ASSERTION: \( C u F e S_{2} \) is concentrated
by froth floatation method.

REASON: \( C u F e S_{2} \) is the main ore of
copper.
A. If both assertion and reason are CORRECT, and reason is the CORRECT explanation of the assertion
B. If both assertion and reason are CORRECT, but reason is NOT the CORRECT explanation of the assertion
c. If assertion is CORRECT but reason is INCORRECT
D. If assertion is INCORRECT but reason is CORRECT


The electronic configuration of silicon is and that of sulphur is
A. silicon - 2, 8, 1; Sulphur - 2, 8, 6
B. Silicon - 2, 8, 4; Sulphur - 2, 8, 3
c. silicon - 2, 8, 2; sulphur - 2, 8, 6
D. silicon - 2, 8, 4; Sulphur - 2, 8, 6


Find the value of \( J K \) in the following
figure if \( \angle \boldsymbol{H} \boldsymbol{L} \boldsymbol{G}=\angle \boldsymbol{J} \boldsymbol{L} \boldsymbol{K} \)
A . 11
3
\( c \cdot 21 \)
D.


f \( \boldsymbol{T} \boldsymbol{r}(\boldsymbol{A})=\boldsymbol{6}, \) then \( \boldsymbol{T} \boldsymbol{r}(\boldsymbol{4} \boldsymbol{A})= \)
\( A \cdot \frac{3}{2} \)
B. 2
c. 12
D. 24


If each side of a rectangle is increased by \( 20 \% \) then the percentage increase in its area is:
A . \( 40 \% \)
B. 20\%
c. \( 44 \% \)
D. 30\%


The IUPAC name of the compound is:
A. 3-chloro-3-phenyl-1-propene
B. 3-benzyl-3-chloro-1-propene
c. 3-phenyl-3-chloro-1-propane
D. 3-chloro propene benzen


Lalita has taken sulphur powder \( (P) \) in a deflagrating spoon, burnt it and put it
in a gas jar. Then she removed the spoon and added water. In another
experiment, she has taken water in one
beaker and added a small piece of
sodium (Q). After some time, she took
both the solutions and checked them
with litmus paper. What result would
she expect?
A. In case \( P \); blue to red, in case \( Q: \) red to blue
B. In both cases, \( P \) and \( Q \) : blue to red
c. In case \( P: \) red to blue, in case \( Q: \) blue to red
D. In both cases, \( P \) and \( Q: \) red to blue


Which is the most stable allotrope of
sulphur?
A. octahedral sulphur
B. Monoclinic sulphu
c. Plastic sulphur
D. colloidal sulphur


The function \( y=\sin ^{-1}(\cos x) \) is not
differentiable at
This question has multiple correct options
\( \mathbf{A} \cdot x=\pi \)
В. \( x=-2 \pi \)
c. \( x=2 \pi \)
D. None of these


Identify the non-diagonal matrix from
the given options.
\( \mathbf{A} \cdot\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right] \)
\( \mathbf{B} \cdot\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 2 & 0 \\ 1 & 9 & 0\end{array}\right] \)
\( \mathbf{C} \cdot\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 4 & 0 \\ 0 & 0 & 1\end{array}\right] \)
D. \( \left[\begin{array}{ccc}1 & 0 & 0 \\ 0 & 4 & 0 \\ 0 & 0 & -1\end{array}\right] \)


Anisole can be prepared by the action of methyl iodide on sodium phenate. The reaction is called:
A. Wurtz reaction
B. Williamson's reaction
c. Fittig's reaction
D. Etard's reaction


Find the square root of a number 529 by Prime Factorisation Method.


Why are danger signals always red in color?
A. Red light is least scattered by fog and smoke
B. It is the color of danger
c. Both A and B
D. None of these


Among the following oxoacids, the correct decreasing order of acid
strength is:
A. \( H C l O_{4}>H C l O_{3}>H C l O_{2}>H O C l \)
в. \( H C l O_{2}>H C l O_{4}>H C l O_{3}>H O C l \)
D. \( H C l O_{4}>H O C l>H C l O_{2}>H C l O_{3} \)


Determine the tension in the left string immediately after the right string is cut


Which of the following catalyst is used in contact process for manufacture of
\( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} ? \)
A. Oxides of nitrogen
в. \( V_{2} \), \( O_{5} \)
\( \mathrm{c} \cdot \mathrm{Fe}_{2} \mathrm{O}_{3} \)
D. Platinised asbestos


Given that \( z^{2}-10 z+25=9, \) what is \( z \)
\( ? \)
A .3,4
в. 1,6
\( c .2,6 \)
D. 2,


Assertion
It is more difficult to push a magnet
into a coil with more loops.
Reason
Emf induced in the current loop resists
the motion of the magnet.
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


Solve: \( \sin \left(-330^{\circ}\right) \cdot \cos \left(-300^{\circ}\right)+ \)
\( \sin \left(-420^{\circ}\right) \cdot \cos 390^{\circ}=-\frac{1}{2} \)


Represent on number line \( \frac{3}{7} \)


Consider the following reaction:
\( \boldsymbol{M}+\boldsymbol{O}_{2} \rightarrow \boldsymbol{M} \boldsymbol{O}_{2} \)
\( M \) is an alkali metal
\( M O_{2} \) is a stable superoxide
A. \( M \) can not be \( L i \) and \( N a \)
B. \( M \) can not be \( C s \) and \( R b \)
c. \( M \) can not be \( L i \) and \( R b \)
D. None of these


Which of the following systems will show Tyndall effect?
A. Aqueous solution of sodium chloride
B. Aqueous solution of aluminium hydroxide
c. Aqueous solution of glucose
D. Aqueous solution of urea


(i) Write down the IUPAC name of the
following complex:
\( \left[\boldsymbol{C r}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{2} \boldsymbol{C l}_{2}(\boldsymbol{e n})\right] \boldsymbol{C l} \)
(en=ethylenediamine)
(ii) Write the formula for the following complex:
Pentaamminentrito-o-cobalt (III)


\( \frac{L}{L} \)


Choose the correct answer from the
alternatives given.
The simple interest on a sum of money
is \( \frac{1}{16} \) of the sum. If the number of years is numerically equal to the rate percent per annum, then the rate percent per annum is
\( A \cdot 3 \frac{1}{3} \)
в. \( 6 \frac{2}{3} \)
\( c \cdot 2 \frac{1}{2} \)
\( D \cdot 7 \frac{1}{2} \)


State True or False.
For two solutions to be isotonic, \( \boldsymbol{C}_{\mathbf{1}}= \)
\( C_{2} \) in all the cases.
A. True
B. False


Assertion
Statement-I: If an aqueous solution of NaCl is electrolysed, the product
obtained at the cathode is \( H_{2} \) gas and
not Na.
Reason
Statement-II : Gases are liberated faster
than the metals.
A. Statement-l is true, Statement-II is true; Statement-II is correct explanation for Statement-I
B. Statement-lis true, Statement-II is true; Statement-II is NOT a correct explanation for statement-
c. Statement-I is true, Statement-II is false
D. Statement-I is false, Statement-II is true


If \( A \) is an invertible matrix of order \( 3 \times 3 \)
such that \( |\boldsymbol{A}|=\mathbf{5}, \) find the value of
\( \left|\boldsymbol{A}^{-1}\right| \)


Which of the following undergo
maximum diffraction?
A. \( \alpha- \)rays
B . \( \gamma- \) rays
c. radio waves
D. light waves


Define a rigid body


12.2 \( g \) of benzoic acid \( (M=122) \) in 100 g water has elevation in the boiling point of \( 0.27 \mathrm{K} . K_{b}=0.54 \mathrm{K} \mathrm{kg} \mathrm{mol}^{-1} . \) If there is
\( 100 \% \) polymerisation, the number of molecules of benzoic acid in the
associated state is:
A.
B. 2
\( c \cdot 3 \)
\( D \)


During electrolytic reduction of alumina, two auxiliary electrolytes \( x \) and Y are added to increase the
electrical conductance and lower the
temperature of melt in order to make fused mixture very conducting. X and Y
are :
A. cryolite and flourspar
B. cryolite and alum
c. alum and flourspar
D. flourspar and bauxite


What is the oxidation number of
underlined element?
\[
\underline{I} C l_{3}
\]


Find the smallest number by which 72 must be multiplied, so that the product is a perfect cube
A . 3
B. 6
c. 12
D. 4


A retired person wants to invest an
amount of Rs. \( 50,000 . \) His broker
recommends investing in two type of bonds A and B yielding 10\% and 9\% return respectively on the invested
amount. He decides to invest at least
Rs.20, 000 in bond A and at least

Rs. 10,000 in bond \( B . \) He also wants to
invest at least as much in bond \( A \) as in
bond B. Solve this linear programming problem graphically to maximize his
returns.
A. 4900
B. 2900
\( c .5400 \)
D. 4000


In the reaction \( C(s)+C O_{2}(g) \rightleftharpoons \)
\( 2 C O(g), \) the equilibrium pressure is
12 atm. If \( 50 \% \) of \( C O_{2} \) reacts till
equilibrium then \( \boldsymbol{K}_{\boldsymbol{p}} \) will be :
A . 12 atm
B. 6 atm
\( c .20 \) atm
D. 24 atm


A radioactive sample has initial
concentration \( N_{0} \) of nuclei. Then
This question has multiple correct options
A. the number of undecayed nuclei present in the sample decays exponentially with time
B. the activity
(R) of the sample at any instant is directly proportional to the number of undecayed nuclei present in the sample at that time
c. the number of decayed nuclei growth exponentially with time
D. the number of decayed nuclei grows linearly with time


State the Kelper's law which is
represented by the relation \( r^{3} \propto T^{2} \)


For the system shown in figure, the cylinder on the left, at \( L, \) has a mass of \( 600 \mathrm{kg} \) and a cross-sectional area of \( 800 c m^{2} . \) The piston on the right, at \( S \)
has cross-sectional area \( 25 \mathrm{cm}^{2} \) and
negligible weight. If the apparatus is filled with oil \( \left(p=0.78 g / c m^{3}\right) \) what is
the force F required to hold the system in equilibrium?


The statement " \( x>5 \) or \( x<3 " \) is true,
if x equals
\( \mathbf{A} \cdot \mathbf{1} \)
B. 3
\( c \cdot 4 \)
D.


Consider Bohr theory for hydrogen atom. The magnitude of angular momentum, orbit radius and velocity of the electron
in \( n^{t h} \) energy state in a hydrogen atom are \( l, r \) and \( v \) respectively. Find out the
value of \( x \) if product of \( v, r \) and \( l \) is
directly proportional to \( n^{x} \)


The line \( 3 x+2 y=0 \)
A \( \cdot \) passes through (3,2) and \( m=-\frac{3}{2} \)
B. passes through (0,0) and \( m=\frac{3}{2} \)
c. passes through (2,3) and \( m=-\frac{3}{2} \)
D. passes through (0,0) and \( m=-\frac{3}{2} \)


The order of elementary reactions can be determined by the number of molecules participating in a collision. Based on this knowledge, which of the following is least likely an elementary reaction?
A. A unimolecular process such as \( C H_{3} N C \rightarrow C H_{3} C N \)
B. A bimolecular reaction such as \( N O+O_{3} \rightarrow N O_{2}+O_{2} \)
C. A tirmolecular process such as \( O+N_{2} O+N \rightarrow \)
\( N O_{2}+N_{2} \)
D. A tetramolecular process such as \( N_{2}+2 H_{2}+C l_{2} \rightarrow \)
\( 2 N H_{4} C l \)


Choose the correct answer from the
alternatives given in the brackets.
The defect myopia can be corrected by
using a
(Convex lens, Concave lens, Concave mirror, Convex mirror)


Find the G.M of 6 and 24


\( 1 m^{3} \) water is brought inside the lake
upto \( 200 m \) depth from the surface of
the lake. What will be change in the volume when the bulk modulus of
elasticity of water is 22000 at \( m ? \) (density of water is \( 1 \times 10^{3} k g / m^{3} \)
atmosphere pressure \( =10^{5} N / m^{2} \) and
\( \boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{2} \)
В. \( 7.8 \times 10^{-3} m^{3} \)
\( \mathbf{c} \cdot 9.1 \times 10^{-4} m^{3} \)
D. \( 8.7 \times 10^{-4} m^{3} \)


On fertilization of egg nucleus with
sperm nucleus
A. First maturation is completed
B. Second maturation is completed
c. Embryo is formed
D. First polar body is formed


Assertion
Active complex is an intermediate
product.
Reason
Active complex is unstable with high
vibrational energy.
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


Fill in the blank:
The system used for describing the position of a is called
Cartesian system.
A. Point
B. Circle
c. Line
D. Square


Compare \( x \) and \( y \) bond angles for the
above given molecules.
A \( . x>y \)
В \( \cdot y>x \)
\( \mathbf{c} \cdot x=y \)
D. None of these


In CGS, the gravitational unit of force is
A. \( k g f \)
B. \( N \)
\( \mathrm{c} \cdot g f \)
D. dyne


Fill in the blanks
The splitting of white light into different
colours (VIBGYOR) is called


A rod of length \( 10 \mathrm{cm} \) made up of
conducting and non-conducting material (shaded part is nonconducting). The rod is rotated with constant angular velocity 10 rad/sec
about point \( O \), in constant and uniform
magnetic field of 2 Tesla as shown in figure. The induced emf between the
point \( A \) and point \( B \) of rod will be
В. \( 0.1 v \)
\( c .0 .051 v \)
D. \( 0.064 v \)


Doctors use stethoscope to hear the sounds produced during each cardiac cycle. The second sound is heard when
A. AV node receives signal from SA node
B. AV valves open up
c. Ventricular walls vibrate due to gushing in of blood from atria
D. semilunar valves close down after the blood flows into vessels from ventricles.


