If \( \boldsymbol{M}=\int_{0}^{\pi / 2} \frac{\cos \boldsymbol{x}}{\boldsymbol{x}+\mathbf{2}} \boldsymbol{d} \boldsymbol{x}, \boldsymbol{N}= \)
\( \int_{0}^{\pi / 4} \frac{\sin x \cos x}{(x+1)^{2}} d x \quad, \) then the value of
\( M-N \) is \( ? \)
\( A \)
в.
c. \( \frac{2}{\pi-4} \)
D. \( \frac{2}{\pi+4} \)


Assertion
Vocal cords consist of three pairs of mucous membrane that extend into the
lumen of the larynx.
Reason
Sound is produced by only two pairs of cords.
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


Given a balanced chemical equation for
each of the following:
Reaction of Ammonia with Nitric acid.


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


When \( \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CHCl}_{2} \) is treated with
\( \mathrm{NaNH}_{2} \), the product formed is
В. \( \mathrm{cH}_{3} \mathrm{c} \equiv \mathrm{cH} \)
\( D \)


Total number of methyl group present in
product \( \boldsymbol{A} \) is:
\[
\underset{\mathrm{Me}}{\mathrm{N}}_{\mathrm{O}}^{\mathrm{OMe}}+2 \bigwedge_{\mathrm{Me}} \widehat{\mathrm{MgBr}} \frac{\mathrm{H}_{3} \mathrm{O}^{\oplus}}{\longrightarrow} \mathrm{A}
\]


Express 0.006006 into scientific
notation in three significant digits:
A \( \cdot 6.01 \times 10^{-3} \)
B . \( 6.0006 \times 10^{-3} \)
c. \( 6.00 \times 10^{-3} \)
D. \( 6.0 \times 10^{-3} \)


A ball of mass m moving with a constant velocity u strikes against a ball of same mass at rest. If e is the
coefficient of restitution, then what will be the ratio of velocity of two balls after collision?
A \( \cdot \frac{1-e}{1+e} \)
в. \( \frac{e-1}{e+1} \)
c. \( \frac{1+e}{1-e} \)
D. \( \frac{e+1}{e-1} \)


Which of the following ions or molecules has a nonzero dipole moment?
A \( \cdot C O_{2} \)
в. \( N O_{3}^{-} \)
\( \mathbf{c} \cdot P O_{4}^{3-} \)
D. \( S O_{2} \)
E \( . S O_{4}^{2} \)


In a triangle of base a, the ratio of the other sides is \( r(<1) . \) Show that the
altitude of the triangle is less than or equal to \( \frac{a r}{1-r^{2}} \)


By graphical method solve the following linear programming problem for maximization.
Objective function \( z=1000 x+600 y \) Constraints \( \boldsymbol{x}+\boldsymbol{y} \leq \mathbf{2 0 0} \)
\( 4 x-y \leq 0 \)
\( x \geq 20, x \geq 0, y \geq 0 \)


Which of the following explains the
effect of a catalyst on the rate of a
reversible reaction?
A. It provides a new reaction pathway with a lower activation energy.
B. It moves the equilibrium position to the right.
c. It increases the kinetic energy of the reacting molecules
D. It decreases the rate of the reverse reaction


When a small uncharged conducting ball of radius \( a=1 c m \) and mass \( m=50 \) g
is dropped from a height h above the
center of another large conducting sphere of radius b \( (=1 \mathrm{m}) \) having charge
\( Q(=100 \mu C), \) it rises to a height \( h_{1} \in \)
\( 2 m \) ) after the collision. The value of h is
\( \mathbf{1 0} \)
Find \( x \)
Assume that during the impact there is no dissipation of energy.


Pitcher is found in
A. Dionaea
B. Drosera
c. Nepenthes
D. Viscum


The vapour pressure of two liquids \( \boldsymbol{P} \)
and \( Q \) are 80 torr and 60 torr
respectively. The total vapour pressure obtained by mixing 3 mole of \( \mathrm{P} \) and 2 mole of \( Q \) would be:
A. 68 torr
B. 20 torr
c. 140 tor
D. 72 torr


Define a diagonal matrix.


Why do adolescents experience mood swings?


Solve:
\( \int \frac{d x}{\sqrt{1-e^{2 x}}} \)


Mendel's law of inheritance composed
of
A. Law of segregation
B. Law of independent assortment
c. Law of dominance
D. All (A), (B) and (C)


The value of magnetic field due to a small element of current carrying conductor at a distance r and lying on
the plane perpendicular to the element of conductor is
A. zero
B. Maximum
c. Inversely proportional to the current
D. None of the above


At high concentration of soap in water, soap behave as:
A. molecular solid
B. associated colloid
c. macromolecular colloid
D. Iyophilic colloid


ABC is a triangle and \( A D \) is median. If \( E \) is any point on \( A D, \) then
\( \mathbf{A} \cdot A r(A B E)=A r(A C E) \)
В. \( B E=C E \)
c. \( A B+B E=A C+C E \)
D. \( A E=\frac{B E+C E}{2} \)


Fundamental theorem of arithmetic is
also called as

Factorization
Theorem.
B. Ambiguous
c. Unique
D. None of these


A particle executes S.H.M with a period of 6 seconds. If the maximum speed is \( 3.14 \mathrm{cm} / \mathrm{sec}, \) then what is its amplitude?
A. \( 3 \mathrm{cm} \)
B. \( 5 \mathrm{cm} \)
\( c \cdot 6 \mathrm{cm} \)
D. \( 9 \mathrm{cm} \)


toppr
Q туре уо
inductance to determine the height of the liquid level in the tank. The inductance of the tank changes from a
value of \( L_{0} \) corresponding to a relative permeability of 1 when the tank is
empty to value \( L_{f} \) corresponding to a
relative permeability \( \boldsymbol{X}_{m} \) (relative permeability of liquid) when the tank is full. The appropriate electronic circuit can determine the inductance
correct upto 5 significant figures and thus the effective relative permeability of the combined air and liquid within the rectangular has height \( D \). The
height of the liquid level in the tank is \( d \) Ignore the fringing effects. Assume tank is fitted with \( \boldsymbol{H} \boldsymbol{g} \boldsymbol{X}_{\boldsymbol{H} \boldsymbol{g}}=\boldsymbol{2} . \boldsymbol{9} \times \mathbf{1 0}^{5} \)
Express \( d \) as a function of \( L \), inductance corresponding to a certain liquid height
\( \boldsymbol{L}_{0}, \boldsymbol{L}_{f} \) and \( \boldsymbol{D} \)
A \( \cdot d=\frac{\left(L-L_{0}\right) D}{L_{f}-L_{0}} \)
в. \( _{d}=\frac{L D}{L_{f}-L_{0}} \)
c. \( _{d=} \frac{\left(L-L_{0}\right) D}{L_{f}} \)
D. None of these


What is the ammeter reading?
A. 0.4
B.
\( c \cdot 0.6 \)
0.12


When honeybee bites, which chemical
enters in to our body?
A. Calcium formate
B. Melittin
c. Formic acid
D. Magnesium hydroxide


Let \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{e}^{\cos ^{-1} \sin (\boldsymbol{x}+\boldsymbol{\pi} / \mathbf{3})} \) Then
This question has multiple correct options
\( \mathbf{A} \cdot f\left(\frac{5 \pi}{9}\right)=e^{5 \pi / 18} \)
B \( \cdot f\left(\frac{8 \pi}{9}\right)=e^{13 \pi / 18} \)
\( ^{\mathbf{C}} \cdot f\left(-\frac{7 \pi}{4}\right)=e^{\pi / 12} \)
D \( \quad f\left(-\frac{7 \pi}{4}\right)=e^{11 \pi / 12} \)


The radii of two cylinders are in the ratio
2: 3 and their heights are in the ratio
\( 5: 3 . \) then what is the ratio of their
volumes?
A . 10: 17
B . 20: 27
c. 10: 27
D. 20: 37


Multiplication of slime moulds occurs
through
A. Binary fission
B. Plasmotomy
c. Multiple fission
D. Both A and B


The following pair of linear equations consistent. State true and false:
\( \boldsymbol{x}+\mathbf{3} \boldsymbol{y}=\mathbf{1 1} ; \mathbf{2}(\mathbf{2} \boldsymbol{x}+\mathbf{6} \boldsymbol{y})=\mathbf{2 2} \)
A. True
B. False


Find the inverse of the following
functions:
\( \boldsymbol{f}(\boldsymbol{x})=\sin ^{-1}\left(\frac{\boldsymbol{x}}{\mathbf{3}}\right), \boldsymbol{x} \in[-\mathbf{3}, \mathbf{3}] \)
\( \operatorname{then} \boldsymbol{f}^{-1}(\boldsymbol{\pi} / \mathbf{2}) \)


The reagent commonly used to determine hardness of water
titrimetrically is:
A. Oxalic acid
B. Disodium salt ot EDTA
c. Sodium citrate
D. Sodium thiosulphate


Farm land tends to erode most rapidly when planted with
A. Wheat
B. Potato
c. saccharum
D. Clover


Define : Acceleration.


In an energy emitting nuclear reaction the binding energies of reactants and
products are \( e_{1}, e_{2} \) respectively.Then which is correct of the following?
\( \mathbf{A} \cdot e_{1}<e_{2} \)
B . \( e_{1}=e_{2} \)
\( \mathbf{c} \cdot e_{1}>e_{2} \)
D. \( e_{1} \geq e_{2} \)


A light bulb has the rating 200 W 220 V
1. Find the peak value of current.
2. If the supply voltage is \( 200 \mathrm{V} \), then power consumed by the bulb.


Convert \( 30^{\circ} C \) to Kelvin scale.
\( A \cdot 323 K \)
в. 313 К
\( c \cdot 303 k \)
D. 293 K


Draw the graph of \( y=\frac{2 x+5}{x-1} \)


The metal which cannot liberate \( H_{2} \) gas
from hydrochloric acid is:
\( A \cdot Z n \)
B. cu
\( \mathrm{c} . \) мв
D. Al


A force exerts a pressure of \( 45 N / m^{2} \)
when it acts on an area of \( 10 m^{2} \)
Calculate the total force
A . \( 4.5 N \)
B. \( 450 N \)
\( c .45 N \)
D \( . .45 N \)


In the adjoining figure, \( B O \) and \( C O \) are
the bisectors of \( \angle B \) and \( \angle C \) of \( \Delta A B C \)
Show that \( \angle B O C=90^{\circ}+\frac{1}{2} \angle A \)


Assertion
An emf is induced in a long solenoid by
a bar magnet that moves while totally inside the solenoid along the axis of the
solenoid.
Reason
As the magnet moves inside the
solenoid the flux through individual turns of the solenoid changes.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


Which of the following organic compound has a bitter almond taste?
A. cinnamaldehyde
B. Benzaldehyde
c. capsaicin
D. Both \( A \) and \( B \)


Which of the following compounds would have significant intermolecular hydrogen bonding?
\( \boldsymbol{H} \boldsymbol{F}, \boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{O} \boldsymbol{H}, \boldsymbol{N}_{2} \boldsymbol{H}_{4}, \boldsymbol{C} \boldsymbol{H}_{4} \)
This question has multiple correct options
A. \( H F, N_{2} H_{4} \)
в. \( H F, C H_{4}, C H_{3} O H \)
\( \mathbf{c} \cdot H F, C H_{3} O H \)
D. \( C H_{3} O H, C H_{4} \)


Identify the final product \( F \)
A. Bakelite
B. Nylon - 6
c. Polyester
D. Natural rubber


\( \boldsymbol{P}_{4}+\mathbf{3} \boldsymbol{N} \boldsymbol{a} \boldsymbol{O} \boldsymbol{H}+\boldsymbol{3} \boldsymbol{H}_{2} \boldsymbol{O} \stackrel{\Delta}{\longrightarrow} \boldsymbol{P} \boldsymbol{H}_{3}+ \)
\( \mathbf{3} N a H_{2} P O_{2} \)
The given reaction is a disproportionation reaction.
If true enter 1 , else enter 0


Assertion
The mobility of sodium ion is lower than
that of potassium ion.
Reason
The ionic mobilities depend on the
effective radius of the ion.
Read the above assertion and reason
and choose the correct option regarding
¡t.
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


Simplify \( \left(2 x+\frac{1}{3 y}\right)^{2}-\left(2 x-\frac{1}{3 y}\right)^{2} \)
A \( \cdot \frac{4 x}{3 y} \)
в. \( 2\left(4 x^{2}+\frac{1}{9 y^{2}}\right) \)
c. \( \frac{8 x}{3 y} \)
D. \( \frac{4 y}{3 x} \)


The equilibrium constant for the reaction
is:
\( 2 F e^{3+}+3 I^{\ominus} \rightleftharpoons F e^{3+}+C e^{3+} \)
Given :
\( E_{C e^{4+1} C e^{3+}}=1.44 \mathrm{V} \)
\( E_{F e^{3+} 1 F e^{2+}}^{\ominus}=0.68 \mathrm{V} \)
A . \( 7.236 \times 10^{12} \)
B . \( 7.386 \times 10^{12} \)
c. \( 7.158 \times 10^{12} \)
D. None of these


\( \ln \operatorname{an} \alpha \) -decay the kinetic energy of \( \alpha \) particle is \( 48 \mathrm{MeV} \) and \( Q \) -value of the
reaction is \( 50 ~ M e V \). The mass number
of the molecular nucleus is \( X \). Find
value of \( \boldsymbol{X} / \mathbf{2 5} \)
(Assume that daughter nucleus is in ground state.)
A .2
B. 4
\( c \cdot 6 \)
D. 8


Which of the following is not expected to show paramagnetism?
\( \mathbf{A} \cdot\left[N i\left(H_{2} O\right)\right]^{2+} \)
B. \( N i(C O)_{4} \)
\( \mathrm{c} \cdot\left[N i\left(N H_{3}\right)_{4}\right]^{2} \)
D \( \cdot\left[\operatorname{Co}\left(N H_{3}\right)_{6}\right]^{2} \)


Consider the potentimeter circuit
arranged as in figure. The potentometer
wire is \( 600 \mathrm{cm} \) long.
(a) At what distance from the point \( \boldsymbol{A} \)
should the jockey touch the wire to get zero deflection in the galvanometer?
(b) If the jockey touches the wire at a
distance of \( 560 \mathrm{cm} \) from \( \mathrm{A} \), what will be
the current in the galvanometer?


The degree of dissociation of an
electrolyte is:
A. directly proportional to its concentration
B. directly proportional to the square of its concentration
C. inversely proportional to its concentration
D. inversely proportional to the square root of its concentration


The diagram of a logic gate circuit is
given below. The output \( Y \) of the circuit
is represented by
A \( . A \cdot(B+C) \)
B. \( A \cdot(B \cdot C) \)
c. \( A+(B \cdot C) \)
\( \mathbf{D} \cdot A+(B+C) \)


Molecule having maximum number of
covalent bonds is:
\( \mathbf{A} \cdot N H_{4} O H \)
в. \( N H_{4} C l \)
c. \( C O\left(N H_{2}\right)_{2} \)
D. \( C H_{3} O H \)


The degree of the term \( x^{3} y^{2} z^{2} \) is:
\( A \cdot 3 \)
B. 2
c. 12
D.


