Use the given figure to find \( n\left(A^{\prime}\right) \)
Given, \( n(\xi)=52, n(A)=43 \) and
\( \boldsymbol{n}(\boldsymbol{B})=\mathbf{2 7} \)


Identify the correct Lewis symbol from the following:
\( A \)
\[
\cdot \mathrm{C}
\]
в. \( \bullet \dot{O} \)
\( c \)
\[
\mathbf{B}
\]
\( D \)
\( \mathbf{N} \)


\( N a+C l \rightarrow N a^{+}+C l^{-} \rightarrow N a^{+} C l^{-} \)
(2,8,1)(2,8,7)(2,8)(2,8,8)
The above equation represents the
formation of sodium chloride. Observe
the equation and answer the following:
a) How many electrons are transferred
from \( N a \) to \( C l ? \)
b) Name the force acting between \( N a^{+} \)
and \( C l^{-} \)
c) Name the nearest noble gas to \( C l^{-} \)
d) Name the bond between \( N a^{+} \) and
\( \boldsymbol{C l}^{-} \)
e) How many electrons are present in
\( N a^{+} \) ion?


Choose the correct statement from the
following.
This question has multiple correct options
A. Liquor ammonia and soda water are examples of liquid-gas type mixtures.
B. Mixture of coconut oil and water can be separated using separating funnel
C. A mixture of iodine and sulphur can be separated using magnetic separation.
D. A mixture of sand and sawdust can be separated using solvent extraction.


Upon hydrolysis, which of the following carbides evolve saturated hydrocarbon gas? This question has multiple correct options
A. \( C a C_{2} \)
в. \( A l_{4} C_{3} \)
c. \( M g_{2} C_{3} \)
D. \( B e_{2} C \)


Seeta is moving due east with a velocity of \( 1 \mathrm{m} / \mathrm{s} \) and Geeta is moving due west with a velocity of \( 2 \mathrm{m} / \mathrm{s} \). What is the
velocity of Seeta with respect of Geeta?


Match the entries of column-I with
appropriate entries of column-II
Column(Metal to be \( \quad \) (Method used for extracted) \( \quad \) reduction of oxide
(i) Reduction with
(A) Iron or Zinc \( \quad \) aluminium
(B) Manganese or
(ii) Reduction with Carbon Chromium
(C) Mercury
(iii) Electrolytic reduction
(D) Aluminium
(iv) Reduction of heating alone
A \( .(A) \longrightarrow(i v) ;(B) \longrightarrow(i) ;(C) \longrightarrow(i i) ;(D) \longrightarrow(i i i) \)
B. \( (A) \longrightarrow(i i i) ;(B) \longrightarrow(i) ;(C) \longrightarrow(i v) ;(D) \longrightarrow(i i) \)
c. \( (A) \longrightarrow(i i) ;(B) \longrightarrow(i) ;(C) \longrightarrow(i v) ;(D) \longrightarrow(i i i) \)
D. \( (A) \longrightarrow(i) ;(B) \longrightarrow(i i) ;(C) \longrightarrow(i i i) ;(D) \longrightarrow(i v) \)


A block slides down an inclined plane of
angle \( 45^{0} \) with constant velocity. If it is
then projected up the same plane with velocity \( 10 m s^{-1}, \) then \( \left[g=10 m s^{-2}\right] \)
a. the retardation while going up is \( 10 \sqrt{2} m s^{-2} \)
b. it comes to rest after moving up for
\( \frac{1}{\sqrt{2}} \mathbf{S} \)
c. it comes to rest after moving up for \( \sqrt{2} \) s.
d. coefficient of friction is 0.5
A. a, b \& dare correct
B. a, c \& dare correct
c. a \& b are correct
D. c \& dare correct


\( 50 L t r \) of a certain liquid is confined in a piston system at the external pressure 100atm. This pressure is suddenly released and liquid is expanded against the constant atmospheric pressure, volume of the liquid increases by 1 Lt \( r \) and the final pressure of the liquid is
100 atm. Find the work done.
A. 1 L. \( a+m \)
B. 5 Latm
c. 500 Latm
D. 50 L.atm


For the reaction:
\( \mathbf{2} N \boldsymbol{H}_{3}(\boldsymbol{g}) \rightarrow \boldsymbol{N}_{2}(\boldsymbol{g})+\mathbf{3} \boldsymbol{H}_{2}(\boldsymbol{g}) \)
if rate of disappearance of of \( \boldsymbol{N} \boldsymbol{H}_{3} \) is
\( 1.7 g m / s e c \) then rate of appearance of
\( N_{2} \) should be:
A \( .0 .85 \mathrm{gm} / \mathrm{sec} \)
B. 3.4 gm/sec
c. \( 1.4 g m / \)sec
D. \( 0.7 \mathrm{gm} / \mathrm{sec} \)


If \( f(x)=x^{4}-2 x^{3}+3 x^{2}-a x+b \) is a
polynomial such that when it is divide by \( (x-1) \) and \( (x+1) \) the remainders
are 5 and 19 respectively the remainder when \( f(x) \) is divisible by \( (x-2) \) is
\( A \cdot 7 \)
B. 8
c. 9
D. 10


The magnitude of the magnetic moment (spin only) of \( \left[N i C l_{4}\right]^{2-} \) will be?
A. 2.82 В.M.
B. 3.25B.M.
c. 1.23 В.М.
D. 5.64 В.М.


Fill in the blanks.
Boiling point of nitrogen


Sum of 4 numbers in GP is \( 60 . \) And the
AM of first and last no. is 18 find the
first term and common difference of the
\( \mathrm{GP} \)
This question has multiple correct options
A \( . a=4, r=2 \)
B. \( a=32, r=\frac{1}{2} \)
c. \( a=3, r=1 \)
D. \( a=6, r=3 \)


What conclusion was drawn by Rutherford based on Geiger-Marsden's experiment on scattering of alpha particles?


Among the following, identify the species with an atom in +6 oxidation
state.
\( \mathbf{A} \cdot\left[M n O_{4}\right]^{-} \)
B . \( \left[\operatorname{Cr}(C N)_{6}\right]^{3-} \)
\( \mathrm{c} \cdot \mathrm{Cr}_{2} \mathrm{O}_{3} \)
D. \( \operatorname{Cr} \mathrm{O}_{2} \mathrm{Cl}_{2} \)


Write short notes on, (a) Biological concentration and magnification,
(b)DDT,
(C) Bordeaux mixture, (d)
IPM,
(e) Natural insecticides,
(f) Biopesticides,
(g) Bioinsecticides


For what value of \( x, 8 x^{2}-7 x+2 \) has
the minimum value?


\( C-O-C \) bond in ethers can be
cleaved by:

This question has multiple correct options
A \( . H_{2} S O_{4} \)
B. \( L i A I H_{4} \)
c. \( K O H \)
D. \( H I \)


Gold is extracted by hydrometallurgical process, based on its property:
A. of being electropositive
B. of being less reactive
c. to form complex which are water soluble
D. None of these


Which of the following compounds has colour but no unpaired electrons?
A. \( K M n O_{4} \)
в. \( K_{2} M n O_{4} \)
\( \mathrm{c} . \) MnSO \( _{4} \)
D. \( M n C l_{2} \)


Factorise: \( 8 a^{3}+b^{3}+12 a^{2} b+6 a b^{2} \)
A \( \cdot(2 a+b)(2 a+b)(2 a+b)(2 a+b)(2 a+b)(2 a+b) \)
B. (2ab)(2a+b)(2a+b)(2ab)(2a+b)(2a+b)
\( c \cdot(2 a-b)(2 a+b) \)
\( D \cdot(2 a+b)(2 a+b) \)


Which of the following will occur if a 1.0 M solution of a weak acid is diluted to
\( 0.01 \mathrm{M} \) at constant temperature:
A. Percentage ionisation will increase
B. [H+] will decrease to 0.01 M
c. \( K_{a} \) will increase
D. pH will decrease by 2 units


The coefficient of friction between a
car's wheels and a roadway is \( 0.5 . \) The least distance in which the car can
accelerate from rest to a speed of 72
\( \boldsymbol{k m p h} \) is \( \left(\boldsymbol{g}=\mathbf{1 0} \boldsymbol{m s}^{-2}\right) \)
A . \( 10 m \)
в. \( 20 m \)
\( c .30 m \)
D. \( 40 m \)


Nuclear power plant is example of invention related to which field?
A. Electricity
B. Education
c. E learning
D. Medication


\( \frac{1}{\boldsymbol{x}^{4}+1}= \)
A. \( \quad\left[\frac{x+\sqrt{2}}{2 \sqrt{2} \sqrt{2}} \frac{x+\sqrt{2}}{2 \sqrt{2}\left(x^{2}-\sqrt{2} x+1\right)}\right] \)
B. \( \quad\left[\frac{x+\sqrt{2}}{x^{2}+\sqrt{2} x+1}-\frac{x+\sqrt{2}}{\left(x^{2}-\sqrt{2} x+1\right)}\right] \)
C \( \quad\left[\frac{x+\sqrt{2}}{2 \sqrt{2}\left(x^{2}+\sqrt{2} x+1\right)} \frac{\sqrt{2}-x}{(-\sqrt{2})}\right] \)
D. \( \frac{1}{2 \sqrt{2}}\left[\frac{x+\sqrt{2}}{\left(x^{2}+\sqrt{2} x+1\right)}+\frac{\sqrt{2}-x}{\left(x^{2}-\sqrt{2} x+1\right)}\right] \)


symmetrical container. Four pistons of
equal area \( A \) are used at the four
openings to keep the water in
equilibrium. Now an additional force \( \boldsymbol{F} \)
is applied at each piston. The increase
in the pressure at the center of the
container due to this addition is
Fig. 4.191
\( A \cdot F \)
\( \bar{A} \)
B. \( \underline{2 F} \)
\( \bar{A} \)
c. \( \frac{4 F}{A} \)
\( D \)


Fascicular cambium found in dicot
stem is a
A. Secondary meristem
B. Primary meristem
c. Intercalary meristem
D. Apical meristem


The unit of Radiation exposure is?


Find the product of three consecutive
odd integers, if one of them is \( (2 m+1) \)


On passing a current through molten KCI \( 19.5 \mathrm{g} \) of \( \mathrm{K} \) is deposited. The amount of \( \mathrm{Al} \) deposited by the same quantity of electricity if passed through molten AlCl
is :
A. \( 4.5 \mathrm{g} \)
B. \( 9.0 \mathrm{g} \)
c. \( 13.5 \mathrm{g} \)
D. 27 g


n the figure given below, \( \Delta B C A \cong \)
\( \Delta B C D . \) Corresponding angle to \( \angle D \) is
\( A \cdot \angle B \)
B. \( \angle C \)
\( c . \angle D \)
0.4


For the process of photosynthesis, all except one of the following items are essential. Point out the exceptions.
A. Water and mineralss
B. Light and chlorophyıl
c. \( \mathrm{co}_{2} \) and optimum temperature
D. Oxygen and sucrose


Let \( \mathbf{S}=\{1,2,3,4\} . \) The total number of unordered pairs of disjoint subsets of \( \mathbf{S} \) is equal to
A . 25
B. 34
\( c \cdot 42 \)
D. 41


A clock fixed on a wall shows time 04:
\( 25: 37 . \) Its image in a plane mirror shows:
\( A \cdot 07: 30: 33 \)
B. 07:43: 32
c. 07: 35: 22
D. 43: 27: 36


Which of the following has pseudo-inert gas configuration in the \( (n-1) \) shell?
A. Typical transition elements
B. Zinc group elements
c. Both of the above
D. None of the above


If \( \tan \left(45^{\circ}+\theta\right)=\sqrt{3} \) and \( 0<\theta<20^{\circ} \)
then the value of \( \theta \) is
A \( .10^{\circ} \)
B . \( 15^{\circ} \)
\( c \cdot 20 \)
D. \( 5^{\circ} \)


Loop of Henle is connected with
A. Dilution of urine
B. Removal of water
c. counter current multiplier system
D. Remove salt


Calculate the concentration of \( \boldsymbol{O} \boldsymbol{H}^{-} \)
ions of \( 0.01 M N H_{4} O H \) solution. The
equilibrium constant of \( N H_{4} O H \) is
\( 1.8 \times 10^{-5} \)


Which congruence criterion do you use
in the following?
Given \( A C=D F, A B=D E, B C=E F, \) so \( \Delta A B C \)
\( \cong \Delta D E F \)


Identify the pollutant gases largely responsible for the discoloured and lustreless nature of marble of the Taj Mahal.
A. \( C O_{2} \) and \( N O_{2} \)
в. \( S O_{2} \) and \( N O_{2} \)
\( \mathrm{c} \cdot \mathrm{O}_{3} \) and \( \mathrm{CO}_{2} \)
\( \mathrm{D} \cdot \mathrm{SO}_{2} \) and \( \mathrm{O}_{3} \)


Solve: \( \frac{-\mathbf{7 P}+\mathbf{1 3}}{\mathbf{6}}=\mathbf{2 P}-\mathbf{1} \)


Which statement is correct regarding
mosses?
A. They have dominant and independent sporophyte.
B. Their antherozoids require water for fertilization.
C. Their archegonia produce many eggs.
D. Their antherozoids are multiflagellated.


Construct \( \triangle P Q R \) such that \( P Q=5 \)
\( \mathrm{cm}, Q R=3 \mathrm{cm} \) and \( \angle Q=95^{\circ} \)


A boy is swinging on a swing such that his lowest and highest position are at heights of \( 2 m \) and \( 4.5 m \) respectively. His velocity at the lowest position is
A \( .2 .5 m s^{-} \)
B. \( 7 m s^{-1} \)
\( \mathrm{c} \cdot 14 \mathrm{ms}^{-1} \)
D. \( 20 m s^{-1} \)


Which of the following process of maintains the existence of the species
on the earth?
A. Metabolism
B. Reproduction
c. Adaptation
D. None of the above


In above shown figure of refrigeration
system. Which of the following
statement explains why work is an input into this system?
A. Work is needed to move thermal energy against temperature gradient.
B. Work is needed to reduce the amount of thermal energy lost during transfer.
c. work uses energy from the cold reservoir to reduce the temperature of the system.
D. Work adds energy to the cold reservoir to increase the flow to the hot reservoir.
E. Work adds heat to the system, causing the temperature of both reservoirs to increase.