The maximum value of function \( x^{3}- \)
\( 12 x^{2}+36 x+17 \) in the interval [1,10]
is
A . 17
в. 17
c. 77
D. None of these


Consider a parallelogram \( A B C D, \) with
angle \( \angle B=120^{\circ} . \) A charge \( +Q \) placed
at the corner \( A \) produces field \( E \) and
potential \( V \) at corner \( D \). If we now add
charges \( -2 Q \) and \( +Q \) at corners \( B \) and
\( C \) respectively, the magnitude of field
and potential at \( D \) will become
respectively
\( ^{A} \cdot \frac{\sqrt{3}}{2} E, V \)
в. \( \frac{\sqrt{3}}{2} E, \) о
\( c . E, 0 \)
D. \( \frac{E}{\sqrt{2}}, \frac{V}{\sqrt{2}} \)


A vertical spring with force constant \( k \)
is fixed on a table. A ball of mass \( \mathrm{m} \) at a
height h above the free upper end of the
spring falls vertically on the spring so that the spring is compressed by a
distance d. The net work done in
the process is
\( ^{\mathbf{A}} \cdot m g(h+d)-\frac{1}{2} k d^{2} \)
B . \( m g(h-d)-\frac{1}{2} k d^{2} \)
c. \( m g(h-d)+\frac{1}{2} k d^{2} \)
D \( m g(h+d)+\frac{1}{2} k d^{2} \)


An electron is released from rest in a
region of uniform electric and magnetic
field acting parallel to each other. The electron will
A. move in a straight line
B. move in a circle
c. remain stationary
D. move in a helical path


The value of van't Hoff factor for \( 0.1 \mathrm{M} \)
\( B a\left(N O_{3}\right)_{2} \) solution is \( 2.74 . \) The degree of dissociation is:
\( \mathbf{A} \cdot 100 \% \)
B. \( 92 \% \)
c. \( 87 \% \)
D. \( 74 \% \)


In Thomsons experiment for determining e/m, the potential difference between the cathode and
the anode is same as that between the
deflecting plates ( in the region of crossed fields). If the
potential difference is doubled. Then the factor by which the magnetic field be increased to ensure that the electron
beam remains undeflected is:
A \( \cdot \sqrt{2} \)
B. 2
\( c \cdot 2 \sqrt{2} \)
\( D \cdot 4 \)


Let for a function \( \boldsymbol{f}(\boldsymbol{x}), \boldsymbol{h}(\boldsymbol{x})= \)
\( (f(x))^{2}+(f(x))^{3} \) for every real
number \( \boldsymbol{x} \). Then

This question has multiple correct options
A. \( h \) is increasing whenever \( f \) is increasing
B. \( h \) is increasing whenever \( f \) is decreasing
C. \( h \) is decreasing whenever \( f \) is decreasing
D. nothing can be said in general


When a Dobereiner triad is considered,
the sum of atomic weights of extreme elements \( X \) and \( Z \) is 177.6 and difference
of \( Z \) and \( Y \) is five times the number of
protons present in a neon atom. Identify \( x, Y \) and \( z \)
\( \mathbf{A} \cdot X \rightarrow C a, Y \rightarrow S r, Z \rightarrow B a \)
в. \( X \rightarrow L i, Y \rightarrow N a, Z \rightarrow K \)
c. \( X \rightarrow K, Y \rightarrow R b, Z \rightarrow C s \)
D. \( X \rightarrow S r, Y \rightarrow B a, Z \rightarrow R a \)


A heat engine operates between \( 2100 \mathrm{K} \) and \( 700 \mathrm{K} \). Its actual efficiency is \( 40 \% \) What percentage of its maximum possible efficiency is this?
A. 33.33\%
B. 66.67\%
c. \( 60 \% \)
D. 40\%


Write the balanced chemical equations for the following reactions and identify
the type of reaction:
limestone is heated strongly to form quicklime and carbon dioxide gas is evolved


Explain the importance of reproduction in organisms.


Find the square root of 7744 by the division method.
\( \mathbf{A} \cdot 82 \)
B. 88
c. 92
D. 98


Saritha bought \( \frac{2}{5} \) metre of ribbon and Lalita \( \frac{3}{4} \) metre of ribbon.What is the total length of the ribbon they bought?


The electric batteries used in small
calculators are?
A. weston cell
B. Leclanche cell
c. Nickel-cadmium batteries
D. Lead acid batteries


The piston in a petrol engine goes up and down 3000 times per minute. For this engine, calculate the period of the piston.
A . \( 0.02 \mathrm{s} \)
B. 0.04 s
c. \( 0.05 \mathrm{s} \)
D. 0.08 s


The fraction occupied by nucleus in an
atom is:
A \( \cdot 1 / 10^{-10} \)
B . \( 1 / 10^{8} \)
\( \mathrm{c} \cdot 1 / 10^{-5} \)
D. \( 1 / 10^{5} \)


Which group elements exhibits highest densities?
A. IIIB
в. Iv
c. vı
D. VIIIB


Name the phenomenon that governs the
following-
A. Green beetels living in green bushes are not eaten by the crows
B. All tall plants are obtained in \( F_{1} \) generation, upon crossing pure tall and dwarf pea plant.
C. Tails of mice were surgically removed for several generation ; still mice have tails in the following generation
D. Numbers of blue beetles on green bushes increase in a fur distant location than green beetles on green bushes, isolated by a river.
E. A migrant beetle reproduces with the local population as a result genes of migrant beetle enter the new population.


If \( P(C)=\frac{2}{7}, \) then \( P(\bar{C})= \)
A
B. \( \frac{2}{7} \)
c. 0
D.


If \( \bar{a}, \bar{b} \) and \( \bar{c} \) are non-coplanar vectors and If \( \bar{d} \) is such that \( \overline{\boldsymbol{d}}=\frac{\mathbf{1}}{\boldsymbol{x}}(\overline{\boldsymbol{a}}+\overline{\boldsymbol{b}}+\overline{\boldsymbol{c}}) \)
and \( \bar{a}=\frac{1}{y}(\bar{b}+\bar{c}+\bar{d}) \) where \( x \) and \( y \) are
non-zero real numbers, then \( \frac{1}{x y}(\bar{a}+ \) \( \overrightarrow{\boldsymbol{b}}+\overline{\boldsymbol{c}}+\overline{\boldsymbol{d}})= \)
A . \( 3 \bar{c} \bar{c} \bar{c} \)
в. \( -\bar{a} \)
c. \( \overline{0} \)
D. \( 2 \bar{a} \bar{a} \bar{a} \)


A solution containing 0.2563 g of naphthalene (molecular mass = 128) in \( 50 \mathrm{g} \) of carbon tetrachloride yields a boiling point elevation of \( 0.201^{\circ} \mathrm{C} \) while a solution of 0.6216 g of an unknown solute in the same mass of the solvent
gives a boiling point elevation of
\( 0.647^{\circ} \mathrm{C} . \) Find the molecular mass of
the unknown solute.


The correct equation of motion is :
A \( . v=u+a S \)
B. \( v=u t+a \)
c. \( S=u t+\frac{1}{2} a t \)
D. \( v=u+a t \)


Which of the following is a basic amino acid?
This question has multiple correct options
A. Leucine
B. Methionine
c. Aspargine
D. Arginine


In an A.C. circuit, the instantaneous
values of e.m.f. and current are \( \boldsymbol{E}= \)
\( 200 \sin 314 t \) volts and \( I=\sin (314 t+ \)
\( \pi / 3) \) ampere then the average power
consumed in watts is
A . 200
B. 100
\( c \cdot 0 \)
D. 50


Draw a circle of radius \( 3.2 \mathrm{cm} . \) At a point on it, draw a tangent to the circle using the tangent-chord theorem.


A point particle of mass \( 0.1 \mathrm{kg} \) is executing SHM with amplitude of 0.1m.When the particle passes through the mean position, its K.E is \( 8 \times 10^{-3} J . \) Obtain the equation of
motion of this particle if the initial
phase of oscillation is \( 45^{\circ} \)
\( \mathbf{A} \cdot y=0.2 \sin (4 t+\pi / 2) \)
B \cdot \( y=0.1 \sin (4 t+\pi / 4) \)
C \( \cdot y=0.2 \sin (4 t+\pi / 4) \)
D. None of these


\( \sec ^{2} 50^{\circ}-\cot ^{2} 40^{\circ}-\sin ^{2} 45^{\circ}=? \)
A \( \cdot 1 / 2 \)
B. 5
\( c \cdot 1 \)
D.


(a) What is an ecosystem? List its two main components.
(b) We do not clean ponds or lakes, but an aquarium needs to be cleaned
regularly. Explain.


Show that \( \int_{0}^{1} \frac{\log x}{\sqrt{\left(1-x^{2}\right)}} d x=\frac{\pi}{2} \cdot \log \frac{1}{2} \)


Find the values of \( K \) so that the
quadratic equations \( x^{2}+2(K-1) x+ \)
\( K+5=0 \) has atleast one positive root
A. \( k \leq-1 \)
B. \( k \leq 1 \)
c. \( k \geq-1 \)
D. \( -1 \leq k \leq 1 \)


Take a thin thermocol sheet. Cut it in
circular discs of different radii like
\( 2 c m, 3 c m, 4 c m, 4.5 c m, 5 c m \) etc and
mark centers with sketch pen. Now take
needles of length nearly 6 cm. Pin a
needle to each disc at its centre
vertically. Take water in a large opaque tray and place the disc with 2 cm radius
in such a way that the needle is inside
the water as shown in fig. Now try to
view the free end (head) of the needle
from surface of the water
Are you able to see the head of the
needle?


\( A D \) is the bisector of BC
Which property of triangle applies here?
A. \( S A S \)
B. \( S S S \)
\( c . A A S \)
D. none


The solution of the differential equation \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\frac{\boldsymbol{y}}{\boldsymbol{x}}+\frac{\boldsymbol{\varphi}(\boldsymbol{y} / \boldsymbol{x})}{\boldsymbol{\varphi}^{\prime}(\boldsymbol{y} / \boldsymbol{x})} \) is :
A \( \cdot x \varphi\left(\frac{y}{x}\right)=k \)
в. \( k \varphi\left(\frac{y}{x}\right)=x \)
c. \( \operatorname{ky\varphi}\left(\frac{y}{x}\right)=y \)
D \( \cdot \varphi\left(\frac{y}{x}\right)=k y \)


The wheel of radius \( r=300 \mathrm{mm} \) rolls to
the right without slipping and has a
velocity \( V_{0}=3 m / s \) of its centre 0. The
speed of the point \( A \) on the wheel for the
instant represented in the figure is :-
\( A \cdot 4.36 m / \)
B. \( 5 m / s \)
\( c \cdot 3 m / s \)
\( \mathbf{D} \cdot 1.5 \mathrm{m} / \mathrm{s} \)


There is no gall bladder in
A . Rat
B. Horse
c. whale
D. All of these


When white phosphorous is stored for longer period it appears yellow due to:
A. the formation of oxide layer
B. conversion to another allotropic form
c. the formation of mixture of its compounds
D. phosphorous concentration


In solid state \( \boldsymbol{P} \boldsymbol{C l} \boldsymbol{l}_{5} \) is a:
A. covalent solid
B. octahedral structure
C . ionic solid with \( \left[P C l_{6}\right]^{+} \) octahedral and \( \left[P C l_{4}\right]^{-} \) tetrahedral
D. ionic solid with \( \left[P C l_{4}\right]^{+} \) tetrahedral and \( \left[P C l_{6}\right] \) octahedral


A cube of edge \( 3 \mathrm{cm} \) of iron weighs \( 12 \mathrm{g} \) What is the weight of a similar cube of
iron whose edge is \( 12 \mathrm{cm} \)
A. 768 g
в. 678 g
c. \( 964 \mathrm{g} \)
D. \( 864 \mathrm{g} \)


A colloidal solution is subjected to an electrical field. The particles move towards anode. The coagulation of same
sol is studied using \( N a C l, B a C l_{2} \) and
\( A l C l_{3} \) solutions. Their coagulation
power should be :
A \( \cdot N a C l>B a C l_{2}>A l C l_{3} \)
в. \( B a C l_{2}>A l C l_{3}>N a C l \)
c. \( A l C l_{3}>B a C l_{2}>N a C l \)
D. \( B a C l_{2}>N a C l>A l C l_{3} \)


(a) An organic compound (A) of
molecular formula \( C_{2} H_{4} O \) is prepared
by the reduction of compound (B) of
molecular formula \( C_{2} H_{3} N \) dissolved in
ether, with \( S n C l_{2} \) and \( H C l . \) Compound
(A) reduces Tollen's reagent. When a
drop of conc. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) is added to
compound (A), it polymerises to give a cyclic compound
(C). Identify (A), (B) and (C). Explain the reactions?
(b) Ionic conductance at infinite dilution of \( A l^{3+} \) and \( S O_{4}^{2-} \) are 189 ohm \( ^{-1} \mathrm{cm}^{2} \) gm.equiv \( ^{-1} \) and
160 ohm \( ^{-1} \mathrm{cm}^{2} \) gm.equiv \( ^{-1} \). Calculate
equivalent and molar conductance of the electrolytes at infinite dilution?


Equipment used to minimize industrial
waste are
A. Electrostatic precipitators
B. Scrubbers
c. Tall chimney
D. All of the above


A dome of a building is in the form of a hemisphere. From inside, it was white-
washed at the cost of \( 498.96 . \) If the costt
of white-washing is 2.00 per square metre, find
(i) the inside surface area of the dome
and
(ii) volume of the air inside the dome.


In what ratio does the point \( \left(\frac{1}{2}, 6\right) \) divide the line segment joining the points (3,5) and (-7,9)\( ? \)


With the help of a well labelled diagram, describe the structure of nephron


Define 1 ampere.


ff \( \boldsymbol{y}=\boldsymbol{e}^{\boldsymbol{a} \boldsymbol{x}} \) cos \( \boldsymbol{b} \boldsymbol{x}, \) then find the value of
\( \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}}-\boldsymbol{2} \boldsymbol{a} \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}+\left(\boldsymbol{a}^{2}+\boldsymbol{b}^{2}\right) \boldsymbol{y} \)
A . 0
B. 1
\( \mathbf{c} \cdot e^{a x} \)
D. 3a


Which is always amphoteric in nature?
A. Electrolytes
B. Lipids
c. Carbohydrates
D. Proteins
E. Nucleic acids


Hardness of water can be detected with:
A. \( N a_{2} C O_{3} \) solution
B. soap water
c. dil. \( H C l \)
D. acidified \( K M n O_{4} \) solution


Select incorrect statement
A \( \cdot \) for any two vectors \( |\vec{A} \cdot \vec{B}| \leq A B \)
B. for any two vectors \( |\vec{A} \times \vec{B}| \leq A B \).
C. a vector is not changed if it is slid parallel to itself.
D. a vector is necessarily changed if it is rotated through an angle


The temperature of water at the surface of a deep lake is \( 2^{0} \) C. The temperature expected at the bottom is
A \( \cdot 0^{0} \mathrm{C} \)
B . \( 2^{0} \) C
c. \( 4^{\circ} \) с
D. \( 6^{\circ} \mathrm{c} \)


Normal force is
A. parallel to the surface
B. perpendicular to the surface
\( c \cdot \) both
D. none


A coin is tossed 1000 times with the
following frequencies:
Head: \( 445, \) Tail: 555
When a coin is tossed at random, what
is the probability of getting a tail?