Choose the correct answer from the
alternatives given The muscular wall that divides the
heart is called:
A . cardial wall
B. hyoglossus
c. trapezius
D. septum


Very short answer type.
Which plant hormone was discovered in
infected rice seedlings that grew extremely tall and slender?


Given the pair of contrasting traits of the following characters in pea plant and mention if it's dominant or
recessive.
Round seed
A. Dominant
B. Recessive
c. Incomplete dominant
D. None of these


f 0 is a point within a quadrilateral
\( A B C D, \) prove that \( ; O A+O B+O C+ \)
\( O D>A C+B D \)


\( \boldsymbol{H}_{2}(\boldsymbol{g})+\frac{1}{2} \boldsymbol{O}_{2}(\boldsymbol{g}) \longrightarrow \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \boldsymbol{\Delta} \boldsymbol{H}= \)
\( -242 k J m o l^{-1} \)
Bond energy of \( H_{2} \) and \( O_{2} \) are 436 and
\( \mathbf{5 0 0} k J \mathrm{mol}^{-1} \) respectively. The bond
energy of \( 0-H \) bond is :
A \( \cdot 434 k J \mathrm{mol}^{-1} \)
B. \( 464 k J \) mol \( ^{-1} \)
\( \mathbf{c} \cdot 452 k J \mathrm{mol}^{-1} \)
D. \( 485 k J \) mol \( ^{-1} \)


Six lead-acid type of secondary cells each of emf \( 2.0 \mathrm{V} \) and internal
resistance of 0.015 are joined in series to provide a supply to a resistance of
\( 8.5 . \) What are the current drawn from the supply and it's terminal voltage?
A. 11.8749
B. 12.8749
c. 13.1749
D. 10.5749


An object is thrown between two tall
buildings \( 180 \mathrm{m} \) from each other. The
object thrown horizontally from a
window \( 55 \mathrm{m} \) above the ground from one
building strikes a window \( 10 \mathrm{m} \) above the tom ground in another building.
Find out the speed of projection.
A. 60
B. 80
\( c .70 \)
D. 90


The only radioactive element among the lanthanoids is:
A. gadolinium
B. holmium
c. promethium
D. neodynium


The IUPAC name of the given compound
is:
A. 2 -(Bromomethyl)-3-oxohexanamide
B. 1 -bromo-2-amino-3-oxohexane
C. 1 -bromo-2-amino-n-propylketone
D. 3-bromo-2-propylpropanamide


Calculate the mass of \( 3.011 \times 10^{23} \)
number of nitrogen atom.


Lassaigne's test for the detection of
nitrogen fails in:
A. \( N H_{2} C O N H N H_{2} . H C l \)
в. \( N H_{2} N H_{2} . H C l \)
c. \( N H_{2} \) СО \( N H_{2} \)
D. \( C_{6} H_{5} N H N H_{2} . H C l \)


Which force is required to maintain a body in uniform circular motion?


Why is anode in galvanic cell considered to be -ve and cathode to be
+ve electrode?


\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}\left[\sin ^{2}\left(\cot ^{-1} \sqrt{\frac{\boldsymbol{1}+\boldsymbol{x}}{1-\boldsymbol{x}}}\right)\right]=? \)


Which of the following is coenocytic?
A. Vaucheria
B. Pseudomonas
c. chlamydomonas
D. All of the above


A parallel plate condenser with a dielectric constant \( K \) between the
plates has a capacity \( C \) and is charged
to a potential \( V \) volt. The dielectric slab is slowly removed from, between the
plates and then reinserted. The net work
done by the system in this process is
A. zero
в. \( \frac{1}{2}(K-1) C V^{2} \)
c. \( \frac{C V^{2}(K-1)}{K} \)
D \( \cdot(K-1) C V^{2} \)


Find out the resultant of the two vectors
one of magnitude 3 directed towards the east and another one of magnitude
4 directed towards the north.
A. 5 northeast
B. 7 northeast
c. 2 southwest
D. 1 northeast
E. 12 northeast.


What cross-sections do you get when you cut a brick vertically?
A . Circle
B. Trianglel
c. cube
D. None of these


The terminal potential difference of a
cell is equal to the emf of the cell when:
A. The cell is an open circuitt
B. The internal resistance of the cell is zero
c. The load resistance \( R \) is much greater than the internal resistance \( r \)
D. All are true


\( f(x)=\{x: x \leq 10, x \in N\}, A=\{x: x \geq 4\} \)
and \( \mathrm{B}=\{x: 2<x<7\} ; \) find the number
of equal sets.


Which of the following element occurs in free form in nature?
A. \( N \)
в. \( P \)
c. \( A s \)
D. \( S b \)


If \( \cot ^{-1} x+\tan ^{-1} 3=\frac{\pi}{2} \) then \( x= \)
A \( -\frac{1}{3} \)
в. \( \frac{1}{4} \)
\( c \cdot 3 \)
D.


Which of the following is found in body? This question has multiple correct options
\( A \cdot P b \)
B. cad
\( c \cdot F e \)
D. co


If the radius of gold (Au) and platinum
\( (P t) \) atoms in \( p m \) is \( 100 \sqrt{2} \) and \( 90 \sqrt{2} \)
respectively, find \( n_{A u} n_{P t} \)
A . 0.52
B. 0.68
c. 0.73
D. 0.74


Match column I with column II and
select the correct option from the codes
given below


The \( p H \) of a \( 10 m l \) aqueous solution of \( H C l \) is \( 4 . \) The amount of water to be
added to this solution in order to
change its \( p H \) from 4 to 5 is?
A. \( 30 m \)
в. \( 60 \mathrm{ml} \)
\( c .90 m l \)
D. \( 120 m l \)


Which of the following actions will help to reduce pollution?
Composting kitchen and garden waste
2. Using unleaded petrol in cars
3. Spraying pesticides on plants to kill
pests
4. Littering chocolates and biscuits
wrappers
A . 1 and 2
B. 3 and 4
C. 1,2 and 3
D. 1,2 and 4


Helium is used in balloons in place of
hydrogen because it is:
A. Incombustible
B. Lighter than hydrogen
c. Radioactive
D. More abundant than hydrogen


Bohr's atom model assumes.
A. The nucleus is of infinite mass and is at rest
B. Electrons in a quantized orbit will not radiate energy
C. Mass of electron remains constant
D. All the above.


Find the value of \( \mathbf{x} \) for which \( \left|\begin{array}{ll}3 & x \\ x & 1\end{array}\right|= \)
\( \left|\begin{array}{ll}3 & 2 \\ 8 & 1\end{array}\right| \)


The \( H \) calories of heat is required to
increase the temperature of one mole of
monoatomic gas from \( 20^{\circ} \mathrm{C} \) to \( 30^{\circ} \mathrm{C} \) at
constant volume. The quantity of heat required to increase the temperature
of 2 moles of a diatomic gas from \( 20^{\circ} \mathrm{C} \)
to \( 25^{\circ} C \) is at constant volume is :
A \( \cdot \frac{4 H}{3} \)
в. \( \frac{5 H}{3} \)
c. \( 2 H \)
D. \( \frac{7 H}{3} \)


What is the percent of composition of the compound that forms when \( 222.7 g \)
of N combines compleletly with \( 77.4 g \) of
O?
A. \( 70 \%, 30 \% \)
B. \( 80 \%, 20 \% \)
c. \( 74.2 \%, 25.8 \% \)
D. \( 72.2 \%, 27.8 \% \)


If \( A \) and \( B \) are symmetric matrices and
\( A B=B A, \) then \( A^{-1} B \) is a
A. Symmetric matrix
B. Skew-symmetric matrix
c. Identity matrix
D. None of these


Formation of which of the sulphides is
most spontaneous?
A. \( H g S \)
в. \( B i_{2} S_{3} \)
\( c . P b S \)
\( \mathrm{D} \cdot \mathrm{CS} \)


The angular velocity of rotation of hour hand of a watch is how many times the angular velocity of Earth's rotation
about its own axis?
A. Three
B. Four
c. Two
D. six


A particle moves in such a manner that
\( \boldsymbol{x}=\boldsymbol{A t}, \boldsymbol{y}=\boldsymbol{B} \boldsymbol{t}^{3}-\boldsymbol{2 t}, \boldsymbol{z}=\boldsymbol{c} \boldsymbol{t}^{2}-\boldsymbol{4} \boldsymbol{t} \)
where \( x, y \) and \( z \) are measured in
metres and \( t \) is measured in seconds,
and \( A, B \) and \( C \) are unknown constants.
Given that the velocity of the particle at \( \boldsymbol{t}=2 \boldsymbol{s} \) is \( \overrightarrow{\boldsymbol{v}}=\left(\frac{\boldsymbol{d} \overrightarrow{\boldsymbol{r}}}{\boldsymbol{d} \boldsymbol{t}}\right)=\boldsymbol{3} \hat{\boldsymbol{i}}+2 \boldsymbol{2} \hat{\boldsymbol{j}} \boldsymbol{m} / \boldsymbol{s} \)
determine the velocity of the particle at
\( \boldsymbol{t}=\mathbf{4} \boldsymbol{s} \)
\( \mathbf{A} \cdot 8 \hat{i}+94 \hat{j}+4 \hat{k} m / s \)
B. \( 6 \hat{i}+94 \hat{j}+6 \hat{k} m / s \)
\( \mathbf{c} \cdot 3 \hat{i}+94 \hat{j}+4 \hat{k} m / s \)
D \( .3 \hat{i}+92 \hat{j}+4 \hat{k} m / s \)


In a N-P-N transistor about \( 10^{10} \)
electrons enter the emitter in \( 2 \mu s, \) when
it is connected to a battery. Then \( \boldsymbol{I}_{\boldsymbol{E}}= \)
\( \boldsymbol{\mu} \boldsymbol{A} \)
A . 200
в. 400
c. 800
D. 1600


Find the angle between the vectors \( \vec{r}_{1}=(4 \hat{i}-3 \hat{j}+5 \hat{k}) \) and \( \vec{r}_{2}=(3 \hat{i}+ \)
\( 4 \hat{j}+5 \hat{k}) \)
A \( \cdot \frac{\pi}{3} \)
B.
\( c \cdot \frac{\pi}{7} \)
D. \( \frac{\pi}{6} \)


Express the rate for the following
reaction in terms of concentration of
reactants and products.
\( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{I}_{2}(\boldsymbol{g}) \rightarrow \boldsymbol{2} \boldsymbol{H} \boldsymbol{I}(\boldsymbol{g}) \)


During the Z scheme, electrons excited absorption of light in PSI are transferred to the primary acceptors, and therefore must be replaced. The replacements come directly from
A. NADP
в. Атр
\( c . \) PS I
D. water


Identify the unknown compounds.
\( \mathbf{A} \cdot A \rightarrow C H_{3} C O C l, B \rightarrow C_{6} H_{5} C l, C \rightarrow N a C N \)
B \( \cdot A \rightarrow C H_{3} C l, B \rightarrow C_{6} H_{5} C H_{2} C l, C \rightarrow K C N \)
\( \mathbf{C} \cdot A \rightarrow C H_{4}, B \rightarrow C_{6} H_{5} C H_{2} C l, C \rightarrow A g C N \)
\( \mathbf{D} \cdot A \rightarrow C H_{3} C l, B \rightarrow C_{6} H_{5} C O C l, C \rightarrow K C N \)


Petiole of Australian Acacia helps in?
A. Respiration
B. Photosynthesis
c. Transpiration
D. Secretion


Solve:
\( \int \frac{\sqrt{x}-\sqrt{a}}{\sqrt{x+a}} d x \)


In a hydrogen spectrum third line of
Balmer's series having wavelength \( \lambda \)
Find the binding energy of the ground
state


Which of the following is the best
measure to save energy?
A. Each individual uses his own vehicle
B. Four colleagues residing in the same colony travel to the office together by the same car
C. Using vehicles to travel small distances
D. Keeping the vehicle engine 'on' during traffic jam


Van't Hoff factor of a mixture of two
moles of KI with 1 mole \( H g I_{2} \) in a
solution of water is :


Which one of the following is not characteristic of Pteridophytes?
A. Dominant gametophytic plant body.
B. Dominant sporophytic plant body.
c. Pinna release spores.
D. Prothallus give rise to gametophytic body


If \( (1+x)^{10}=a_{0}+a_{1} x+a_{2} x^{2}+\dots+ \)
\( a_{10} x^{10}, \) then the value of
\( \left(a_{0}-a_{2}+a_{4}-a_{6}+a_{8}-a_{10}\right)^{2}+ \)
\( \left(a_{1}-a_{3}+a_{5}-a_{7}+a_{9}\right)^{2} \) is
\( \mathbf{A} \cdot 2^{10} \)
B . 2
\( c \cdot 2^{20} \)
D. None of these


Evaluate \( : \lim _{x \rightarrow 1} \frac{\sqrt{5 x-4}-\sqrt{x}}{x^{3}-1} \)


For gaseous reaction, rate \( \boldsymbol{k}[\boldsymbol{A}][\boldsymbol{B}] . \) If volume of container is reduced to \( 1 / 4 \) of initial, then the rate of reaction will be
times of initial.
A . \( 1 / 8 \)
B. 8
c. \( 1 / 16 \)
D. 16


What is correct about the movement of
substance across the membrane in
facilitated diffusion?
A. It is an active transporttt
B. It doesn't cause transport of molecules from lower concentration to higher
c. it does not require a carrier protein
D. It works against concentration gradient


What are damped vibrations? How do they differ from free vibrations ? Give one example of each.


