An open end manometer consists of
0.75 moles of \( X_{g} \) taken in a container of
volume 24.63 lit at \( 300 K . \) The level of
mercury in the open tube is found to be \( 14 \mathrm{cm} \) lower. The height difference when manometer is heated to \( 450 K \) will be:
A . \( 14.5 \mathrm{cm} \)
B. \( 21 \mathrm{cm} \)
\( \mathbf{c} \cdot 13 c m \)
D. \( 17 \mathrm{cm} \)


For a reaction \( \boldsymbol{A} \stackrel{\boldsymbol{K}_{1}}{\longrightarrow} \boldsymbol{B} \stackrel{\boldsymbol{K}_{2}}{\longrightarrow} \boldsymbol{C} . \) If the
reaction are of \( 1^{s t} \) order then \( \frac{\boldsymbol{d}[\boldsymbol{B}]}{\boldsymbol{d} \boldsymbol{t}} \) is
equal to:
A . \( -k[B] \)
B. \( +k_{1}[A] \)
\( \mathbf{c} \cdot k_{1}[A]-k_{2}[B] \)
D. \( k_{1}[A]+k_{2}[B] \)


Curved portion of Henle's loop is lined by
A. Columnar epithelium
B. Cuboidal epithelium
c. Squamous epithelium
D. cinated epithelium


Show that each of the three given vectors is a unit vectors. also Show that
they are mutually \( \perp \) to each other \( \vec{a}=\frac{1}{7}(2 \hat{i}+3 \hat{j}+6 \hat{k}) \)
\( \vec{b}=\frac{1}{7}(3 \hat{i}-6 \hat{j}+2 \hat{k}) \)
\( \overrightarrow{\boldsymbol{c}}=\frac{1}{7}(6 \hat{i}+2 \hat{j}-3 \hat{k}) \)


Which one of the following statements
is incorrect about soaps?
A. Soaps are biodegradable
B. Soaps are sodium salts of higher fatty acids
C. Soaps are prepared from natural oils and fats
D. Soaps can be used in acidic solutions


Van't Hoff factor for \( \boldsymbol{T} \boldsymbol{H}\left(\boldsymbol{N} \boldsymbol{O}_{3}\right)_{4} \) in an
aqueous solution is :


The strength of sigma bonds formed by axial overlap of \( s \) - orp-orbitals of 2 nd
shell of participating atoms decreases
as:


Factorise the following: \( 2 a^{3}-54 b^{3} \)
\( \mathbf{A} \cdot 2(a b+3 b)\left(a^{2}+3 b+9 a b^{2}\right) \)
B \( \cdot 2(a+2 b)\left(a^{3}+3 a b-9 b^{3}\right) \)
C \( \cdot(a-3 b)\left(a^{2}+3 b+9 a b^{2}\right) \)
D \( \cdot 2(a-3 b)\left(a^{2}+3 a b+9 b^{2}\right) \)


A plank of mass \( m_{1} \) with a bar of mass
\( m_{2} \) placed on it lies on a smooth
horizontal plane. A horizontal force growing with time \( t \) as \( \boldsymbol{F}=\boldsymbol{a t}(\boldsymbol{a} \) is
constant) is applied to the bar. Find how
the accelerations of the plank \( w_{1} \) and of
the bar \( w_{2} \) depend on \( t, \) if the
coefficient of friction between the plank and the bar is equal to \( k \)


If \( \left(x^{2}+y^{2}\right)^{2}=x y, \) find \( \frac{d y}{d x} \)


Figure shows two large cylindrical
shells having uniform linear charge
densities \( +a \lambda \) and \( -\lambda . \) Radius of inner
cylinder as 'a' and that o outer cylinder
is 'b'. A charged particle of mass m,
charge q revolves in a circle of radius
r.Then its speed 'v' is : (Neglect gravity and assume the radii of both the
cylinders to be very small in
comparision to their length)
A \( \cdot \sqrt{\frac{\lambda q}{2 \pi \epsilon_{0} m}} \)
B. \( \sqrt{\frac{2 \lambda q}{\pi \epsilon_{0} m}} \)
c. \( \sqrt{\frac{\lambda q}{\pi \epsilon_{0} m}} \)
D. \( \sqrt{\frac{\lambda q}{4 \pi \epsilon_{0} m}} \)


Predict the direction of the reaction
from the comparison of \( Q_{c}, K_{c} . \) Mark the
incorrect statement.
A \( \cdot \) If \( Q_{c}<K_{c} \), reaction goes from left to right.
B. If \( Q_{c}=K_{c} \), reaction goes from right to left
\( \mathrm{c} \cdot \) If \( Q_{c}>K_{c} \), net reaction goes from right to left
D. If \( Q_{c}=K_{c} \), reactants and products are at equilibrium.


Mention two limitations of Ohm's law.


The split of white light into its constituent colours, by a triangular prism, is known as:
A. scattering
B. dispersion
c. refraction
D. deviation


In resonance tube experiment, the velocity of sound is given by \( \boldsymbol{v}= \)
\( 2 f_{0}\left(l_{1}-l_{1}\right) . \) We found \( l_{1}=25.0 c m \) and
\( l_{2}=75.0 c m . \) If there is no error in
frequency, what will be the maximum
permissible error in the speed of sound? \( \left(\text {Take} f_{0}=\mathbf{3 2 5 H z}\right) \)


Let \( A \) and \( B \) be two events such that \( P(\overline{A \cup B})=\frac{1}{6}, P(A \cap B)=\frac{1}{4} \) and
\( P(\bar{A})=\frac{1}{4}, \) then events \( A \) and \( B \) are
A. equally likely, but not independent
B. equally likely and mutually exclusive
c. mutually exclusive and independent
D. independent but not equally likely


Drugs that bind to the receptor sites and inhibit its natural function, are
called:
A. antipyretics
B. analgesics
c. agonist
D. antagonist


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


Assertion
The points on the curve \( y^{2}=x+\sin x \)
at which tangent is parallel to x-axis lies on a straight line.
Reason Tangent is parallel to \( x \) -axis then \( \frac{d y}{d x}= \)
0 or \( \frac{d x}{d y}=\infty \)
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


A beam of light converges towards a point \( 0, \) behind a convex mirror of focal length \( 20 \mathrm{cm} . \) Find the magnification
and nature of the image when point 0 is \( 30 \mathrm{cm} \) behind the mirror.
A. 2 (virtual, inverted)
B. 3 (real, inverted)
c. 3, (virtual, enlarged)
D. +1 (real, enlarged)


Name the following compound according to the IUPAC system or nomenclature:
\( \boldsymbol{C H}_{3} \boldsymbol{C H}\left(\boldsymbol{C H}_{3}\right) \boldsymbol{C H}_{2} \boldsymbol{C}\left(\boldsymbol{C H}_{3}\right)_{2} \boldsymbol{C O C H}_{3} \)


What is coagulation? Explain.


Which of the following correctly represents symbol for chlorine in Berzelius system?
A.
в. с
\( c . \) мп
D.