The gold leaf electroscope is charged so that its leaves somewhat diverge. If \( X \) rays are incident on the electroscope
then
A. the divergence will decrease
B. the divergence of leaves will remain unchanged
c. the gold leaves will melt
D. the divergence will increase


With the help of a neat and labeled diagram describe Waston and Crick's
model of DNA.


Acetic acid and Ammonium hydroxide
are and \( \ldots \ldots . . . \) respectively.
A. Weak acid, weak base
B. Weak acid,Strong base
c. Strong acid, strong base
D. Strong acid. Weak base


Why can \( M n O_{2} \) be reduced by ' \( A l^{\prime} \) and not by carbon?


Define haemocoel and true coelom.


A charge particle of charge \( q, \) mass \( m \) is projected with a velocity \( \vec{v}=v \hat{i} \). The electric field \( \overrightarrow{\boldsymbol{E}}=\boldsymbol{E} \hat{\boldsymbol{k}} \) and magnetic
field \( \vec{B}=B \hat{j} \) is applied. The
acceleration of the particle is then
A \( \frac{q v B}{m} \)
в. \( \frac{q E}{m} \)
c. \( \frac{q(E+v B) \hat{k}}{m} \)
\( D \)


If the mass of the body on the surface of the earth is \( 50 k g, \) its mass at the
centre of the earth is:
A. zero
B. More than \( 50 \mathrm{kg} \)
c. Less than \( 50 \mathrm{kg} \)
D. Equal to \( 50 \mathrm{kg} \)


Drum B undergoes
A. translational motion
B. rotational motion
c. rotational as well as transaltional motion
D. none of the above


When a charged balloon is brought near a charged silk thread, the two bodies
A. Repel each other
B. Attract each other
c. Neither attract nor repel
D. None of the above


Nitrogen does not show pentacovalency because of:
A. absence of s-orbitals
B. absence of d-orbitals
c. its small size
D. none of these


Population explosion is the main cause of pollution. Explain


Calculate angular velocity of earth so
that acceleration due to gravity at \( 60^{\circ} \)
latitude becomes zero. (Radius of earth
\( =6400 \mathrm{km}, \) gravitational acceleration
at poles \( \left.=10 m / s^{2}, \cos 60^{\circ}=0.5\right) \)
A . \( 7.8 \times 10^{-2} r a d / s \)
B. \( 0.5 \times 10^{-3} \mathrm{rad} / \mathrm{s} \)
c. \( 1 \times 10^{-3} r a d / s \)
D. \( 2.5 \times 10^{-3} \mathrm{rad} / \mathrm{s} \)


On crossing two heterozygous tall plants (Tt), a total of 500 plants were
Obtained in \( F_{1} \) generation. What will be
the respective number of tall and
dwarf plants obtained in \( F_{1} \) generation?
A. 375, 125
B. 250, 250
c. 475,25
D. 350, 150


Which of the following is a monomer of natural rubber?
A. Chloroprene
c. urea
D. None of these


Free radical has electron
A. Unpaired and extremely reactive
B. Paired and extremely inactive
C. Unpaired and extremely inactive
D. Paired and extremely reactive


\( f\left(x^{2}+y^{2}\right)^{2}=x y, \) then \( \left(\frac{d y}{d x}\right) \) is


Find: \( \int_{-\pi}^{\pi} \frac{\cos ^{2} x d x}{1+a^{x}} \) where \( a>0 \)


A non-relativistic proton beam passes without deviation through a region of space where there are uniform
transverse mutually perpendicular electric and magnetic fields with \( \boldsymbol{E}= \)
\( 120 k V m^{-1} \) and \( B=50 m T . \) Then the
beam strikes a grounded target. Find the force imparted by the beam on the target if the beam current is equal to
\( \boldsymbol{i}=\mathbf{0 . 8} \boldsymbol{m} \boldsymbol{A} \)
Mass of protons \( =1.67 \times 10^{-27} k g \)


Evaluate the definite integral \( \int_{0}^{1} \frac{\boldsymbol{d} \boldsymbol{x}}{\sqrt{1-\boldsymbol{x}^{2}}} \)


If the dark period is interrupted by flashes of light, short day type plant will not flower.
A. True
B. False
c. Ambigous
D. Data insufficient


is used to create a vacuum to
show anaerobic respiration.


When sufficient force is applied, ionic crystals and covalent solids also break. But, metals can be made into thin
sheets or foils by the application of the same amount. of force. Give reason(s)


Find the sum of \( 1^{2}-2^{2}+3^{2}-4^{2}+ \)
\( +19^{2}-20^{2}=\dots \dots \)
\( \mathbf{A} \cdot-210 \)
в. 120
\( c \cdot 210 \)
D. -120


Surface tension of liquid
A. Increases with area
B. Decreases with area
C. Increases with temperature
D. Decreases with temperature


If the point \( P(2,2) \) is equidistant from the points \( A(-2, k) \) and \( B(-2 k,-3) \) find \( k \)


The angular part of the wave function
depends on the quantum numbers are:
This question has multiple correct options
\( A \cdot n \)
B. \( l \)
\( c . m \)
D.


An ore on heating in air forms \( S O_{2} \)
State the process that will be used for
its concentration.
A. Hydrautic washing
B. Magnetic separation
c. Froth floatation
D. None of the above


What should be added to \( x^{5}-1 \) to be
completely divisible by \( x^{2}+3 x-1 ? \)


If \( \boldsymbol{P}=\left[\begin{array}{cc}\frac{\sqrt{\mathbf{3}}}{\mathbf{2}} & \frac{\mathbf{1}}{\mathbf{2}} \\ -\frac{\mathbf{1}}{\mathbf{2}} & \frac{\sqrt{\mathbf{3}}}{\mathbf{2}}\end{array}\right], \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{1} & \mathbf{1} \\ \mathbf{0} & \mathbf{1}\end{array}\right] \) and
\( \boldsymbol{Q}=\boldsymbol{P} \boldsymbol{A} \boldsymbol{P}^{T}, \) then \( \boldsymbol{P}^{T} \boldsymbol{Q}^{2015} \boldsymbol{P} \) is:
A. \( \left[\begin{array}{cc}0 & 2015 \\ 0 & 0\end{array}\right] \)
B. \( \left[\begin{array}{cc}2015 & 0 \\ 1 & 2015\end{array}\right] \)
c. \( \left[\begin{array}{cc}2015 & 1 \\ 0 & 2015\end{array}\right] \)
D. \( \left[\begin{array}{cc}1 & 2015 \\ 0 & 1\end{array}\right] \)


The maximum value of the function
\( 2 x^{3}-15 x^{2}+36 x+4 \) is attained at
\( \mathbf{A} \cdot \mathbf{0} \)
B. 3
\( c \cdot 4 \)
D. 2
E. 5


Most of the blood proteins are
A. Acidic
B. Basic
c. Neutral
D. All the above in equal proportions


Which yields isopropyl methyl ether as the major product with little or no by products?
A \( \cdot\left(C H_{3}\right)_{2} C H O^{-} N a^{+}+C H_{3} I \longrightarrow \)
в. \( C H_{3} O N a+\left(C H_{3}\right)_{2} C H I \)
c. \( \left(C H_{3}\right)_{2} C H O H+C H_{3} O H \stackrel{H_{2} S O_{4}}{\longrightarrow} \)
D. All three gives isopropyl methyl ether as the major product


In \( n-p-n \) transistor circuit, the collector current is \( 5 \mathrm{mA} \). If \( 98 \% \) of electrons
emitted reach the collector then the
emitter current will be
A . \( 5.1 \mathrm{mA} \)
B. 8.1 mA
\( c \cdot 6.5 \mathrm{mA} \)
D. \( 10 \mathrm{mA} \)


What is the percentage of India's population to the world population?
A. 6 percent
B. 17.5 percent
c. 26 percent
D. 36 percent


State True or False.
figure, \( \angle P Q R=\angle P R Q \), then
\( \angle P Q S=\angle P R T \)
4. True
3 falss


Assertion
Water kept in an open vessel will quickly evaporate on the surface of the
moon.
Reason
The temperature at the surface of the moon is much higher than the boiling point of water
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 energy band gap (distance between the conduction band and valence band) in conductor is.
\( \mathbf{A} \cdot \mathbf{0} \)
в. 4 А
\( c \cdot 10^{\circ} \)
\( \mathbf{D} \cdot_{100 A}_{A}^{\circ} \)


'Mycorrhizae' are useful for the plants
mainly due to
A. Fixing atmospheric nitrogen
B. Enhanced absorption of nutrients from soil
c. killing insects and pathogens
D. Providing resistance against abiotic stresses


A body is brought near a negatively charged gold leaf electroscope. If the divergence of leaves remains
unchanged, state the kind of charge on body in this case.
A. positive
B. Negative
c. no charge
D. cant say


A capacitor of capacitance \( 10 \mu F \) is
charged a potential \( 50 V \) with a battery. The battery is now disconnected and an additional charge \( 200 \mu C \) is given to the positive plate of the capacitor. The potential difference across the
capacitor will be :
A . \( 50 V \)
B. \( 80 V \)
\( \mathbf{c} \cdot 100 V \)
D. \( 60 V \)


Crossing over takes place in
A. Prophase
B. Metaphase
c. Anaphase
D. Prophase I


toppr \( t \)
Q Type your question
speed. Which one of the following
graphs best depicts the variation of its
speed \( \boldsymbol{v} \) with time \( t ? \)
\( A \)
\( B \)
\( c \)
\( D \)


Universal indicator shows yellow colour
when added to a solution at \( 25^{0} C . \) If its
concentration is changed such that the same indicator shows red colour, then
identify the correct statement.
A. The solution is diluted to 100 times
B. The solution is concentrated by 100 times
c. The solution is concentrated 10,000 times
D. The solution is concentrated 1,00,000 times


Air is a conductor of
electricity.
A. Good
B. Badd
c. Both
D. None


Due to acid rain, the \( p H \) of soil in your backyard will be
A. less than 7
B. greater than 7
c. equal to 7
D. equal to or greater than 7


Simplify the multiplication of complex numbers: \( \boldsymbol{a} \times(\boldsymbol{c}, \boldsymbol{d}) \)
\( \mathbf{A} \cdot(a c, a d) \)
B. \( (-a d, a c) \)
c. \( (a d, a c) \)
D. None of these


The area enclosed in a hysteresis loop
is
A. strain energy per unit volume
B. strain energy per unit volume absorbed in each loading cycle
c. strain energy per unit volume released as heat in each loading cycle
D. total strain energy


If \( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{4} & \mathbf{2} \\ \mathbf{3} & \mathbf{3}\end{array}\right], \) then adj \( (\operatorname{adj} \boldsymbol{A}) \) is equal
to
\( \mathbf{A} \cdot\left[\begin{array}{cc}3 & -2 \\ -3 & 4\end{array}\right] \)
в. \( \left[\begin{array}{ll}4 & 2 \\ 3 & 3\end{array}\right] \)
D. None of these


Define resolving power of microscope. Write its formula. How will it vary, when
(a) wavelength of incident light is decreased?
(b) aperture of the objective lens is decreased?


In solar cells, a silicon solar cell \( (\mu= \)
3.5) is coated with a thin film of silicon
monoxide \( \boldsymbol{S} \boldsymbol{i} \boldsymbol{O}(\boldsymbol{\mu}=\mathbf{1 . 4 5}) \) to minimise
reflective losses from the surface.
Determine the minimum thickness of
SiO that produces the least reflection
at a wavelength of \( 550 n m, \) near the centre of the visible spectrum.


The bacteria in a culture grows by \( 10 \% \) in the first hour, decreases by \( 10 \% \) in the second hour and again increases by \( 10 \% \) in the third hour. If the original count of the bacteria in a sample is
10000, find the bacteria count at the
end of 3 hours.


T-bacteriophages possess
A. Rounded shape
B. Tadpole shape
C . Irregular shape
D. Rhomboid shape


The mixed solution of pthallic acid and potassium hydrogen pthallate is
A. Basic buffer
B. Acid buffer
c. Not a buffer
D. An acid


The \( e / m \) ratio of cathode rays is different for different gases.
(True/False)


topp


An inductive coil has a resistance of
100 \( \Omega \). When an a.c. signal of frequency \( 1000 H z \) is fed to the coil, the applied
voltage leads the current by \( 45^{\circ} . \) What
is the inductance of the coil?
\( \mathbf{A} \cdot 10 m H \)
в. \( 12 m H \)
c. \( 16 m H \)
D. \( 20 m H \)


A body starts from rest with uniform acceleration. If its velocity after \( \boldsymbol{n} \) seconds is \( \boldsymbol{v} \) then assuming straight line motion, its displacement in last two seconds is
A \( \cdot \frac{v(n-1)}{n} \)
B. \( \frac{2 v(n-1)}{n} \)
c. \( \frac{2 v(n+1)}{n} \)
D. \( \frac{v(n+1)}{n} \)


\( 2 C H_{3} C O O K+2 H_{2} O \longrightarrow C_{2} H_{6}+ \)
\( 2 C O_{2}+2 K O H+H_{2} \)
During the above reaction, the pH of the
solution:
A. increases
B. decreases
c. remains constant
D. cannot be predicted


A rational number \( \frac{-2}{3} \)
A. Lies to the left side of 0 on the number line.
B. Lies to the right side of 0 on the number line.
C. Is not possible to represent on the number line.
D. None of these.