If the series limit of Lymen series for hydrogen atom is equal to the series limit of Balmer series for a hydrogen
like atom, then atomic number of this
hydrogen like atom is
A . 1
B. 2
\( c .3 \)
D. 4


In which of the following orbits are the TV broadcasting satellites placed?
A. Semi-synchronous orbitt
B. Sun-synchronous orbit
c. Geostationary orbitt
D. Geo-synchronous orbit


For the elements:
\( \boldsymbol{C l}, \boldsymbol{B r}, \boldsymbol{F}, \boldsymbol{A l}, \boldsymbol{C}, \boldsymbol{L} \boldsymbol{i}, \boldsymbol{C s} \) \& \( \boldsymbol{X} \boldsymbol{e} \)
Choose the best option. The element having 8 electrons in the outermost shell is:
A. \( X e \)
в. \( C s \)
\( c \cdot B r \)
D. \( C \)


The reaction \( N_{2} O_{5}\left(\text { in } C C l_{4}\right) \rightarrow \)
\( 2 N O_{2}+1 / 2 O_{2}(g) \) is first order in
\( N_{2} O_{5} \) with rate constant \( 6.2 \times 10^{-4} \)
What is the value of rate of reaction
when \( \left[N_{2} O_{5}\right]=1.25 \) mole \( L^{-1} \)
A \( \cdot 7.75 \times 10^{4} \) mol \( L^{-1} S^{-1} \)
B. \( 6.35 \times 10^{3} \) mol \( L^{-1} S^{-1} \)
c. \( 5.15 \times 10^{5} \) mol \( L^{-1} S^{-1} \)
D. \( 3.85 \times 10^{4} \) mol \( L^{-1} S^{-1} \)


Superphosphate of lime is obtained by treating:
A. calcium phosphate with \( H C l \)
B. calcium phosphide with \( H C l \)
C. calcium phosphate with \( H_{2} S O_{4} \)
D. calcium phosphate with \( N a O H \)


The velocity - time graph of a body is
given in figure. The maximum
acceleration in \( m / s^{2} \) is
4
\( B \)
\( c \)
\( D \)


Find the sum of series up to \( n \) terms:
\( \frac{1^{3}}{1}+\frac{1^{3}+2^{3}}{1+3}+\frac{1^{3}+2^{3}+3^{3}}{1+3+5}+\dots \)


n given figure the interior opposite
angles of the exterior angle \( \angle A C D \) are:
\( A \cdot \angle B, \angle C \)
в. \( \angle A, \angle C \)
\( \mathbf{c} \cdot \angle A, \angle B \)
D. \( \angle B, \angle E \)


A uniform magnetic field of 1.5 T exists in a cylindrical region of radius \( 10.0 \mathrm{cm} \) its direction parallel to the axis along east to west. A wire carrying current of \( 7.0 \mathrm{A} \) in the north to south direction passes through this region. What is the magnitude and direction of the force on the wire if,(a) the wire intersects the axis,(b) the wire is turned from N-S to northeast-northwest direction,(c) the
wire in the N-S direction is lowered from
the axis by a distance of \( 6.0 \mathrm{cm} \) ?


\( \operatorname{Let} \boldsymbol{f}(\boldsymbol{x}):\left\{\begin{array}{llll}\boldsymbol{x}, & \boldsymbol{x} & \boldsymbol{i} \boldsymbol{s} & \boldsymbol{r} \boldsymbol{a} \boldsymbol{t} \boldsymbol{i} \boldsymbol{o} \boldsymbol{n} \boldsymbol{a} \boldsymbol{l} \\ \boldsymbol{0}, & \boldsymbol{x} & \boldsymbol{i} \boldsymbol{s} & \boldsymbol{i} \boldsymbol{r} \boldsymbol{r} \boldsymbol{a} \boldsymbol{t} \boldsymbol{i} \boldsymbol{o} \boldsymbol{n} \boldsymbol{a} \boldsymbol{l}\end{array}\right. \)
and
\( \boldsymbol{g}(\boldsymbol{x}):\left\{\begin{array}{llll}\mathbf{0}, & \boldsymbol{x} & \boldsymbol{i} \boldsymbol{s} & \boldsymbol{r} \boldsymbol{a} \boldsymbol{t} \boldsymbol{i} \boldsymbol{o} \boldsymbol{n} \boldsymbol{a} \boldsymbol{l} \\ \boldsymbol{x}, & \boldsymbol{x} & \boldsymbol{i} \boldsymbol{s} & \boldsymbol{i} \boldsymbol{r} \boldsymbol{r} \boldsymbol{a} \boldsymbol{t} \boldsymbol{i} \boldsymbol{o} \boldsymbol{n} \boldsymbol{a} \boldsymbol{l} \boldsymbol{l}\end{array}\right. \)
ff \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) and \( \boldsymbol{g}: \boldsymbol{R} \rightarrow \boldsymbol{R}, \) then \( (\boldsymbol{f}- \)
\( \boldsymbol{g}) \) is
A. one-one and into
B. neither one-one nor onto
c. many-one and onto
D. one-one and onto


Using the differentials, the approximate
value of \( (627)^{1 / 4} \) is
A . 5.002
B. 5.003
c. 5.005
D. 5.004


The velocity of an object varies with time as \( V=A t^{2}+B t+C . \) Taking the
unit of time as \( s \) and velocity as \( m s^{-1} \) the units of \( A, B, C \) respectively are :
\( \mathbf{A} \cdot m s^{-3}, m s^{-2}, m s^{-1} \)
B . \( m s^{-2}, m s^{-1}, m s^{-3} \)
c. \( m s^{-1}, m s^{-2}, m s^{-3} \)
D. \( m s^{-1}, m s^{-1}, m s^{-1} \)


If the straight line \( a x+b y+p=0 \) and
\( x \cos \alpha+y \sin \alpha=p \) enclosed an angle
of \( \frac{\pi}{4} \) and the line \( x \sin \alpha-y \cos \alpha=0 \)
meets them at the same point, then
\( a^{2}+b^{2} \) is
A .4
B. 3
\( c \cdot 2 \)
D.


Temporary hardness is caused due to
the presence of:
A. magnesium sulphate
B. magnesium chloride
c. calcium sulphate
D. magnesium carbonate


BOD of eutrophied lake will be
A . Lower
B. Moderate
c. Higher
D. Same as any other lake


The complex compound in which metal is not present in zero oxidation state?
\( \mathbf{A} \cdot M n_{2}(C O)_{10} \)
В \( \cdot\left[N i(C O)_{4}\right] \)
\( \mathbf{c} \cdot\left[\operatorname{Cr}\left(C_{6} H_{6}\right)_{2}\right] \)
D \( \cdot_{K}\left[P t C l_{3}\left(C_{2} H_{4}\right)\right] \)


Construct a quadrilateral ABCD, if \( A B=4.5 \mathrm{cm}, \mathrm{BC}=5.5 \mathrm{cm}, \mathrm{CD}=5 \mathrm{cm}, \mathrm{DA}=4.8 \)
\( \mathrm{cm}, \) and \( \angle A B C=60^{\circ} \)


Let \( \boldsymbol{f}(\boldsymbol{x})=\sin \left(\tan ^{-1} \boldsymbol{x}\right) . \) Then
\( [\boldsymbol{f}(-\sqrt{\mathbf{3}})], \) where [.] denotes the
greatest integer function, is
\( ^{\mathrm{A}}-\frac{\sqrt{3}}{2} \)
B.
c. -1
D. none of these


Bullet proof helmets are made from:
A. lexan
B. saran
c. glyptal
D. thiokol


The rate constant of reaction changes
when:
A. volume is changed
B. concentration of the reactants are changed
c. temperature is changed
D. pressure is changed


The image which can not be taken on the screen is called
A. a real image
B. a virtual image
c. either a real or a virtual image
D. neither a real nor a virtual image


The compound which reacts fastest
with Lucas reagent at room temperature, is
A . butan-1-ol
B. butan-2-ol
c. 2-methyl propan-1-ol
D. 2-methyl propan-2-ol


Calculate the pH of a buffer prepared by mixing 300 cc of \( 0.3 \mathrm{M} N H_{3} \) and \( 500 \mathrm{cc} \)
of \( 0.5 \mathrm{M} N H_{4} C l . K_{b} \) for \( N H_{3}=1.8 \times \)
\( 10^{-5} \)
A . 8.1187
B. 9.8117
c. 8.8117
D. None of these


The following equilibrium are given
\( N_{2}+3 H_{2} \rightleftharpoons 2 N H_{3} \quad K_{1} \)
\( N_{2}+O_{2} \rightleftharpoons 2 N O \)
\( H_{2}+\frac{1}{2} O_{2} \rightleftharpoons H_{2} O \)
The equilibrium constant of the reaction
\( \mathbf{2} N \boldsymbol{H}_{3}+\frac{\mathbf{5}}{\mathbf{2}} \boldsymbol{O}_{2} \rightleftharpoons \mathbf{2} \boldsymbol{N} \boldsymbol{O}+\mathbf{3} \boldsymbol{H}_{2} \boldsymbol{O}, \) in
terms of \( K_{1}, K_{2} \) and \( K_{3} \) is :
A. \( \frac{K_{1} K_{2}}{K_{3}} \)
B. \( \frac{K_{1} K_{3}^{2}}{K_{2}} \)
\( ^{\mathrm{C}} \cdot \frac{K_{2} K_{3}^{3}}{K_{1}} \)
D. \( K_{1} K_{2} K_{3} \)


The different zones of a candle flame
are marked by the letters, \( A, B \) and
C. Which of the following is correct?
A. \( B \) is the hottest part of the flame
B. \( C \) is moderately hot.
\( \mathrm{C} \). A is the hottest part of the flame
A is moderately hot whereas \( C \) is the coldest partt


Production of ICs is preferred in
industrial scales because:
A. it reduces the cost of production.
B. it makes the task of fabrication of a circuit easier
c. it improves the efficiency of the circuit.
D. specifications of a circuit is same for all applications


Reaction occurring in lead storage battery is a kind of:
A. disproportionation
B. comproportionation
c. oxidation
D. reduction


Pick the incorrect statement from the
following:
A. Iris is the part of the eye which gives it, its distinctive colour
B. The most comfortable distance at which one can read
with a normal eye is about \( 50 \mathrm{cm} \)
C. If still images of a moving object are flashed on the eye at a rate faster than \( 16 / s \), then, the eye perceives this object as moving
D. Eye lens becoming cloudy is called cataract


State, whether the following statement is True or False:

The systematic names of the acids are formed by dropping the -e of the name of parent alkane and adding suffix -oic
acid.


Diazotization of \( n-B u-N H_{2} \) with
\( N a N O_{2} / H C l \) gives
isomeric butene.
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D.


The distance between the two parallel chords of length \( 8 \mathrm{cm} \) and \( 6 \mathrm{cm} \) in a circle of diameter \( 10 \mathrm{cm} \) if the chords lic
on the same side of the centre is
A. \( 1 \mathrm{cm} \)
B. 2 \( \mathrm{cm} \)
\( c \cdot 3 \mathrm{cm} \)
D. \( 4 \mathrm{cm} \)


\( \frac{\sigma}{\partial x} \)
0


Invert sugar is:
A. a type of cane sugar
B. optically inactive form of sugar
C. mixture of glucose and galactose
D. mixture of glucose and fructose in equimolar quantities


Exhaust motor vehicle is the main
source of:
A. manganese
B. carbon monoxide
c. sulfur dioxide
D. nitrogen oxide


Find the value of the unknown exterior
angle \( x \) in the following diagram


The structures participating in the air
inhalation are
A. Diaphragm and internal intercoastal
B. Diaphragm and external intercoastal
c. Abdominal muscles and intercoastal
D. All of the above


Which of the following pairs of ions are isoelectronic as well as isostructural?
A \( \cdot C l O^{-}, S O_{2}^{-4} \)
в. \( \operatorname{ClO}_{3}^{-2}, \operatorname{SO}_{4}^{-2} \)
\( \mathrm{c} \cdot \mathrm{ClO}_{3}^{-}, \mathrm{NO}_{3}^{-} \)
D. \( S O_{4}^{2-}, P O_{4}^{3} \)


The sum of the infinite series \( \frac{1.3}{2}+ \) \( \frac{3.5}{2^{2}}+\frac{5.7}{2^{3}}+\frac{7.9}{2^{4}}+\dots \dots \dots . .0 . \)


Represent the solution of each of the
following inequalities on the real number line:
\( 7-x \leq 2-6 x \)


Nitrogen exists as diatomic molecule
and phosphorus as \( \boldsymbol{P}_{4} \). Why?


Among the following groupings, which represents the collection of isoelectronic species?
A \( \cdot C O, N O^{+}, C N^{-}, C_{2}^{2} \)
B. \( N_{2}, C_{2}^{2-}, C O, N O \)
c. \( N O, C N, N_{2}, O_{2}^{-} \)
D. \( N O^{+}, C_{2}^{2-}, O_{2}^{-}, C O \)


Which of the following is an example of liquid dishwashing detergent?
A \( \cdot C H_{3}\left(C H_{2}\right)_{10}-C H_{2} O S O_{3}^{-} N a^{+} \)
в.
\( c \)
\( ^{\mathrm{D} \cdot}\left[\begin{array}{cc}C H_{3} & \\ C H_{3}\left(C H_{2}\right)_{15}-N & N \\ C H_{3} & C H_{3}\end{array}\right]^{+} B r \)


Which of the following industries are responsible for water pollution? This question has multiple correct options
A. Oil refineries
B. Paper factories
c. textile and sugar mills
D. chemical factories


N divisions on the main scale of vernier
callipers coincide with (N+1) divisions on the vernier scale. If each divisions on
the main scale of a units, determine the
least count of instrument.
A. (N+1) Main scale division
B . (N + 1) -1 Main scale divisions
c. N Main scale division
D. (1-N) Main scale divisions


A sound wave travelling in air is made to propagate through a liquid such that the velocity of sound is quadrupled. If the frequency of he sound wave is constant, find the change in the wavelength of the sound wave.
A \( \cdot \lambda_{a i r} \)
B. \( 2 \lambda_{\text {ar }} \)
c. \( 3 \lambda_{\lambda i} \)
D. \( 4 \lambda_{\text {ar }} \)


State true or false.
Given universal set= \( = \) \( \left\{-\mathbf{6},-\mathbf{5} \frac{\mathbf{3}}{\mathbf{4}},-\sqrt{\mathbf{4}},-\frac{\mathbf{3}}{\mathbf{5}},-\frac{\mathbf{3}}{\mathbf{8}}, \mathbf{0}, \frac{\mathbf{4}}{\mathbf{5}}, \mathbf{1}, \mathbf{1} \frac{\mathbf{2}}{\mathbf{3}}\right. \)
From the given set, find set of non-
negative integers is \{0,1\}
A. True
B. False


The concept of solid angle is a natural extension of a \( \underline{\text { angle to }} \) dimensions.
\( A \). plane, two
B. line, three
c. plane, three
D. line, two


Let \( A \) be the \( 2 \times 2 \) matrices given by
\( \boldsymbol{A}=\left[\boldsymbol{a}_{i j}\right] \) where \( \boldsymbol{a}_{i j}=\{\mathbf{0}, \mathbf{1}, \mathbf{2}, \mathbf{3}, \mathbf{4}\} \)
such that \( \boldsymbol{a}_{11}+\boldsymbol{a}_{12}+\boldsymbol{a}_{21}+\boldsymbol{a}_{22}=\boldsymbol{4} \)
Find the number of matrices \( A \) such
that the trace of \( A \) is equal to 4
\( A \cdot 3 \)
B. 4
\( c \cdot 5 \)
D. 6


A man running along a straight road with uniform velocity \( \vec{u}=u \hat{i} \) feels that
the rain is falling vertically down along \( -\hat{\boldsymbol{j}} \). If he doubles his speed,he finds that
the rain is coming at an angle \( \theta \) with the vertical. The velocity of the rain with respect to the ground is :
A \( . u i-u \tan \theta \hat{j} \)
B. \( u i-\frac{u}{\tan \theta} \)
c. \( u \tan \theta-u \vec{j} \)
D. \( \frac{u}{\tan \theta} \vec{i}-u \vec{j} \)


Binomial expansion of \( \left(\boldsymbol{x}^{k}+\frac{\mathbf{1}}{\mathbf{2}^{\mathbf{2 k}}}\right)^{\mathbf{3 n}} \)
where \( n \) is a positive integer, always contains a term which is independent of
\( \mathbf{A} \cdot x^{2} \)
B. \( x \)
\( \mathbf{c} \cdot x^{3} \)
D. none of the above


Light from a denser medium 1 passes
to a rarer medium 2. When the angle of incidence is \( \theta \) the partially reflected and
refracted rays are mutually perpendicular. The critical angle will be
A \( \cdot \sin ^{-1}(\cot \theta) \)
B. \( \sin ^{-1}(\tan \theta) \)
c. \( \sin ^{-1}(\cos \theta) \)
D. \( \sin ^{-1}(\sec \theta) \)


Sulphuric acid is used in lead-acid storage batteries.
A. True
B. False


What is a tissue?


