Consider the following reaction
\( \boldsymbol{R} \boldsymbol{C} \boldsymbol{H}=\boldsymbol{C} \boldsymbol{H}_{2}+\boldsymbol{I} \boldsymbol{N}_{3}^{\ominus} \rightarrow \boldsymbol{A} \)
\( A \) is :
A . \( R C \) \( _{i}^{C H C H_{2} N_{3}} \)
в. \( \underset{N_{3}}{R C H C H_{2} I} \)
c. Both are possible
D. None of these


If \( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{3} & \boldsymbol{x} \\ \mathbf{0} & \mathbf{1}\end{array}\right] \) and \( \boldsymbol{B}=\left[\begin{array}{ll}\mathbf{9} & \mathbf{1 6} \\ \mathbf{0} & -\boldsymbol{y}\end{array}\right], \) find
\( x \) and \( y \) when \( A^{2}=B \)


Uniform circular motion is called
continuously accelerated motion mainly because its :
A. direction of motion changes
B. speed remains the same
c. velocity remains the same
D. direction of motion does not change


The refractive index of a prism is 2. The prism can have a maximum refracting angle of
A \( .90^{\circ} \)
B. 60
c. 45
D. \( 30^{\circ} \)


Elements \( P \) and \( Q \) react to form a
compound \( P_{x} Q_{y} . \) R and P react to form
\( \boldsymbol{R}_{\boldsymbol{y}} \boldsymbol{P}_{\boldsymbol{z}} \)
If \( P_{x} Q_{y} \) is a binary acid with \( x=2 y \) then the acid is:
A. sulphuric acid
B. hydrochloric acid
c. chloric acid
D. hydrogen sulphide


\( \frac{\boldsymbol{d}}{d x}\left(e^{\tan x}\right) \)
\( \mathbf{A} \cdot e^{\tan x} \cdot \sec ^{2} x \)
B \( \cdot e^{\cot x} \cdot \sec ^{2} x \)
\( \mathbf{C} \cdot e^{\cos x} \cdot \sec ^{2} x \)
D \( \cdot e^{\sin x} \cdot \sec ^{2} x \)


Construct a \( \triangle X Y Z \) such that:
\( \boldsymbol{Y} \boldsymbol{Z}=\mathbf{5} \boldsymbol{c m}, \angle \boldsymbol{Z} \boldsymbol{Y} \boldsymbol{X}=\mathbf{3 0}^{\boldsymbol{o}} \) and
\( \angle Y Z X=75^{\circ} \)


The sum of first \( p \) -terms of a sequence
is \( p(p+1)(p+2) . \) The \( 10^{t h} \) term of the
sequence is
A . 396
в. 600
\( c .330 \)
D. 114


John notices that a standard piece of
paper is a rectangle \( \ldots \) how many lines of symmetry does it have?
A . 1
B . 2
\( c .3 \)
D. 4


\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}\left[(\boldsymbol{x}+\mathbf{1})\left(\boldsymbol{x}^{2}+\mathbf{1}\right)\left(\boldsymbol{x}^{4}+\mathbf{1}\right)\left(\boldsymbol{x}^{\boldsymbol{8}}+\right.\right. \)
1) \( ] \)
\( =\frac{\left(15 x^{p}-16 x^{q}+1\right)}{(x-1)^{2}} \Rightarrow(p, q)= \)
A . (12,11)
B. (15, 14)
\( c \cdot(16,14) \)
D. (16, 15)


The angular velocity \( (\omega \) of a particle is
related to the linear velocity \( v \) of the particle moving in a circular motion or radius R using the formula
\( \mathbf{A} \cdot v=R \omega \)
B. \( v=2 R \omega \)
c. \( v=R \omega^{2} \)
D. \( v=R \sqrt{(} \omega) \)


Lanthanoid for which +2 and +3
oxidation states are common is:
A . La
B. Eu
\( c \cdot c e \)
D. Nd


Due to irreversibility of a process,
A. initial state of the process cannot be restored
B. final state is not in equilibrium with the initial state.
C. the intermediate states are not in equilibrium with each other.
D. All of the above.


Write the degree of each of the following polynomials:
\( \frac{1}{2} y^{7}-12 y^{6}+48 y^{5}-10 \)


A street car moves rectilinearly from station \( \boldsymbol{A} \) (here car stops) to next
station \( B \) (here also car stops) with an acceleration varying according to the \( \operatorname{law} f=a-b x, \) where \( a \) and \( b \) are
positive constants and \( x \) is the distance
from station \( A \). If the maximum
distance between the two stations is \( \boldsymbol{x}=\frac{\boldsymbol{N} \boldsymbol{a}}{\boldsymbol{b}} \) then find \( \boldsymbol{N} \)


Explain the significance of meiocytes in a diploid organism.


Assertion
Cu doesn't give \( \boldsymbol{H}_{2} \) when treated with
dil. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) or dil. \( \boldsymbol{H} \boldsymbol{C l} \)
Reason
Less active metals like \( C u \) do not give
\( \boldsymbol{H}_{2} \)
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


ff \( g(x) \) is a polynomial satisfying \( \boldsymbol{g}(\boldsymbol{x}) \boldsymbol{g}(\boldsymbol{y})=\boldsymbol{g}(\boldsymbol{x})+\boldsymbol{g}(\boldsymbol{y})+\boldsymbol{g}(\boldsymbol{x} \boldsymbol{y})-2 \) for
all real \( x \) and \( y \) and \( g(2)=5 \) then \( g(3) \) is equal to -
A . 10
B . 24
\( c \cdot 21 \)
D. none of these


Which substance is not used for
preparing Iyophilic cols?
A. Starch
B. Gum
c. Gelatin
D. Metal sulphide


At \( ^{0} C \) water has its
maximum density and its minimum volume
A . 40
B. 4
c. 14
D . 24


Assertion
The value of acceleration due to gravity does not depend upon the mass of the body.
Reason
Acceleration due to gravity is a constant quantity.
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


\( \int_{1}^{\sqrt{3}} \frac{d x}{1+x^{2}} \)


Nitrogen gas is prepared:
A. by heating ammonium nitrate.
B. by reacting chlorine with liquor ammonia.
C. by passing \( H N O_{3} \) vapours on red hot copper
D. by beating lead nitrate.


Coal is a fossil fuel and it cannot be
prepared in a laboratory or industry because the formation of coal.
(A) is a very slow process.
(B) needs very low pressure and low
temperature
(C) needs very high pressure and high temperature
(D) causes air pollution Select the correct alternatives.
A. A and B
B. B and
\( c \cdot c \) and \( A \)
D. D and A


In \( n \) simillar thin prisms of same material and refractive index are
arranged in series as shown:
A. if \( n \) is even number, no net deviation and no net dispersion
B. if \( n \) is odd number, no net deviation and no net dispersion
c. it depends upon angle of prism
D. no sufficient information


In this \( I-V \) characteristic curve of a
zener diode, regions 1 and 2 respectively
indicate
A. forward bias and reverse bias regions
B. reverse bias and forward bias regions
C. forward bias regions only
D. reverse bias regions only


\( \boldsymbol{I}=\int_{0}^{1} \frac{(1-\boldsymbol{x}) \boldsymbol{d} \boldsymbol{x}}{(\mathbf{1}+\boldsymbol{x})} \)


A fielder on the ground throws a ball at an angle of \( 15^{\circ} \) to the horizontal with
velocity \( V_{A} \) at the wicket to dismiss the
batsman. Had he thrown the ball at \( 45^{\circ} \)
with a speed \( V_{B} \) to hit the wicket, then \( \frac{V_{B}}{V_{A}} \) is
\( ^{A} \cdot \frac{1}{\sqrt{3}} \)
в. \( \sqrt{2} \)
c. \( \sqrt{3} \)
D. \( \frac{1}{\sqrt{2}} \)


Consider a block sliding down a frictionless inclined plane with acceleration a . If we double the mass of
the block, what is its acceleration?
\( A \cdot \) a 14
в. а /2
\( c \)
D. 2a
E. \( 4 a \)


The Sl unit of inductance, henry can be written as:
a) \( \frac{\text { weber }}{\text { ampere }} \)
b) \( \frac{V o l t-\text { second }}{\text { ampere }} \) c) \( \frac{\text {joule}}{\text {ampere}^{2}} \)
d) Ohm - second
A. a \& c are correct
B. a \& b are correct
c. a, b \& c are correct
D. all are correct


No. of 5 membered ring in \( \left[(\boldsymbol{C a}(\boldsymbol{E} \boldsymbol{D} \boldsymbol{T} \boldsymbol{A})]^{-2} \boldsymbol{i s}\right. \)
A . 5
B. 6
\( c \cdot 7 \)
D. 8


Which of the underlined atoms in the
molecules shown below have \( s p \)
hybridization?
(u) \( C H_{2} C H C H_{3} \)
(v) \( C H_{2} \) CCHCl
\( (w) C H_{3} C H_{2}^{+} \)
\( (x) H-C=C-H \)
\( (y) C H_{3} C N \)
(z) \( \left(\boldsymbol{C H}_{3}\right)_{2} \boldsymbol{C} \underline{\boldsymbol{N}} \boldsymbol{N} \boldsymbol{H}_{\boldsymbol{z}} \)
A. \( x \) and \( z \)
B. \( x, y \) and \( z \)
c. u, w and \( x \)
D. \( v, x \) and \( y \)


Number of diagonals in parallelogram is/are:
A. 0
B.
\( c \cdot 2 \)
D. none of these


Which of these does not require a medium?
A. Conduction
B. Convection
c. Radiation
D. None of these


\( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{X}+\boldsymbol{K O H}(\boldsymbol{a l} \boldsymbol{c}) \rightarrow \)
\( \boldsymbol{C H}_{2}=\boldsymbol{C H}_{2}+\boldsymbol{K} \boldsymbol{X}+\boldsymbol{H}_{2} \boldsymbol{O} \)
These type of reactions are called
A. addition reactions
B. substitution reactions
c. elimination reactions
D. molecular rearrangement


Choose the correct statement(s).
This question has multiple correct options
A. The shape of an atomic orbital depends upon azimuthal quantum number
B. The orientation of an atomic orbital depends upon the magnetic quantum number
C. The energy of an electron in an atomic orbital of multielectron atom depends upon principal quantum number only
D. The number of degenerate atomic orbitals of one type depends upon the value of azimuthal quantum number


If \( \vec{a}=\hat{i}+\hat{j}+\hat{k}, \vec{b}=4 \hat{i}+3 \hat{j}+4 \hat{k} \) and
\( \vec{c}=\hat{i}+\alpha \hat{j}+\beta \hat{k} \) are linearly dependent
vectors and \( |\vec{c}|=\sqrt{3} \) then the value of \( \alpha \)
may be.
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
c. -3
D. 4


Which of the following can be used to prepare chloroform?
A. Methane
B. Ethyne
c. Ethanol
D. Both \( A \) and \( C \)


A radio active element has a half life of
20 min.The time that should elapse
before the element is reduced \( 1 / 8 \) th of the original mass is:
A. 40 min
B. 60 min
c. 80 min
D. 160 min


Two opposite vertices of a square are (2,-3,4) and \( (4,1,-2) . \) The length of the side of the square is
A \( \cdot \sqrt{58} \)
B. \( 2 \sqrt{7} \)
c. \( \sqrt{14} \)
D. \( \sqrt{7} \)


State two uses of a cathode ray tube


Why is red phosphorus less reactive
than white phosphorus?


Assertion
The standard unit for expressing the
mass of atom is amu.
Reason
amu is also called as avogram.
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


Which one of the following statements is wrong?
A. PVC stands for poly vinyl chloride.
B. PTFE stands for Teflon
c. PMMA stands for polymethyl methacrylate.
D. Buna-S stands for natural rubber.


An emulsifier is a substance:
A. which stabilises an emulsion
B. which breaks the emulsion into its constituent liquids
C. which can convert liquid into an emulsion
D. which bring about coagulation of an emulsion


The plates of a parallel plate condenser are pulled apart with a velocity v. If at any instant their mutual distance of
separation is \( x, \) the magnitude of the time of rate of change of capacity depends on \( x \) as follows:
\( A \cdot 1 / x \)
B . \( 1 / x^{2} \)
c. \( x^{2} \)
D.


Find the derivative of
\( x^{-4}\left(3-4 x^{-5}\right) \)


Erythrocyte maturing factor is
A. Folic acid
B. Cyanocobalamine
c. Vitamin \( B_{2} \)
D. Vitamin C


A body is dropped from a height \( h \), if it acquires a momentum p, then the mass of the body is:
A \( \cdot \frac{p}{\sqrt{2 g h}} \)
в. \( \frac{P^{2}}{2 g h} \)
c. \( \frac{2 g h}{p} \)
D. \( \sqrt{2 g h / p} \)


The peptizing agent used in Peptization is a/an:
A. stabilizer
B. electrolyte
c. proton donor
D. promoter


The angle between the line \( 2 x=3 y= \)
\( -z \) and \( 6 x=-y=-4 z \) is
A \( .90^{\circ} \)
B . \( 0^{\circ} \)
\( c \cdot 30^{0} \)
D. \( 45^{\circ} \)


When elements are placed in the order of their increasing atomic number, the elements having the same number of \( _{-1} \) is repeated in such a
way, so as to fall under the same group. since, the electronic configuration of the valence shell electrons is same they
show similar properties.
A. valence shell electrons
B. inner electrons
c. electrons present in inner shell
D. protons and neutrons


What is the general solution of the
differential equation \( x^{2} d y+y^{2} d x=0 ? \)
A. \( x+y=c \) where \( c \) is the constant of integration
B. \( x y=c \) where \( c \) is the constant of integration
c. \( c(x+y)=x y \) where \( c \) is the constant of integration
D. None of the above


If three points with position vectors as \( (1, a, b) ;(a, 2, b) \) and \( (a, b, 3) \) are
collinear in space, then the value of \( a+ \)
\( \boldsymbol{b} \) is
\( A \cdot 3 \)
B. 4
\( c \cdot 5 \)
D. none


The average speed of an object is defined to be
A. One half of the sum of the maximum and the minimum speeds
B. Distance it travels multiplied by the time it takes
c. The distance it travels divided by the time it takes
D. The speed determined over an infinitesimally small time interval
E. The value of the speed at the midpoint of the time interval


Number of visible lines in Balmer
series.
A . 2
B. 4
\( c .3 \)
\( D \)


Two vertices of a rectangle are on the
positive \( \mathbf{x} \) -axis. The other two vertices lie on the lines \( y=4 x \) and \( y=-5 x+6 \)
Then the maximum area of the
rectangle is?
\( A \cdot \frac{2}{3} \)
B. \( \frac{2}{4} \)
\( c \cdot \frac{1}{3} \)
D. \( \frac{4}{3} \)


Which of the following does not define reduction?
A. Gain of electron and addition of hydrogen
B. Removal of oxygen
c. Decrease in oxidation state
D. Removal of electron, removal of hydrogen, addition of oxygen and increase in oxidation state