In an ecosystem which of the following are important components?
A. Energy flow and food chain
B. Mineral recycling and energy flow
c. Food chain and decomposers
D. All of the above


\( C_{6} H_{5} C l \frac{N a O H(a q .)}{625 K, 300 a t m} \)
The product can be:
A. benzal
B. sodium benzoate
C . benzol
D. sodium phenate


A cricket ball and a ping-pong ball are dropped from the same height in a vacuum chamber. When they have
fallen half way down, they have the
same:
A. velocity
B. potential energy
c. kinetic energy
D. rest energy


Give the IUPAC name for the following alcohols. Classify as primary or secondary or teritiary alcohol \( \boldsymbol{C H}_{3} \)
\( \boldsymbol{C H}_{3}-\boldsymbol{C} \boldsymbol{H}-\boldsymbol{C H}-\boldsymbol{C H}_{3} \)
\( \boldsymbol{O H} \)


Methylphenyl ether can be obtained by reacting:
A. phenolate ions and methyl iodide
B. methoxide ions and bromobenzene
c. methanol and phenol
D. bromo benzene and methyl bromide


Sea water is \( 3.5 \% \) by mass of common
salt and has a density \( 1.04 g \mathrm{cm}^{-3} \) at \( 298 K . \) Assuming the salt to be sodium chloride, then osmotic pressure of sea water will be: (assume complete
ionisation of the salt)
A . 25.45 atm
B. \( 11.56 a t m \)
c. \( 15.13 a t m \)
D. \( 30.40 a t m \)


The radii of curvature of the surfaces of
a double convex lens are \( 20 \mathrm{cm} \) and 40
\( \mathrm{cm} \) respectively, and its focal length is \( 20 \mathrm{cm} . \) What is the refractive index of
the material of the lens?
A \( \cdot \frac{5}{2} \)
в. \( \frac{4}{3} \)
\( c \cdot \frac{5}{3} \)
D. \( \frac{4}{5} \)


In a transformer number of turns in
primary circuit is 500 and in secondary circuit number of turns is 10 and load
resistance is \( 10 \Omega \) and voltage of secondary coil is \( 50 \mathrm{V} \) then find the
current in primary circuit.
A . \( 0.2 \mathrm{A} \)
B. \( 0.3 \mathrm{A} \)
c. 0.4 A
D. 0.1A


The substance used in the birth control
pills is?
A. Tetracycline
B. Sulphadiazine
c. Novestrol
D. Penicillin


In a crystal, cations and anions are held together by:
A. electrons
B. electrostatic forces
c. nuclear forces
D. covalent bonds


Which of the processes is not associate with plant growth and development?
A. Cell enlargement
B. Cell movement
c. Cell division
D. cell differentiation


IUPAC name of \( \left(\mathbf{C H}_{3}\right)_{2} \mathbf{C H}- \)
\( \mathbf{C H}\left(\mathbf{C H}_{3}\right)_{2} \)
A. 1,1,2,3 -Tetra ethyl ethane
B. 1,2, - -Diisopropyl ethane
c. 2,3 -Dimethyl butane
D. 2, 3, 3-Trimethyl butane


A motor car is going due north at a speed of \( 50 \mathrm{km} / \mathrm{hr} \). It makes a \( 90^{\circ} \) left
turn without changing the speed. The change in the velocity of the car is about.
A. \( 50 \sqrt{2} \mathrm{km} / \mathrm{hr} \)
B. \( 70 \mathrm{km} / \mathrm{hr} \)
c. \( 80 \mathrm{km} / \mathrm{hr} \)
D. zero


The function
\( f(x)=\frac{\cos x-\sin x}{\cos 2 x} \) is not defined at
\( x=\frac{\pi}{4} . \) The value of \( f\left(\frac{\pi}{4}\right) \) so that \( f(x) \)
is continuous everywhere, is
\( A \)
B.
\( c \cdot \sqrt{2} \)
D. \( \frac{1}{\sqrt{2}} \)


quantıties for the pictured circult. What is the current flowing through the
resistor \( 3 ? \)
Battery Terminal Voltage \( \quad 16.0 \mathrm{v} \)
Voltmeter 1 Reading
Ammeter 1 Reading
Ammeter 2 Reading \( 7.0 \mathrm{A} \)
\( A \cdot 8.0 A \)
B. 13.0 A
\( c \cdot 7.0 A \)
D. 16.0 A
E. 6.0


Find the points of the maxima or local minima of the following function, using the first derivative test. Also, find the
local maximum or local minimum
values, as the case may be. \( f(x)=x^{3}(x-1)^{2} \)


If \( \boldsymbol{d}=\mathbf{0 . 5 m m}, \boldsymbol{\lambda}=\mathbf{5 0 0 0} \boldsymbol{A} \) and \( \boldsymbol{D}= \)
100 \( c m \), find the value of \( n \) for the
closest second bright ring.
\( A \cdot 888 \)
В. 83
\( c .914 \)
D. 998


How many of the following ions have the same magnetic moments?
\( \mathrm{Fe}^{2+} \mathrm{Mn}^{2+} \mathrm{Cr}^{2+} \mathrm{Ni}^{2+} \)
A
B. 2
\( c \cdot 3 \)
D. 4


In the problem below, \( f(x)=x^{2} \) and
\( \boldsymbol{g}(\boldsymbol{x})=\boldsymbol{4} \boldsymbol{x}-\boldsymbol{2} \)

Find the following function: \( (\boldsymbol{f}+\boldsymbol{g})(\boldsymbol{x}) \)
A \( \cdot x^{2}+4 x-2 \)
B. \( x^{2}-4 x-2 \)
c. \( x^{2}-4 x+2 \)
D. \( x^{2}-2 \)


Assertion: A quick collision between two bodies is more violent than a slow
collision; even when the initial and final velocities are identical.
Reason: The momentum is greater in first case
A. If both assertion and reason are true but the reason is the correct explanation of assertion.
B. If both assertion and reason are true but the reason is not the correct explanation of assertion
c. If assertion is true but reason is false
D. If both the assertion and reason are false.
E . If reason is true but assertion is false


Compute the energy stored in the
inductor at \( t=2.00 m s \)
A. \( 0.0094 \mu J \)
B. \( 0.0940 \mu J \)
c. \( 0.9400 \mu J \)
D. \( 9.4000 \mu J \)


The following table shows the scores of
a group of 20 football players. Identify
the modal class.
\( \begin{array}{lllll}\text { Scores } & 7- & 14- & 21- & 28- \\ & 14 & 21 & 28 & 35\end{array} \)
Football 30 \( 40 \quad 20 \) players
A. \( 28-35 \)
B. \( 21-28 \)
c. \( 7-14 \)
D. \( 35-42 \)


Three particles, each of mass \( 10^{-2} \mathrm{kg} \)
are brought from infinity to the vertices of an equilateral triangle of side \( 0.1 m \) the work done is:
A \( .2 \times 10^{-8} \mathrm{J} \)
В. \( 2 \times 10^{-11} J \)
c. \( 2 \times 10^{-12} J \)
D. \( 2 \times 10^{-13} \mathrm{J} \)


\( \int_{0}^{\pi} \frac{\boldsymbol{d} \boldsymbol{x}}{\boldsymbol{3}+\boldsymbol{2} \sin \boldsymbol{x}+\cos \boldsymbol{x}}= \)
A . \( \pi / 3 \)
B . \( \pi / 4 \)
c. \( \pi / 6 \)
D . \( \pi / 2 \)


In the statement of Fleming's left hand rule, what do the direction of centre
finger represents
A. motion
B. magnetic field
c. current
D. none


\( p_{1}, p_{2} \) are the lengths of the
perpendiculars from any point on \( 2 x+ \)
\( 11 y=5 \) upon the lines \( 24 x+7 y= \)
\( \mathbf{2 0}, \mathbf{4 x}-\mathbf{3 y}=\mathbf{2}, \) then \( \boldsymbol{p}_{\mathbf{1}}= \)
\( A \cdot p_{2} \)
B . \( 2 \mathrm{p}_{2} \)
c. \( \frac{1}{2} p_{2} \)
D. \( \frac{1}{3} p_{2} \)


The number of stationary points of \( \mathbf{f}(\mathbf{x})=\sin \mathbf{x} \operatorname{in}[\mathbf{0}, \mathbf{2} \boldsymbol{\pi}] \) are
A
B. 2
\( c \cdot 3 \)
D.


Through which mode of transfer, we receive heat from burning wood?
A. Convection
B. Conduction
c. Radiation
D. None


What is the function of leucoplasts?
A. To store starch grains, oil drops and protein granules
B. To store nucleoprotein
C . To store glycoprotein
D. To synthesize glycogen


What are ambident nucleophiles?


What are \( \boldsymbol{f} \) -block elements?
Distinguish between lanthanoid and
actinoid.


The de-Broglie wavelength of an electron in the ground state of the hydrogen atom is :
A \( \cdot \pi r^{2} \)
в. \( 2 \pi r \)
\( c . \pi r \)
D. \( \sqrt{\pi r} \)


A satellite is changes it orbit from
radius of \( \mathrm{R} \) to radius of \( 2 \mathrm{R} \). If its initial
kinetic energy is \( K_{1} \) then calculate the
new kinetic energy.
A \( \cdot \frac{K_{1}}{4} \)
в. \( \frac{K_{1}}{2} \)
c. \( K_{1} \)
D. \( 2 K_{1} \)
E \( .4 K_{1} \)


The study of the vertical section of the
layers of the soil is known as
A. Soil study
B. Soil profile
c. Soil layering
D. Soil weathering


The output of an AND gate is connected to both the inputs of a NOR gate, then this circuit will act as a
A. or gate
B. NOR gate
c. AND gate
D. NOT gate
E. NAND gate


Mark the incorrect statement.
A. The rate of enzymes catalysed reaction also depend upon enzymes concentration.
B. The rate of enzymes catalysed reaction depend upon ionic strength.
C. The rate of enzymes catalysed reaction first increases with temperature
D. The increase in activity of protein as enzymes is due to denaturation.


What reading would you expect of a square-wave current, switching rapidly between \( +0.5 A \) and \( -0.5 A, \) when
passed through an ac ammeter?
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( 0.5 A \)
c. 0.25
D. \( 1.0 A \)


In humans the alveoli are the
functioning units of external
respiration.
A. True
B. False


ETC of photosynthesis process is
A. Bound to thylakoid membrane
B. Present in stroma
C. Bound to outer chloroplast membrane
D. Dispersed in cytosol


Find the common difference of the A.P.
and write the next two terms:
1. \( , 2.0,2.2,2.4, \dots . \)


Find the equation of circle passing through the points where the circles
\( x^{2}+y^{2}+6 x-8 y-11=0 \) and
\( x^{2}+y^{2}-8 x+14 y+56=0 \) subtend
equal angles and cut the first of these circles orthogonally.


If \( \hat{i}, \hat{j} \) and \( \hat{k} \) represent unit vectors along the \( x, y \) and \( z \) -axes respectively, then the angle \( \theta \) between the vectors \( (\hat{i}+\hat{j}+\hat{k}) \) and \( (\hat{\mathbf{i}}+\hat{\mathbf{j}}) \) is equal to:
A \( \cdot \sin ^{-1}\left(\frac{1}{\sqrt{3}}\right) \)
B. \( \sin ^{-1}(\sqrt{\frac{2}{3}}) \)
c. \( \cos ^{-1}\left(\frac{1}{\sqrt{3}}\right) \)
D. \( 90^{\circ} \)


The oxidation states of most
electronegative elements in the
products obtained from the reaction between \( B a O_{2} \) and dil. \( H_{2} S O_{4} \) are:
A. 0,-1
B. -1,-2
c. -2,0
D. -2,+1


Carbon dioxide is transported via blood to lungs mostly
A. As carbaminohaemoglobin and as carbonic acid
B. In the form of carbonic acid only.
c. In combination with haemoglobin only.
D. Dissolved in blood plasma


Find the magnitude of the angular
acceleration at the moment \( t=10.0 s \)
A. \( 1.3 \mathrm{rad} / \mathrm{s} \)
B. 3 rad / \( s \)
c. 1 rad \( / s \)
D. \( 0.3 \mathrm{rad} / \mathrm{s} \)


\[
\operatorname{Let} f(x)=x+\frac{1}{2 x+\frac{1}{2 x+\frac{1}{2 x+\ldots . . \infty}}}
\]
Compute the value of \( \boldsymbol{f}(\mathbf{1 0 0}) \cdot \boldsymbol{f}^{\prime}(\mathbf{1 0 0}) \)


f \( a, b \in R, \) perpendicular distance
between planes \( x=a \) and \( x=b \) is
\( \ldots(a \neq b) \)


possess the lowest
first ionization energy in their respective period.
A . Alkali metals
B. Alkaline earth metals
c. Noble gases
D. Halogens


A liquid P of specific heat capacity \( 1800 J k g^{-1} K^{-1} \) and \( a t 80^{\circ} C \) is mixed
with a liquid \( R \) of specific heat capacity \( 1200 J k g^{-1} K^{-1} \) and at \( 30^{\circ} \mathrm{C} . \) After
mixing, the final temperature of
mixture is \( 50^{\circ} \mathrm{C} \). In what proportion by weight are the liquids mixed?