Consider \( \boldsymbol{x}=\mathbf{4} \tan ^{-1}\left(\frac{\mathbf{1}}{\mathbf{5}}\right), \boldsymbol{y}= \)
\( \tan ^{-1}\left(\frac{1}{70}\right) \) and \( z=\tan ^{-1}\left(\frac{1}{99}\right) \)
What is \( x \) equal to?
A \( \cdot \tan ^{-1}\left(\frac{60}{119}\right) \)
в. \( \tan ^{-1}\left(\frac{120}{119}\right) \)
\( ^{\mathbf{c}} \cdot \tan ^{-1}\left(\frac{90}{169}\right) \)
D. \( \tan ^{-1}\left(\frac{170}{169}\right) \)


Le-Chatelier principle is not applicable
to:
A \( \cdot H_{2}(g)+I_{2}(g) \rightleftharpoons 2 H I(g) \)
В. \( F e(s)+S(s) \rightleftharpoons F e S(s) \)
C. \( N_{2}(g)+3 H_{2}(g) \rightleftharpoons 2 N H_{3}(g) \)
D. \( N_{2}(g)+O_{2}(g) \rightleftharpoons 2 N O(g) \)


Construct a triangle \( A B C \) in which
\( A B=5.8 c m, B C+C A=8.4 \mathrm{cm} \) and
\( \angle B=60^{\circ} \)


When we inflate cycle tubes, the volume
of tube as well as the pressure of air inside tube increases.
A. It is an exceptional case of Boyle's Law
B. It happens because air is not ideal gas
c. It happens because mass of air is not constant
D. It happens because external force is applied in inflating the tubes


A proton goes undeflected in a crossed electric and magnetic field (the fields
are perpendicular to each other) at a speed of \( 10^{5} \mathrm{m} / \mathrm{s} \). The velocity is
perpendicular to both the fields. When
the electric field is switched off, the
proton moves along a circle of radius 2
\( \mathrm{cm} . \) Find the magnitude of the electric and the magnetic fields. Take the mass of the proton \( =1.6 \times 10^{-27} \mathrm{kg} \)


A telephone cable at a place has four long straight horizontal wires carrying a current of \( 1.0 \mathrm{A} \) in the same direction
east to west. The earth's magnetic field at the place is \( 0.39 \mathrm{G} \), and the angle of dip is \( 35^{0} . \) The magnetic declination is nearly zero. What are the resultant
magnetic fields at point \( 4.0 \mathrm{cm} \) below the cable?
B. 0.50 G
c. 1.25 G
D . 2.50 G


Consider the following isomerism:
(i) ionization (ii) hydrate (iii) coordination (iv) geometrical (v) optical Which of the above isomerisms are
exhibited by \( \left[\boldsymbol{C r}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{2}(\boldsymbol{O} \boldsymbol{H})_{2} \boldsymbol{C l}_{2}^{-} ?\right. \)
\( A \cdot \) (i) and (v)
B. (ii) and (iii)
c. (iii), (ii) and (i)
D. (iv) and (v)


A flat coil, \( C, \) of \( n \) turns, area \( A \) and
resisitance \( R \) is placed in a uniform
magnetic field of magnitude B. The plane of the coil is initially perpendicular to B. If the coil is rotated by an angle about the axis \( \mathrm{XY} \), charge of amount Q flows through it. if the coil rotates about XY with a constant
angular velocity \( \omega, \) the emf induced in
¡t.
This question has multiple correct options
A. is zero
B. changes nonlinearly with time
c. has a constant value \( =\mathrm{BAn} \omega \)
D. has a maximum value \( = \) BAn


A nucleus of mass \( M+\Delta m \) is at rest
and decays into two daughter nuclei of equal mass of \( \frac{M}{2} \) each. The speed of light is c,Then speed of daughter nuclei is?
A \( \cdot c \frac{\Delta \mathrm{m}}{\mathrm{M}+\Delta \mathrm{m}} \)
B. \( \mathrm{c} \sqrt{\frac{2 \Delta \mathrm{m}}{\mathrm{M}}} \)
\( ^{c} \cdot c \sqrt{\frac{\Delta m}{M}} \)
D \( \cdot \sqrt{\frac{\Delta m}{M+\Delta m}} \)


Mark the correct statement.
A. Some metals are found in earth's crust in the free state
B. Metals at the bottom of activity series are least reactive
C. Gold, silver can never be found in free state
D. Both A and B


The velocity \( v \) of sound can be assumed
as dependent on density of medium and modulus of elasticity of medium ,so which of the following can be considered as correct formula for
calculating velocity of sound, \( (\rho \) =density, \( E \) =modulus of elasticity
\( \mathbf{A} \cdot v=\rho^{0.5} \times E^{0.5} \)
В . \( v=\rho^{0.5} \times E^{-0.5} \)
C \( \cdot v=\rho^{-0.5} \times E^{0.5} \)
D. none of the above


A rigid body in shape of a triangle has
\( \boldsymbol{v}_{\boldsymbol{A}}=\mathbf{5} \boldsymbol{m} / \boldsymbol{s}^{2} \) down, \( \boldsymbol{v}_{\boldsymbol{B}}=\mathbf{1 0 m} / \boldsymbol{s} \) down
Find velocity of point \( \boldsymbol{C} \)
\( \mathbf{A} \cdot 5 \hat{i}+10 \hat{j} \)
B . \( -5 \hat{i}-10 \hat{j} \)
c. \( -5 \hat{i}+10 \hat{j} \)
D. \( 5 \hat{i}-10 \hat{j} \)


This species has \( s p^{2} \) hybrid orbitals
A. \( B e F_{2} \)
в. \( N H_{3} \)
\( \mathrm{c} \cdot \mathrm{CH}_{4} \)
D. \( C H_{2} C H_{2} \)
E \( \cdot C C l_{4} \)


Fill in the blanks by choosing the appropriate word/words from those given in the brackets:
(square pyramidal, electrical, 74, 26, \( s p^{3} d^{2}, s p^{3} d, \) chemical, 68,32
tetrahedral, yellow, white, iodoform, Lucas)
The shape of \( X e O F_{4} \) molecule is
and the
hybridisation of xenon atom in the
molecule is


Deforestation is the major causal agent
of
A. Depletion of natural resources
B. Environmental pollution
c. Desertification of habitatt
D. All of the above


Let \( \boldsymbol{f}: \boldsymbol{N} \rightarrow \boldsymbol{N}(\boldsymbol{N} \) being the set of
positive integers) be a function defined by \( f(x)= \) the biggest positive integer
obtained by reshuffling the digits of \( x \) For example, \( \boldsymbol{f}(\mathbf{2 9 6})=\mathbf{9 6 2} \)
\( f \) is
A. One-one and onto
B. One-one and into
c. Many-one and onto
D. Many-one and into


Initiation codon is
A. UUU
B. UGA
c. AUG
D. UAG


A straight conductor of uniform cross-
section carries a current \( I . \) If \( s \) is the
specific charge of an electron, the momentum of all the free electrons per unit length of the conductor, due to
their drift velocity only is
A . \( 1 s \)
в. \( \sqrt{\frac{I}{s}} \)
c. \( \frac{I}{s} \)
\( ^{\mathrm{D} \cdot}\left(\frac{I}{s}\right)^{2} \)


Lymph transports white blood cells from
A. Spleen
B. Pancreas
c. Lymph nodes
D. liver


The vertical height of mercury which a simple barometer can support at sea level is
\( \mathbf{A} \cdot 76 \mathrm{cm} \)
B. more than \( 76 \mathrm{cm} \)
c. less than \( 76 \mathrm{cm} \)
D. none of these


The elevation in boiling point of a
solution \( d T_{b} \) is related with molality of
solution \( (\mathrm{m}) \) by the relation:
\( \boldsymbol{d} \boldsymbol{T}_{\boldsymbol{b}}=\left[\frac{\boldsymbol{R} \boldsymbol{T}_{\boldsymbol{b}}^{2}}{\boldsymbol{\Delta} \boldsymbol{H}_{\boldsymbol{v a p}}}\right]\left[\frac{\boldsymbol{M}_{\mathbf{1}}}{\mathbf{1}+\boldsymbol{m} \boldsymbol{M}_{\mathbf{1}}}\right], \) where
\( M_{1} \) is molar mass of solvent and \( \Delta \boldsymbol{H}_{\boldsymbol{v} \boldsymbol{a} \boldsymbol{p}} \)
is heat of vaporisation of solvent. For a dilute solution, the relation \( \left(\frac{\partial T_{b}}{\partial m}\right)_{m \rightarrow 0} \)
gives:
A. molal ebullioscopic constant
B. elevation in boiling point
C. elevation in boiling point \( \partial T_{b} \) becomes more predominant
D. boiling point of solvent


Which of the following complementary base pairing does not exist?
A. A DNA adenine to a DNA thymine
B. A DNA adenine to an RNA thymine
C. A DNA guanine to an RNA cytosine
D. A DNA adenine to an RNA uracil
E. A DNA guanine to a DNA cytosine


Find all points of discontinuity of \( \boldsymbol{f} \)
where \( f \) is defined by \( f(x)= \)
\( \left\{\begin{array}{ll}2 x+3, & x \leq 2 \\ 2 x-3, & x>2\end{array}\right. \)


The probability that Dhoni will hit
century in every ODI matches he plays is \( \frac{1}{5} \). If he plays 6 matches in World Cup \( 2011, \) the probability that he will score 2 centuries is:
A \( \cdot \frac{768}{3125} \)
в. \( \frac{2357}{3125} \)
c. \( \frac{2178}{3125} \)
D. \( \frac{412}{3125} \)


Choose the correct answer from the
alternatives given
Active transport
A. Requires an input of ATP
B. Is involved in diffusion
c. occurs in osmosis and facilitated transport
D. All of the above


What results in the weak catenation
property of nitrogen?
A. Smaller size
B. Repulsion between non-bonded electrons
C. Repulsion between protons
D. High electronegativity


Assertion
For nuclear reactor, it is desirable to
have (Multiplication Factor) \( k=1 \)
Reason
Sustained chain reaction occur at this
critical condition.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Assertion
\( Y b^{+2} \) is more stable in compare to
\( G d^{+2} \)
Reason
The electron configuration of \( G d \) is
\( [\boldsymbol{X} \boldsymbol{e}] \boldsymbol{4} \boldsymbol{f}^{7} \boldsymbol{5} \boldsymbol{d}^{2} \boldsymbol{6} \boldsymbol{s}^{2} \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


What lubricates the freely movable joint at the shoulder?


Which of the quantity consists of unit
as m/sec?
A. Speedd
B. Distance
c. weight
D. Time period


Assertion
Heavy nuclides tend to have more
number of neutrons than protons.
Reason
In heavy nuclei, as there is coloumbic
repulsion between protons, so excess of
neutrons are preferable.
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


Which of the following movements is
not related to change in auxin levels?
A. Nyctinastic leaf movement
B. Movement of roots towards soil
C. Movements of sunflower tracking the direction of the
sun
D. Movement of shoot towards light


Find the \( 9^{t h} \) term of a G.P.: \( 3,6,12,24, \dots \)


Order of paramagnetic character among following elements is/are:
This question has multiple correct options
\( \mathbf{A} \cdot M n>F e>C r \)
в. \( F e>Z n>C r \)
c. \( C r>F e>Z n \)
\( \mathrm{D} \cdot \mathrm{Cr}>\mathrm{Mn}>\mathrm{Fe} \)


Assuming \( i=i_{0} \) at \( t=0 ; \) The current at
any instant in the loop is after
the external field has stopped changing
A. \( _{i=i_{0} e^{\frac{-2 R t}{\mu_{0} \pi a}}} \)
в. \( \quad_{i=i_{0} e^{\frac{-R t}{\mu_{0} \pi a}}} \)
\( \mathrm{c} \cdot_{i=i_{0} e^{\frac{2 R t}{\mu_{0} \pi a}}} \)
D. \( _{i=i_{0} e^{\frac{-R t}{2 \mu_{0} \pi a}}} \)


The family of elements which is least
reactive is:
A. alkali metalss
B. alkaline earth metals
c. noble gases
D. halogens
E. transition metals


How deforestation will lead to ecological imbalance?


What will be the magnitude of e.m.f. induced in a 200 turns coil with cross
section area \( 0.16 m^{2} ? \) The magnetic field through the coil changes from 0.10 Wb \( m^{-2} \) to \( 0.30 \mathrm{Wb} \), at a uniform rate over a
period of \( 0.05 \mathrm{s} \)
A . \( 128 v \)
B. 130v
\( c \cdot 118 v \)
D. 1320


The fraction, \( \frac{1}{3} \)
A. equals 0.33333333
B. is less than 0.33333333 by \( \frac{1}{3.10^{8}} \)
c. is less than 0.33333333 by \( \frac{1}{3.10^{9}} \)
D ' is greater than 0.33333333 by \( \frac{1}{3.10^{8}} \)
E \( \cdot \) is greater than 0.33333333 by \( \frac{1}{3.10^{9}} \)


Product of two integers with
unlike signs is
A. Negative
B.
c. Positive
D. None of these


\( 1 \mathrm{u} \) is equivalent to an energy of
\( A \cdot 9.315 \mathrm{MeV} \)
B. 931.5 Kev
c. 93.15 Mev
D. 931.5 Mev


Examine the applicability of Mean Value
Theorem for the following function. \( \boldsymbol{f}(\boldsymbol{x})=[\boldsymbol{x}] \) for \( \boldsymbol{x} \boldsymbol{\epsilon}[\boldsymbol{2}, \boldsymbol{2}] \)


Evaluate \( \frac{\sin ^{2} 63^{\circ}+\sin ^{2} 27^{\circ}}{\cos ^{2} 17^{\circ}+\cos ^{2} 73^{\circ}} \)


The circumference of the second Bohr
orbit of electron in the hydrogen atom is
\( 600 n m . \) Calculate the potential
difference to which the electron has to
be subjected so that the electron stops. The electron had the de Broglie
wavelength corresponding to the circumference.


