When \( 20 m l \) of ethanol is mixed with
10 \( m l \) of water, the total volume of the
solution will be:
A. \( 30 m l \)
в. \( >30 m l \)
\( c \cdot<30 m l \)
D. not definite


A body of mass \( 1 k g \) tied to one end of string is revolved in a horizontal circle of
radius \( 0.1 m \) with a speed of
3evolution/ sec, assuming the effect of gravity is negligible, then linear velocity, acceleration and tension in the string be :
A \( \cdot 1.88 m / s, 35.5 m / s^{2}, 35.5 N \)
B . 2.88m/s,45.5m/s \( ^{2} \), 45.5 \( N \)
c. \( 3.88 m / s, 55.5 m / s^{2}, 55.5 N \)
D. None


A ball is thrown vertically downwards with velocity \( \sqrt{2 g h} \) from a height \( h \) After colliding with the ground it just reaches the starting point. Coefficient of restitution is :
A. \( 1 / \sqrt{2} \)
B. \( 1 / 2 \)
c. 1
D. \( \sqrt{2} \)


Find the value of \( \lambda \) for which the four
points \( A, B, C, D \) with position vectors \( -\widehat{\boldsymbol{j}}-\widehat{\boldsymbol{k}} ; \boldsymbol{4} \hat{\boldsymbol{i}}+\boldsymbol{5} \hat{\boldsymbol{j}}+\boldsymbol{\lambda} \hat{\boldsymbol{k}} ; \boldsymbol{3} \hat{\boldsymbol{i}}+\boldsymbol{9} \hat{\boldsymbol{j}}+\boldsymbol{4} \widehat{\boldsymbol{k}} \) and
\( -4 \hat{i}+4 \widehat{j}+4 \widehat{k} \) are coplanar.


The ionising power of \( \alpha \) -particles is
roughly times that of \( \boldsymbol{\beta} \)
particle. Fill in the blank.
A \( \cdot 10^{4} \)
B . 10
c. 10
D. 1/16


Fluorobenzene \( \left(C_{6} H_{5} F\right) \) can be
synthesized in the laboratory:
A. By heating phenol with \( H F \) and \( K F \)
B. From aniline by diazotization, followed by heating the diazonium salt with \( H B F_{4} \)
c. By direct fluorination of benzene with \( F_{2} \) gas
D. By reacting bromobenzene with \( N a F \) solution


Consider the following \( v_{x}=t \) graph to
be parabolic. Plot the acceleration-time
graph and analyze the motion of the particle from A to E.


If \( \boldsymbol{x}=\boldsymbol{a} \cos ^{3} \boldsymbol{\theta} \) and \( \boldsymbol{y}=\boldsymbol{a} \sin ^{3} \boldsymbol{\theta}, \) then find
the value of \( \frac{d^{2} y}{d x^{2}} \) at \( \theta=\frac{n}{6} \)


If in a plano-convex lens, the radius of curvature of the convex surface is \( 10 \mathrm{cm} \)
and the focal length of the lens is \( 30 \mathrm{cm} \) then the refractive index of the material
fo lens will be
A . 1.5
B. 1.66
c. 1.33
D. 3


If \( x \) is acute and \( \sin \left(x+10^{0}\right)= \)
\( \cos \left(3 x-68^{\circ}\right), \) find \( x \) in degrees


Identify following \( A, B \& C \) structures in
given diagram:-
A. \( A \) - Right lobe, \( B \) - Left lobe \( C \) - Diaphragm
B. A - Left lobe, B - Right lobe C - Diaphragm
C. A - Diaphragm, B - Left lobe C - Right lobe
D. A - Diaphragm, B - Right lobe C - Left lobe


An atom emits a spectral line of wavelength \( \lambda \) when an electron makes a
transition between levels of energy \( \boldsymbol{E}_{1} \)
and \( E_{2} . \) Which expression correctly
relates \( \lambda, E_{1} \) and \( E_{2} ? \)
A \( \cdot \lambda=\frac{h c}{E_{1}+E_{2}} \)
B. \( \lambda=\frac{2 h c}{E_{1}+E_{2}} \)
c. \( \lambda=\frac{2 h c}{E_{1}-E_{2}} \)
D. \( \lambda=\frac{h c}{E_{1}-E_{2}} \)


Which of the following are example(s) of non-contact force?
A. Muscular force
B. Gravitation force
c. Magnetic force
D. Both (B) and (C)


In the figure, \( C D \) and \( R S \) are
respectively the medians of \( \triangle A B C \) and
\( \triangle P Q R \) If \( \triangle A B C \sim \triangle P Q R, \) prove that
(i) \( \triangle A D C \sim \triangle P S R \)
(ii) \( \frac{C D}{R S}=\frac{A B}{P Q} \)


If \( \tan (A+B)=p, \tan (A-B)=q \)
then prove that \( \tan 2 A=\frac{p+q}{1-p q} \)


Which of the following groups contains only easily biodegradable items? This question has multiple correct options
A. Grass, flower and leather
B. Grass, wood and plastic
c. Fruits, peel cake and lime juice
D. Cake, wood and grass


The hybridization and shape of \( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{\mathbf{5}}^{-} \)
is :
A. \( s p^{3} \), tetrahedron
B . \( s p^{3} \), trigonal pyramidal
\( \mathbf{c} \cdot s p^{3} d^{2} \), trigonal bipyramidal
D. \( s p^{3} d^{3} \), pentagonal planar


Calculate the cell potential (in V) if \( \triangle G=-96.5 k J / m o l \) and \( n=1 \)


The most electro positive metal among the following is:
A. \( Z n \)
в. \( F e \)
\( c . C a \)
D. Na


\( \int_{\mathbf{A}}^{\boldsymbol{A}} \cdot \frac{\mathbf{1}}{\boldsymbol{x}^{2}} \sqrt{\frac{\boldsymbol{x}-\mathbf{1}}{\boldsymbol{x}+\mathbf{1}}} \boldsymbol{d} \boldsymbol{x}= \)
B. \( \cos ^{-1} \frac{1}{|x|}-\frac{\sqrt{x^{2}-1}}{x}+c \)
C \( \cdot \sin ^{-2} \frac{1}{|x|}-\frac{\sqrt{x^{2}-1}}{x}+c \)
D. \( \sin ^{-1} \frac{1}{|x|}+\frac{\sqrt{x^{2}-1}}{x}+c \)


The volume of liquid flowing per second
out of an orifice at the bottom of the
tank does not depend upon:
A. the density of the liquid
B. acceleration due to gravity
c. the height of the liquid above orifice
D. the area of the orifice


When magnesium burns in steam, the formulae of the products are:
A \( \cdot M g(O H)_{2}, H_{2} \)
\( \mathbf{B} \cdot \mathrm{MgO}, H_{2} \)
с. \( M g O_{2}, H_{2} \)
D. \( M g(O H)_{2}, O_{2} \)


The presence of thymine at the place of uracil also confers additional stability
to DNA. How?


To an acidified dichromate solution, a
pinch of \( N a_{2} O_{2} \) and ether is added and
shaken.What is observed?
A. Deep violet colour
B. Red colour changing to green
C. AgF is insoluble, others are soluble
D. All are insoluble


A. Natural rubber is an elastomer.
R. The inter-molecular forces of
attraction between the polymer chains
are weak vander Waals forces.
A. Both A and R are correct and R is the correct explanation of the \( A \)
B. Both A and R are correct but R is not the correct explanation of the \( A \)
\( \mathrm{c} \). A is correct but \( \mathrm{R} \) is in correct
D. A is incorrect but R is correct


The equilibrium constant in a reversible
reaction at a given temperature which:
A. Depends on initial concentration, of the reactants
B. Depends on the concentration of the products at equilibrium
C. Does not depend on the initial concentration
D. His not characteristic of the reaction


Energy is being emitted from the
surface of black body at \( 127^{\circ} \mathrm{C} \) at the
rate of \( 1.0 \times 10^{6} J / s m^{2} . \) The
temperature of black body at which the rate of energy is \( 16.0 \times 10^{6} J / s m^{2} \) will
be:
\( \mathbf{A} \cdot 754^{\circ} C \)
B. \( 527^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 254^{\circ} C \)
D. \( 508^{\circ} \mathrm{C} \)


Here an extraction process is given in steps. Identify the suitable ores
corresponding to the process. Pulverisation \( \rightarrow \) Calcination \( \rightarrow \)
Smelting \( \rightarrow \) Vacuum \( \rightarrow \) Distillation This question has multiple correct options
A. zinc blend
B. Calamine
c. Magnesite
D. zincite


When domestic sewage mixes with
river water,
A. Small animals like rats will die after drinking river water
B. The increased microbial activity released micronutrients such as iron
C. The increased microbial activity uses up dissolved oxygen
D. The river water is still suitable for drinking as impurities are only about \( 0.1 \% \)


Two positive charges \( q_{1} \) and \( q_{2} \) are
moving with velocities \( v_{1} \) and \( v_{2} \) when
they are at points \( A \) and \( B \), respectively,
as shown in figure. The magnetic force
experienced by charge \( q_{1} \) due to the
other charge \( \boldsymbol{q}_{2} \) is :
\( A \)
B. \( \frac{\mu_{0} q_{1} q_{2} v_{1} v_{2}}{4 \sqrt{2} \pi a^{2}} \)
\( \overbrace{\frac{\mu_{0} \pi_{1} q_{2}}{2 \sqrt{2}} v_{1} v_{2}^{2}} \)
D. \( \frac{\mu_{0} q_{1} q_{2} v_{1} v_{2}}{\sqrt{2} \pi a^{2}} \)


Stool of a person contain whitish grey colour is due to malfunction of
organ
A. Pancrease
B. Spleen
c. Kidney
D. Liver


If \( \boldsymbol{x}, \boldsymbol{y} \in(\mathbf{0}, \boldsymbol{3} \boldsymbol{0}) \) such that \( \left[\frac{\boldsymbol{x}}{\mathbf{3}}\right]+\left[\frac{\boldsymbol{3} \boldsymbol{x}}{\mathbf{2}}\right]+ \)
\( \left[\frac{\boldsymbol{y}}{\mathbf{2}}\right]+\left[\frac{\mathbf{3} \boldsymbol{y}}{\boldsymbol{4}}\right]=\frac{\mathbf{1 1} \boldsymbol{x}}{\mathbf{6}}+\frac{\mathbf{5} \boldsymbol{y}}{\boldsymbol{4}}(\text { where }[\mathbf{x}] \)
denote greatest integer \( \leq x \) ) then the
number of ordered pairs \( (x, y) \) is
A . 10
B. 20
\( c \cdot 24 \)
D. 28


Arrange the points: \( \mathbf{A}(1,2- \) \( \mathbf{3}), \mathbf{B}(-\mathbf{1}, \mathbf{2},-\mathbf{3}), \mathbf{C}(-\mathbf{1},-\mathbf{2}-\mathbf{3}) \) and
\( \mathbf{D}(\mathbf{1},-\mathbf{2},-\mathbf{3}) \) in the increasing order of
their octant numbers:
A. \( A, B, C, D \)
в. \( B, C, D, A \)
c. \( C, D, A, B \)
D. \( D, C, B, A \)


Soap action is due to:
A. micelle formation
B. colloidal dispersion of micelles in water
C . oil drop dispersal
D. All of these


For what distance is ray optics a good approximation when the aperture is \( 4 m m \) and the wavelength of light is
\( 400 n m ? \)
A \( .24 m \)
в. \( 40 m \)
\( c .18 m \)
D. 30m


Which is correctly paired?
A. Aspergillus niger-Production of lactic acid
B. Trichoderma polysporum - Lowers blood cholesterol
C. Saccharomyces cerevisiae-Production of citric acid
D. Methanogenic bacteria - Gobar gas formation


Twinkling of stars is on account of
A. Large distance of stars and storms in air
B. Small size of stars
C. Large size of stars
D. Large distance of stars and fluctuations in the density of air


The change that occurs in apex at the time of flowering is
A. Meristem gets destroyed
B. Vegetative apex changes into reproduction apex
c. Meristem decreases its activity
D. All of the above


Assertion
Capillary water is not readily available
to the plants as it lies below the level of
roots.
Reason
Gravitational water constitutes the only
water available to the plants.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A vehicle registration number consists
of 2 letters of English alphabet followed by 4 digits, where the first digit is not zero. Then, the total number of vehicles
with distinct registration numbers is
A \( \cdot 26^{2} \times 10^{4} \)
В. 26 \( P_{2} \times \) 10 \( P_{4} \)
c. \( 26 P_{2} \times 9 \times 10 P_{3} \)
D . \( 26^{2} \times 9 \times 10^{3} \)


Given standard electrode potentials:
\( F e^{3+}+3 e^{-} \rightarrow F e ; E^{0}=-0.036 V \)
\( F e^{2+}+2 e^{-} \rightarrow F e ; E^{0}=-0.440 V \)
The standard electrode potential \( E^{o} \) for
\( F e^{3+}+e \rightarrow F e^{2+} \) is:
A. \( 0.476 v \)
B. 0.404 v
c. \( 0.40 v \)
D. +0.772 V


How many gm of solid \( K O H \) must be
added to \( 100 m L \) of a buffer solution,
which is \( 0.1 ~ M \) each with respect to
acid \( H A \) and salt \( K A \) to make the \( p H \)
of the solution \( 6.0 ? \)
\( \left[\text { Given: } \boldsymbol{p} \boldsymbol{K}_{\boldsymbol{a}}(\boldsymbol{H} \boldsymbol{A})=\mathbf{5}\right] \)
A .0 .458
B. 0.327
c. 5.19
D. None of the above


A particle executes S.H.M. of period
\( 6.28 s \) and amplitude \( 3 \mathrm{cm} . \) Its maximum acceleration is
A \( .2 .14 \mathrm{cm} / \mathrm{s}^{2} \)
в. 3 ст / \( s^{2} \)
c. \( 9.42 \mathrm{cm} / \mathrm{s}^{2} \)
D. \( 1.5 \mathrm{cm} / \mathrm{s}^{2} \)


Choose the correct answers from the
alternatives given

Root pressure can be measured by
A. Osmometer
B. Potometer
c. Manometer
D. Porometer


Which enzyme converts glucose to ethanol?
A . Diesterase
B. Invertase
c. zymase
D. Both (2) and (3)


If the angle of incidence is \( 70^{\circ}, \) then
calculate the angle between the incidence ray and the reflected ray.
A \( .50^{\circ} \)
B . \( 140^{\circ} \)
\( \mathrm{c} \cdot 130^{\circ} \)
D. \( 80^{\circ} \)


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


The cost of fencing a rectangular field at \( R s 18 \) per metre is \( R s 1980 . \) If the
width of the field is \( 23 m \) find its length.