The number of ways of choosing 10 balls from infinitely many white, red , blue and green balls is:
\( A \cdot 70 \)
B. 84
\( c \cdot 286 \)
D. 86


A fricionless wire \( A B \) is fixed on
sphere of radius R. A very small particle slips on the wire. The journey from \( A \) to \( B \) is performed in time
A .2 Rg \( \cos \theta \)
B. \( 2 \sqrt{R g} \cos \theta \)
\( c \cdot 2 \sqrt{\frac{R}{g}} \)
\( 0.2 \sqrt{\frac{9}{2}} \)


Substract \( x^{2} \) from \( x^{2}+y^{2}-3 y \)


The velocity of the body at any instant is
A \( \cdot \frac{M+2 N t^{4}}{4} \)
B. 2N
c. \( \frac{M+2 N}{4} \)
D. \( 2 N t^{3} \)


Electromagnetic waves travel only
through.
\( \mathbf{A} \). material medium
B. vacuum
C. oscillating electric and magnetic fields
D. oscillating electric and magnetic fields whose directions are perpendicular to each other


Is the point (0,3) lie on the graph of the
linear equation \( 3 x+4 y=12 ? \)


The standard enthalpies of n-pentane, isopentane and neopentane are -35.0,-37.0 and \( -40.0 K \) cal / mole
respectively. The most stable isomer of
pentane in terms of energy is
A. n-pentane
B. isopentane
c. neopentane
D. n-pentane and isopentane


The number of neutrons accompanying the formation of 139
54 \( \mathrm{Xe} \) and 94
38 \( \mathrm{Sr} \) from
the absorption of a slow neutron by 235 92 followed by nuclear fission is:
\( A \cdot O \)
B. 2
\( c \)
D. 3


Which of the following is not a carbonate mineral?
A. siderite
B. Calamine
c. limestone
D. Fluorospar


The standard electrode potential \( \left(E^{\circ}\right) \)
for Daniel cell is \( +1.1 \mathrm{V} \). Calculate \( \Delta G^{\circ} \)
for the reaction.
\( \boldsymbol{Z} \boldsymbol{n}(\boldsymbol{s})+\boldsymbol{C} \boldsymbol{u}_{(a q)}^{2+} \rightarrow \boldsymbol{Z} \boldsymbol{n}_{(a q)}^{2+}+\boldsymbol{C u}(\boldsymbol{s}) \)
\( (1 F=96500 C / m o l) \)


A ball is projected upwards from a height h above the surface of the earth with velocity v.The time at which the ball trikes the ground is This question has multiple correct options
A \( \cdot \frac{v}{g}+\frac{2 h g}{\sqrt{2}} \)
в. \( \frac{v}{g}[1-\sqrt{1+\frac{2 h}{g}}] \)
c. \( \frac{v}{g}[1+\sqrt{1+\frac{2 g h}{v^{2}}}] \)
D. \( \frac{v}{g}[1+\sqrt{v^{2}+\frac{2 g}{h}}] \)


A positive test charge is released from rest in a uniform electric field. Which of
the following best describes its initial
motion?
A. It will move with constant velocity along an equipotential line
B. It will move with constant acceleration along an equipotential line
c. It will move with constant acceleration along an electric field line
D. It will move with constant velocity along an electric field line


From 2011 to \( 2016, \) find the difference
between the total number of people who
preferred to play Basketball and Badminton (in millions)?
(Preferences of people in playing different games over the years.
A . 525
В. 275
\( c .730 \)
D. 250


All meteors reach the surface of the
Earth. This statement is
A. True
B. False


A restaurant owner has a few bottles of
soft drink in his restaurant. But, unfortunately, these are not labelled. He
has to serve the drinks on the
demand of customers. One customer
wants acidic drink, another wants basic
and the third wants neutral drink. How
will the restaurant owner decide which
drink is to be served to whom?


Chemical agent that has important role in flowering is
A. Fluorocarbon
B. GA \( _{3} \)
c. Florigen
D. Auxins


Construct a \( 2 \times 2 \) matrix \( A=\left[a_{i j}\right] \)


The mean score of 1000 students for an
examination is 34 and \( S . D . \) is 16
(i) How many candidates can be
expected to obtain marks between 30
and 60 assuming the normality of the distribution and
(ii) determine the limit of the marks of
the central \( 70 \% \) of the candidates:
\( \{\boldsymbol{P}[\mathbf{0}<\boldsymbol{z}<\mathbf{0 . 2 5}]=\mathbf{0 . 0 9 8 7} \boldsymbol{P}[\mathbf{0}<\boldsymbol{z}<\mathbf{1} \)


Q туре your question
3.
\( c \)
D.


Explain the effects of pressure on the following equilibria.
\( \boldsymbol{L}(\boldsymbol{g})+\boldsymbol{M}_{(\boldsymbol{g})} \rightleftharpoons \boldsymbol{N}_{(\boldsymbol{g})}+\boldsymbol{O}_{(g)} \)


If \( \frac{x+3 i}{2+i y}=1-i, \) then the value of
\( (5 x-7 y)^{2} \) is
A . 1
B. 0
\( c \cdot 2 \)
D.


In the following diagram, the Potential
difference across \( 6 V \) cell is:
\( \mathbf{A} \cdot 6 V \)
\( \mathbf{B} \). \( 5.6 V \)
\( \mathbf{c} .8 .2 V \)
D. \( 8.4 V \)


You have two solutions, \( A \) and \( B \). The
\( p H \) of solution \( A \) is 6 and \( p H \) of
solution \( B \) is \( 8 . \) Which solution has
more hydrogen ion concentration? Which of this acidic and which one is
basic?
A. A \( p H \) value less then 7 indicates an acidic solution, while greater than 7 indicates a basic solution. Therefore, the solution with \( p H=6 \) is acidic and has more hydrogen ion concentration than the solution of \( p H=8 \) which is basic.
B. A \( p H \) value less then 7 indicates an basic solution, while greater than 7 indicates a acidic solution. Therefore, the solution with \( p H=8 \) is acidic and has more hydrogen ion concentration than the solution of \( p H=6 \) which is basic
C. A \( p H \) value less then 7 indicates an acidic solution, while greater than 7 indicates a basic solution. Therefore, the solution with \( p H=8 \) is acidic and has
more hydrogen ion concentration than the solution of \( p H=6 \) which is basic.
D. None of the above


By what factor the velocity of an electron in a Bohr's orbit for a hydrogen atom will change, if the principal quantum number is doubled:
A. velocity is doubled
B. velocity is halved
C . velocity is reduced to \( \frac{1}{3} \)
D. velocity remains unchanged


\( \dots \)
the function \( Z \) of \( X \) and \( Y \) represented by
given figure is :
\( A \)
\begin{tabular}{|c|c|c|}
\hline\( X \) & \( Y \) & \( Z \) \\
\hline 0 & 0 & 0 \\
0 & 1 & 0 \\
1 & 0 & 1 \\
1 & 1 & 1 \\
\hline
\end{tabular}
B. \begin{tabular}{|c|c|c|}
\hline\( X \) & \( Y \) & \( Z \) \\
\hline 0 & 0 & 1 \\
0 & 1 & 1 \\
1 & 0 & 0 \\
1 & 1 & 0 \\
\hline
\end{tabular}
\( c \)
\begin{tabular}{|c|c|c|}
\hline\( X \) & \( Y \) & \( Z \) \\
\hline 0 & 0 & 1 \\
0 & 1 & 0 \\
1 & 0 & 1 \\
1 & 1 & 0 \\
\hline
\end{tabular}
D. None of these