Which of the following plant hormone promotes cell division?
A . Auxin
B. Cytokinin
c. Ethylene
D. Gibberellin


The mole fraction of \( H N O_{3} \) in an
aqueous binary solution is \( 0.15> \) The
ratio of moles of \( H N O_{3} \) to \( H_{2} O \) in the
solution is nearly:
\( \mathbf{A} \cdot 17: 3 \)
B. 3: 17
c. 1: 1
D. 15: 100


In the following circuit the values of
\( \boldsymbol{L}, \boldsymbol{C}, \boldsymbol{R} \) and \( \boldsymbol{E}_{\mathbf{0}} \) are \( 0.01 \mathrm{H}, \mathbf{1 0}^{-\mathbf{5}} \boldsymbol{F}, \mathbf{2 5 \Omega} \)
and 220 volt respectively. The value of current flowing in the circuit at \( \boldsymbol{f}=\mathbf{0} \)
and \( \boldsymbol{f}=\infty \) will respectively be
\( A \cdot 8 A \) and \( 0 A \)
B. \( 0 A \) and \( 0 A \)
\( c \cdot 8 A \) and \( 8 A \)
D. o \( A \) and \( 8 A \)


What is the hybridisation state of xenon
in \( X e O F_{4} ? \)
\( A \cdot s p^{3} \)
B. \( s p^{3} d \)
c. \( s p^{3} d^{2} \)
D. \( s p^{3} d^{3} \)


An infinite number of charges each
equal to \( q \) are placed along the \( x \) -axis at \( \boldsymbol{x}=\mathbf{1}, \boldsymbol{x}=\mathbf{2}, \boldsymbol{x}=\mathbf{4}, \boldsymbol{x}=\mathbf{8} \) and \( \mathbf{s} \mathbf{o} \) on
Find the potential and electric field at the point \( x=0 \) due to this set of
charges.
A \( \cdot_{5 k q}, \frac{4 k g}{3} \)
в. \( 2 k q, \frac{4 k g}{3} \)
c. \( _{3 k q}, \frac{4 k g}{3} \)
D. \( 7 k q, \frac{4 k g}{4} \)


If a unit charge is taken from one point to another over an equipotential surface,
then
A. work is done on the charge
B. work is done by the charge
c. work on the charge is constant
D. no work is done


\( C r_{2} O_{3} \)
\( C_{7} H_{16} \frac{F e_{2} O_{3}}{773 K} A \frac{K M n O_{4} / H^{\oplus}}{ } B \)
10 atm
Then what is the incorrect statement?
A. \( B \) will give effervescence with \( N a H C O_{3} \)
B. \( A \) has degree of unsaturation equal to 4
c. \( B \) with slaked lime gives a symmetrical ketone
D. None of these


Comparing the L-C oscillations with the oscillations of a spring block system (force constant of spring \( =k \) and mass
of the block \( =m \) ), the physical quantity
\( m k \) is equal to :
A . \( C L \)
в. \( 1 / C L \)
c. \( C / L \)
D. \( L / C \)


The mean deviation from the mean of
the series \( a, a+d, a+2 d, \dots a+2 n d \)
is
A \( \cdot n(n+1) d \)
B. \( \frac{n(n+1) d}{2 n+1} \)
c. \( \frac{n(n+1) d}{2 n} \)
D. \( \frac{n(n-1) d}{2 n+1} \)


Calculate the amount of \( N H_{3} \) and
\( N H_{4} C l \) required to prepare a buffer
solution of \( p H 9.0 \) when total
concentration of buffering reagents is \( 0.6 \operatorname{mol} L^{-} \cdot p K_{b} \) for \( N H_{3}= \)
\( 4.7, \log 2=0.30 \)


Find the mean of the following frequency distribution:
\( \begin{array}{lllll}\text { Class } & 10- & 30- & 50- & 70- \\ \text { interval: } & 30 & 50 & 70 & 90\end{array} \)
Frequency: \( \quad 5 \quad 8 \) 12 20


Suppose values taken by a variable \( \boldsymbol{X} \)
are such that \( a \leq x_{i} \leq b \) where \( x_{i} \)
denotes the value of \( X \) in the \( i^{i h} \) case
for \( \boldsymbol{i}=\mathbf{1}, \mathbf{2}, \dots . \boldsymbol{n} . \) Then
\( ^{\text {A } \cdot} \frac{a^{2}}{4} \leq \operatorname{Var}(X) \)
В . \( (b-a)^{2} \geq \operatorname{Var}(X) \)
c. \( a \leq \operatorname{Var}(X) \leq b \)
D \( \cdot a^{2} \leq \operatorname{Var}(X) b^{2} \)


A wire of length \( 28 \mathrm{cm} \) is to be cut into 2 pieces, 1 piece is to be made into a
square \( \& \) the other one into a circle
what should be the length of 2 piece so that the combined area of the square \( \& \) the circle is min?


f \( y=\tan ^{-1}\left(\frac{1}{1+x+x^{2}}\right)+ \)
\( \tan ^{-1}\left(\frac{1}{x^{2}+3 x+3}\right)+ \)
\( \tan ^{-1}\left(\frac{1}{x^{2}+5 x+7}\right)+---+ \) upto
n terms, then \( \boldsymbol{y}^{\prime}(\mathbf{0})= \)
A \( \cdot \frac{-1}{1+n^{2}} \)
в. \( \frac{-n^{2}}{1+n^{2}} \)
c. \( \frac{n^{2}}{1+n^{2}} \)
D.


Complete the following, so as to make a
true statement:
A quadrilateral has vertices, no three of which are


Evaluate the definite integral:
\( \int_{0}^{\pi / 2} \cos ^{2} x d x \)


If \( I_{n}=\int_{0}^{\pi / 4} \tan ^{n} x d x \) then \( \lim _{n \rightarrow \infty} n\left(I_{n}+\right. \)
\( \left.\boldsymbol{I}_{n-2}\right)= \)
\( \mathbf{A} \cdot \mathbf{1} \)
B. 1/2
\( c \cdot \infty \)
D.


The bulk modulus of a metal is
\( 10^{10} N / m^{2} \) and Poisson's ratio \( 0.20 . \) If average distance between the
molecules is \( 3 A \) then the inter
atomic force constant :
A. \( 5.4 N / m \)
в. \( 7.5 N / m \)
c. \( 7.6 N / m \)
D. 30N/m


Solve the equation \( \tan ^{-1}\left[\frac{1-x}{1+x}\right]= \)
\( \frac{1}{2} \tan ^{-1} x,(x>0) \)


\( \mathrm{CaSO}_{4} \) is somewhat soluble in water.
I. When \( H_{2} S O_{4} \) is added to a solution
of \( C a S O_{4}, \) the solubility of the \( C a S O_{4} \)
will be increased.
II. The addition of \( H_{2} S O_{4} \) will lower the
\( p H \) of the solution
A. Statement \( I \) is true, Statement \( I I \) is true
B. Statement I is true, Statement \( I I \) is false
c. statement \( I \) is false, statement \( I I \) is true
D. Statement I is false, Statement II is false


If \( \int e^{2 x} f^{\prime}(x) d x=g(x) \), then
\( \int_{\text {A }}\left(e^{2 x} f(x)+e^{2 x} f^{\prime}(x)\right) d x \)
\( \quad \frac{1}{2}\left[e^{2 x} f(x)-g(x)\right]+C \)
B \( \cdot \frac{1}{2}\left[e^{2 x} f(x)+g(x)\right]+C \)
c. \( \frac{1}{2}\left[e^{2 x} f(2 x)+g(x)\right]+C \)
D. \( \frac{1}{2}\left[e^{2 x} f^{\prime}(x)-g(x)\right]+C \)


Which one of the following shows intramolecular \( \boldsymbol{H}- \) bonding?
A \( . H_{2} \)
B. o-Nitro phenol
c. \( H F \)
D. \( C H_{3} \) СООН


The relationship between \( Y, \eta \) and \( \sigma \) is
\( \mathbf{A} \cdot Y=2 \eta(1+\sigma) \)
B \( . \eta=2 Y(1+\sigma) \)
c. \( \sigma=\frac{2 Y}{(1+\eta)} \)
D. \( Y=\eta(1+\sigma) \)


A particle moves a distance \( x \) in time
according to equation \( \boldsymbol{x}=(\boldsymbol{t}+\mathbf{5})^{-1} \)
The acceleration of particle is
proportional to
A . (velocity) \( ^{3 / 2} \)
B. (distance) \( ^{2} \)
c. (distance) \( ^{-2} \)
D. (velocity) \( ^{2 / 3} \)


In vinyl acetylene \( \boldsymbol{C H} \equiv \boldsymbol{C}-\boldsymbol{C H}= \)
\( C H_{2} \) type of overlapping in \( \left(C_{2} \sigma C_{3}\right) \)
bond is :
\( \mathbf{A} \cdot s p^{2}-s p \)
B. \( s p-s p^{2} \)
\( \mathbf{c} \cdot s p^{3}-s p^{3} \)
D. \( s p^{3}-s p^{2} \)


The half life of radium is 1600 years. The
fraction of radium atoms that remain
undecayed after 4800 years will be
A \( \cdot \frac{1}{4} \)
в. \( \frac{1}{16} \)
\( c \cdot \frac{1}{8} \)
D. \( \frac{1}{32} \)


If \( \omega \) is an imaginary cube root of unity
then \( \left(1+\omega-\omega^{2}\right)^{7} \) equals?
A. \( 128 \omega \)
B. \( -128 \omega \)
c. \( -128 \omega^{2} \)
D. None of these


A fish is looking at a \( 1.0 m \) high plant of the edge of the pond. Will the plant appear shorter or taller than its actual
height, to the fish
A. taller
B. shorter
c. no change
D. can't say


Bleaching properties of bleaching powder are due it its:
A. Oxidizing properties
B. Reducing properties
c. Basic properties
D. Disinfecting properties


For the circuit shown in figure, the
direction and magnitude of the force on
PQR is:
A . zero
B. ILB out of the page
c. ILB/2 into the page
D. ILB into the page


Identify the gas evolved when:
Sulphur is treated with concentrated
nitric acid :
A. Sulphur dioxide
B. Nitrogen dioxide
c. Hydrogen
D. oxygen


\( H C l \) gas is covalent and \( N a C l \) is an
ionic compound. This is because:
A. sodium is highly electropositive
B. hydrogen is a non-metal
c. \( H C l \) is a gas
D. electronegativity difference between \( H \) and \( C l \) is less than \( 2 . \)


Which does not have a carboxyl group?
A . Picric acid
B. Ethanoic acid
c. Salicylic acid
D. Benzoic acid


Among alcohols and phenols which one is more acidic and why?


If \( \mathbf{A}=\left[\mathbf{a}_{\mathbf{i} \mathbf{j}}\right] \) is a scalar matrix of order
\( \boldsymbol{n} \times \boldsymbol{n} \) such that \( \mathbf{a}_{\mathbf{i j}}=\mathbf{k} \) for all \( \mathbf{i}=\boldsymbol{j}, \) then
trace of \( \mathbf{A}= \)
\( A \cdot \) nk
B. \( n+k \)
c. \( \frac{n}{k} \)
D.


Evaluate
\( \int_{0}^{\sqrt{3}} \frac{1}{1+x^{2}} \cdot \sin ^{-1}\left(\frac{2 x}{1+x^{2}}\right) d x \)
A \( \cdot \frac{5}{72} \pi^{2} \)
в. \( \frac{13}{144} \pi^{2} \)
c. \( \frac{7}{72} \pi^{\text {? }} \)
D. \( \frac{1}{12} \pi^{2} \)


How many covalent bonds are there in a molecule of ethane \( \left(C_{2} H_{6}\right) ? \)


Evaluate: \( \lim _{x \rightarrow \infty} \frac{4 x-3}{2 x+3} \)


Which of the following gives the correct increasing order of the atomic radii of 0, F and N?
\( A \cdot O, F, N \)
B. N, O, F
c. \( 0, \) N, \( F \)
D. F, O, N


Carbon dioxide is used in fire
extinguishers.


If the surface is placed parallel to the electric field, then
A. infinite electric flux will pass through the surface
B. no electric flux will pass through the surface.
c. finite electric flux will pass through the surface.
D. variable electric flux will pass through the surface


\( \boldsymbol{C H}_{3}-\boldsymbol{C l}+\boldsymbol{N} \boldsymbol{H}_{3} \rightarrow \)
\( \boldsymbol{C}_{2} \boldsymbol{H}_{5}-\boldsymbol{C l}+\boldsymbol{N} \boldsymbol{H}_{3} \rightarrow \)
Complete the reaction.


Verify lagrange's mean value theorem
for the function
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2}+\boldsymbol{2} \boldsymbol{x}+\boldsymbol{3} \) where \( \boldsymbol{x} \in[\boldsymbol{4}, \boldsymbol{6}] \)


Write about your favourite scientist/physicist


\( \cos ^{-1}\left\{\frac{1}{2} x^{2}+\sqrt{1-x^{2}} \cdot \sqrt{1-\frac{x^{2}}{4}}\right\}= \)
\( \cos ^{-1} \frac{x}{2}-\cos ^{-1} x \) holds for
A \( \cdot|x| \leq 1 \)
В. \( x \in R \)
c. \( 0 \leq x \leq 1 \)
D. \( -1 \leq x \leq 0 \)


Prove that \( \frac{\sin \theta-\cos \theta+1}{\sin \theta+\cos \theta-1}= \)
\( \frac{1}{\sec \theta-\tan \theta}, \) using the identity
\( \sec ^{2} \theta=1+\tan ^{2} \theta \)


Express the following as a rational number i.e. in the form \( \frac{a}{b} ; \) where \( a, b \in I \) and \( \boldsymbol{b} \neq \mathbf{0} \)
\( 0.4375=? \)
A \( \cdot \frac{5}{16} \)
в. \( \frac{7}{16} \)
\( c \cdot \frac{3}{16} \)
D. \( \frac{9}{16} \)


The first ionization potentials \( (e V) \) of
\( B e \) and \( B \) respectively are:
A. 8.29,9.32
В. 9.32,9.32
c. 8.29,8,29
D. 9.32,8.29


What is the basicity of \( \boldsymbol{H}_{4} \boldsymbol{P}_{2} \boldsymbol{O}_{7} \) ?
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot 3 \)
D. 4


Freundlich equation for adsorption of gases (in amount of \( g \) ) on a solid (in
amount of \( \mathrm{mg} \) ) at constant temperature can be expressed as:
\( ^{\mathbf{A}} \cdot \log \frac{x}{m}=\log P+\frac{1}{n} \log K \)
B. \( \log \frac{x}{m}=\log K+\frac{1}{n} \log P \)
c. \( \frac{x}{m} \propto P^{n} \)
D \( \cdot \frac{x}{m}=P+\frac{1}{n} \log K \)


A super saturated solution is a meta
stable state of solution in which solute
concentration:
A. is equal to the solubility of that substance in water
B. is more than its solubility
c. is less than its solubility
D. continuously changes


In how many ways three different rings
can be worn in four fingers with at most
one in each finger?


\( X e O F_{4} \) contains:
A. six electron pairs forming an octahedron with two positions occupied by lone pairs
B. two \( \pi \) -bonds and the remaining six electron pairs forming an octahedron
C. three \( \pi \) -bonds and the remaining four electron pairs forming a tetrahedron
D. one \( \pi \) -bonds and the remaining six electron pairs forming an octahedron with one position occupied by \( a \)
lone pair


If \( A \) and \( B \) are two points having coordinates (3,4) and (5,-2)
respectively and \( P \) is a point such that \( P A=P B \) and area of \( P A B=10 \) sq. units, then coordinates of \( \mathrm{P} \) are
в. (7,2)\( \&(1,0) \)
c. (2,7)\( \&(4,13) \)
D. (7,4)\( \&(13,4) \)


A body at rest with initial displacement can be shown in the displacement \( (s) \) versus time (t) graph given above.
A. True
B. False


What are interhalogen compounds? Explain with two examples.


