\frac{4-\eta}{4+\eta} v \)
D. \( v^{\prime}=\frac{4+\eta}{4-\eta} v \)


The charge through a conductor of
resistance \( R \) varies with time as \( \boldsymbol{q}= \)
\( a t-b t^{2} \) where a and \( b \) are constant.
Total heat produced in \( R \) is
A \( \cdot R a^{3} / 3 b \)
в. \( R a / 6 b \)
c. \( R a^{2} / 9 b \)
D. \( R a^{3} / 6 b \)


Describe an experiment that would demonstrate that growth stimulating
hormone is produced at the tip of coleoptile.


The potential difference between points \( A \) and \( B, \) in a section of a circuit shown,
is
A. 5 volt
B. 1 Volt
c. 10 volt
D. -16volt


\( K_{m} \) value of enzyme is substrate
concentration at
\( A \cdot 10 \vee_{\max } \)
B. \( 0.5 / 1 \mathrm{V}_{\max } \)
c. \( 1 / 2 \mathrm{v}_{\max } \)
D. \( 4 / 5 \mathrm{V}_{\max } \)


If \( A \) and \( B \) are two matrices such that
\( A B=0 \) and \( A \) is non-singular, then
\( \mathbf{A} \cdot B=0 \)
B. \( B \) is singular
c. \( B \) is non-singular
D. \( B=A \)


Obtain the value of \( \frac{\cos 45^{\circ}}{\sec 30^{\circ}+\operatorname{cosec} 30^{\circ}} \)


Solve \( \int \frac{1-\sqrt{x}}{1+\sqrt{x}} d x \)
A \( \cdot 3 \sqrt{x}+\frac{x}{2}-3 \log (1+\sqrt{x})+c \)
B \( 3 \sqrt{x}+3 \log (1+\sqrt{x})-\frac{1}{2} x+c \)
c. \( 3 \sqrt{x}-\frac{1}{2} x-3 \log (1+\sqrt{x})++c \)
D. \( 4 \sqrt{x}-x-4 \log (1+\sqrt{x})+c \)


Coal mining has been known, since:
\( A . \quad 1750 \) A.D.
B. 675 A.D
c. Roman times
D. Mediaeval times


An engine moving away from a vertical cliff blows a horn at frequency f. Its speed is \( 0.5 \% \) of the speed of sound in air. The frequency of the reflected sound received at the engine is :
A . 0.990
B. 0.995 f
\( c .1 .005 f \)
D. 1.010


What is the simplified value of \( \frac{\sin 2 A}{1+\cos 2 A} ? \)
\( \mathbf{A} \cdot \tan A \)
B. \( \cot A \)
\( c \cdot \sin A \)
D. \( \cos A \)


What is the solution used for the
preparation of hydrogen peroxide by electrolytic procedure?
A \( .0 .2 N N a O H \)
в. \( 50 \% \) Н \( _{2} \) S \( O_{4} \)
c. \( 20 \% \) NaOH
D. \( 5 \% \) NaCl


In the reaction \( x \) and \( y \) are:
\( \mathbf{A} \cdot x=H_{2} \cdot P d / B a S O_{4} ; y=N a O A c, A c_{2} O \)
B \( \cdot x=L i A l H_{4} ; y=N a O A c, A c_{2} O \)
C \( \cdot x=H_{2}, P d / C ; y=N a O H, A c_{2} O \)
\( \mathbf{D} \cdot x=L i A l H_{4} ; y=N a O H, A c_{2} O \)


\( \Delta H>\Delta E \)
Which of the following reaction follows
the above relation?
\( \mathbf{A} \cdot C H_{4}(g)+2 O_{2}(g) \rightarrow C O_{2}(g)+2 H_{2} O(g) \)
B \( . N_{2}(g)+3 H_{2}(g) \rightarrow 2 N H_{3}(g) \)
\( \mathbf{c} \cdot C_{2} H_{4}(g)+3 O_{2}(g) \rightarrow 2 C O_{2}(g)+2 H_{2} O(g) \)
D. \( \operatorname{CaCO}_{3}(s) \rightarrow \operatorname{CaO}(s)+C O_{2}(g) \)


Define chemical twins. Write general
electronic configuration of actinoids.


Which is the correct for the following reaction:
\( \boldsymbol{B}(\boldsymbol{O} \boldsymbol{H})_{3}+\boldsymbol{H}_{2} \boldsymbol{O} \rightarrow\left[\boldsymbol{B}(\boldsymbol{O} \boldsymbol{H})_{4}\right]^{-}+ \)
\( \boldsymbol{H}^{+} \)
A. \( B(O H)_{3} \) is a Lewis acid
B. \( B(O H)_{3} \) is a Lewis base
C. \( B(O H)_{3} \) is amphoteric
D. None of the above


Which physical quantities remain constant in U.C.M?