Sea and land breezes are
caused because of :
A. convection
B. cyclones
c. rains
D. conduction


The end-product in the reaction sequence would be:
Ethyl amine \( \frac{H N O_{2}}{\longrightarrow} A \stackrel{P C l_{5}}{\longrightarrow} B \stackrel{N H_{3}}{\longrightarrow} C \)
A. Ethyl cyanide
B. Ethyl amine
c. Methyl amine
D. Acetamide


Which of the following is not a feature of an efficient gas exchange surface?
A . thick walls
B. close proximity to blood capillaries
c. moist lining
D. large surface area


solve
\( x d y-y d x=\sqrt{x^{2}+y^{2} d x} \)


An aldehyde on oxidation gives
A . an acid
B. an alcohol
c. an ether
D. a ketone


Assertion
In an elastic collision between two bodies, the relative speed of the bodies after collision is equal to the relative speed before the collision.
Reason
In an elastic collision, the linear momentum of the system is conserved.
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


\( \int \frac{1-x}{1+x} \)


Q Type your question-
respectively as shown in figure.
Assuming that these are placed in the same plane, the magnetic fields will be zero at the centre of the loop when the
separation H is
\( A \cdot \frac{1_{e}}{I_{I} \pi} \)
В \( \cdot \frac{I_{c} R}{I_{e}} \)
\( c \cdot \frac{\pi 1}{I F} \)
D. \( \frac{1_{e}}{I_{R}} \)


The molecule \( X e O_{3} \) has:
A. Three double bonded 0 -atoms
B. Trigonal pyramidal geometry
c. one lone pair and
\( s p_{3} \) hybridisation
D. All of these


In the below shown reaction
sequence, the compound B formed is :
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{O H} \stackrel{\boldsymbol{P C l}_{3}}{\longrightarrow} \boldsymbol{A} \stackrel{\text {alc. } \boldsymbol{K O H}}{\boldsymbol{N}} \boldsymbol{B} \)
A. propane
B. propanol
c. propene
D. propyne


Curd taste sour because this is a/an:
A. base
B. salt
c. acid
D. liquid


Solve the following simultaneous equations:
\( \frac{27}{x-2}+\frac{31}{y+3}=85 ; \quad \frac{31}{x-2}+ \)
\( \frac{27}{y+3}=89 \)
A \( \cdot x=\frac{3}{4}, y=4 \)
B. \( x=\frac{5}{2}, y=-2 \)
c. \( _{x}=\frac{4}{3}, y=3 \)
D. \( x=\frac{7}{2}, y=6 \)


The wavelength of ultraviolet light absorbed by nucleic acid is
\( A \cdot 26 n m \)
B. 75 nm
\( c .260 \mathrm{nm} \)
D. 1500 \( \mathrm{nm} \)


Calculate the pH of the following mixture given \( \boldsymbol{K}_{a}=\mathbf{1 . 8} \times \mathbf{1 0}^{-\mathbf{5}} \) and \( \boldsymbol{K}_{\boldsymbol{b}}=\mathbf{1 . 8} \times \)
\( \mathbf{1 0}^{-\mathbf{5}}\left(\boldsymbol{p} \boldsymbol{K}_{\boldsymbol{a}}=\boldsymbol{p} \boldsymbol{K}_{\boldsymbol{a}}=\mathbf{4 . 7 4 4 7}\right) \)
\( 50 m L 0.05 M N a O H+50 m L \) of
\( \mathbf{0 . 1} \boldsymbol{M} \boldsymbol{C H}_{3} \boldsymbol{C O O H} \)


Dissociation of water takes place in two
steps:
\( \boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \boldsymbol{H}^{+}+\boldsymbol{O} \boldsymbol{H}^{-} ; \boldsymbol{\Delta} \boldsymbol{H}=+497.8 \mathrm{kJ} \)
\( O H^{-} \rightarrow H^{+}+O^{2-} ; \Delta H=+428.5 \mathrm{kJ} \)
What is the bond energy of \( 0-H \) bond?
A . \( 463.15 \mathrm{kJ} \mathrm{mol}^{-1} \)
В. 428.5 k \( \mathrm{mol}^{-1} \)
c. \( 69.3 \mathrm{kJ} \mathrm{mol}^{-1} \)
D. 926.3 kJ \( m o l^{-1} \)


Knowing that the chemistry of lanthanids \( (\mathrm{Ln}) \) is dominated by its +3
oxidation state, which of the following statements are correct?
(1) The ionic sized of \( L n(\| I) \) decreases in general with increasing atomic
number.
(II) \( \mathrm{Ln}(\mathrm{III}) \) compounds are generally colourless.
(III) \( \operatorname{Ln}(\| I) \) hydroxides are mainly basic in character
(IV) Because of the large size of the Ln
(III) ions, the bonding in its compounds is predominently ionic in character.
A. I, III and III
B. II, III and IV
c. ।, ॥ and IV
D. I, III and IV


The insertion of a dielectric between the
plates of a parallel-plate capacitor always
A. increases its capacitance
B. decreases its capacitance
c. remains same its capacitance
D. none of the above


A coil of inductance \( 1 H \) and resistance
\( 10 \Omega \) is connected to a resistanceless
battery of emf \( 50 V \) at time \( t=0 . \) The
ratio of the rate at which magnetic energy is stored in the coil to the rate at
which energy is supplied by the battery
at \( t=0.1 s \) is \( \frac{37}{n} . \) Find \( x \)


Find the square of the following numbers without actual multiplication
\( \mathbf{3 9} \)


A metal sphere is kept on an insulating stand. A negatively charged rod is
brought near it, then the sphere is
earthed as shown. On removing the earthing, and taking the negatively
charged rod away, what will be the
nature of charge on the sphere? Give
reason for your answer.

Ground


Distance between plane \( 3 x+4 y- \)
\( \mathbf{2 0}=\mathbf{0} \) and point \( (\mathbf{0}, \mathbf{0},-\mathbf{7}) \) is
A. 4 units
B. 3 units
c. 2 units
D. 1 units


The given graph shows potential energy and kinetic energy plotted against time of a ball thrown straight up from the 10 storey building.
At what point on the graph does the kinetic energy of the object decrease
while the potential energy increases?
A. True
B. False


A block is released from rest at the top
of a frictionless inclined plane \( 16 \mathrm{m} \) long. It reaches the bottom 4 sec later. \( A \)
second block is projected up the plane from the bottom at the instant the block
is released in such a way that it returns
to the bottom simultaneously with first block. The acceleration of each block on
the incline is
A \( \cdot 1 m / s^{2} \)
в. \( 2 m / s^{2} \)
\( \mathbf{c} \cdot 4 m / s^{2} \)
D. \( 9.8 m / s^{2} \)


Assertion
Horse has to pull a cart harder during the first few steps of his motion.
Reason
The first few steps are always difficult.
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


Potato is a modified
A. Petiole
B. Stem
\( c . \) Root
D. Leaf


The electron in a hydrogen atom makes
a transition \( n_{1} \rightarrow n_{2} \) whose \( n_{1} \) and \( n_{2} \)
are the principal quantum numbers of the two states. Assume the Bohr model
to be valid. The frequency of orbital
motion of the electron in the initial
state is \( 1 / 27 \) of that in the final state.
The possible value of \( n_{1} \) and \( n_{2} \) are
\( \mathbf{A} \cdot n_{1}=4, n_{2}=2 \)
B \( . n_{1}=3, n_{2}=1 \)
\( \mathbf{c} \cdot n_{1}=8, n_{2}=1 \)
\( \mathbf{D} \cdot n_{1}=6, n_{2}=3 \)


A hemispherical bowl of radius unity is
filled up with water upto the depth \( \frac{1}{2} \)
The volume of water in the bowl is
A \( \cdot \frac{27 \pi}{24} \)
в. \( \frac{5 \pi}{24} \)
c. \( \frac{3 \pi}{4} \)
D. None of these


The declaration experienced by a moving motor boat, after its engine is cut-off is given by \( \frac{\mathrm{dv}}{\mathrm{dt}}=-\mathrm{kv}^{3} \) where \( \mathrm{k} \)
is constant If \( \mathbf{v}_{\mathbf{0}} \) is the magnitude of the velocity at cut-off, the magnitude of the velocity at a time \( t \) after the cut off is
\( A \cdot \frac{v_{0}}{2} \)
B . v
c. \( \mathrm{v}_{0} \mathrm{e}^{-\mathrm{ti}} \)
D. \( \frac{v_{0}}{\sqrt{\left(2 v_{v}^{2} \mathrm{kt}+1\right)}} \)


Each pair forms ideal solution except :
A. \( C_{2} H_{5} B r \) and \( C_{2} H_{5} I \)
в. \( C_{6} H_{5} C l \) and \( C_{6} H_{5} B r \)
c. \( C_{6} H_{6} \) and \( C_{6} H_{5} C H_{3} \)
D. \( C_{2} H_{6} I \) and \( C_{2} H_{5} O H \)


A small hollow sphere, which has a small hole in it, is immersed in water to
a depth of \( 0.5 \mathrm{m} \) before any drop
penetrates into it. If surface tension for water is \( 0.073 \mathrm{N} / \mathrm{m} \), the radius of the
hole is :
[Assume pressure inside the sphere to be atmospheric pressure]
\( A .0 .06 \mathrm{mm} \)
B. \( 0.03 \mathrm{mm} \)
c. \( 0.09 \mathrm{mm} \)
D. 0.15 mm.


Which process occurs when the
pressure or the volume of a system changes so dramatically and instantaneously that the other (pressure or volume in this case) does not have time to catch up.
A . Reversible
B. Irreversible
c. Isothermal
D. Adiabatic


Convert \( 1 \frac{4}{11} \) into improper fraction?


For the reaction
\( \boldsymbol{C u} \boldsymbol{S O}_{4} \cdot \boldsymbol{5} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{s}) \rightleftharpoons \)
\( \boldsymbol{C u} \boldsymbol{S O}_{4} \cdot \boldsymbol{3} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{s})+\boldsymbol{2} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \)
which one is correct representation:
A \( \cdot K_{P}=\left(P_{H_{2}} \partial\right)^{2} \)
в. \( K_{C}=\left[H_{2} O\right]^{2} \)
\( \mathbf{c} \cdot K_{p}=K_{c}(R T)^{2} \)
D. all of these


Consider the following compounds.
\( (i) I C I(i i) I B r(i i i) I C I_{3}(i v) S F_{4} \)
\( (v) B r F_{3}(v i) I F_{3}(v i i) B r F_{5}(v i i i) I F_{7} \)
Calculate the value of \( \left[\frac{\boldsymbol{P}^{2}-\boldsymbol{Q}^{2}}{\boldsymbol{R}+\boldsymbol{S}}\right] \)
Here,
\( \boldsymbol{P}: \) Total number of polar compounds
\( Q: \) Total number of planar compounds
\( R: \) Total number of non polar compounds
\( \boldsymbol{S}: \) Total number of non planar compounds
A. 6
B. 7
\( c \cdot 4 \)
D.


\( \operatorname{Let} \rho(r)=\frac{Q r}{4 \pi R^{4}} \) be the charge density
distribution of a solid sphere of radius \( R \) and total charge \( Q . \) Find the magnitude of electric field at a point \( \boldsymbol{P} \)
inside the sphere at a distance \( r_{1} \) from
the centre of the sphere.
A \( \cdot \frac{Q}{4 \pi^{2} \epsilon_{6} r_{1}^{2}} \)
в. \( \frac{Q r_{1}^{2}}{4 \pi^{2} \epsilon_{\epsilon} R^{4}} \)
c. \( \frac{Q r_{1}^{2}}{16 \pi \epsilon_{1} R^{4}} \)
D. 0


Which of the following statements are
correct about phenol-formaldehyde
resin?
This question has multiple correct options
A. Novolac or resin is a liner polymer and is used in the manufacture of adhesive.
B. Bakelite is a cross-linked polymer and is used in making switches and plugs.
C. Novolac is prepared when (P/F) (phenol/formaldehyde) ratio is greater than 1 , whereas bakelite is prepared when (P/F) ratio is less than 1
D. Novolac is prepared when \( \mathrm{P} / \mathrm{F}<1 \) and bakelite is prepared when \( \mathrm{P} / \mathrm{F}>1 \)


\( \int_{1}^{3} \log x d x=\ldots \ldots\left(x>0 \in R^{+}\right) \)
A. \( -2+\log 27 \)
B. \( -2+\log 9 \)
c. \( 2+\log 27 \)
\( ^{\mathrm{D}} \cdot \log \left(\frac{27}{e}\right) \)


For the given situation irrespective of the magnitude of charge and their
separation it is found that total energy of the system (i.e. electric potential energy and their K.E.) is related to K.E. by the equation total energy = -kinetic energy \( (k) \) Which of the following gives the correct value of potential energy of the system?
A \( \cdot \frac{q^{2}}{4 \pi \varepsilon_{0} R} \)
В. \( \frac{q^{2}}{8 \pi \varepsilon_{0} R} \)
\( ^{\mathbf{C}}-\frac{q^{2}}{4 \pi \varepsilon_{0} R} \)
\( ^{\mathrm{D}}-\frac{q^{2}}{8 \pi \varepsilon_{0} R} \)


Solve \( \cos ^{2} x^{3} \)


Solve:
\( x^{4}+\frac{1}{x^{4}} \)


T-distribution is symmetrical like
normal distribution and its mean value
is
A. zero
B. - -
\( c \)
D.


(a) A person cannot read newspaper placed nearer than \( 50 \mathrm{cm} \) from his eyes. Name the defect of vision he is
suffering from. Draw a ray diagram to illustrate this defect. List its two
possible causes. Draw a ray diagram to
show how this defect may be corrected using a lens of appropriate focal length.
(b) We see advertisements for eye donation on television or in newspapers.
Write the importance of such advertisements.


Evaluate: \( \int 3 x-5 d x \)
A \( \frac{3 x^{2}}{2}-5 x+C \)
B. \( \frac{3 x^{2}}{2}-7 x+C \)
c. \( \frac{3 x^{2}}{2}-4 x+C \)
D. \( \frac{3 x^{2}}{2}-6 x+C \)


When a steady current of \( 2 A \) was
passed through two electrolytic cells \( \boldsymbol{A} \)
and \( B \) containing electrolytes \( Z n S O_{4} \)
and \( C u S O_{4} \) connected in series, \( 2 g \) of
\( C u \) were deposited at the cathode of
cell \( B \)
How long did the current flow?
What mass of \( Z n \) was deposited at
cathode of cell \( \boldsymbol{A} \) ?
[Atomic mass: \( C u= \)
\( \mathbf{6 3 . 5 g} \mathbf{m o l}^{-\mathbf{1}}, \mathbf{Z n}=\mathbf{6 5 g} \mathbf{m o l}^{-\mathbf{1}} ; \mathbf{1} \mathbf{F}= \)
\( \left.96500 C m o l^{-1}\right] \)


Modes of controlling pollution in large
cities include
A. Cleanliness and less use of insecticides
B. Proper disposal of organic wastes, sewage and industrial effluents
c. Broader roads and shifting of factories out of the residential areas
D. All of the above


If \( a x+b y^{2}=\cos y, \) then find \( \frac{d y}{d x} \)


The process of accumulating higher and higher amounts of a toxic material such as PCBs within the body of any animal is called
A. Bioaccumulation
B. Biological amplification
c. Biological half-life
D. None of the above


Cyclic form of Fructose is called as:
A. D-fructopyranose
B. D-fructofuranose
c. D-glucofuranose
D. dextrose


Toby invested Rs. 1200 for 2 years in a
savings account. His account depreciates by \( 8 \% \) per annum
compound interest. How much did Toby
have in his savings account after 2
years?