The most basic oxide among
\( M n O, M n_{2} O_{3}, M n O_{2} \) and \( M n_{2} O_{7} \) is :
\( \mathbf{A} \cdot M n O \)
в. \( M n O_{2} \)
\( \mathrm{c} \cdot M n_{2} O_{3} \)
D. \( M n_{2} O_{7} \)


The tube in simple barometer is filled with mercury.
A. Half
B. Three-fourth
c. completely
D. Two-third


Which of the following is an example of a disproportionation reaction?
A. \( C a C O_{3} \rightarrow C a O+C O_{2} \)
в. \( 2 H C u C l_{2} \rightarrow C u+C u^{2+}+4 C l^{-}+2 H^{+} \)
c. \( P C l_{5} \rightarrow P C l_{3}+C l_{2} \)
D. \( 2 H_{2} S+S O_{2} \rightarrow 2 H_{2} O+3 S \)


Which property of DNA double helix led Watson and Crick to hypothesise semiconservative mode of DNA replication? Explain.


In which of the following option, covalent bond is having maximum \( s \% \) character?
A. \( S-H \) bond in \( H_{2} S \)
B. \( P-H \) bond in \( P H_{3} \)
c. \( N-H \) bond in \( N H_{3} \)
D. All have equal \( s \% \) character


\( i f \angle A=\angle B=45^{\circ} \) verify that \( , \sin \)
\( (A+B)=\sin A \cos B+\cos A \sin B \)


The properties of medicine is/are:
This question has multiple correct options
A. it cures the diseases
B. it does not causes addiction
C . it has negligible toxicity
D. none of the above


If \( \sin ^{-1} x=y, \) then
A. \( 0 \leq y \leq \pi \)
B. \( -\frac{\pi}{2} \leq y \leq \frac{\pi}{2} \)
c. \( 0<y<\pi \)
D. \( -\frac{\pi}{2}<y<\frac{\pi}{2} \)


During denaturation of proteins which structure is destroyed?
A. secondaary
B. primary
c. tertiary
D. secondary and tertiary


Which of the following statements is true?The entropy of the universe:
A. increases and tends towards maximum value
B. decreases and tends to be zero
c. remains constant
D. decreases and increases with a periodic rate


What are the major change significant at the stage of adolescents?


A common device which can supply
small electric current continuously for a sufficient time


Find the number of sides of a regular
polygon if each exterior angle
measures: \( 45^{\circ} \)


The compound \( \left[\boldsymbol{P t} \boldsymbol{C l}_{2}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{2}\right] \) can
form:
A. geometrical isomers.
B. coordination isomers.
c. linkage isomers.
D. optical isomers.


In the Leibigs method, if \( w \) is the mass of compound taken and \( x \) is the amount
of \( C O_{2} \) formed then
\( \mathbf{A} \cdot \% C=\frac{12 \times x}{16 \times w} \)
B . \% \( C=\frac{12}{44} \times \frac{w}{x} \times 100 \)
C \( \cdot \) \% \( C=\frac{12}{44} \times \frac{x}{w} \times 100 \)
D・\% \( C=\frac{12}{44} \times \frac{x}{w} \)


Solve \( \int \boldsymbol{a}^{\boldsymbol{m} \boldsymbol{x}} \boldsymbol{b}^{\boldsymbol{n} \boldsymbol{x}} \boldsymbol{d} \boldsymbol{x} \)


If in the expansion of \( \left(\frac{1}{x}+x \tan x\right)^{5}, \) the ratio of \( 4^{t h} \) term to the \( 2^{n d} \) term is \( \frac{2}{27} \pi^{4} \) then the value of \( x \) can be
A \( \cdot \frac{-\pi}{6} \)
в. \( \frac{-\pi}{3} \)
c.
D. \( \frac{\pi}{12} \)


toppr
Q Type your question
heat with the liquid. The bubble
contains n moles of gas. The
temperature of the gas when the
bubbles is at the bottom is \( T_{0}, \) the
height of the liquid is \( \mathrm{H} \) and the
atmospheric pressure is \( P_{0} \) (neglect
surface tension). When the gas bubble
is at height \( y \) from the bottom, its
temperature is:
A \( \cdot \quad T_{0}\left(\frac{P_{0}+\rho_{1} g H}{P_{0}+\rho_{1} g y}\right)^{\frac{2}{5}} \)
\( ^{\mathbf{B}} T_{0}\left(\frac{P_{0}+\rho_{1} g(H-y)}{P_{0}+\rho_{1} g H}\right)^{\frac{2}{3}} \)
c.
\[
T_{0}\left(\frac{P_{0}+\rho_{1} g H}{P_{0}+\rho_{1} g y}\right) \overline{5}
\]
\( P_{0}\left(\frac{P_{0}+\rho_{1} g(H-y)}{P_{0}+\rho_{1} g y}\right)^{\frac{3}{5}} \)


A Shell following a parabolic path explodes somewhere in its flight. The centre of mass of fragments will continue to move in
A. vertical direction
B. any direction
c. horizontal direction
D. same parabolic path


Derivative of which function is \( \boldsymbol{f}^{\prime}(\boldsymbol{x})= \)
\( x \sin x ? \)
This question has multiple correct options
A. \( x \sin x+\cos x \)
B. \( x \cos x+\sin x \)
c. \( x \sin \left(\frac{\pi}{2}-x\right)+\cos \left(\frac{\pi}{2}-x\right) \)
D. \( x \cos \left(\frac{\pi}{2}-x\right)+\sin \left(\frac{\pi}{2}-x\right) \)


The oxide of an element whose
electronic configuration \( 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{1} \)
is:
A. Neutral
B. Atmospharic
c. Basic
D. Acidic


Let \( \boldsymbol{f}:\{\boldsymbol{x}, \boldsymbol{y}, \boldsymbol{z}\} \rightarrow\{1,2,3\} \) be a one-one
mapping such that only one of the following three statements and remaining two are false : \( \boldsymbol{f}(\boldsymbol{x}) \neq \) \( \mathbf{2}, \boldsymbol{f}(\boldsymbol{y})=\mathbf{2}, \boldsymbol{f}(\boldsymbol{z}) \neq 1, \) then
A \( . f(x)>f(y)>f(z) \)
в. \( f(x)<f(y)<f(z) \)
c. \( f(y)<f(y)<f(z) \)
D. \( f(y)<f(z)<f(x) \)


Construct a \( \triangle A B C \) in which \( A C= \)
\( \mathbf{5} c m, \) and \( \angle B A C=60^{\circ} \) and \( A B- \)
\( B C=1.2 \mathrm{cm} \)


(a) Obtain an expression for the mutual
inductance between a long straight
wire and a square loop of side a as
shown in Fig.
(b) Now assume that the straight wire
carries a current of \( 50 \mathrm{A} \) and the loop is moved to the right with a constant velocity, \( v=10 \mathrm{m} / \mathrm{s} \). Calculate the induced emf in the loop at the instant
when \( x=0.2 \mathrm{m} . \) Take \( a=0.1 \mathrm{m} \) and
assume that the loop has a large
resistance.