The spieces that undergoes disproportionation in an alkaline medium is:
A \( . M n O_{4}^{2} \) мпо4
B. \( C l O_{4}^{-} \)
c. \( N O_{2} \)
D. all of the above


The conservation of electric charge
implies that
This question has multiple correct options
A. charge cannot be created
B. charge cannot be destroyed
C. the number of charged particles in the universe is constant
D. simultaneous creation of equal and opposite charges is permissible


The mode of the following distribution is
Size \( \mathbf{3} \) and 4
20 Frequency \( \quad 10 \quad 12 \quad 25 \)
A. Only 4
B. Only 6
c. Both 4 and 6
\( D \)


GC / AT ratio in E. coli is
A . 0.93: 1
B. 1: 0.93
c. 1: 1.52
D. 1.52:


A body of mass \( m \) is lifted up from the
surface of earth to a height three times the radius of the earth \( R \) The change in
potential energy of the body is
A. \( 3 m g R \)
в. \( \frac{5}{4} \) mg \( R \)
c. \( \frac{3}{4} m g R \)
D. \( 2 m g R \)


If \( \boldsymbol{E} \) and \( \boldsymbol{F} \) be events in a sample space
such that \( \boldsymbol{P}(\boldsymbol{E} \cup \boldsymbol{F})=\mathbf{0 . 8}, \boldsymbol{P}(\boldsymbol{E} \cap \boldsymbol{F})= \)
0.3 and \( P(E)=0.5, \) then \( P(F) \) is
A . 0.6
B.
\( c .0 .8 \)
D. None


The number of \( \pi \) -electrons present in
naphthalene is:
\( \mathbf{A} \cdot \mathbf{6} \)
B. 4
c. 10
D. 14


In the chemical reaction \( N_{2}+ \)
\( \mathbf{3} \boldsymbol{H}_{2} \rightleftharpoons \mathbf{2} \boldsymbol{N} \boldsymbol{H}_{3} \) at equilibruim:
A. equal volumes of \( N_{2} \& H_{2} \) are reacting
B. equal masses of \( N_{2} \& H_{2} \) are reacting
c. the reaction has stopped
D. the same amount of ammonia is formed as is decomposed into \( N_{2} \) and \( H_{2} \)


When water boils the temperature
remains constant. Give reasons.


A particles performing uniform circular motion. Its angular frequency is doubled and its kinetic energy halved, then the new angular momentum is
A \( \cdot \frac{L}{4} \)
B. \( 2 L \)
c. \( 4 L \)
D. \( \frac{L}{2} \)


In dilute alkaline solution \( M n O_{4}^{-} \)
changes to:
A \( \cdot M n O_{4}^{2} \)
в. \( M n O_{2} \)
c. \( M n_{2} O_{3} \)
D. \( M n O \)


Find the value of \( \sin ^{-1} x+\sin ^{-1} \frac{1}{x}+ \)
\( \cos ^{-1} x+\cos ^{-1} \frac{1}{x} \)


Rutherford said that electrons revolve
around the nucleus in circular paths called:
A . circles
B. orbits
c. wheels
D. sphere


The soil in field is highly acidic. list any two materials which can be added to
this soil to reduce its acidity. give the
reason for your choice.


Two metallic spheres \( A \) and \( B \) kept on
insulating stands are in contact with
each other. A positively charged rod \( P \) is
brought near the sphere \( A \) as shown in
the figure. The two spheres are
separated from each other, and the rod
\( P \) is removed. What will be the nature of
charges on spheres \( \boldsymbol{A} \) and \( \boldsymbol{B} \) ?


If the volume of a cuboid is \( 880 \mathrm{cm}^{3} \) and
area of base is \( 88 \mathrm{cm}^{2} \). Find the height.


Virus with nucleic acid but without
protein coat is
A. Virion
B. Viroid
c. capsid
D. Prion


We know that friction depends upon
mass of the body. When we roll down an
iron ball and a football on the ground, which ball will travel more distance?
Why?


The graph of the equation \( 4 y^{2}+x^{2}= \)
25 is
A . a circle
B. an ellipse
c. a hyperbola
D. a parabola
E . a straight line


Find the angles between the lines \( \sqrt{3} x+y=1 \) and \( x+\sqrt{3} y=1 \)


For an \( L-R \) circuit, the inductive
reactance is equal to the resistance \( \boldsymbol{R} \)
of the circuit. An emf \( \boldsymbol{E}=\boldsymbol{E}_{0} \cos (\boldsymbol{w} \boldsymbol{t}) \) is
applied to the circuit. Then, the power consumed in the circuit is :
A \( \cdot \frac{E_{0}}{R} \)
в. \( \frac{E_{0}^{2}}{4 R} \)
c. \( \frac{4 R}{E_{0}} \)
D. \( \frac{R}{E_{0}} \)


When zinc is reacted with dil. sulphuric acid,which gas is evolved?
\( A \cdot O_{2} \)
в. \( H_{2} \)
\( c \cdot S O_{2} \)
D. \( S O_{3} \)


If \( M=\{x: x \in N, 1<x \leq 4\} \) and
\( N=\{y: y \in W, y<3\} \)


In the extraction of nickel by Monds process, the metal is obtained by:
A. Electrochemical reduction
B. Thermal decomposition
c. Chemical reduction by aluminium
D. Reduction by carbon


By changing the metal electrodes and gas inside the cathode ray tube,
A. The same particles-electrons were produced.
B. The same particles-neutrons were produced.
c. The same particles-protons were produced
D. New particles were produced