A solution containing \( B r^{-} \) ions is treated with each of the following.
Which of these will not liberate bromine
\( \operatorname{gas}( \) in acidic medium)
This question has multiple correct options
A \( \cdot C l_{2} \)
в. \( H I \)
\( \mathbf{c} \cdot I_{2} \)
D. \( S O_{3} \)


The formula for calculating \( \bar{M}_{w} \) of a polymer is:
A. \( \frac{\sum N i M i}{\sum N i} \)
в. \( \frac{\sum N i M i}{\sum M i} \)
c. \( \frac{\sum_{N i M i}^{2}}{\sum M i} \)
D. \( \frac{\sum N i M i^{2}}{\sum N N M i} i \)


Ozone requires atoms
of oxygen.
\( A \cdot 8 \)
B. 3
\( c \cdot 1 \)
\( D \)


A boy stands on the ground. The area
below his feet is \( 70 \mathrm{cm}^{2} \). The pressure he
exerts on the ground is \( 7 N / c m^{2} \)
Calculate the total force acting on the ground.
A . \( 0.1 N \)
в. \( 10 N \)
c. \( 490 N \)
D. \( 4.9 N \)


Which of the following behaves as both oxidising and reducing agents?
A. \( H_{2} S O_{4} \)
в. \( S O_{4} \)
c. \( H_{2} \)
D. \( H N O_{3} \)


The number of electrons in an atom
with atomic number 105 having \( (n+ \) \( l)=8 \) are:
A . 30
B. 17
c. 15
D. 21


In hot summer day, plant cooling is due
to
A. Loss of water vapours from leaf
B. Transport of water in plant
c. Loss of liquid water
D. Loss of water from entire plant


\( \angle \boldsymbol{A}+\angle \boldsymbol{B}=\mathbf{6 5}^{\circ}, \angle \boldsymbol{B}+\angle \boldsymbol{C}=\mathbf{1 4 0}^{\circ} \)
Find measure of each angle of \( \Delta \)


A series \( L C R \) circuit containing a
resistance of \( 120 \Omega \) has angular
resonance frequency \( 4 \times 10^{5} \) rad \( s^{-1} \)
At resonance the voltages across
resistance and inductance are \( 60 V \)
and \( 40 \mathrm{V} \), respectively. The value of
inductance \( L \) is
A. \( 0.1 \mathrm{mH} \)
в. \( 0.2 \mathrm{mH} \)
c. \( 0.35 \mathrm{mH} \)
D. \( 0.4 \mathrm{mH} \)


If \( \sin \theta-\operatorname{cosec} \theta=\sqrt{5}, \) then the value of
\( \sin \theta+\operatorname{cosec} \theta \) is:
A. \( \sqrt{3} \)
B.
\( c \cdot 3 \)
D.


Integrate \( \int_{1}^{2} x^{2} d x \)


Construct a quadrilateral \( \boldsymbol{P} \boldsymbol{N} \boldsymbol{K} \boldsymbol{J} \)
where \( \mathrm{PN}=7 \mathrm{cm}, \mathrm{NK}=8 \mathrm{cm}, \mathrm{JK}=10 \mathrm{cm} \)
\( P J=5 \mathrm{cm} \) and \( \angle J=75^{\circ} \)
Then, the measure of \( \angle N \) is
A . \( 65^{\circ} \)
B. \( 95^{\circ} \)
\( c \cdot 75^{\circ} \)
D. \( 85^{\circ} \)


Graph shows the number of units
consumed by a family for six months.
Find the cost of energy for four months
from March to June if M.S.E.B increased
its unit rate from Rs.3.50 to Rs. 4.50 for
April and May and again decreased by
Rs.2 for June:
A. Rs.6000
B. Rs.6, 030
c. Rs.6, 300
D. Rs.6, 200


If \( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{3} & -\mathbf{2} \\ \mathbf{4} & -\mathbf{2}\end{array}\right], \) find \( \boldsymbol{K} \) such that \( \boldsymbol{A}^{\mathbf{2}}= \)
\( \boldsymbol{K} \boldsymbol{A}-\boldsymbol{2} \boldsymbol{I}, \) where \( \boldsymbol{I} \) is the identity
element.


Let \( \boldsymbol{y}=\sin ^{-1} \boldsymbol{x}, \) then find \( \left(\mathbf{1}-\boldsymbol{x}^{2}\right) \boldsymbol{y}_{2} \)
\( \boldsymbol{x} \boldsymbol{y}_{1} \)
Where \( y_{1} \) and \( y_{2} \) denote the first and
second order derivatives respectively.
\( \mathbf{A} \cdot \mathbf{1} \)
в. - 1
c. 0
D.


Bioluminescence is shown by
A. Ceratium
B. Chlorella
c. Hirudinaria
D. chlamydomonas


From the adjacent figure find the values
of \( \angle P R S(\text { in degree }) \)
\( A \cdot 85 \)
B. 75
\( c \cdot 65 \)
D. 55


Chlorine has \( _{\text {一一一一一一詔 }} \)
A. 1 (one) () \( ) \) )
B. 2 (two)
c. 3 (three)
D. 4 (four)


Find the domain of the following
function:
\( f(x)=\sqrt{1-\sqrt{1-\sqrt{1-x^{2}}}} \)
the domain is \( [-a, a], \) then a is?


Which of the following supports most satisfactorily the organic
evolution?
A. Fossils
B. Neoteny
c. connecting links
D. None of the above


The equilibrium constants for the
reaction, \( B r_{2} \rightleftharpoons 2 B r \) at \( 500 \mathrm{K} \) and 700
K are \( 1 \times 10^{-10} \) and \( 1 \times 10^{-5} \)
respectively. The reaction is:
A. endothermic
B. exothermic
\( c . \) fast
D. slow


Respiration initiated in chloroplasts and occurring in light is called
A. Aerobic respiration
B. Anaerobic respiration
c. Fermentation
D. Photorespiration


The ends of a circular coil of radius \( r \)
and number of turns \( n \) is connected to
the two terminals of a cell. The
magnetic field at the centre of the coil is \( B \). If the number of turns be made \( 2 n \)
keeping the radius same, the magnetic field at the centre of the coil will be:
A. \( B \)
в. \( 2 B \)
\( c .3 B \)
D. \( 4 B \)


\( f-2 x=4 y+6 \) and \( 2(2 y+3)=3 x- \)
5What is the solution \( (x, y) \) to the
system of equation above?


Motion of bodies \( A \) and \( B \) is depicted by the \( x \) -t graph. Now consider the following statements (a), (b), (c) and (d) and select the incorrect option.
(a) A has uniform motion
(b) \( \mathrm{B} \) has less velocity than A initially
(e) B crosses A at a displacement X
(d) A comes to rest at a displacement \( x \)
\( A \cdot \) Only \( (a) \)
B. (b) and (c)
\( c \cdot(b),(c) \) and \( (d) \)
D. All of them


An atmosphere
A. is a unit of pressure
B. is a unit of force
C . gives us an idea of composition of air
D. is the height above which there is no air


If \( f(x)=\left\{\begin{array}{l}x: x<0 \\ 1: x=0 \quad \text { then } \lim _{x \rightarrow 0} f(x)= \\ x^{2}: x>0\end{array}\right. \)
A .
B.
\( c \cdot 2 \)
D. does not exist


For the process
\( \boldsymbol{A}\left(\boldsymbol{l}, \mathbf{0 . 0 5} \boldsymbol{a t m}, \boldsymbol{3} \boldsymbol{2}^{\circ} \boldsymbol{C}\right) \rightarrow \)
\( \boldsymbol{A}\left(\boldsymbol{g}, \boldsymbol{0 . 0 5} \boldsymbol{a t m}, \boldsymbol{3} \boldsymbol{2}^{\circ} \boldsymbol{C}\right) \)
The correct set of thermodynamic
parameters is :
A \( . \Delta G=0 \) and \( \Delta S=-v e \)
B. \( \Delta G=0 \) and \( \Delta S=+v e \)
c. \( \Delta G=+v e \) and \( \Delta S=0 \)
D. \( \Delta G=-v e \) and \( \Delta S=0 \)
E . \( \Delta G=0 \) and \( \Delta S=0 \)


If \( P \) and \( Q \) are two points on the
diagonal \( D B \) such that \( D P=P Q= \)
\( Q B \) then area of the \( \Delta C P Q \) in square
units is
A \( \cdot \frac{1}{3} \)
B. \( \frac{1}{2} \)
\( c \cdot \frac{1}{4} \)
D.


\( \lim _{x \rightarrow 0} \frac{(x+2)^{10}-2^{10}}{(x+2)^{5}-2^{5}} \) is
A . 16
B. 32
\( c \cdot 64 \)
D. 128


The perimeter of a triangle formed by points \( (\mathbf{0}, \mathbf{0}),(\mathbf{6}, \mathbf{0}),(\mathbf{0}, \mathbf{6}) \) is
A. \( 6(2+\sqrt{2}) \) units
B. \( 2+\sqrt{2} \) units
c. \( 6 \sqrt{2} \) units
D. None of the above


The oxidation state of nitrogen in ammonia molecule is -3.
A. True
B. False


\( \ln \Delta A B C, \) a line is drawn parallel to
\( B C \) to meet sides \( A B \) and \( A C \) in \( D \) and
\( E \) respectively. If the area of the \( \Delta A D E \) is \( \frac{1}{9} \) times area of the \( \Delta A B C, \) then the value of \( \frac{A D}{A B} \) is equal to:
A \( \cdot \frac{1}{3} \)
B.
\( c \cdot \frac{1}{5} \)
D.


The figure given below
represents experimental set up with a
weighing machine to demonstrate a
particular process in plants. The experimental set up was placed in
bright sunlight. Study the diagram and
answer the following questions:

What is the purpose of keeping the test
tube \( \mathrm{B} \) in the experimental set up?


The nucleus obtained after \( \alpha \) -emission
from the nucleus \( _{y} \mathbf{A}^{x} \) is
A・ \( _{y-2} \mathrm{B}^{x-2} \)
В. \( _{y+2} \mathrm{B}^{x+4} \)
\( \mathbf{c} \cdot_{y} \mathbf{B}^{x} \)
D. \( _{y-2} \mathrm{B}^{x-4} \)


In a thermostat device which parameter
remains approximately constant
A. Volume
B. Pressure
c. Temperature
D. Mass


Differentiate the following functions
with respect to \( \boldsymbol{x} \) \( \frac{e^{x} \sin x}{\left(x^{2}+2\right)^{3}} \)


\( \operatorname{Let} h(x)=f(x)-(f(x))^{2}+(f(x))^{3} \) for
every real number \( x, \) then
A. \( h \) is increasing whenever \( f \) is increasing and decreasing whenever \( f \) is decreasing
B. \( h \) is increasing whenever \( f \) is decreasing
c. \( h \) is decreasing whenever \( f \) is increasing
D. Nothing can be said in general


Classify the following curve as open or
closed


The cost price of 11 pens is equal to the
selling price of 10 pens. Find the loss or gain percent.


State whether the following statements are true or false, spiny ant-eater is the most primitive mammal
A. True
B. False


The latus rectum subtends a right angle at the centre of the ellipse then its eccentricity is
\( A \cdot 2 \sin 18^{\circ} \)
B. \( 2 \cos 18^{\circ} \)
\( c \cdot 2 \sin 54^{\circ} \)
\( D \cdot 2 \cos 54^{\circ} \)


The sum of 7 terms of the series \( 1^{2}- \)
\( \mathbf{2}^{2}+\mathbf{3}^{2}-\mathbf{4}^{2}+\mathbf{5}^{2}-\mathbf{6}^{2}+\dots \) is
A . -21
B. 15
c. 28
D. -35


If \( f(x)=|x|^{3} . \) show that \( f^{\prime \prime}(x) \) exists for
all real \( x \) and find it.


The human eye part which can be used again and again for forming different images is called
A . Iriss
B. Puil
c. cornea
D. Retina


The other name of comproportionation
is:
A. disproportionation
B. proportionation
c. symproportionation
D. antiproportionation


Find the height from the earth's surface where \( g \) will be \( 25 \% \) of its value on the
surface of earth \( (\mathrm{R}=\mathbf{6 4 0 0} \mathrm{km}) . \) (b) Find
the percentage increase in the value of \( \mathrm{g} \) at a depth h from the surface of earth.