If the error committed in measuring the radius of the circle is \( 0.05 \% \), then the
corresponding error in calculating the area is:
\( \mathbf{A} \cdot 0.05 \% \)
B. \( 0.025 \% \)
c. \( 0.25 \% \)
D. \( 0.1 \% \)


A uniformly charged ring of radius R carrying q is rotating with angular speed \( \omega . \) The magnetic field at the centre of ring is:
A \( \cdot \frac{\mu_{o} q \omega}{2 \pi R} \)
в. \( \frac{\mu_{0} q \omega}{4 \pi R} \)
c. \( \frac{\mu_{q} q \omega}{8 \pi R} \)
D. zero


If \( x_{0}=10 \mathrm{cm} \) and the object is given
velocity \( 18 \mathrm{m} / \mathrm{s} \) towards left, then the
speed of the image at that instant is
A. \( 2 \mathrm{m} / \mathrm{s} \)
B. \( 6 \mathrm{m} / \mathrm{s} \)
\( c .9 \mathrm{m} / \mathrm{s} \)
D. 162 \( \mathrm{m} / \mathrm{s} \)


If the time and displacement of particle along the positive X-axis are related as \( \boldsymbol{t}=\left(\boldsymbol{x}^{2}-\mathbf{1}\right)^{\frac{1}{2}}, \) then find the
acceleration in terms of \( x \)
A \( \cdot \frac{1}{x^{4}} \)
в. \( \frac{1}{x^{7}} \)
c. \( \frac{1}{x} \)
D. \( \frac{1}{x^{3}} \)


When the face of a coil towards an
observer seems to carry current in direction, north polarity is induced on
that face.
A. electromagnet
B. right angles
c. permanent
D. anticlockwise


Which of the statements about the
reaction below are incorrect?
\( 2 P b O(s)+C(s) \rightarrow 2 P b(g)+C O_{2}(g) \)
(I) Lead is getting reduced.
(II) Carbon dioxide is getting oxidized.
(III) Carbon is getting oxidized.
(IV) Lead oxide is getting reduced.
A . I and II
B. I and III
c. ।, ॥ and III
D. All are incorrect


Write each of the following as decimals
\( \mathbf{2 0 0}+\mathbf{6 0}+\mathbf{5}+\mathbf{1} / \mathbf{1 0} \)


A person standing on the floor of an elevator drops a coin. The coin reaches the floor of the elevator-
a) in a time \( t_{1} \) if the elevator is
stationary and
b) in time \( t_{2} \) if it is moving uniformly,
then
A \( \cdot t_{1}=t_{2} \)
в. \( t_{1}>t_{2} \)
c \( \cdot t_{1}<t_{2} \)
D. \( t_{1}<t_{2} \) or \( t_{1}>t_{2} \) depending on whether the lift is going
up or down


Match list I with list II and select the
correct answer using the codes given below the lists:
\( \begin{array}{ll}\text { List I } & \text { List II } \\ \text { A. }\left(\frac{\delta G}{\delta P}\right)_{T} & \text { 1. } \mu_{H} \\ \text { B. }\left(\frac{\delta G}{\delta T}\right)_{P} & \text { 2. } T \\ \text { C. }\left(\frac{\delta H}{\delta S}\right)_{P} & \text { 3. }-S \\ \text { D. }\left(\frac{\delta T}{\delta P}\right)_{H} & \text { 4. } P \\ & \text { 5. } V\end{array} \)
A. \( A-5, B-1, C-2, D-4 \)
B . \( A-5, B-3, C-2, D-4 \)
\( \mathbf{c} \cdot A-3, B-5, C-2, D-1 \)
D . \( A-5, B-3, C-2, D-1 \)


Monika answered \( \frac{3}{4} \) of the questions on her quiz correctly. What percent of the questions did she answer correctly?
A . \( 25 \% \) \%
B. 34\%
c. \( 50 \% \)
D. 75\%


The velocity of a particle moving with
constant acceleration at an instant \( t_{0} \) is
\( 10 m / s . \) After 5 seconds of that instant
the velocity of the particle is \( 20 m / s \)
The velocity at 3 second before \( t_{0} \) is:
A. \( 8 \mathrm{m} / \mathrm{s} \)
B. \( 6 m / s \)
c. \( 4 m / s \)
D. \( 7 \mathrm{m} / \mathrm{s} \)


Which of the following cannot be polarised?
A. Radio waves
B. \( \beta \) rays
c. Infrared rays
D. \( \gamma \) rays


Two dice are thrown. The probability that the sum of the numbers coming up
on them is 9 , if it is known that the
number 5 always occurs on the first die, is
A \( \cdot \frac{1}{6} \)
B. \( \frac{1}{3} \)
\( c \cdot \frac{1}{2} \)
D. \( \frac{5}{6} \)


Define diameter.


The chromosome replication occurs
during
A. s phase
B. G_phase
c. Metaphase
D. Anaphase


Write the formula for area of a triangle
where \( A\left(x_{1}, y_{1}\right), B\left(x_{x}, y_{2}\right) \) and
\( C\left(x_{3}, y_{3}\right) \) are the vertices of a triangle
\( A B C \)


What is the number of isomers possible for decane?
A. 5
B. 25
\( c .50 \)
D. 75


The spores of Bacillus thuringiensis
are used as bioinsecticide. Comment.


If \( \sin \theta=0.47, \) then \( \sin (\pi-\theta)= \)
A . -0.47
B . -0.43
c.
D. 0.43
E . 0.47


For \( a, b, c \in Q \) and \( b+c \neq a, \) the roots of
\( \boldsymbol{a} \boldsymbol{x}^{2}-(\boldsymbol{a}+\boldsymbol{b}+\boldsymbol{c}) \boldsymbol{x}+(\boldsymbol{b}+\boldsymbol{c})=\mathbf{0} \) are
A. Rational and unequal
B. rational and equal
c. complex numbers
D. none


A \( 1 \mathrm{kg} \) block is attached by light string
to another block of mass 2 kg. The
string is passed over a pulley of
negligible mass and friction. Calculate the acceleration of the masses?
\( A \cdot 5 m / s^{2} \)
B. \( 6.7 m / s^{2} \)
\( \mathbf{c} \cdot 10 m / s^{2} \)
D. \( 20 m / s^{2} \)
E. \( 30 m / s^{2} \)


Choose the correct set.
\begin{tabular}{ll|l|l}
& Column I & & Column \\
\hline I. & Gross primary productivity & A. & Total ass \\
II. & Secondary productivity & B. & Remains and does not situ \\
III. & Transducers & C. & Green ple \\
IV. & Foodweb & D. & Interlock \\
\hline
\end{tabular}
\( \mathbf{A} \)
।- \( A,\|-B,\|-C, I V-D \)
B. I-B, II-C. III-D, IV-A
C. \( \mid-\mathrm{C}, \) ।I- \( \mathrm{D}, \) III- \( \mathrm{A}, \mathrm{IV}-\mathrm{B} \)
D. \( |-A,||-C,|||-B, \mid V-D \)


If \( \vec{a} \) and \( \vec{b} \) are unit vectors such that \( \vec{a}+3 \vec{b} \) is perpendicular to \( 7 \vec{a}-5 \vec{b} \) and \( \vec{a}-4 \vec{b} \) is perpendicular to \( 7 \vec{a}-2 \vec{b} \) then
the angle between \( \vec{a} \) and \( \vec{b} \) is
A \( \cdot \frac{\pi}{6} \)
B.
\( c \cdot \frac{\pi}{2} \)
D. \( \frac{\pi}{3} \)


Name the following. Flight - or - fight hormones.


The positive value of parameter' \( a \) ' for
which the area bounded by parabolas \( y=x-a x^{2} \& a y=x^{2} \) attains its the
maximum value is


Two blocks each of mass M are resting
on a frictionless inclined plane as
shown in figure. Then
A. The block A moves down the plane.
B. The block B moves down the plane.
c. Both the blocks remain at rest.
D. Both the blocks move down the plane


The secondary precursors of photochemical smog are:
A. \( S O_{2} \) and \( N O_{2} \)
B. \( N O_{2} \) and hydrocarbons
\( \mathrm{c} \cdot O_{3} \) and hydrocarbons
D. \( C O_{2} \) and \( O_{2} \)


If the four letter words (need not to
meaningful) are to be formed using the letter from the word "MEDITERRANEAN"
such that the first letter is \( R \) and the fourth letter is \( \mathrm{E} \), then the total number
of all such words is:
A . 110
B . 59
c. \( \frac{11 !}{(2 !)^{3}} \)
D. 56


How many 3 -digit even numbers are
formed using the digits \( 0,1,2, \ldots ., 9, \) if the repetition of digits is not allowed?


2 moles of \( P C l_{5} \) were heated in a closed
vessel of 2 liter capacity. At
equilibrium, \( 40 \% \) of \( P C l_{5} \) dissociated
into \( P C l_{3} \) and \( C l_{2} \)

The value of equilibrium constant is:
\( \mathbf{A} \cdot 0.267 \)
в. 0.53
\( c .2 .63 \)
D. 5.3


If / the last term, d the common difference and 's' the sum of n terms
\( (n \neq 1) \) and 'a' the first term of an A.P.
be connected by the eqution \( 8 d s= \)
\( (d+2 l)^{2}, \) then \( d= \)
A . \( 2 a \)
в.
c. за
D. \( 4 a \)


If the area bounded by the curve \( |\boldsymbol{y}|= \)
\( \sin ^{-1}|x| \) and \( x=1 \) is \( a(\pi+b), \) then
the value \( a-b \) is:
A \( . \)
B. 2
\( c \cdot 3 \)
D. 4


The disk has a weight of \( 100 \mathrm{N} \) and rolls without slipping on the horizontal surface as it oscillates about its
equilibrium position. If the disk is displaced, by rolling it counterclockwise 0.4 rad, determine the
equation which describes its oscillatory motion when it is released.
A \( \cdot \theta=-0.2 \cos (16.16 t) \)
B \( \cdot \theta=0.2 \cos (16.16 t) \)
c. \( \theta=-0.4 \cos (16.16 t) \)


When the band gap for a semiconductor
is low
A. conductivity of that material is low
B. conductivity of that material is highh
c. the resistance of that material is highh
D. none of the above


determine the total work done on the
block
A . 12.45
B . 24.9
c. 49.8
D. 99.6


Match the List I with the List II.


An object thrown upwards with a
velocity \( u \) from the top of a tower of
height \( \boldsymbol{H} \) reaches the ground in \( \boldsymbol{t}_{\mathbf{1}} \) seconds. When thrown downwards with
the same speed it reaches the ground in
\( t_{2} \) seconds. When dropped from the top
of tower it reaches in \( t_{3} \) seconds. Then \( t_{3} \)
is equal to (in terms of \( t_{1} \) and \( t_{2} \) )
\( \mathbf{A} \cdot t_{1}+t_{2} \)
B. \( \sqrt{t_{1} t_{2}} \)
c. \( t_{1}-t_{2} \)
D. \( t_{1} / t_{2} \)


Which of the following statement is/are
correct?
This question has multiple correct options
A. Phosphoric acid is transparent solid.
B. Phosphoric acid melts as \( 44^{\circ} \mathrm{C} \).
C. Phosphoric acid absorbs water.
D. Phosphoric acid forms coloured syrupy mass.


In the above reaction, \( Z \) is:
A. toulene
B. biphenyl
c. 4 -chlorotoulene
D. ethyl benzene


Which of the following is the characteristic of Nostoc?
A. Non-cellulosic cell wall
B. Uniflagellate zoospore
c. chlorophyll e
D. Sexual reproduction


\( 1.5 \mathrm{g} \) of a hydrocarbon on combustion gave \( 4.4 g \) of \( C O_{2} \) and \( 2.7 g \) of \( H_{2} O . \) The vapour density of the compound is 15 Calculate the molecular formula.
A \( \cdot C_{2} H_{6} \)
в. \( C H_{4} \)
\( c \cdot O_{2} \)
D. \( N_{2} \)


Name the type of isomerism exhibited by the following isomers:
\( \left[\boldsymbol{C r}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{6}\right]\left[\boldsymbol{C o}\left(\boldsymbol{C N}_{6}\right)\right] \) and
\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{6}\right]\left[\boldsymbol{C r}(\boldsymbol{C N})_{6}\right] \)


A current-carrying conductor when placed in a magnetic field always experiences a force. Is the given statement true or false?


Expand \( \left(\boldsymbol{x}+\frac{\mathbf{1}}{\boldsymbol{x}}\right)^{\boldsymbol{6}} \)


Very short answer type. Normally a vein opens into a larger vein
or into the heart but does not end
in capillaries. Which vein/ veins in humans is/are exception to this rule?


Multiplication of 3 with the matrix \( \left[\begin{array}{lll}\mathbf{4} & \mathbf{1} & \mathbf{1}\end{array}\right] \) gives
\( \mathbf{A} \cdot\left[\begin{array}{lll}12 & 3 & 3\end{array}\right] \)
B \cdot \( \left[\begin{array}{lll}12 & 1 & 1\end{array}\right] \)
\( \mathbf{c} \cdot\left[\begin{array}{lll}4 & 3 & 1\end{array}\right] \)
D. \( \left[\begin{array}{lll}4 & 1 & 3\end{array}\right] \)


How did Darwin explain the existence of
different varieties of finches on the
Galapagos Islands?


Write the name of reactant used for the
preparation ethyl t-butyl ether


Part of pistil which receives pollen is
A. Ovary
B. Style
c. stigma
D. Ovule


In a burette, the zero mark on the
graduation scale is near its mouth.
A. True
B. False


Recently discovered element with atomic number 115 is:
A. Uun
в. \( U u b \)
c. \( U u p \)
D. Uus


According to the I. U.P. A. C. nomenclature, sodium nitroprusside is named as :
A. sodium nitro-ferrocyanide
B. sodium pentacyanidonitrosylferrate (II)
c. sodium nitroferricyarride
D. sodium pentacyanonitrosylferrate (III)


A sprinter runs 6 meters in the first second of a certain race and increase
her speed by \( 25 \mathrm{cm} / \mathrm{sec} \). in each succeeding second. (This means that she goes \( 6 \mathrm{m} 25 \mathrm{cm} \). the second second, \( 6 \mathrm{m} 50 \mathrm{cm} . \) the third second, and so on.)
How far does she go during the eight second?
A. \( 8.75 \mathrm{m} \)
B. 7.75 m
\( c .8 .25 \mathrm{m} \)
D. 9.25 m


The number of electrons in an element
with atomic number \( X \) and mass
number Y will be:
A. \( x-y \)
B. Y-X
\( c \cdot x+y \)
D. x


The degree of dissociation of an electrolyte depends on:
A. nature of the electrolyte
B. nature of solvent
c. temperature
D. all the above


You are able to see in shaded areas,
such as under a tree, because light has undergone:
\( A \). refraction
B. incident bending
c. a change in speed
D. diffused reflection


In which of the following situations, the magnetic field can accelerate a charge particle at rest?
I. When the magnetic field is uniform with respect to time as well as position
11. When the magnetic field is time varying but uniform w.r.t position
III. When the magnetic field is time independent but position dependent.
A. I, II and II
B. III only
c. ॥ only
D. None of these


The general electronic configuration of f-block elements is:
A \( \cdot(n-2) f^{1-14}(n-1) d^{0-1} n s^{2} \)
B . \( (n-2) f^{1-14}(n-1) d^{0-10} n s^{1} \)
C. \( (n-2) f^{1-10}(n-1) d^{0-1} n s^{2} \)
D \( \cdot(n-2) f^{1-14}(n-1) d^{0-1} n s^{1} \)


A copper ring is moved towards the
north pole of a bar magnet. Then
A. the ring will not be affected
B. the ring all tend to get warm
c. an alternating current will flow in the ring
D. the ring will be positively charged


Write any two differences between step growth polymerisation and chain growth polymerisation.