\( A B C D \) is a square of length \( a, a \in \)
\( N, a>1 . \) Let \( L_{1}, L_{2}, L_{3} \dots \dots, \) be point on
BC such that \( \boldsymbol{B} \boldsymbol{L}_{1}=\boldsymbol{L}_{1} \boldsymbol{L}_{2}=\boldsymbol{L}_{2} \boldsymbol{L}_{3}= \)
\( \ldots=1 \) and \( M_{1}, M_{2}, M_{3} \ldots \ldots \ldots \) be points
on CD such that \( \boldsymbol{C} \boldsymbol{M}_{\mathbf{1}}=\boldsymbol{M}_{\mathbf{1}} \boldsymbol{M}_{\mathbf{2}}= \)
\( =1 . \) Then \( \sum_{n=1}^{a-1}\left(A L_{2}^{2}+L_{n} M_{n}^{2}\right) \) is
equal to
A \( \cdot \frac{1}{2} a(a-1)^{2} \)
B.
\[
\frac{1}{2}(a-1)(2 a-1)(4 a-1)
\]
c.
\[
\frac{1}{2} a(a-1)(4 a-1)
\]
D. None of these


The volume of a largest sphere that can be cut from cylindrical log of wood of
base radius \( 1 m \) and height \( 4 m \) is:
A \( \cdot \frac{8}{3} \pi m^{3} \)
в. \( \frac{10}{3} \pi m^{3} \)
c. \( \frac{16}{3} \pi m^{3} \)
D. \( \frac{4}{3} \pi m^{3} \)


In the bandgap between valence band and conduction band in a material is
\( \mathbf{5} . \mathbf{0} e \boldsymbol{V}, \) then the material is
A. semiconductor
B. good conductor
c. superconductor
D. insulator


\( \lim _{x \rightarrow a} \frac{x^{7}-a^{7}}{x-a} \)


Which scientist synthesised 1st organic compound in lab?
A. Friedrich Wohler
B. Antoine Lavoisier
c. Robert Boyle
D. Willard Gibbs


Assertion
\( \left(H_{2}+O_{2}\right) \) fuel cell gives a constant
voltage throughtout its life.
Reason In this fuel cell, \( H_{2} \) reacts with \( \stackrel{\ominus}{O H} \) ions, yet the over all \( [\stackrel{\ominus}{O} \boldsymbol{H}] \) does not change.
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


A graph and the system of inequalities are shown above. Which region of the
graph could represent the solution for
the system of in equations?
\( \boldsymbol{y}>\boldsymbol{x} \)
\( \mathbf{3} \boldsymbol{y} \leq-\mathbf{4} \boldsymbol{x}+\mathbf{6} \)
\( A \cdot A \)
в. \( B \)
\( c . c \)
D. \( D \)


Which of the following is(are) the merit(s) of Mendeleev's periodic table?
A. Could also predict the properties of these unknown elements
B. Grouping of chemically dissimilar elements.
c. Position given to isotopes.
D. Presence of anomalous pairs


For what value of \( a \), the function
\[
\boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{ll}
\frac{1-\cos 4 x}{\boldsymbol{x}^{2}}, & \boldsymbol{i f} \quad \boldsymbol{x}<0 \\
\boldsymbol{a}, \quad \boldsymbol{i f x}=\mathbf{0} & \\
\frac{\sqrt{\boldsymbol{x}}}{\sqrt{\mathbf{1 6 + \sqrt { \boldsymbol { x } }}-\boldsymbol{4}}}, & \boldsymbol{i f} \boldsymbol{x}>0
\end{array}\right.
\]
continuous at \( \boldsymbol{x}=\mathbf{0} \)


The most abundant organic compound in the world is:
A . cellulose
B. alkaloids
c. methane
D. chlorophyll


In a parallel plate capacitor, the region between the plates is filled by a delectric slab. The capacitor is connected to a cell and the slab is taken
out.
A. Some charge is drawn from the cell
B. Some charge is returned to the cell
c. The potential difference across the capacitor is reduced
D. No work is done by an external agent in taking the slab out


Select the incorrect order(s) among
the following:
This question has multiple correct options
\( \mathbf{A} \cdot C l O^{-}<B r O^{-}<I O^{-} \) - disproportionation
B \( \cdot C l O_{4}^{-}<B r O_{4}^{-}<l O_{4}^{-} \) - oxidising power
c. \( H C l O<H C l O_{2}<H C l O_{3}<H C l O_{4} \) - acid strength
D. \( H O C l>H O I>H O B r \) -acid strength


The result of the operation \( 2.5 \times 1.25 \) should be which of the following on the basis of significant figures?
A . 3.125
B. 3.13
c. 3.
D. 31.25


Calculate \( \gamma\left(\text { ratio of } C_{p} \text { and } C_{v}\right) \) for triatomic linear gas at high
temperature. Assume that the
contribution of the vibrational degree of freedom is \( 75 \% ? \)
A. 1.222
B. 1.121
c. 1.18
D. 1.33


Assertion
If the bodies in question have spatial extent (rather than being theoretical point masses), then the gravitational force between them is calculated by summing the contributions of the notional point masses which constitute the bodies.
Reason
Every point mass attracts every single other point mass by a force pointing along the line intersecting both points.
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


If \( A=\left|\begin{array}{ll}2 & 3 \\ 6 & 9\end{array}\right| \) then \( |A|= \)
A .
B. 1
\( c \cdot 2 \)
D.


A positively charged particle in a uniform magnetic field moves in a circular path in the clockwise direction,
parallel to the plane of the page. In what direction do the magnetic field lines point?
A. Out of the page
B. Into the page
c. To the left
D. To the right
E. In a clockwise pattern parallel to the plane of the page


The length of the perpendicular from the
vertex \( D \) on the opposite face is
A \( \cdot \frac{14}{\sqrt{6}} \)
в. \( \frac{2}{\sqrt{6}} \)
c. \( \frac{3}{\sqrt{6}} \)
D. none of these


Evaluate the following:
\( \sin ^{-1}(\sin 5) \)


Which of the following pigments is present in brown algae?
A. Anthocyanin
B. Fucoxanthin
c. Phycobilins
D. Biliverdin


Himanshu borrowed \( \boldsymbol{R} \boldsymbol{s} \mathbf{1 2}, \mathbf{0 0 0} \) at
\( 15 \frac{1}{2} \% \) rate of simple interest for certain years. At the end of the period, he paid a total sum of \( \boldsymbol{R} \boldsymbol{s} \boldsymbol{2} \boldsymbol{0}, \boldsymbol{3} \boldsymbol{7} \boldsymbol{0} . \) Find the period.