The wrong statement about \( N_{2} O \) is :
A . it is nitrous oxide
B. it is least reactive oxide of nitrogen
c. it is not a linear molecule
D. it is known as laughing gas


10,20,40,80 is an example of
A . fibonacci sequence
B. harmonic sequence
C. arithmetic sequence
D. geometric sequence


The solution of \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\frac{\boldsymbol{x} \boldsymbol{y}}{\boldsymbol{x}^{2}+\boldsymbol{y}^{2}} \) is
A. \( \quad \frac{x^{2}}{y^{2}} \)
\[
x=c e^{\frac{1}{2}}
\]
в. \( \quad y=c e^{\frac{x^{2}}{y^{2}}} \)
c.
\[
y=c e^{\frac{x^{2}}{2 y^{2}}}
\]
D. \( \quad x=c e^{\frac{2 x^{2}}{y^{2}}} \)


\( \mathbf{A} \mathbf{5 0} \boldsymbol{W}, \mathbf{1 0 0} \boldsymbol{V} \) lamp is to be connected
to an \( A C \) mains of \( 200 V, 50 H z . \) What capacitance is essential to be put in series with the lamp?
A . 9.2
B. 8
c. 10
D. 12


\( \left|\begin{array}{ccc}\boldsymbol{x}+\boldsymbol{\alpha} & \boldsymbol{\beta} & \gamma \\ \boldsymbol{\alpha} & \boldsymbol{x}+\boldsymbol{\beta} & \gamma \\ \boldsymbol{\alpha} & \boldsymbol{\beta} & \boldsymbol{x}+\boldsymbol{\gamma}\end{array}\right|=\mathbf{0}, \) then \( \boldsymbol{x} \) is
equal to
\( \mathbf{A} \cdot 0,-(\alpha+\beta+\gamma) \)
B. \( 0, \alpha+\beta+\gamma \)
c. \( 1, \alpha+\beta+\gamma \)
D. \( 0, \alpha^{2}+\beta^{2}+\gamma^{2} \)


Evaluate \( \left(\frac{7}{8} x+\frac{4}{5} y\right)^{2} \)
A. \( \frac{49}{64} x^{2}+\frac{6}{25} y^{2}+\frac{7}{5} x y \)
B \( \cdot \frac{18}{77} x^{2}+\frac{16}{5} y^{2}+\frac{1}{5} x y \)
c. \( \frac{13}{22} x^{2}+\frac{16}{25} y^{2}+\frac{1}{5} x y \)
D. \( \frac{49}{64} x^{2}+\frac{16}{25} y^{2}+\frac{7}{5} x y \)


Assertion
Heavy metals such as cadmium,
mercury, nickel etc. are water
pollutants.
Reason
Heavy metals are not harmful to
humans.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Assertion
Plastics are non-biodegradable.
Reason
As they cannot be decomposed by micro-organisms.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


If the vectors \( \vec{a}, \vec{b}, \vec{c} \) are coplanar, then the value of \( \left|\begin{array}{ccc}\overrightarrow{\boldsymbol{a}} & \overrightarrow{\boldsymbol{b}} & \overrightarrow{\boldsymbol{c}} \\ \overrightarrow{\boldsymbol{a}} \cdot \overrightarrow{\boldsymbol{a}} & \overrightarrow{\boldsymbol{a}} \cdot \overrightarrow{\boldsymbol{b}} & \overrightarrow{\boldsymbol{a}} \cdot \overrightarrow{\boldsymbol{c}} \\ \overrightarrow{\boldsymbol{b}} \cdot \overrightarrow{\boldsymbol{a}} & \overrightarrow{\boldsymbol{b}} \cdot \overrightarrow{\boldsymbol{b}} & \overrightarrow{\boldsymbol{b}} \cdot \overrightarrow{\boldsymbol{c}}\end{array}\right|= \)
\( \mathbf{A} \cdot \mathbf{1} \)
B.
\( c \cdot-1 \)
D. \( \vec{a}+\vec{b}+\vec{c} \)


Find the molecular mass of:
(a) \( \boldsymbol{H}_{2} \boldsymbol{S}(\mathbf{b}) \boldsymbol{H} \boldsymbol{C l}(\mathbf{c}) \boldsymbol{N} \boldsymbol{H}_{3} \)
(d) \( C l_{2} \)
\( \boldsymbol{C H}_{3} \boldsymbol{C O O H}(\mathrm{f}) \boldsymbol{C H}_{3} \boldsymbol{C H O} \)


Ferrimagnetic those expected to have large magnetism but actually have small net magnetic moment e.g. magnetic \( \left(\boldsymbol{F} \boldsymbol{e}_{3} \boldsymbol{O}_{4}\right), \) ferrites \( \left(\boldsymbol{M}^{2}+\right. \)
\( F e_{2} O_{4} \) ). This is because of unequal
number of domains in opposite direction.


What is refining of metals? Explain with
diagram the method of electrolysis by which copper is purified.