A ray of light travelling in a transparent medium falls on a surface separating the medium from air at an angle of
incidence \( 45^{\circ} \) and undergoes total
internal reflection. If \( \mu \) is the refractive
index of medium the possible values of
\( \mu \) are
This question has multiple correct options
A \( . \mu=1.3 \)
в. \( \mu=1.4 \)
c. \( \mu=1.5 \)
D. \( \mu=1.6 \)


The band gaps of an insulator, conductor and semi conductor are
respectively \( \boldsymbol{E}_{\boldsymbol{g} 1}, \boldsymbol{E}_{\boldsymbol{g} \mathbf{2}} \) and \( \boldsymbol{E}_{\boldsymbol{g} \mathbf{3}} . \) The
relationship between them is given as
A \( . E_{g 1}>E_{g 2}<E_{g 3} \)
В. \( E_{g 1}>E_{g 2}>E_{g 3} \)
C \( . E_{g 1}<E_{g 2}>E_{g 3} \)
D. \( E_{g 1}<E_{g 2}<E_{g 3} \)


Explain the mechanism of cleansing action of soaps.


If \( \vec{V}_{1}=\hat{i}-2 \hat{j}+3 \hat{k} \) and \( \vec{V}_{2}=a \hat{i}+b \hat{j}+ \)
\( \boldsymbol{c} \hat{\boldsymbol{k}} \) where \( \boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c} \in\{-\mathbf{1}, \boldsymbol{0}, \boldsymbol{1}, \boldsymbol{2}, \boldsymbol{3}\} \) then
find the numbers of non-zero vectors \( \vec{V}_{2} \)
which are normal to \( \vec{V}_{1} \)


The van't hoff factor for a very dilute
solution of \( \boldsymbol{F e}_{2}\left(\boldsymbol{S O}_{4}\right)_{3} \) is:
\( \mathbf{A} \cdot \mathbf{9} \)
B. 5
\( c \cdot 24 \)
D. 16


The value of \( f(0) \) so that the function \( f(x)=\frac{\sqrt{1+x}-(1+x)^{1 / 3}}{x} \) becomes
continuous is equal to
\( A \cdot \frac{1}{6} \)
B.
c. 2
D.


Electrometallurgy is the field concerned with the processes of metal electrodeposition.
A. True
B. False


The points (2,3,4),(-1,-2,1),(1,2,5)
and (4,7,8) are the vertices of a
A. rhombus
B. square
c. a parallelogram
D. none of these


Choose the correct answers from the
alternatives given. Which of the following is the correct order of classification?
A. Domain - Kingdom - Phylum - Class - Order - FamilyGenus - Species
B. Kingdom - Domain - Class - Phylum - Order - Family Genus - Species
c. Kingdom - Domain - class - Phylum - Order - Genus Species - Family
D. Kingdom - class - Phylum - Domain - Genus - Order Family - species


A very long cylindrical wire of radius \( \mathrm{R} \)
carries a current \( \boldsymbol{I}_{\mathbf{0}} \) uniformly
distributed across the cross-section of
the wire, calculate the magnetic flux
through a rectangle that has one side of length w s running down the centre of the wire and another side of length \( R \),
shown in figure
A \( \cdot \frac{\mu_{0} I_{0} \times w R}{4 \pi} \)
B. \( \frac{\mu_{0} I_{0} w}{4 \pi} \)
с. \( \frac{\mu_{0} I_{0} R}{4 \pi w} \)
D. None of these


The A.M. of \( a+2, a, 2-a \) is
A . \( a \)
в. \( \frac{a+4}{3} \)
c. \( \frac{a-4}{3} \)
D.


Avogadro's number is?
\( \mathbf{A} \cdot 6.023 \times 10^{23} \)
B . \( 6.066 \times 10^{-19} \)
C \( \cdot 6.032 \times 10^{24} \)
D. \( 6.203 \times 10^{18} \)


For cadium plating, electrolyte used is:
A. cadmium sulphate and sulphuric acid
B. cadmium hexa metaphosphate
C. sodium cyanide, cadmium and caustic soda
D. all of the above


If the product of the matrices
\[
\left[\begin{array}{ll}
1 & 1 \\
0 & 1
\end{array}\right]\left[\begin{array}{ll}
1 & 2 \\
0 & 1
\end{array}\right]\left[\begin{array}{ll}
1 & 3 \\
0 & 1
\end{array}\right]
\]
\( \left[\begin{array}{cc}\mathbf{1} & \boldsymbol{n} \\ \mathbf{0} & \mathbf{1}\end{array}\right]=\left[\begin{array}{cc}\mathbf{1} & \mathbf{3 7 8} \\ \mathbf{0} & \mathbf{1}\end{array}\right], \) then \( \boldsymbol{n} \) is
equal to
\( A \cdot 27 \)
B . 26
\( c .37 \)
D. 37


Blood pressure is defined as the force with which blood
A. Comes out of the atrium
B. Is pushed to the legs
c. Pushes against wall of blood vessels
D. comes out of the ventricle


The mass of two pieces of brass is 60
kg. The first piece contains \( 10 \mathrm{kg} \) of pure copper and the second piece
contains 8 kg of pure copper. What is
the percentage of copper in the first piece of brass if the second piece
contains 15 per cent more copper than the first?


Find the scaler product of vectors \( 3 \hat{i}+ \) \( 4 \hat{j}-7 \hat{k} \) and \( 5 \hat{i}+3 \hat{j}+4 \hat{k} \)


(-1,-5,-7) lies in Octant
\( A \)
B. VII
\( c \cdot v \)
D. II


Two equal charges \( q \) are kept fixed at \( a \)
and \( +a \) along the \( x \) -axis. A particle of mass \( m \) and charge \( \frac{q}{2} \) is brought to the origin and given a small displacement along the \( x \) -axis, then:
A. the particle executes oscillatory motion
B. the particle remains stationary
c. the particle executes, SHM along x-axis
D. the particle executes SHM along y-axis


Compound (D) is:
\( \mathbf{A} \cdot C H_{3}-\underset{C H_{3}}{C H}-C_{D H_{3}}-C H_{2} O H \)
\( \mathbf{B} \)
\[
C H_{3}-\underset{_{C H_{3}}^{\mathrm{I}}}{C}-C H_{2} C H_{2} O H
\]
\( \mathbf{c} . C H_{3}-C H-C H_{2}-C H O H \)
\( _{C H_{3}} \)


A circular current carrying coil has a
radius r. Find the distance from the
centre of coil, on its axis, where the
magnetic induction will be \( 1 / 8 \) th of its
value at the centre of coil.


If \( A \) is an \( m \times n \) matrix and \( B \) is \( n \times p \)
matrix, then does \( A B \) exist? If yes, write
its order.


Sum \( 1.3,-3.1,-7.5, \dots \) to 10 terms


A block of mass \( 2.0 \mathrm{kg} \) is pushed down
an inclined plane of inclination \( 37^{\circ} \) with
a force of \( 20 N \) acting parallel to the incline. It is found that the block moves
on the incline with an acceleration of
\( 10 m / s^{2} . \) If the block started from rest, find the work done
(a) by the applied force in the first second
A . 100
B. 105
c. 150
D. 200


Which of the following is an explopive
omp
4
topp
\( B \)
Happy Father's Day
3
\( D \)


Assertion
The Sl unit of volume is \( m^{3} \)
Reason
Volume is a derived quantity of length.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is
not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


When NPN transistor is used as an
amplifier?
A. Electrons move from base to emitter
B. Electrons move from emitter to collector
c. Electrons moves from base to emitter
D. Holes moves from base to emitter


The value of \( \frac{\left(\cot ^{2} 5\right)\left(\cos ^{2} 5\right)}{\left(\cot ^{2} 5-\cos ^{2} 5\right)} \).is equal to


Sum of the numbers 0.5,12.56 and
\( \mathbf{0 . 0 0 3} \) is
A . 13.063
в. 31.063
c. 12.063
D. none of these


Write the formulae of the following coordination compounds. triamminetrinitrocobalt(III)


Match the species in Column I with their corresponding property(ies) in Column II.


On changing a capacitor with charge \( \mathrm{Q} \) stored energy is W. If charge is doubled then stored energy will be:-
A \( .2 W \)
в. \( 4 W \)
c. \( 8 W \)
D. \( \frac{1}{2} W \)


\( \int \frac{2 x+3}{\sqrt{4 x+3}} d x= \)
A \( \cdot \frac{1}{12}(4 x-3)^{\frac{3}{2}}+\frac{1}{4} \sqrt{4 x+3}+c \)
B \( \frac{1}{12}(4 x+3)^{\frac{3}{2}}+\frac{3}{4} \sqrt{4 x+3}+c \)
C \( \frac{1}{12}(4 x+3)^{\frac{3}{2}}-\frac{3}{4} \sqrt{4 x-3}+c \)
D \( \quad \frac{1}{12}(4 x+3)^{\frac{3}{2}}-\frac{1}{4} \sqrt{4 x-3}+c \)


Let \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) be defined as
\( \left\{\begin{array}{lll}2 x & \text { if } & x>3 \\ x^{2}, & \text { if } & 1<x \leq 3 \text { . Then, find } \\ 3 x, & \text { if } & x \leq 1\end{array}\right. \)
\( \boldsymbol{f}(-1)+\boldsymbol{f}(2)+\boldsymbol{f}(4) \)
\( A \cdot S \)
B . 14
\( c .5 \)
D. none of these


If \( (0, b, 0) \) is the centroid of the triangle
formed by the points (4,2,-3) \( (a,-5,1) \) and \( (2,-6,2) . \) If \( a, b \) are the
roots of the quadratic equation \( x^{2}+ \)
\( \boldsymbol{p} \boldsymbol{x}+\boldsymbol{q}=\mathbf{0}, \) then \( \boldsymbol{p}, \boldsymbol{q} \) are
A .9,18
в. -9,-18
c. 3,-18
D. -3,18


f current \( \boldsymbol{I}_{1}=\mathbf{3} \boldsymbol{A} \sin \omega \boldsymbol{t} \) and \( \boldsymbol{I}_{2}= \)
\( 4 A \cos \omega t, \) then \( I_{3} \) is
A \( \cdot 5 a \sin \left(\omega t+53^{\circ}\right) \)
B. \( 5 a \sin \left(\omega t+37^{\circ}\right) \)
c. \( 5 a \sin \left(\omega t+45^{\circ}\right) \)
D. \( 5 a \sin \left(\omega t+30^{\circ}\right) \)


A \( 60 k g \) man is inside a lift which is moving up with an acceleration of
\( 2.45 m s^{-2} . \) The apparent percentage change in his weight is:
A . \( 20 \% \)
B. 25\%
c. \( 50 \% \)
D. \( 75 \% \)


State whether true or false:
The pattern of the magnetic field
around a conductor due to electric
current flowing through it depends on the shape of the conductor
A. True
B. False


Which of the following statements is/are correct for generating nonbiodegradable waste?
A. Thermal power plants producing fly ash
B. Iron and steel plants producing blast furnace slag
c. Metal industries producing mud and tailings
D. All of the above


Which of the following does not represent redox reaction?
A \( \cdot C r_{2} O_{7}^{2-}+2 O H^{-} \rightarrow 2 C r O_{4}^{2-}+H_{2} O \)
B \( \cdot S O_{5}^{2-}+I^{-} \rightarrow I_{2}+S O_{4}^{2} \)
c. \( C a(O H)_{2}+C l_{2} \rightarrow C a(O C l)_{2}+C a C l_{2} \)
D. \( P C l_{5} \rightarrow P C l_{3}+C l_{2} \)


If the phase difference between two
component waves of different
amplitudes is \( 2 \pi, \) their resultant
amplitude will become
A. sum of the amplitudes
B. difference of the amplitudes
c. product of the amplitudes
D. ratio of their amplitudes


The frequency of vibration (v) of a string may depend upon length (I) of the string, tension (T) in the string and mass per unit length (m) of the string. Use method of dimensions for
establishing the formula for frequency


Xenon fluoride act as fluoride acceptor
with :
A. \( R b F \)
в. \( C s F \)
c. Both (A) and (B)
D. None of these


The value of valance electrons of N is:
\( \mathbf{A} \cdot \mathbf{1} \)
B. 3
\( c \cdot 4 \)
D. 5


The process of depositing thin layer of a metal over an another metal with a help of electric current is called:
A. electrorefining
B. electroplating
c. thermoplating
D. none of the above


The curie weiss law is obeyed by iron
A. at all temperatures
B. above the curie temperature
C . below the curie temperature
D. at the curie temperature


Find the area of the parallelogram whose diagonals are \( \vec{a}=\hat{i}-2 \hat{j}+3 \hat{k} \) and \( \vec{b}=3 \hat{i}-2 \hat{j}+\hat{k} \)


What is the IUPAC name for the
following compound? \( O \)
\( \boldsymbol{H} \stackrel{\|}{\boldsymbol{C}}-\boldsymbol{O}-\stackrel{\|}{\boldsymbol{C} \boldsymbol{H}} \)
A. propanoic anhydride
B. methanoic anhydride
c. formyl formate
D. oxomethanoate


The strong reducing agent is:
A . \( N H_{3} \)
в. \( B i H_{3} \)
c. \( P H_{3} \)
D. \( A s H_{3} \)


A neutron moving with velocity u collides with a stationary \( \boldsymbol{\alpha}- \) particle
The velocity of the neutron after collision is
A. \( -\frac{30}{5} \)
в. \( \frac{30}{5} \)
c. \( \frac{20}{5} \)
D. \( -\frac{2 U}{5} \)


The IUPAC name of given compound is :
A. 4 -Methylpentanenitril
B. 3-Methylnocypentane
c. 3 -Methylpentancyanide
D. 3-Methylpentanenitril


Convert the following rupees into paise:
\( \boldsymbol{R} \boldsymbol{s} \boldsymbol{9} \boldsymbol{0} \)


\( \operatorname{Let} A=\{1,2,3\}, B=\{4,5,6,7\} \) and
let \( \boldsymbol{f}=\{(\mathbf{1}, \boldsymbol{4}),(\mathbf{2}, \mathbf{5}),(\mathbf{3}, \mathbf{6})\} \) be a
function from \( A \) to \( B \). State whether \( f \) is
one-one or not.