A machine gun fires a bullet of mass
\( 40 g \) with a velocity \( 1200 m s^{-1} . \) The man
holding it can exert a maximum force of
144N on the gun. How many bullets can he fire per second at the most?
A. \( O n e \)
B. Four
c. \( T w o \)
D. Three


\( 146 k J \) work is performed in order to compress 1 kilomole of gas adiabatically and in this process the temperature of the gas increases by
\( \mathbf{7}^{o} \mathbf{C} . \) The gas is:
(Take \( \left.\boldsymbol{R}=\mathbf{8 . 3} \boldsymbol{J} \boldsymbol{m} \boldsymbol{o l} \boldsymbol{e}^{-1} \boldsymbol{K}^{-1}\right) \)
A. monoatomic
B. diatomic
c. triatomic
D. a mixture of monoatomic and diatomic


n the following figure, \( \tan ^{2} \boldsymbol{A}-\sec ^{2} \boldsymbol{A} \)
\( A \)
3. -2
\( c \)
\( D \)


If \( I^{2}+\mathbf{m}^{2}=1, \) then the max values of
\( \boldsymbol{I}+\mathbf{m} \) is
\( A \cdot 1 \)
B. \( \sqrt{2} \)
c. \( \frac{1}{\sqrt{2}} \)
D. 2


In a single throw of three dice, if the
probability of getting a total of 17 or 18 is \( \frac{1}{a} . \) Find \( a \)


Axon is characterised by
A. Transformation of energy
B. Receiving the impulse
C . Providing energy for impulse
D. Conduction of impulse


The anhydride of \( \mathbf{H C l O}_{4} \) is:
A \( \cdot \mathrm{ClO}_{4} \)
в. \( \mathrm{Cl}_{2} \mathrm{O}_{7} \)
\( \mathrm{c} \cdot \mathrm{ClO}_{2} \)
D. \( \mathrm{ClO}_{3} \)


Assertion
Both cis-1,3-dimethyl cyclobutane and trans-1,3-dimethyl cyclobutane are optically inactive.
Reason
cis-1,3-Dimethyl cyclobutane has the plane of symmetry, where as trans form has the centre of symmetry.
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


From band of cilia identify this figure.
A. Tornaria larva
B. Trochophore larva
c. Planeria larva
D. None of the above


Two cells of emfs \( E_{1} \) and \( E_{2} \) are
connected in series. Their internal
resistances are \( r_{1} \) and \( r_{2} \) respectively. Compute the equivalent emf and equivalent internal resistance.


Choose the correct sequence of tissues
containing \( C O_{2} \) from highest
concentration level to the lowest.
A. Pulmonary veins-left atrium- tissues-right ventricle
- pulmonary arteries
B. Left atrium- tissues - right ventricle-pulmonary veins-pulmonary arteries
C. Pulmonary arteries- right ventricle- tissues-left atrium- pulmonary veins
D. Right ventricle- pulmonary arteries- pulmonary veins-left atrium- tissues
E. Tissues-pulmonary veins-pulmonary arteries-left atrium-right ventricle


The capacitor of an oscillatory circuit of negligible resistance is enclosed in a evacuated container. The frequency of the circuit is \( 150 \mathrm{kHZ} \) and when the
container is filled with a gas, the frequency changes by 100 HZ. The dielectric constant of the gas.
\( A \cdot 2 \)
B. 1.53
c. 1.0012
D. 3


Electromagnetic waves of wavelength ranging from \( 100 \dot{A} \) to \( \dot{A} \) comes under
A. X-rays
B. UV regions
c. Visible region
D. Infrared region


Explain S.I units


Very short answer type.
Name two organs of the digestive system that secrete the most fluid


Solve the differential equation \( \boldsymbol{x} \boldsymbol{d} \boldsymbol{y}+ \)
\( 2 y d x=0 \) when \( x=2, y=1 \)


Acne and pimples on the face are due to the secretion of
A. Bile from liver
B. Oil glands during puberty
C. Enzymes in the digestive tract
D. Tear from tear glands


What type of gate is this,


The reagent used in Wolff-Kishner
reduction is:
A. \( N H_{2}-N H_{2} \) and \( K O H \) in ethylene glycol
в. \( Z n-H g / \) сопс. \( H C l \)
c. \( N a B H_{4} \)
D. \( N a-H g / H_{2} O \)


Write the value of \( \lim _{x \rightarrow 0} \frac{\sin x}{\sqrt{1+x}-1} \)


Buna-N rubber' is a coploymer of butadiene and acrylonitrile. In comparison to natural rubber it:
A. is delicate and soft
B. has better resistance to wear and tear
c. is a poor substitute for natural rubber
D. does not last for a long time


Find the correct statements related to
the image formed by the plane mirror form the given below.
A. The image formed is laterally inverted, virtual and erect
B. The size of the image is equal to the size of the object.
C. The object distance from the plane mirror is equal to the image distance from the plane mirror
D. All the above


Draw the structures of the following organic halogen compounds:
(i) \( 4- \) tert-buty \( -3- \) idoheptane
(ii) \( 4- \) bromo \( -3- \) methylpent \( -2- \)
ene


Brine solution conducts electricity because it contains oppositely charged
ions.

If the statement is true, enter 1 if false
enter 0


Cross bridges between actin and myosin is broken up by
A. Hydrolysis of AP
B. Binding of ATP to the myosin head
c. Binding of calcium to the subunit of troponin
D. Exposure of tropomyosin


If \( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{cl}\frac{1-\sqrt{2} \sin x}{\pi-4 x}, & \text { if } x \neq \frac{\pi}{4} \\ a, & \text { if } x=\frac{\pi}{4}\end{array}\right. \)
is continuous at \( \frac{n}{4} \) then \( a= \)
\( A \)
B. 2
c. 1
\( 0 . \frac{1}{1} \)


A magnetising force of \( 360 A m^{-1} \) produces a magnetic flux density of
\( 0.6 T \) in a ferromagnetic material. The susceptibility of the material is:
A . 1625
в. 1329
c. 2105
D. 1914


A hemispherical bowl made of wood has
inner diameter of \( 10.5 \mathrm{cm} \). Find the cost
of painting it on the inside at the rate of
Rs.12 per \( 100 \mathrm{cm}^{2} \)


The I.U.P.A.C name for \( \left[\boldsymbol{F e}(\boldsymbol{C N})_{\mathbf{6}}\right]^{\mathbf{3}-} \) ion
is :
A. hexacyanidoferrate(II) ion
B. hexacyanidoferrate(III) ion
C. hexacyanideiron(II) ion
D. iron(III) hexacyanide ion


If \( A \) is symmetric as well as skew-
symmetric matrix, then \( \boldsymbol{A} \) is
A. diagonal matrix
B. null matrix
c. triangular matrix
D. none of these


Calculate the area of the figure given
below: which is not drawn to scale.
\( \mathbf{A} .630 \mathrm{sq.cm} \)
B. 620 sq. \( \mathrm{cm} \)
c. 640 sq. \( \mathrm{cm} \)
D. 600 sq. \( \mathrm{cm} \)


A. \( C C l_{4} \) does not act as lewis acid.
B. Silanes are strong reducing agents.
C. Crystalline silica will have Diamond
like structure.

Which of the above statement(s) is/are
true?
\( A \cdot A \& B \)
B. only 'A'
c. only's'
D. \( A, B \& C \)


topp
\( Q \) тур
An ice-cream shop notices the variation between outside temperature and number of customers attending the
shop in the table given above. From the graphs, determine the best possible relationship between the temperature and number of customers attending the
shop
\( A \)
Number of Customers
3.
Number of Customers
\( c \)
Number of Customers
D.
Number of Customers


Which one of the following can form
micelle?
A. \( N a C o o----R----C o o N a \)
B.
c. \( N a C O O-R-C O O N a \)
D. R-R-R


Find the coordinates of the focus, axis
of the parabola, the equation of directrix and the length of the rectum for \( y^{2}= \)
\( 12 x \)


The progress of reaction \( \boldsymbol{A}(\boldsymbol{g}) \rightleftharpoons \)
\( \boldsymbol{x} \boldsymbol{B}(\boldsymbol{g})+\boldsymbol{y} \boldsymbol{C}(\boldsymbol{g}) \) with time is presented
in figure. What is the value of \( \boldsymbol{K}_{c}^{0} \) at
\( \mathbf{3 0 0 K} ? \)
\( A \)
B.
\( c .3 \)
\( D \)


If collector current is \( 120 m A \) and base
current is \( 2 m A \) and resistance gain is 3
what is power gain?
A . 180
B. 10800
c. 1.8
D. 18


A compound which is having hydrogen and carbon is called hydrocarbon. A hydrocarbon is heated in an excess of oxygen to produce 58.67 g of \( C O_{2} \) and 27 g of \( H_{2} O . \) What is the empirical formula of the hydrocarbon?
A. \( C_{3} H_{9} \)
в. \( C_{4} H_{12} \)
\( \mathbf{c} \cdot C_{8} H_{18} \)
D. \( C_{4} H_{9} \)


The total energy of a vibrating particle in SHM is \( E \). If its amplitude and time
period are doubled, its total energy will
be :
\( \mathbf{A} \cdot 16 E \)
в. \( 8 E \)
\( c .4 E \)
D. \( E \)


For which vitamin liver is not the
source?
A. Vitamin - \( B_{1} \)
B. Vitamin - \( B_{2} \)
c. vitamin - \( B_{12} \)
D. Vitamin- \( H \)


EDTA is hexadentate ligand and is used
to remove hardness in water.
A. True
B. False


Adsorption is a surface phenomenon
A. True
B. False


Substances which have identical
chemical properties but differ in atomic weight are called.
A. Isothermals
B. Isotopes
c. Isotropics
D. Elementary particles


Write Newland's Law of 'Octaves' for
classification of elements.


Explain chemical constituents of DNA


Which of this have same chemical
properties, but their physical properties may be different?
A. Atomic number
B. Mass number
c. Isotopes
D. Isobars


One spherical ball of radius \( R \), density
released in a liquid of density \( d / 2 \)
attains a terminal velocity \( V \). Another ball of radius \( 2 R \) and density \( 1.5 d \) released in the liquid will attain a terminal velocity
A \( .2 V \)
в. \( 4 V \)
\( c .6 V \)
D. 8V


What will be the reaction of \( N a N H_{2} \)
and \( N H_{3} \) with alkyne?


A high molecular weight molecule which does not contain repeating structural units is called a:
A. polymer
B. macromolecule
c. both \( (A) \) and \( (B) \)
D. none of the above


During the quantitative estimation of phosphorous present in an organic compound, phosphorous is:
A. Reduced
B. Oxidized
c. Both Oxidized and reduced
D. None of these


Coal tar is obtained as a by product during:
A. Destructive distillation of wood
B. Destructive distillation of coal
c. Destructive distillation of bones
D. Steam distillation of light oil


A series AC circuit containing an inductor \( (20 \mathrm{mH}), \) a capacitor \( (120 \mu F) \) and a resistor \( (60 \Omega) \) is driven by an \( A C \) source of \( 24 \mathrm{V} / 50 \mathrm{Hz} \). The energy dissipated in the circuit in 60 s is :
A \( \cdot 2.26 \times 10^{3} J \)
В . \( 3.39 \times 10^{3} J \)
c. \( 5.65 \times 10^{2} J \)
D. \( 5.17 \times 10^{2} J \)


State the observations made by
Oerested on the basis of his
experiments with current carrying conductor.


Which of the following is not a polymer?
A. Sucrose
B. Teflon
c. starch
D. Enzyme


Which of the following statements
regarding fuel cell is (are) true? This question has multiple correct options
A. They have efficiency of about \( 60-70 \% \)
B. There efficiency is less then conventional methods
C. They do not cause pollution
D. They can supply indefinite amount of energy until outside supply of reactants is maintained


The strongest acid among the following acids is :
\( \mathbf{A} . \quad H C O O H \)
в. \( C H_{3} \)СООН
c. \( \left(C H_{3}\right)_{2} C H C O O H \)
D. \( \left(C H_{3}\right)_{3} C C O O H \)


A cord is wound around the
circumference of wheel of radius 'r'. The
axis of the wheel is horizontal and
moment of inertia about it is 'l'. The
weight 'mg' is attached to the end of the cord and falls from rest. After falling
through a distance 'h', the angular
velocity of the wheel will be
\( \mathbf{A} \cdot[m g h]^{1 / 2} \)
B. \( \left[\frac{m g h}{I+2 m r^{2}}\right]^{1 / 2} \)
c. \( \left[\frac{2 m g h}{I+m r^{2}}\right]^{1 / 2} \)
D. \( \left[\frac{m g h}{I+m r^{2}}\right]^{1 / 2} \)


In the mineral, barium ion can be identified by :
A. green colour in ame
B. yellow precipitate with \( C r O_{4}^{2-} \) solution
C. white precipitate with \( S O_{4}^{2} \)
D. all of the above


State true or false
if \( z \) is a complex number then \( z \bar{z} \) is
purely real
A. True
B. False


Write the names of any two ores of iron.