Which of the following is an EAN of iron in potassium ferricyanide?
A . 28
B. 36
c. 35
D. 39


The conversion of atomic hydrogen into ordinary hydrogen is:
A. Exothermic reaction
B. Endothermic reaction
c. Nuclear change
D. Photochemical change


If collision between the block and the
incline is completely elastic, the the vertical (upward) component of the velocity of blocks at point \( \boldsymbol{B} \)
immediately after it strikes the second
incline is
A \( . \sqrt{30} \mathrm{m} / \mathrm{s} \)
B. \( \sqrt{15} \mathrm{m} / \mathrm{s} \)
\( c .0 \)
D. \( -\sqrt{15} \mathrm{m} / \mathrm{s} \)


If \( x^{2}+\frac{1}{x^{2}}=51, \) find the value of \( x^{3}- \)
1
\( \overline{x^{3}} \)


Let \( y=2^{x}+x^{2}+2 \) then find \( \frac{d y}{d x} \)


In which of the following molecules, the central atom does not have \( s p^{3} \) hybridization?
A \( . C H_{4} \)
в. \( S F_{4} \)
\( \mathbf{c} \cdot B F_{4} \)
D. \( N H_{4}^{+} \)


In the given figure, the triangles are
congruent, Find the values of \( x \) and \( y \)


The electronic arrangements of four elements i, ii, iii, iv are:
(iii) \( 1 s^{2} 2 s^{2} 2 p^{5} \) (iv)
(i) \( 1 s^{2} \) (ii) \( 1 s^{2} 2 s^{2} 2 p^{2} \) \( 1 s^{2} 2 s^{2} 2 p^{6} \)
The tendency to form ionic bond is maximum in:
\( A \)
B. i i
c. iii
\( D . \) iv


A free nucleus of mass 24 amu emits a
gamma photon (when initially at rest). The energy of the photon is 7 MeV. The recoil energy of the nucleus in KeV is:
(Assuming 1 amu \( =931 \) MeV )
A . 2.2
B. 1.
c. \( 3 . \)
D. 22


Phosphine is not evloved when:
A. White phosphorus is boiled with a strong
solution of
\( \mathrm{Ba}(\mathrm{OH})_{2} \)
B. Phosphorus acid is heated
C. Calcium hypophosphite is heated
D. Metaphosphoric acid is heated


In displacement method, the distance
between object and screen is 96 cm.
The ratio of lengths of two images
formed by a converging lens placed
between them is \( 4 . \) Then
This question has multiple correct options
A. Ratio of the length of object to the length of shorter image is 2
B. Distance between the two positions of the lens is \( 32 \mathrm{cm} \)
C. Focal length of the lens is \( 64 / 3 \mathrm{cm} \)
D. When the shorter image is formed on screen, distance of the lens from the screen is \( 32 \mathrm{cm} \)


If the vector \( O P \) in \( X Y \) plane whose
magnitude is \( \sqrt{3} \) makes an angle \( 60^{\circ} \)
with \( Y- \) axis, the length of the
component of the vector in direction of
\( X- \) axis is :
A . 1
B. \( \sqrt{3} \)
\( c \cdot \frac{1}{2} \)
D. \( \frac{3}{2} \)


The number of turns per unit length of a
long solenoid is \( 10 . \) If its average radius is \( 5 \mathrm{cm} \) and it carries a current of \( 10 \mathrm{A} \)
then the ratio of flux densities obtained
at the centre and at one endpoint will be
A .1: 2
B . 2: 1
c. 1: 1
D. 1: 4


An unpolarized beam of intensity \( 2 a^{2} \) passes through a thin Polaroid. Assuming zero absorption in the Polaroid, the intensity of emergent planes polarized light will be
\( \mathbf{A} \cdot 2 a^{2} \)
в. \( a^{2} \)
\( c \cdot \sqrt{2} a \)
D. \( \frac{a^{2}}{\sqrt{2}} \)


A glass hemisphere of radius \( R \) and of
material having refractive index 1.5 is
silvered on its flat face as shown in
figure. A small object of height \( h \) is
located at a distance \( 2 R \) from the
surface of hemisphere as shown in figure. The final image will form.
A. At a distance of \( R \) from silvered surface, on the right side
B. On the object itself
C. At hemisphere surface
D. At a distance of \( 2 R \) from the silvered surface, on left
side


LPG can be used as a power source for:
A. combined heat and power technologies (CHP)
B. combined heat and energy technologies ( CHP)
C . combined heat and coal technologies (CHP)
D. heat and power technologies


If \( A \) is \( (-1,2,0), B \) is (1,2,3) and \( C \) is \( (4,2,1), \) then prove that \( \Delta A B C \) is an isosceles right triangle.


If certain decomposition reaction found to obey equation in term of partial pressure (P) of reactant : \( \frac{\boldsymbol{a}-\boldsymbol{p}^{2}}{\boldsymbol{p}^{2}}=\boldsymbol{b k t} \)
what is order of reaction if \( a, b \) and \( k \)
are constant (t represents time)?
\( A \cdot 3 \)
B. 6
\( c \cdot 2 \)
\( D \)


Any point on the circumference of a
rigid body which is rolling without slipping undergoes :
A. a circular path
B. an elleptic path
c. a cycloid path
D. an parabolic path


Write any two rational numbers which
are between 2.3 and 2.4


'The extent to which a solute is
dissociated or associated can be
expressed by Van 't Hoff factor'. Substantiate the statement.


Mark the correct reason/s why
nichrome is used for making heating element of electrical appliances.
A. Nichrome does not oxidize
B. Nichrome doesn't burn easily at high temperatures as it has higher melting and boiling point than metals
C. Nichrome has higher resisistivity and consequently a higher resistance
D. All


If a galvanometer has full scale
deflection current \( I_{G} \) and resistance \( G \)
A shunt resistance \( R_{A} \) is used to
convert it into an ammeter of range \( \boldsymbol{I}_{\mathbf{0}} \)
and a resistance \( R_{V} \) is connected in series to convert it into a voltmeter of
range \( V_{0} \) such that \( V_{0}=I_{0} G \) then
\( R_{A} R_{V} \) and \( \frac{R_{A}}{R_{V}} \) respectively are
\( ^{\mathbf{A}} \cdot G^{2} \) and \( \frac{I_{G}^{2}}{\left(I_{0}-I_{G}\right)^{2}} \)
в. \( G^{2} \) and \( \frac{I_{0}^{2}}{\left(I_{0}-I_{G}\right)^{2}} \)
\( ^{\mathrm{c}} \cdot G^{2} \) and \( \frac{I_{G}}{\left(I_{0}-I_{G}\right)^{2}} \)
D. \( G^{2} \) and \( \frac{I_{G}^{2}}{\left(I_{0}+I_{G}\right)^{2}} \)


f the brass wire were replaced by
another brass wire of diameter 1 m \( m \)
where should the mass be suspended
so that \( A B \) would remain horizontal?
\( \mathbf{A} \cdot x=0.06 m \)
В . \( x=0.12 \) т
c. \( x=0.24 m \)
D. \( x=0.48 m \)


Calculate the number of molecules of
oxygen gas that occupies a volume Of 22
\( \mathrm{ml} \) at \( 273 \mathrm{K} \) and 3 atm pressure.