Through a non-uniform pipe, a nonviscous liquid is flowing from section \( \mathbf{A} \) to B as shown in figure.Which of following is correct?
A. since liquid is flowing from A to B, therefore, pressure at A is greater than at
B. Velocity at B is greater than that at
C. Total energy per unit volume of the liquid is greater at than that at
D. Axis of pipe can be horizonta


Which of the following reactions does
not show the correct products of the
reaction?
\( \mathbf{A} \cdot C H_{3}-C H=C H_{2} \frac{H B r}{\text {Peroxide}} C H_{3}-C H_{2}-C H_{2} B r \)
B \( \cdot C H_{3}-C H=C H_{2} \frac{H C l}{\text {Peroxide}} C H_{3}-C H_{2}-C H_{2} C l \)
C. \( \quad B r \)
\[
C H_{3}-C H=C H_{2} \stackrel{H B r}{\longrightarrow} C H_{3}-C H-C H_{3}
\]
D. \( C H_{3}-C H=C H_{2} \stackrel{H C l}{\longrightarrow} C H_{3}-C H-C H_{3} \)
\( C l \)


Solve the following pair of an equation by elimination the coefficient method:
\( x+2 y=11 \)
\( 2 x-y=2 \)


A polygon with minimum number of
sides is called as ?
A. pentagon
B. square
c. triangle
D. angle


The absolute maximum and minimum
value of \( \boldsymbol{f}(\boldsymbol{x})=\sin \boldsymbol{x}+\cos \boldsymbol{x}, \boldsymbol{x} \in[\mathbf{0}, \boldsymbol{\pi}] \)
are respectively
A \( \cdot \sqrt{2},-1 \)
B. \( \sqrt{2}, 1 \)
c. \( \sqrt{2},-\sqrt{2} \)
D. \( \sqrt{3}, \sqrt{2} \)


In the Davisson and Germer experiment, the velocity of electrons emitted from
the electron gun can be increased by
A. increasing the potential difference between the anode and filament
B. increasing the filament current
c. decreasing the filament current
D. decreasing the potential difference between the anode and filament


A bag of wheat weighs 100 kg. To what height should it be raised, so that its potential energy may be \( 9800 \mathrm{J}(g= \)
\( \left.9.8 m s^{-2}\right) \)


The 'pupil' in human eye can be dilated by:
A . retina
B. choroid
c. optic nerve
D. iriss


In a first-order reaction, \( \boldsymbol{A} \longrightarrow \boldsymbol{B} \), if \( \boldsymbol{k} \) is
rate constant and initial concentration
of the reactant \( A \) is \( 0.5 ~ M \) then half-life
is:
A \( \cdot \frac{\log 2}{k} \)
в. \( \frac{\log 2}{k \sqrt{0.5}} \)
\( c \cdot \frac{\ln 2}{k} \)
D. \( \frac{0.693}{0.5 k} \)


A triangle and a parallelogram have the same base and some area. If the sides
of the triangle are \( 26 \mathrm{cm}, 28 \mathrm{cm} \) and 30 \( \mathrm{cm} \) and the parallelogram stands on the
base \( 28 \mathrm{cm} . \) Find the height of the parallelogram.


f point \( (x, y) \) is equidistant from points
(7,1) and (3,5) show that \( y=x-2 \)


What do you mean by elastic bodies and plastic.


Describe the different types of hydrides which are formed.


In the metallurgy of sodium by electrolysis, excess of calcium chloride is mixed with sodium chloride to:
A. make the latter a good conductor
B. make the latter soft
c. generate more energy for the electrolytic cell
D. assist liquefaction of the latter at a much lower temperature


Metal was formed under high
temperature and pressure from:
A. black rock and iron
B. burnt rocks and clay
C. marine matter
D. giant forests and vegetable matter


Which set of terms correctly identifies the carbohydrate shown?
(1) Pentose
(2) Pentulose
(3) Hexulose
(4) Hexose
(5) Aldose
(6) Ketose
Pyranose
(8) Furanose
A. 2,6,8
в. 2,6,7
\( c \cdot 1,5,8 \)
D. A set of terms other than these


\( 4 g m s \) of steam at \( 100^{\circ} \mathrm{C} \) is added to
\( 20 g m s \) of water at \( 46^{\circ} \mathrm{C} \) in a container
of negligible mass. Assuming no heat is lost to surrounding, the mass of water in container at thermal equilibrium is.
Latent heat of vaporisation \( = \)
\( \mathbf{5 4 0} \) cal / gm. Specific heat of water \( = \)
\( \mathbf{1} \boldsymbol{c a l} / \boldsymbol{g m}-^{\circ} \boldsymbol{C} \)
\( \mathbf{A} \cdot 18 g m \)
в. \( 20 g m \)
c. \( 22 g m \)
D. \( 24 g m \)


The angle of dip at equator is
\( \mathbf{A} \cdot 0^{\circ} \)
В . \( 45^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 90^{\circ} \)


Simplify : \( \left(\frac{3}{2} x-0.45 y\right)^{2} \)
A. \( 2.25 x^{2}-1.35 x y+0.2015 y^{2} \)
B. \( 2.15 x^{2}-1.35 x y+0.2025 y^{2} \)
c. \( 2.25 x^{2}-1.35 x y+0.2025 y^{2} \)
D. \( 2.25 x^{2}-1.25 x y+0.2025 y^{2} \)


Which of the following carbonyl compounds is most polar?
A. \( C_{2} H_{5}-\stackrel{I}{C}-C_{2} H_{5} \)
B. \( \quad o \)
\( C H_{3}-C-C H_{3} \)
c.
\[
C H_{3}-C-H
\]
D.
\[
H-C-H
\]


The resistance of a coi is \( 4.2 \Omega \) at
\( 100^{\circ} \mathrm{C} \) and the temperature coefficient
of resistance of its material is
\( 0.004 /^{\circ} \mathrm{C} . \) Its resistance at \( 0^{\circ} \mathrm{C} \)
A . \( 6.5 \Omega \)
B. 3\Omega
\( c .5 \Omega \)
D. 4\Omega


A small object is placed 5 U cm to the
left of a thin convex lens of focal length
\( 30 \mathrm{cm} . \) A convex spherical mirror of
radius of curvature \( 100 \mathrm{cm} \) is placed to
the right of the lens at a distance of
\( 50 \mathrm{cm} . \) The mirror is tilted such that the
axis of the mirror is at an angle \( \boldsymbol{\theta}=\mathbf{3 0}^{\circ} \)
to the axis of the lens, as shown in
figure. If the origin of the coordinates system is
taken to be at the centre of the lens, the
coordinates \( (\text { in } c m) \) of the point \( (x, y) \)
at which the image is formed are
\( \mathbf{A} \cdot(28 \mathrm{cm}, 38 \mathrm{cm}) \)
B . \( (125 / 3,25 / \sqrt{3}) \)
C. \( (50-25 \sqrt{3}, 25) \)
D. \( 0, \)


The truth table given is for which gate?
\( \begin{array}{ccc}\mathbf{A} & \mathbf{B} & \mathbf{Y} \\ 0 & 0 & 1 \\ 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0\end{array} \)
\( A \cdot X O R \)
B. OR
C . AND
D. NAND


A three-digit code for certain locks uses the digits 0,1,2,3,4,5,6,7,8,9
according to the following constraints. The first digit cannot be 0 or 1 the second digit must be 0 or \( 1, \) and the second and third digits cannot both be
0 in the same code. How many different codes are possible?
A. 144
в. 152
c. 160
D. 168
E. 176


Two capillaries of same length and radii in the ratio 1: 2 are.connected in series.
A liquid flows through them in streamlined condition. If the pressure across the two extreme ends of the combination is \( 1 \mathrm{m} \) of water, the pressure difference across first
capillary is
\( A \cdot 9.4 \mathrm{m} \)
B. 4.9 \( m \)
c. \( 0.49 \mathrm{m} \)
D. 0.94 m


A ball of mass \( m \) is thrown upward and
another ball of same mass is thrown
downward so as to move freely under
gravity. The acceleration of centre of mass is
\( \mathbf{A} \cdot g \)
B. \( \frac{g}{2} \)
\( c \cdot 2 g \)
D. Zero


Which of the following descriptions apply
to a lightning conductor?
A. It is usually fixed at the top of tall buildings
B. It has several metal stripes connected to a copper strip
C. One end of the conductor is buried deep under the ground
D. All of the above


The two surfaces \( A \) and \( B \) are at the same
potential and separated by a distance \( r \) The work done in carrying a charged particle \( (q) \) from \( A \) to \( B \) will be:
A \( \cdot \frac{K q}{r^{2}} \)
в. \( \frac{K q}{r} \)
c. \( -\frac{K q}{r} \)
D. zero


A motor car is moving with the speed of
\( 20 m s^{-1} \) on a circular track of radius
\( 100 \mathrm{m} . \) If its speed is increasing at the
rate of \( 3 m s^{-} 2, \) the resultant
acceleration is
\( A \cdot 3 m s^{-2} \)
B. \( 5 m s^{-2} \)
c. \( 2.5 m s^{-2} \)
D. \( 3.5 m s^{-2} \)


Which of the following term means the difference between the mass of the
nucleus and the sum of each individual
nucleon?
A. mass defect
B. nucleon difference
c. nucleon defect
D. mass difference
E. nuclear difference


Let \( A_{1}, A_{2} \) and \( A_{3} \) be subsets of a set \( X \)
Which one of the following is correct?
A. \( A_{1} \cup A_{2} \cup A_{3} \) is the largest subset of \( X \) containing
elements of each of \( A_{1}, A_{2} \) and \( A_{3} \)
B. \( A_{1} \cup A_{2} \cup A_{3} \) is the smallest subset of \( X \) containing
either \( A_{1} \) or \( A_{2} \cup A_{3} \) but not both
C. The smallest subset of \( X \) containing \( A_{1} \cup A_{2} \) and \( A_{3} \)
equals the smallest subset of \( X \) containing both \( A_{1} \) and \( A_{2} \cup A_{3} \) only if \( A_{2}=A_{3} \)
D. None of these


In the figure \( P Q \) is tangent to the circle
at \( p t \)
Find the radius, if \( P Q=8 \mathrm{cm} \) and
\( \boldsymbol{O} \boldsymbol{R}=\mathbf{1 0} \boldsymbol{c m} \)


Transfusion tissue replaces the veins in
A. Cycas and Ferns
B. Cycas and Pinus
c. cycas
D. Selaginella


The temperature of a radiating body increase by \( 30 \% \). Then the increase in the amount of radiation is
\( \mathbf{A} \cdot 185 \% \)
B. \( 285 \% \)
c. \( 325 \% \)
D. \( 130 \% \)


Which of the following cannot be dissolved in water?
A . Ice
B. Sugar
c. wood
D. salt


The IUPAC name of
\( \left[\boldsymbol{F e}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{5}(\boldsymbol{N O})\right] \boldsymbol{S} \boldsymbol{O}_{4} \) is penta
aquanitrosylium iron
(I) sulphate.
A. True
B. False


The vector \( \bar{x} \) which is perpendicular to
(2,-3,1) and (1,-2,3) and which satisfies the condition
\( \bar{x}(\bar{i}+\overline{2} \bar{j}-7 k)=10 \) is


Left \( \boldsymbol{f} \) be an odd function defined on the
set of real numbers such that for \( x \geq \)
\( \mathbf{0}, \boldsymbol{f}(\boldsymbol{x})=\mathbf{3} \sin \boldsymbol{x}+\mathbf{4} \cos \boldsymbol{x} \)
Then \( f(x) \) at \( x=-\frac{11 \pi}{6} \) is equal to
A \( \cdot-\frac{3}{2}-2 \sqrt{3} \)
B. \( \frac{3}{2}-2 \sqrt{3} \)
c. \( \frac{3}{2}+2 \sqrt{3} \)
D. \( -\frac{3}{2}+2 \sqrt{3} \)


Which of the following gases is responsible for the flame at the mouth of Bessemer converter?
A. Carbon monoxide
B. Carbon dioxide
c. Chlorine
D. oxygen


A projectile at any instant during its
flight has velocity \( 5 ~ m / s \) at \( 30^{\circ} \) above
the horizontal. How long after this
instant, will it be moving at right angle to the given direction?


The function \( \boldsymbol{f}(\boldsymbol{x})=\log _{e}\left[\boldsymbol{x}^{3}+\sqrt{\boldsymbol{x}^{6}+\mathbf{1}}\right] \)
is an
This question has multiple correct options
A. even function
B. odd function
c. increasing function
D. decreasing function


The maximum number of different
possible non-zero entries in a skew-
symmetric matrix of order 'n' is
A \( \cdot \frac{1}{2}\left(n^{2}-n\right) \)
B \( \cdot \frac{1}{2}\left(n^{2}+n\right) \)
\( c \cdot n^{2} \)
D. \( \left(n^{2}-n\right) \)


Subtract \( 0.2 J \) from \( 7.26 J \) and express
the result with correct number of
significant figures.
A . 7.1
B . 7.06
c. 7.0
D. 7 J


Which of the one is true for this
reaction:
\( 2 F e C l_{3}+S n C l_{2} \rightarrow 2 F e C l_{2}+S n C l_{4} \)
A \( \cdot F e^{+3} \) reduced to \( F e^{+2} \)
B. \( S n^{+2} \) is reduced to \( S n^{+4} \)
\( c \cdot S n^{+2} \) oxidized to sn
D. \( F e^{+3} \) gains two electrons


The position vectors of \( \boldsymbol{A}, \boldsymbol{B}, \boldsymbol{C}, \boldsymbol{D} \) are
\( \bar{a}, \bar{b}, \bar{c}, \bar{d} \) respectively and \( |\bar{a}-\overline{\boldsymbol{d}}|= \)
\( |\bar{b}-\bar{d}|=|\bar{c}-\bar{d}|, \) then for the triangle
\( A B C, D \) is
A. Ortho centre
B. Centroid
c. circumcentre
D. Incentre


\( \operatorname{Given} \mathbf{3}\left[\begin{array}{cc}\boldsymbol{x} & \boldsymbol{y} \\ \boldsymbol{z} & \boldsymbol{w}\end{array}\right]=\left[\begin{array}{cc}\boldsymbol{x} & \boldsymbol{6} \\ -\mathbf{1} & \boldsymbol{2} \boldsymbol{w}\end{array}\right]+ \)
\( \left[\begin{array}{cc}4 & x+y \\ z+w & 3\end{array}\right], \) find the values of
\( \boldsymbol{x}, \boldsymbol{y}, \boldsymbol{z} \) and \( \boldsymbol{w} \)


The angular velocity of a wheel is 70 rad/s. If the radius of the wheel is
\( \mathbf{0 . 5} \boldsymbol{m}, \) then linear velocity of the whee
is
A. \( 70 \mathrm{m} / \mathrm{s} \)
B. \( 35 \mathrm{m} / \mathrm{s} \)
c. \( 30 m / s 30 m / s \)
D. 20m/s2om/s


Construct a triangle \( P Q R \) in which
\( Q R=7 c m, \angle Q=75^{\circ} \) and \( P Q+ \)
\( \boldsymbol{P R}=13 \mathrm{cm} \)


DDT residues are rapidly passed through food chain causing biomagnification because DDT is
A. water soluble
B. Lipid soluble
c. Moderately toxic
D. Non-toxic to aquatic animals