The transverse nature of light waves is verified by
A. reflection of light
B. polarisation of light
c. refraction of light
D. interference of light


Concentration by froth floatation is applicable for which of the following ores?
A. \( A l_{2} O_{3} \)
в. \( T e_{3} O_{4} \)
c. \( T e_{2} O_{3} .3 H_{2} O \)
D. \( Z n S \)


Ensheathing tissue of muscles is called
A. Tendon
B. Ligament
c. Peritoneum
D. Fascia


The complex number \( e^{i \theta} \) can be
expressed in vector form by
\( A \cdot \sin \theta+i \cos \theta \)
\( \mathbf{B} \cdot \cos \theta+i \sin \theta \)
c. both \( (a) \) and \( (b) \)
D. none of these


Which of the following gas, when ignited, burns with a blue flame and is not very soluble in water?
\( A \cdot O_{2} \)
в. \( C O_{2} \)
c. \( N_{2} \)
D. \( H e \)


Conditions which affect the
decomposition of nitric acid is/are:
A. room temperature
B. presence of sunlight.
c. high temperature
D. both \( A \) and \( B \)


If \( \mathrm{M} \) and \( \mathrm{N} \) are any two events, the
probability that atleast one of them
occurs is
A \( \cdot P(M)+P(N)-2 P(M \cap N) \)
B . \( P(M)+P(N)-P(M \cap N) \)
c. \( P\left(M^{c}\right)+P\left(N^{c}\right)-2 P\left(M^{c} \cap N^{c}\right) \)
D - \( P\left(M \cap N^{c}\right)-P\left(M^{c} \cap N\right) \)


The geometries of the ammonia
complexes of \( N i^{2+}, P t^{2+} \) and \( Z n^{2+} \)
respectively, are:
A. octahedral, square planar and tetrahedral
B. square planar, octahedral and tetrahedral,
C . tetrahedral, square planar and octahedral
D. octahedral, tetrahedral and square planar


Which of the following has the lowest ionization energy?
A \( . L i \)
в. \( N a \)
c. \( K \)
D. \( R b \)
ह. \( C s \)


\( C l O_{2} \) reacts with \( O_{3} \) to give :
A. \( C l_{2} O_{4} \)
в. \( C l_{2} O \)
c. \( C l O_{3} \)
D. \( C l O_{4} \)


The solution of the equations \( 2 x- \)
\( 3 y=7 \) and \( 4 x-6 y=20 \) is
A. \( x=18, y=12 \)
В. \( x=0, y=0 \)
c. No solution
D. \( x=8, y=5 \)


Assertion: Oxygen is more
electronegative than sulphur, yet \( \boldsymbol{H}_{2} \boldsymbol{S} \)
is acidic, while \( H_{2} O \) is neutral

Reason: H-S bond is weaker than 0-H
bond.
\( A \). if (A) is true, (R) is true and (R) is correct explanation
(A)
B. if both (A) and (R) are true but (R) is not correct explanation of (A)
\( \mathrm{c} \). if (A) is true but (R) is false
D. if (A) is false and (R) is true


For a certain type of computers, the length of time between charges of the
battery is normally distributed with a
mean of 50 hours and a standard
deviation of 15 hours. John owns one of
these computers and wants to know the
probability that the length of time will
be between 50 and 70 hours.
A .0 .4082
B. 0.4025
c. 0.4213
D. 0.4156


Which type of biological waste effect soil?
A. Urine
B. Feces
c. Both a and \( b \)
D. None of these


A body of mass \( m_{1}=4 k g \) moves at
\( \mathbf{5 i} \boldsymbol{m} / \boldsymbol{s} \) and another body of mass
\( \boldsymbol{m}_{2}=2 k g \) moves at \( 10 i m / s . \) The
kinetic energy of centre of mass is
A \( \cdot \frac{200}{3} J \)
в. \( \frac{500}{3} J \)
c. \( \frac{400}{3} J \)
D. \( \frac{800}{3} J \)


If \( x \) changes from 4 to 4.01 then find the
approximate change in \( \log x \)


Halogenation of halo arenes follows which of the following mechanism?
A. Nucleophilic sustitution
B. Electrophillic substitution
c. Addition
D. Elimination


Two spheres of mass \( M \) and \( 7 M \) are
connected by a rod whose mass is negligible, and the distance between
the centers of each sphere is \( d \). How far
from the center of the \( 7 M \) sphere is the
Center of Mass for this object?
A \( \cdot d / 8 \)
B. \( d / 7 \)
c. \( d / 2 \)
D. \( 6 d / 7 \)
E \( .7 d / 8 \)


\( f \frac{x}{a}+\frac{y}{b}=1 \) and \( \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=\frac{a b}{a+b} \)
then prove that \( \frac{\boldsymbol{x}^{\boldsymbol{n}+\mathbf{1}}}{\boldsymbol{a}}+\frac{\boldsymbol{y}^{\boldsymbol{n}+\mathbf{1}}}{\boldsymbol{b}}= \)
\( \left(\frac{a b}{a+b}\right)^{n} \)


The moment \( P\left(\text { in } k g m s^{-1}\right) \) of a particle
is varying with time \( t \) (in second) as
\( \boldsymbol{p}=\mathbf{2}+\mathbf{3} \boldsymbol{t}^{2} . \) The force acting on the
particle at \( t=3 s \) will be
\( A \cdot 18 N \)
B. 54
\( c \cdot 9 N \)
D. 15 N


In angiosperms, normally after
fertilisation.
A. The zygote divides earlier than the primary endosperm nucleus
B. The primary endosperm nucleus divides earlier than the zygote
C. Both the zygote and primary endosperm nuclei divide simultaneously
D. Both the zygote and primary endosperm nuclei undergo a resting period


Find the roots of the equations by the method of completing the square. \( \boldsymbol{x}^{2}+\mathbf{7} \boldsymbol{x}-\mathbf{6}=\mathbf{0} \)


Water \( \left(\boldsymbol{H}_{2} \boldsymbol{O}\right) \) is liquid while all other
molecules of equivalent and even higher molecular weight are present in
gaseous state because of
A. covalent bonding between Hydrogen and Oxygen
B. Electrostatic attraction among water molecules
c. Hydrogen bonds.
D. lonic bonds


In a class of 100 students, 60 students
drink tea, 50 students drink coffee and
30 students drink both. A student from
class is selected at random, find the
probability that student takes at least one of the two drinks (i.e. tea or coffee or both)
\( A \cdot 1 \)
5
B. \( \frac{2}{5} \)
\( c \cdot \frac{3}{5} \)
D. \( \frac{4}{5} \)


The radius of a wavefront as the waves
propagate
A. decreases
B. increases
c. becomes zero
D. sometimes decreases and sometimes increases


A concentrated solution contains high
amount of
A. solvent
B. solute
c. both solute and solvent
D. none of these


In a forward-biased photo-diode with increase in incident light intensity, the diode current:
A . increases
B. remains constant
c. decreases
D. none of the above


The two position-time graphs time in seconds pictured below on the same grid represents the position of a motorized car (red) and a cart coasting
down a ramp (blue). At what time are
their velocity closures to being the
same?
A. 1 second
B. 2 second
c. 3 second
\( D \)
E. 3 second


A family has five girls and no son, the probability of the occurance of son in 6
\( t h \) child is
A \( \cdot 1 / 2 \)
B. 1/5
\( c \)
D. No chance


Draw a plot showing the variation of (i)
electric field \( (\boldsymbol{E}) \) and (ii) electric
potential \( (V) \) with distance \( r \) due to a
point charge \( Q \)


The plot shows the variation of \( -\ln \boldsymbol{K}_{\boldsymbol{p}} \)
versus temperature for the two
reactions.
\( M(s)+\frac{1}{2} O_{2}(g) \rightarrow M O(s) \) and
\( C(s)+\frac{1}{2} O_{2}(g) \rightarrow C O(s) \)
Identify the correct statement?
A. \( A t T>1200 K, \) carbon will reduce \( M O(s) \) to \( M(s) \)
B. At \( T<1200 \mathrm{K} \), oxidation of carbon is unfavourable.
C. At \( T<1200 \) K, the reaction \( M O(s)+C(s) \rightarrow M(s)+ \)
\( C O(g) \) is spontaneous
D. Oxidation of carbon is favourable at all temperatures


A ray of light incident normally on face \( A B \) of an isosceles prism travels as
shown in figure. The least value of the
refractive index the prism must be:


The deflection in galvanometer falls to \( \left[\frac{1}{4}\right]^{t h} \) when it is shunted by \( 3 \Omega \). If additional shunt of \( 2 \Omega \) is connected to earlier shunt, the deflection in galvanometer falls to
A \( \cdot \frac{1}{2} \)
B. \( \frac{1^{r d}}{3} \)
c. \( \frac{1}{4}^{t h} \)
D. \( \frac{1}{8.5} \)


In Down's process for the extraction of sodium, the melting point of \( N a C l \) is
lowered from \( 803^{0} C \) to \( 600^{0} C \)
Choose the correct statement(s)
regarding this.
a) It is done in order to avoid
vapourisation of metallic sodium.
b) It is done in order to avoid corrosive
action of sodium and chlorine on the
vessel at the high temperature.
c) It is done by mixing sufficient
amounts of \( \boldsymbol{C a} \boldsymbol{C l}_{2} \)
A. Only a is correct
B. Only a and b are correct
c. Only a and c are correct
D. All a, b and c are correct


The curved surface area and height of a
cylinder are \( 110 \mathrm{cm}^{2} \) and \( 5 \mathrm{cm} \)
respectively. Find the radius of a cylinder.


Result of ozone hole is
A. UV radiation reaching earth
B. Green house effect
C. Acid rain
D. Global warming


For construction of a \( \triangle P Q R, \) where
\( Q R=6 \mathrm{cm}, P R=10 \mathrm{cm} \) and \( \angle Q= \)
\( 90^{\circ}, \) its steps for construction is given
below in jumbled form. Identify the first step from the following.
1. At point \( Q \), draw an angle of \( 90^{\circ} \)
2. From \( R \) cut an arc of length \( P R= \)
\( 10.0 \mathrm{cm} \) using a compass.
3. Name the point of intersection of the
\( \operatorname{arm} \) of the angle \( 90^{\circ} \) and the arc drawn
in step \( 3, \) as \( P \)
4. Join \( P \) to \( Q . P Q R \) is the required
triangle.
5. Draw the base side \( Q R=6 \mathrm{cm} \)
\( A \cdot 2 \)
B. 1
\( c \cdot 3 \)
D. 5
E. 4


Statement: A homogeneous mixture of solute and solvent is known as solution.
State whether the given statement is
true or false.
A. True
B. False


The pressure in water pipe at the ground floor of a building is \( 120000 P a \)
where as the pressure on a third floor is
\( 30000 P a . \) What is the height of third
floor?
(Take \( g=10 m s^{-2} \), density of water \( = \)
\( \left.1000 k g m^{-3}\right) \)


If a body moves with uniform retardation, the velocity-time graph is a straight line
A. inclined to the time axis with a positive slope
B. inclined to the time axis with a negative slope
c. parallel to the time axis
D. parallel to the velocity axis


Create a set of 8 observations with
mean 14.


If the sum to \( n \) terms of an A.P. is \( 3 n^{2}+ \)
\( \mathbf{5} n \) while \( T_{m}=164, \) then value of \( m \) is
A . 25
B . 26
c. 27
D . 28


SLV-3 rockets use
A. solid propellants
B. liquid propellants
C. hybrid propellants
D. composite solid propellants
\( E \). none of the above


The IUPAC name of :
A. 2 -Chlorocarbonyl ethylbenzoate
B. 2-Carboxyethyl benzoyl chloride
C. Ethyl-2-(chlorocarbonyl) benzoate
D. Ethyl-1-(chlorocarbonyl) benzoate


The position of three elements \( A, B \) and
\( \mathrm{C} \) in the Periodic Table are shown below-
Group 16
\( B \)
\( \begin{array}{ll}6 & \text { Group17 } \\ & \\ & \mathrm{A} \\ & \\ & \\ & \mathrm{C}\end{array} \)
(a) State whether A is a metal or non-
metal.
(b) State whether \( C \) is more reactive or
less reactive than \( \mathbf{A} \)
(c) Will \( C \) be larger or smaller in size than B?
(d) Which type of ion, cation or anion, will be formed by element A?


When propyne is treated with aqueous
\( H_{2} S O_{4} \) in presence of \( H g S O_{4} \) the major product is:
A. propanal.
B. propyl hydrogensulphate.
c. acetone.
D. propanol.


What is the resistance of the portion of
a circuit between \( A \) and \( B \) in the figure
given below. Points ' \( \boldsymbol{A} \) ' and ' \( \boldsymbol{a} \) ' are
connected by a copper wire of negligible resistance. Similarly, points ' \( B \) ' and ' b'
are also connected by a copper wire of negligible resistance.
\( A .3 R \)
в. \( \frac{R}{3} \)
c. \( \frac{3 R}{2} \)
D. \( \frac{2 R}{3} \)


Choose the INCORRECT options:-
This question has multiple correct options
A. If relative velocity of one object with respect to other is towards the line joining them, then they must collide.
B. If relative velocity of one object with respect to other is towards the line joining them, then they may collide.
C . A particle staring from rest under the action of constant acceleration must follow a straight line trajectory
D. Motion under constant magnitude acceleration can never result in a closed path trajectory with some area enclosed.


For car battery which one is correct
statement?
A. Cathode is lead dioxide \( \left(P b O_{2}\right) \) and anode is copper \( (C u) \)
B. Cathode is copper \( (C u) \) and anode is lead dioxide \( \left(P b O_{2}\right) \)
C. Cathode is copper \( (C u) \) and anode is lead \( (P b) \)
D. cathode is lead dioxide \( \left(P b O_{2}\right) \) and anode is lead \( (P b) \)


Volume of urine is regulated by
A. Aldosterone
B. Aldosterone and testosterone
C . ADH
D. Aldosterone and ADH


If \( \frac{2 y+5}{3}=3 y-10, \) then the value of \( y \)
is-
A . 4
B. 3
\( c \cdot 2 \)
D. None of these


In the figure, \( D E \| B C \)
(i) Prove that \( \triangle A D E \) and \( \triangle A B C \) are
\( \operatorname{similar} \)


The equilibrium constant for the redox change
\( \left[2 A g\left(N H_{3}\right)_{2}^{+}+C_{6} H_{12} O_{6}+H_{2} O \rightarrow\right. \)
\( \boldsymbol{C}_{6} \boldsymbol{H}_{12} \boldsymbol{O}_{7}+\boldsymbol{2} \boldsymbol{A} \boldsymbol{g}(\boldsymbol{s})+\boldsymbol{C}_{6} \boldsymbol{H}_{12} \boldsymbol{O}_{2}+ \)
\( \left.\mathbf{2} \boldsymbol{H}^{+}\right] \) is:
\( \mathbf{A} \cdot 5.15 \times 10^{9} \)
В. \( 4,2 \times 10^{5} \)
c. \( 1.72 \times 10^{-11} \)


How many elements are possible for the
\( 1^{s t} \) period of periodic table if azimuthal quantum number can have integral values from 0 to \( (n+1) .[n= \) shell number and other rules are remaining same to form period table?
A . 4
B. 6
\( c \cdot 2 \)
\( D \cdot 8 \)


For a positive numbers \( x, y \) and \( z \) the numerical value of the determinant \( \left[\begin{array}{ccc}1 & \log _{x} y & \log _{x} z \\ \log _{y} x & 1 & \log _{y} z \\ \log _{z} x & \log _{z} y & 1\end{array}\right] \) is:
A. 0
B. 1
\( \mathbf{c} \cdot \log _{e} x y z \)
\( \mathbf{D} \cdot-\log _{e} x y z \)


Derive the formula \( \frac{\boldsymbol{F}}{\boldsymbol{l}}=\frac{\boldsymbol{\mu}_{o}}{\mathbf{2} \boldsymbol{\pi}} \cdot \frac{\boldsymbol{i}_{1} \boldsymbol{i}_{2}}{\boldsymbol{r}} \) as
the force per unit length between two parallel wires each of length I meter,
carrying currents \( i_{1} \) and \( i_{2} \) amperes and separated by a distance r meters. Define ampere with the help of this formula.