The dimensions of \( \frac{\alpha}{\beta} \) in the equation \( \boldsymbol{F}=\frac{\boldsymbol{\alpha}-\boldsymbol{t}^{2}}{\beta \boldsymbol{v}^{2}}, \) where \( \mathrm{F} \) is the force, \( \mathrm{v} \) is
velocity and t is time, is
A \( \cdot\left[M L T^{-1}\right] \)
В \( \cdot\left[M L^{-1} T^{-2}\right] \)
c. \( \left[M L^{3} T^{-4}\right] \)
D・ \( \left[M L^{2} T^{-4}\right] \)


Which of the following semiconductor is electrically positive?
A. Intrinsic semiconductor
B. P-type semiconductor
c. N-type semiconductor
D. None of these


If \( D \) is a point on the side \( A B \) of \( \triangle A B C \) such that \( A D: D B=3: 2 \) and \( E \) is a point
on BC such that DE \( \| \) AC. Find the ratio of areas of \( \triangle \mathrm{ABC} \) and \( \triangle \mathrm{BDE} \)


At \( 1100^{\circ} \mathrm{C} \), which reaction is
spontaneous to a maximum extent?
A. \( M g O+C \rightarrow M g+C O \)
B. \( Z n O+C \rightarrow Z n+C O \)
c. \( M g O+Z n \rightarrow M g+Z n O \)
D. \( Z n O+M g \rightarrow M g O+Z n \)


Discribe about structure of proteins.


Select the incorrect statement(s):
A. An activated complex is a high-energy, unstable, short lived configuration of reactant atoms
B. An endothermic reaction always has a greater activation energy and a slower rate than the opposing exothermic reaction
C. Threshold energy level decreases on heating the reaction mixture
D. The geometrical shape and the collision geometry of reacting molecules affects reaction rate


Liquid oxygen remains suspended between two pole forces of a magnet because it is:
A. diamagnetic
B. paramagnetic
c. ferromagnetic
D. antiferromagnetic


The number of chromosomes in parents
and offsprings of a particular species remains constant due to
A. Doubling of chromosomes after zygote formation
B. Halving of chromosomes during gamete formation
c. Doubling of chromosomes after gamete formation
D. Halving of chromosomes after gamete formation


Show that the maximum volume of the
cylinder which can be inscribed in a sphere of radius \( 5 \sqrt{3} \mathrm{cm} \) is \( 500 \pi c m^{3} ? \)


Let \( M \) and \( m \) be respectively the
absolute maximum and the absolute
minimum values of the function,
\( f(x)=2 x^{3}-9 x^{2}+12 x+5 \) in the
interval \( [0,3] . \) Then \( M-m \) is equal to.
A . 1
B. 5
\( c \cdot 4 \)
D. 9


The \( n^{t h} \) term of an \( A P \) is \( a=2=n+1 \)
find its sum.


\( P\left(A / B^{\prime}\right) \) is defined only when
\( A \cdot B \) is not a sure event
B. \( B \) is a sure event
c. \( B \) is an impossible event
D. \( B \) is not an impossible event


toppr
Q Type your question.
rumu ac shape ACB such that \( d<<l \). The
tension in the string is \( \mathrm{T} \) and the strain
produced in it is \( \varepsilon . \) If the Youngs modulus of the material of wire is \( Y \).
Then
This question has multiple correct options
A \( \cdot_{\varepsilon}=\frac{d}{2 l} \)
B. \( _{\varepsilon}=\frac{d^{2}}{2 l^{2}} \)
c. \( T=a Y\left(\frac{d}{2 l}\right) \)
D. \( T=a Y\left(\frac{d^{2}}{2 l^{2}}\right) \)


PUC certificate stands for
A. Pollution Under Control Certificate
B. Population Under Control Certificate
C. Population Under Coordinate Certificate
D. All of the above


A film of water is formed between two
straight parallel wires of length \( 10 \mathrm{cm} \)
each separated by \( 0.5 \mathrm{cm} \). If their separation is increased by \( 1 m m \) while still maintaining their parallelism how much work will have to be done of
water (Surface tension of water \( = \)
\( \left.7.2 \times 10^{-2} N / m\right) \)
A \( \cdot 7.22 \times 10^{-6} \mathrm{J} \)
В. \( 1.44 \times 10^{-5} \mathrm{J} \)
c. \( 2.88 \times 10^{-5} \mathrm{J} \)
D. \( 5.76 \times 10^{-5} J \)


\( 3.24636363 \ldots \) is
A. An integer
B. An irrational number
C. A rational number
D. Not a real number


Calculate the degree of ionization and \( \left[\boldsymbol{H}_{3} \boldsymbol{O}^{+}\right] \) of \( \mathbf{0 . 0 1} \boldsymbol{M} \boldsymbol{C H}_{3} \boldsymbol{C O O H} \)
solution. The equilibrium constant of acetic acid is \( 1.8 \times 10^{-5} \)


Evaluate: \( 96 a b c(3 a-12)(5 b-30) \div \)
\( \mathbf{1 4 4}(\boldsymbol{a}-\mathbf{4})(\boldsymbol{b}-\mathbf{6}) \)
\( \mathbf{A} \cdot 10 a b c \)
B. 2abc
\( c \cdot 2 a b \)
D. \( 2 b c \)


The F-Xe-F bond angle in \( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{4} \) is:
\( \mathbf{A} \cdot 109^{\circ} \)
B. \( 103^{\circ} \)
\( c .90^{\circ} \)
D. \( 60^{\circ} \)


The perimeter of a rhombus is \( 100 \mathrm{cm} \) and one of the diagonals is \( 40 \mathrm{cm} \) Then the area of the rhombus is
A. \( 1000 \mathrm{cm}^{2} \)
В. \( 500 \mathrm{cm}^{2} \)
c. \( 1200 \mathrm{cm}^{2} \)
D. \( 600 \mathrm{cm}^{2} \)


The cell functionally associated with sieve tube is
A. Phloem fibres
B. Phloem parenchyma
c. companion cell
D. collenchyma


Adrenaline is equivalent to which neurotransmitter?
\( A \cdot \) GABA
B. Serotonin
c. Epinephrine
D. None of the abaov


If \( e \) and \( e^{\prime} \) be the eccentricities of two
conics \( S=0 \) and \( S^{\prime}=0 \) and if \( e^{2}+ \)
\( e^{\prime 2}=3, \) then both \( S \) and \( S^{\prime} \) can be
A. hyperbolas
B. ellipses
c. parabolas
D. none of these


(a) Give two differences between Ideal
and non-Ideal solutions.
(b) Find out osmotic pressure of Glucose solutions of \( 5 \% \) solution at
\( 25^{\circ} \mathrm{C} \) temperature while molecular
mass of Glucose 180 and \( R=0.0821 \)
Litre Atmosphere.