A cast iron column has an internal
diameter of 200 mm. What should be
the minimum external diameter (in
\( \mathrm{m} \) so that it may carry a load of
1.6 million \( N \) without the stress
exceeding \( 90 N / m m^{2} ? \) (round off your answer to nearest integer)


Define atrial natriuretic factor


Name any six domestic appliances
based on the heating effect of electric
current


On passing electric current in two long straight conductors in mutually opposite directions, the magnetic force acting between them will be
A. attractive
B. repulsive
c. both attractive and repulsive
D. neither attractive nor repulsive


Chemical linkage into chains of atoms of the same element is known as
catenation.
A. True
B. False


Rayon or artificial silk is obtained from :
A. cocoon
B. petroleum
c. silk fibre
D. wood pulp


The general method of asexual reproduction, in yeast is
A. By spores
B. By budding
c. Binary fission
D. Multiple fission


A dynamo converts:
A. electrical energy into mechanical energy
B. electrical energy into heat energy
C. mechanical energy into electrical energy
D. heat energy into electrical energy


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


To determine BOD value, what is the time period of sample for incubation?
A. 4 hours
B. 2 hours
c. 3 days
D. 5 days


Identify which of the following should be used for polarised light waves?
I. Sunglasses
Il. Remove ultraviolet light
III. Reveal stress patterns
A. I only
B. II only
c. I and III only
D. II and III only
E. I, II, and III


If \( z_{1} \) and \( z_{2} \) are two complex numbers satisfying the equation \( \left|\frac{z_{1}+z_{2}}{z_{1}-z_{2}}\right|=1 \) then \( \frac{z_{1}}{z_{2}} \) is a number which is
A . Positive real
B. Negative real
c. zero or purely imaginary
D. none of these


If \( z(1+a)=b+i c \) and \( a^{2}+b^{2}+c^{2}= \)
1, then \( \frac{1+i z}{1-i z}= \)
A \( \cdot \frac{a+i b}{1+c} \)
в. \( \frac{b-i c}{1+a} \)
c. \( \frac{a+i c}{1+b} \)
D. None of these


\( \lim _{x \rightarrow 0} \frac{e^{x^{2}}-\cos x}{\sin ^{2} x} \) is equal to :
\( A \cdot 2 \)
B. \( \frac{3}{2} \)
\( c \cdot 3 \)
\( D \cdot \frac{5}{4} \)


Consider a track having frictional
coefficient \( \mu . A \) block of mass \( m \) is released from point \( \boldsymbol{P} \) situated at
height \( h . \) Which of the following is
correct?
A. It can reach at \( V \)
B. It cannot reach at \( V \)
c. It can reach at \( V \), if \( \mu \) is reduced to \( \mu / 2 \)
D. It can reach at \( V \), if \( \mu \) is increased to \( 2 \mu \)


Add an express the sum as a mixed
fraction:
\( \frac{101}{6} \) and \( \frac{7}{8} \)


Consider the points \( \boldsymbol{A}(\mathbf{0}, \mathbf{1}) \) and \( \boldsymbol{B}(\mathbf{2}, \mathbf{0}) \)
and the \( P \) be a point on the line \( 4 x+ \)
\( 3 y+9=0 . \) Coordinates of \( P \) such that
\( |\boldsymbol{P} \boldsymbol{A}-\boldsymbol{P} \boldsymbol{B}| \) is maximum are
\( \mathbf{A} \cdot\left(-\frac{12}{5}, \frac{17}{5}\right) \)
B \( \cdot\left(-\frac{18}{5}, \frac{9}{5}\right) \)
\( ^{\mathbf{C}} \cdot\left(-\frac{6}{5}, \frac{17}{5}\right) \)
D \( \cdot(0,-3) \)


Molecule(s) possessing two-centre-two electron bonds and three-centre-two
electron bonds would include:
A. \( B_{2} H_{6} \) and \( S i F_{4} \)
B. \( X e F_{6} \) and \( B F_{6} \)
\( \mathbf{c} \cdot B_{2} H_{6} \) and \( X e F_{6} \)
D. \( B_{2} H_{6} \) alone


In a city, electricity costs \( \$ 0.12 \) per kilowatt-hour. A bulb of 150-watt
operates for 5 hours. Calculate the cost
of electricity which is consumed by the bulb.
A. \( \$ 0.009 \)
в. \$0.09
c. \( \$ 0.90 \)
D. \$9.00
E. \( \$ 90.00 \)


Which Newton's law of motion defines
force?
A. First
B. second
c. Third
D. None


The number of \( A \) in \( T_{p} \) such that the trace of \( A \) is not divisible by \( p \) but \( \operatorname{det}(A) \) divisible by p is ?[Note: The trace of matrix is the sum of its diagonal entries].
A \( \cdot(p-1)\left(p^{2}-p+1\right) \)
B . \( p^{3}-(p-1)^{2} \)
c. \( (p-1)^{2} \)
D. \( (p-1)\left(p^{2}-2\right) \)


When alpha particle are sent through a thin metal foil, most of them go straight through the foil because
A . a-particles are much heavier than electrons
B. a- particles are positively charged
c. most part of the atom is empty space
D. a-particle move with high velocity


An A.C. of \( 50 \mathrm{Hz} \) and \( 1 \mathrm{A} \) peak value flows
in primary coil transformer whose mutual inductance is \( 1.5 \mathrm{H} \). Then peak
value of induced emf in the secondary coil is:
A. \( 150 v \)
B. \( 150 \pi v \)
c. \( 300 \vee \)
D. 200 V


toppr
Q Type your question.
\( \boldsymbol{H}_{2} \boldsymbol{O}_{2(l)} \rightarrow \boldsymbol{H}_{2} \boldsymbol{O}_{(l)}+\frac{1}{2} \boldsymbol{O}_{2(g)} ; \boldsymbol{\Delta}_{r} \boldsymbol{G}^{o}= \)
\( -122.6 k J / m o l \)
As the reaction from left to right is accompanied by a decrease in free
energy, it is a spontaneous process.
However, its decomposition at \( 25^{\circ} \mathrm{C} \) in
the absence of catalysts is slow. The
catalysts which accelerate
decomposition are \( \mathrm{Pt}, \) Ag, cobalt, iron,
copper, manganese dioxide and light.
Concentrated \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) solution can result
into uncontrolled decompositions
leading to explosion. \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) thus stored
in colored wax-lined bottles (as rough
glass surfaces) also causes its decomposition. A few stabilizers such
as acids acetanilide, pyrophosphates,
and stannates are added to slow down
the decomposition of \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \)
\( H_{2} O_{2} \) is stored in colored wax-lined
bottles because:
A. it is radioactive
B. it produced uncontrolled decompositions leading to explosion
C. it is non-polar molecule
D. none of these


Evaluate: \( \int_{0}^{\frac{\pi}{2}} \log \left(\frac{4+3 \sin x}{4+3 \cos x}\right) d x \)


How much electricity in terms of Faraday is required to produce:
(i) \( 20 g \) of \( C a \) from molten \( C a C l_{2} \)
(ii) \( 40 g \) of \( A l \) from molten \( A l_{2} O_{3} \)
[Given : Molar mass of calcium \&
Aluminium are 40 g \( m o l^{-1} \& 27 g \) mol \( \left.^{-1} \text {respectively }\right] \)


The volume occupied by \( 8 ~ g m ~ o f ~ o x y g e n ~ \) at S.T.P. is
A . 11.2 lit
B. 22.4 lit
c. 2.8 lit
D. 5.6 lit


A monochromatic light source of frequency \( 6 \times 10^{14} H z \) is emitting
energy at the rate \( 2 \times 10^{-3} J / s \)
Calculate the number of photons emitted per second by the source.


In the reaction \( I_{2}+I^{-} \rightarrow I_{3}^{-}, \) the Lewis
base is
A \( \cdot I_{3} \)
В. \( I_{2} \)
\( c \cdot I^{-} \)
D. None of the above


Consider the reversible reaction
\( \boldsymbol{H} \boldsymbol{C} \boldsymbol{N}(\boldsymbol{a} \boldsymbol{q}) \leftrightharpoons \boldsymbol{H}^{+}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{C} \boldsymbol{N}^{-}(\boldsymbol{a} \boldsymbol{q}) \) at
equilibrium. The addition of \( C N^{-}(a q) \)
at equilibrium would:
A. reduce \( H C N \) (aq) concentration
B. decrease \( H^{+} \) ion concentration
c. increase equilibrium constant
D. decrease equilibrium constant


Reaction of monochloro ethane is
hydrolysed with aqueous KOH as follows:
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{\boldsymbol{x}} \boldsymbol{C l}+\boldsymbol{a q} \cdot \boldsymbol{K O H} \rightarrow \)
\( \boldsymbol{C}_{2} \boldsymbol{H}_{\boldsymbol{y}} \boldsymbol{O} \boldsymbol{H}+\boldsymbol{K} \boldsymbol{C l} \)
Find \( x \) and \( y \)
A. \( x=1, y=3 \)
B. \( x=1, y=5 \)
c. \( x=2, y=3 \)
D. \( x=2, y=5 \)


Factorise the expression and divide them as directed.
\( 5 p q\left(p^{2}-q^{2}\right) \div 2 p(p+q) \)


In a nuclear reactor, what is the
function of the moderator?


Who among the following did not provide experimental proof for the semiconservative model of DNA
replication?
A. Meselson \& Stahl
B. Cairns
c. Watson \& Crick
D. Taylor


lodine reacts with conc. \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \) and
gives:
\( A \). iodic acid
B. hydrogen iodide
c. nitrous oxide
D. nitrogen dioxide


Where would you locate the element
with electronic configuration 2,8 in the modem period table?
A. Group 8
B. Group 2
c. Group 10
D. Group 18


Gas Density
\( A \)
\[
\begin{array}{l}
0,82 g L^{-1} \\
0,26 g L^{-1}
\end{array}
\]
\( 0.51 g L^{-1} \)
Pick up the correct statement/
statements.
1. Gas \( A \) will tend to lie at the bottom.
2. The number of atoms of various
\( \operatorname{gases} A, B \) and \( C \) are same.
3. The gases will diffuse to form homogeneous mixture.
4. Average kinetic energy of each gas is
same.
\( \mathbf{A} \cdot 2,3 \)
в. 1,4
\( c \cdot 1 \)
D. 3,4


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


Smoke precipitator works on the
principle of :
A. distribution law
B. neutralization of charge on colloids
C . Le-Chaterlier's principle
D. addition of electrolytes


The electrons identified by quantum
numbers \( n \) and \( l, \) are as follows:
I. \( \boldsymbol{n}=\mathbf{4}, \boldsymbol{l}=\mathbf{1} \)
Il. \( \boldsymbol{n}=\mathbf{4}, \boldsymbol{l}=\mathbf{0} \)
III. \( \boldsymbol{n}=\mathbf{3}, \boldsymbol{l}=\mathbf{2} \)
IV. \( n=3, l=1 \)
If we arrange them in order of increasing energy, i.e. from lowest to highest, the correct order is:
A. \( I V<I I<I I I<I \)
B. \( I I<I V<I<I I \)
c. \( I<I I I<I I<I V \)
D. III \( <I<I V<I I \)


Which logic gate produces LOW output when any of the inputs is HIGH?
A. AND
в. ов
c. NAND
D. NOR


(a) Obtain a relation for equivalent capacitance of the series combination
of capacitors. Draw a circuit diagram
(b) 10 capacitors each of capacity \( 10 \mu F \) are joined first in series and then
in parallel. Write the value of product of equivalent capacitances.
(c) What will be the value of
capacitance of a \( 4 \mu F \) capacitor if a
dielectric of dielectric constant 2 is
inserted fully between the plates of parallel plate capacitor.


Show that the height of a closed right circular cylinder of given surface and
maximum volume, is equal to the diameter of its base.


Which of the following is solid at room temperature?
A. Acetaldehyde
B. Paraldehyde
c. Metaldehdye
D. All of the above.


Consider the following statements
regarding halides of \( \boldsymbol{S} \)
(i) \( S F_{4} \) and \( S C l_{4} \) act as Lewis acid only.
(ii) \( S F_{4} \) and \( S C l_{4} \) act as Lewis base
only.
(iii) \( S F_{4} \) and \( S C l_{4} \) act both as Lewis acid and Lewis base.
The correct option is:
A. both (ii) a (iii) are correct
B. both (i) a (ii) are correct
c. only (iii) is correct
D. all are correct


The function \( x(x-1)(x-2) \) attains its
maximum value when \( x \) is
\( \mathbf{A} \cdot \mathbf{1} \)
B. \( 1+\frac{1}{\sqrt{3}} \)
c. \( _{1-} \frac{1}{\sqrt{3}} \)
D. \( 1 \pm \sqrt{3} \)


For a single slit of width "a", the first
minimum of the interference pattern of
a monochromatic light of wavelength \( \lambda \) occurs at an angle of \( \frac{k}{a} . \) At the same angle of \( \frac{k}{a}, \) we get a maximum for two narrow slits separated by a distance "a" Explain.


The ratio of the inertial mass to
gravitational mass is equal to:
A . 0.5
B.
c. 1.5
\( D \)


If \( 684 g \) of sucrose \( (M M=342 g) \) is
dissolved in \( 2000 g \) of \( H_{2} O \) (essentially
\( 2 L), \) what will be the freezing point of this solution?
A . -0.51
B . -1.86
c. -3.72
D. - 6.58


Group II. A elements are extracted from their chlorides by
A. Magnetic
B. Static
c. Electrolytic
D. Dymanic


A block of mass \( m=1 k g \) has speed
\( v=4 m / s \) at \( \theta=60^{\circ} \) on a circular track
of radiu \( R=2 m \) as shown in figure.
Coefficient of kinetic friction between
the block and the track is \( \mu_{k}=0.5 \) tangential acceleration of the block at this instant is approximately.
A \( .2 .1 m / s^{2} \)
В \( \cdot 5 m / s^{2} \)
\( \mathrm{c} \cdot 1.2 \mathrm{m} / \mathrm{s}^{2} \)
D. \( 3 m / s^{2} \)


In a mixture of weak acid and its salt,
the ratio of the concentration of salt to
acid is increased tenfold.The pH of the solution would increase by:
A. 0.5
B.
\( c \cdot 10 \)
D.


If \( f \) is a real-valued differentiable
function such that \( f(x) f^{\prime}(x)<0 \) for all
real \( x, \) then
A. \( f(x) \) must be a increasing function
B. \( f(x) \) must be a decreasing function
c. \( |f(x)| \) must be a increasing function
D. \( |f(x)| \) must be a decreasing function


picometer is centimeter
A \( \cdot 10^{-8} \)
B. \( 10^{-9} \)
c. \( 10^{-10} \)
D. \( 10^{10} \)


What is the power of concave lens?
A. Positive
B. Negative
c. Neutral
D. None


The hydrogen-like species \( L i^{2+} \) is in a
spherically symmetric state \( S_{1} \) with one
radial node and its energy is equal to the ground state energy of the hydrogen atom.