The near point for a young adult with normal vision is:
A . \( 2.5 \mathrm{cm} \)
B. 25 cm
c. \( 2.5 \mathrm{m} \)
D. 25 m


The heavier stable nuclei tend to have
larger N/Z ratio because
This question has multiple correct options
A. A neutron is heavier than a proton
B. A neutron is an unstable particle
C. A neutron does not exert electric repulsion
D. Coulomb forces have longer range compared to nuclear forces


Which of the following statements is
true?
A \( \cdot \frac{-5}{8} \) lies to the left of 0 on the number line
B. \( \frac{3}{7} \) lies to the right of 0 on the number line.
C the rational numbers \( \frac{1}{3} \) and \( \frac{-7}{3} \) are on opposite sides of 0 on the number line
D. All the above


An isolated metal body is illuminated with monochromatic light and is
observed to becomes charged to a steady positive potential \( 1.0 \mathrm{V} \) with respects to the surrounding. the work function of the metal is \( 3.0 \mathrm{eV} \). The
frequency of the incident light is


Calculate the minimum number of
balloons each of volume 82.1 L required to lift a mass of \( 1 \mathrm{kg} \) to a height of 831
\( \mathbf{m} \)
Given: molar mass of air \( =29 \mathrm{g} / \mathrm{mol} \), the temperature is constant at \( 290 \mathrm{K} \) and mass of each balloon is 40 g. \( \left[\text { Use } e^{-01}=0.9, \text { pressure at sea level }=1\right. \) atm, acceleration due to gravity \( (g)=10 \) \( \left.\mathrm{m} / \mathrm{s}^{2}\right] \)
A . 10
в. 20
\( c \cdot 25 \)
D. 50


Assertion
If \( \tan A+\tan B+\tan C=3 \sqrt{3}, \) then
triangle is equilateral
Reason
\( \ln \Delta A B C, \tan A+\tan B+\tan C= \)
\( \tan A \tan B \tan C \)
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 false but Reason is true


Give the IUPAC name of the following:
\[
\begin{array}{c}
\mathrm{CH}_{3} \\
\mathrm{CH}_{3}-\mathrm{CH}-\mathrm{CH}_{2}-\mathrm{CH}_{2}-\mathrm{CH}_{2}^{3} \frac{\mathrm{CH}_{3}}{\mathrm{CH}_{2}-\mathrm{CH}-\mathrm{CH}_{3}} \\
\mathrm{8}_{7}-\mathrm{CH}_{2}-\mathrm{CH}_{2}-\mathrm{CH}_{3}
\end{array}
\]


A cyclist wants to loop the loop inside the death globe of diameter 5 m. Find
the minimum velocity, that he should have at the lowest point and calculate the height from which he should start it.
\( \left(\boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{2}\right) \)


The probability of selecting a red ball at random from a jar that contains only red, blue and orange balls is \( \frac{1}{4} . \) The probability of selecting a blue ball at random from the same jar \( \frac{1}{3} . \) If the jar contains 10 orange balls, find the total number of balls in the jar.


The function \( \boldsymbol{f}(\boldsymbol{x})=-\frac{\boldsymbol{x}}{\mathbf{2}}+\sin \boldsymbol{x} \)
defined on \( \left[-\frac{\pi}{3}, \frac{\pi}{3}\right] \) is
A. increasing
B. decreasing
c. constant
D. none of these


\( \operatorname{Let} \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R}, \boldsymbol{g}(\boldsymbol{x})=\boldsymbol{f}(\boldsymbol{x})+\mathbf{3} \boldsymbol{x}-\mathbf{1} \)
then the least value of function \( y= \)
\( \boldsymbol{g}(|\boldsymbol{x}|) \) is
A. \( -\frac{9}{4} \)
B. \( -\frac{5}{4} \)
c. -2
D. -


By increasing the speed of a car by 10 \( k m / h r, \) the time of journey for a distance of \( 72 k m \) is reduced by 36
minutes. Write an equation for the given information and check if it is a
Quadratic Equation?


Find the value of \( f(0) \) so that the
function \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \frac{\mathbf{9 6}\left[\log \left(1+\frac{\boldsymbol{x}}{\mathbf{1 2}}\right)-\log \left(\mathbf{1}-\frac{\boldsymbol{x}}{\mathbf{8}}\right)\right]}{\boldsymbol{x}}, \boldsymbol{x} \neq \)
0 is continuous on [0,8]


The mean weight of 500 male students in a certain college is 151 pounds and the standard deviation is 15 pounds. Assuming the weights are normally distributed, find the approximate number of students weighing.
(i) between 120 and 155 pounds,
\[
\begin{array}{llll}
z & 0.2667 & 2.067 & 2.2667 \\
& & & \\
\text { Area } & 0.1026 & 0.4803 & 0.4881
\end{array}
\]
(ii) more than 185 pounds.


Find the real numbers \( x \) and \( y, \) if \( (x- \) \( i y)(1+i) \) is the conjugate of \( -3-2 i \)


Driver of a train travelling at \( 115 k m / h \) sees on a same track, \( 100 m \) infront of him, a slow train travelling in the same direction at \( 25 k m / h \). The least
retardation that must be appiled to faster train to avoid a collision is
A. \( 3.125 \mathrm{m} / \mathrm{s}^{2} \)
в. \( 3.5 m / s^{2} \)
\( \mathbf{c} \cdot 2.75 m / s^{2} \)
D. \( 3.0 m / s^{2} \)


Which of the following reptilian is regarded as living fossil?
A. crocodilus
B. Testudo
c. sphenodon
D. varanus


Which of the following matches is
correct?
(1)
Mucor Reproduction
by
conjugation Ascor
parasitic
fungus Basidi
(2) Agaricus
(3) Basidi Basidi \( \begin{array}{ll}\text { Phytophthora } & \begin{array}{l}\text { Aseptate } \\ \text { mycelium }\end{array} \\ \text { Alternaria } & \begin{array}{l}\text { Sexual } \\ \text { reproduction } \\ \text { absent }\end{array}\end{array} \)
(4) Deute
\( A \cdot 3 \)
\( B .2 \)
\( c \cdot 1 \)
\( D \cdot 4 \)


Hydrogen atoms usually contain a single neutron. Deuterium and tritium
are isotopes of hydrogen containing two and three neutrons, respectively. How many electrons orbit the tritium
nucleus if the atom is electrically neutral?
A. 0
B.
\( c \cdot 2 \)
D. 3


Growth in human brain from new born
to adult is
A. \( 100 \mathrm{gm} \) to \( 1 \mathrm{kg} \)
B. \( 400 \mathrm{gm} \) to \( 1.4 \mathrm{kg} \)
c. \( 0.2-1.4 \mathrm{kg} \)
D. 1.4 to 2.4 kg


If \( C \) is the mid point of \( A B \) and \( P \) is any
point outside \( A B, \) then
\( \mathbf{A} \cdot \overline{P A}+\overline{P B}+\overline{P C}=0 \)
в. \( \overline{P A}+\overline{P B}+2 \overline{P C}=\overline{0} \)
c. \( \overline{P A}+\overline{P B}=\overline{P C} \)
D. \( \overline{P A}+\overline{P B}=2 \overline{P C} \)


A ball is thrown upward with a velocity of \( 100 \mathrm{m} / \mathrm{s} \) it will reach the ground after
:-
A . 10 s
B. 20
\( c \cdot 5 s \)
D. 40 s


What is the use of keeping food in air tight containers?


\( \boldsymbol{K}_{s p} \) of \( \boldsymbol{P b C l}_{2} \) is \( \mathbf{1 0}^{-13} \cdot\left[\boldsymbol{P b}^{2+}\right] \) in solution
prepared by mixing \( 100 m L \) of \( 0.1 M \)
\( P b\left(N O_{3}\right)_{2} \) and \( 1 m L \) of \( 1 M H C l \) will
be:
\( \mathbf{A} \cdot\left[P b^{2+}\right]=9.4 \times 10^{-2} \) mollitre \( ^{-1} \)
B . \( \left[P b^{2+}\right]=8.4 \times 10^{-2} \) mollitre \( ^{-1} \)
C \( \cdot\left[P b^{2+}\right]=9.0 \times 10^{-2} \) mollitre \( ^{-1} \)
D \( \cdot\left[P b^{2+}\right]=9.2 \times 10^{-2} \) mollitre \( ^{-1} \)


State whether true or false.
Magnetic lines of force are primarily curved lines.
A. True
B. False


One gas bleaches the colour of flowers by reduction while the other gas by
oxidation. The two gases are,
respectively:
A \( \cdot \cos 2 l_{2} \)
в. \( H_{2} S \& B r_{2} \)
\( \mathrm{c} \cdot \operatorname{SO}_{2} \& C l_{2} \)
D. \( N H_{3} \& S O_{3} \)


Choose the correct answers from the
alternatives given:
It is important that the centromere does
not divide until the end of metaphase
because it
A. contains the genes that control prophase
B. holds the replicated DNA molecules together
\( \mathrm{C} \). is connected to the nuclear membrane
D. produces the spindle fibres


\( (+76)-(-34)= \)
A. -110
B. -42
\( \mathbf{c} \cdot+110 \)
D. None of these


Select the correct statements.
(I) Increase in relative humidity decreases the density of air
(II) Increase in relative humidity decreases the rate of evaporation of
water
(III) Increase in relative humidity
decreases the velocity of sound
(IV) Increase in relative humidity increases the velocity of sound
A . ।, ॥, । v
в. ।, и, III
\( c \cdot 1,1 \)
D. I, IV


Which of the following alkyl halide is most reactive towards substitution on
reaction by \( S_{N} 1 \) mechanism?
\( \mathbf{A} \cdot\left(C H_{3}\right)_{3} C-B r \)
B \( \cdot\left(C H_{3}\right)_{2}-C H-B r \)
c. \( C H_{3}-B r \)
D. \( C H_{3}-C H_{2}-B r \)


A rectangular coil of area \( A \), having the
number of turns \( N \) is rotated at \( f \)
revolutions per second in a uniform
magnetic field \( B \) the field is perpendicular to the coil. Prove that the maximum emf induced in the coil is
\( 2 \pi f N B A \)


Respiration is an anabolic and
catabolic both. Justify the statement by giving example.


Which of the following is/are Iyophobic
colloids?
This question has multiple correct options
A. Gold sol
в. \( A s_{2} S_{3} \) sol
\( \mathrm{c} \cdot \mathrm{Fe}(\mathrm{OH})_{3} \) sol
D. starch sol


Colloidal solution can be purified by :
This question has multiple correct options
A. dialysiss
B. electrodialysis
c. electrophoresis
D. ultrafiltration


The ends of a stretched string of length
\( L \) are fixed at \( x=0 \) and \( x=L . \) In one
experiment, the displacement of the wire is \( y_{1}=2 A \sin \left(\frac{\pi x}{L}\right) \sin \omega t \) and
energy \( \boldsymbol{E}_{1} \) and in another experiment,
its displacement is \( y_{2}= \) \( A \sin \left(\frac{2 \pi x}{L}\right) \sin 2 \omega t \) and energy \( E_{2} \)
then
\( \mathbf{A} \cdot E_{2}=E_{1} \)
B . \( E_{2}=2 E_{1} \)
\( \mathbf{c} \cdot E_{2}=4 E_{1} \)
D. \( 16 E_{1} \)


The equation of the circle which touches the lines \( x=0, y=0 \) and
\( 4 x+3 y=12 \) is
A \( \cdot x^{2}+y^{2}-2 x-2 y-1=0 \)
В . \( x^{2}+y^{2}-2 x-2 y+3=0 \)
c. \( x^{2}+y^{2}-2 x-2 y+2=0 \)
D. \( x^{2}+y^{2}-2 x-2 y+1=0 \)
E . \( x^{2}+y^{2}-2 x-2 y-3=0 \)


The distance travelled by light in one year is called
A . Light Year
B. Light Distance
c. Both (a) and (b)
D. None of these


Which of the following exhibit highest
boiling point?
\( A \)
B.
\( c \)
\( D \)


Construct a bisector of an angle of \( 60^{\circ} \)


A scorpion stalks kills and then eats a spider. Based on its behaviour which ecological terms describe the scorpion?
A. Producer, Herbivore, Decomposer
B. Producer, Carnivore, Heterotroph
c. Predator, Carnivore, Consumer
D. Predator, Autotroph, Herbivore


The time after which the cone is empty
is
\( \mathbf{A} \cdot H / 2 k \)
в. \( H / k \)
\( \mathbf{c} \cdot H / 3 k \)
D. \( 2 H / k \)


Pi bond is formed between the two
atoms when their is a:
A. donation of electron pair from one atom to another
B. axial overlapping of atomic orbitals
C. transfer of one or more than one electron from one atom to another
D. lateral overlapping of atomic orbitals


Assertion
Bond order for both \( N O^{+} \) and \( N O^{-} \) is
\( \mathbf{2 . 5} \)
Reason
\( N O^{+} \) is more stable than \( N O^{-} \)
Read the above assertion and reason and choose the correct option regarding
it.
A. Assertion is true, Reason is true and Reason is correct explanation for Assertion
B. Assertion is true, Reason is true and Reason is NOT the correct explanation for Assertion
c. Assertion is true, Reason is false
D. Assertion is false, Reason is true


The \( P \) - \( V \) diagram of a system
undergoing a thermodynamic process is shown in figure. Work done by the
system in going from \( \boldsymbol{A} \rightarrow \boldsymbol{B} \rightarrow \boldsymbol{C} \) is 30
and \( 40 \mathrm{J} \) heat is given to the system.
The change in internal energy of the gas
if the gas is directly taken from \( A \) to \( C \)
is
A . 10
B. 70 J
c. 84
D. 134


The value of \( 60^{g} \) in circular measure is
A \( \cdot \frac{\pi^{c}}{10} \)
в. \( \frac{3 \pi^{c}}{10} \)
c. \( \frac{2 \pi^{c}}{5} \)
D. \( \frac{\pi^{c}}{2} \)


A solid at temperature \( T_{1} \) is kept in an evacuated chamer at temperature
\( T_{2}>T_{1} . \) The rate of increase of
temperature of the body is proportional
to
A \( \cdot T_{2}-T_{1} \)
B . \( T_{2}^{2}-T_{1}^{2} \)
\( \mathbf{c} \cdot T_{2}^{3}-T_{1}^{3} \)
D. \( T_{2}^{4}-T_{1}^{4} \)


The largest value of the non-negative
integer \( a \) for which
\( \lim _{x \rightarrow 1}\left\{\frac{-a x+\sin (x-1)+a}{x+\sin (x-1)-1}\right\}^{\frac{1-x}{1-\sqrt{x}}}= \)
\( \mathbf{1} \)
\( \overline{4}^{\text {is }} \)


Let \( A \) be a finite set containing \( n \)
distinct elements. The number of
relations that can be defined on A is:
A \( \cdot 2^{n} \)
B \( \cdot n^{2} \)
\( c \cdot 2^{n^{2}} \)
D. 2n


Lead storage battery contains:
A. \( P b \) rod as anode
B. \( P b \) plates coated with \( P b O_{2} \) act as cathode
C . electrolyte is \( H_{2} S O_{4} \)
D. all are currect


The value of \( \left|\begin{array}{ccc}\boldsymbol{y} \boldsymbol{z} & \boldsymbol{z} \boldsymbol{x} & \boldsymbol{x} \boldsymbol{y} \\ \boldsymbol{p} & \boldsymbol{2} \boldsymbol{q} & \boldsymbol{3} \boldsymbol{r} \\ \boldsymbol{1} & \boldsymbol{1} & \boldsymbol{1}\end{array}\right| \) where \( \boldsymbol{x}, \boldsymbol{y}, \boldsymbol{z} \)
are respectively, \( p t h,(2 q) t h, a n d(3 r) t h \)
terms of an H.P., is
A . -1
B.
c. 1
D. none of these


Internal ear is filled with
A. Perilymph
B. Endolymph
c. Lymph
D. Both A and B


The force \( \boldsymbol{f} \) acting after time \( t \) on the
bottom of a beaker of area \( A \) when
water of density \( \rho \) falls from a tap at a
height \( h \) at uniform rate \( v \) is:
\( ^{\mathbf{A}} \cdot_{v \rho}\left[g t+2 g A\left(h-\frac{v t}{A}\right)\right] \)
B \( \cdot v \rho[g t+\sqrt{2 g h}] \)
c. v\( \rho g h \)
D \( \cdot \operatorname{ve}[g t+\sqrt{2 g\left(h+\frac{v t}{A}\right)}] \)


Let the positive numbers \( a, b, c, d \) be in
A.P. Then \( a b c, a b d, a c d, b c d \) are
A. Not in A.P./G.P/H.P.
B. in A.P.
c. in G.P.
D. in H.P.