A woolen cloth when rubbed against
plastic object acquires
charge.
A. Sometimes positive and sometimes negative
B. Negative
c. Positive
D. None of the these


\( f\left(\begin{array}{ccc}2 & -1 & 3 \\ -5 & 3 & 1 \\ -3 & 2 & 3\end{array}\right], \) then
\( A .(A d j A)= \)
A \( \cdot\left(A d j \cdot A^{T}\right) \)
B. \( (\text {Adj.A}) . A \)
c. \( |A| . A \)
D. None of these


A rectangular tank containing water is \( 5 \mathrm{m} \) long, \( 3 \mathrm{m} \) broad and \( 2 \mathrm{m} \) deep. Find how much the water will rise, if a block
of lead \( 1 \mathrm{m} \times 45 \mathrm{cm} \times 30 \mathrm{cm} \) is put in the
tank?
A. \( 9 \mathrm{cm} \)
B. \( 90 \mathrm{cm} \)
\( \mathrm{c} .9 \mathrm{mm} \)
D. 9 m


The IUPAC name of:
A. 3,4 -dimethylpentanoyl chloride
B. 1 -chloro-1-oxo- 2,3 -dimethylpentane
C. 2 -ethyl-3-methylbutanoyl chloride
D. 2,3 -dimethylpentanoyl chloride


Match the column I with column II and
select the correct option
colun column 1 1
(i)
Central National
Herbarium
(ii)
Royal Botanical
Garden \( \quad(\mathrm{q}) \quad \) Delhi
(iii) National Museum
of National History (r) Kolkata
(iv) Rajiv Gandhi
Zoological Park (s) Pune
A. (a) (i)-(r), (ii)-(s), (iii)-(p), (iv)-(q)
B. (b) (i)-(r), (ii)-(p), (iii)-(q), (iv)-(s)
C. (c) (i)-(p), (ii)-(s), (iii)-(q), (iv)-(r)
D. (d) (i)-(q), (ii)-(r), (iii)-(p), (iv)-(s)


Find the area of the region in the first quadrant enclosed by x-axis, the line \( x=\sqrt{3} y \) and the circle \( x^{2}+y^{2}=4 \)


iso-butylene when subjected to hydroboration oxidation reaction,
yields:
A. iso-butyl alcohol
B. sec-butyl alcohol
c. n-butyl alcohol
D. tert-butyl alcohol


Which of the following is not an ambident nucleophile?
\( \mathbf{A} \cdot O H^{-} \)
B. \( N O_{2}^{-} \)
c. \( C N^{-} \)
D. \( S C N^{-} \)


n figure OPQR is a rhombus, three of whose vertices lie on the circle with
centre \( 0 . \) If the area of rhombus is 32
\( \sqrt{3} \mathrm{cm}^{2}, \) find the radius of the circle.
\( 4.6 \mathrm{cm} \)
B. 2 cm
\( c .4 \mathrm{cm} \)
\( D \)


At absolute zero temperature:
A. only para hydrogen exists
B. only ortho hydrogen exists
C. both para and ortho hydrogen exist
D. none of these


A lawn roller in the form of a thin-walled
hollow cylinder of mass \( M \) is pulled horizontally with a constant horizontal
force \( \boldsymbol{F} \) applied by a handle attached to
the axle. Ifit rolls without slipping, find the acceleration and the friction force.


Na and Al are the examples of two metals which are manufactured by the electrolysis of their fused salts.
If true enter 1 , else enter 0 .


Five moles of Hydrogen initially at STP is compressed adiabatically so that its temperature becomes 673 K. The
increase in internal energy of the gas, in
\( \boldsymbol{k} \boldsymbol{J} \) is:
\( [R=8.3 J / m o l e-K ; \gamma=1.4 \) for
diatomic gas
A . 80.5
B. 21.55
c. 41.50
D. 65.55


Find the values of \( x \) for which \( \left|\begin{array}{ll}3 & x \\ x & 1\end{array}\right|= \) \( \left|\begin{array}{ll}\mathbf{3} & \mathbf{2} \\ \mathbf{4} & \mathbf{1}\end{array}\right| \)


The hormone involved in the active
water reabsorption in renal tubules
A. Anti-diuretic hormone
B. Vasopressin
c. Both A and B
D. Adrenaline


Prove that the eccentricity of the conic given by the general equation satisfies the relation \( \frac{e^{4}}{1-e^{2}}+4= \)
\( \frac{(a+b-2 h \cos \omega)^{2}}{\left(a b-h^{2}\right) \sin ^{2} \omega}, \) where \( \omega \) is the
angle between the axes.


The delay in recovery on removal of the
deforming force is called


Which of the following gases is used as preservative injuice of fruits \( \& \) jams?


Force that enable us to perform all activities like movement or bending of the body is
A . Gravitational force
B. Frictional force
c. Muscular force
D. Magnetic force


In the electrochemical cell shown above,
which of the following half-reactions
occurs at the anode?
\( \mathbf{A} \cdot C u^{2+}+e \rightarrow C u^{-} \)
B \( \cdot Z n(s) \rightarrow Z n^{2+}+2 e \)
\( \mathbf{c} \cdot Z n^{2+}+2 e \rightarrow Z n(s) \)
\( \mathbf{D} \cdot C u(s) \rightarrow C u^{2+}+2 e \)
E \( \cdot C u^{2+}+2 e \rightarrow C u(s) \)


\( \triangle A B C \sim \triangle D E F \) and their perimeters
are \( 32 \mathrm{cm} \) and \( 24 \mathrm{cm} \) respectively. If
\( A B=10 \mathrm{cm}, \) Find \( D E \)


Let \( \boldsymbol{\alpha}, \boldsymbol{\beta}, \boldsymbol{\gamma}, \boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c}, \boldsymbol{x} \boldsymbol{\epsilon} \boldsymbol{R} \) and let
\( \Delta= \)
\( \left|\begin{array}{ccc}\sin (x+\alpha) & \cos (x+\alpha) & a+x \sin \alpha \\ \sin (x+\beta) & \cos (x+\beta) & b+x \sin \beta \\ \sin (x+\gamma) & \cos (x+\gamma) & c+x \sin \gamma\end{array}\right| \)
then \( \Delta \) is
This question has multiple correct options
A. independent of \( x \)
B. dependent of \( \alpha, \beta, \),
c. dependent on \( a, b, c, c \)
D. \( a \) constant


How many significant figures will be there in the calculated solution of
following problem:
\( \frac{(29.2-20.2) \times\left(1.97 \times 10^{5}\right)}{1.39} ? \)
A. 3
B.
\( c \cdot 4 \)
D.


Animal dung contains:
A. Phosphorus
B. Nitrogen
c. sulphur
D. A and


Two particles \( A \) and \( B \) are placed as
shown in figure. The particle A on the
top of a tower of height H is projected horizontally with a velocity u and the particle B is projected along the horizontal surface towards the foot of
the tower, simultaneously. When particle A reaches at ground, it simultaneously hits particle B. Then the speed of projected particle B is:(neglect any type of friction)
A \( \cdot d \sqrt{\frac{g}{2 H}} \)
B. \( d \sqrt{\frac{g}{2 H}}-u \)
\( c \)
\[
\sqrt[d]{\frac{g}{2 H}+u}
\]
D.