The energy of the state \( S_{2}( \) next state ) in units of the hydrogen atom ground state energy is:
A . 7.5
в. 1.50
c. 2.25
D. 4.50


The gas released when baking soda is mixed with vinegar, is:
A. \( C O \)
в. \( C O_{2} \)
c. \( C H_{4} \)
D. \( O_{2} \)


Which of the following is incorrect in a galvanic cell?
A. Oxidation occurs at anode
B. Reduction occurs at cathode
c. The electrode at which electrons are gained is called cathode
D. The electrode at which electrons are lost is called cathode


In triangle \( A B C, \angle B=90^{\circ} \) and \( D \) is
the mid-point of side Be. Prove that:
\( A C^{2}=A D^{2}+3 C D^{2} \)


A less reactive metal displaces a more
reactive metal from its salt solution.
A. True
B. False


Consider the reaction equilibrium Ice\( \rightleftharpoons_{\text {Lesservier}}-\boldsymbol{X k c a l} \)
Greatervolume
The favourable condition for forward
reaction are:
A. low temperature, high pressure and excess of ice
B. low temperature, low pressure and excess of ice
c. high temperature, low pressure and excess of ice
D. high temperature, high pressure and excess of ice


Classify the following materials with regard to magnetism:
Manganese, Cobalt, Nickel, Bismuth,
Oxygen and Copper


A thin, symmetric double convex lens of
power \( \boldsymbol{P} \) is cut into three parts \( \boldsymbol{A}, \boldsymbol{B} \)
and \( C \) as shown. The power of
This question has multiple correct options
A \( . A \) is \( P \)
B. \( A \) is \( 2 P \)
\( \mathbf{c} \cdot B \) is \( P / 2 \)
D. \( C \) is \( P / 4 \)


A letter lock consists of three rings each marked with fifteen different letters; find in how many ways it is possible to make an unsuccessful attempt to open the lock.


Indicate which of the following
statement is true or false.
The reaction between hydrogen and nitrogen to form ammonia is reversible.
A. True
B. False


Which of the following statements are
correct?
This question has multiple correct options
A. In gas phase, the basic character of amine is \( 3>2>1 \)
Due to the +1effect of (R-), the availability of \( L P e^{-^{\prime}} s \) on N increases.
B. In aqueous medium, the basic character of amines is \( M e_{2} N H>M e_{3} N>M e N H_{2}>N H_{3} \)
C. In aqueous medium, the addition of protons increases crowding and thus strains setup, which being the highest in 3 amine decreases its basic character.
D. In aqueous medium, the ammonium ions in solution are stabilised not only by alkyl groups but also by \( \mathrm{H}- \) bond donation to the solvent.


Define 1 Newton


The displacement current is
A \( \cdot_{\varepsilon_{o}} \frac{d \phi_{E}}{d t} \)
в. \( \frac{\varepsilon_{o}}{R} \frac{d \phi_{E}}{d t} \)
\( \mathbf{c} \cdot_{\varepsilon_{o}} \frac{E}{R} \)
D. \( \varepsilon_{o} q \frac{C}{R} \)


What do Ka and Kb vales say about acid
and base strength?
A. The higher Ka and Kb values, the stronger the acid or base
B. The higher the Ka and Kb values, the weaker the acid o base
c. When Ka values equal Kb values, the acid is strong.
D. ka and Kb values do not provide information about acid and base strength.


Lattice energy of ionic compounds depend upon:
A. packing of ions only
B. charge and size of ions
c. charge on ion only
D. size of ions only


In electrolytic refining of any metal impure metal is taken as
A. anode
B. cathode
c. solution
D. both B and C


The sample space in the set
representing an event more than one element is called
A. compound
B. simple
c. impossible
D. complementary


Compare the chemistry of actinoids
with that of the lanthanoids with
special reference to:
(i) electronic
configuration
(ii) atomic and ionic
sizes and (iii) oxidation state (iv)
chemical reactivity.


Evaluate the following integral:
\( \int_{0}^{5} x^{2} d x \)


A magnetic field exists in the region surrounding a magnet, in which the force of the magnet can be detected. Is the given statement true or false?


Allium cepa belongs to the family
A. Solanaceae
B. Liliaceae
c. Cruciferae
D. compositae


A telescope is used to resolve two stars
separated by \( 4.6 \times 10^{-6} \) rad. If the wavelength of light used is \( 5460 A \) what should be the aperture of the objective of the telescope?
A. \( 0.1488 \mathrm{m} \)
B. 0.567 m
\( c \cdot 1 m \)
D. 2 \( m \)


The reduction potential of hydrogen electrode at \( p H=10 \) is:
A \( .-0.059 \mathrm{V} \)
B. -0.59
c. \( 0.59 v \)
D. \( 0.0 \mathrm{V} \)


Name the reagents used in the
following reaction:
Dehydration of propan-2-ol to propene.


How much current is drawn by the primary of a transformer connected to \( 220 V \) supply when it delivers power to
a \( 110 V-550 W \) refrigerator?


Suppose(God forbid) due to some
reason, the earth expands to make its volume eight-fold. What you expect your
weight to be?
A. Two-fold
B. One-half
c. one-fourth
D. Unaffected


What are ecosystem services? What lessons do they give to human society?


The mass of the moon is \( 1 \% \) of mass of
the earth.The ratio of gravitational pull of earth on moon to that of moon on
earth will be:
A . 1:
B. 1: 10
c. 1: 100
D. 2:1


Source of maximum sulphur is
A. Ocean
B. Land
c. Rocks
D. Lakes


If \( \int \frac{1}{(x+2)\left(x^{2}+1\right)} d x= \)
\( a \log \left|1+x^{2}\right|+b \tan ^{-1} x+ \)
\( \frac{1}{5} \log |x+2|+C \)
A. \( a=-\frac{1}{10} b=-\frac{2}{5} \)
B. \( a=\frac{1}{10} b=-\frac{2}{5} \)
c. \( a=-\frac{1}{10} b=\frac{2}{5} \)
D. \( a=\frac{1}{10} b=\frac{2}{5} \)


Devendra invested in a national saving certificate scheme. In the first year he
invested Rs.1000 in second year Rs.
\( 1400, \) in the third year \( R s .1800 \) and \( s 0 \)
on. Find the total amount that he
invested in 12 years


A cylinder rolls down an inclined plane
of inclination \( 30^{\circ}, \) the acceleration of
cylinder is
A \( \cdot \frac{g}{3} \)
B. \( g \)
c. \( \frac{g}{2} \)
D. \( \frac{2 g}{3} \)


If \( ^{n} \boldsymbol{P}_{r}=\mathbf{3 0 2 4 0} \) and \( ^{n} \boldsymbol{C}_{r}=\mathbf{2 5 2}, \) then the
ordered pair \( (n, r) \) is equal to:
A. (12,6)
в. (10,5)
c. (9,4)
(年. \( 9,4,4) \)
D. (16,7)


Out of the elements \( C, S, G e, S n \) and
\( P b, \) only +4 oxidation state is shown by how many element(s)?


Assertion
High energy particles from outer space, on entering the earth's atmosphere
causes ionisation of the atoms of the
gases present in the atmosphere.
Reason

One goes higher the atmospheric
pressure decreases.
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 volume of two spheres is in the ratio 64: 27 and the sum of their radiiis
7 cm. The difference in their total
surface areas is
\( \mathbf{A} \cdot 38 c m^{2} \)
B. \( 58 c m^{2} \)
\( \mathbf{c} \cdot 78 c m^{2} \)
D. \( 88 \mathrm{cm}^{2} \)


\( K M n O_{4} \) can be prepared from
\( K_{2} M n O_{4} \) as per the reaction:
\( \mathbf{3} M n O_{4}^{2-}+2 H_{2} O \rightleftharpoons 2 M n O_{4}^{-}+ \)
\( M n O_{2}+4 O H^{-} \)
The reaction can go to completion by
removing \( \boldsymbol{O H}^{-} \) ions by adding:
A. \( H C l \)
в. КОН
\( \mathrm{c} \cdot \mathrm{CO}_{2} \)
D. \( S O_{2} \)


\( 4.6 \mathrm{cm}^{3} \) of methyl alcohol is dissolved in
\( 25.2 \mathrm{g} \) of water. Calculate mole fraction of methyl alcohol.
A. 0.1232
B. 0.0759
c. 0.0932
D. 0.0562


0.1890 g of an organic compound containing chlorine, gave in Carius determination 0.2870 g of \( A g C l \)
Calculate the percentage of chlorine in the compound.
\( \mathbf{A} \cdot 32.89 \)
B. 37.56
c . 35.45
D. 40.1


Fuse wire is made of :
A. Platinum
B. Copper
C. Aluminium
D. Alloy in tin and lead


A ball is dropped on to a horizontal plate from a height \( h=9 \) m above it. If the coefficient of restitution is \( e=1 / 2, \) the
total distance travelled before the ball
comes to rest is:
A. \( 10 \mathrm{m} \)
B. 15
\( c \cdot 20 m \)
D. 25 m


How can soil erosion by river floods be controlled?
A. By making canals
B. By pumping water from river
c. By constructing dams across the rivers
D. By letting water flow freely at high speed


In how many ways is it possible to choose a white square and a black square on a chessboards, so that the squares must not lie in the same row or
column?
A . 56
в. 896
c. 60
D. 768


For constructing a triangle when the base, one base angle and the difference between lengths of other two sides are given, the base length is equals to:
A. The difference between lengths of other two sides
B. The given base length
c. The largest side
D. None of these


In human female, immature eggs are seen for the first time in the ovary during which stage?
A. At puberty
B. Before birth, at the fetus stage
c. During the first menstrual cycle
D. After the first year of birth


Distance between \( \vec{r}=\hat{i}+\lambda(\hat{j}+\hat{k}) \)
and \( \vec{r}=\hat{j}+\mu(\hat{j}+\hat{k}) \) is equal to


Four light waves are represented by
\( (i) y=a_{1} \sin \omega t \)
\( (i i) y= \)
\( a_{2} \sin (\omega t+\varepsilon) \)
\( (i i i) y=a_{1} \sin 2 \omega t \quad(i v) y= \)
\( \boldsymbol{a}_{2} \sin 2(\boldsymbol{\omega} \boldsymbol{t}+\boldsymbol{\varepsilon}) \)
Interference fringes may be observed due to superposition of This question has multiple correct options
A \( \cdot(i) \) and \( (i i) \)
B. ( \( i \) ) and (iii)
c. ( \( i i \) ) and \( (i v) \)
D. (iii) and (iv)


Larva of Bombyx mori is
A . Caterpillar
B. Trochophore
c. Nymph
D. cocoon


Solve \( \frac{2}{3}+\frac{1}{7} \)


Find the angular speed of the rod as the
function of angle \( \theta \) of rotation \( \omega=f(\theta) \)
if the rod is allowed to rotate freely


Mark the correct alternative of the
following.
n figure, if \( A B \| C D, \) then the values of \( x \)
and y are?
A. \( x=106, y=307 \)
B. \( x=307, y=106 \)
c. \( x=107, y=306 \)
D. \( x=105, y=308 \)


A cyclist moves in such a way that he
takes \( 72^{\circ} \) turn towards left after
travelling \( 200 \mathrm{m} \) in straight line. What is the displacement when he takes just takes fourth turn?
A. zero
B. 600 \( m \)
c. \( 400 \mathrm{m} \)
D. 200 \( \mathrm{m} \)


Integrate the following
i) \( \log x \)
ii) \( \cos ^{-1}(\sqrt{x}) \)


Write general configuration of
inner transition element. what is the
important of the element?


Select the correct option:
Identify the types of vascular bundle in the figures (i) and (ii) and select the correct option.
conjoint
(A) Conjoint collateral - \( \quad \) bicollatera
(B) Conjoint bicollateral- - conjoint collateral
C) Conjoin Conjoin open
D) Conjoint collatera conjoint closed
\( A \)
B. B
\( c \cdot c \)
\( D \cdot D \)


The temperature coefficient of
resistance of platinum is \( \boldsymbol{\alpha}=\mathbf{3 . 9 2} \times \)
\( 10^{-1} K^{-1} \) at \( 20^{\circ} C . \) Find the
temperature at which the increase in the resistance of platinum wire is \( 10 \% \)
of its value at \( 20^{\circ} C \)
A \( .40 .5^{\circ} \mathrm{C} \)
в. \( 45.5^{\circ} \mathrm{C} \)
c. \( 48.5^{\circ} \mathrm{C} \)
D. \( 43.5^{\circ} \mathrm{C} \)


Hydrogen peroxide oxidises \( \left[\boldsymbol{F e}(\boldsymbol{C} \boldsymbol{N})_{\boldsymbol{6}}\right]^{4-} \) to \( \left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{\boldsymbol{6}}\right]^{3-} \) in acidic
medium but reduce \( \left[\boldsymbol{F} e(\boldsymbol{C} \boldsymbol{N})_{\boldsymbol{6}}\right]^{3-} \) to
\( \left[\boldsymbol{F} e(\boldsymbol{C} \boldsymbol{N})_{6}\right]^{4-} \) in alkaline medium. The
other products formed are, respectively:
\( \mathbf{A} \cdot H_{2} O \) and \( \left(H_{2} O+O_{2}\right) \)
B. \( H_{2} O \) and \( \left(H_{2} O+O H^{-}\right) \)
\( \mathrm{c} \cdot\left(\mathrm{H}_{2} \mathrm{O}+\mathrm{O}_{2}\right) \) and \( \mathrm{H}_{2} \mathrm{O} \)
D. \( \left(H_{2} O+O_{2}\right) \) and \( \left(H_{2} O+O H^{-}\right) \)


The distance between two magnetic poles is doubled and their pole-strength is also doubled. The force between them
A. Increases to three times
B. Decreases by half
c. Remains unchanged
D. Increases to two times


An electron does not suffer any
deflections while passing through a region. This makes sure that there is no
magnetic field in that region. Is the
given statement true or false?