The resultant of two forces acting at an
angle of \( 150^{\circ} \) is \( 10 \mathrm{N} \) and its
perpendicular to one of the forces.The
two other force is:
A \( \cdot \frac{20}{\sqrt{3}} N \)
в. \( \frac{10}{\sqrt{3}} N \)
c. \( 20 N \)
D. \( \frac{20}{3} N \)


In a circular table corner of radius
\( 32 \mathrm{cm}, \) a design is formed leaving an
equilateral triangle \( A B C \) in the middle as shown in Fig. Find the area of the design


The vibrations of a string of length
\( 60 \mathrm{cm} \) fixed at both ends are
represented by the equation \( \boldsymbol{y}= \) \( 4 \sin \left[\frac{\pi x}{15}\right] \cos (96 \pi t) \) where \( x \) and \( y \) are
in \( \mathrm{cm} \) and \( t \) in sec. The equation of
component waves whose superposition gives the above wave are
A \( \cdot y_{1}=2 \sin \left(96 \pi t+\frac{\pi x}{5}\right), y_{2}=-2 \sin \left(96 \pi t-\frac{\pi x}{5}\right) \)
B・ \( y_{1}=2 \sin \left(\frac{\pi \mathrm{x}}{5}+96 \pi t\right), y_{2}=-2 \sin \left(\frac{\pi \mathrm{x}}{5}-96 \pi t\right) \)
c. \( y_{1}=2 \operatorname{sm}\left(\frac{\pi \mathrm{x}}{15}+96 \pi t\right), y_{2}=-2 \sin \left(96 \pi t-\frac{\pi x}{15}\right) \)
D. \( y_{1}=2 \sin \left(\frac{\pi \kappa}{15}+96 \pi t\right) y_{2}=-2 \sin \left(\frac{\pi \mathrm{x}}{15}-96 \pi t\right) \)


If a rigid body is subjected to two forces \( \vec{F}_{1}=2 \hat{i}+3 \hat{j}+4 \hat{k} \) acting at (3,3,4)
and \( \overrightarrow{\boldsymbol{F}}_{2}=-2 \hat{\boldsymbol{i}}-\boldsymbol{3} \hat{\boldsymbol{j}}-\boldsymbol{4} \hat{\boldsymbol{k}} \) acting at
(1,0,0) then which of the following is
(are) true?
A. The body is in equilibriumm
B. The body is under the influence of a torque only
C. The body is under the influence of a single force
D. The body is under the influence of a force together with torque


Without actually dividing find if \( \frac{11}{18} \)
is terminating decimal


Find the maximum velocity of the bar over its motion.
A \( \cdot v_{\max }=\sqrt{\frac{g}{a} \cos \alpha \tan \alpha} \)
B. \( v_{\max }=\sqrt{\frac{2 g}{a} \sin \alpha \tan \alpha} \)
c. \( v_{m a x}=\sqrt{\frac{g}{a} \sin \alpha \tan \alpha} \)
D. \( v_{\max }=\sqrt{\frac{2 g}{a} \cos \alpha \tan \alpha} \)


AB IS a resistanceless conaucting roa
which forms a diameter of a conducting
ring of radius \( r \) rotating in a uniform
magnetic field \( B \) as shown in figure.
The resistors \( R_{1} \) and \( R_{2} \) do not rotate.
Then the current through the resistor
\( \boldsymbol{R}_{1} \)
\( ^{\mathbf{A}} \cdot \frac{B \omega r^{2}}{2 R_{1}} \)
B. \( \frac{B \omega r^{2}}{2 R_{2}} \)
\( ^{\mathbf{C}} \frac{B \omega r^{2}}{2 R_{1} R_{2}}\left(R_{1}+R_{2}\right) \)
D. \( \frac{B \omega r^{2}}{2\left(R_{1}+R_{2}\right)} \)
E. answer required


Assertion: Two \( \Delta \) s are said to be
congruent if two sides and an angle of the one triangle are respectively equal to the two sides and an angle of the other triangle.

Reason: Two \( \Delta \) s are congruent if two sides and the included angle of the one
triangle are equal to the corresponding two sides and included angle of the other triangle.

Two statements A and R are given above. Which of the following statements is correct?
A. A is false and R is the correct explanation of A
B. A is true and R is the correct explanation of a A
c. \( A \) is false and \( R \) is true
D. None of these


the wavelength in Angstroms of the photon that is emitted when an electron in Bohr orbit \( n=2 \) returns to the orbit \( n= \)
in the hydrogen atom. The ionisation potential of the ground state hydrogen atoms is \( 2.17 \times 10^{-11} \) ergs per atom:
A \( \cdot 1220 A^{\circ} \)
B . \( 1350 A^{\circ} \)
c. \( 610 A^{\circ} \)
D. \( 570 A^{\circ} \)


From the thermochemical reactions,
\( \boldsymbol{C}_{(\text {graphite})}+\frac{\mathbf{1}}{\mathbf{2}} \boldsymbol{O}_{2} \rightarrow \boldsymbol{C O} ; \boldsymbol{\Delta} \boldsymbol{H}= \)
\( -110.5 k J \)
\( \boldsymbol{C O}+\frac{\mathbf{1}}{\mathbf{2}} \boldsymbol{O}_{2} \rightarrow \boldsymbol{C O}_{2} ; \boldsymbol{\Delta} \boldsymbol{H}=-\mathbf{2 8 3 . 2 k} \boldsymbol{J} \)
the heat of reaction of \( C_{(g r a p h i t e)}+ \)
\( \boldsymbol{O}_{2} \rightarrow \boldsymbol{C} \boldsymbol{O}_{2} \) is:
\( \mathbf{A} \cdot+393.7 k J \)
B . \( -393.7 k J \)
\( \mathbf{c} .-172.7 k J \)
\( \mathbf{D} .+172.7 k J \)


Two charged conducting spheres of
radii a and b are connected to each
other by a wire. What is the ratio of
electric fields at the surfaces of the two
spheres? Use the result obtained to explain why charge density on the sharp and pointed ends of a conductor is higher than on its flatter portions.


Assertion: In the compound \( C H_{3} C I I_{2} C I=N, \) the most
electroegative carbon is II. Reason: Carbon atom II has more s-
character.
A. Assertion is True, Reason is True and Reason is the correct explanation for Assertion
B. Assertion is True, Reason is True and Reason is NOT a correct explanation for Assertion
c. Assertion is True, Reason is False
D. Assertion is False, Reason is True


State whether given statement is True or False. An object moving on a frictionless horizontal surface should move with
constant velocity
A. True
B. False


A problem in mathematics is given to 4 students whose chances of solving individually are \( \frac{1}{2}, \frac{1}{3}, \frac{1}{4} \) and \( \frac{1}{5} . \) The probability that the problem will be solved at least by one student is?
A \( \cdot \frac{2}{3} \)
в. \( \frac{3}{5} \)
\( c \cdot \frac{4}{5} \)
D. \( \frac{3}{4} \)


Which of the following does not react
with oxygen directly? \( Z n, T i, P t, F e \)


A spherical cavity made in a informaly
changed non-conducting sphere and a
positive charge in released from
position \( P \) as shown in fig. Then path
followed by particle is
A . A straight line along radically upward of cavity
B. A straight line along radially outward of cavity
c. A straight line along positive \( X \) - direction.
D. A straight line along radially outward of sphere


R.Q. is ratio of
\( \mathbf{A} \cdot \mathrm{CO}_{2} \) produced to substrate consumed
B. \( \mathrm{CO}_{2} \) produced to \( \mathrm{O}_{2} \) consumed
c. Oxygen consumed to water produced
D. Oxygen consumed to \( \mathrm{CO}_{2} \) produced.


If a curve passes through the point
(1,0) and has slope \( \left(1+\frac{1}{x^{2}}\right) \) at any point \( (x, y) \) on it, then the ordinate of point on the curve whose abscissa is
\( -3, \) is?
A \( \cdot \frac{3}{8} \)
B. \( \frac{-8}{3} \)
c. \( \frac{-3}{8} \)
D. \( \frac{8}{3} \)


Let \( [x] \) denote the greatest integer less than or equal to \( x \)
If \( f(x)=[x \sin \pi x], \) then \( f(x) \) is
This question has multiple correct options
A. continuous at \( x=0 \)
B. continuous in (-1,0)
c. differentiable at \( x=1 \)
D. differentiable in (-1,1)
E. none of these


\( \lim _{x \rightarrow \infty} \frac{2 \sqrt{x}+3 \sqrt[3]{x}+4 \sqrt[4]{x}}{\sqrt{(2 x-3)}+\sqrt[3]{(2 x-3)}+\sqrt[4]{(2}} \)
is equal to
A . 1
B. \( \alpha \)
c. \( \sqrt{2} \)
D. None of these


Antichlor is a compound:
A. which absorbs chlorine
B. which removes excess of \( C l_{2} \) from a material
C . which liberates \( C l_{2} \) from bleaching powder
D. which acts as a catalyst in the manufacture of \( C l_{2} \)


Deforestation leads to an increase in
the amount of \( C O_{2} \) in the air:
A. because the number of trees which consume \( C O_{2} \) is increased
B. because the number of trees which consume \( C O_{2} \) is reduced
c. because the number of trees which fix \( C O_{2} \) is reduced
D. None of the above


Capacity of a parallel plate condenser is \( 10 \mu F \) when the distance between its
plates is \( 8 \mathrm{cm} \). If the distance between the
plates is reduced to \( 4 \mathrm{cm} \), its capacity will
be:
A. \( 10 \mu F \)
B. \( 15 \mu F \)
c. \( 20 \mu F \)
D. \( 40 \mu F \)


Which one among the following is strongest acid?
A) Dil. \( \boldsymbol{H} \boldsymbol{C l} \)
B) Con. \( \boldsymbol{H}_{2} \boldsymbol{C O}_{3} \)


ype your questio
speed of the body is zero?
\( A \)
B.
\( c \)
\( D \)


\( (-1)(-1)(-1)(-1)(-1)=\dots \dots \)


Fill in the blanks
A tower is observed from two stations \( A \)
and \( B \) where \( B \) is East of \( A \) at a distance
100 metres. The tower is due North of \( A \)
and due North-West of
B. The angles of elevation of the tower from \( A \) and \( B \) are
complementary, the height of the tower
is


The eight species that follow all have covalent bonds. In which pair do the
species have different shapes from each other?
A. \( B e C l_{2} \) and \( C O_{2} \)
B. \( C H_{4} \) and \( N H_{4}^{+} \)
c. \( N H_{3} \) and \( B F_{3} \)
D. \( S C l_{2} \) and \( H_{2} O \)


A circuit contains a battery with
terminal voltage of 4 volts and a four-
ohm resistor
f the internal resistance is two ohms,
what is emf?
A. 4 volt
B. 5volt
c. 6 volt
D. \( 7 v o l t \)


The radius of any circle touching the \( \operatorname{lines} 3 x-4 y+5=0 \) and \( 6 x-8 y- \)
\( \mathbf{9}=\mathbf{0} \) is
A . 1.9
B. 0.95
c. 2.9
D. 1.45


A thin spherical conducting shell of radius \( R \) has a charge \( q \). Another charge
\( Q \) is placed at the centre of the shell. The electrostatic potential at a point \( \mathrm{P} \) at a distance \( \boldsymbol{R} / \mathbf{2} \) from the centre of the
shell is :
\( ^{A} \cdot \frac{2 Q}{4 \pi \varepsilon_{\Omega} R} \)
в. \( \frac{2 Q}{4 \pi \varepsilon_{0} R}-\frac{2 q}{4 \pi \varepsilon_{0} R} \)
c. \( \frac{2 Q}{4 \pi \varepsilon_{0} R}+\frac{q}{4 \pi \varepsilon_{0} R} \)
D. \( \frac{(q+Q) 2}{4 \pi \varepsilon R R} \)


Find the mean of the following.
All the factors of 48


Find solution of following inequality, also show it graphically:
\( \boldsymbol{x}-\mathbf{5} \geq-\mathbf{7}, \boldsymbol{x} \in \boldsymbol{Z} \)
\( A \)
\begin{tabular}{lllllll}
\hline-2 & -1 & 0 & 1 & 2 & 3
\end{tabular}
B.
\( \quad-3 \quad-2-1 \quad 0 \quad+\quad \bullet \quad \longrightarrow \rightarrow \)
\( \quad-3 \quad-1 \quad 0 \quad 1 \quad 2 \quad 3 \quad 4 \)
\( c \)
\begin{tabular}{ccccccc}
& & & & & \( \rightarrow \) & \( \rightarrow \) \\
\hline-2 & -1 & 0 & 1 & 2 & 3 & 4
\end{tabular}
\( D \)
\begin{tabular}{rrrrrr}
\hline & 1 & 1 & 1 & & & 1 \\
-2 & -1 & 0 & 1 & 2 & 3
\end{tabular}


In a muonic atom, a muon of mass of
200 times of that of electron and same
charge is bond to the proton. The wavelengths of its Balmer series are in
the range of
A. X-rays
B. infrared
c. \( \gamma \) rays
D. microwaves


On the basis of the graphs shown in the
figure, answer the following question:
(a) Which physical parameter is kept constant for the three curves?
(b) Which is the highest frequency
among \( \boldsymbol{v}_{1}, \boldsymbol{v}_{2} \) and \( \boldsymbol{v}_{3} ? \)


A condition of failure of function of
kidney to form urine is
A. Creatinine
B. Hematuria
c. Anuria
D. Alkaptonuria


The decomposition of \( 2 N_{2} O_{5} \rightarrow \)
\( 2 N_{2} O_{4}+O_{2} \) is at \( 200^{\circ} C . \) If the initial
pressure is \( 114 \mathrm{mm} \) and after \( 25 \mathrm{min} \). of
the reaction the total pressure of gaseous mixture is \( 133 \mathrm{mm} \). Calculate
the average rate of the reaction in
a) \( \operatorname{atm} \min ^{-1} \)
b) \( \operatorname{mol} L^{-1} s^{-1} \)
respectively.
A \( .0 .002,8.58 \times 10^{-7} \)
В. \( 0.001,8.58 \times 10^{-7} \)
c. \( 0.002,8.58 \times 10^{-4} \)
D. \( 0.001,8.58 \times 10^{-3} \)


\( C O_{2} \) and \( C H_{4} \) have critical
temperatures of \( 304 \mathrm{K} \) and \( 190 \mathrm{K} \)
respectively. \( P_{C} \) for \( C O_{2}=72 \) atm and
\( P_{C} \) for \( C H_{4}=45 \) atm. The ratio \( b_{C O_{2}}: \)
\( b_{C H_{4}} \) is?
A .2: 3
B. 1: 1
\( c \cdot 2: 1 \)
D. 3: 2


If \( \boldsymbol{A}=\left[\begin{array}{c}\mathbf{2} \\ -\mathbf{4} \\ \mathbf{1}\end{array}\right], \boldsymbol{B}=\left[\begin{array}{lll}\mathbf{5} & \mathbf{3} & -\mathbf{1}\end{array}\right] \) then
verify that \( (\boldsymbol{A} \boldsymbol{B})^{\prime}=\boldsymbol{B}^{\prime} \boldsymbol{A}^{\prime} \)


Which of the following test is used to detect halogens?
A . Lead acetate test
B. Beilstein's test
c. oxidation test
D. None of the above


A man weighs \( 75 k g \) on the surface of the earth. His weight in a geostationary satellite is:
A . infinity
в. \( 150 k g \)
c. zero
D. \( 75 / 2 k g \)


Two matrices \( A \) and \( B \) are added if
A. both are rectangular
B. both have same order
C. no of columns of \( A \) is equal to columns of \( B \)
D. no of rows of A is equal to no of columns of B


Which is responsible for ozone
depletion?
A . \( C F C s \)
B. Hydrocarbons
\( c \cdot C O_{2} \)
D. \( C O \)


\( \mathbf{A} \)
\( 3 \mathrm{M} \)
3L solution of NaOH is mixed with
another \( 3 \mathrm{M} \) 5L solution of \( \mathrm{NaOH} \). How
much should the mixture be diluted so
that the final molarity of the solution becomes 1M?


Match these words /sentences with
appropriate statements given below:
(methanol, fermentation, catenation,
homologous series, hydrogen gas)
i) The ability of carbon to form a large number of compounds through selflinking property.
ii) Alcohols react with sodium to give
this element.
iii) This series helps in giving knowledge and enables a systematic study of members.
iv) Formation of simple molecules from complex organic compounds using enzymes.
v) Unlike ethanol, the intake of this compound in very small quantities can cause death.