An infinite non-conducting sheet of
charge has a surface charge density of \( 10^{-7} C / m^{2} . \) The separation between two
equipotential surfaces near the sheet whose potential difference by \( 5 V \) is
A \( .0 .88 \mathrm{cm} \)
В. \( 08.8 m m \)
c. \( 0.88 m \)
D. \( 5 \times 10^{-7} m \)


The following are some equations about Nernst equations.
I) For metal electrode: \( E=E^{0}- \)
\( \frac{2.303 R T}{n F} \log \frac{[M]}{\left[M^{n+}\right]} \)
II) For metal electrode: \( E=E^{0}+ \)
\( \frac{2.303 R T}{n F} \log c \)
III) For non-metal electrode: \( E=E^{0}- \)
\( \frac{0.059}{n} \log c\left[A^{n-}\right] \)
IV) For non-metal electrode: \( E=E^{0}- \)
\( \frac{2.303 R T}{n F} \log c\left[A^{n-}\right] \)
The correct answer is :
A. only I and III are correct
B. only II and IV are correct
C. only I and IV are correct
D. all are correct


A partition divides a container having insulated walls into two components
and II The same gas filled in both components whose initial parameters
are given The partition is conducting wall which can freely move without
friction Choose the correct statements
(is/are) with respect to the final
equilibrium position:

This question has multiple correct options
A. The pressure in two compartments are equal
B. Volume of compartment I is \( 3 v / 5 \)
c. Volume of compartment II is \( 12 \% / 5 \)
D. Final pressure in compartment lis 5P/3


Water softening by Clark's process
uses:
\( \mathbf{A} \cdot C a H C O_{3} \)
в. \( \operatorname{NaH} \mathrm{CO}_{3} \)
\( \mathbf{c} \cdot N a_{a} C O_{3} \)
\( \mathbf{D} \cdot \operatorname{Ca}(O H)_{2} \)


toppr
Q Type your question
wires have same length, but thickness
of wire \( \mathrm{B} \) is twice that of wire \( \mathrm{A} \). The
conducting wires connecting \( A \) and \( B \)
to the ideal cell are resistance less. The
dependence of electric potential on
position along the length of two wires is given in option.
\( A \)
B.
\( c \)
D.
\( E \)


The negation of \( \boldsymbol{q} \vee \sim(\boldsymbol{p} \wedge \boldsymbol{r}) \) is?
\( \mathbf{A} \cdot \sim q \wedge \sim(p \vee r) \)
В \( . \sim q \wedge(p \wedge r) \)
\( \mathbf{c} \cdot \sim q \vee(p \wedge r) \)
D. \( r \vee(p \wedge r) \)


For a set of positive numbers, consider
the following statements:
1. If each number is reduced by \( 2, \) then the geometric mean of the set may not always exists.
2. If each number is increased by 2 , then the geometric mean of the set is increased by 2 Which of the above statements is/are
correct?
A. 1 only
B. 2 only
c. Both 1 and 2
D. Neither 1 nor 2


Mark the correct statement:
A. Resistivity is the measure of a materials ability to oppose the flow of current
B. Unit of resistivity is Ohm meter
C. Resistivity is constant for a particular range of temperature
D. All


A compound \( X \) consists of only
molecules. Hence \( \boldsymbol{X} \) will have :
A. a crystalline hard structure
B. a low melting point and low boiling point
\( c . \) an ionic bond
D. a strong force of attraction between its molecules


Subcellular level of body organisation is found in
A. Protozoans
B. Porifers
c. Prokaryotes
D. Non living organisms


A proton moves with a speed of \( 5.0 \times \) \( 10^{6} \mathrm{m} / \mathrm{s} \) along the \( \mathrm{x} \) -axis. It enters a
region where there is a magnetic field of magnitude \( 2.0 . \) Tesla directed at an
angle of \( 30^{\circ} \) to the \( x \) -axis and lying in the xy-plane. The magnitude of the magnetic force on the proton is?
A. \( 0.8 \times 10^{-13} \mathrm{N} \)
В. \( 1.6 \times 10^{-13} \mathrm{N} \)
c. \( 8.0 \times 10^{-13} \mathrm{N} \)
D. \( 8.01 \times 10^{-13} \mathrm{N} \)
E \( .16 \times 10^{-13} \mathrm{N} \)


Example of positive geotropism is
A. closing of flowers
B. Upward growth of stem
c. Downward growth of root
D. Lateral growth of root


Why do we see a rainbow in the sky only
after rainfall?
A. The water droplets behave like prism and reflects sunlight
B. The water droplets behave like convex lens and disperses sunlight.
C. The water droplets behave like prism and disperses sunlight.
D. The water droplets behave like concave lens and disperses sunlight.


Assertion
Derivative of \( 3 \cot x+5 \operatorname{cosec} x \) is
\( -\operatorname{cosec} x(3 \operatorname{cosec} x+5 \cot x) \)
Reason
\( \boldsymbol{f}^{\prime}(\boldsymbol{a})=\lim _{\boldsymbol{h} \rightarrow \mathbf{0}} \frac{\boldsymbol{f}(\boldsymbol{a}+\boldsymbol{h})-\boldsymbol{f}(\boldsymbol{a})}{\boldsymbol{h}} \)
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


Study the following bar chart and
answer the questions based on it. The histogram below shows the marks
of 50 students in an examination.
Examine the diagram and answer the
questions.
If the minimum marks for passing is 40
then what percentage of students have
failed in the examination?
A . \( 5 \% \)
B . \( 10 \% \)
c. \( 14 \% \)
D . 28\%