The value of \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2}+\boldsymbol{3} \) when \( \boldsymbol{x}=\boldsymbol{3} \)
is


the angular acceleration of the ball about its centre of mass is \( =\frac{x \mu g \cos \theta}{2 R} \)


Assertion
Benzyl bromide when kept in acetone
and \( H_{2} O \) produces benzyl alcohol.
Reason
The reaction follows \( S_{N} 2 \) mechanism.
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 are correct


A coil of inductance \( 0.1 \mathrm{H} \) is connected to
\( 50 V, 100 H z \) generator and current is found to be 0.5A. The potential
difference across resistance of the coil
is
A . \( 15 v \)
B. 20V
c. \( 25 v \)
D. 39V


What is the current (I) in the circuit?
A \( \cdot \frac{1}{2} A \)
\( B .2 A \)
\( c \cdot \frac{3}{2} A \)
D. none of these


The potential difference between two parallel plates \( 1 \mathrm{cm} \) apart is \( 100 \mathrm{V} \). The electric field strength between them is :
A. \( 100 V / m \)
в. \( 1000 V / m \)
c. \( 10^{4} V / m \)
D. \( 50 V / m \)


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


What is the work done in moving a
charge of \( 50 n C \) between two points on an equipotential surface?


Let \( \boldsymbol{E}_{1}(\boldsymbol{r}), \boldsymbol{E}_{2}(\boldsymbol{r}) \) and \( \boldsymbol{E}_{3}(\boldsymbol{r}) \) be the
respective electric fields at a distance from a point charge \( Q, \) an infinitely long wire with constant linear charge density
\( \lambda, \) and an infinite plane with uniform
surface charge density \( \sigma . \) If \( E_{1}\left(r_{0}\right)= \)
\( E_{2}\left(r_{0}\right)=E_{3}\left(r_{0}\right) \) at a given distance \( r_{0} \)
then :
A \( \cdot Q=4 \sigma \pi r_{0}^{2} \)
B. \( r_{0}=\frac{\lambda}{2 \pi \sigma} \)
c. \( E_{1}\left(\frac{r_{0}}{2}\right)=2 E_{2}\left(\frac{r_{0}}{2}\right) \)
D. \( E_{2}\left(\frac{r_{0}}{2}\right)=4 E_{3}\left(\frac{r_{0}}{2}\right) \)


A sphere of mass \( M \) and radius \( r \) slips
on a rough horizontal plane. At some
instant it has translation velocity \( \boldsymbol{v}_{0} \) and rotational velocity about the centre
\( v_{0} / 2 r . \) The translation velocity after the
sphere starts pure rolling
A \( \cdot 6 v_{0} / 7 \) in forward direction
B. \( 6 v_{0} / 7 \) in backward direction
\( c \cdot 7 v_{0} / 6 \) in forward direction
D. \( 7 v_{0} / 6 \) in backward direction


According to laws of refraction,
refraction of light at the boundary
between two different regions follow:
A. that the incident ray, the normal at the point of incidence and the refracted ray, all lie in the same plane.
B. that for a given pair of media and given colour of light. the ratio of the sine of angle of incidence to the sine of angle of refraction is constant.
C. both \( A \) and \( B \)
D. neither A nor B


Assertion (A) : A freely falling body experiences a constant horizontal force due to wind velocity, its path is a straight line Reason (R) : The motion is decided by the unbalanced force acting on it
A. Both Assertion
(A) and Reason (R) are correct and R is the correct explanation
B. Both Assertion
(A) and Reason
(R) are correct but the reason does not give the correct explanation
c. Assertion
(A) is true but Reason
(R) is false
D. Assertion
(A) is false but Reason
(R) is true


type of entertainment device sold at
three of their branch stores so that they
can monitor their purchases of
supplies. The sales in two weeks are
shown in the following spreadsheets.
Find the sum of the items sold out in
two weeks using matrix addition.


Write the IUPAC name of
\( \left(\boldsymbol{C H}_{3}\right)_{2} \boldsymbol{C H C H O} \)


Assertion
In tetrahedral complexes low spin
configurations are rarely observed.
Reason
\( \Delta_{t}=\left(\frac{4}{9}\right) \Delta_{0} \)
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 radius of a solid hemisphere is \( 2 r \)
Find its surface area.


Male heterogametic sex, \( X X, X O \) type of sex determination is found in
A. Butterflies
B. Moths
c. Grasshoppers
D. Drosophila


State whether the given statement is
True or False :
Positive electrification is due to
deficiency of electrons.
A. True
B. False


A system consists of two identical
small balls of mass 2 kg each
connected to the two ends of a 1 m long light rod. The system is rotating about a fixed axis through the centre of the rod and perpendicular to it at an angular speed of 9 rad/s. An impulsive force of
average magnitude \( 10 N \) acts on one of the masses in the direction of its
velocity for \( 0.20 s . \) Calculate the new
angular velocity of the system.


The function \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{ll}2 x^{2}-1, & \text { if } 1 \leq x \leq 4 \\ 151-30 x, & \text { if } 4<x \leq 5\end{array} \) is not \right.
suitable to apply Rolle's theorem, since
B. \( f(1) \neq f(5) \)
c. \( f(x) \) is continuous only at \( x=4 \)
D. \( f(x) \) is not differentiable in (4,5)
E. \( f(x) \) is not differentiable at \( x=4 \)


Thickness of mantle of Earth is
approximately:
\( A \cdot 4,000 \mathrm{km} \)
B. 3,500 km
c. \( 3,200 \mathrm{km} \)
D. \( 2,890 \mathrm{km} \)


A net force \( \sum F_{x}(t)=A+B t^{2} \) in the \( +x \)
direction is applied to a girl of mass \( \mathrm{m} \) The force starts at \( t=0 \) and continues
until time t.
This question has multiple correct options
A. Impulse of the force is \( 2 B t \)
B. Her speed at time t is \( \frac{A}{m} t+\left(\frac{B}{3 m}\right) t^{3} \)
C. Impulse of the force is \( A t+\left(\frac{B}{3}\right) t^{3} \)
D. Her speed at time tis \( \left(\frac{2 B}{m}\right) t \)


A diode made of silicon has a barrier
potential of \( 0.7 ~ V \) and a current of
\( 20 m A \) passes through the diode when
a battery of emf \( 3 V \) and a resistor
is connected to it. The power dissipated across the resistor and diode are
A. \( 0.046 \mathrm{W}, 0.014 \mathrm{W} \)
в. \( 4.6 \mathrm{W}, 0.14 \mathrm{W} \)
c. \( 0.46 W, 0.14 W \)
D. \( 46 W, 14 W \)


atmosphere means how many Pascal?


A ball is shot vertically upward with a
given initial velocity. It reaches a maximum height of \( 100 \mathrm{m} \). If on a second shot, the initial velocity is doubled then the ball will reach a maximum height of
\( A .70 .7 \mathrm{m} \)
B. \( 141.4 \mathrm{m} \)
c. \( 200 \mathrm{m} \)
D. \( 400 \mathrm{m} \)


Which equation represents the line that
passes through the point (6,2) and is parallel to the \( y \) -axis?
\( \mathbf{A} \cdot y=6 \)
B. \( x=2 \)
c. \( x=6 \)
D. \( y=2 \)


Arrange the following ions in increasing
order of their radius:
\( \mathbf{A} \cdot M n^{+7}<V^{+5}<C a^{+2}<K^{+} C l^{-}<S^{2}<P^{3-} \)
B \( \cdot M n^{+7}<C a^{+2}<V^{+5}<K^{+} C l^{-}<S^{2}<P^{3-} \)
\( \mathbf{c} \cdot M n^{+7}<V^{+5}<C a^{+2}<K^{+} C l^{-}<P^{3-}<S^{2} \)
D. \( V^{+5}<M n^{+7}<C a^{+2}<K^{+} C l^{-}<S^{2}<P^{3-} \)


State True or False :
For correction of defects in human eye, spectacles form virtual images only.
A. True
B. False


Assertion
Resonance is exhibited by a circuit only
if both L and \( C \) are present in the circuit
Reason
Only then the voltage across L and \( C \) cancel each other, both being out of
phase
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


What is a line passing through two points on a circle called?
A. secant
B. Digonal
c. Radius
D. tangent


Green plants during day time absorb:
A. \( O_{2} \)
в. \( C O_{2} \)
\( c \cdot c o \)
D. \( N_{2} \)


Radiation from hydrogen gas excited to first excited state is used for
illuminating certain photoelectric plate. When the radiation from some unknown
hydrogen-like gas excited to the same level is used to expose the same plate, it is found that the de Broglie wavelength of the fastest photoelectron has decreased 2.3 times. It is given that the energy corresponding to the longest wavelength of the Lyman series of the unknown gas (13.6 eV). Find the work function of the photoelectric plate in eV.
\( \left[\text { take }(2.3)^{2}=5.25\right] \)


Dolly was given birth by
A. Finn dorset sheep
B. Scottish blackface ewe
C. Polled Dorset sheep
D. None of these


The phase change in reflected wave,
when light wave suffers reflection at the interface from air to glass is
A .
в. \( \frac{\pi}{2} \)
\( c . \pi \)
D. \( 2 \pi \)


If the standard deviation of \( n \)
observations \( x_{1}, x_{2}, \dots, x_{n} \) is 4 and
another set of \( n \) observations
\( \boldsymbol{y}_{1}, \boldsymbol{y}_{2}, \dots, \boldsymbol{y}_{n} \) is \( 3 . \) The standard deviation
of \( n \) observations \( x_{1}-y_{1}, x_{2}- \)
\( \boldsymbol{y}_{2}, \dots, \boldsymbol{x}_{\boldsymbol{n}}-\boldsymbol{y}_{n} \) is
A . 1
в. \( \frac{2}{\sqrt{3}} \)
\( c .5 \)
D. data insufficient


\( N_{2}(g)+3 H_{2}(g) \rightarrow \)
\( \mathbf{2} \boldsymbol{N} \boldsymbol{H}_{3}(\boldsymbol{g}) ; \quad \boldsymbol{\Delta} \boldsymbol{H}^{O}=-\boldsymbol{4} 4 \boldsymbol{K} \boldsymbol{c a l} \)
For the above reaction, the correct
statement is:
\( \begin{array}{lll}\text { A } . \Delta H & <\Delta E\end{array} \)
в. \( \Delta H \quad=\Delta E \)
\( c . \Delta H \quad>\Delta E \)
D. none of these


During denaturation of proteins, only ........... structure of protein is retained


An object of height \( 4 c m \) is placed at a
distance of \( 15 \mathrm{cm} \) in front of a concave
lens of power, -10 dioptres. Find the
size of the image.


Why are bryophytes called amphibians of plant kingdom?


A compound microscope consists of an objective of focal length \( 2 \mathrm{cm} \) and an eye-piece of focal length \( 5 \mathrm{cm} \). When an object is kept \( 2.4 \mathrm{cm} \) from the objective, final image formed is virtual and is at \( 25 \mathrm{cm} \) from the eye-piece. Determine magnifying power of this compound microscope in this set up, i.e., in normal
use.


Mrs. Verma has an autosomal gene pair Bb' and she contain x-linked gene 'd'
What is the percentage of gamete, which contain 'bd' genes?
A. \( 1 / 2 \) or \( 50 \% \)
B. 1/4 or 25\%
c. 3/4 or 75\%
D. 1 or \( 100 \% \)


A moving coil galvanometer A has 100
turns and resistance \( 10 \Omega \). Another
galvanometer B has 50 turns and 5 \( \Omega \)
The other quantities are same in both the cases. Then the voltage sensitivity of :
A. A is greater than that of
B. B is greater than that of
c. \( A \) and \( B \) is same
D. Cannot be compared


Solve for \( x \) and \( y: \) \( \boldsymbol{x}+\boldsymbol{y}=\frac{\boldsymbol{7} \boldsymbol{\pi}}{\boldsymbol{4}}, \frac{\sin \boldsymbol{x}}{\cos \boldsymbol{y}}=-\sqrt{\boldsymbol{2}} \)


What are the shapes of the molecules of
water and boron trifluoride?
\begin{tabular}{lll}
& \( \boldsymbol{H}_{2} \boldsymbol{O} \) & \( \boldsymbol{B} \boldsymbol{F}_{3} \) \\
\cline { 1 - 3 }\( _{\mathrm{A}} \) & linear & pyramidal \\
B & linear & trigonal \\
C & non-linear & pyramidal \\
D & non-linear & trigonal
\end{tabular}
\( A \)
B. B
\( c \cdot c \)
D.


A laser beam passes through the air
into a piece of plexiglass. Find out the possible change in property of the laser beam
A. The velocity decreases
B. The wavelength increases
c. The frequency decreases
D. The period decreases
E. None of the above is true


The isoclinic lines on magnetic map
represent lines of
A. zero dip
B. equal declination
c. equal dip
D. equal horizontal field


What is the angle between the electric
dipole moment and the electric field due to it on the axial line?
A \( \cdot 0^{\circ} \)
B. \( 90^{\circ} \)
\( c \cdot 180^{\circ} \)
D. none of these


What is denaturation of protein and
name the two diseases caused due to
deficiency of protein?


What is the order of rotational symmetry
of the above pattern?
\( A \)
\( B \)
\( c \cdot 12 \)
\( D \)


State whether the given statement is true or false \( \overline{\left(z^{-1}\right)}=(\bar{z})^{-1} \)


Metal carbonyls can have formula
\( \left.M(C O)_{x}\right), \) where \( x= \) number of \( C O \) units coordinated to metal \( M \)

What is the formula of the carbonyl of \( F e(26) \) if \( E A N \) of \( F e \) in metal carbonyl
is \( 36 ? \)
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. 5


In anaerobic respiration of yeast
\( A \cdot O_{2} \) is given out
B. \( C O_{2} \) is given out
\( \mathrm{c} \cdot \mathrm{CO}_{2} \) is taken in
\( D \cdot O_{2} \) is taken in


A mRNA coding for a secretory protein, when translated using free ribosome under in vitro conditions, resulted in a
\( 40 k D a \) protein. The same mRNA when translated using the rough endoplasmic reticulum resulted in a
\( 36 k D a \) protein. The difference in the
molecular weight of the two
polypeptides is due to the loss of a
A \( .2 k D a \) peptide from \( N \) -terminus and a \( 2 k D a \) peptide from the C-terminus
B. \( 1 k D a \) peptide from \( N \) -terminus and a \( 3 k D a \) peptide from the C-terminus
C. \( 4 k D a \) peptide from the N-terminus
D. \( 4 k D a \) peptide from the C-terminus


Higher value of decay constant
indicates
A. faster decay
B. high half-life period
c. slower decay
D. both (A) and (B)


The internal bisectors of \( \angle Q \) and \( \angle R \) of
\( \triangle P Q R \) meet at \( C . \) If \( \angle P=70^{\circ}, \) then
\( \angle P=70^{\circ} \) is
A \( \cdot 110^{\circ} \)
B . \( 125^{\circ} \)
\( \mathbf{c} \cdot 130^{\circ} \)
D. \( 140^{\circ} \)


In figure the cylinder of mass \( 10 k g \) and
radius \( 10 \mathrm{cm} \) has a tape wrapped round
¡t. The pulley weighs \( 100 N \) and has a
radius \( 5 c m . \) When the system is
released, the \( 5 k g \) mass comes down
and the cylinder rolls without slipping.
Calculate the acceleration and velocity of the mass as a function of time.