Explain why the given names in the following are wrong. Give the correct name in each case:
2-ethylbutane


What is the resistivity of a pure
semiconductor at absolute zero?
A. Zero
B. Infinity
C. Same as that of conductors at room temperature
D. Same as that of insulators at room temperature


Assume that each diode as shown in
the figure has a forward bias resistance
of \( 50 \Omega \) and an infinite reverse bias
resistance. The current through the
resistance \( 150 \Omega \) is:
A \( .0 .66 A \)
B. \( 0.05 A \)
c. zero
D. \( 0.04 A \)


What are furs?
A. A bunch of threads
B. A bunch of plastics
C. A bunch of fluffy hairs
D. None of these


The value of
\( \lim x \rightarrow \infty x^{2} \sin (\operatorname{en} \sqrt{\cos \frac{\pi}{x}}) \) is
\( A \cdot-\frac{\pi^{2}}{2} \)
B. \( -\frac{\pi}{1} \)
c. \( \frac{\pi^{2}}{2} \)
D. \( \frac{\pi^{2}}{4} \)


Which is used to measure the rate of
transpiration?
A. Atmometer
B. Psychrometer
c. Potometer
D. Porometer


Mark the incorrect statement:
A. Light travels along a straight line.
B. Mirror changes the direction of light falling on it
C. Things are only visible when light from our eyes reaches the object.
D. All are true.


The following table shows the
distribution of weights of 100 candidates appearing for a competition Determine the model weight.
\( \begin{array}{llll}\text { Weight } & \mathbf{5 0}- & \mathbf{5 5}- & \mathbf{6 0}- \\ (\mathbf{i n k g}) & \mathbf{5 5} & \mathbf{6 0} & \mathbf{6 5}\end{array} \)
Number of 13 candida
18


The converse of: "If two triangles are
congruent then they are similar" is
A. If two triangles are similar then they are congruent.
B. If two triangles are not congruent then they are not similar.
C. If two triangles are not similar then they are not congruent
D. None


A parallel plate capacitor is given a
definite potential difference. Keeping the potential difference same, a slab of
thickness \( 3 \mathrm{mm} \) is placed between the plates. To do this, the distance between the plates is increased by \( 2.4 \mathrm{mm} \)
Calculate the dielectric constant of the
slab.
\( (\mathbf{a}) \)
(b)
\( A \cdot 10 \)
В. 15
\( c .5 \)
\( D \)


Conversion of \( \mathrm{SO}_{2} \) to \( \mathrm{SO}_{3} \) is:
A. exothermic reaction
B. endothermic reaction
c. photochemical reaction
D. reduction reaction


Find the equation of the line passing
through the point (2,3) and perpendicular to the straight line \( 4 x- \) \( \mathbf{3} \boldsymbol{y}=\mathbf{1 0} \)


Solve the equation:
\( \mathbf{7} \boldsymbol{x}-\mathbf{9}=\mathbf{1} 6 \)


Prove that
\( y=2 e^{x}+3 e^{2} x \) is not g.s. of differential
equation \( \boldsymbol{y}^{2}-\mathbf{3} \boldsymbol{y}+\mathbf{2} \boldsymbol{y}=\mathbf{0} \)


Construct a quadrilateral \( J U M P \)
when: \( J U=3.5 \mathrm{cm}, U M= \)
\( \mathbf{4} \boldsymbol{c m}, \boldsymbol{M} \boldsymbol{P}=\mathbf{5} \boldsymbol{c m}, \boldsymbol{P} \boldsymbol{J}= \)
\( 4.5 \mathrm{cm}, P U=6.5 \mathrm{cm} \)


Calculate \( p H \) of a buffer solution that
contains \( 0.1 M N H_{4} O H\left(K_{b}=10^{-5}\right) \)
and \( 0.1 m N H_{4} C l \)
A . 10
B. 9
\( c .3 \)
D. 7


Determine the number of neutrons in an isotope of 'H' (mass no. 3).
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot 0 \)
D.


Let for \( \boldsymbol{a} \neq \boldsymbol{a}_{1} \neq \mathbf{0}, \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{a} \boldsymbol{x}^{2}+\boldsymbol{b} \boldsymbol{x}+ \)
\( \boldsymbol{c}, \boldsymbol{g}(\boldsymbol{x})=\boldsymbol{a}_{1} \boldsymbol{x}^{2}+\boldsymbol{b}_{1} \boldsymbol{x}+\boldsymbol{c}_{1} \) and \( \boldsymbol{p}(\boldsymbol{x})= \)
\( \boldsymbol{f}(\boldsymbol{x})-\boldsymbol{g}(\boldsymbol{x}), \) If \( \boldsymbol{p}(\boldsymbol{x})=\mathbf{0} \) only for \( \boldsymbol{x}= \)
-1 and \( p(-2)=2, \) then the value of
\( p(2) \) is :
A . 3
B. 9
\( c \cdot 6 \)
D. 18


f velocity of C immediately after
collision becomes \( v_{0} / 2 \) in the initial
direction of motion, the impulse due to
string on sphere \( A \) is :
A. \( \frac{m v_{0}}{8} \)
в. \( \frac{m v_{0}}{2} \)
c. \( \frac{\sqrt{m v_{0}}}{4} \)
D. none of thes


The magnetic quantum number of the valence electron of sodium is:
A . 2
B. 3
c. 1
\( D \)


\( C H C l_{3} \) and \( H_{2} O \) from two separate
immiscible layers. \( B r_{2}(\text { orange }) \) and \( I_{2} \) (violet) are soluble in organic layer to a greater extent. In test tube \( \boldsymbol{A}(\boldsymbol{K} \boldsymbol{I}+ \)
\( \left.\boldsymbol{C H C l}_{3}+\boldsymbol{H}_{2} \boldsymbol{O}\right) \) and \( \boldsymbol{B}(\boldsymbol{K} \boldsymbol{B r}+ \)
\( \left.\boldsymbol{C H} \boldsymbol{C l}_{3}+\boldsymbol{H}_{2} \boldsymbol{O}\right), \boldsymbol{C l}_{2} \) gas is passed
then:
Given:
\( \frac{1}{2} C l_{2}+e^{-} \longrightarrow C l^{-} \quad E^{o}=1.40 \mathrm{V} \)
\( \frac{1}{2} B r_{2}+e^{-} \longrightarrow B r^{-} \quad E^{o}=1.09 \mathrm{V} \)
\( \frac{1}{2} I_{2}+e^{-} \longrightarrow I^{-} \quad E^{o}=0.62 \mathrm{V} \)
This question has multiple correct options
A. organic layer in \( A \) appear violet
B. organic layer in \( A \) appear orange
c. organic layer in \( B \) appear orange
D. organic layer in \( B \) first appear violet then orange


If \( f(x) \) is a polynomial function and
\( \boldsymbol{f}^{\prime}(\boldsymbol{x})>\boldsymbol{f}(\boldsymbol{x}), \forall \boldsymbol{x} \geq 1 \) and \( \boldsymbol{f}(1)=\mathbf{0} \)
then
A. \( f(x) \geq 0, \forall x \geq 1 \)
B. \( f(x)<0, \forall x \geq 1 \)
c. \( f(x)=0, \forall x \geq 1 \)
D. None of the above


Which of the following configurations represents the most electronegative
element?
A \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{1} \)
B \( \cdot 1 s^{2} 2 s^{2} 2 p^{5} \)
C \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{5} \)
D \( \cdot 1 s^{2} 2 s^{2} 2 p^{4} \)


Find the \( A . M . \) of the series
\( \mathbf{1}, \mathbf{2}, \mathbf{4}, \mathbf{8}, \mathbf{1 6}, \dots \dots \mathbf{2}^{n} \)


Which of the following is/are true?
A. Profitability Index (PI) is a variation of the NPV rule
B. Even in case of mutually exclusive projects a conflict of ranking will not arise between PI and NPV
C. A project should be accepted when both PI and NPV are positive
D. All of the above
E. Both (A) and
(C) above


Mention the benefits of rain water
harvesting at coastal cities.


Which reactions are used for the
preparation of the halogen acid? This question has multiple correct options
\( \mathbf{A} \cdot 2 K B r+H_{2} S O_{4} \rightarrow K_{2} S O_{4}+2 H B r \)
(conc.)
B \( \cdot C a F_{2}+H_{2} S O_{4} \rightarrow C a S O_{4}+2 H F \)
(conc.)
c. \( N a C l+H_{2} S O_{4} \rightarrow N a H S O_{4}+H C l \)
(conc.)
D. \( 2 K I+H_{2} S O_{4} \rightarrow K_{2} S O_{4}+2 H I \)
(conc.)


In free space, a particle A of charge \( 1 \mu C \) is held fixed at a point P. Another particle B of the same charge and mass \( 4 \mu g \) is kept at a distance of 1 mm from
P. if \( \mathrm{B} \) is released, then its velocity at a distance of \( 9 \mathrm{mm} \) from \( \mathrm{P} \) is :
\( \left[\text { Take } \frac{1}{4 \pi \varepsilon_{0}}=9 \times 10^{9} N m^{2} C^{-2}\right] \)
A \( .2 .0 \times 10^{3} \mathrm{m} / \mathrm{s} \)
в. \( 3.0 \times 10^{4} \mathrm{m} / \mathrm{s} \)
c. \( 1.5 \times 10^{2} m / s \)
D. \( 1.0 m / s \)


What is corrosion? Explain whether gold ornaments corrode or not


Given: All seniors are mature students.
Which statement expresses a
conclusion that logically follows from
the given statement?
A. All mature students are seniors
B. If Bill is a mature student, then he is a senior
C. If Bill is not a mature student, then he is not a senior
D. If Bill is not a senior, then he is not a mature student
E. All sophomores are not mature students.


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


Which of the following are the limitations of Bohr's model?
(i) It could not explain the intensities or
the fine spectrum of the spectral lines.
(ii) No justification was given for the
principle of quantisation of angular
momentum.
(iii) It could not explain why atoms should combine to form bond.
(iv)It could not successfully applied to single electron atoms.
\( A \cdot(i),(i i),(i v) \)
B . (ii), (iii)
c. (i), (iii), (iv)
D. (i),(ii),(iii)


For current entering at \( \mathbf{A}, \) the electric
field at a distance \( \mathbf{r} \) ' from A is:
A \( \cdot \frac{\rho \mathrm{I}}{2 \pi \mathrm{r}^{2}} \)
в. \( \frac{\rho \mathrm{I}}{4 \pi^{2}} \)
c. \( \frac{\rho \mathrm{I}}{8 \pi \mathrm{r}^{2}} \)
D. \( \frac{\rho}{\mathrm{r}^{2} \mathrm{I}} \)


Neither q nor w is a state function but
\( q+w \) is a state function. Why?


If in \( N \times N, R \) is a relation defined by
the formula \( (x, y) R(p, q) \) if and only if
\( \boldsymbol{x}+\boldsymbol{q}=\boldsymbol{y}+\boldsymbol{p}, \) show that \( \mathrm{R} \) is an
equivalence relation


Using IUPAC norms, write the formulae
for the following:
(i) Potassium trioxalatoaluminate (III)
(ii) Dichloridobis (ethane-1,2-diamine) cobalt (III).


Unpolarized light falls first on polarizer
\( (P) \) and then on analyzer \( (A) . \) If the
intensity of the transmitted light from the analyser is \( \frac{1}{8} \) th of the incident unpolarized light. What will be the angle between optic axes of \( \boldsymbol{P} \) and \( \boldsymbol{A} \) ?
A \( \cdot 45^{\circ} \)
B. \( 30^{\circ} \)
c. zero
D. \( 60^{\circ} \)


Which is a stronger reducing agent,
\( \boldsymbol{S b H}_{3} \) or \( \boldsymbol{B i H}_{3}, \) and why?


For two acute angled \( \triangle A B C \) and \( \triangle P Q R \) if \( \triangle A B C \sim \triangle P Q R \) then prove
\( \operatorname{that} \frac{\operatorname{area}(\triangle A B C)}{\operatorname{area}(\triangle P Q R)}=\frac{A B^{2}}{P Q^{2}}=\frac{B C^{2}}{Q R^{2}}= \)
\( \frac{A C^{2}}{P R^{2}} \)


A lens is made of flint glass (refractive index \( =1.5 \) ). When the lens is immersed
in a liquid of refractive index \( 1.25, \) the
focal length:
A. Increases by a factor of 1.25
B. Increases by a factor of 2.5
c. Increases by a factor of 1.2
D. Remains same


\( \int_{\log 1 / 2}^{\log 2} \sin \left(\frac{e^{x}-1}{e^{x}+1}\right) d x \) is equal to
A \( \cdot \cos \frac{1}{3} \)
B.
c. \( 2 \cos 2 \)
D. none of these


Solve the equations using graphical
method: \( \boldsymbol{x}-\boldsymbol{y}=\mathbf{3} \) and \( \boldsymbol{x}+\boldsymbol{y}=\mathbf{1 1} \)
A \( .(7,4) \)
в. (-7,3)
c. (7,-4)
D. (-7,4)


The chief enzyme found in yeast cells is
A. Invertase
B. Maltase.
c. zymase.
D. Amylase.


ff \( x=2 \) and \( y=-8 \) find the value of
\( (x-y)^{3} \)


If the diagonal of cube is \( \sqrt{300} \mathrm{cms} \) then the surface area (in sq. cm) is
A. 300
B. 600
\( c \cdot 1200 \)
D. 2400


A particle of mass \( m \) is made to move
with uniform speed \( v_{0} \) along the perimeter of a regular hexagon, inscribed in a circle of radius R. The
magnitude of impulse applied at each corner of the hexagon is :
A \( \cdot 2 m v_{0} \sin \frac{\pi}{6} \)
В. \( m v_{0} \sin \frac{\pi}{6} \)
c. \( _{m v_{0} \sin \frac{\pi}{3}} \)
D. \( 2 m v_{0} \sin \frac{\pi}{3} \)


Calculate the mean of the following data, using direct method:
\( \begin{array}{lllll}\text { Class } & \begin{array}{l}25- \\ 35\end{array} & \begin{array}{l}35- \\ 45\end{array} & \begin{array}{l}45- \\ 55\end{array} & \begin{array}{l}55- \\ 65\end{array}\end{array} \)
10
8
Frequency 6


If \( z=\frac{1+i}{\sqrt{2}}, \) then the value of \( z^{1929} \) is
A. \( 1+i \)
B. -
c. \( \frac{1+i}{2} \)
D. \( \frac{1+i}{\sqrt{2}} \)


At some planet 'g' is \( 1.96 m / s^{2} . \) If it is safe to jump from a height of \( 2 m \) on
earth, then what should be
corresponding safe height for jumping on that planet
A. \( 5 m \)
в. \( 2 m \)
\( c .10 m \)
D. 20m


In the given triangle the value of \( x \) is
A .55
B. \( 110^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 30^{\circ} \)


In metabisulphite method, the resulting sulphuric acid is bubbled through nitric acid which will release
A. yellow liquid
B. colorless gas
c. brown/red vapors
D. yellow/green vapors


Biochemical Oxygen Demand (BOD) in a
river water
A. Remains unchanged when algal bloom occurs.
B. Has no relationship with concentration of oxygen in the water.
C. Gives a measure of salmonella in the water.
D. Increases when sewage gets mixed with river water.