The points \( A(2 a, 4 a), B(2 a, 6 a) \) and
\( \boldsymbol{C}(\mathbf{2} \boldsymbol{a}+\sqrt{\mathbf{3}} \boldsymbol{a}, \mathbf{5} \boldsymbol{a}),(\mathbf{w h e n} \boldsymbol{a}>\boldsymbol{o}) \)
vertices of


In an experiment, it was observed that when the length of a wire in an electrical circuit is doubled. everything else remaining same, the current becomes half. On the other hand, if the thickness
(diameter) of the wire is doubled, the
current becomes 4 imes. Two wires \( W_{1} \)
and \( W_{2} \) of the same metal have the
same current passing through them
The thickness of wire \( W_{2} \) is twice that
of \( W_{1}, \) then the length wire \( W_{2} \) is
A. sixteen times that of \( S W_{1} \)
B. Four times that of wire \( W_{1} \)
C. Two times that of wire \( W_{1} \)
D. Same as that of wire \( W_{1} \)


Isotopes of an element have:
This question has multiple correct options
A. the same physical properties.
B. same chemical properties.
C. different number of neutrons.
D. different atomic numbers.


Active transport
A. Releases energy
B. Requires energy
C. Produces ATP
D. Produces a toxic substance


Which of the following reacts with water to give ethane?
A \( \cdot C H_{4} \)
в. \( C_{2} H_{5} M g B r \)
\( \mathbf{c} \cdot C_{2} H_{4} O H \)
D. \( C_{2} H_{5} O C_{2} H_{5} \)


Identify the Indian breeds of sheep:
A . Lohi
B. Marwari
c. Nal
D. All of these


ff \( y=y(x) \) and it follows the relation \( \mathbf{2} e^{x y^{2}}+\boldsymbol{y} \cos \left(x^{2}\right)=4, \) then \( \left|\boldsymbol{y}^{\prime}(\mathbf{0})\right| \) is
equal to


State whether true or false:
The thermal capacity of 10 g of a substance is 8 calories then its specific
heat is 1.25 cal \( g^{-1 o} C^{-1} \)
A. True
B. False


Which of the following can be beaten into thin sheet?
A. coal
B. Phosphorus
c. Aluminium
D. Sulphur


Which of the following forest tree is
used for medicinal purpose?
A . Neem
B. Oak
c. Turmeric
D. Basil


What is the remainder, when
\( \left(4 x^{3}-3 x^{2}+2 x-1\right) \) is divided by
\( (x+2) ? \)
A . - 49
B. 55
\( c \cdot-30 \)
D. 37


Which pair do not have equal
dimensions?
A. Energy and torque
B. Force and impulse
C. Angular momentum and Planck's constant
D. Elastic modulus and pressure


The human eye can focus objects at different distances by adjusting the focal length of the eye lens. This is due
to
A. presbyopia
B. accomodation
c. near-sightedness
D. far-sightedness


Which microbe is used to extract
ethanol from fruit juices and sugar
molasses?


Pericycle in roots is never thick and sclerenchymatous because
A. it does not act as mechanical tissue in roots
B. it gives rise to root hairs
c. it is place o f origin of lateral roots
D. it gives rise both to root hairs and root branches


Went demonstrated the role of auxins
using
A. Root tips
B. Coleoptiles
c. callus tissue
D. Lateral meristems


In any \( \Delta A B C, \sum\left(\frac{\sin ^{2} A+\sin A+1}{\sin A}\right) \) is
always greater than
A . 9
B. 3
c. 27
D.


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


A body of mass \( m \) is raised from the
surface of the earth to a height \( n R\left(R^{-}\right. \)
radius of earth). Magnitude of the change in the gravitational potential energy of the body is \( \left(g^{-}\right. \) acceleration due to gravity on the surface of earth)
A \( \cdot\left(\frac{n}{n+1}\right) m g R \)
\( ^{\mathbf{B}} \cdot\left(\frac{n-1}{n}\right) m g R \)
c. \( \frac{m g R}{n} \)
D. \( \frac{m g R}{(n-1)} \)


If expiratory reserve volume is \( 1100 \mathrm{ml} \) residual volume is \( 1200 \mathrm{ml} \) and tidal
volume is \( 500 \mathrm{ml} \), what shall be the
functional residual capacity?
A . \( 1600 \mathrm{ml} \)
B. 2800 m!
c. \( 2300 \mathrm{ml} \)
D. \( 1200 \mathrm{ml} \)


Reaction rate increases
with
A. concentration
B. pressure
c. both a and \( b \)
D. none of above


A compound contains \( 28 \% \) of nitrogen and \( 72 \% \) metal by mass. 3 atoms of the metal combine with 2 atoms of the
nitrogen. Find the atomic mass of the
metal.
A . 24
B. 25
\( c \cdot 23 \)
D. 21


The structure A represents Wedge-Dash Notation of a compound. The structures to IV represents Fischer Projections for the same compound. Which Fischer
Projection is correct representation of
structure A?
\( A \)
B. I
\( c \)
\( D \cdot 1 v \)