The Venn diagram shows sets \( P, Q \) and \( R \)
with regions labelled, I, II, III and IV.
State the region which represents set
\( \left[\boldsymbol{P} \cap(\boldsymbol{Q} \cup \boldsymbol{R})^{\prime}\right] \)
\( A \)
B.
\( c . \| \)
D. IV


Two S.H.M.'s are represented by the relations \( \boldsymbol{x}=\mathbf{4} \sin (\mathbf{8 0} \boldsymbol{t}+\boldsymbol{\pi} / \mathbf{2}) \) and \( \boldsymbol{y}= \)
\( 2 \cos (60 t+\pi / 3) \)
The ratio of their time periods is
A . 2:
B. 1:
c. 4: 3
D. 3:


If \( \alpha \) is a real number for which \( f(x)= \)
\( \log _{e} \cos ^{-1} x \) is defined, then a possible
value of \( [\boldsymbol{\alpha}] \) (where [] denotes the
greatest function) is This question has multiple correct options
A . 0
B.
\( c \cdot-1 \)
D. - -


The maximum value of \( x^{1 / x} \) is
A \( \cdot \frac{1}{e^{e}} \)
B.
\( \mathbf{c} \cdot e^{1 / e} \)
D.


The element used for coating in galvanisation:
A . tin
B. leadd
c. zinc
D. copper


Choose the correct answer from the
alternatives given
Plants are green because they
A. absorb only green wavelengths of light
B. absorb only yellow and blue wavelengths of light
c. reflect green wavelengths of light
D. reflect yellow and blue wavelengths of light


An uncharged electroscope can be charged by holding a charged body near its cap. True/False?


The distance of a particle as a function
of time is shown below. The graph indicates that
A. the particle starts with certain velocity but the motion is retarded and finally the particle stops
B. the acceleration of the particle varies
c. the acceleration of the particle is constant throughout
D. the particle starts with another constant velocity the motion is in acceleration and finally the particle moves with another constant velocity


A hydrocarbon has molecular formula
\( C_{6} H_{8} \) and it can be resolved into enantiomers However, catalytic hydrogenation of the above hyhdrocarbon gives 3-methyl pentane.Deduce structure of
hydrocarbon.


What will be the stable state of
aggression of carbon at \( 298 K \) and 1 atm
pressure?
A. Graphite
B. Diamond
c. Amorphous carbon
D. None of these


Evaluate the following:
\( \left|\begin{array}{ccc}\boldsymbol{x}+\boldsymbol{\lambda} & \boldsymbol{x} & \boldsymbol{x} \\ \boldsymbol{x} & \boldsymbol{x}+\boldsymbol{\lambda} & \boldsymbol{x} \\ \boldsymbol{x} & \boldsymbol{x} & \boldsymbol{x}+\boldsymbol{\lambda}\end{array}\right| \)


The zero of the polynomial \( x^{2}-1 \) is
A. True
B. False


Three equal resistors connected in series across a source of e.m.f. together dissipate 10 watt of power. What would be the power dissipated if the same resistors are connected in parallel across the same source of e.m.f.?
A. 90 watts
B. 80 watts
c. 70 watts
D. 75 watts


An electron and a photon each have a
wave length 1nm. Find the momenta.


Vectors \( \vec{a}, \vec{b} \) and \( \vec{c} \) are such that \( \vec{a}+\vec{b}+ \) \( \vec{c}=\overrightarrow{0} \) and \( |\vec{a}|=3, \mid \vec{b}=5 \) and \( |\vec{c}|=7 \)
Find the angle between \( \vec{a} \) and \( \vec{b} \)


Rutherford's scattering experiment led
to the conclusion that:
A. nucleus is very small in size
B. nucleus is very heavy and carries positive charge
C. most of the space in the atom is empty
D. all of these


Consider a spherical shell of radius \( \boldsymbol{R} \) at
temperature \( T . \) The black body radiation inside it can be considered as
an ideal gas of photons with internal energy per unit volume \( u=\frac{U}{V} \propto T^{4} \) and pressure \( \boldsymbol{P}=\frac{1}{\mathbf{3}}\left(\frac{\boldsymbol{U}}{\boldsymbol{V}}\right) . \) If the shell
now undergoes an adiabatic expansion the relation between \( T \) and \( R \) is :
A \( \cdot T \propto e^{-R} \)
В . \( T \propto e^{-3 R} \)
\( c \cdot T \propto \frac{1}{R} \)
D. \( T \propto \frac{1}{R^{3}} \)


Calculate approximately the diameter
of an atom of mercury, assuming that each atom is occupying a cube of edge length equal to the diameter of the mercury atom. The density of mercury is \( 13.6 \mathrm{g} / \mathrm{cc} \)


Newton's \( 3^{r d} \) law of motion gives idea
about the:
A. inertia
B. momentum
c. cause and effect of motion
D. force


The transducer used in television
transmission works on the principle of
A. Electromagnetic induction
B. Photoelectric effect
c. Raman's effect
D. Rayleigh's effect


If benzoic acid (mol. mass = 122) is associated into double molecules when
dissolved in benzene and the osmotic
pressure of a solution of 5 g of benzoic acid in \( 100 \mathrm{mL} \) benzene is 5.73 atm at
\( 10^{\circ} \mathrm{C}, \) what is the percentage
association of benzoic acid?
\( \mathbf{A} \cdot 60 \% \)
B. \( 70 \% \)
\( c .80 \% \)
D. \( 85 \% \)


The value of \( ^{\prime} g^{\prime} \) at a depth of \( 80 k m \) will
be (Radius of earth \( =\mathbf{6 4 0 0 k m} \) and
value of \( ^{\prime} g^{\prime} \) on the surface of earth is
\( \left.10 m / s^{2}\right) \)
A. \( 990 \mathrm{cm} / \mathrm{s}^{2} \)
В \( .980 \mathrm{cm} / \mathrm{s}^{2} \)
\( \mathrm{c} \cdot 970 \mathrm{cm} / \mathrm{s}^{2} \)
D. \( 1000 \mathrm{cm} / \mathrm{s}^{2} \)


Name the principal mineralocorticoid secreted by the adrenal cortex.


Which of the following will produce \( C O_{2} \)
on heating? This question has multiple correct options
A. \( B a C O_{3} \)
в. \( N a_{2} C O_{3} \)
с. \( M g C O_{3} \)
D. \( C a C O_{3} \)


Phenol is an organic compound even though it is soluble in water due to the
presence of:
A. ionic bonding
B. covalent bonding
c. hydrogen bonding
D. coordinate bonding


The force of repulsion between two parallel wires is \( f \) when each one of
them carries a certain current I. If the
current in each is doubled, the force
between them would be
A \( \cdot 4 / f \)
B. \( 4 f \)
\( c \cdot 2 f \)
\( D \)


What is the best pH of the soil for cultivation of plants?
A . \( 3.5-5 \)
B. 6.5 - 7
c. \( 4.5-8 \)
D. 5.5 - 7


The centripetal force \( \boldsymbol{F} \) acting on a particle moving uniformly in a circle may depend upon mass \( (\boldsymbol{m}), \) velocity
\( (v) \) and radius \( (r) \) of the circle. Derive
the formula for \( \boldsymbol{F} \) using the method of dimensions.
\( \left.^{\mathrm{A}} \cdot_{F}=\frac{m v^{2}}{r} \text { (where } k=1\right) \)
B . \( F=m v^{2} \times r \) (where \( k=1 \) )
C \( \cdot F=m v^{3} \times r \) (where \( k=1 \) )
D. \( F=\frac{m v^{3}}{r} \) (where \( k=1 \) )


In meiosis , replication of DNA occurs in
A . Mesiosis I
B. Meiosis II
c. Between meiosis II and Meiosis
D. Both meiosis I and Meiosis I


A circular area having a radius \( 20 \mathrm{cm} \) is divided into two equal parts by a concentric circle of radius 'r'. The value
of 'r' will be
A. \( 5 \mathrm{cm} \)
B. 10 \( \mathrm{cm} \)
\( \mathrm{c} \cdot 5 \sqrt{2} \mathrm{cm} \)
D. \( 10 \sqrt{2} \mathrm{cm} \)


Find the median for the data set.
22,45,56,56,45,123,122,56,103,56
A . 103
в. 102
\( c \cdot 122 \)
D. 56


Match column I with column II and
select the correct option from the codes
given below.
Column I
A. Suicide bag of the \( \quad \) column \( \| \) cell
1. Mitochondria
B. Powerhouse of the
2. Ribosome cell
3. Lysosome
C. Protein factory of the
4. Endoplasmic cell \( \quad \) reticulum
D. Kitchen of the cell
E. Circulatory system of
5. Chloroplast
the cell
A. A- \( 3, \) B- \( 1, \) C- \( 2, \) D- \( 5, \) E- 4
B. A- 3, B-1, C- 5, D-2, E-4
c. \( A-3, B-2, C-1, D-5, E-4 \)
D. A-1,B-3,C-2,D-5,E-4


A stone is dropped into a quiet lake and waves move in circles at a speed of 4 \( \mathrm{cm} / \mathrm{sec} . \) At the instant when the radius
of the circular wave is \( 10 \mathrm{cm}, \) how fast is the enclosed area increasing?


The pH of an aqueous solution of
\( \boldsymbol{C H}_{3} \boldsymbol{C O O N} \boldsymbol{a} \) of concentration \( \boldsymbol{C}(\boldsymbol{M}) \) if
given by
A \( \cdot \quad 7-\frac{1}{2} p K_{a}-\frac{1}{2} \log C \)
B. \( \frac{1}{2}^{p K_{w}}+\frac{1}{2} p K_{b}+\frac{1}{2} \log C \)
\( ^{\mathrm{c}} \cdot \frac{1}{2}^{p} K_{w}-\frac{1}{2} p K_{b}-\frac{1}{2} \log C \)
\( ^{\mathrm{D} \cdot \frac{1}{2} p K_{w}+\frac{1}{2} p K_{a}+\frac{1}{2} \log C} \)


The length of the side is \( 3.9 \mathrm{ft} \). Find the
surface area of a cube .
A \( \cdot 41.82 f t^{2} \)
B. \( 94.16 f t^{2} \)
c. \( 91.26 f t^{2} \)
D. \( 40.41 f t^{2} \)


Gasoline is the name given to :
A. diesel oil
B. petrol
c. natural gas
D. crude oil


What is the electric potential at a
distance \( ^{\prime} x^{\prime} \) from the centre, inside a
conducting sphere having a charge \( Q \)
and radius \( R ? \)
A. \( \frac{1}{4 \pi \epsilon_{0}} \frac{Q}{R} \)
в. \( \frac{1}{4 \pi \epsilon_{6}} \frac{Q}{x} \)
c. \( \frac{1}{4 \pi \epsilon_{0}} \frac{Q X}{R^{2}} \)
D. zero


Let \( f \) be function defined on \( [a, b] \) such
that \( f^{\prime}(x)>0, \) for all \( x \in(a, b) . \) Then
prove that \( f \) is an increasing function on \( (a, b) \)


The acceleration of the object over the
interval (2,4) will be :
A. \( 4 m / s^{2} \)
B \( \cdot 2 m / s^{2} \)
c. \( 8 m / s^{2} \)
D. \( 6 m / s^{2} \)


Solve;
\( \lim _{x \rightarrow 0} \frac{(1+x)^{6}-1}{(1+x)^{2}-1} \)


Evaluate \( \int \frac{x \cos ^{-1} x}{\sqrt{1-x^{2}}} d x \)


Multiple Choice Questions Photochemical smog consists of
A. \( S O_{2}, C O_{2} \) hydrocarbons
B. \( O_{3}, S O_{2} \) hydrocarbons
\( \mathrm{c} \cdot O_{3}, P A N, N O_{X} \)
D. \( S O_{2}, P A N, \) smoke


Arrange the following electromagnetic waves in increasing order of their frequencies (i.e., begin with the lowest frequency): Visible light, \( \gamma \) rays, X rays
micro waves, radio waves, infrared radiations and ultraviolet radiations.


Glycosuria is the condition, where a
man
A. Eats more sugar
B. Excretes sugar in urine
c. sugar is excreted in faeces
D. Has low sugar level in blood


\( 33 \frac{1}{3} \% \) of \( 1 \frac{1}{2} \) minute is equal to
A. 2000 seconds
B. 5000 seconds
c. 3000 seconds
D. 6000 seconds


Which of the following is a linear molecule?
A \( . H_{2} O \)
в. \( H_{2} O_{2} \)
\( c \cdot D_{2} O \)
D. \( N_{2} \),


Two trains \( 121 \mathrm{m} \) and \( 99 \mathrm{m} \) in length are running in opposite directions with velocities \( 40 \mathrm{km} \mathrm{h}^{-1} \) and \( 32 \mathrm{km} \mathrm{h}^{-1} \). In
what time they will completely cross each other?
A . 9 s
B. 11 s
\( c \cdot \) 13 \( s \)
D. 15 s


Which of the following relationships is not correct for the reaction between
\( \Delta H \) and \( \Delta U ? \)
A. When \( \Delta n_{g}=0 \) then \( \Delta H=\Delta U \)
B. When \( \Delta n_{g}> \) O then \( \Delta H>\Delta U \)
C. When \( \Delta n_{g}<0 \) then \( \Delta H<\Delta U \)
D. when \( \Delta n_{g} R T=0 \) then \( \Delta H>\Delta U \)


The maximum vertical distance
through which a full dressed astronaut canjump on the earth is \( 0.5 \mathrm{m} \)
Estimate the maximum vertical
distance through which he can jump on the moon, which has a mean density \( 2 / 3 \) rd that of the earth and radius one
quarter that of the earth.
A . \( 1.5 \mathrm{m} \)
B. 3 m
\( c \cdot 6 m \)
D. 7.5 \( m \)


Vapour pressure of water at certain
temperature is \( 155 \mathrm{mm} \) Hg and that of the another solvent 'X' is 'p' mm Hg. Molecular weight of 'X' is 128. An
aqueous solution of 'X'(64\% by wt) has
a vapour pressure of \( 145 \mathrm{mm} \) Hg. What is 'p'?