The difference in maximum kinetic
energy of photoelectrons from the \( A \) and
from B
A. increases with increases in \( E \)
B. decreases with decreases in \( E \)
c. first increases than decrease with increase in \( E \)
D. remain constant


Ratio of shaded fraction to whole is
\( \mathbf{A} \cdot 1: 2 \)
B. 1: 3
\( \mathbf{c} \cdot 3: 4 \)
D. 2: 3


Mendeleev corrected the atomic weight
of :
\( A \cdot B e \)
B. \( N \)
\( c \cdot O \)
D. \( C l \)


If \( \boldsymbol{x}^{\boldsymbol{y}}=\boldsymbol{e}^{\boldsymbol{x}-\boldsymbol{y}}, \) then find \( \frac{d \boldsymbol{y}}{d \boldsymbol{x}} \) at \( \boldsymbol{x}=\mathbf{1} \)


Chemical oxygen demand of a sample
of \( H_{2} O \) is the amount of oxygen:
A . liberated when excess of \( H_{2} O \) is added to a known volume of \( H_{2} O \)
B. consumed by 1 litre of the sample of \( H_{2} O \) at 1 atm \( 27^{0} C \)
c. required to chemically oxidize the organic content of polluted water by \( K_{2} C r_{2} O_{7}+50 \% H_{2} S O_{4} \) in given sample of \( H_{2} O \)
D. any of the above


If accuracy of weighing machine is better than \( 1 / 2 \) percent, a student record his own mass. Choose the option that
explains the recording most accurately.
A. \( 6.43 \mathrm{kg} \)
B. 60 kg
\( c \cdot 64.3 \mathrm{kg} \)
D. 600kg
E. \( 643 \mathrm{kg} \)


Give reasons:
Aliphatic amines are stronger bases
than ammonia.


The temperature of equal masses of three different liquids \( A, B, C \) are
\( 12^{\circ} \mathrm{C}, 19^{\circ} \mathrm{C} \) and \( 28^{\circ} \mathrm{C} \) respectively. The
temperature, when \( A \) and \( B \) are mixed,
is \( 16^{\circ} \mathrm{C} \) and when \( B \) and \( C \) are mixed,
is \( 23^{\circ} \mathrm{C} \). What will be the temperature
when \( A \) and \( C \) are mixed?


In the given distance-time graph, what
is the distance corresponding to 4 min ?
\( A \cdot 2 k m \)
3. \( 3 k m \)
\( c .4 k m \)
\( D .5 k m \)


Select the correct statement.
A. Carbon-carbon bond order in graphite is more than diamond
B. Carbon-carbon bond order in graphite is less than diamond
C . Hybridization of each carbon in diamond is \( s p^{2} \)
D. Hybridization of each carbon in graphite is \( s p^{3} \)


Find the product of \( \frac{k^{2}+13 k+42}{k^{2}+15 k+56} \) and \( \frac{\boldsymbol{k}^{2}+\mathbf{8} \boldsymbol{k}}{\boldsymbol{k}^{2}+\mathbf{1 1} \boldsymbol{k}+\mathbf{3 0}} \)
A \( \cdot \frac{k^{2}+8 k}{k+5} \)
в. \( \frac{k}{k+5} \)
c. \( \frac{k}{k^{2}+15 k+56} \)
D. \( \frac{1}{k+5} \)


Two liquids \( A \) and \( B \) have vapour
pressures in the ratio \( P_{A}^{0}: P_{B}^{0}=2: 3 \) at
a certain temperature. Assuming that \( \mathbf{A} \) and \( \mathrm{B} \) form an ideal solution and ratio of
mole fractions of \( A \) and \( B \) in the vapour
phase is \( 1: 3, \) then the mole fraction of \( \mathbf{A} \) in the solution at the same temperature
is :
A \( \cdot \frac{1}{3} \)
B. \( \frac{2}{3} \)
c. \( \frac{1}{4} \)
D. \( \frac{3}{4} \)


What is the product formed when ozone reacts with mercury?
A. \( H g O \)
в. \( H g_{2} O_{2} \)
\( \mathrm{c} \cdot \mathrm{Hg}_{2} \mathrm{O} \)
D. All of the above


A vector \( \vec{B} \) which has magnitude 8 is added to a vector \( \vec{A} \) which lies along the
x-axis. the sum of their two vectors is a
third vector which lies along the y-axis and has a magnitude that is twice the magnitude of \( \vec{A} \). Find the magnitude of \( \boldsymbol{A} \)


A current of 3A flows in a circuit shown
in the figure. The potential difference between A and B is
A \( \cdot 4 v \)
B. 3v
\( c \cdot 2 v \)
D. \( 5 v \)


If a determinant is of the \( n^{t h} \) order, and
if the constituents of its first, second,
third, \( \ldots n^{t h} \) rows are the first \( n \) figurate
numbers of the first, second, third, \( \ldots n^{t h} \) orders, show that its value is unity,


What is reflection of light?


The wave equation is \( y= \) \( 0.30 \sin (314 t-1.57 x) \) where \( t, x \) and \( y \)
are in second, metre and centimetre
respectively. The speed of the wave is
A. \( 400 \mathrm{m} / \mathrm{s} \)
в. \( 100 \mathrm{m} / \mathrm{s} \)
c. \( 200 m / s \)
D. \( 50 \mathrm{m} / \mathrm{s} \)


\( \int \sec ^{8 / 9} x \operatorname{cosec}^{10 / 9} x d x \) is equal to
A. \( -(\cot x)^{1 / 9}+c \)
B. \( 9(\tan x)^{1 / 9}+c \)
\( \mathbf{c} \cdot-9(\cot x)^{1 / 9}+c \)
D. \( -\frac{1}{9}(\cot x)^{1 / 9}+c \)


Enzymes are \( _{---} \) -specific in action
A . highly
B. not
c. may be
D. may not


In the figure the boundary of the shaded region consists of four semicircular
\( \operatorname{arcs}, \) the smallest two being equal. If the
diameter of the largest is \( 14 \mathrm{cm} \) and of
the smallest is \( 3.5 \mathrm{cm}, \) find
1. The length of the boundary
2. The area of the shaded region


Name the individual isomers of each of
the following:
(a) \( \left[\boldsymbol{P t}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{2} \boldsymbol{C l}_{2}\right] \)
(b) \( C r C l_{3} .6 H_{2} 0 \)
\( (c)\left[C o\left(N H_{3}\right)_{5} N O_{2}\right]\left(N O_{3}\right)_{2} \)
\( (\mathrm{d}) \mathrm{Co}\left(\mathrm{N} \boldsymbol{H}_{3}\right)_{5}\left(\boldsymbol{S} \boldsymbol{O}_{4}\right)(\boldsymbol{C l}) \)
\( (\mathrm{e})\left\{\begin{array}{cc}\boldsymbol{N} \boldsymbol{H}_{2} & \\ (\boldsymbol{e n})_{2} \boldsymbol{C} \boldsymbol{o} & \boldsymbol{C o}(\boldsymbol{e n})_{2} \\ \boldsymbol{N} \boldsymbol{O}_{2} & \boldsymbol{B r}_{4}\end{array}\right) \)
\( (f) C o(e n)_{2} N H_{3} B r S O_{4} \)
\( \left.(g)\left[\boldsymbol{P t}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)\left(\boldsymbol{H}_{2}\right)\right)\left(\boldsymbol{C}_{5} \boldsymbol{H}_{5} \boldsymbol{N}\right)\left(\boldsymbol{N} \boldsymbol{O}_{2}\right)\right] \boldsymbol{C l} \)


If two waves of length \( 50 \mathrm{cm} \) and \( 51 \mathrm{cm} \)
produced 12 beats per second, the
velocity of sound is:
A . 360
в. 340
\( c .306 \)
D. none of the above


State whether True or False.
Factorization of \( (2 x-y)^{3}-(2 x-y) \) is
\( (2 x-y)(2 x-y+1)(2 x-y-1) \)
A. True
B. False


A particle is moving on a straight line path with constant acceleration
directed along the direction of instantaneous velocity. Which of following statements are false about the motion of particle?
A. Particle may reverse the direction of motion
B. Distance covered is not equal to magnitude of displacement
c. The magnitude of average velocity is less than average speed
D. All the above


A lightning conductor is a
A. piece of wire with spikes through which current can flow
B. sbstance that can be charged by clouds
C. metal rod with spikes, ending in a copper plate buried in the ground, fixed to a building to protect it from lightning
D. copper plate buried in the ground below a building to protect it from lightning.


Solve: \( \sqrt{e^{4 x}-e^{2 x}} \)


HB H bond angle in \( B H_{4}^{-} \) is
A \( .180^{\circ} \)
B . \( 120^{\circ} \)
\( c \cdot 109^{\circ} \)
D. \( 90^{\circ} \)


Calculate the energy associated with
the first orbit of \( H e^{+} . \) What is the
radius of this orbit?


In the arrangement of capacitors shown
in Figure, if each capacitor is \( 9 \mathrm{pF} \), the effective capacitance between \( A \) and \( B \)
is
A . \( 10 p \)
В. 15 p
\( c .20 p F \)
D. \( 5 p F \)


The reaction \( \boldsymbol{C a} \boldsymbol{C O}_{3}(\boldsymbol{s}) \Leftrightarrow \boldsymbol{C a O}(\boldsymbol{s})+ \)
\( C O_{2}(g) \) goes to completion in lime kiln.
A. True
B. False


An object \( A \) is dropped from rest from the top of a \( 30 \mathrm{m} \) high building and at the same moment another object B is projected vertically upwards with an initial speed of \( 15 \mathrm{m} / \mathrm{s} \) from the base of
the building. Mass of the object A is 2 kg while mass of the object B is 4 kg. The maximum height above the ground level attained by the center of mass of
the \( A \) and \( B \) system is \( (\text {take } g= \)
\( \left.10 m / s^{2}\right) \)
\( \mathbf{A} \cdot 15 \mathrm{m} \)
B. 25 m
c. 30 \( m \)
D. 35 m


If \( \mathbf{M}(\mathbf{A}, \mathbf{Z}), \boldsymbol{M}_{\boldsymbol{p}}, \boldsymbol{a} \boldsymbol{n} \boldsymbol{d}, \boldsymbol{M}_{\boldsymbol{n}} \)
denote the masses of
the nucleus
respectively in units of
\( \left(1 u=931.5 M e V / C^{2}\right) \)
and BE represents its bonding energy in
MeV,
then -
A \( . M(A, Z)=Z M_{p}+(A-Z) M_{n}-B E \)
B. \( M(A, Z)=Z M_{p}+(A-Z) M_{n}+B E / C^{2} \)
C \( . M(A, Z)=Z M_{p}+(A-Z) M_{n}-B E / C^{2} \)
D. \( M(A, Z)=Z M_{p}+(A-Z) M_{n}+B E \)


In a Bainbridge mass spectrometer positive rays of the same element produce different traces. The traces
correspond to:
A. isotopes
B. isobars
c. isotones
D. none of the above


Ketosis is due to
A. High insulin level
B. Low insulin level
C. Low thyroxine level
D. Low level of glucagon


A solid cylinder of length L and radius \( r \)
is heat upto same temperature as that of a cube of edge length a. If both have
same material, volume and allowed to
cool under similar conditions, then ratio
of amount of radiations radiated will be
(Neglect radiation emitted from flat surfaces of the cylinder)
A \( \cdot \frac{a}{3 r} \)
B. \( \frac{2 a}{r L} \)
c. \( \frac{a^{2}}{r L} \)
D. \( \frac{\pi a^{2}}{2 r L} \)


Which of the following theories could not explain completely the behaviour of conductors, insulators, and
semiconductors.
A. energy band theory
B. free electron theory
c. valence electron theory
D. None


Oxygen dissociation curve in mammals
is
A. J-shaped
B. Sigmoid shapeddped
c. T-shaped
D. L-shaped


\( \cot ^{-1}(2+\sqrt{3})= \)
\( A \cdot \frac{\pi}{12} \)
B. \( \frac{\pi}{15} \)
\( c \cdot \frac{\pi}{5} \)
\( D \cdot \frac{3 \pi}{10 \pi} \)


Find the equation of the ellipse whose
vertices are \( (\pm \mathbf{5}, \mathbf{0}) \) and foci are
\( (\pm \mathbf{3}, \mathbf{0}) \)


The figure shows a circuit containing a
coil wound over a long and hollow thin
tube. Copy the diagram and show the polarity required by each face of the
solenoid.
A. Current enters the solenoid from face \( B \), hence this end of solenoid is south pole and the face \( A \) is north pole
B. Current enters the solenoid from face \( B \), hence this
end of solenoid is north pole and the face \( A \) is south pole.
c. current enters the solenoid from face \( A \), hence this
end of solenoid is south pole and the face \( B \) is north pole
D. None of these


If \( \boldsymbol{y}=\cos ^{-1} \boldsymbol{x} \) then \( \left(1-\boldsymbol{x}^{2}\right) \boldsymbol{y}^{\prime \prime}-\boldsymbol{x} \boldsymbol{y}^{\prime}=? \)
where \( \boldsymbol{y}^{\prime}=\frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \)
A . 1
B.
\( c \cdot 2 x \)
D. \( 2 y \)


The adrenal glands consist of :
A. lower adrenal and upper paradrenal sections
B. ACTH and BCTH sections
C. the inner and outer layer of the kidney
D. the inner medulla and the outer cortex


The area bounded by \( y=x^{2} \) and \( y= \)
\( 1-x^{2} \) is
A \( \cdot \frac{\sqrt{8}}{3} \)
в. \( \frac{16}{3} \)
c. \( \frac{32}{3} \)
D. \( \frac{17}{3} \)


Answer the following. State the function of iris and ciliary muscles in human eye.


Give for rational numbers equivalent to:
\( \frac{\mathbf{5}}{-3} \)


A mixture has 18 g water and 414 g ethanol. The mole fraction of water in
mixture is (assume ideal behaviour of
the mixture):
A . \( 0 . \)
B. 0.4
\( c . \) о.
D. 0.9


Moment of inertia of a hollow sphere of
mass \( \mathrm{M} \) and diameter \( \mathrm{D} \) about its
diameter
A \( . M D^{2} / 5 \)
В. \( 2 M D^{2} / 5 \)
c. \( M D^{2} / 6 \)
D. \( 5 M D^{2} / 2 \)


\( A P \) bisects angle \( A \)


A tuning fork of frequency 500 Hz is sounded on a resonance tube. The first
and second resonances are obtained at
\( 17 \mathrm{cm} \) and \( 52 \mathrm{cm} . \) The velocity of sound
is
A. \( 170 \mathrm{m} / \mathrm{s} \)
B. \( 350 \mathrm{m} / \mathrm{s} \)
c. \( 520 \mathrm{m} / \mathrm{s} \)
D. \( 850 \mathrm{m} / \mathrm{s} \)


Which of the following applies most
appropriate to \( B ? \)
A. Instead of containing some strongly activating groups, it is very less reactive towards electrophilic aromatic substitution reaction
B. It is highly reactive towards electrophilic aromatic substitution reaction
C. It is highly reactive towards aromatic nucleophilic substitution reaction
D. It is inert toward any substitution reaction.