Two point charges \( +q \) and \( -q \) are
located at points \( (0,0,-a) \) and \( (0,0, a) \) respectively. The potential at a point \( (0,0, z) \) where \( z>a \) is
A \( \cdot \frac{2 q a}{4 \pi \epsilon_{0}\left(z^{2}+a^{2}\right)} \)
в. \( \frac{q}{4 \pi \epsilon_{0} a} \)
c. \( \frac{q a}{4 \pi \epsilon_{0} z^{2}} \)
D. \( \frac{2 q a}{4 \pi \epsilon_{0}\left(z^{2}-a^{2}\right)} \)


In the given figure, find the value of capacitance \( C \) if the equivalent capacitance between \( A \) and \( B \) is \( \frac{32}{17} \mu F \) Values shown are in \( \mu \boldsymbol{F} \)


\( \ln \) a \( H_{2}-O_{2} \) fuel cell, combustion of
hydrogen occurs to:
A. remove adsorbed oxygen from electrode surface
B. create potential difference between the two electrodes
c. produce high purity water
D. generate heat


Which one is not supplied exclusively with involuntary muscles?
A. Iriss
B. Gland ducts
c. Urethra
D. coats of blood vessels


An object is placed \( 25 \mathrm{cm} \) from a convex lens whose focal length is \( 10 \mathrm{cm} \). The
image distance is \( (50 c m, 16.66 c m, 6.66 c m, 10 c m) \)


Using the above approximation, the
value of \( \cos 40^{\circ} \) is
A \( \cdot \frac{1}{\sqrt{2}}-\frac{\pi}{\sqrt{2} 36} \)
в. \( \frac{1}{\sqrt{2}}+\frac{\pi}{36 \sqrt{2}} \)
c. 0.747
D. 0.7267


Air is a good conductor of heat. True or false.
A . True
B. False


Solve:
\( \frac{\cos 70}{\sin 20}+\cos 59 \csc 31 \)


If \( f(x)=\left|x^{2}-4 x+3\right|, \) then \( f^{\prime}(x) \) is
A. \( 2 x-4 \) for \( 1<x<3 \)
B. \( 4-2 x \) for \( 1<x<3 \)
c. \( 2 x-4 \) for \( 1 \leq x \leq 3 \)
D. \( 4-2 x \)


The only ctenophoran to bear
cnidoblasts is
A. Bolinopsis
B. Beroe
c. ctenoplana
D. Euchlora


With reference to Haber's process, write
the equation and the conditions
required.


\( \boldsymbol{C}_{6} \boldsymbol{H}_{5} \boldsymbol{C O N} \boldsymbol{H}_{2} \frac{\boldsymbol{H}_{3} \boldsymbol{O}^{+}}{\Delta} \boldsymbol{A}+\boldsymbol{N} \boldsymbol{H}_{3} \)
In this reaction, \( \boldsymbol{A} \) is
\( \mathbf{A} \cdot C_{6} H_{6} \)
в. \( C_{6} H_{5} \)СООН
\( \mathbf{c} \cdot C_{6} H_{5} N H_{2} \)
D. \( C_{6} H_{5} C N \)


Complete the diagram of the transformer and connections by labelling all parts joined by you.


In Vanda, velamen helps in
A. Moisture absorption from air
B. Gaseous exchange
c. Give support
D. water absorption from soil


Which is the lightest gas?
A. Helium
B. Oxygen
c. Hydrogen
D. Nitrogen


State the location and function of
different types of meristematic tissues in plants.


The surface area of a spherical balloon
is increasing at the rate of \( 2 \mathrm{cm}^{2} / \mathrm{sec} \)
At what rate is the volume of the balloon
is increasing when the radius of the
balloon is \( 6 \mathrm{cm} ? \)


The protein \( \alpha 1- \) antitrypsin is used to treat the disease.
A. Cancer
B. Rheumatoid arthritis
c. Alzhelmer's disease
D. Emphysema


The Group VA element that makes up part of bones and teeth is:
A.
B.
c. As
D. sb


How many ATP is produced in the pay off phase of glycolysis?
\( \mathbf{A} \cdot \mathbf{1} \)
B. 5
\( c \cdot 4 \)
D.


If \( \vec{a}, \vec{b} \) and \( \vec{c} \) are mutually perpendicular vectors of equal magnitudes, If the angles which the vector \( 2 \vec{a}+\vec{b}+2 \vec{c} \) makes with the vectors \( \vec{a} \) is \( \cos ^{-1} \sqrt{\frac{2}{m}} \) Find \( \boldsymbol{m} \)


When but- \( 2- \) yne is treated with \( N a \) in liquid ammonia:
A . cis- 2 -butene is obtained
B. trans- 2 -butene is formed
c. \( n \) -butane is the major product
D. it rearranges to but-1-yne
E. there is no reaction


The distance of the closest approach of an alpha particle fired at a nucleus with
kinetic energy \( \boldsymbol{K} \) is \( \boldsymbol{r}_{0} . \) The distance of
the closest approach when the \( \alpha \) particle is fired at the same nucleus
with kinetic energy \( 2 K \) will be
\( ^{A} \cdot \frac{r_{0}}{2} \)
B. \( 4 r_{0} \)
c. \( \frac{r_{0}}{4} \)
D. \( 2 r_{0} \)


Mention two main functions of water for
living organisms.


A lens of focal length \( 20.0 \mathrm{cm} \) and aperture radius \( 2.0 \mathrm{cm} \) is placed at a distance \( 30.0 \mathrm{cm} \) from a point source of light. On the other side a screen is placed at a distance \( 50.0 \mathrm{cm} \) from the lens. The radius of spot of light formed on screen is (neglect spherical abberation through lens)
A. \( 1 / 2 \mathrm{cm} \)
B. \( 1 / 3 \mathrm{cm} \)
\( c \cdot 1 / 5 \mathrm{cm} \)
D. 1.0 \( \mathrm{cm} \)


Assuming the earth to be a uniform
sphere of radius \( 6400 \mathrm{km} \) and density \( 5.5 \mathrm{g} / \mathrm{c} . \mathrm{c}, \) find the value of \( \mathrm{g} \) on its
surface. \( G=6.66 \times 10^{-11} N m^{2} k g^{-2} \)
\( \mathbf{A} \cdot=3.82 m s^{-2} \)
В. \( =9.82 m s^{-2} \)
\( \mathbf{c} .=19.82 m s^{-2} \)
\( \mathrm{D} \cdot=2 m s^{-2} \)


For a Zener diode.
A. Both p and n regions are heavily doped
B. p region is heavily doped but n region is lightly doped
C. \( n \) region is heavily doped but p region is lightly doped
D. Both p and n regions are lightly doped
E. Depletion region is very thick


Calculate the range and coefficient of range from the following data:

Marks scored by 12 students in a test:
\( \mathbf{3 1}, \mathbf{1 8}, \mathbf{2 7}, \mathbf{1 9}, \mathbf{2 5}, \mathbf{2 8}, \mathbf{4 9}, \mathbf{1 4}, \mathbf{4 1}, \mathbf{2 2}, \mathbf{3 3}, \mathbf{1} \)


Species acting as Bronsted acid and
base is:
A. \( H S O_{4}^{-} \)
в. \( N a_{2} C O_{3} \)
c. \( N H_{3} \)
D. \( O H^{-} \)


Metals that are refined by liquation are:
This question has multiple correct options
A. si
B. Pb
\( c \cdot s n \)
D. Bi


Find the value of \( \mathrm{K} \)


Materials which allow larger currents to flow through them are called:
A. insulators
B. conductors
c. semiconductors
D. alloys


The objective lens of a compound microscope produces magnification of
10. In order to get an overall
magnification of 100 when image is formed at \( 25 \mathrm{cm} \) from the eye, the focal
length of the eye lens should be : (in \( c m \) )
A . 4
B. 10
c. \( \frac{25}{9} \)
D. 9


Factorise the following:
\( 3\left(x^{2}-5 x\right)^{2}-2\left(x^{2}-5 x+5\right)-6 \)
A \( \cdot\left(x^{2}-5 x+2\right)\left(3 x^{2}-5 x-8\right) \)
B. \( \left(x^{2}-5 x+2\right)\left(3 x^{2}-15 x-8\right) \)
C. \( \left(x^{2}-5 x-2\right)\left(3 x^{2}-15 x+8\right) \)
D. \( \left(x^{2}-5 x-2\right)\left(3 x^{2}-5 x+8\right) \)


In Figure circuit section, \( A B \) absorbs
energy at a rate of 50W when a current
\( =1.0 \mathrm{A} \) passes through it in the indicated direction. What is the
potential difference between \( A \) and \( B \) ?
A \( .10 V \)
в. \( 50 V \)
\( c \cdot 20 V \)
D. 30V


Assertion
We can live very happily if the friction is
not present in nature.
Reason
Aeroplane shape is stream lined to
reduce the effort of frictional force.
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


Factorise: \( \boldsymbol{p}^{2}-\boldsymbol{3} \boldsymbol{p} \boldsymbol{q}+\boldsymbol{2} \boldsymbol{q}^{2} \)


A system has two charges \( \boldsymbol{q} \boldsymbol{A}=\mathbf{2 . 5} \times \)
\( \mathbf{1 0}^{-7} \boldsymbol{C} \) and \( \boldsymbol{q} \boldsymbol{B}=-\boldsymbol{2 . 5} \times \mathbf{1 0}^{-\mathbf{7}} \boldsymbol{C} \)
located at point \( \boldsymbol{A}(\mathbf{0}, \mathbf{0},-\mathbf{1 5}) \) cm and
\( B(0,0,15) c m \) respectively. What are the total charge and electric dipole
moment vector of the system?


Plane figure with four sides is known as
\( \mathbf{a} \)
A. Pentagon
B. Trianglel
c. Quadrilateral
D. none of these


Consider the cell:
\( \boldsymbol{C d}(\boldsymbol{s})\left|\boldsymbol{C} \boldsymbol{d}^{2+}(\mathbf{1} . \boldsymbol{0} \boldsymbol{M}) \| \boldsymbol{C} \boldsymbol{u}^{2+}(\mathbf{0 . 1} \boldsymbol{M})\right| \boldsymbol{C} \)
If we wish to make a cell with a more
positive voltage using the same substance, we should:

This question has multiple correct options
A \( \cdot \) increase both \( \left[C d^{2+}\right] \) and \( \left[C u^{2+}\right] \) to 2.0 M
B. decrease the \( \left[C d^{2+}\right] \) to \( 0.1 \mathrm{M} \)
c. increase the \( \left[C u^{2+}\right] \) to \( 1.0 \mathrm{M} \)
D. decrease both the \( \left[C d^{2+}\right] \) and \( \left[C u^{2+}\right] \) to 0.01 M


The molecular formula of sodium
carbonate is:
A. \( N a C O_{3} \)
в. \( \left(N H_{4}\right) S O_{4} \)
\( \mathbf{c} \cdot N a_{2} C O_{3} \)
D. \( \left(N H_{4}\right)_{2} S O_{4} \)


If \( \cos ^{-1} x= \)
\( \left\{\begin{array}{r}a \pi-b \cos ^{-1}\left(2 x^{2}-1\right), i f-1 \leq x< \\ c \cos ^{-1}\left(2 x^{2}-1\right), \text { if } 0 \leq x \leq 1\end{array}\right. \)
Find the value of \( a+b+c \)
A . 1
B. 2
\( c .3 \)
D. 4


Chloroform reacts with NaOH to form
sodium formate. This is a/an:
A. oxidation reaction
B. hydrolysis reaction
c. reduction reaction
D. addition reaction


In the given figure, \( A B \| \) EF \( \| \) CD. If \( A B= \)
\( 22.5 \mathrm{cm}, \mathrm{EP}=7.5 \mathrm{cm}, \mathrm{PC}=15 \mathrm{cm} \) and DC
\( =27 \mathrm{cm} . \) Find \( \mathrm{AC} \)
\( A \cdot A C=37.5 \mathrm{cm} \)
B. AC = 22.5 cm
\( c \cdot A C=13.5 \mathrm{cm} \)
D. \( A C=27 \mathrm{cm} \)


Electromagnetic radiation of wavelength \( 242 \mathrm{nm} \) is just sufficient to ionise the sodium atom. What should
be ionization energy of sodium atom in
order of \( 10^{-19} ?\left(c=3 \times 10^{8} \mathrm{ms}^{-1}, h=\right. \)
\( 6.626 \times 10^{-34} \mathrm{Js} \)
A . 8.2
B. 8
c. 9
D. 9.2


Find the center and radius of the circle.
\( (x+5)^{2}+(y-3)^{2}=36 \)


Equilibrium constant for the reaction
\( \mathbf{2} N \boldsymbol{O}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g}) \rightleftharpoons 2 \boldsymbol{N} \boldsymbol{O} \boldsymbol{C l}(\boldsymbol{g}) \) is
correctly given by the expression:
\( ^{\mathbf{A}} \cdot_{K}=\frac{[2 N O C l]}{[2 N O]\left[C l_{2}\right]} \)
в. \( _{K}=\frac{[N O C l]^{2}}{[N O]^{2}\left[C l_{2}\right]} \)
\( ^{\mathbf{c}}_{K}=\frac{[N O]^{2}[C l]^{2}}{[N O]^{2}+\left[C l_{2}\right]} \)
\( K=\frac{[N O]^{2}+[C l]^{2}}{[N O C l]} \)


Sodium metal is prepared
commercially by electrolysis of fused \( N a C l \) by:
A. Down's process
B. Nelson cell
c. Solvay process
D. castner and Kellner's cell


When a photon of energy \( 7 e V \) is made incident on a metal then the emitted
electron is stopped by a stopping potential of \( -5.5 V . \) The work function
of metal will be :
A. \( -1.5 e V \)
B. \( 1.5 e V \)
c. \( 12.5 e V \)
D. \( 37.5 e V \)


According to Hess's law, the thermal
effects of a reaction depends on
\( \mathbf{A} \cdot \) Initial and final conditions of the reacting substances
B. Initial concentration of reactants
C. Final conditions of the reacting substances
D. Not on initial and final conditions of the reacting substance


Find the equation of the plane passing through the intresection of the planes \( x-2 y+z=1 \) and \( 2 x+y+z=8 \)
and parallel to the line with direction ratio proportional to \( 1,2,1, \) find also the perpendicular distance of (1,1,1) from this plane.