The phase difference between the instantaneous velocity and acceleration of a particle executing simple harmonic motion is:-
A. zero
в. \( 0.5 \pi \)
\( c \)
D. \( 0.707 \pi \)


The sum of the oxidation state of the
nitrogen atom in hyponitrous acid, nitric acid and nitrous acid is


\( \operatorname{Let} f(x)=\left\{\begin{array}{cc}x^{2} / 2 & 0<x \leq 1 \\ 2 x^{2}-3 x+3, & 1<x<2\end{array}\right. \)
then which is incorrect
This question has multiple correct options
A. \( f \) is continuous in (0,2)
B. \( f \) is not continuous at all points in (0,2)
c. \( f \) is differentiable in (0,2)
D. \( L t_{x \rightarrow 1^{+}} f(x)=L t_{x \rightarrow 1^{-}} f(x) \)


For the points on the circle \( x^{2}+y^{2}- \)
\( 2 x-2 y+1=0, \) the sum of maximum
and minimum values of \( 4 x+3 y \) is
A \( \cdot \frac{26}{3} \)
B . 10
c. 12
D. 14


An aeroplane flying at a constant speed
releases a bomb. As the bomb moves
away from the aeroplane, it will
A. always be vertically below the aeroplane only if the aeroplane was flying horizontally
B. always be vertically below the aeroplane only if the aeroplane was flying at an angle of \( 45^{\circ} \) to the horizontal
c. always be vertically below the aeroplane
D. gradually fall behind the aeroplane if the aeroplane was flying horizontally


The reagent used for getting trans
alkene from alkyl substituted acetylene with hydrogen is :
\( \mathbf{A} \cdot N a \) in liq. \( N H_{3} \)
B. anhy. AlCla
c. \( Z n+H C l \)
D. \( H_{2} \) in presence of \( N i \) (or) \( P t \) (or) \( P d \)


If \( x \) and \( y \) are sides of two squares such
that \( y=x-x^{2} \). Find the rate of change
of area of second square (side \( y \) ) with respect to area of the first square (side
\( x) \) when \( x=1 \mathrm{cm} \)


Compare the imbibing capacities of pea
and wheat seeds.


Which of the following compounds contain(s) no covalent bonds?
\( \boldsymbol{K} \boldsymbol{C l}, \boldsymbol{P H}_{3}, \boldsymbol{O}_{2}, \boldsymbol{B}_{2} \boldsymbol{H}_{6}, \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \)
A. \( K C l \)
в. \( K C l, B_{2} H_{6} \)
c. \( K C l, B_{2} H_{6}, P H_{3} \)
D. \( K C l, H_{2} S O_{4} \)


The rate of increase of length of the
shadow of a man 2 metres height, due
to a lamp at 10 metres height, when he is moving away from it at the rate of \( 2 m / s e c, \) is
A \( \cdot \frac{1}{2} \mathrm{m} / \mathrm{sec} \)
B. \( \frac{2}{5} \) m/sec
c. \( \frac{1}{3} \mathrm{m} / \mathrm{sec} \)
D. \( 5 m / s e c \)


Let \( R \) be a relation from a set \( A \) to a set
\( B, \) then:
\( \mathbf{A} \cdot R=A \cup B \)
В . \( R=A \cap B \)
c. \( R \subset A \times B \)
D. \( R \subseteq B \times A \)


The maximum potential energy / length increases with:
A. Amplitude
B. wavelength
c. Frequency
D. Velocity


Answer the following question:
Write the general electronic
configuration of lanthanoids.
2. Why are most of the compounds of transition metals coloured?


The average velocity of an ideal gas
molecule at \( 27^{\circ} C \) is \( 0.3 m / \) sec. The
average velocity at \( 927^{\circ} \mathrm{C} \) will be:
A. \( 0.6 m / s e c \)
в. \( 0.3 m / \)sec
\( \mathbf{c} \cdot 0.9 m / \)sec
D. \( 3.0 m / s e c \)


Classify the following proteins
(a) Keratin
(b) Haemoglobin \( (c) \) Albumin
(d) Myosin
(e) Collagen Insulin


State whether given statement is True or False
Electricity is power.
A. True
B. False


Which of the following is a correct Irving-
Williams order (tendency of complex
formation)?
\( \mathbf{A} \cdot M n^{2+}<F e^{2+}<C o^{2+}<N i^{2+} \)
B. \( N i^{2+}<C o^{2+}<F e^{2+}<M n^{2+} \)
\( \mathbf{c} \cdot F e^{2+}<M n^{2+}<N i^{2+}<C o^{2+} \)
D \( \cdot C o^{2+}<M n^{2+}<F e^{2+}<N i^{2+} \)


A compound contains two dissimilar asymmetric carbon atoms. The number of optically active isomers is:
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. 5


The degree of the differential equation \( \boldsymbol{y}_{3}^{2 / 3}+\mathbf{2}+\mathbf{3} \boldsymbol{y}_{2}+\boldsymbol{y}_{1}=\mathbf{0} \) is:
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c .3 \)
D. none of these


In the wall of alimentary canal, which is correct sequence from outer to inner?
A. Serosa, longitudinal muscle, mucosa, sub mucosa
B. Mucosa, serosa, long muscle
c. serosa, long muscle, circular, sub-mucosa, mucosa
D. Serosa, Iong muscle, sub-mucosa, mucosa


Calculate the number of molecules of
\( H F \) which are contained in gaseous
form due to hydrogen bonding if the
density of \( H F \) is gaseous phase at 1 \( \operatorname{atm}, 300 K \) is 3.248 g/litre?


\( \sqrt{\mathbf{2}}+\sqrt{\mathbf{2}}+\sqrt{\mathbf{2}}+\ldots+\boldsymbol{n} \) terms
\( \mathbf{2} \cos \frac{\boldsymbol{\pi}}{\mathbf{2}^{n+1}}, \boldsymbol{n} \boldsymbol{\epsilon} \boldsymbol{N} \)


Out of the following, select Lux-Flood Acid.
A. \( C O_{2} \)
в. \( B F_{3} \)
\( \mathrm{c} \cdot H^{+} \)
D. \( A l\left(C H_{3}\right)_{3} \)


Find the area of the triangle for the following
(i) base \( =6 \mathrm{cm}, \) height \( =8 \mathrm{cm} \)


Define relaxation time of the free
electrons drifting in a conductor: How is it related to the drift velocity of free electrons? Use this relation to deduce
the expression for the electrical resistivity of the material.


A parallel plate capacitor consists of
two circular plates each of radius \( 12 \mathrm{cm} \)
and separated by \( 5.0 m m . \) The capacitor is being charged by an external source. The charging current is constant and is
equal to \( 0.15 A \). The rate of change of potential difference between the plates will be :
A. \( 8.173 \times 10^{7} V / s \)
В . \( 7.817 \times 10^{8} V / s \)
C \( .1 .873 \times 10^{9} \mathrm{V} / \mathrm{s} \)
D. \( 3.781 \times 10^{10} V / s \)


Which of the following is not true about
the formation of winds due to uneven
heating of land at Equator and Polar
regions?
A. The winds blow from the \( 0-30^{\circ} \) latitudes, taking
place of the warm air at the equator that has risen up, towards the equator and constitute the Polar winds.
B. The cool air at the poles rushes in to take place of the
warmer winds in the \( 60^{\circ} \) belt and constitute the Polar
winds.
C. The winds of the wind is not exactly in the North-South direction because of the rotation of the Earth.
D. The pressure difference between the equatorial and polar regions leads to the formation of winds in the North-South direction


Answer the following:
What is the value of impedance of a resonant series LCR circuit?


\( \cot ^{-1}(\cot 5 \pi / 4)= \)
\( \mathbf{A} \cdot \pi / 4 \)
В . \( -\pi / 4 \)
c. \( 3 \pi / 4 \)
D. none of these


What is the specific heat of a \( 2.0 g \) sample of metal which requires the addition of \( 8 J \) to be heated from \( 293 K \)
to \( 303 K ? \)
A . 0.4
B. 0.02
c. 0.6
D. 2.5


Evaluate the integral \( \int_{2}^{3} \frac{\sqrt{\boldsymbol{x}}}{\sqrt{\mathbf{5}-\boldsymbol{x}}+\sqrt{\boldsymbol{x}}} \boldsymbol{d} \boldsymbol{x} \)
A \( \cdot 1 / 2 \)
B . \( 3 / 2 \)
\( c \cdot 5 / 2 \)
D. 0


A resistor, an indicator and a capacitor are connected in series with a \( 120 \mathrm{V}, 100 \) \( \mathrm{Hz} \) ac source. Voltage leads the current
by \( 35^{\circ} \) in the circuit. If the resistance of
the resistor is \( 10 \Omega \) and the sum of
inductive and capacitive reactance is \( 17 \Omega, \) calculate the self-inductance of
the inductor.


The masses of three copper wires are in the ratio 1: 3: 5 and their lengths are
in the ratio \( 5: 3: 1 . \) The ratio of their
resistance is
A . 15: 1: 125
B. 1: 125: 15
c. 125: 1: 15
D. 125: 15: 1


The electronic configuration of
gadolinium is:
\( \mathbf{A} \cdot[X e] 4 f^{3} 5 d^{5} 6 s^{2} \)
\( \mathbf{B} \cdot[X e] 4 f^{6} 5 d^{2} 6 s^{2} \)
\( \mathbf{c} \cdot[X e] 4 f^{8} 5 d^{9} 6 s^{2} \)
\( \mathbf{D} \cdot[X e] 4 f^{7} 5 d^{1} 6 s^{2} \)


A student prepares for an
experiment involving a voltaic cell. Which of the following is needed the least to perform the experiment?
A. Burette
B. Salt bridge
c. Strip of zinc metal
D. copper wire
E. Solution of zinc sulfate


Three cards are drawn at random from a
pack of 52 cards. What is the probability that all the three cards are kings?


The price of petrol is increased by \( 25 \% \)
By how much precent a car owner should reduce his consumption of petrol so that the expenditure on petrol would not be increased?
A . \( 25 \% \)
B . 30\%
c. \( 50 \% \)
D . 20\%


Prove that \( \frac{\left(\boldsymbol{a}^{\boldsymbol{p}+\boldsymbol{q}}\right)^{2}\left(\boldsymbol{a}^{\boldsymbol{q}+\boldsymbol{r}}\right)^{2}\left(\boldsymbol{a}^{\boldsymbol{r}+\boldsymbol{p}}\right)^{\mathbf{2}}}{\left(\boldsymbol{a}^{\boldsymbol{p}} \cdot \boldsymbol{a}^{\boldsymbol{q}} \boldsymbol{a}^{\boldsymbol{r}}\right)^{\boldsymbol{4}}}=\mathbf{1} \)


How can saline hydrides remove traces of water from organic compounds?


Monoecious plant of Chara shows
OCCUrrence of
A. Stamen and carpel on the same plant
B. Upper antheridium and lower oogonium on the same plant
C. Upper oogonium and lower antheridium on the same plant
D. Antheridiophore and archegoniophore on the same plant


The height at which the weight of a body becomes \( \frac{1}{16} t h, \) its weight on the surface of earth (radius \( \boldsymbol{R} \) ), is
\( A .3 R \)
в. \( 4 R \)
\( c .5 R \)
D. \( 15 R \)


A source of wave vibrates with a
frequency \( 500 H z . \) The wave travels 33
\( \mathrm{m} \) in \( 0.1 s . \) How far does the waves
travels when the source executes 150
vibrations?
A . \( 11 m \)
B. \( 99 m \)
\( c .66 m \)
\( \mathbf{D} \cdot 128 m \)


Check whether the following are
Quadratic equations
\( x^{2}+3 x+1=(x-2)^{2} \)


Embryophyta includes
A . Algae
B. Fungi
c. Bryophyta
D. All of the above


If the point (3,2) lies on the graph of the
equation \( 5 x+a y=19, \) then find \( a \)
\( \mathbf{A} \cdot \mathbf{5} \)
B. 7
\( c . \)
D. 2


Which statement(s) about cathode rays
is/are correct?
This question has multiple correct options
A. They travel in straight lines towards cathode.
B. They produce fluorescent discharge through the walls of the tube
C. They produce heating effect.
D. They can effect photographic plate.


A photo-cell employs photoelectric
effect to convert:
A. change in the frequency of light into a change in electric voltage.
B. change in the intensity of illumination into a change in photoelectric current.
C. change in the intensity of illumination into a change in the work function of the photocathode.
D. change in the frequency of light into a change in the electric current.


A particle of mass \( m \) is made to move
with uniform speed \( v \) along the perimeter of a regular hexagon. The magnitude of impulse applied at each
corner is:
A . \( m v \)
B. \( m v \sqrt{3} \)
c. \( \frac{m v}{2} \)
D. \( \frac{m v}{\sqrt{3}} \)


A p-njunction diode cannot be used
A. as a rectifier.
B. for converting light energy to electric energy.
C . for getting light radiation.
D. for increasing the amplitude of an AC signal.


A thermometer has a low thermal
capacity. Why is this an advantage?
A. The thermometer does not absorb much thermal energy to raise its own temperature
B. The thermometer does not conduct much thermal energy to the surroundings
C. The thermometer does not melt when it gets hot
D. The thermometer does not radiate much thermal
energy to the surroundings


What is \( Q \) factor of a RC circuit?
A \( \cdot \frac{1}{R} \)
в. \( \frac{X_{C}}{R} \)
\( c .1 \)
D.


The angles of a triangle are in the ratio
of \( 1: 2: 3 . \) Find the measure of each
angle of the triangle
A \( \cdot 30^{\circ}, 60^{\circ}, 90^{\circ} \)
B . \( 20^{\circ}, 60^{\circ}, 90^{\circ} \)
c. \( 30^{\circ}, 30^{\circ}, 90^{\circ} \)
D. None of these


The resistance of \( 1 \mathrm{N} \) solution of acetic
acid is \( 250 \Omega \) when measured in a cell
having a cell constant of \( 1.15 \mathrm{cm}^{-1} . \) The
equivalent conduction (in oh \( m^{-1} c m^{2} e q u i v^{-1} \) ) of \( 1 N \) acetic acid is
A . 2.3
B. 4.6
c. 9.2
D. 18.4


Parallel venation occurs in dicot
A . corymbium
B. Ageratum
c. Carthamus
D. Centipeda


The line PX perpendicular to PQ in the
plane of PQR.


117 grams of \( N a C l \) are dissolved
in water to make \( 500 m L \) of
solution. Water is then added to this
solution to make a total of one liter
of solution. The final molarity of
the solution is :
\( A \cdot 4 M \)
в. 2 М
\( c \cdot 1 M \)
D. \( 0.5 ~ M \)
E . 0.585 М


In a certain region of space, electric field is along the z-direction throughout The magnitude of electric field is, however, not constant but increases
uniformly along the positive z-direction, at the rate of \( 10^{5} N C^{-1} m^{-1} \) per metre. What are the force and torque
experienced by a system having a total
dipole moment equal to \( 10^{-7} \mathrm{Cm} \) in the negative z-direction?