The position vectors of the points \( A, B, C \) and \( \mathrm{D} \) are \( 3 \hat{i}-2 \hat{j}-\hat{k}, 2 \hat{i}-3 \hat{j}+ \)
\( \mathbf{2} \hat{\boldsymbol{k}}, \mathbf{5} \hat{\boldsymbol{i}}-\hat{\boldsymbol{j}}+\mathbf{2} \hat{\boldsymbol{k}} \) and \( \mathbf{4} \hat{\boldsymbol{i}}-\hat{\boldsymbol{j}}+\boldsymbol{\lambda} \hat{\boldsymbol{k}} \)
respectively. If the points \( A, B, C \) and \( D \) lie on a plane, the value of \( \lambda \) is?
\( A \cdot 0 \)
B.
\( c \cdot 2 \)
D. -4


Which is not an electrophile?
\( \mathbf{A} \cdot \mathrm{NO}_{2} \)
в. \( \mathrm{CH}_{3}-\mathrm{OH}_{2} \)
c. \( \mathrm{PCl}_{5} \)
D. \( \mathrm{CH}_{3} \)


Which one has a copulatory organ?
A. Squirrel
B. Snake
\( c . \) Toad
D. Parrot


Atomic hydrogen is excited to the nth energy level.The maximum number of
spectral lines which it can emit while
returing to the ground state, is
A \( \cdot \frac{1}{2} n(n-1) \)
B . \( \frac{1}{2} n(n+1) \)
c. \( n(n+1) \)
D. \( n(n-1) \)


Three long straight parallel wires
\( X, Y, Z \) carry currents as shown; the
resultant force on \( Y \) is
A. Towards \( X \)
B. Towards \( Z \)
C. Perpendicular to the plane of the figure
D. Zero


f \( a, b, c>1, \Delta= \)
\( \left|\begin{array}{ccc}\log _{a}(a b c) & \log _{a} b & \log _{a} c \\ \log _{b}(a b c) & 1 & \log _{b} c \\ \log _{c}(a b c) & \log _{c} b & 1\end{array}\right| \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B \( \cdot \log _{a} b+\log _{b} c+\log _{c} a \)
\( \mathbf{c} \cdot \log _{a b c}(a+b+c) \)
D. none of these


Which term of the GP \( 2,8,32, \dots \) is
\( \mathbf{1 3 1 0 7 2} ? \)
\( \mathbf{A} \cdot 6^{t h} \)
B. \( 7^{\text {th }} \)
\( c \cdot 8^{t h} \)
\( \mathbf{D} \cdot 9^{t h} \)


In the diagram, \( O \) is the centre of the
circle. Given that \( O Q= \)
\( 5 \mathrm{cm} \) and \( A N=8 \mathrm{cm}, \) find the length
of \( \boldsymbol{P Q} \)


The most abundant metal among the following is:
A . \( A l \)
в. \( C a \)
c. \( F e \)
D. \( K \)


The fraction \( \frac{1}{5} \) converted to percentage
is
A . \( 20 \% \)
B. 30\%
c. \( 40 \% \)
D. \( 50 \% \)


The prime factor of 128 is
A. 0
B. 1
\( c \cdot 2 \)
D. 3


The method for separation of mixture of common salt and ammonium chloride
is:
A. Fractional distillation
B. Sublimation
c. chromatography
D. crystallization


Let \( A \) be the sum of the first 20 terms
and \( B \) be the sum of the first 40 terms
of the series \( 1+2.2^{2}+3^{2}+2.4^{2}+5^{2}+ \)
\( 2.6^{2}+\ldots . . . . . \) Find the value of \( \boldsymbol{A} \)
A . 496
в. 232
c. 248
D. 464


Two particles of equal mass go around
a circle of radius \( R \) under the action of
their mutual gravitational attraction.The speed of each particle is
\( ^{\mathbf{A}} \cdot_{v}=\frac{1}{2 R} \sqrt{\left(\frac{1}{G m}\right)} \)
в. \( v=\sqrt{\left(\frac{G m}{2 R}\right)} \)
\( ^{\mathrm{c}} v=\sqrt{\left(\frac{G m}{R}\right)} \)
D. \( v=\sqrt{\left(\frac{4 G m}{R}\right)} \)


A box of negligible mass containing 2
moles of an ideal gas of molar mass \( M \)
and adiabatic exponent \( \gamma \) moves with
constant speed \( \boldsymbol{v} \) on a smooth
horizontal surface. If the box suddenly
stops, then change in temperature of
gas will be
A \( \cdot \frac{(\gamma-1) M v^{2}}{4 R} \)
B. \( \frac{\gamma M v^{2}}{2 R} \)
c. \( \frac{M v^{2}}{2(\gamma-1) R} \)
D. \( \frac{(\gamma-1) M v^{2}}{2 R} \)


If the frequency of a sound wave is increased by \( 25 \% \), then the change in its wavelength will be
A. 25\% decrease
B. 20\% decrease
c. 20\% increase
D. 25\% increase


Which of the following industries may be a reason for water scarcity?
A. Chemical industry
B. Pharmaceutical industry
C. Textile industry
D. All of the above.


A small sphere starts falling from a very large height and after falling a distance
of \( 100 m \) it attains the terminal velocity
and continues to fall with this velocity. The work done by the atmosphere during the first fall of \( 100 m \) is:
A. Greater than the work done for next fall of 100 m
B. Less than the work done for next fall of 100 m
c. Equal to \( 100 \mathrm{mg} \)
D. Greater than \( 100 \mathrm{mg} \)


Solve the following determinant :
\( \begin{array}{|ccc|}15 & 11 & 7 \\ 11 & 17 & 14 \\ 10 & 16 & 13\end{array} \)


Which of the following represents the poisonous gas which caused the tragedy in Bhopal in \( 1984 ? \)
A. \( C H_{3} C=N=S \)
в. \( C H_{3}-N=C=O \)
c. \( C H_{3}-N=C=S \)
D. \( C H_{3}-O-N=C \)


In a potentiometer of 10 wires, the
balance point is obtained on the \( 7^{t h} \)
wire. To shift the balance point to \( 9^{t h} \) wire, we should.
A. Decrease resistance in the main circuit
B. Increase resistance in the main circuit
c. Decrease resistance in series with the cell whose emf is to be measured
D. Increase resistance in series with the cell whose emf is to be determined


In the following diagram an arrow
shows the motion of the coil towards the
bar magnet.
(i) State in which direction the current
flows: \( A \) to \( B \) or \( B \) to \( A \) ?
(ii) Name the law used to come to the
conclusion.


Oxygen has number of
electrons in the outermost shell.


Protein denaturation results in:
A. change of primary structure
B. change of secondary structure
c. change of tertiary structure
D. change in both secondary and tertiary structures


Two pipes running together can fill a cistern in \( 3 \frac{1}{13} \) minutes. If one pipe take
3 minutes more than other to fill it,
find the time in which each pipe can fill
the tank.


The graph of the electrical activity of heart versus time produced by the noninvasive medical procedure is called
A. Electroencephalogram
B. Electrocardiogram
c. stethoscope
D. None of the above


Swinging of table fan is an example of which type of motion?
A. Oscillatory motion
B. One dimenetional motion
c. Projectile motion
D. None of the above


Which of the following statement is true as per the second law of thermodynamics for an isolated, ordered system?
A. Heat will flow into the system
c. work will be done by the system
D. Work will be done on the system
E. The entropy withing the system will increase


The co-ordination number of \( N a \) in
solid \( N a H \) is:
A .4
B. 6
\( c \cdot 8 \)
D. 12


What type of deviation from Raoult's law is exected?
(a) when equal volume of acetone and
ethanol is mixed?
(b) when equal volume of acetone and chloroform is mixed?


The rate of the first order reaction is
\( 0.69 \times 10^{-2} \) mol \( L^{-1} \) min \( ^{-1} \) and the
initial concentration is \( 0.2 m o l L^{-1} \). The
half life period is:
A . \( 1205 s \)
в. 330
c. \( 600 s \)
D. \( 1 s \)


Evaluate:
\( \int_{0}^{2}\left[x^{2}\right] d x \)


Evaluate the following limits. \( \lim _{x \rightarrow 0} \frac{x\left(e^{x}-1\right)}{1-\cos x} \)


Three point charges \( 3 n C, 6 n C \) and \( 9 n C \)
are placed at the corners of an
equilateral triangle of side 0.1 m. The
potential energy of the system is :
A \( .8910 n J \)
в. \( 89100 \mathrm{mJ} \)
c. \( 9910 J \)
D. \( 99100 K J \)


If \( n^{t h} \) term of \( A P \) is \( 4 n+1 \), then \( A M \) of
\( 11^{t h} \) to \( 20^{t h} \) terms is
A . 61.5
B. 63
\( c .63 .5 \)
D. 62


A circuit \( A B C D \) is held perpendicular
to the uniform magnetic field of \( \boldsymbol{B}= \)
\( 5 \times 10^{-2} T \) extending over the region
\( P Q R S \) and directed into the plane of
the paper. The circuit is moving out of
the field at a uniform speed of \( 0.2 m s^{-1} \)
for \( 1.5 s . \) During this time, the current in
the \( 5 \Omega \) resistor is
\( \mathbf{A} \cdot 0.6 m A \) from \( B \) to \( C \)
B. \( 0.9 m A \) from \( B \) to \( C \)
c. \( 0.9 m A \) from \( C \) and \( B \)
D. \( 0.6 m A \) from \( C \) to \( B \)
E. \( 0.8 m A \) from \( C \) to \( B \)


The vitamin responsible for biosynthesis of co-enzyme Q is:
\( A \cdot A \)
B.
\( c \cdot E \)
\( D \)


The formula for permutit or zeolite which is used as softer in ion-exchange
method is:
A. \( N a A l S i O_{4} \)
B. \( N a A l O_{2} \)
c. both \( A \) and \( B \)
D. \( N a_{2} S O_{4} \)


Solve:
\( \frac{x+2}{6}-\left(\frac{11-x}{3}-\frac{1}{4}\right)=\frac{3 x-4}{12} \)


The mean of four observations is \( 3 . \) If the
sum of the squares of these observations is 48 then their standard
deviation is
A. \( \sqrt{7} \)
B. \( \sqrt{2} \)
\( c \cdot \sqrt{3} \)
D. \( \sqrt{5} \)


State whether given statement is True or False.

Is it possible to move in a curved path in the absence of a force?
A. True
B. False


Two blocks of masses \( 2 k g \) and \( 1 k g \)
respectively are tied to the ends of a
strings which passes over a light
frictionless pulley. The masses are held
at rest at the same horizontal level and
then released. The distance traversed by
centre of mass in 2 seconds is: \( (g= \)
\( \left.10 m / s^{2}\right) \)
A \( .1 .42 m \)
B. \( 2.22 m \)
c. \( 3.12 m \)
D. \( 3.33 m \)


Atmospheric pressure decreases with increase in height.
A. True
B. False


The halogen which can form both cations and anions is:
A.
B. Cl
\( c \cdot B r \)
\( D \)


Which of the following is incorrect for
\( C_{2} \) molecule?
A. Its bond order is 2
B. Both bonds are \( \pi \) bonds
c. one bond is \( \sigma \) and other bond is \( \pi \)
D. It is diamagnetic


The total number of metals discovered
so far are:
\( \mathbf{A} \cdot 92 \)
B. 82
c. 80
D. 11


Disposable plastic plates should not be used because:
A. They are made of materials with light weight
B. They are made of toxic materials
c. They are made of biodegradable materials
D. They are made of non-biodegradable materials


The atomic number of an element \( X \) is
13.What will be the number of electrons
in its ion \( X^{34} \)


The STP volume of oxygen liberated by 2 ampere of current when passed through acidulated water for 3 minutes and 13
seconds, is:
A . 120 \( c c \)
B. 22.4 cc
c. \( 11.2 \mathrm{c} \)
D. 44.8 сс


If the speed of longitudinal wave equals
10 times the speed of the transverse waves in a stretched wire of material
which has modulus of elasticity \( \mathrm{E} \), then the stress in the wire is
\( \mathbf{A} \cdot 100 E \)
в. \( \frac{E}{100} \)
c. \( \frac{E}{10} \)
D. \( 10 E \)


Q Type your question-
-
liquid of density \( \rho=1000 k g / m^{3} \) and
refractive index \( \mu=4 / 3 . \) Afish is at rest
at the bottom of the container and a
humming bird is at rest in air at some distance above the surface of the liquid.
At \( t=t_{0}, \) the level of the liquid is \( h= \)
\( \frac{3}{5} m \) as shown in the figure. Neglect
viscous effects and take \( g=10 m / s^{2} \)
Q43. What is the speed of top surface of liquid in the container at the given instant:
\( A \)
\[
\frac{1}{2} \mathrm{m} / \mathrm{s}
\]
B. \( 2 \mathrm{m} / \mathrm{s} \)
\( c \cdot 3 m / s \)
\( D \)
\[
\frac{1}{4} m / s
\]


1.375 g of cupric oxide was reduced by heating in a current of hydrogen and the weight of copper obtained was 1.098 g. In another experiment, 1.156 g of copper was dissolved in nitric acid and the
resulting solution was evaporated to dryness. The residue of copper nitrate
when strongly heated was converted
into 1.4476 g of cupric oxide. State the law illustrated by these chemical
combinations.
A. Law of reciprocal proportion
B. Law of multiple proportion
C. Law of constant composition
D. None of these


A circular coil has 500 turns of wire and
its radius is \( 5 \mathrm{cm} \). The self inductance of
the coil is:-
A \( \cdot 25 \times 10^{-3} m H \)
в. \( 25 m H \)
c. \( 50 \times 10^{-3} H \)
D. \( 50 \times 10^{-3} \mathrm{mH} \)


The curve \( y-e^{x y}+x=0 \) has a vertical
tangent at
A \( .(1,1) \)
в. (0,1)
c. (1,0)
(i) 5
D. (0,0)


A particle of mass \( \mathrm{m} \) is revolving in a horizontal circle of radius r with
constant angular speed \( \omega . \) The areal
velocity of the particle is:
A \( \cdot r^{2} \omega \)
B . \( r^{2} \theta \)
\( ^{c \cdot \frac{r^{2} \omega}{2}} \)
D. \( \frac{r \omega^{2}}{2} \)


Which one is correct for a solution?
A. Saturated and dilute
B. Supersaturated and saturated
C. Saturated and unsaturated
D. Dilute and concentrated


In the extraction of iron, the most
preferred ores are :
A. hematite and limonite
B. copper pyrites an dsiderite
c. magnetite and iron pyrites
D. limonite and copper pyrites


A single electron system has ionization energy \( 11180 k J \) mol \( ^{-1} \). Find the
number of protons in the nucleus of the
system.