Which of the following relationship is correct for the following figure:
This question has multiple correct options
A \( . x=y=z \)
В. \( x=y>z \)
C \( . x>120^{\circ} \)
D. \( z<120^{\circ} \)


A block of mass \( \mathrm{m} \) is placed on a rough horizontal surface. The coefficient of
friction between them is \( \mu . \) An external
horizontal force is applied to the block
and its magnitude is gradually increased. The force exerted by the block on the surface is \( \mathrm{R} \) then :
This question has multiple correct options
A. the magnitude of R will gradually increase
B . \( R \leq m g \sqrt{\mu^{2}+1} \)
c. the angle made by R with the vertical will gradually increase.
D. the angle made by R with the vertical \( \leq \tan ^{-1} \mu \)


Rutherford's \( \alpha- \) particle scattering
experiment led to the discovery of
A. electrons
B. protons
c. neutrons
D. atomic nucleus


How many coulomb are required for the
oxidation of 1 mole of \( H_{2} O_{2} \) to \( O_{2} ? \)
A \( \cdot 9.65 \times 10^{4} C \)
B. \( 93000 C \)
c. \( 1.93 \times 10^{5} C \)
D. \( 19.3 \times 10^{2} C \)


We do not sense any pain when we clip
our nails or cut our hair. Why?
A. They are made up of dead cells.
B. These parts are senseless.
C. They are very strong to tolerate pain.
D. None of these.


Give the structures of \( c i s- \)
\( \left[\boldsymbol{C o C l}_{2}(\boldsymbol{e n})_{2}\right] \) and \( \boldsymbol{f a c i a l}- \)
\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{3}\left(\boldsymbol{N} \boldsymbol{O}_{2}\right)_{3}\right] \) isomers


Column-1 Column-2
P) Opening of the leaf blade
¡) Epinasty
Q) Closing of leaves
ii)hyponasty
R) zigzag movement in the
iii) nutation apical bud
S) spiral and helical growth \( \quad \) iv)circumnutation of tendrilar plants
of
T) pulsation in leaflets
v) variation Indian telegraph plant
\( A \cdot(P-i)(Q-i i)(R-i i i)(S-i v)(T-v) \)
B. (P-v) (Q-iv) (R-iii) (S-ii) (T-i)
C \( .(P-v)(Q-i)(R-i v)(S-i i i)(T-i i) \)
D. (P-v) (Q-i) (R-iv) (S-II) (T-iii)


The phosphorus present in an organic compound of mass 75 g is oxidized to phosphoric acid by heating with fuming nitric acid. The phosphoric acid so obtained is precipitated as \( M g N H_{4} P O_{4}, \) which on ignition is
converted into \( M g_{2} P_{2} O_{7} \). If the mass of
Mg2P207 is 50 g, the percentage composition of phosphorus present in the sample of the organic compound is:
A . 19.5
в. 18.
\( c \cdot 20 \)
D. 18.6


Statement-1: Superposition principle is applicable only for small disturbances
Statement-2: Superposition principle is applicable only for non-linear waves.
A. If both the statements are true and statement- 2 is the correct explanation of statement-
B. If both the statements are true but statement-2 is not the correct explanation of statement-
c. If statement-1 is true and statement- 2 is false
D. If statement-1 is false and statement-2 is true


The difference between the
circumference and the radius of a circle
is \( 74 \mathrm{cm}, \) find the area of the circle.


A light charged particle is resolving in a circle of radius 'r' in electrostatic
attraction of a static heavy particle with opposite charge. How does the magnetic field 'B' at the centre of the circle due to the moving charge depend
on 'r'?
A \( \cdot B \propto \frac{1}{r} \)
в. \( B \propto \frac{1}{r^{2}} \)
c. \( _{B} \propto \frac{1}{r^{\frac{3}{2}}} \)
D. \( B \propto \frac{1}{r^{\frac{5}{2}}} \)


Assertion
In some solids, the valence band is
completely filled while the next higher band separated by an energy gap of few electrons-volts is completely empty.
Reason
In insulators the energy band completely filled with electrons( the valence band) and above it is empty
band (the conduction band)
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 strongest bonding out of the following is :
A. vander Waal
B. ionic
c. covalent
D. metallic


\( \frac{228}{88} X-3 \alpha-\beta \longrightarrow Y . \) The element \( Y \)
is:
\( \mathbf{A} \cdot_{82}^{216} P b \)
в \( \cdot \) за้ใ \( P b \)
\( \mathbf{c} \cdot_{83}^{218} B i \)
D \( \cdot_{83}^{216} B i \)


The velocity of the CM of the rod
A \( \frac{5}{7} v_{0} \) at \( \tan ^{-1} \frac{4}{3} \) below horizonta
B. \( 5_{0} \) at \( \tan ^{-1} \frac{3}{4} \) below horizonta
\( 7^{0} \) a
C \( \cdot \frac{5}{8} v_{0} \) at \( \tan ^{-1} \frac{3}{4} \) below horizontal
\( \stackrel{-5}{-} \frac{5}{6} 0 \) at \( \tan ^{-1} \frac{4}{3} \) below horizonta


If a loop in a basic dc generator suddenly begins rotating at a faster speed, the induced voltage
A. remains unchanged
B. reverses polarity
c. increases
D. decreases


EMP is also known as
A . Glycolysis
B. Krebs cycle.
c. ЕTS
D. Fermentation.


\( \int \frac{\cos ^{2} x}{2+\sin x} d x \)


In a metre bridge, the gaps are closed by two resistances \( \mathrm{P} \) and \( \mathrm{Q} \) and the
balance point is obtained at \( 40 \mathrm{cm} \)
When \( Q \) is shunted by a resistance of 10
\( \Omega, \) the balance point shifts to \( 50 \mathrm{cm}, \) The
values of \( P \) and \( Q \) arc
A \( \cdot \frac{10}{3} \Omega, 5 \Omega \)
B. \( 20 \Omega, \) 30\Omega
c. \( 10 \Omega, \) 15\Omega
D. \( 5 \Omega, \frac{15}{2} \Omega \)


If order of a matrix is \( 3 \times 3, \) then it is a
A. square matrix
B. rectangular matrix
c. unit matrix
D. None of these


The cost of 2 meter cloth is \( 10 . \) Find the
\( \operatorname{cost} \) of \( 100 m \) cloth.
A . 400
в. 500
\( c .1000 \)
D. 1500


Which of the following \( a \& b \) are in direct proportion?
A \( \cdot a=\frac{2}{b} \)
В. \( a=2 b \)
c. \( a=b^{3} \)
D. \( a=\frac{1}{b^{2}} \)


A cube has a side of length \( 1.2 \times \)
\( 10^{-2} m . \) Calculate its volume
A \( .1 .7 \times 10^{-6} m^{3} \)
В. \( 1.73 \times 10^{-6} m^{3} \)
C. \( 1.70 \times 10^{-6} m^{3} \)
D. \( 1.728 \times 10^{-6} \mathrm{m}^{3} \)


Write the integrating factor of the following differential equation:
\( \left(1+y^{2}\right)+(2 x y-\cot y) \frac{d y}{d x}=0 \)


On the basis of the following observations made with aqueous
solutions, assign secondary valences to metals in the following compounds:
Moles of \( A g C l \) precipitated per Formula mole of the compounds with
\[
\operatorname{excess} A g N O_{3}
\]
(i)
\[
P d C l_{2} .4 N H_{3}
\]
(i)
\[
\mathrm{NiCl}_{2} \cdot 6 \mathrm{H}_{2} \mathrm{O}
\]
(iii)
\[
P t C l_{4} .2 H C l
\]
(iv)
\[
\mathrm{CoCl}_{3} .4 \mathrm{NH}_{3}
\]
\( (v) \)
\[
P t C l_{2} \cdot 2 N H_{3}
\]


Which chloride is the most reactive
towards aqueous NaOH in:
A. Methyl chloride
B. Chlorobenzene
c. vinyl chloride
D. Benzyl chloride


Which statements are correct?
This question has multiple correct options
A. Phenol and aniline give coupling reaction with diazonium salt.
B. Phenol couples with diazonium salt in mild basic conditions \( (p H=8-10) \)
C. Aniline couples with diazonium salt in mild acidic condition \( (p H=4-6) \)
D. Both phenol and aniline couple with diazonium salt in neutral condition \( (p H=7) \)


Eccentricity of the ellipse \( 4 x^{2}+y^{2}-8 y-8=0 \) is
A \( \frac{\sqrt{3}}{2} \)
в. \( \frac{\sqrt{3}}{4} \)
\( c \cdot \frac{\sqrt{3}}{\sqrt{2}} \)
D. \( \frac{\sqrt{3}}{8} \)
E \( \cdot \frac{\sqrt{3}}{16} \)


Thorns differ from prickles in having
A. Vascular supply
B. Endogenous origin
\( c . \) Bark
D. All of the above


Two acids \( H_{2} S O_{4} \) and \( H_{3} P O_{4} \) are
neutralized separately by the same
amount of an alkali when sulphate and
dihydrogen phosphates are formed respectively.Find the ratio of the
masses of \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) and \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4} \)


80
\( g_{i} \)
90
\( 90^{\circ} \)
\( \int_{0}^{\infty} \)


Interference is produced with two coherent sources of the same intensity If one of the sources is covered with a
thin film so as to reduce the intensity of light coming out of it to half, then:
A. bright fringes will be less bright and dark fringes will be less dark
B. bright fringes will be more bright and the dark fringes will be more dark
c. brightness of both types of the fringes will remain the same
D. dark region will spread completely


Consider the following statements: The system of equations \( .2 x-y=4 \) and
\( \boldsymbol{p} \boldsymbol{x}-\boldsymbol{y}=\boldsymbol{q} \)
I. has a unique solution if \( y \neq 2 \)
Il. has infinitely many solutions if \( \boldsymbol{p}= \)
\( 2, q=4 \) Of these statements:
A. I alone is correct
B. II alone is correct
c. I and II are correct
D. I and II are false


The method of dispersal in Amoeba is
A. Locomotion
B. Sporulation
c. Encystment
D. Binary fission


The projection of the vector \( \hat{\mathbf{i}}-\mathbf{2} \hat{\mathbf{j}}+\hat{\boldsymbol{k}} \)
on the vector \( 4 \hat{i}-4 \hat{j}+7 \hat{k} \) is
A \( \cdot \frac{5}{19} \sqrt{5} \)
в. \( \frac{19}{9} \)
c. \( \frac{9}{19} \)
D. \( \frac{1}{19} \sqrt{6} \)


UV radiations cause
A. Formation of thymine dimers
B. Addition of base pairs
C . Deletion of base pairs
D. Methylation of bases


Consider the graph given.
The distance travelled by an object in a
given direction as time increases is
given by the given graph

In this context which of the following
statements is correct?
A. The velocity decreases during DE
B. The velocities during DE and BC are in opposite directions
c. Total distance travelled is AF
D. During CD the body is moving with uniform velocit


The remainder obtained when \( t^{6}+ \) \( 3 t^{2}+10 \) is divided by \( t^{3}+1 \) is:
A \( \cdot t^{2}-11 \)
B . \( t^{3}-1 \)
\( c \cdot 3 t^{2}+11 \)
D. none of these


Classify the following numbers as rational or irrational.
\( \mathbf{1 1} . \mathbf{2 1 3 2} \mathbf{4 3 5 4 6 5} \)


Assign oxidation number to the
underlined element in \( \boldsymbol{H}_{2} \underline{S}_{2} \boldsymbol{O}_{7} \)


Calculate the pressure exerted by water at the bottom of a lake of depth \( 6 m \)
(Density of water \( =1000 k g m^{-3}, g= \)
\( \left.10 m s^{-2}\right) \)


A projectile is fired 30.0 degrees above the horizontal with speed \( \left|\boldsymbol{v}_{1}\right|=\mathbf{4 0 m} / \boldsymbol{s} \)
and a second one 60.0 degrees above
the horizontal with speed \( \left|\boldsymbol{v}_{2}\right|=\mathbf{3 0 m} / \boldsymbol{S} \)
simultaneously. After 2 seconds, how far apart will the two projectiles be? Assume no air resistance and that they are fired from
the same spot, and that each moves independent of the outer projectile. Take \( \boldsymbol{g}=\mathbf{9 . 8 1 m} / \boldsymbol{s}^{2} \)
A . \( 11.96 m \)
в. \( 28.11 m \)
\( \mathrm{c} .39 .28 \mathrm{m} \)
D. 41.06 m
E . \( 41.99 \mathrm{m} \)


The volume of air that can be breathed
in by maximum forced inspiration over and above the normal inspiration is
called
A. Expiratory reserved volume
B. Inspiratory reserved volume
c. vital capacity
D. Inspiratory capacity


A variable plane at a distance of 1 unit from the origin cuts the co-ordinate axes at \( A, B \) and \( C . \) If the centroid \( D(x, y, z) \) of triangle \( A B C \) satisfies the relation \( \frac{1}{x^{2}}+ \) \( \frac{1}{y^{2}}+\frac{1}{z^{2}}=k, \) then the value of \( k \) is
A . 3
B. 1
c. \( 1 / 3 \)
D.


Give reasons:
(a) A gas fills completely the vessel in which it is kept
(b) A gas exerts pressure on the walls of the container.
(c) A wooden table should be called a
solid
(d) We can easily move our hand in air but to do the same through a solid block of wood we need a karate expert.


If \( 1 \mathrm{mg} \) of \( U^{235} \) is completely annihilated,
the energy liberated is
\( \begin{array}{ll}\text { A. } & 9 \times 10^{10} J\end{array} \)
в. \( \quad 9 \times 10^{19} J \)
\( \begin{array}{ll}\text { с. } & 9 \times 10^{18} J\end{array} \)
D. \( \quad 9 \times 10^{17} J \)


Plant roots grow downwards and show
A. Positive geotropic
B. Negative geotropic
c. Positive phototropic
D. Negative hydrotropic


Atoms of different elements having the same mass number are known as:
A. isotopes
B. isobars
c. isotones
D. isoelectronic


Diagram shows stress-strain graph for two material A \& B. The graphs are
drawn to scale.