Leptome is used for
A. Phloem
B. Xylem
c. Fibres
D. Parenchyma


Main constituents of coal gas are
A. \( H_{2} O, C_{2} H_{6}, O_{2} \)
в. \( C H_{4}, C O_{2}, O_{2} \)
\( \mathrm{c} \cdot C H_{4}, H_{2}, C O \)
D. \( C_{2} H_{6}, N_{2}, O_{2} \)


n the given figure, it is given that
\( \boldsymbol{R T}=\boldsymbol{T} \boldsymbol{S}, \angle \mathbf{1}=\mathbf{2} \angle \mathbf{2} \) and \( \angle \mathbf{4}=\mathbf{2} \angle \mathbf{3} \)
Prove that \( \Delta R B T \cong \Delta S A T \)


\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{I} \) is an:
A. iodine derivative of alkanes
B. derivative of iodo alkanes
c. both \( A \) and \( B \)
D. None of these


The linear equations that converts Fahenheit \( \left(^{o} F\right) \) to Celsius \( \left(^{o} C\right) \) is given
by the relation:
\( o_{C}=\frac{5^{o} F-160}{9} \)
Find \( ^{o} \boldsymbol{F}, \) if \( ^{o} \boldsymbol{C}=\mathbf{1} \mathbf{6}^{\mathbf{0}} \boldsymbol{C} \)


Is this a negative rational number? \( \frac{6}{11} \)


State True Or False, if the following expression is a quadratic polynomial:
\( \boldsymbol{x}^{2}+\boldsymbol{x} \)
A . True
B. False


A conducting loop in the shape of a right angled isosceles triangle of height
\( 10 \mathrm{cm} \) is kept such that the \( 90^{\circ} \) vertex
is very close to an infinitely long conducting wire (see the figure). The wire is electrically insulated from the loop. The hypotenuse of the triangle is parallel to the wire. The current in the triangular loop is in counter clockwise direction and increased at a constant
rate of \( 10 A s^{-1} . \) Which of the following
statement (s) is (are) true?
This question has multiple correct options
A. There is a repulsive force between the wire and the loo
B. If the loop is rotated at a constant angular speed about the wire, an additional emf of \( \left(\frac{\mu_{0}}{\pi}\right) \) volt is induced in the wire
C . The magnitude of induced emf in the wire is \( \left(\frac{\mu_{0}}{\pi}\right) \) vo
duced current in the wire is in opposite directic to the current along the hypo


Suppose the entire system of the
previous question is kept inside an elevator which is coming down with an
acceleration \( a<g \). Repeat parts (a) and
(b).


Vishal goes to a shop to buy a radio
costing Rs. \( 2568 . \) The rate of sales tax is
\( 7 \%, \) he tells the shop keeper to reduce the price of radio to such an extent that
he has to pay Rs. 2568 inclusive of sales tax. Find the reduction needed in the
price of the radio
A. Rs. 179
B. Rs. 170
c. Rs. 168
D. Rs. 169


In fig name all the pairs of adjacent angles.


If \( \boldsymbol{y}=\cos ^{-1}\left(\frac{5 \cos x-12 \sin x}{13}\right), x \in \)
\( \left(0, \frac{\pi}{2}\right), \) then find the value of \( d y / d x \)


\( \boldsymbol{C H}_{3} \boldsymbol{O H} \stackrel{\boldsymbol{P}+\boldsymbol{I}_{2}}{\longrightarrow} \boldsymbol{A} \frac{M \boldsymbol{g} / \text {dryether}}{\boldsymbol{\}} \)
\( \boldsymbol{B} \stackrel{\boldsymbol{H C H O}}{\longrightarrow} \boldsymbol{C} \stackrel{\boldsymbol{H}^{+} / \boldsymbol{H}_{2} \boldsymbol{O}}{\longrightarrow} \boldsymbol{D} \)
What are \( B \& D \) respectively?
A. \( C H_{3} M g I, C H_{3} C H O \)
B. \( C H_{3} M g I, C H_{3} C H_{2} O H \)
c. \( C H_{3} M g I, C H_{3} C O O H \)
D. \( C H_{3} M g I, C H_{3} C O C H_{3} \)


Which of the following correctly describes meta-formaldehyde?
A. It is a dimer of HCHO
B. It is a trimer of formaldehyde.
c. It is a tetramer of formaldehyde.
D. It is a polymer in which number of HCHO unit is more than 100


A chord \( A B \) is at a distance of \( 6 \mathrm{cm} \)
from the centre of a circle whose radius
is \( 6 \mathrm{cm} \) less than that of the chord \( A B \)
Then the length of the chord \( A B \) is
\( A \cdot 8 \mathrm{cm} \)
B. \( 32 \mathrm{cm} \)
c. \( 24 \mathrm{cm} \)
D. \( 16 \mathrm{cm} \)


Convectional currents are set up, giving
rise to :
A. Land breezes
B. Land clean
c. Sea water heated up
D. None


A copper wire of negligible mass, \( 1 \mathrm{m} \) length and cross-sectional area
\( l 0^{-6} m^{2} \) is kept on a smooth horizontal
table with one end fixed. A ball of mass
kg is attached to the other end. The wire and the ball are rotating with an angular velocity of 20 rad/s. If the
elongation in the wire is \( 10^{-3} \mathrm{m} \)
a. Find the Young's modulus of the wire (in terms of \( \left.\times 10^{11} N / m^{2}\right) \)


If \( 5,0.5,0.05, \ldots \) are in GP, then its fourth term is
A . 0.05
B. 0.5
c. 0.005
D. 0.0005


If the cardinality of a set \( A \) is 4 and that
of a set \( B \) is 3 , then what is the cardinality of the \( \operatorname{set} A \Delta B \)
A .
B. 5
\( c \cdot 7 \)
D. Cannot be determined


A particle with initial velocity \( v_{0} \) moves with constant acceleration in a straight
line. Find the distance travelled in \( n^{t h} \)
second


If \( y^{2}=p(x) \) is a polynomial of degree 3
\( \operatorname{then} 2 \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}\left(\boldsymbol{y}^{3} \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}}\right) \) is equal to
A \( \cdot p^{\prime \prime \prime}(x) \cdot p^{\prime}(x) \)
B \cdot \( p^{\prime \prime}(x) \cdot p^{\prime \prime \prime}(x) \)
c. \( p(x) \cdot p^{\prime \prime \prime}(x) \)
D. None of these


A plane sound wave travelling with velocity' \( v^{\prime} \) in a medium A reaches a
point on the interface of medium A and medium B. If velocity of sound in medium B is \( 2 v \), the angle of incidence for total internal reflection of the wave
will be greater than \( \left(\sin 30^{\circ}=\right. \)
\( \left.0.5 \text { and } \sin 90^{\circ}=1\right) \)
A \( \cdot 15^{\circ} \)
B. \( 30^{\circ} \)
\( \mathbf{c} \cdot 45^{\circ} \)
D. \( 90^{\circ} \)


Among which of the following pairs of halogen compounds, the first
compound undergoes faster \( \boldsymbol{S}_{N} \mathbf{2} \)
reaction compared to the second?
This question has multiple correct options
A. \( (a) \)
()
в. \( (b) \)
c. \( (c) \)
D. \( (d) \)


Write True or False and justify your answer in each of the following:
If a number of circles touch a given line segment PQ at a point \( A, \) then their centres lie on the perpendicular bisector of PQ.
A. True
B. False
c. Ambiguous
D. Data Insufficient


A block of mass \( m \) moving at a speed \( v \) collides with another block of mass \( 3 m \)
at rest. If the light block comes to rest after collision, the coefficient of restitution is :
A \( \cdot \frac{1}{3} \)
B. \( \frac{1}{6} \)
\( c \cdot \frac{1}{2} \)
D.


In the above shown sequence, the final
product \( \boldsymbol{F} \) is :
A. bakelite
B. nylon - 6
c. polyester
D. natural rubber


toppr
Q Type your question.
them in a sequence.
(a) Thus, an electron pair is shared between \( C \) and \( C l . \) This is the Lewis
electron dot diagram for \( \boldsymbol{C C l}_{4} \)
(b) Write the symbol of chlorine and
represent its valence electrons with the help of crosses, that is,
(c) Write the symbol of carbon and represent its valence electrons with the
help of dots, that is,
(d) When carbon combines with four
chlorine atoms, the carbon atom contributes four electrons for sharing whereas each chlorine atom
contributes only one electron for
sharing. Thus, both the atoms in \( C C l_{4} \)
attain an octet.
(c)
\( A \cdot a \cot d \)
B. b a c d
\( c \cdot d c b a \)
\( D \cdot c b d a \)


Krebs cycle takes place in the
A. Vesicles of E.R.
B. Mitochondrial matrix.
c. Dictyosomes
D. Lysosomes


The major constituent of natural gas is :
A. methane
B. propane
c. butane
D. hexane


The green plastids contain
A. Carotenoids
B. xanthophyll
c. chlorophyll
D. All the above


What are the different elements of
earth's magnetism? What is the relation between them?


f \( y=x^{x}+(\sin x)^{\cot x} \). find \( \frac{d y}{d x} \)


The positive vector of a particle is
determined by the expression \( \vec{r}= \) \( 3 t^{2} \hat{i}+4 t^{2} \hat{j}+7 \hat{k} . \) The distance
traversed in first 10 sec is:
A. \( 500 \mathrm{m} \)
B. 300 \( m \)
c. \( 150 \mathrm{m} \)
D. \( 100 \mathrm{m} \)


The concentration of a solution is the
mass of the solute in grams, which is present in:
A. \( 10 \mathrm{g} \) of solvent
B. 10 g of solution
c. 100 g of solvent
D. 100 g of solution


Assertion
The atomic radii of the elements of
oxygen family are smaller than the atomic radii of corresponding elements of the nitrogen family.
Reason
The members of oxygen family are all more electronegative and thus have
lower value of nuclear charge than
those of the nitrogen family.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


If \( \frac{1}{\sqrt{2}}<x<1 \) then \( \cos ^{-1} x+ \)
\( \cos ^{-1}\left(\frac{x+\sqrt{1-x^{2}}}{\sqrt{2}}\right) \) is equal to
A \( \cdot 2 \cos ^{-1} x-\frac{\pi}{4} \)
B. \( 2 \cos ^{-1} x \)
\( c \cdot \frac{\pi}{4} \)
\( D \)


Which of the following was not a conclusion of Rutherford's gold foil
experiment?
A. The atom is mainly empty space.
B. The nucleus has a negative charge
c. The atom has a dense nucleus.
D. Alpha particles can pass through a thin sheet of gold foil
E. All of the above are correct regarding the gold foil experiment.


Mark true statement about apoplast
pathway.
A. Apoplast pathway may be aided by cytoplasmic streaming
B. Apoplast pathway is continuous throughout the plant without any exception
C. Apoplast pathway is faster than symplast pathway
D. In Apoplast pathway mass flow of water occurs through plasmodesmata


The value of
\( \lim _{x \rightarrow 0} \frac{1}{x}\left(\tan ^{-1}\left(\frac{x+1}{2 x+1}\right)-\frac{\pi}{4}\right) \) is equal
to.
A .
B.
\( c \cdot \frac{-1}{2} \)
\( D \)


State the whether given statement is true or false

Show that area of a rhombus is half the product of the length of its diagonals.
A. True
B. False


Which of the following cause a substance
to change into an entirely new substance
with a new chemical formula?
A. Physical change
B. Chemical change
c. Both A and B
D. None of these


Thrombokinase is associated with
A. Ellimination of urea and other excreatory products from the body.
B. Production of erythrocytes from the bone marrow.
C. Pulmonary and systematic circulation.
D. Cardiac cycle and its regulation
E. Enzymatic reactions in coagulation of blood.


Complete the following reaction:
\( \boldsymbol{S O}_{2}+\boldsymbol{N O}+\boldsymbol{H}_{2} \boldsymbol{O} \longrightarrow \boldsymbol{?} \)
\( \mathbf{A} \cdot S O_{2}+2 N O+H_{2} O \longrightarrow N_{2} O+S O_{4}^{2-}+2 H^{+} \)
B. \( S O_{2}+4 N O+2 H_{2} O \longrightarrow 2 N_{2} O+S O_{4}^{2-}+4 H^{+} \)
\( \mathrm{c} \cdot S O_{2}+2 N O+4 H_{2} O \longrightarrow N_{2} O+S O_{4}^{2-}+4 H^{+} \)
D. None of these


A system of logic gates is shown in the figure. From the study of truth table it can be found that to produce a high output (1) at \( R, \) we must have
в. \( X=1, Y=1 \)
c. \( X=1, Y=0 \)
D. \( X=0, Y=0 \)
0


Nodal plane is found in which orbital?
A \( . n=2, l=0 \)
B. \( n=3, l=0 \)
c. \( n=2, l=1 \)
D. \( n=1, l=0 \)


Write down the reaction involved in
preparation of Potassium dichromate from chromine ore.


If the mass of one molecule of water is
18 amu. What is the mass of one mole of
water molecules?


Find the least value of \( 2 \sin ^{2} \theta+3 \cos ^{2} \theta \)


Which of the following is unique to
mitosis and not a part of meiosis?
A. Homologous chromosomes behave independently
B. Chromatids are separated during anaphase
C. Homologous chromosomes pair and form bivalents
D. Homologous chromosomes crossover


Assertion
Time-dependent magnetic field generates electric field
Reason
Direction of electric field generated
from time variable magnetic field does
obey Lenz's law.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


Assertion
Dodecyl pyridinium chloride forms
positive micelles in water.
Reason
Dodecyl pyridinium chloride possesses hydrophobic and hydrophilic moities in
its cationic part.
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


Assertion
Density of a substance is the ratio of
mass of the substance to its volume
Reason
Relative density is the ratio of density of
substance to the density of water at \( 4^{\circ} \mathrm{C} \)
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


Aspirine is a an:
A. Antiseptic
B. Antipyretic
C. Antimalarial
D. Narcotic