If \( \boldsymbol{x}=\boldsymbol{a} \sin 2 \boldsymbol{t}(1+\cos 2 t) \) and \( \boldsymbol{y}= \)
\( b \cos 2 t(1-\cos 2 t), \) find the values of
\( \frac{d y}{d x} \) at \( t=\frac{\pi}{4} \) and \( t=\frac{\pi}{3} \)
OR
If \( \boldsymbol{y}=\boldsymbol{x}^{x}, \) prove that \( \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}}-\frac{1}{\boldsymbol{y}}\left(\frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}\right)^{2}- \)
\( \frac{\boldsymbol{y}}{\boldsymbol{x}}=\mathbf{0} \)


Principles or laws of inheritance were
enunciated by
A. Mendel
B. Morgan
c. Bateson
D. Punnet


Illustrate with examples the limitations
of Williamson's synthesis for
the preparation of certain types of
ethers.


A projector lens has a focal length 10
\( \mathrm{cm} . \) It throws an image of a \( 2 \mathrm{cm} \times 2 \mathrm{cm} \)
Slide on a screen 5 meter away from the
lens. Find
(i) The size of the picture on the screen
and
(ii)ratio of illuminations of the slide and
of the picture on the screen.


For a plane convex lens \( (\mu=1.5) \) having radius of curvature \( 10 \mathrm{cm} . \) It is silvered on its plane surface. Find focal length after silvering:
\( A \cdot 10 \mathrm{cm} \)
B. 20 cm
c. \( 15 \mathrm{cm} \)
D. 25 cm


Work function is
A. energy necessary to eject the electron from its orbit
B. energy necessary to eject an electron from within a metal body
C. minimum necessary energy to eject an electron from a metal surface
D. wavelength necessary for releasing an electron from a body


Identify \( A, B, \) and \( C \)
i) Isomeric alcohols \( (A),(B), \) and \( (C) \)
\( \left(\boldsymbol{C}_{5} \boldsymbol{H}_{12} \boldsymbol{O}\right) \)
ii) \( (A) \) and
(B) react with chromic acid
solution.
(B) gives an acid (D).
iii) Reactivity with HBr is: \( C>A \gg B \)
All give the same compound,
\( \boldsymbol{C}_{5} \boldsymbol{H}_{11} \boldsymbol{B} \boldsymbol{r}(\boldsymbol{E}) \)
iv) Only (A) is oxidised by NaOI.


List I and List II contains four entries
each. Entries of Column I are to be
matched some entries of List II. One or
more than one entries of List I may
match with the same entry of List II


The product of \( t_{5} \) and \( t_{6} \) of the progress \( \frac{1}{4}, \frac{1}{2}, 1, \dots \dots \) is
A \( \cdot t_{8} \)
в. \( t_{11} \)
c. \( t_{1} \)
D. \( t \)


The solubility of salt \( \boldsymbol{X} \boldsymbol{Y}_{2} \) is:
\( \mathbf{A} \cdot 4 K_{s p} \)
в. \( \frac{K_{s p}}{4} \)
D. \( \sqrt{\frac{K_{s p}}{4}} \)


A body is heated at \( 110^{\circ} \mathrm{C} \) and placed in
air at \( 10^{\circ} \mathrm{C} \). After 1 hour its
temperature is \( 60^{\circ} \mathrm{C} \). How much
additional time is required for it to cool
to \( 35^{\circ} \) C?


A galvanic cell is constructed using the
redox reaction, it is represented as:
\( \frac{1}{2} H_{2}(g)+A g C l(s) \rightleftharpoons H^{+}(a q)+ \)
\( \boldsymbol{C l}^{-}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{A} \boldsymbol{g}(\boldsymbol{s}) \)
\( \mathbf{A} \cdot P t\left|H_{2}(g)\right| H C l(s o l n .) \| A g N O_{3}(s o l n .) \mid A g \)
B \( \cdot A g|A g C l(s)| K C l(s o l n .) \mid H C l(\text {soln.}), H_{2}(g) \mid P t \)
\( \mathbf{c} \cdot P t\left|H_{2}(g)\right| K C l(s o l n .) \| A g C l(s) \mid A g \)
\( \mathbf{D} \cdot P t\left|H_{2}(g), H C l(s o l n .) \| A g C l(s)\right| A g \)


A chord of a circle of radius \( 12 \mathrm{cm} \)
stands an angle of \( 120^{\circ} \) at the centre.
Find the area of the corresponding
segment of the circle.


A wheel starting from rest is uniformly accelerated at 4 rad \( / s^{2} \) for 10 seconds. It is allowed to rotate uniformly for the
next 10 seconds and is finally brought to rest I the next 10 seconds. Find the
total angle rotated by the wheel


If the radius of the hydrogen atom is 53 \( \mathrm{pm}, \) the radius of the \( H e^{+} \) ion is closest
to:
A \( .108 \mathrm{pm} \)
B. \( 81 \mathrm{pm} \)
c. 27 pm
D. 13 pm


\( \ln \) a reaction \( \boldsymbol{A}+\boldsymbol{B} \rightleftharpoons \boldsymbol{C}+\boldsymbol{D}, \) the
rate constant of forward reaction and
backward reaction is \( K_{1} \) and \( K_{2}, \) then
the equilibrium constant (K) for reaction is expressed as
\( ^{\mathrm{A}} \cdot_{K_{c}}=\frac{K_{2}}{K_{1}} \)
в. \( K_{c}=\frac{K_{1}}{K_{2}} \)
\( \mathbf{c} \cdot K_{c}=K_{1} \times K_{2} \)
D. \( K_{c}=K_{1}+K_{2} \)


A solution of \( 50 \% \) of \( A \) and \( 50 \% \) of \( B \) on
distillation results into
A. Seperation of an azeotropic mixture and pure \( A \)
B. Seperation of an azeotropic mixture and pure B.
C. Seperation of both pure \( A \) and pure \( B \)
D. None.


toppr \( t \)
Q Type your question
supply \( ): \)
\( A \)
B.
\( c \)
\( D \)


Resolve \( \frac{6 x^{4}+11 x^{3}+18 x^{2}+14 x+6}{(x+1)\left(x^{2}+x+1\right)^{2}} \)
into partial fractions.
A \( \frac{5}{x+1}+\frac{(x-1)}{\left(x^{2}+x+1\right)}+\frac{(3 x+2)}{\left(x^{2}+x+1\right)^{2}} \)
в. \( \frac{5}{x+1}-\frac{(x-1)}{\left(x^{2}+x+1\right)}+\frac{(3 x+2)}{\left(x^{2}+x+1\right)^{2}} \)
c. \( \frac{5}{x+1}+\frac{(x-1)}{\left(x^{2}+x+1\right)}-\frac{(3 x+2)}{\left(x^{2}+x+1\right)^{2}} \)
D. \( \frac{5}{x+1}+\frac{(x+1)}{\left(x^{2}+x+1\right)}+\frac{(3 x+2)}{\left(x^{2}+x+1\right)^{2}} \)


Determine whether or not each of the
definition of \( * \) given below gives a
binary operation. In the event that \( * \) is not a binary operation, given justification for this
(i) \( \operatorname{On} Z^{+}, \) define \( * \) by \( a * b=a-b \)
(ii) \( \operatorname{On} Z^{+}, \) define \( * \) by \( a * b=a b \)
(iii) On \( R, \) define \( * \) by \( a * b=a b^{2} \)
(iv) On \( Z^{+}, \) define \( * \) by \( a * b=|a-b| \)
On \( Z^{+}, \) define \( * \) by \( a * b=a \)


Sex chromosomes of birds are
B. zz-ww
c. \( x x-x y \)
D. xo-xxx


Find the radius of a circle whose
circumference is \( 39.6 \mathrm{cm} \)


When \( 100 g \) of saturated solution is
evaporated at \( 50^{\circ} \mathrm{C}, 50 \mathrm{g} \) of solid is left over. Find the solubility of the
substance at \( 50^{\circ} \mathrm{C} \)
A . 100
B. 50
c. 75
D. 25


A thinwalled, spherical conducting shel S of radius \( R \) is given charge \( Q \). The same amountof charge is also placed at its centre C. Which of the following
statements are correct?
This question has multiple correct options
A \( \cdot \) on the outer surface of \( \mathrm{S} \), the charge density is \( \frac{Q}{2 \pi R^{2}} \)
B. The electric field is zero at all points inside
c. At a point just outside \( S \), the electric field is double the field at a point just inside
D. At any point inside S, the electric field is inversely proportional to the square of its distance from


Find the equation of the hyperbola satisfying the give conditions: Vertices
(0,±5) foci (0,±8)


The kinetic energy of an electron in the second Bohr orbit of a hydrogen atom is:
\( \left(a_{0} \) is Bohr radius) \right.
A \( \cdot \frac{h^{2}}{4 \pi^{2} m a_{0}^{2}} \)
B. \( \frac{h^{2}}{16 \pi^{2} m a_{0}^{2}} \)
c. \( \frac{h^{2}}{32 \pi^{2} m a_{0}^{2}} \)
D. \( \frac{h^{2}}{64 \pi^{2} m a_{0}^{2}} \)


The surface of some material is
radiated in turn by waves of \( \lambda=3.5 \times \) \( 10^{-7} \) and \( \lambda=5.4 \times 10^{-7} m \) respectively
The ratio of the stopping potential in the two cases in \( 2: 1 . \) The work function of
the metal is:
A . \( 1.05 e V \)
B. \( 1.5 e V \)
c. \( 2.05 e V \)
D. \( 2.5 e V \)


Which one of the following is not related to guttation?
A. Water is given out in the form of droplets
B. Water given out is impure
c. water is given out early morning
D. Guttation is of universal occurrence


A block is pushed with some velocity up a rough inclined plane. It stops after
ascending few meters and then
reverses its direction and returns back
to point from where it started. If angle of
inclination is \( 37^{\circ} \) and the time to climb
up is half of the time to return back
then coefficient of friction is:
\( \mathbf{A} \cdot \frac{9}{20} \)
B. \( \frac{7}{5} \)
c. \( \frac{7}{12} \)
D. \( \frac{5}{7} \)


Which of the following properties of light conclusively support wave theory of light?
A. Light obeys laws of reflection
B. Speed of light in water is smaller than the speed in vacuum
c. Light doesn't show interferrence
D. Light shows photoelectric effect


Maximum value of \( \prod\left(1+\frac{b-c}{a}\right)^{a} \) is \( \lambda \) where \( a, b, c \) are integral sides of a
triangle, \( \lambda+2 \) is/are divisible by
This question has multiple correct options
A . 2
B. 3
c. 1
D. 5


Two infinite long wires, each carrying
current \( I, \) are lying along \( x \) -axis and \( y \)
axis, respectively. \( A \) charged particle,
having a charge \( q \) and mass \( m \), is
projected with a velocity \( u \) along the
straight line \( O P . \) The path of the
particle is (neglect gravity) a:
A. straight line
B. circle
c. helix
D. cycloid


Find the concentration of \( \boldsymbol{H}^{+}, \boldsymbol{H} \boldsymbol{C O}_{3}^{-} \)
and \( C O_{3}^{2-} \) in a \( 0.01 M \) solution of
carbonic acid if the pH of the solution is \( \mathbf{4 . 1 8}, \mathbf{K}_{\mathbf{1}}=\mathbf{4 . 4 5} \times \mathbf{1 0}^{-\mathbf{7}}, \mathbf{K}_{\mathbf{2}}=\mathbf{4 . 6 9} \times \)
\( 10^{-11} \)


Fill in the blank space by choosing the correct word.

Water stored in the reservoirs of hydroelectric dams has .................... energy.
A. tidal
B. fossill
c. potential
D. biomass


The wave-like character was
experimentally proved for light by
A. Newton
B. Young
c. мaxwell
D. Huygens


Which of the following statements are
correct?
This question has multiple correct options
A \( \cdot \) The angular momentum of \( 3 p \) -orbital is \( \frac{h}{\sqrt{2} \pi} \)
B. The sixth electron of carbon atom has the quantum numbers \( n=2, \ell=1, m=0, s=+\frac{1}{2} \) or \( -\frac{1}{2} \)
C. Magnetic moment of \( V^{4+} \) ions is 1.73 BM \( (\mathrm{V}=23) \)
D. For azimuthal quantum number \( \ell=3 \), the maximum
number of electrons is 6


Draw and label the diagram showing various regions of Electro-magnetic spectrum and their wavelength ranges.


Area bounded by \( \mathbf{y}=\{\mathbf{x}\},\{.\} \) is
fractional part of function and \( \mathbf{x}=\pm \mathbf{1} \)
is in sq. units
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot 3 \)
D. 4


Which name is invalid?
A. Name not published in Species Plantarum.
B. Name proposed prior to 1961
C. Name which is not in Latin.
D. Name for which holotype is not designated.


Find the angle between \( 3 \vec{i}+4 \vec{j}, 2 \vec{j}-5 \vec{k} \)
\( ^{\mathrm{A}} \cdot \cos ^{-1} \frac{8}{5 \sqrt{29}} \)
B. \( \sin ^{-1} \frac{8}{5 \sqrt{29}} \)
c. \( \cos ^{-1} \frac{-1}{5 \sqrt{29}} \)
D. \( \sin ^{-1} \frac{-1}{5 \sqrt{29}} \)


The electric potential decreases uniformly from \( 120 \mathrm{V} \) to \( 80 \mathrm{V} \) as one
moves on the X-axis from \( x=-1 c m \) to
\( \boldsymbol{x}=+1 \mathrm{cm} . \) The electric field at the
origin.
A. must be equal to \( 20 V / c m \)
B. must be equal to \( 2.0 \mathrm{V} / \mathrm{cm} \)
c. must be greater than \( 20 V / \mathrm{cm} \)
D. must be less than \( 20 \mathrm{V} / \mathrm{cm} \)


Identify the incorrect statement about a
planet revolving around Sun
A. The gravitational attraction provides the centripetal force for a revolving planet
B. The total energy of a planet is always negative
c. The total energy of a planet is always more than potential energy of the system
D. Kinetic energy of revolving planet is sometimes zero


Which one of the following pentafluorides cannot be formed?
A. \( P F_{5} \)
B. \( A s F_{5} \)
\( \mathrm{c} . S b F_{5} \)
D. \( B i F_{5} \)


Voltaic cell is same as:
A. galvanic cell
B. electrolytic cell
C. fuel cell
D. lead cell


At what distance from a convex lens of
focal length \( 0.15 m \) must an object be
placed so that the image must be twice the size of the object, when the image is
a) real
b) virtual


In mammals connection between fetus
and uterine wall form
A. Placenta
B. Inguinal canal
c. Ureter
D. Eustachian cana


Establish the relation between torque
and angular acceleration Hence define moment of inertia.


A charged particle is moving through uniform magnetic field, then magnetic
field :
A. Always exerts a force on the particle
B. Never exerts a force on the particle
c. Exerts a force, if the particle is moving along the field.
D. Exerts a force, if the particle is moving perpendicular to the direction of the field