Glomerulus and Bowmans capsule constitute
A. Blood vessels
B. Malpighian body
c. Green gland
D. Malpighian tubule


Which of the following comes under
laws of refraction?
A. Angle of incidence is equal to angle refraction
B. Angle of refraction is greater than angle of incidence
C value of \( \frac{\sin i}{\sin r} \) is known as refractive index of the medium
D. All


A student performs a titration with different burettes and finds titre values
of \( 25.2 \mathrm{ml}, 25.25 \mathrm{ml} \) and \( 25.0 \mathrm{ml} \). The
number of significant figures in the average titre value is:
A . 3
B. 4
\( c \cdot 6 \)
D. 8


Measure of one angle of linear pair is given. Find the measure of another
angle:
\( \mathbf{5 0}^{\circ} \)


The IUPAC name for the complex
\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{5}\left(\boldsymbol{N} \boldsymbol{O}_{2}\right)\right] \boldsymbol{C l}_{2} \) is:
A. Nitrito - N - pentaammine cobalt( (II) chloride
B. Nitrito - N - pentaammine cobalt(II) chloride
c. Pentaammine nitrito - N - cobalt( II) chloride
D. Pentaammine nitrito - N - cobalt (III) chloride


Benzene carbaldehyde is reacted with concentrated \( N a O H \) solution to give the products \( A \) and \( B \). The product \( A \) can be used as food preservative and the product \( B \) is an aromatic hydroxy compound where \( O H \) group is linked to
\( s p^{3} \) hybridised carbon atom next to
benzene ring. The products \( A \) and \( B \) respectively are :
A. sodium benzoate and phenol
B. sodium benzoate and phenyl methanol
c. sodium benzoate and cresol
D. sodium benzoate and picric acid


Two men, each of mass \( m \), stand on the
edge of a stationary car and jump off with a horizontal velocity u relative to
the car, first simultaneously and then one after the other. If friction be
negligible, in which case will they
impart greater speed to the car?


From following where all SONAR is used?
A. Measure depth of sea bed
B. Locate scraps
c. locate submarines
D. All of the above


Give half cell equation of Daniel cell takes place at cathode.


If \( P(A)=0.4, P(B)=0.3 \) and
\( P(B / A)=0.5, \) find \( P(A \cap B) \) and
\( P(A / B) \)


Find the complement of each of the
following angles:


The area of a segment of a circle of
radius \( 21 \mathrm{cm} \) if the arc of the segment
has a measure of \( 60^{\circ} \) is
(Take \( \sqrt{\mathbf{3}}=\mathbf{1 . 7 3} \) )
A. 45.27 sq. \( \mathrm{cm} \)
B. 40.27 sq. \( \mathrm{cm} \)
c. 40.8 sq. \( \mathrm{cm} \)
D. none of these


Complete the following Table:
Electronic

Bo
Element configuration \( \quad \) forms
Magnesium
Oxygen
Chlorine


Find \( A M \) of 2 and 16


Number of rational term is the
expansion of \( \left(7^{1 / 3}+11^{1 / 9}\right)^{729} \)
\( A \cdot 81 \)
B. 82
c. 730
D. None of these


The oxidation number of Cr is +6
in

This question has multiple correct options
A \( \cdot \operatorname{Fe} C r_{2} O_{4} \)
в. \( K C r O_{3} C l \)
c. \( C r O_{5} \)
D. \( \left[C r(O H)_{4}\right]^{-} \)


A lead block is suspended from your hand by a string. The reaction due to the force of gravity on the block is the force exerted by :
A. The string on the block
B. The block on the string
c. The string on the hand
D. The block on Earth


Which one of the following is a simple
ether?
A. \( C H_{3}-O-C_{2} H_{5} \)
в. \( C_{6} H_{5}-O-C H_{3} \)
c. \( C_{2} H_{5}-O-C_{2} H_{5} \)
D. \( C_{3} H_{7}-O-C_{2} H_{5} \)


A photoelectric cell is lightened by a light source, situated at a distance \( d \) from the cell. If distance becomes \( \boldsymbol{d} / \mathbf{2} \)
then number of electrons emitted per sec will be:-
A. Remains same
B. Four times
c. Two times
D. One fourth


Q Type your question
fundamental idea of VSEPR theory?
\( A \)
\( B \)
\( c \)
\( D \)


Particles and their anti-particles have
A. Same masses but opposite spins
B. Same masses but opposite magnetic moments
C. Same masses and same magnetic moments
D. Opposite spins and same magnetic moments


Draw a neat labelled diagram of L.S. of
tooth.


ntegrate the function \( \frac{\mathbf{5 x}}{(x+1)\left(x^{2}+9\right)} \)


Expand \( \left(x^{2}+2 a\right)^{5} \) by binomial
theorem.


Which of the following is a coenzyme?
A. NAD
B. NADP
c. FAD
D. All the above


Why are microwaves used in radars?


If suddenly the gravitational force of attraction between earth and a satellite
revolving aroung it becomes zero, then the satellite will
A. continue to move in its orbit with same velocity
B. Move tangentialy to the original orbit with the same velocity
c. Become satationary in its orbit
D. Move towards the earth


A long, straight wire of radius a carries a current distributed uniformlt over its
cross-section. The ratio of the magnetic fields due to the wire at distance \( \frac{a}{3} \) and
\( 2 a, \) respectively from the axis of the
wire is?
A \( \cdot 2 / 3 \)
B. \( 3 / 2 \)
c. \( 1 / 2 \)
D. 2


Curved surfaces which are used in big hall to direct the sound waves towards
the people sitting in a hall are known as:
A. megaphone
B. hydrophone
c. bulb horn
D. none of the above


In the hysteresis cycle, the value of \( \boldsymbol{H} \) needed to make the intensity of magnetism zero is called
A. Retentivity
B. Coercive force
c. Lorentz force
D. None of the above


Which of the following reactions will get
affected by increasing the pressure? Also, mention whether change will
cause the reaction to go into forward or backward direction.
(i) \( \boldsymbol{C O C l}_{2}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{C O}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g}) \)
(ii) \( \boldsymbol{C H}_{4}(\boldsymbol{g})+\mathbf{2 S}_{2}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{C S}_{2}(\boldsymbol{g})+ \)
\( 2 H_{2} S(g) \)
(iii) \( \boldsymbol{C O}_{2}(\boldsymbol{g})+\boldsymbol{C}(\boldsymbol{s}) \rightleftharpoons \mathbf{2} \boldsymbol{C O}(\boldsymbol{g}) \)
\( (\text { iv }) 2 H_{2}(g)+C O(g) \rightleftharpoons C H_{3} O H(g) \)
\( (v) C a C O_{3}(s) \rightleftharpoons C a O(s)+C O_{2}(g) \)
\( (v i) 4 N H_{3}(g)+5 O_{2}(g) \rightleftharpoons 4 N O(g)+ \)
\( \boldsymbol{6} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \)


\( \mathrm{CO}_{2} \) is carried in blood by hemoglobin in the form of
A. Sodium bicarbonate
B. Potassium bicarbonate
c. Carbamino compound
D. Methaemoglobin


Adam's apple is a
A. Large developed voice box in males
B. Apple which is eaten by Adam
c. special class of apple
D. None of the above


What is the range of wavelength of the spectrum of white light in \( \boldsymbol{A}^{o} \) ?
A \( .4000 A^{\circ} \) to \( 5000 A^{\circ} \)
B. \( 5000 A^{\circ} \) to \( 6000 A^{\circ} \)
c. \( 6000 A^{\circ} \) to \( 8000 A^{\circ} \)
D. All the above


toppr \( E \)
Q Type your question
\( B \)
\( c \)
\( D \)


In insulators (CB is conduction band
and VB is valence band)
A. VB is partially filled with electrons
B. CB is partially filled with electrons
c. \( \mathrm{cB} \) is empty and \( \mathrm{VB} \) is filled with electrons
D. CB is filled with electrons and VB is empty


A body of mass \( M \) moves in outer space
with velocity \( V . \) It is desired to break the body into two parts so that the mass of one part is one-tenth of the total mass. After the explosion, the heavier part comes to rest while the lighter part continues to move in the original
direction of motion. The velocity of the small part will be
A. \( V \)
B. \( (V / 2) \)
c. \( (V / 10) \)
D. 10V


Distinguish between dot product and cross product.


A point charge is placed at the corner of a cube. The electric flux through the
shaded surface is
\( A \cdot \frac{q}{8 c_{0}} \)
B. \( \frac{q}{\varepsilon_{0}} \)
\( c \cdot \frac{q}{24 c} \)
\( D \cdot \frac{q}{12 \varepsilon 0} \)


Two lenses of power \( 10 D \) and \( -10 D \) are in contact, find power, focal length and nature of lens combination.


Assertion
Acetone-Carbon disulphide solution shows positive deviation from Raoult's
law.
Reason
Acetone \( + \) Aniline solution shows
positive deviation from Raoult's law.
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


Constant a quadrilateral \( \boldsymbol{A B C D} \), where \( A B=4 c m, B C=5 c m, C D=6.5 \mathrm{cm} \)
and \( \angle B=105^{\circ} \) and \( \angle C=80^{\circ} \)


n which of the following pairs, indicated bond is of greater strength?
\( (I) \)
\( A \)
B.
c. Both are equal
D. cannot determine


The rate constant for the forward
reaction \( \boldsymbol{A}(\boldsymbol{g}) \rightleftharpoons 2 \boldsymbol{B}(\boldsymbol{g}) \) is \( 1.5 \times \)
\( 10^{-3} s^{-1} \) at \( 100 \mathrm{K} \). If \( 10^{-5} \) moles of \( \mathrm{A} \) and
100 moles of \( \mathrm{B} \) are present in a 10 litre
vessel at equilibrium then rate
constant for the backward reaction at
this temperature is:
\( \begin{array}{ll}\text { A } \cdot 1.50 \times 10^{4} L & \text { mol- }^{-1} s^{-1}\end{array} \)
В. \( 1.5 \times 10^{11} L \quad \) mol \( ^{-1} s^{-1} \)
C. \( 1.5 \times 10^{10} L \quad \) mol \( ^{-1} s^{-1} \)
D. \( 1.5 \times 10^{-11} L \quad \) mol \( ^{-1} s^{-1} \)


Who coined the term zymase for
enzymes in yeast?
A. Kuhne
B. Sumner
c. Louis Pasteur
D. Eduard Buchner


When \( 3 g \) of carbon is burnt in \( 8 g \) of oxygen, \( 11 g \) of carbon dioxide is
produced. What mass of carbon dioxide will be formed when \( 3 g \) of carbon is burnt in \( 50 g \) oxygen?
A . \( 12 g \)
в. 13 g
c. \( 11 g \)
D. \( 10 g \)


A vessel contains a mixture consisting
of \( m_{1}-7 g \) of nitrogen \( \left(M_{1}=28\right) \) and \( m_{2}= \)
11 g of carbon dioxide \( \left(M_{2}=44\right) \) at
temperature \( T-300 K \) and pressure \( P_{0}= \) atm. The density of the mixture is
A. \( 1.46 g \) per litre
B. \( 2.567 g \) per litre
c. \( 3.752 g \) per litre
D. \( 4.572 g \) per litre


Name the compounds used in preparation of nylon-66.
A. E-caprolactum
B. Hexamethylenediamine and adipic acid
C. Dimethyl tetraphthalate
D. Hexamethylene diamine


Calcium phosphate can be prepared by mixing solution containing calcium ions and hydrogen phosphate ions in the presence of an alkali.
A . True
B. False


The magnetising field required to be applied in opposite direction to reduce residual magnetism to zero is called
A. retentivity
B. coercivity
c. hysteresis
D. flux


The formula of Haematite is:
\( \mathbf{A} \cdot F e_{3} O_{4} \)
в. \( F e O_{4} \)
\( \mathrm{c} \cdot \mathrm{Fe}_{2} \mathrm{O}_{3} \)
\( \mathrm{D} \cdot \mathrm{Fe}_{3} \mathrm{O}_{2} \)


at the walls of the pipe?


The \( p K_{a} \) values of four carboxylic acids
are 4.76,4.19,0.23 and 3.41
respectively. The \( p K_{a} \) value of strongest carboxylic acid among them is:
A . 4.19
в. 3.41
c. 0.23
D. 4.76


According to the laws of reflection, \( \ldots \). is
equal to
A. incidence, reflection
B. deviation, reflection
c. incidence, deviation
D. All


Solve the differential equation \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}= \)
\( \frac{x^{2}+5 x y+4 y^{2}}{x^{2}} \)


In the minimum deviation position of a prism, the refracted ray is always parallel to its base.
A. True
B. False


Calculate the formula unit mass of
\( \boldsymbol{C a} \boldsymbol{S O}_{4 .} \mathbf{2 H}_{2} \boldsymbol{O} \)


The number of lone pairs in
\( X e F_{2}, X e F_{4} \) and \( X e F_{6} \)
respectively are :
\( A \cdot 1,2,3 \)
B. 3, 2,1
c. 1,3,2
D. 2, 1, 3


Crystalloids differ from colloids mainly in respect of :
A. electrical behaviour
B. particle nature
c. particle size
D. solubility


A bipolar neuron has
A. Two axons and two dendrons
B. One axon and one dendron
C. Two axons and one dendron
D. One axon and two dendrons


State Hess's law of constant heat
summation and explain it with an
example.


Two \( 30 \mathrm{kg} \) blocks rest on a massless
belt which passes over a fixed pulley
and is attached to a 40 kg block. If
coefficient of friction between the belt
and the table as well as between the
belt and the blocks \( \mathrm{B} \& \) block \( \mathrm{C} \) is \( \mu . \) The
system is released from rest from the
position shown, the speed with which
the block \( \mathrm{B} \) falls off the belt is
This question has multiple correct options
\( \mathbf{A} \cdot 2 \sqrt{2} m / s \) if \( \mu=0.2 \)
B. \( 2 m / s \) if \( \mu=0.2 \)
\( c: \quad \) । \( / s \) if \( \mu=0.5 \)
D. \( 2.5 m / s \) if \( \mu=0.5 \)


\( 100 \mathrm{mL} \) of a solution contains \( 2 \mathrm{g} \) of acetic acid and 3 g of sodium acetate providing \( K_{a}=1.8 \times 10^{-5} . \) Choose the
correct option.
A. This solution is basic in nature
B. This solution is acidic in nature
c. This solution is amphoteric in nature
D. This solution is neutral in nature


Which reagent can be used to convert
ethanol to diethyl ether?
A. \( A l_{2} O_{3} \) at \( 250^{\circ} C \)
B. conc. \( H_{2} S O_{4} \) at \( 170^{\circ} C \)
c. conc. \( H_{2} S O_{4} \) at \( 130^{0}-140^{0} C \)
D. \( A l_{2} O_{3} \) at \( 350^{\circ} C \)


Short Answer
Give an account of the composition of
the atmosphere


Which of the following is not true?
A \( \cdot P_{700}>2 / 3 \)
В. \( P_{101}<2 / 3 \)
C. \( P_{100} P_{101}>2 / 3 \)
D. none of these


Given below are four methods (A-D) and
their modes of action (i-iv) in
achieving contraception. Select their
correct matching from the four options
that follow.