The ratio of young modulli of \( A \) to
material B is


An alkyl halide in which halogen atom is
attached to that \( C \) atom which is
attached to only one \( C \) in molecule is
called as:
A. primary alkyl halide
B. secondary alkyl halide
c. tertiary alkyl halide
D. none of these


ABCD a parallelogram. \( \boldsymbol{E} \) is a point on \( A D \) and \( C E \) is produced to meet \( B A \) at
\( F . \) If \( A E=4 c m, A F=8 \mathrm{cm} \) and
\( A B=12 \mathrm{cm} . \) Find the perimeter (in \( \mathrm{cm} \)
of parallelogram \( \boldsymbol{A B C D} \)


Three isotopes of an element have mass
numbers, \( M,(M+1) \) and \( (M+2) . \) If
the mean mass number is \( (M+0.5) \)
then which of the following ratios may
be accepted for \( M,(M+1),(M+2) \)
in that order?
A. 1: 1: 1
B. 4: 1: 1
\( \mathrm{c} .3: 2: 1 \)
D. 2: 1: 1


What is meant by magnification of a lens? Write its expression.


The decreasing order of \( p K_{a} \) value of the given is:
(I) \( \mathbf{C H} \equiv \mathbf{C H} \)
\( (\mathbf{I I}) \)
A \( .(I I I)>(I)>(I I) \)
в. \( (I I)>(I)>(I I I) \)
c. \( (I)>(I I I)>(I I) \)
D. \( (I)>(I I)=(I I I) \)


Find the value of \( (a+b)^{2}-(a-b)^{2} \)
\( \mathbf{A} \cdot a b \)
в. \( 2 a \)
\( c \cdot 3 a b \)
D. \( 4 a \)


The modulus of charge of electron is :
A \( .1 .6 \times 10^{-19} \mathrm{c} \)
B. 3.2 \( \times 10^{-19} \mathrm{C} \)
c. \( 1.8 \times 10^{-19} \mathrm{c} \)
D. \( 1.6 \times 10^{-21} \mathrm{c} \)


N, the set of natural numbers, is
partitioned into subsets \( \boldsymbol{S}_{1}= \) \( \{1\}, S_{2}=\{2,3\}, S_{3}=\{4,5,6\}, S_{4}= \)
\( \{7,8,9,10\} . \) The last term of these
groups is \( 1,1+2,1+2+3,1+2+ \)
\( 3+4, \) so on. Find the sum of the
elements in the subset \( S_{50} \)


If \( f(x)=e^{x}, \) then \( \lim _{x \rightarrow 0} f(f(x))^{\frac{1}{(f(x))}} \) is
equal to (where \( \{x\} \) denotes fractional
part of \( \boldsymbol{x} \) ).
A. \( f(1) \)
B. \( f(0) \)
\( c .0 \)
D. Does not exist


Equation of the parabola with its vertex at (1,1) and focus (3,1) is
A \( \cdot(x 1)^{2}=8(y-1) \)
B . \( (y-1)^{2}=8(x-3) \)
c. \( (y-1)^{2}=8(x-1) \)
D. \( (x-3)^{2}=8(y-1) \)


The electric field between the inside
and outside layers is:
A \( \cdot 10^{6} V m^{-1} \)
В. \( 5 \times 10^{6} V m^{-1} \)
c. \( 0.2 \times 10^{7} V m^{-1} \)
D. \( 10^{7} V m^{-1} \)


If the common chord of the circle \( x^{2}+ \)
\( (y-\lambda)^{2}=16 \) and \( x^{2}+y^{2}=16 \)
subtend a right angle at the origin then \( \lambda \) is equal to
\( A \cdot 4 \)
B. \( 4 \sqrt{2} \)
\( c \cdot \pm 4 \sqrt{2} \)
\( D .8 \)


Differentiate between regular and
diffused reflection. Does diffused
reflection mean the failure of the laws of
reflection?


What is the value of \( R_{4}(\text { in ohm }) \) in figure (a) and (b) ?
(a) \( -4 w w-w w w w w w=-w w w \)
\( 20 \Omega+3.5 \Omega+4.92=\quad R_{42} \)
(b)
A. 28.4,0.58
B. 0.58, 28
c. 7.1,1.85
D. 6.15,1.80


A pair of starts rotates about a common
centre of mass. One of the stars has a
mass \( M \) and the other \( m \). Their centres
are a distance \( d \) apart, \( d \) being large
compared to the size of either star. Derive an expression for the period of
revolution of the stars about their
common centre of mass. Compare their angular momenta and kinetic energies.


A transition metal x has the electronic
configuration [Ar]3d \( ^{4} \) in its +3 oxidation
state. The element is:
A. Mn
B. Fe
c. Ti
D.


Which of following statements related
to center of gravity is/are false?
A. If an object is placed in a uniform gravitational field, center of gravity coincides with center of mass.
B. The center of gravity of an object is defined as point through which its whole weight appears to act.
C. The center of gravity is sometimes confused with center of mass.
D. The center of gravity always lies inside object.


Find the solution of \( \frac{d y}{d x}+\frac{y}{x}= \)
\( \frac{1}{(1+\log x+\log y)^{2}} \)
A \( \cdot x y\left[1-(\log x y)^{2}\right]=-\frac{x^{2}}{2}+C \)
B. \( x y\left[1+(\log x y)^{2}\right]=\frac{x^{2}}{2}+C \)
c. \( x y\left[1+(\log x y)^{2}\right]=-\frac{x^{2}}{2}+C \)
D. \( x y\left[1-(\log x y)^{2}\right]=\frac{x^{2}}{2}+C \)


Two elements M and X have electronic
configurations 2,8,3 and 2,8,6 respectively. Identify the correct formula of the compound formed.
\( A \cdot M x_{2} \)
B. \( M_{2} x \)
\( \mathrm{c} \cdot \mathrm{M}_{2} \mathrm{x}_{3} \)
D. \( M_{3} x_{2} \)


A rectangular block of mass \( M \) and
height \( a \) is resting on a smooth leve
surface. A force \( \boldsymbol{F} \) is applied to one
corner as shown in figure. At what point
should a parallel force \( 3 F \) be applied in
order that the block shall undergo pure translational motion? Assume normal
contact force between the block and
surface passes through the centre of
gravity of the block.
A \( \cdot \frac{a}{3} \) vertically above centre of gravity
B \cdot \( \frac{a}{6} \) vertically above centre of gravity
\( c . \) no such point exists
D. it is not possible


For the matrices \( A \) and \( B \), verify that
\( (A B)^{\prime}=B^{\prime} A^{\prime} \) where
(i) \( \boldsymbol{A}=\left[\begin{array}{c}\mathbf{1} \\ -\mathbf{4} \\ \mathbf{3}\end{array}\right], \boldsymbol{B}=\left[\begin{array}{lll}-\mathbf{1} & \mathbf{2} & \mathbf{1}\end{array}\right] \)
(ii) \( \boldsymbol{A}=\left[\begin{array}{l}\mathbf{0} \\ \mathbf{1} \\ \mathbf{2}\end{array}\right], \boldsymbol{B}=\left[\begin{array}{lll}\mathbf{1} & \mathbf{5} & \mathbf{7}\end{array}\right] \)


Fill in the blanks.
The traces of impurity added for doping are called


For any prism, show that refractive
index of its material is given by:
\( \operatorname{nor} \mu=\frac{\sin \left(\frac{A+\delta m}{2}\right)}{\sin \left(\frac{A}{2}\right)} \)
where the terms have their usual
meaning.


\( \boldsymbol{Z} \boldsymbol{n}\left|\begin{array}{c}\boldsymbol{Z} \boldsymbol{n}\left(\boldsymbol{N} \boldsymbol{O}_{3}\right)_{2}(\boldsymbol{a} \boldsymbol{q}) \\ \boldsymbol{1} \mathbf{0} \boldsymbol{0} \boldsymbol{m} \boldsymbol{L}, \boldsymbol{1} \boldsymbol{M}\end{array}\right|\left|\begin{array}{c}\boldsymbol{C u}\left(\boldsymbol{N} \boldsymbol{O}_{3}\right)_{2}(\boldsymbol{a} \boldsymbol{q}) \\ \boldsymbol{1} \mathbf{0} \boldsymbol{0} \boldsymbol{m} \boldsymbol{L}, \mathbf{1} \boldsymbol{M}\end{array}\right| \)
The following galvanic cell was operated as an electrolytic cell using Cu as anode
and \( \mathrm{Zn} \) as cathode. A current of 0.48
ampere was passed for 10 hour and then the cell was allowed to function as
galvanic cell. The e.m.f. of the cell at \( 25^{\circ} \)
\( \mathrm{C} \) is (write the nearest integer value):
Assume that the only electrode reactions occurring were those
involving \( \boldsymbol{C} \boldsymbol{u} / \boldsymbol{c u}^{2+} \) and \( \boldsymbol{Z} \boldsymbol{n} / \boldsymbol{Z} \boldsymbol{n}^{2+} \)
Given
\( E_{C u^{2+}, C u}^{o}=0.34 V \) and \( E_{Z n, Z n^{2+}}^{o}= \)
\( -0.76 V \)


Which fraction on the number line
below is in the wrong place?
\( A \cdot \frac{1}{4} \)
B.
\( c \cdot \frac{1}{2} \)
D.
E. None of the above


The sales of Lux in 2010 was by what
percent more than the sales of Rexona
in 2007?
A. \( 60 \% \)
3. \( 50 \% \)
\( c .80 \% \)
\( 0.90 \% \)


Rainbow is a natural phenomenon showing dispersion of light.
A. True
B. False


A uniform meter rule balances
horizontally on a knife edge placed at the \( 58 \mathrm{cm} \) mark when a weight of 20 gf is suspended from one end.


For the reaction \( C_{2} H_{5} O H+B r^{-} \leftrightharpoons \)
\( C_{2} H_{5} B r+O H^{-}, \) equilibrium will shift
to the right on:
A. exposing the system to light
B. adding an alkali
c. adding an acid
D. adding \( C_{2} H_{5} B r \)


A thin diamagnetic rod is placed vertically between the poles of an electromagnet. When the current in the electromagnet is switched on, then the diamagnetic rod is pushed up, out of the horizontal magnetic field. Hence the rod gains gravitational potential energy. The work required to do this comes
from
A. The lattice structure of the material of the rod
B. The current source
c. The induced electric field due to the changing magnetic field
D. The magnetic field


If \( \delta_{1} \) and \( \delta_{2} \) are the angles of dip observed in two vertical planes at right angles to each other and \( \delta \) is the true
value of dip then :
A \( \cdot \tan ^{2} \delta=\tan ^{2} \delta_{1}+\tan ^{2} \delta_{2} \)
B . \( \cot ^{2} \delta=\cot ^{2} \delta_{1}+\cot ^{2} \delta_{2} \)
\( ^{\mathrm{C}} \tan ^{2} \delta=\frac{\tan ^{2} \delta_{1}+\tan ^{2} \delta_{2}}{\tan ^{2} \delta_{1} \tan ^{2} \delta_{2}} \)
D. \( \cot ^{2} \delta=1+\cot ^{2} \delta_{1} \cos ^{2} \delta_{2} \)


Find sum of all odd integers between 2 and 100 divisible by 3


How many hydrogen bonded water molecules are associated with
\( \boldsymbol{C u} \boldsymbol{S O}_{4} \cdot \boldsymbol{5} \boldsymbol{H}_{2} \boldsymbol{O} \)
A. five
B. one
c. four
D. three


Write two properties of magnetic field
lines.


Which of the following is/are true for "magnetic lines of force around a bar magnet"?
A. are closed continuous curves
B. travel from north to south outside the magnet
c. bend around the length of magnet
D. all the above


Two coils \( A \) and \( B \) are separated by a certain distance. If a current of \( 4 \mathrm{A} \)
flows through \( A, \) a magnetic flux of \( 10^{-3} \)
Wh passes through B (no current through B).If no current passes through A and a current of 2 A passes through \( B \), then the flux through \( A \) is then
A \( .5 \times 10^{-3} \)
B . \( 4 \times 10^{-4} \)
c. \( 5 \times 10^{-4} \)
D. \( 2 \times 10^{-3} \)


Which of the following represents the four main categories of tissues?
A. Epithelial, skeletal, adipose, nervous
B. Connective, epithelial, muscle, nervous
c. Blood, connective, muscle, nervous
D. Bone, muscle, striated, nervous


Q Type
elevation of the top \( P \) of the tower \( O P \) at
a point \( A \) on the ground is \( \alpha, \) he then
walks a distance \( A B \) towards the foot \( O \)
of the tower and finds the angle of
elevation as \( \beta, \) he again walks a
distance \( B C \) in the same direction and
observes the angle of elevation now is \( \gamma \)
He notices that \( \boldsymbol{a}+\boldsymbol{\beta}+\boldsymbol{\gamma}= \)
\( 180^{\circ} ; \alpha, \beta, \gamma \) are in A.P. and the distance
of \( C \) from the foot of the tower is half the
distance of \( B \) from the foot \( O \) of the
tower. If the height of tower is \( h \), the distance of \( A \) from the foot \( O \) is \( \frac{5 h}{3 \sqrt{3}} \)
Reason

If the angles of elevation of the top of a
tower at three points on the ground are in A.P. then the distance of the points from the foot of the tower are also in A.P.
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


The AM of multiple of 5 from numbers 1
to 500 is
\( \mathbf{A} \cdot 250 \)
в. \( \frac{500}{2} \)
c. \( \frac{505}{2} \)
D. 252.5


Which out of following hydrocarbons undergo addition reactions?
\( C_{2} H_{6}, C_{3} H_{8}, C_{3} H_{6}, C_{2} H_{2} \) and \( C H_{4} \)
A. \( C_{2} H_{6} \) and \( C_{3} H_{8} \)
B. \( C_{3} H_{6} \) and \( C_{2} H_{2} \)
c. \( C H_{4} \) and \( C_{2} H_{6} \)
D. \( C_{3} H_{8} \) and \( C_{2} H_{2} \)


Find the slope of a line parallel to the line \( \boldsymbol{y}=\frac{\mathbf{2}}{\mathbf{3}} \boldsymbol{x}-\mathbf{4} \)
A . -4
в. \( -\frac{3}{2} \)
\( c \cdot 2 \)
D. \( \frac{3}{2} \)
\( E \cdot \frac{2}{3} \)


\( \int\left(\cot ^{n+2} x+\cot ^{n} x\right) d x= \)
A. \( \quad \frac{-\cot ^{n+1} x}{n+1}+c \)
B \( \cdot \frac{-\cot ^{n-1} x}{n-1}+C \)
c. \( \frac{-\cot ^{n+3} x}{n+3}+c \)
D. \( \frac{-\cot ^{2 n} x}{2 n}+C \)


Water is flowing through a horizontal tube. The pressure of the liquid in the portion where velocity is \( 2 m / s \) is \( 2 m \)
of \( H g . \) What will be the pressure in the portion where velocity is \( 4 m / s \)


Predict the increasing order of acidity in the following compounds.
A. Phenol
B. Paracresol
c. Metanitrophenol
D. Paranitrophenol


The percentage change in the pressure of a given mass of a gas filled in a container at constant temperature is
100\%. Calculate the percentage change in its volume.


The weight of a boy on the surface of moon is \( 300 N . \) The weight of this boy on
the surface of earth is:
\( \mathbf{A} \cdot 300 N \)
в. \( 5 N \)
\( c .50 N \)
D. \( 1800 N \)


The movement or growth of any part of a
plant in response to an external stimulus is called tropism or tropic
movement.
A . True
B. False