Construct a quadrilateral \( P Q R S \) in which \( \boldsymbol{P Q}=\mathbf{5} \boldsymbol{c m}, \boldsymbol{Q} \boldsymbol{R}=\mathbf{7 . 5 c m}, \boldsymbol{R S}= \)
\( P S=6.5 c m, \) and \( P R=10 c m \)
Measure the diagonal \( Q S \)


Free services provided to humans by
ecosystems include
A. control of atmospheric carbon dioxide concentration
B. prevention of soil erosion
c. filtering of pollutants from water and air.
D. all of the above


An enzyme which can only act in acidic medium is
A. Pepsin
B. Trypsin
c. Renin
D. Amylase


If a letter is chosen at random from the
English alphabet, if the probability that the letter is a consonant is \( \frac{a}{26}, \) then
what is the value of \( a ? \)


A ray of light is incident normally on one
face of a \( 30^{\circ}-60^{\circ}-90^{\circ} \) prism of
refractive index \( \frac{\mathrm{t}}{\text { imersed in water of }} \) \( \mathbf{Z} \)
refractive index \( \frac{-}{2} \) as shown \( \overline{\mathbf{3}} \)
This question has multiple correct options
A \( \cdot \) the exit angle \( \theta_{2} \) of the ray is \( \sin ^{-1}\left(\frac{5}{8}\right) \)
B \( \cdot \) the exit angle \( \theta_{2} \) of the the ray is \( \sin ^{-1}\left(\frac{5}{4 \sqrt{3}}\right) \)
C. total internal reflection at point P ceases if the
refractive index of water is increased to \( \frac{5}{2 \sqrt{3}} \) by
dissolving some substance
D. Total internal reflection at point P ceases if the
refractive index of water is increased to \( \frac{-b y}{y} \)
dissolving some substance.


At \( 400 \mathrm{K}, \) the half-life of a sample of a gaseous compound initially at 56.0 \( k P a \) is 340 s. When the pressure is 28.0
\( k P a, \) the half-life is 170 s. The order of
the reaction is:
A. 0
B. 2
\( c \)
D. \( 1 / 2 \)


One mol of a gas at NTP is suddenly expanded to three times its initial
volume. If \( C_{v}=2 R, \) the ratio of initial to
final pressure of gas will nearly be
A . 5
B. 4
\( c \cdot 3 \)
D. 2


Describe one experiment to demonstrate the phenomenon of electromagnetic induction.


The values of coefficients to balance the
following reaction are:
\( \boldsymbol{C r}(\boldsymbol{O H})_{3}+\boldsymbol{C l O}^{-}+\boldsymbol{O H}^{-} \rightarrow \)
\( \boldsymbol{C r} \boldsymbol{O}_{4}^{2-}+\boldsymbol{C l}^{-}+\boldsymbol{H}_{2} \boldsymbol{O} ? \)
A \( \cdot \operatorname{Cr}(O H)_{3}-(2), C l O^{-}-(3), C r O_{4}^{2-}-(3), C l^{-}-(3) \)
B. \( \operatorname{Cr}(O H)_{3}-(2), C l O^{-}-(4), C r O_{4}^{2-}-(3), C l^{-}-(2) \)
c. \( \operatorname{Cr}(O H)_{3}-(2), \operatorname{ClO}^{-}-(4), \operatorname{Cr} O_{4}^{2-}-(4), C l^{-}-(2) \)
D. \( \operatorname{Cr}(O H)_{3}-(2), C l O^{-}-(3), C r O_{4}^{2-}-(2), C l^{-}-(3) \)


If the polarizing angle of a piece of glass
for green light is \( 54.74^{\circ}, \) then the angle of minimum deviation for an equilateral prism made of same glass is :
\( \left[\mathrm{GIVEN}, \tan 54.74^{\circ}=1.414\right] \)
A \( \cdot 45^{\circ} \)
B. 54.74
\( c \cdot 60 \)
\( D \cdot 30^{\circ} \)


Freons are:
A. highly stable
B. unreactive
C . easily liquefiable gases
D. All the above


Urine formation occurs in
A . Liver
B. Kidney
c. spleen
D. Heart


Verify whether \( \boldsymbol{A} \subset \boldsymbol{B} \) for the sets \( \boldsymbol{A}= \)
\( \{\{a, b, c\}\}, B=\{1,\{a, b, c\}, 2\} \)


Which of the following is absent in the DNA of bacterial prokaryotes?
A. Histone proteins
B. Acidic proteins
c. Double stranded nature
D. None of the above


A rectangular block \( 5 \mathrm{m} \times 4 \mathrm{m} \times 2 \mathrm{m} \) lies
on a table with its largest surface in contact with the table. The work done to
keep it so that the block rests on the smallest surface is, if its density is 600 \( \mathbf{k} \boldsymbol{m}^{-\mathbf{3}} \)
A . 352800 J
B. zero
c. \( 376000 \mathrm{J} \)
D. \( 24,0000 \mathrm{J} \)


If the value of \( b^{2}-4 a c^{\prime} \) is greater than
zero, the quadratic equation \( a x^{2}+b x+ \)
\( c=0 \) will have
A. Two Equal Real Roots.
B. Two Distinct Real Roots.
c. No Real Roots.
D. No Roots or Solutions.