Method \( \quad \) Mode of Action
A. Prevents sperms
Oral pill \( \quad \) (i) \( \quad \) reaching cervix
B. Condom
(ii) Prevents fertilisation
C. Vasectomy
(iii) Prevents ovulation
Semen contains no
D. CopperT \( \quad \) (iv) \( \quad \) sperms
\( A \)
A - (iii), B - (iv) \( C-(i), D-( \) ii)
B. \( A-(i i), B-(i i i), C-(i), D-(i v) \)
\( c \)
\( A-(\text { iii) }, B-(i), C-(i v), D-(i i) \)
D. A - (iv), B - (i), C - (ii), D- (iii)


Equilibrium constant for following
reactions respectively \( \boldsymbol{K}_{1}, \boldsymbol{K}_{2} \) and \( \boldsymbol{K}_{3} \)
\( N_{2}+3 H_{2} \rightleftharpoons 2 N H_{3} \quad K_{1} \)
\( N_{2}+O_{2} \rightleftharpoons 2 N O \quad K_{2} \)
\( \boldsymbol{H}_{2}+\frac{1}{2} \boldsymbol{O}_{2} \rightleftharpoons \boldsymbol{H}_{2} \boldsymbol{O} \quad \boldsymbol{K}_{3} \)
\( \mathbf{2} N \boldsymbol{H}_{3}+\frac{5}{2} \boldsymbol{O}_{2} \rightleftharpoons \mathbf{2} \boldsymbol{N} \boldsymbol{O}+\mathbf{3} \boldsymbol{H}_{2} \boldsymbol{O} \quad \boldsymbol{K}_{4} \)
Which of the following relation is
correct?
\( \mathbf{A} \cdot K_{1}=\frac{K_{2} \times\left(K_{3}\right)^{3}}{K_{4}} \)
B \( \cdot K_{4}=K_{1} \times K_{2} /\left(K_{3}\right)^{3} \)
\( \mathbf{C} \cdot K_{2}=\frac{K_{4}+K_{1}}{\left(K_{3}\right)^{3}} \)
D. None of these


If \( (x+1) \) is a factor of \( x^{3}+11 x^{2}+15 x+ \)
\( a \) then the value of 'a' is
\( A \cdot 2 \)
B. 3
\( c \cdot 5 \)
D. 4


Which of the following is a good conductor of electricity?
A. Anhydrous \( H C l \)
в. Aqueous \( H C l \)
c. HCl gas
D. crystalline \( H C l \)


Below, three different arrangement of identical capacitors are shown. What is the correct order of total capacitance
values for the arrangements, greatest first?
\( \mathbf{A} \cdot 1,2,3 \)
в. 3,2,1
\( c \cdot 3,1,2 \)
D. 2,3,1
E .2,1,3


The roots of \( a^{2} x^{2}+a b x=b^{2}, a \neq \)
\( \mathbf{0}, \boldsymbol{b} \neq \mathbf{0} \) are:
A. Equal
B. Non- real
c. Unequal
D. None of these


The plant ash is an indication of
A. organic matter of plant
B. Waste product
C. Mineral salts absorbed by plants
D. None of the above


The displacement \( y \) in centimeters is
given in terms of time \( t \) in second by the
equation: \( y=3 \sin 3.14 t+4 \cos 3.14 t \)
then the amplitude of SHM is
\( A \cdot 3 \mathrm{cm} \)
B. \( 4 \mathrm{cm} \)
\( c \cdot 5 \mathrm{cm} \)
D. \( 7 \mathrm{cm} \)


Identify the wrong statement.
A. \( A \) body can have momentum without energy
B. A body can have energy without momentum.
C. The momentum can conserved in an elastic collision.
D. Kinetic energy is not conserved in an inelastic collision


a. Caprolactum\( \stackrel{\text {hydrolysis}}{ } \boldsymbol{A} \)
b. \( \boldsymbol{A}+\boldsymbol{G} \) lycine \( \rightarrow \boldsymbol{B}(\text { Polymer }) \)
Here, \( \boldsymbol{B} \) is :
I. Condensation Polymer
II. Addition Polymer
III. Polyamide Polymer
IV. Polyester Polymer
V. Biodegradable Polymer
A . I, III, v are corect
B. II, IV are correct.
c. ॥, ॥ा, IV are correct.
D. II, IV, V are correct.


What is the oxidation state of \( \boldsymbol{T} \boldsymbol{h} \) in
organometallic compound
\( \left[T h H O R\left(C_{5} M e_{5}\right)_{2}\right] ? \)
A \( .+1 \)
B. +2
\( c \cdot+4 \)
D. +3


Find the coordinates of the foci, the
vertices, the length of major axis, the
minor axis, the eccentricity and the length of the latus rectum of the ellipse \( \frac{x^{2}}{49}+\frac{y^{2}}{36}=1 \)


During photorespiration which compounds are formed having \( 2 C \) anc
\( 3 \mathrm{C} \) respectively in peroxisome?
A. Glycolate and glycine
B. Glycine and glycerate
c. Serine and glycine
D. Phosphoglycerate and glycolate


In a system where \( \Delta \boldsymbol{E}=-\mathbf{5 1 . 0} \mathrm{kJ}, \) a
piston expanded against a \( P_{e x t} \) of 1.2 atm giving a change in volume of \( 32.0 \mathrm{L} \) what was the change in heat of this
system?
A. -36 k) J.
B. -13 k.
c. -47 k
D. 24 kJ


Multiple photoelectric effect
experiments were conducted by
applying a variety of visible wavelengths to a metal surface and
recording the electrical current
produced. Data from these experiments provided evidence for which of the following
claims?
A. Electromagnetic radiation exhibit wave-like characteristics.
B. Electromagnetic radiation exhibit particle-like characteristics.
C. Electrons have quantized energies in an atom.
D. Electrons behave like waves in an atom.


Which of the following is not a cell?
A. Red Blood Corpuscle (RBC)
B. Bacterium
c. spermatozoa
D. Virus


Factorise the following expressions:
\( \boldsymbol{x} \boldsymbol{y}-\boldsymbol{a b}(\boldsymbol{x}+\boldsymbol{y})+\boldsymbol{a}^{2} \boldsymbol{b}^{2} \)


Two mutually exclusive events are always independent always.
A. True
B. False


\( X \) and \( Y \) are two elements which form
\( X_{2} Y_{3} \) and \( X_{3} Y_{4} . \) If 0.2 mol of \( X_{2} Y_{3} \)
weighs 32 g and 0.4 mole of \( X_{3} Y_{4} \) weighs \( 92.8 \mathrm{g} \), the atomic weights of \( \boldsymbol{X} \)
and \( Y \) respectively are :
A. 16,56
B. 16,16
\( \mathbf{c} \cdot 56,16 \)
D. 56,56


The reaction, \( 2 N O+O_{2} \rightarrow 2 N O_{2} \)
proceeds in two steps. If one elementary
reaction is \( N O+O_{2} \rightarrow N O_{3}, \) write the
second elementary reaction. Write the rate law of the reaction.


Show that the function \( \boldsymbol{f}(\boldsymbol{x})= \) \( \sin (2 x+\pi / 4) \) is decreasing on
\( (3 \pi / 8,5 \pi / 8) \)


Which of the following statement is not in accordance with the International
Code of Botanical Nomenclature?
A. Colour of flower is a criteria for classification
B. Tautonyms can be used in nomenclature.
c. Two genera can have same name.
D. All of the above


Let \( P(n): n^{2}+n \) is an odd integer. It is
seen that truth of \( P(n) \Rightarrow \) the truth of \( P(n+1) . \) Therefore, \( P(n) \) is true for all
\( A \cdot n>1 \)
B.
\( c \cdot n>2 \)
D. none of these


Differentiate the following function w.r.t.
\( \boldsymbol{x} \)
\( \sqrt[3]{\left(2 x^{2}-7 x-4\right)^{5}} \)


Premature leaf fall is caused due to the
deficiency of


Define a binary operation \( * \) on the set
\{0,1,2,3,4,5\} as
\( \boldsymbol{a} * \boldsymbol{b}=\left\{\begin{array}{ll}\boldsymbol{a}+\boldsymbol{b}, & \boldsymbol{i f} \quad \boldsymbol{a}+\boldsymbol{b}<\mathbf{6} \\ \boldsymbol{a}+\boldsymbol{b}-\boldsymbol{6} \quad \boldsymbol{i} \boldsymbol{f} \quad \boldsymbol{a}+\boldsymbol{b} \geq \boldsymbol{6} & \boldsymbol{6}\end{array}\right. \)
Show that zero is the identity for this
operation and each element \( a \neq 0 \) of
the set is invertible with \( 6-a \) being the
inverse of \( a \)


Number of moles of oxygen that one
mole of benzoic acid uses in the
production of phenol by oxidative decarboxylation?
\( A \cdot 3 / 2 \)
B.
c. \( 1 / 2 \)
D.


Show that no translator forces act on an
electric dipole held in uniform electric
field.


Fill in the blank-
An electric fuse works on the
effect of current.
A. heating
B. magnetic
c. chemical
D. none of these


Which of the following systems is responsible for producing enzymes that aid in breaking down of complex substances to be absorbed for the
body's growth and repair?
A. Respiratory system
B. Digestive system
D. Nervous system


A body of mass \( 5 k g \) starts motion form the origin with an initial velocity \( \vec{u}= \) \( (30 \hat{i}+40 \hat{j}) m s^{-1} \) If a constant force \( \vec{F}=-(-\hat{6} i-5 \hat{j}) N \) acts on the body than the time in which the Y-component of the velocity becomes zero is
\( \mathbf{A} \cdot 5 s \)
в. \( 20 s \)
\( c .40 s \)
D. 80


\( f(x)=\left|\begin{array}{ccc}\cos x & 1 & 0 \\ 1 & \cos x & 1 \\ 0 & 1 & \cos x\end{array}\right| \) the
\( f^{\prime}\left(\frac{\pi}{3}\right) \) equals
A \( \frac{11 \sqrt{3}}{8} \)
\( B \cdot \frac{5 \sqrt{3}}{8} \)
\( c \cdot-\frac{5 \sqrt{3}}{8} \)
D. none of these


Molten sodium chloride conducts
electricity due to the presence of:
A. free electrons
B. free molecules
c. atoms
D. free ions


Choose the correct alternative(s)
regarding standing waves in a string
This question has multiple correct options
A. particles near the antinode have lesser potential energy than the particles near the node when they reaches at its extreme position
B. All the particles crosses their mean position simultaneously
C. Energy and momentum can transmitted through node
D. Particles near the antinode have lesser kinetic energy than the particles near the node when they crosses their mean position


The acid rain destroys vegetation because it contains
A. Nitrates
B. \( \mathrm{H}_{2} \mathrm{SO}_{4} \)
\( c \cdot 0_{3} \)
D. co


Find the values of \( x \) and \( y \) in the figure
given below


Three elements \( X, Y \) and \( Z \) form a Dobereiner triad. The ratio of the atomic
weight of \( X \) to that of \( Z \) is 7: 25
If the sum of the atomic weights of \( x \) and \( Z \) is 160 , find the atomic weights of \( X, Y \) and \( Z \)
A \( . x \rightarrow 35, Y \rightarrow 80, Z \rightarrow 125 \)
в. \( x \rightarrow 125, Y \rightarrow 80, z \rightarrow 35 \)
c. \( x \rightarrow 80, Y \rightarrow 35, Z \rightarrow 125 \)
D. \( x \rightarrow 80, Y \rightarrow 125, z \rightarrow 35 \)


Simplify:
\( \frac{1+\frac{1}{2}}{1-\frac{1}{2}} \div \frac{4}{7}\left(\frac{2}{5}+\frac{3}{10}\right) \) of \( \left(\frac{\frac{1}{2}+\frac{1}{3}}{\frac{1}{2}-\frac{1}{3}}\right) \)


A coil of insulated copper wire is connected to a galvanometer. What would happen if a bar magnet is (i) Pushed into the coil?
A. The galvanometer shows deflection
B. The galvanometer do not show any deflection
c. Current increases inside the coil
D. none


In a weather map, lines joining all those regions with same atmospheric
pressure are called
A. Bars
B. Millibars
c. Isobars
D. None


Which of the following electrolytic solutions has the least specific
conductance?
A. \( 0.02 N \)
n
B. \( 0.2 N \)
\( c \cdot 2 N \)
D. \( 0.002 N \)


Susceptibility is small and negative for
A. para magnetio
B. diamagnetic
C. ferro magnetic
D. electromagnetic


Let \( \boldsymbol{f} \) be a positive function. If \( \boldsymbol{I}_{\mathbf{1}}= \) \( \int_{1-k}^{k} x f x(1-x) d x, I_{2}= \)
\( \int_{1-k}^{k} f x(1-x) d x, \) where \( 2 k-1>0 \)
then \( \frac{\boldsymbol{I}_{1}}{\boldsymbol{I}_{2}} \) is
A . 2
B. \( k \)
\( c \cdot \frac{1}{2} \)
D.


In histogram, the height of rectangle shows
A. width of the class
B. upper limit of the class
c. lower limit of the class
D. frequency of the class


n the given figure, 0 is the centre of the
circle. If \( \angle B A D=75^{\circ} \) and \( B C=C D \)
find \( \angle B O D, \angle B C D, \angle O B D \)


The conjugate complex number of \( \frac{2-i}{(1-2 i)^{2}} \) is
A \( \cdot \frac{2}{25}+\frac{11}{25} i \)
в. \( \frac{2}{25}-\frac{11}{25} i \)
c. \( -\frac{2}{25}+\frac{11}{25} i \)
D. \( -\frac{2}{25}-\frac{11}{25} i \)


Group 16 elements have a lower value of first ionization enthalpy as compared to group 15 elements because:
A. half filled p-orbitals in group 15 elements are more stable
B. group 16 elements have smaller size than group 15 elements
c. group 16 elements contain double bond while group 15 elements have a triple bond
D. group 16 elements have more number of electrons in p-orbitals


If \( \boldsymbol{A}=\{\boldsymbol{x}, \boldsymbol{y}\} \) and \( \boldsymbol{B}=\{\mathbf{3}, \mathbf{4}, \mathbf{5}, \mathbf{7}, \mathbf{9}\} \) and
\( \boldsymbol{C}=\{\mathbf{4}, \mathbf{5}, \mathbf{6}, \mathbf{7}\}, \) find \( \boldsymbol{A} \times(\boldsymbol{B} \cap \boldsymbol{C}) \)
A \( \cdot\{(x, 4),(x, 5),(x, 7),(y, 4),(y, 5),(y, 7)\} \)
B - \( \{(x, 3),(x, 5),(x, 7),(y, 4),(y, 5),(y, 7)\} \)
c \( \cdot\{(x, 4),(x, 5),(x, 7),(y, 4),(y, 5),(y, 9)\} \)
D. none of the above


The triangle formed by the tangent to
the curve \( f(x)=x^{2}+b x-b \) at the
point (1,1) and the co-ordinate axes
lies in the first quadrant.lf its area is 2 sq.unit, then the value of \( b \) is:
A. -3 sq.unit
B. - 2 sq.unit
c. -1 sq.unit
D. 0 sq.unit


In Millikan's oil drop experiment, we make use of:
A. Ohm's law
B. Ampere's law
c. Stoke's law
D. Faraday's law


Two wires of equal length, one of aluminium and the other of copper have
the same resistance. Which of the two
wires is lighter? Hence explain why aluminium wires are preferred for
overhead power cables. \( \left(\rho_{A I}=2.63 \times\right. \)
\( 10^{-8} \Omega m, \rho_{C u}=1.72 \times 10^{-8} \Omega m \)
Relative density of \( A I=2.7, \) of \( C u=8.9 . \)


The most acidic is:
A. \( A s_{2} O_{3} \)
в. \( P_{2} O_{3} \)
\( \mathrm{c} \cdot \mathrm{Sb}_{2} \mathrm{O}_{3} \)
D. \( B i_{2} O_{3} \)


The point (0,3) lies on
A. \( + \) ve \( x \) -axis
B. + -ve y-axis
c. - ve \( x \) -axis
D. - ve y-axis


The drain cleaner, Drainex contains
small bits of aluminium which react
with caustic soda to produce dihydrogen.What volume of dihydrogen
at \( 20^{\circ} C \) and one bar will be released
when \( 0.15 g \) of aluminium reacts?