Which of the following statements is
false?
A. Vegetables conduct electricity
B. Passage of electric current will not change the colour of a solution
C. An electrode conducts electricity
D. Electroplating is one of the applications of chemical effects of electrical current


Draw a circle with center \( \boldsymbol{O} \) and radius
\( 6 \mathrm{cm} . \) Take a point \( P \) outside the circle
at a distance of \( 10 \mathrm{cm} \) from \( O . \) Draw
tangents to the circle from point \( P . \) Let
the tangents intersect the circle in points \( A \) and \( B . \) Find the approximate
value of \( \angle O P B \)
A \( .37^{\circ} \)
B. \( 53^{\circ} \)
\( c \cdot 45^{\circ} \)
D. None of these


Induced abortion is also called
A. STD
в. мтр
\( c \cdot \mid u D \)
D. PID


Find the value of \( (64)^{-\frac{1}{3}} \)


Mammals have negative -pressure breathing.


Simplify the following expressions:
(A) \( 7 i^{2} \)
(B) \( -6 i^{8} \)
\( (C) 8 i^{7} \)


Simplify:tan \( ^{-1}(1 / 2)+\tan ^{-1}(1 / 3) \)


Prove that
\[
\begin{array}{l}
(\cos \alpha+\cos \beta)^{2}+(\sin \alpha+\sin \beta)^{2}= \\
4 \cos ^{2}\left(\frac{\alpha-\beta}{2}\right)
\end{array}
\]


Aluminium foils are used to wrap food items.
A . True
B. False


The isoelectronic pair is:
A. \( C O, N_{2} \)
в. \( O, N O \)
c. \( C_{2}, H F \)
D. \( H F, H C l \)


Give reasons
A heavy truck is filled with 6 to 14 wheels.


Define the term 'conductivity' of a metallic wire. write its Sl unit.


Select the correct option, among \( \boldsymbol{S} \boldsymbol{c}(\boldsymbol{I} \boldsymbol{I} \boldsymbol{I}), \boldsymbol{T} \boldsymbol{i}(\boldsymbol{I} \boldsymbol{V}), \boldsymbol{P} \boldsymbol{d}(\boldsymbol{I} \boldsymbol{I}) \) and \( \boldsymbol{C} \boldsymbol{u}(\boldsymbol{I} \boldsymbol{I}) \)
ions.
A. All are paramagnetic
c. \( S c(I I I), T i(I V) \) are paramagnetic and \( P d(I I I), C u(I I) \) are diamagnetic
D. \( S c(I I I), T i(I V) \) are diamagnetic and \( P d(I I), C u(I I) \) are paramagnetic


What is the product in the given
reaction?


Find the common difference and write
the next four terms of each of the
following arithmetic progression:
\( -1,-\frac{5}{6},-\frac{2}{3}, \dots \)


Concentration 1 microgram per gram is \( \boldsymbol{x} \) ppm. Then, the value of \( \boldsymbol{x} \) is :


\( 1.4 \mathrm{g} \) of acetone dissolved in \( 100 \mathrm{g} \) of benzene gave a solution which freezes
at \( 277.12 \mathrm{K} . \) Pure benzene freezes at
\( 278.4 \mathrm{K} .2 .8 \mathrm{g} \) of a solid
(A) dissolved in
\( 100 \mathrm{g} \) of benzene gave a solution which froze at \( 277.76 \mathrm{K} \). Calculate the molar mass of \( (A) \)


The ratio (R) of output resistance \( r_{0} \)
and and the input resistance \( r_{i} \) in
measurements of input and output
characteristics of a transistor is
typically in the range:
A . \( R \sim 10^{2}-10^{3} \)
В. \( R \sim 1-10 \)
c. \( R \sim 0.1-1.0 \)
D. \( R \sim 0.1-0.01 \)


Read the following graph and answer the question given below
What is the percentage obtained by the
student ?
\( A \cdot 80 \% \)
B. \( 63 \% \)
\( c .57 \% \)
\( 0.90 \% \)


Number of 9 digits numbers divisible by
nine using the digits from 0 to 9 if each digit is used almost once is \( \boldsymbol{K}=\mathbf{8 !} \)
then \( K \) has the value equal to


The type of bond that is most important in maintaining secondary structure of a protein is
A. disulphide bridges
B. hydrogen bonding within the backbones
c. hydrogen bonding between \( R \) group
D. salt bridges


Which of these are the characteristics
of wave function \( \mathbf{\Psi} ? \)
This question has multiple correct options
A. \( \Psi \) must be single valued
в. \( \int_{-\infty}^{+\infty} \Psi^{2} d x d y d z=1 \)
c. \( \Psi \) must be finite and continous
D. \( \Psi \) represents a standing wave


Write the value of \( \tan ^{-1}\left(\frac{1}{x}\right) \) for \( x<0 \) in terms of \( \cot ^{-1}(x) \)


Assertion \( \operatorname{Let} A=\left[\begin{array}{ll}a & b \\ b & a\end{array}\right] \) and \( B=\left[\begin{array}{ll}p & q \\ r & s\end{array}\right] \)
If \( b=0, \) then \( A B=B A \)
Reason

If \( b \neq 0, \) then \( A B=B A \)
\( \Leftrightarrow \boldsymbol{p}=\boldsymbol{s} \boldsymbol{a} \boldsymbol{n} \boldsymbol{d} \boldsymbol{q}=\boldsymbol{r} \)
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


The volume of an air bubble increases
by \( x \% \) as it rises from the bottom of a lake to its surface. If the height of the water barometer is \( \mathrm{H} \), the depth of the lake is
\( ^{\mathrm{A}} \cdot\left(\frac{H+x}{100}\right)^{2} \)
В. \( \frac{H x}{(100+x)} \)
c. \( \frac{H x}{100} \)
D. \( \frac{100 H}{x} \)


The minimum number of carbon atoms
that should be present in a monosaccharide is:


How many diagonals does each of the following have?
(a) A convex quadrilateral
(b) A regular hexagon
(c) A triangle


If ball of steel (density \( \rho=7.8 \mathrm{cm}^{-3} \) )
attains a terminal velocity of \( 10 \mathrm{cms}^{-1} \)
when falling in a tank of water
(coefficient of viscosity \( \boldsymbol{\eta}_{\boldsymbol{w} \text {ater}}=\mathbf{8 . 5} \times \)
\( 10^{-4} \) Pa.s then its terminal velocity in
glycerin \( \left(\rho=1.2 g c m^{-3} \eta=13.2 P a . s\right) \)
would be nearly:
A \( .1 .5 \times 10^{-5} \mathrm{cms}^{-1} \)
в. \( 1.6 \times 10^{-5} \mathrm{cms}^{-1} \)
c. \( 6.25 \times 10^{-4} \mathrm{cms}^{-1} \)
D. \( 6.45 \times 10^{-4} \mathrm{cms}^{-1} \)


\( (\sin \theta+\cos \theta)(1-\sin \theta \cos \theta) \) can be
written as:
\( \mathbf{A} \cdot \sin \theta+\cos \theta \)
\( \mathbf{B} \cdot \sin ^{3} \theta-\cos ^{3} \theta \)
\( \mathbf{c} \cdot \sin ^{3} \theta+\cos ^{3} \theta \)
\( \mathbf{D} \cdot \sin \theta-\cos \theta \)


Polar satellites:
A. are high altitude satellite
B. are widely used for telecommunication
C. are used for environmental studies
D. go around the Earth in a East-West direction
E. have time-period of rotation of 24 hours


Let \( T_{r} \) be the \( r^{t h} \) term of an A.P for \( r= \)
\( 1,2,3, \dots \) if for some positive integers \( \boldsymbol{m}, \boldsymbol{n}, \) we have \( \boldsymbol{T}_{\boldsymbol{m}}=\frac{\mathbf{1}}{\boldsymbol{n}} \) and \( \boldsymbol{T}_{\boldsymbol{n}}=\frac{\mathbf{1}}{\boldsymbol{m}} \)
then \( T_{m n} \) equals
A \( \cdot \frac{1}{m n} \)
B. \( \frac{1}{m}+\frac{1}{n} \)
c. 1
D.


toppr
Q Type your question
Glucose
Glyceraldehyde
Lactic
\( +\mathrm{CO}_{2} \)
\( \mathbf{A} \cdot \mathbf{A}-N A D H+H^{+} \rightarrow N A D^{+} ; \mathrm{B}-N A D^{+} \rightarrow N A D H+ \)
\( H^{+} ; \mathrm{C}-N A D^{+} \rightarrow N A D H+H^{+} \)
B. A-NADH \( +H^{+} \rightarrow N A D^{+} ; \) B-N \( A D H+H^{+} \rightarrow \)
\( N A D^{+} ; \mathrm{C}-N A D^{+} \rightarrow N A D H+H^{+} \)
C \( \cdot \mathrm{A}-N A D^{+} \rightarrow N A D H+H^{+} ; \mathrm{B}-N A D H+H^{+} \rightarrow \)
\( N A D^{+} ; \mathrm{C}-N A D H+H^{+} \rightarrow N A D^{+} \)
D. \( A-N A D^{+} \rightarrow+H^{+} ; B-N A D H+H^{+} \rightarrow N A D^{+} ; C- \)
\( N A D^{+} \rightarrow N A D H+H^{+} \)


Find the product. Write the answer in standard form
\( i(6-2 i)(7-5 i) \)
A. \( 52+16 i \)
B. \( 10 i^{3}+44 i^{2}+42 i \)
c. \( -44-32 i \)
D. \( 44+32 i \)


\( \{3 x-2 \leq 10 \text { and } x \) belongs to natural numbers
Find the range of \( x \)


Gorilla like man with large head and hands and protruding jaws, is produced due to
A. Over secretion of thyroxin
B. Over secretion of growth hormone since maturity
c. Excess of vitamin 'C' in diet
D. Excess secretion of TSH


OABC is a current carrying square loop
an electron is projected from the centre
of loop along its diagonal \( A C \) as shown.
Unit vector in the direction of initial
acceleration will be
\( A \cdot \hat{k} \)
B. \( -\left(\frac{\hat{i}+\hat{j}}{\sqrt{2}}\right) \)
\( c .-\hat{k} \)
\( \frac{\hat{i}+\hat{j}}{\sqrt{2}} \)


Which of the following statements is not true about low density polythene?
A. They are tough
B. They are hard
c. Poor conductor of electricity
D. Highly branched structure


is the major source of
fresh water
A. Ground water
B. Sea water
c. Lake
D. None of the above


The coefficient of superficial expansion of rod is \( 4 \times 10^{-5} /^{\circ} \mathrm{C} \). The percentage
increase in the volume of a cube of that
metal when it is heated from \( 0^{\circ} \mathrm{C} \) to
\( 100^{\circ} \mathrm{C} \) is :
A . 0.4\%
в. 0.8\%
c. 1.2\%
D. 0.6\%


Find the time period of a periodic
motion having frequency as \( 100 H z \)
A \( \cdot T=\frac{1}{25} s \)
в. \( T=\frac{1}{20} s \)
c. \( T=\frac{1}{100} s \)
D. \( T=\frac{100}{25} s \)


The van't Hoff factor for a dilute solution
of \( \boldsymbol{K}_{3}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{6}\right] \) is likely to be:
A . 10
B. 4
\( c \cdot \frac{1}{4} \)
D.


If \( \boldsymbol{f}=\{(\boldsymbol{4}, \boldsymbol{5}),(\boldsymbol{5}, \boldsymbol{6}),(\boldsymbol{6},-\boldsymbol{4})\} \) and \( \boldsymbol{g}= \)
\( \{(\boldsymbol{4},-\boldsymbol{4}),(\boldsymbol{6}, \boldsymbol{5}),(\boldsymbol{8}, \boldsymbol{5})\} . \) Then \( |\boldsymbol{f}-\boldsymbol{g}|=? \)


Which is the order of tulsi?
A . Lamiaceae
B. Lamiales
c. Poales
D. Sapindales


Which of the following molecular formulae represent the ore carnallite?
A. \( N a_{2} A l_{2} O_{4} \)
в. \( N a_{3} A l F_{6} \)
c. \( K C l M g C l_{2} \cdot 6 H_{2} O \)
D. \( F e_{3} O_{4} \)


A \( 10 V \) olts battery of internal resistance
one ohm is connected to a \( 20 \mathrm{V} \) olt
battery of internal resistance 2ohm. The
combination is put across a resistance
of 30 oh \( m . \) Find the current through
each battery


Sedimentation potential is reverse of:
A. electro-osmosis
B. electrophoresis
c. electrokinetic potential
D. streaming potential


A wire lying along y-axis from \( y=0 \) to \( y=1 \) m carries a current of \( 2 \mathrm{mA} \) in the
negative y-direction.The wire lies in a non-uniform magnetic field given by \( \vec{B}=(0.3 T / m) y \hat{i}+(0.4 T m) y \hat{j} . \) The
magnetic force on the entire wire is
A \( \cdot-3 \times 10^{-4} \hat{j} N \)
В. \( 6 \times 10^{-3} \hat{k} N \)
c. \( -3 \times 10^{-4} \hat{k} N \)
D. \( 3 \times 10^{-4} \hat{k} N \)


The number of hydrogen atoms attached to phosphorus atom in hypophosphorous acid is :
A. zero
B. two
c. one
D. three


Pepsin acts in
A. Basic medium
B. Acidic medium
C. Neutral medium
D. All types of media


If a function such that \( \boldsymbol{f}(\mathbf{0})= \)
\( \mathbf{2} ; \boldsymbol{f}(\mathbf{1})=\mathbf{3} \) and \( \boldsymbol{f}(\boldsymbol{x}+\mathbf{2})=\mathbf{2} \boldsymbol{f}(\boldsymbol{x})- \)
\( \boldsymbol{f}(\boldsymbol{x}+\mathbf{1}) \forall \boldsymbol{x} \in \boldsymbol{R} \) then \( \mathrm{f}(5)= \)
\( A \cdot 7 \)
B. 13
\( c \)
D.


Which plating is done on bicycle handle bars and wheel rims?
A. Iron plating
B. Gold plating
c. silver plating
D. Chromium plating


The number of molecules of water of
crystallisation present in washing soda crystals is:
A . five
B. two
\( c . \) ten
D. seven


Total population of a district is 3,540 out of which 2,065 are males. Find the ratio of males to females.


Which of the following is an energydependent process?
A. Facilitated diffusion
B. Active transportt
c. Endosmosis
D. Exosmosis


The decreasing leaving group order of the following compounds is:
\( \boldsymbol{i} . \boldsymbol{F}_{3} \boldsymbol{C} \boldsymbol{S} \boldsymbol{O}_{3}^{\ominus} \quad \boldsymbol{i} \boldsymbol{i} . \boldsymbol{C l}_{3} \boldsymbol{C}-\boldsymbol{C O O}^{\ominus} \)
iii. Ph \( S O_{3}^{\ominus} \) iv. \( M e S O_{3}^{\ominus} \)
A \( \cdot(i)>(i i)>(i i i)>(i v) \)
B. \( (i v)>(i i i)>(i i)>(i) \)
c. \( (i i i)>(i)>(i i)>(i v) \)
D. \( (i)>(i i i)>(i v)>(i i) \)