Three resistances \( 2 \Omega, 4 \Omega, 5 \Omega \) are combines in series and this
combination is connected to a battery
of \( 12 \mathrm{V} \) emf and negligible internal resistance. The potential drop across these resistances are.
A . (5.45,4.36,2.18) V
B. (2.18,5.45,4.36) \( \mathrm{v} \)
c. (4.36,2.18,5.45) v
D. (2.18,4.36,5.45)\( \vee \)


AD is an altitude of an isosceles
triangle \( A B C \) in which \( A B=A C . \) show
that
(i) AD bisects BC
(ii) AD bisects \( \angle A \)


Express the following angle into radians
\( \mathbf{5 0}^{\circ} \mathbf{3 7}^{\prime} \mathbf{3 0}^{\prime \prime} \)


Which of the following is 100 times sweeter than sugar?
A. sucrolose
B. Saccharin
c. Aspartame
D. Alitame


If \( y=\log (\sec x+\tan x), \) then \( \frac{d y}{d x}= \)
\( \mathbf{A} \cdot \sec x \)
в. \( \frac{1}{\sec x+\tan x} \)
C. \( \log \left(\cos x+\sec ^{2} x\right) \)
D. none of these


The Sl units of thrust and pressure are
respectively given by :
A. \( N, N m^{2} \)
В. \( N, N m^{-2} \)
c. \( N m^{-1}, N m^{-2} \)
D. \( N m^{-2}, N \)


Greater the \( _{---} \) value, better is the
fuel.
A. gold
B. iodine
c. calorific
D. decane


The percentage error in the \( 11^{t h} \) root of
the number 28 is approximately times the
percentage error in 28
A \( \cdot \frac{1}{28} \)
в. \( \frac{1}{11} \)
c. 11
D. 28


Prepare hydrogen from dil. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \)
A \( \cdot 2 Z n+H_{2} S O_{4}(d i l) \rightarrow 2 Z n S O_{4}+H_{2} \)
B. \( Z n+H_{2} S O_{4}(d i l) \rightarrow Z n S O_{4}+H_{2} \)
c. \( Z n+2 H_{2} S O_{4}(d i l) \rightarrow 2 Z n S O_{4}+H_{2} \)
D. \( 2 Z n+2 H_{2} S O_{4}(d i l) \rightarrow 2 Z n S O_{4}+2 H_{2} \)


If the frequency or revolution of the electron in first Bohr orbit of a H-atom
is \( 6.6 \times 10^{15} \mathrm{Hz} \), the frequency in the
next orbit is
A \( \cdot 13.2 \times 10^{15} \) Н 2
В. \( 43.50 \times 10^{30} \) Нz
c. \( 0.8 \times 10^{15} \) Н \( z \)
D. \( 1.65 \times 10^{15} \) Н \( z \)


Which type of fiber is flax?
A. Leaf fiber
B. Bast fiber
c. Animal fiber
D. Fruit fiber


Temperature can be expressed as a
derived quantity in terms of :
A. length and mass
B. mass and time
c. length, mass and time
D. none of these


The values of \( k \) for which the equation
\( 2 x^{2}+k x+x+8=0 \) will have real and
equal roots are
\( A \cdot 10 \) and -6
B. 7 and -9
\( c \cdot 6 \) and -10
D. -7 and 9


\( e\left(\lim _{x \rightarrow \beta}(\tan x \cot \beta-1)\right) \)
is equal to
A \( \cdot \frac{1}{\sin \beta \cos \beta} \)
\( \mathbf{B} \cdot \sin \beta \cos \beta \)
c. \( \frac{-1}{\sin \beta \cos \beta} \)
D \( \cdot e^{\sec ^{2} \beta \cot \beta} \)


When a number \( x \) is subtracted from
each of the numbers \( 8,16, \) and \( 40, \) the resulting three numbers form a geometric progression. Find the value of
\( \boldsymbol{x} \)
A . 3
B. 4
c. 6
D. 12
E . 18


Though friction can provide necessary centripetal force, the banking of roads is considered as advantageous in
highways:
A . True
B. False


Explain how Corpuscular theory predicts the speed of light in a medium,
say, water, to be greater than the speed of light in vacuum. Is the prediction confirmed by experimental determination of the speed of light in water? If not, which alternative picture of light is consistent with experiment?


A line through \( \boldsymbol{A}(-\mathbf{5},-\mathbf{4}) \) meets the
line \( \boldsymbol{x}+\mathbf{3} \boldsymbol{y}+\mathbf{2}=\mathbf{0}, \mathbf{2} \boldsymbol{x}+\boldsymbol{y}+\mathbf{4}=\mathbf{0} \)
and \( x-y-5=0 \) at the point \( B, C \) and
\( D \) respectively. If \( \left(\frac{15}{A B}\right)^{2}+ \) \( \left(\frac{10}{A C}\right)^{2}=\left(\frac{6}{A D}\right)^{2} . \) Find the equation
of the line.