Solanine is
A. Not known to be harmful to humans
B. A naturally occurring toxin found in green potatoes
C. A naturally occurring toxin found in shellfish
D. A toxin that grows on corn and peanut products


Let \( a=2 i+j-2 k \) and \( b=i+j . \) If \( c \) is
a vector such that \( \quad \boldsymbol{a} . \boldsymbol{c}=|\boldsymbol{c}| \cdot|\boldsymbol{c}-\boldsymbol{a}|= \)
\( 2 \sqrt{2} \) and the angle between \( (a \times b) \) and
\( c \) is \( 30^{\circ}, \) then \( |(a \times b) \times c| \) is equal to
A \( \cdot \frac{2}{3} \)
B. \( \frac{3}{2} \)
c. 2
D. 3


When electrons in sample of H-atom make transitions from 5th excited state
to ground state, then the maximum number of spectral lines which belong to visible region is:
A . 10
B. 4
c. 15
D. 5


The ordered pair (a,b) such that \( f(x)= \) \( \left\{\begin{array}{ll}\frac{b e^{x}-\cos x-x}{x} & , x>0 \\ a & , x=0 \\ \frac{2 \tan ^{-1}\left(e^{x}\right)-\frac{\pi}{4}}{x} & , x<0\end{array}\right. \)
continuous at \( x-0 \) is


If \( \vec{E}=3 \hat{i}+4 \hat{j}-5 \hat{k}, \) calculate the
electric flux through a surface of area 50 units in z-x plane


Which one of the following erosion processes is a natural process?
A. Geological erosion
B. Accelerated erosion
c. Gully erosion
D. Rill erosion


If the weight of a body on the earth is 12 Newtons (N), its weight on the moon will be:
A. २N
B. 24 kg
c. 12N
D. \( 12 \mathrm{kg} \)


The hybridisation of \( N i \) in \( N i(C O)_{4} \) is:
\( A \cdot s p^{2} \)
В. \( d s p^{2} \)
\( c \cdot s p^{3} \)
D. \( s p^{3} d \)


IUPAC name of the compound is:
\( \boldsymbol{C H} \)
A. 6 -Chloro-4-ethyl-5-methyl hept-5-en-1-yne
B. 6-Chloro-4-ethyl-5-methyl hept-1-yn-Hne
c. 2-chloro-4-ethyl-3-methyl hept-2-en-6-yne
D. 2-Chloro-4-ethyl-3-methyl hept-4, 3-yn-2-ene


Evaluate
\( ^{4} \boldsymbol{C}_{3}+^{4} \boldsymbol{C}_{4}=? \)


Which of the following is responsible for synthesis of enzyme in seed germination?
A. \( I A A \)
B. Gibberellin
c. Cytokinin
D. Ethylene.


A step up transformer operates on a 230 volt line and supplies to a load of 2 amp. The ratio of primary to secondary windings is \( 1: 25 . \) Determine the primary
current
A. 12.5 amp
B. 50 amp
c. 8.8 amp
D. 25 amp


N moles of a monoatomic gas is carried
round the reversible rectangular cycle
ABCDA as shown in the diagram. The
temperature at \( \boldsymbol{A} \) is \( \boldsymbol{T}_{\mathbf{0}} . \) The
thermodynamic efficiency of the cycle
is
A. \( 15 \% \)
B. \( 50 \% \)
\( c \cdot 20 \% \)
D. \( 25 \% \)


Which of the following statements is
not correct about methanol?
A. It is used for drinking purposes.
B. It is highly poisonous compound.
C. It can be prepared by reduction of formaldehyde with \( L i A l H_{4} \)
D. It is miscible with water in all proportions.


A body initially at rest travels a
distance \( 100 \mathrm{m} \) in \( 5 \mathrm{s} \) with a constant
acceleration. Find the acceleration.
A \( \cdot 20 m s^{-2} \)
B. \( 4 m s^{-2} \)
\( \mathbf{c} \cdot 8 m s^{-2} \)
D. \( 10 m s^{-2} \)


The angular frequency of the damped oscillator is given by \( \omega=\sqrt{\left(\frac{k}{m}-\frac{r^{2}}{4 m^{2}}\right)} \) where \( k \) is the
spring constant, \( m \) is the mass of the oscillator and \( r \) is the damping constant. If the ratio \( \frac{r^{2}}{m k} \) is \( 80 \%, \) the change in time period compared to the undamped oscillator is approximately
as follows:
A. increases by 8\%
B. decreases by 8\%
C. increases by \( 1 \% \)
D. decreases by 1\%


The weight of a freely falling body is always constant.
A . True
B. False


State whether given statement is True
or False.

The actual force applied by the brakes may be slightly less than the calculated
value.
A. True
B. False


Assertion
A charged particle is moving in a
circular path under the action of
uniform magnetic field as shown in fig.
During motion kinetic energy of
charged particle is constant.
Reason
During the motion, magnetic force
acting on the particle is perpendicular
to instantaneous velocity.
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


\( 50 W / m^{2} \) energy density of sunlight is normally incident on the surface of a
solar panel. Some part of incident energy \( (25 \%) \) is reflected from the surface and the rest is absorbed. The
force exerted on \( 1 m^{2} \) surface area will
be close to? \( \left(c=3 \times 10^{8} m / s\right) \)
\( \mathbf{A} \cdot 15 \times 10^{-8} \mathrm{N} \)
B . \( 35 \times 10^{-8} \) N
c. \( 10 \times 10^{-8} \mathrm{N} \)
D. \( 20 \times 10^{-8} \mathrm{N} \)


The probability that an automobile will be stolen and found within one week is
\( 0.0006 . \) The probability that an
automobile will be stolen is \( 0.0015 . \) The
probability that a stolen automobile will be found in one week is
A . 0.3
B. 0.4
\( c .0 .5 \)
D. 0.6


An object is placed in front of a thin convex lens of focal length \( 30 \mathrm{cm} \) and a plane mirror is placed \( 15 \mathrm{cm} \) behind the lens. If the final image of the object coincides with the object, the distance of the object from the lens is :
\( A \cdot 60 \mathrm{cm} \)
B. 30 cm
c. \( 15 \mathrm{cm} \)
D. 25 cm


Insert three rational of number between
\( \frac{3}{7} \) and \( \frac{4}{7} \)


A sample of chloroform which is used by doctors as an anaesthetic is generally
tested by:
A. \( A g N O_{3}(a q .) \)
B. Fehling's solution
c. \( A g N O_{3}(a q .) \) after boiling with \( K O H \)
D. Any of the above


A particle is moving with a constant speed in a circular path. The ratio of average velocity to its instantaneous velocity when the particle describe an angle \( \frac{\pi}{2} \) is?
A. \( 3 / 2 \pi \)
B. \( \frac{2 \sqrt{2}}{\pi} \)
\( c \cdot \frac{2}{\pi} \)
D.


\( \operatorname{Let} f\left(x+\frac{1}{x}\right)=x^{2}+\frac{1}{x^{2}}(x \neq 0), \) then
\( \boldsymbol{f}(\boldsymbol{x}) \) equals:
A \( \cdot x^{2}-2 \)
B . \( x^{2}-1 \)
\( \mathbf{c} \cdot x^{2} \)
D. None of these


Cumene process is the most important
commercial method for the
manufacture of phenol. Cumene is:
A. (1-methylethyl ) benzene
B. ethyl benzene
c. vinyl benzene
D. propyl benzene


The equation of the circle passing through (4,5) having the centre at (2,2) is
A \( \cdot x^{2}+y^{2}+4 x+4 y-5=0 \)
B . \( x^{2}+y^{2}-4 x-4 y-5=0 \)
c. \( x^{2}+y^{2}-4 x=13 \)
D. \( x^{2}+y^{2}-4 x-4 y+5=0 \)


An old man cannot see objects closer than \( 1 \mathrm{m} \) from the eye clearly. Name the
defect of vision he is suffering from. How can it be corrected? Draw ray
diagram for the
(i) defect of vision and
also
(ii) for its correction.


The initial velocity of a particle is u and the acceleration is given by (kt), where k is a positive constant. The distance
traveled in time t is :
A \( . s=u t^{2}+k t^{2} \)
B. \( s=u t+\left(\frac{k t^{3}}{6}\right) \)
c. \( _{s}=u t+\left(\frac{k t^{3}}{2}\right) \)
D. \( s=\left(\frac{u t^{2}}{2}\right)+\left(\frac{k t^{3}}{6}\right) \)


A sound wave is passing through air column in the form of compression and rarefaction. In consecutive compression
and rarefaction:
A. density remains constant
B. Boyle's law is obeyed
c. bulk modulus of air oscillates
D. there is no transfer of heat


Point of intersection of the point
(2,4,5)(3,6,-4)


Which of the following aldehyde is very much used in perfumery and in dye industries?
A. Formaldehyde
B. Acetaldehyde
c. Benzaldehyde
D. Butyraldehyde


Find \( : \int \frac{\sin 2 x}{\left(\sin ^{2} x+1\right)\left(\sin ^{2} x+3\right)} d x \)


Oil \( A \) is at \( 300^{\circ} \) C whereas oil \( B \) is at
\( 530^{\circ} \) F. Which one is hotter?
A. \( A \)
в. \( B \)
c. Both are same
D. Can not be predicted


A gas at \( 27^{\circ} \mathrm{C} \) and pressure of \( 30 \mathrm{atm} \)
is allowed to expand to atmospheric pressure and volume 15 times larger. The final temperature of gas is
\( A \cdot 123^{0} C \)
B . - \( 123^{\circ} \mathrm{C} \)
c. \( 400 \mathrm{k} \)
D. None


In which of the following sets, the central atom of each member involves
\( \boldsymbol{s} \boldsymbol{p}^{3} \) hybridisation?
\( \mathbf{A} \cdot I O_{4}^{-}, I C l_{4}^{-}, I F_{4}^{+} \)
в. \( X e O_{3}, X e O_{4}, X e F_{4} \)
\( \mathrm{c} \cdot \mathrm{SO}_{3}, \mathrm{SO}_{3}^{2-}, \mathrm{SO}_{4}^{2} \)
D. \( P C l_{4}^{+}, B F_{4}^{-}, C l O_{4} \)


In housefly, the excretory organs are
A. Nephridia
B. Flame cells
c. Malpighian tubules
D. Kidneys


When dilute aqueous solution of
\( A g N O_{3}(\text { excess }) \) is added to \( K I \) solution, positively charged sol particles of \( A g I \) are formed due to
adsorption of ion:
A \( . K^{\text {t }} \)
в. \( A g^{+} \)
c. \( I^{-} \)
D. \( N O_{3}^{-} \)


The number of \( \angle F I F \) angles which are
less than \( 90^{\circ} \) in \( I F_{5} \) are :
\( A \cdot 8 \)
B. 7
\( c \cdot 6 \)
D. 5


IUPAC name of given compound is :
A. 3 -bromo-2-chlorocyclohexene
B. 3-bromo-1-chlorocyclohexane
c. 3 -bromo-1-chlorocyclohexene
D. none of these


If water kept in an insulated vessel at
\( -10^{\circ} C \) suddenly freezes, the entropy change of the system:
A. decrease
B. increase
c. is zero
D. equals to that of the surrouding


Which intermolecular force binds aqua
\( \left(H_{2} O\right) \) together in water?
A. Iondon force
B. Hydrogen bond
c. dipole-dipole force
D. All of these


The serial management of taxa is known as
A. Natural classification
B. Keys
c. Hierarchy
D. taxonomy


A \( 50 ~ m H \) coil carries a current of \( 2 A \)
The energy stored in joule is
A . \( 0 . \)
B. 0.5
c. \( 1 . \)
D. 5.0


State one relevant observation for each
of the following reactions:
Action of dilute hydrochloric acid on
iron
(II) sulphide.


A liquid will NOT wet the surface of a solid if its angle of contact is
A. Zero
B. Less than 90
c. More than 90
D. \( 90^{\circ} \)


Account for the following:
(i) Primary amines \( \left(\boldsymbol{R}-\boldsymbol{N} \boldsymbol{H}_{2}\right) \) have
higher boiling point than tertiary
\( \operatorname{amines}\left(\boldsymbol{R}_{3} \boldsymbol{N}\right) \)
(ii) Aniline does not undergo Friedel-
Crafts reaction.
(iii) \( \left(C H_{3}\right)_{2} N H \) is more basic than
\( \left(C H_{3}\right)_{3} N \) in an aqueous solution


The velocity of central maxima at \( t=5 s \)
\( \mathbf{i} \mathbf{S} \)
A \( .50 m s^{-1} \) along Y-axis
B. \( 50 m s^{-1} \) along negative Y-axis
\( \mathrm{c} \cdot 3 \times 10^{8} \mathrm{m} \mathrm{s}^{-1} \) along \( \mathrm{Y} \) -axis
D. \( 3 \times 10^{8} \mathrm{m} \mathrm{s}^{-1} \) along negative Y-axis


Suppose the kinetic energy of a body oscillating with amplitude \( A \) and at a distance \( x \) is given by \( K=\frac{B x}{x^{2}+A^{2}} \)
The dimensions of \( B \) are the same as
that of :
A \( \cdot \frac{\text {work}}{\text {time}} \)
B. work \( \times \) distance
c. \( \frac{\text { work }}{\text { distance }} \)
D. work \( \times \) time


Which of the following are correct for
co-ordianate covalent compounds?
A. Their M.P. is more than purely covalent bond
B. Their B.P. is more than ionic compounds
C. They are soluble in polar solvent
D. They are good conductor of electricity


The oxidation number of chlorine is
maximum in
A . \( H O C l \)
в. \( C l_{2} O_{6} \)
c. \( K C l O_{4} \)
D. \( N a C l O_{3} \)


The chemical process in the production of steel from haematite ore involves
A. reduction
B. oxidation
c. reduction followed by oxidation
D. oxidation followed by reduction


What is potential energy?
A. Energy of an abject due to its position or arrangement in a system
B. Energy of an abject due to its nature or arrangement in a system
C. Energy of an abject due to its shape or arrangement in a system
D. None


\( \boldsymbol{C a} \boldsymbol{C O}_{3}(\boldsymbol{s}) \longrightarrow \boldsymbol{C a O}(\boldsymbol{s})+\boldsymbol{C O}_{2}(\boldsymbol{g}) \)
For this reaction relate \( \Delta H \) and \( \Delta U \)
A. \( \Delta H=\Delta U \)
в. \( \Delta H>\Delta U \)
c. \( \Delta H<\Delta U \)
D. None of these


State the energy conversion taking place in a solar cell.


IUPAC name of given compound is :
A. But-2-en-3-oic acid
B. But-3-eneoic acid
c. But-2-eneoic acid
D. none of these


The motion a particle is given by \( y= \) \( U t+\frac{1}{2} g t^{2} . \) Whose \( y \) is the
displacement along \( y \) is calculate what kind of acceleration the particle is going through.


Which of the following statements is
true?
A. Cube root of a positive number may be a negative number
B. Cube root of a number ending with 8 ends with 2 .
C. Cube root of an odd number may be an even number.
D. All above statements are false


An electric motor exerts a constant
torque \( 5 N m \) on a flywheel by which it is
rotated at the rate of 420 rpm. The
power of motor is:
A. \( 110 w a t t \)
B. 150watt
c. 220 watt \( t \)
D. 300watt


A prisoner escapes from a jail and is equally likely to choose one of the four roads I, II, III or IV to reach away from the hands of law. If he choose I road, he is successful with probability \( 1 / 6 \) and for
I, III and IV this is \( 1 / 8,1 / 10 \) and \( 1 / 12 \). If the prisoner is successful, the probability that he chose road


Name the unit in which the laudness or
the sound is expressed.


A function \( f \) is defined by \( f(x)= \) \( \frac{1}{2^{r-1}}, \frac{1}{2 r}<x \leq \frac{1}{2^{r-1}}, r=1,2,3, \dots . \)
then the value of \( \int_{0}^{1} f(x) d x \) is equal
A
B.
\( c \cdot \frac{2}{3} \)
D.


The reaction of \( t \) -butyl bromide with
sodium methoxide mainly produces:
\( A \). isobutane
B. isobutylene
c. \( t \) -butyl methyl ether
D. sodium tert-butoxide


The Sl unit of G is.
A \( \cdot N^{2} m^{2} / k g \)
B. \( N m^{2} / k g \)
c. \( N \) ml \( k g \)
D. \( N m^{2} / k g^{2} \)


Write IUPAC name of the following complex compounds
\( (\mathrm{i})\left[\boldsymbol{N} \boldsymbol{i}(\boldsymbol{C} \boldsymbol{O})_{4}\right] \)
(ii) \( \boldsymbol{K}_{\mathbf{2}}\left[\boldsymbol{H} \boldsymbol{g} \boldsymbol{I}_{4}\right] \)


The values of \( x \) for which the angle
between the vectors \( a=x i-3 j-k \)
and \( b=2 x i+x j-k \) is acute, and the
angle between the vector \( b \) and the axis
of ordinates is obtuse, are
This question has multiple correct options
A . 1,2
в. -2,-3
c. all \( x<0 \)
D. all \( x>0 \)


What type of leaf margin is found in
grasses?
A. Crenate
B. Dentate
c. Entire
D. serrate


If \( E_{F e^{2+} / F e}^{0}=-0.441 \mathrm{V} \) and \( E_{F e^{3+} / F e^{2+}}^{0}= \)
\( 0.771 \mathrm{V}, \) the standard \( \boldsymbol{E} \boldsymbol{M} \boldsymbol{F} \) of the
reaction,
\( \boldsymbol{F} \boldsymbol{E}+\mathbf{2} \boldsymbol{F} \boldsymbol{E}^{3+} \rightarrow \mathbf{3} \boldsymbol{F} \boldsymbol{E}^{2+} \) will be:
A \( .0 .330 V \)
\( V \)
B. \( 1.653 V \)
c. \( 1.212 V \)
D. \( 0.111 V \)


If \( \mathrm{E} \) is the energy of the combining
atomic orbitals, \( E_{1} \) and \( E_{2} \) are the
energies of molecular orbitals formed,
then:
A. \( E-E_{1}>E_{2}-E \)
B. \( E-E_{1}<E_{2}-E \)
c. \( E-E_{1}=E_{2}-E \)
D. Any one of the above


\( 0.1 m^{3} \) of water at \( 80^{\circ} \) is mixed with
\( 0.3 m^{3} \) of water at \( 60^{\circ} . \) The final
temperature of mixture is :
A \( \cdot 80^{\circ} \mathrm{C} \)
B . \( 70^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 60^{\circ} \mathrm{C} \)
D. \( 75^{\circ} \mathrm{C} \)


\( f(a)=\frac{-1+i \sqrt{3}}{2}, b=\frac{-1-i \sqrt{3}}{2} \) then
show that \( a^{2}=b \) and \( b^{2}=a \)


Differentiate the following
function with respect to \( x \)
\( \tan h^{-1}(3 x+1) \)


What is the value of \( \sec ^{2}\left(\tan ^{-1}\left(\frac{5}{11}\right)\right) ? \)
A . \( 121 / 96 \)
B. 217/921
\( c \cdot 146 / 121 \)
D. 267/121


The freezing point of a 0.05 molal solution of non-electrolyte in water is:
\( \left[\boldsymbol{K}_{f}=\mathbf{1 . 8 6} \boldsymbol{K} \boldsymbol{m}^{-1}\right] \)
\( \mathbf{A} \cdot-1.86^{\circ} \mathrm{C} \)
B. \( -0.93^{\circ} \mathrm{C} \)
с. \( -0.093^{\circ} \mathrm{C} \)
и. \( -0.093^{\circ} \).
D. \( 0.093^{\circ} \mathrm{C} \)


When we hear a sound, we can identify
it source from
A. The frequency of the sound
B. The amplitude of the soundd
c. The wavelength of the sound
D. The overtones present in the sound


A body is executing SHM. If the force
acting on the body is \( 6 \mathrm{N} \) when the displacement is \( 2 \mathrm{cm}, \) then the force acting on the body when the displacement is \( 3 \mathrm{cm} \) in newton is:
A. 6 N
B. 9 N
\( c .4 \mathrm{N} \)
D. \( \sqrt{6} \) N


Consider the function \( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{ll}2 \boldsymbol{x}-\mathbf{1}, & \boldsymbol{0} \leq \boldsymbol{x}<\mathbf{2} \\ \boldsymbol{x}+\boldsymbol{a} & \boldsymbol{2} \leq \boldsymbol{x} \leq \mathbf{4} \\ \boldsymbol{3} \boldsymbol{x}+\boldsymbol{b} & \boldsymbol{4}<\boldsymbol{x} \leq \mathbf{6}\end{array}\right. \)
(i) Find \( f(2-) \) and \( f(2+) \)
(ii) Find \( a \) if \( f \) is continuous at \( x=2 \)
(iii) Find \( b \) if \( f \) is continuous on [0,6]


A system changes from state \( X \) to \( Y \) with a change in internal energy
measuring to \( 25 \mathrm{kJ} \mathrm{mol}^{-1}, \) by a
reversible path and returns from Y to X by an irreversible path, What will be the net change in internal energy?
A. \( 25 \mathrm{kJ} \)
J.
B . >25 kJ
c. \( <25 \mathrm{kJ} \)
D. zero


Draw a circuit diagram of a transistor amplifier in CE configuration
Define the terms:
(i) Input resistance and
(ii) Current
amplification factor. How are these determined using typical input and output characteristics?


A carbon sample from the frame of
picture gives 7 counts of \( C^{14} \) per minute
per gram of carbon. If freshly cut wood
gives 15.3 counts of \( C^{14} \) per minute,
calculate the age of frame. \( \left(t_{1 / 2} \text { of } C^{14}=\right. \) 5570 years
A . 6286 years
B. 5527 years
c. 5570 years
D. 4570 years


If a line makes an angle of \( \frac{\pi}{4} \) with the positive direction of each of \( x \) -axis and
\( \boldsymbol{y} \) -axis, then the angle that the line
makes with the positive direction of \( z \)
axis is-
A \( \cdot \frac{\pi}{3} \)
в.
c. \( \frac{\pi}{2} \)
D.


Three resistors of resistances \( 6 \Omega \)
each are connected as shown:
The effective resistance between \( A \) and
\( B \) is:
\( \mathbf{A} \cdot 18 \Omega \)
B. 2\Omega
\( c .9 \Omega \)
D. \( 4 \Omega \)


The velocity of an electron in a certain
Bohr orbit of H-atom bears the ratio
1: 275 to the velocity of light. The quantum number (n) of the orbit is :
\( A \cdot 3 \)
B. 2
\( c \)
\( D \cdot 4 \)


Evaluate the following integral:
\( \int \frac{\left(e^{\sin ^{-1} x}\right)^{2}}{\sqrt{1-x^{2}}} d x \)


Find the values of the unknown \( x \) and \( y \)
in the following diagram


If \( \frac{(x+1)^{2}}{x^{3}+x}=\frac{A}{x}+\frac{B x+C}{x^{2}+1}, \) then
\( \csc ^{-1}\left(\frac{1}{A}\right)+\cot ^{-1}\left(\frac{1}{B}\right)+\sec ^{-1} C= \)
A \( \cdot \frac{5 \pi}{6} \)
B.
c.
D. \( \frac{\pi}{2} \)


The potential of a hydrogen electrode in
a solution with \( \mathrm{pH}=5 \) at \( 25^{\circ} \mathrm{C} \) is:
A \( .+0.059 \)
B. 0.59
c. -0.295
D. 0.295


\( \left[\begin{array}{ccc}1 & 0 & 2 \\ -1 & 1 & -2 \\ 0 & 2 & 1\end{array}\right]+\left[\begin{array}{ccc}5 & 1 & -2 \\ 1 & 1 & 0 \\ -2 & -2 & 1\end{array}\right] \)
What will be the sum of the diagonal
elements of the resultant matrix.
A . 10
B. 6
\( c \)
\( D \)


Assertion
The second dissociation constant of fumaric acid is greater than maleic
acid.
Reason
Higher the dissociation constant of acid
more is the acidic character.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The sides of a triangle (in cm) are given
below:

In which case, the construction of \( \triangle \) is
not possible?
\( A \cdot 8,7,3 \)
B. 8,6,4
c. 8,4,4
D. 7,6,5


Evaluate :
\( \boldsymbol{I}=\int \frac{\boldsymbol{2} \boldsymbol{x}}{\boldsymbol{x}^{2}-\boldsymbol{6} \boldsymbol{x}+\boldsymbol{6}} \boldsymbol{d} \boldsymbol{x} \)


Sprain involves
A. Overstretching of ligament
B. Overstretching of tendon
C. Dislodging of bone
D. Both A and B


State True or False.
Depositive zinc exhibits para-
magnetism due to loss of two electrons from \( 3 d \) -orbital of neutral atom.
A. True
B. False


Select the correct statements for
Ellingharn diagram:
This question has multiple correct options
A. The slope of the curves of the formation of metal oxide is +ve because \( \Delta \hat{G} \) becomes less negative or increases with the rise in temperature
B. Each curve is a straight line except when some change takes place in phase \( (s \rightarrow \operatorname{lor} l \rightarrow g) \)
C. Each curve is not a straight line except when some change takes place in phase \( (s \rightarrow \operatorname{lor} l \rightarrow g) \)
D. The slope of the curves of the formation of metal oxide is -ve because \( \Delta G \) becomes less negative or increases with the rise in temperature


Reproductive leaves are found in
A. Allium
B. Bryophyllum
c. saccharum
D. Argemone


If the \( 6^{t h} \) term in the expansion of
\( \left[\frac{1}{x^{8 / 3}}+x^{2} \log _{10} x\right]^{8} \) is \( 5600, \) then \( x= \)
A . 10
B. 8
\( c \cdot 11 \)
\( D \)


The direction of magnetic lines of forces close to a straight conductor carrying current will be -
A. A long the length of the conductor
B. Radially outward
c. circular in a plane perpendicular to the conductor
D. Helical


A police inspector in a jeep is chasing a pickpocket on a straight road. The jeep is going at a maximum speed \( v \) (assume uniform). The pickpocket rides on the motorcycle of a waiting friend
when the jeep is at a distance \( d \) away
and the motorcycle starts with a constant acceleration \( a \). What should
be the speed of the jeep so that the
pickpocket will be caught?
A \( \cdot v \geq \sqrt{\frac{3}{2} a d} \)
B. \( v \geq \sqrt{2 a d} \)
C \( . v \geq \sqrt{6 a d} \)
D. \( v>2 a d \)


Assertion
A 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


Name the device which is used to
measure temperature.
A. Caloriemeter
B. Thermometer
c. vermier calliper
D. None


I.C.S.H. in male acts on
A. Cells of Leydig
B. Sertoli cells
c. Spermatids
D. spermatogonia


The weight in \( \mathrm{Kg} \) of 13 students in a class are
42.5,47.5,48.6,50.5,49,46.2,49.8,45.8
Find the coefficient of range.
A. 0.077
B. 0.213
c. 0.0803
D. 0.093


The symbol for metre is written as:
A . \( m \)
в. \( M \)
\( c \cdot \mu \)
D. All of the above


Find a G.P. for which sum of the first two
terms is -4 and the fifth term is 4
times the third term.


A sum of \( R s .9600 \) is invested for 3
years at \( 10 \% \) per annum at compound interest, then what is the sum due at the end of the first year?