Find the measures of the missing angle
in the given triangle.
A \( \cdot 30^{\circ} \)
В. \( 60^{\circ} \)
\( c \cdot 90^{\circ} \)
D. \( 12^{\circ} \)


The importance of the Kreb's cycle is
A. Production of amino acid
B. Production of vitamin
C. Production of ATP molecule through oxidative phosphorylation
D. ATP formation through oxidative and substrate level phosphorylation


Which one yields drug for malaria?
A. Penicillium
B. Algae
c. Bacteria
D. cinchona bark


Two boys are standing at the ends \( A \) and B of a ground, where \( A B=a \). The boy at \( B \) starts running in a direction perpendicular to AB with velocity \( v_{1} \). The boy at A starts running simultaneously with velocity \( v \) and catches the other boy in a time \( t, \) where \( t \) is
A. \( \frac{a}{\sqrt{v^{2}+v_{1}^{2}}} \)
в. \( \sqrt{\frac{a^{2}}{v^{2}-v_{1}^{2}}} \)
c. \( \frac{a}{\left(v-v_{1}\right)} \)
D. \( \frac{a}{\left(v+v_{1}\right)} \)


How much energy is needed to convert \( 100 g \) of ice at \( 263 K \) to liquid water at
a temperature of \( 283 K ? \)
\( \boldsymbol{C}_{\boldsymbol{i c e}}=\mathbf{0 . 4 9} \boldsymbol{c a l} /\left(\boldsymbol{g}^{o} \boldsymbol{C}\right) \)
\( \boldsymbol{C}_{\boldsymbol{w} \text {ater}}=\mathbf{1 . 0 0} \boldsymbol{c a l} /\left(\boldsymbol{g}^{\boldsymbol{o}} \boldsymbol{C}\right) \)
\( \Delta H_{f u s}=79.8 \mathrm{cal} / g \)
\( \boldsymbol{\Delta} \boldsymbol{H}_{\boldsymbol{v a p}}=\mathbf{5 4 0} \boldsymbol{c a l} / \boldsymbol{g} \)
A .9470 call \( l \)
B. 3288 cal
c. 2288 cal
D. 727.3 cal


Which of the following compounds
would react most readily by the \( S_{N} 2 \)
mechanism?
\( A \)
в. \( H_{2} C=C H-B r \)
\( c \)
D. None of these


Assertion
An element (X) with an atomic number
of 16 has 14 electrons in \( X^{2-} \)
Reason
Two protons bind the two outermost electrons
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


Fuel obtained from biomass are:
A. Charcoal (from wood)
B. Bio-gas from animal waste (cow-dung etc).
C. Bio-diesel (from sugar cane and oilseed crops).
D. All of above


\( \boldsymbol{C H}_{3} \boldsymbol{C H O}+ \)
\( \boldsymbol{H}_{2} \boldsymbol{C}(\boldsymbol{C O O R})_{2} \frac{(i) \boldsymbol{P i p}}{(i i) \boldsymbol{H}_{3} O \oplus, \boldsymbol{\Delta}} \boldsymbol{A} \)
If \( \mathbf{A} \) is \( \boldsymbol{C} \boldsymbol{H}_{\boldsymbol{p}}-\boldsymbol{C} \boldsymbol{H}=\boldsymbol{C} \boldsymbol{H}-\boldsymbol{C} \boldsymbol{O}_{\boldsymbol{q}} \boldsymbol{H} \)
Then find the value of \( \boldsymbol{p}+\boldsymbol{q} \)


Which fossil man had cranial capacity almost equal to modern man?
A. Australopithecus
B. Java ape man
c. Neanderthal man
D. Peking man


Study the image above. How are the
elements arranged in the modern
periodic table?
A. Elements are arranged by their atomic numbers
B. Elements are arranged by their atomic mass
C. Elements are arranged by their valence electron configurations.
D. Electrons are arranged in alphabetical order


The pressure exerted by real gas is:
A. Lower than ideal gas
B. More than ideal gas
C. Equal to ideal gas
D. Can't be calculated.


The work done by electric field in
carrying a point charge of \( 5 \mu C \) from a
point \( A \) to point \( B \) is 10 mJ. The potential
difference \( \boldsymbol{V}_{\boldsymbol{A}}-\boldsymbol{V}_{\boldsymbol{B}} \) is the:
\( A \cdot+2 k V \)
B. -2 kV
\( c \cdot+2000 v \)
D. -2000V


element has one electron
in the outermost shell and attains
duplet configuration after accepting one more electron and attains stability.
A. Helium
B. Hydrogen
c. Lithium
D. carbon


\( \frac{\boldsymbol{x}-\boldsymbol{y}}{\boldsymbol{x}}+\frac{1}{2}\left(\frac{\boldsymbol{x}-\boldsymbol{y}}{\boldsymbol{x}}\right)^{2}+\frac{1}{3}\left(\frac{\boldsymbol{x}-\boldsymbol{y}}{\boldsymbol{x}}\right)^{3}+ \)
\( \ldots= \)
\( \mathbf{A} \cdot \log _{e}(x+y) \)
B \( \cdot \log _{e} \frac{x}{y} \)
\( \mathbf{c} \cdot \log _{e}(x-y) \)
D \( \cdot \log _{e} \frac{y}{x} \)


Mean free time of electrons are
expressed in picosecond\( (\boldsymbol{p s}) . \) 1ps \( =? \)
\( \mathbf{A} \cdot 10^{-12} s \)
B \( \cdot 10^{-9} s \)
\( \mathbf{c} \cdot 10^{-3} s \)
D. None of these