Under the same conditions of pressure
and temperature, which property is the
same for \( \boldsymbol{H}_{2} \) and \( \boldsymbol{D}_{2} ? \)
A. rate of reaction with other substances
B. average kinetic energy per mole
c. most probable velocity
D. maximum density


A point object is placed at a distance of
\( 20 \mathrm{cm} \) from a thin plano-convex lens of
focal
length \( 15 \mathrm{cm} \), if the plane surface is
silvered. The image will form at:
A. \( 60 \mathrm{cm} \) left of \( A B \)
B. \( 30 \mathrm{cm} \) left of \( A B \)
c. \( 12 \mathrm{cm} \) left of \( A B \)
D. \( 60 \mathrm{cm} \) right of \( A B \)


A ball of mass \( 100 g m \) is hit by hockey stick giving an impulse of \( 0.083 N m \) with what velocity does the ball move?


n the given circuit, find the potential
difference across the 6 \( \mu \) F capacitor in
steady state
4.4
3.22
\( c \cdot 6 v \)
D


Name the process for ethanol to ethene
conversion and reactants used.
A. hydrogenation of ethanol in the presence of concentrated \( H_{2} S O_{4} \)
B. dehydration of ethanol in the presence of concentrated \( H_{2} S O_{4} \)
C. oxidation of ethanol in the presence of concentrated
\( H_{2} S O_{4} \)
D. reduction of ethanol in the presence of concentrated \( H_{2} S O_{4} \)


if \( \frac{1}{1^{2}}+\frac{1}{2^{2}}+\frac{1}{3^{2}}+\ldots . . . . . \) upto \( \infty=\frac{\pi^{2}}{6} \)
\( \operatorname{then} \frac{1}{1^{2}}+\frac{1}{3^{2}}+\frac{1}{5^{2}}+\ldots \)
A \( \cdot \pi^{2} / 8 \)
в. \( \pi^{2} / 12 \)
c. \( \pi^{2} / 3 \)
D . \( \pi^{2} / 9 \)


\( 5 \% \) of a number is \( 9 . \) The number is
A . 45
B. 90
c. 135
D. 180


The percentage increase in the surface area of a cube when each side is increased to \( \frac{3}{2} \) times the original length is
A . 225
в. 200
c. 175
D. 125


A car is moving along a straight line say OP in the figure. It moves from \( \boldsymbol{O} \) to \( \boldsymbol{P} \)
in 18 sec and returns from \( P \) and \( Q \) in
6 sec. What are average velocity of the
car in going from
(a) \( O \) to \( P ?(b) \) from \( O \) to \( P \) and back to
\( Q ? \)
A \( \cdot 10 m s^{-1}, 20 m s^{-1} \)
B . \( 20 \mathrm{ms}^{-1}, 10 \mathrm{ms}^{-1} \)
C \( .10 m s^{-1}, 10 m s^{-1} \)
D \( \cdot 20 m s^{-1}, 20 m s^{-1} \)


The differential equation of system of concentric circles with centres (1,2) is
A \( \cdot \frac{d y}{d x}=\frac{x-1}{x-2} \)
B. \( \frac{d y}{d x}=\frac{x-1}{2-x} \)
c. \( \frac{d y}{d x}=\frac{x-1}{2-y} \)
D. \( \frac{d y}{d x}=\frac{x-1}{y-2} \)


Evaluate: \( i^{24}+\left(\frac{1}{i}\right)^{26} \)
\( A \cdot 0 \)
B.
\( c \cdot-1 \)
D.


The substance known as soda ash is
\( N a_{2} C O_{3} \)
A. True
B. False


\( \lim _{x \rightarrow \infty}\left(\frac{\sqrt{x^{2}+1}}{x}\right) \)


A particle is moving on a circular track with uniform speed. Its motion is
A. periodic and simple harmonic
B. periodic but not simple harmonic
c. damped
D. none of the above


Which of the following lead to pregnancy and development of embryo.
(i) Fertilization of egg
(ii) Maturation of egg
(iii) Release of egg
(iv) Embedding of embryo in thickened uterine wall.

Which of the following options gives the correct order of sequence in which they
occur?
A \( \cdot(i),(i \text { i) },(i i),(i v) \)
B. (ii), (i), (iii), (iv)
\( c \cdot(i),(i v),(i),(\text { iii) }) \)
D. None of the above


An electric bulb is rated \( 220 V \) and
\( 100 W, \) when it is operated on \( 110 V \)
the power consumed will be
A . \( 100 \mathrm{W} \)
в. \( 75 \mathrm{W} \)
\( \mathbf{c} .50 W \)
D. \( 25 W \)


If \( \boldsymbol{y}(\boldsymbol{n})=\boldsymbol{e}^{\boldsymbol{x}} \boldsymbol{e}^{\boldsymbol{x}^{2}} \ldots \boldsymbol{e}^{\boldsymbol{x}^{n}}, \boldsymbol{0}<\boldsymbol{x}<1 . \) Then
\( \lim _{n \rightarrow \infty} \frac{\boldsymbol{d} \boldsymbol{y}(\boldsymbol{n})}{\boldsymbol{d} \boldsymbol{x}} \) at \( \boldsymbol{x}=\frac{\mathbf{1}}{\mathbf{2}} \) is
\( A \cdot e \)
в. \( 4 € \)
\( c \cdot 2 e \)
D. \( 3 e \)


The triangle formed by the points \( A \) ( \( 2 a \), 4a),B (2a,6a) and C (2a+\sqrt{3a,5a) is : }
A. right angled
B. isosceles
c. equilateral
D. None of these


If for a gas \( \frac{\boldsymbol{R}}{\boldsymbol{C}_{\boldsymbol{V}}}=\mathbf{0 . 6 7}, \) this gas is made
up of molecules which are.
A. Monatomic
B. Diatomic
c. Polyatomic
D. Mixture of diatomic and polyatomic molecules


What is correct about mean value
theorem?
A. It states that given a planar arc between two endpoints, there is at least one point at which the tangent to the arc is parallel to the secant through its endpoints.
B. It tells us when certain values for the derivative must
exist.
C. Both A and B
D. Only B


The inversion temperature \( \boldsymbol{T}_{\boldsymbol{i}}(\boldsymbol{K}) \) of
hydrogen is:
[Given: Van der Waal's constants a and b
\( \operatorname{are} 0.244 \operatorname{atm} L^{2} m o l^{-2} \) and
\( \left.0.027 L m o l^{-1} \text {respectively }\right] \)
A \( \cdot 440 \)
в. 220
c. 110
D. 330


Endocrine structure of kidney is
A. Cortex
B. Medulla
c. Juxtaglomerular apparatus
D. Pelvis


The molecular formula of a
compound having a molecular weight of 92 and containing \( 30.5 \% \) of nitrogen
and \( 69.5 \% \) of oxygen by weight is:
A. \( N_{2} O_{4} \)
is
в. \( N O_{2} \)
\( \mathrm{c} \cdot N_{2} O_{3} \)
D. \( N_{2} \) O


Ascending imbricate corolla is found in
A. Pisum
B. Tamarindus
c. Mimosa
D. Datura


A point object is placed at distance of \( 20 \mathrm{cm} \) from a lens as shown in figure.
The position of final image from the
lens is


Find the coordinates of the focus axis of
the parabola the equation of directrix
and the length of the latus rectum for \( y^{2} \)
\( =-8 x \)


Urn \( A \) contains 6 red and 4 black balls
and urn \( B \) contains 4 red and 6 black
balls. One ball is drawn at random from
urn \( A \) and placed in urn \( B \). Then one bal
is drawn at random from urn \( B \) and
placed in urn \( A \). If one ball is now drawn at random from urn \( A \), the probability
that it is found to be red is \( 4 k / 55 . \) Find
the value of \( k \)


The number of solutions of \( 3 \sec \theta-5= \)
\( 4 \tan \theta \operatorname{in}[0,4 \pi] \) be \( k . \) Find \( k ? \)


A particle is an linear simple harmonic motion between two extreme point \( \mathbf{A} \) and B. \( 10 \mathrm{cm} \) apart(See figure below) If the direction from \( A \) to \( B \) is taken as
positive direction, what are signs of displacement \( x, \) velocity \( V \) and acceleration a, when the particle is at
\( \mathbf{A} ? \)
A \( . x=-v e, V=-v e, a=-v e \)
в. \( x=+v e, V=0, a=-v e \)
c. \( x=+v e, V=-v e, a=+v e \)
D. \( x=-v e, V=0, a=+v e \)


A particle is moved from (0,0) to \( (a, a) \) under a free force \( \overrightarrow{\boldsymbol{F}}=(3 \hat{\boldsymbol{i}}+4 \hat{\boldsymbol{j}}) \) from
two paths, I is OP and path 2 is OQP. Let
\( W_{1} \) and \( W_{2} \) be the work done by this force in these two paths. Then:
A. \( W_{1}=W_{2} \)
в. \( W_{1}, W_{2} \)
c. \( W_{2}-2 W_{1} \)
D. \( W_{2}-4 W_{1} \)


If a is A symmetric matrix and B is a skew symmetric matrix such that \( \boldsymbol{A}+ \) \( B=\left[\begin{array}{cc}2 & 3 \\ 5 & -1\end{array}\right], \) then \( A B \) is equal to?
A. \( \left[\begin{array}{ll}-4 & 2 \\ 1 & 4\end{array}\right] \)
B. \( \left[\begin{array}{cc}-4 & -2 \\ -1 & 4\end{array}\right] \)
\( \mathbf{c} \cdot\left[\begin{array}{cc}4 & -2 \\ -1 & -4\end{array}\right] \)
D. \( \left[\begin{array}{ll}4 & -2 \\ 1 & -4\end{array}\right] \)


A body at rest starts from a point at a distance \( r(>R) \) from the center of the
earth. If \( \mathrm{M} \) and \( \mathrm{R} \) stand for the mass and
the radius of earth respectively, then the speed of the body when it reaches the Earth surface is
\( ^{\mathrm{A}} \cdot \sqrt{\frac{2 G M}{R}} \)
в. \( \sqrt{\frac{2 G M}{R-r}} \)
c. \( \sqrt{\frac{2 G M(r-R)}{R r}} \)
D. zero


Assertion
Noble gases are considered unreactive
elements.
Reason
Group 18 elements have complete octet
except Helium.
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


Read the statements 1 and 2 . Choose the
correct option:
Statement 1: RNAi take place in all prokaryotic and eukaryotic organisms as a method ofcellular defence.

Statement 2: RNA interference is a pre-
translational process.
A. Both statements are correct
B. Statement I correct, statement 2 incorrect
c. Both statements are incorrect
D. Statement-1 incorrect, statement 2 correct.


What is incorrectly matched?
\( \mathbf{A} \cdot C s B r_{3} \rightleftharpoons C s^{\oplus}+B r_{3}^{\ominus} \rightleftharpoons C s^{\oplus}+B r^{\ominus}+B r_{2} \)
B \( \cdot I_{4} O_{9} \rightleftharpoons I^{3}+3\left(I O_{3}\right)^{\ominus} \)
\( \mathbf{c} \cdot A g B r O_{3} \rightleftharpoons A g^{\oplus} B r_{3}^{\ominus} \)
\( \mathbf{D} \cdot I_{2} O_{4} \rightleftharpoons I O_{2}^{\oplus}+I O_{2}^{\ominus} \)


In \( K O_{2}, \) the nature of oxygen species
and the oxidation state of oxygen atom
are, respectively.
A. Superoxide and -1
B. superoxide and - \( \frac{1}{2} \)
c. peroxide and \( -\frac{1}{2} \)
D. Oxide and -2


Find mode for given data:
\( \begin{array}{lllll}\text { Class } & 20- & 30- & 40- & 50- \\ 29 & 39 & 49 & 59 \\ \text { Frequency } & 15 & 20 & 50 & 30\end{array} \)


The relative reactivity of \( 1^{\circ} H, 2^{\circ} H \) and
\( 3^{\circ} H \) in bromination reaction has been
found to be 1: 82: 1600 respectively. In
the reaction the percentage yields of the products (A) and (B) are expected to be:
\( (A) \)
A . 99.4\%, 0.6\%
B . 50\%, 50\%
c. 0.6\%, 99.4\%
D. 80\%, 20\%


Tonoplast is
A. Permeable membrane
B. Semi permeable membrane
C. Impermeable membrane
D. Selectively permeable membrane


\( \mathbf{A} \)
\( 60 \mathrm{kg} \) mass is pushed with a enough
force to start it moving and the same force is continued to act afterward. If
the coefficient of static friction and
sliding friction are 0.5 and 0.4 respectively, then the acceleration of
the body will be
A \( \cdot 1 \mathrm{ms}^{-2} \)
B. \( 3.9 \mathrm{ms}^{-2} \)
c. \( 4.9 \mathrm{ms}^{-2} \)
D. \( 6 m s^{-2} \)


Which gas creates greenhouse effect in the atmosphere?


Let \( \omega \) be a complex cube root of unity
with \( \omega \neq 1 . \) A fair die is thrown three
times. If \( r_{1}, r_{2} \) and \( r_{3} \) are the numbers
obtained on the die then the probability
that \( \omega^{r_{1}}+\omega^{r_{2}}+\omega^{r_{3}}=\mathbf{0} \) is
A \( \cdot \frac{1}{18} \)
в. \( \frac{1}{9} \)
\( c \cdot \frac{2}{9} \)
D. \( \frac{1}{36} \)


Highly volatile metal is:
\( A \cdot v \)
B. cr
\( c . \) мn
D. zn


According to Oswald Tippo, Angiosperms are placed under
A. Atracheata
B. Thallophyta
c. Tracheophyta
D. spermatophyta


The activity of a radioisotope falls to \( 12.5 \% \) in 90 days. The half-life of the isotope is \( 5 X . \) Then \( X \) is:


0.1 mole of \( N_{2} O_{4}(g) \) was sealed in a
tube under one atmospheric conditions
at \( 25^{0} C . \) Calculate the number of moles
of \( N O_{2}(g) \) present, if the equilibrium \( N_{2} O_{4}(g) \rightleftharpoons 2 N O_{2}(g)\left(K_{p}=0.14\right) \) is
reached after some time.
A \( .1 .8 \times 10^{2} \)
B . \( 2.8 \times 10^{2} \)
c. 0.034
D. \( 2.8 \times 10^{-2} \)


If it rains a dealer in rain coats can earn
Rs.500/- a day. If it is fair he will lose Rs. \( 40 /- \) a day. His mean profit if the probability of a fair day is 0.6 is:
A. Rs. \( 230 /- \)
B. Rs. \( 460 /- \)
c. Rs. \( 176 /- \)
D. Rs. 88/-


Write the following equation in the general form of a linear equation in two variables:
\( 7 x=3 y+23 \)


In figure, \( A, B, C \) are collinear points.
Name two linear pairs.


What is the velocity of centre of mass after the collision?
\( A \cdot \vec{V}_{0} \)
в. \( \frac{\vec{V}_{0}}{3} \)
\( c \cdot \frac{\vec{V}_{0}}{6} \)
\( D \)


The chemical which are produced by
host plants due to infection as a defence reaction to pathogen, are called
as
A. Phytotoxin
B. Toxin
c. Phytotron
D. Phytoalexins


How does surface tension of a liquid
vary with temperature?
or
Define v viscosity of fluid, write its \( \mathrm{S} \)
unite.


When two individual of \( \mathrm{F} 1 \)
generation are crossed with each other the phenomenon is called
A. Test cross
B. Back cross
c. Self cross
D. None of the above


Assertion
A given transformer can be used to
step-up or step-down the voltage
Reason
The output voltage depends upon the
ratio of the number of turns of the two
coils of the transformer
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