In the given figure, \( A D=B C, A C= \)
BD. Then \( \triangle P A B \) is
A . equilateral
B. right angled
\( c . \) scalene
D. isosceles


The displacement-time graph of a
particle executing SHM is shown in the
figure. Then
This question has multiple correct options
A. the velocity is maximum at \( t=T / 2 \)
B. the acceleration is maximum at \( t=T \)
C. the force is zero at \( t=3 T / 4 \)
D. the potential energy equals the oscillation at t=T/2


Sound waves do not travel through:
A. solids
B. liquids
c. gases
D. vacuum


Novolac is:
A. a linear condensation product of phenol and formaldehyde
B. a cross linked condensation product of urea and formaldehyde
C . a cross linked condensation product of phenol and formaldehyde
D. a linear condensation product of urea and formaldehyde


Find the derivative of the following function at the indicated points. \( 2 \cos x \) at \( x=\frac{\pi}{2} \)


If a botanist want to study nomenclature of a similar species, the scientist will study
A. Syntype
B. Isotype
c. Neotype
D. Mesotype


Solve for \( \boldsymbol{x} \)
\( 2 \tan ^{-1} \frac{2 x}{1-x^{2}}=\pi \)


The diagram shown above represents the applied force per unit area with the
corresponding change \( \boldsymbol{X} \) (per unit length) produced in a thin wire of uniform cross-section in the curve
shown. The region in which the wire behaves like a liquid is :
\( A \cdot a \)
в. \( b c \)
\( c \cdot c d \)
D. \( O a \)


What kind of eclipse do we see when the moon is entirely within the Earth's umbral shadow?
A. Partial lunar
B. Total solar
c. Total lunar
D. Partial solar


Which one of the following features is shared by algae and fungi?
A. Autotrophism
B. Parenchymatous thallus
c. Embryo absent in life cycle
D. Reserve food matter in starch


The presence of carbon in an organic
compound is detected by heating it
with :
A. sodium metal to convert it to \( N a C N \)
B. \( C a O \) to convert it into \( C O \) which burns with a blue flame
c. \( C u O \) to convert it into \( C O_{2} \) which turns lime water milky
D. \( C u \) wire to give a bluish-green flame


Find the general solution of the
equation \( \sin 2 x+\sin 4 x+\sin 6 x=0 \)


mole of an ideal gas is subjected to a
reversible process as shown in the
figure. Calculate the work done (in
joule) in this process. \( [\ln 2=0.7] \)
A. 0.5 Joule
B. 6 Joule
c. 8 Joule
D. 0.8 Joule


How are the two atoms \( _{92}^{235} P \) and \( _{92}^{238} P \) similar?
(i) They have the same number of
protons
(ii) They have the same number of
neutrons
(iii) They have the same number of
electrons
A. Only (i)
B. Only (i) and (ii)
c. only (i) and (iii)
D. (i), (ii) and (iii)


\( \frac{\sigma}{\sigma} \)
\( \frac{\sigma}{\sigma} \)
\( \sigma \)


\( 1.5 \mathrm{g} \mathrm{Cd} \mathrm{Cl}_{2} \) was found to contain \( 0.9 \mathrm{g} \)
Cd. Calculate MO, atomic weight of Cd.
A . 118
B. 112
c. 106.5
D. 53.25


Name the property under multiplication used in each of the following. \( \frac{-19}{29} \times \frac{29}{-19}=1 \)


List two essential roles of ribosome
during translation.


Secondary cortex is derived from?
A . Intercalary meristem
B. Protoderm
c. Procambium
D. Phelloderm


Boyle's law holds good for an ideal gas during:
A. Isobaric changes
B. Isothermal changes
c. Isochoric changes
D. Isotopic changes


\( \mathbf{A} \)
1.00 molal aqueous solution of trichloroacetic acid \( \left(C C l_{3} C O O H\right) \) is heated to its boiling point. The solution
has the boiling point of \( 100.18^{\circ} \mathrm{C} \) Determine the van't Hoff factor for
trichloroacetic acid. \( \left(K_{b} \text { for water }=\right. \)
\( 0.512 \mathrm{K} \mathrm{kg} \mathrm{mol}^{-1} \) )


Two concentric hollow spherical shells have radii \( r \) and \( R(R>>r) . \) A charge
\( Q \) is distributed on them such that the
surface charge densities are equal. The electric potential at the centre is:
A \( \cdot \frac{Q(R+r)}{4 \pi \epsilon_{0}\left(R^{2}+r^{2}\right)} \)
B. \( \frac{Q\left(R^{2}+r^{2}\right)}{4 \pi \epsilon_{0}(R+r)} \)
c. \( \frac{Q}{R+r} \)
D.


The phenomenon of production of magnetic field on passing an electric current in a straight conducting wire is based on the law of
A. Faraday
B. Coulomb
c. Ampere
D. oersted


The first ionisation potential of \( \boldsymbol{N}, \boldsymbol{P}, \boldsymbol{O} \) and \( S \) are in the order of
\( \mathbf{A} \cdot S>P<O>N \)
В . \( N>O>P>S \)
c. \( N>O<P>S \)
D. \( N<O<P<S \)


Fresh water snakes are commonly
A. Viviparous
B. Less poisonous
c. Deadly poisonous
D. Non-poisonous


Fill in the blanks
\begin{tabular}{lllll}
S. no & cost price & Selling price & Profit & Loss \\
\hline (a) & Rs 1,200 & Rs Rs & Rs \\
(b) & 2,000 & & 800 & 180 \\
(c) & & Rs & Rs & \\
(d) & Rs & 5,100 & 850 & \\
& 10,800 & & Rs & 216
\end{tabular}


The magnet is strongest near the
A. Poles of the magnet
B. Ends of the magnet
C. Centre of the magnet
D. One quarter point from the poles of the magnet


Evaluate \( \lim _{x \rightarrow 0} \frac{\tan x}{x} \)


Lianas are
A. Weak stemmed trailers
B. Woody stemmed climbers and twiners
C . Trees with twisted stems
D. Plants with woody stems and medium height


The internal centre of similitude of two
circles \( (x-3)^{2}+(y-2)^{2}= \)
\( \mathbf{9},(\boldsymbol{x}+\mathbf{5})^{2}+(\boldsymbol{y}+\mathbf{6})^{2}=\mathbf{9} \) is
A \( \cdot(-1,-2) \)
B. (-2,-1)
c. (3,2)
(年. (3,2)
D. (-5,-6)


Let 'f' be a function defined from
\( \boldsymbol{R}^{+} \longrightarrow \boldsymbol{R}^{+} \cdot \boldsymbol{I} \boldsymbol{f}(\boldsymbol{f}(\boldsymbol{x} \boldsymbol{y}))=\boldsymbol{x}(\boldsymbol{f}(\boldsymbol{y}))^{2} \) for
all positive numbers \( x \) and \( y . I f f(2)= \) \( \operatorname{find} f(50)= \)
A . 20
B. 30
\( c .3 \)
D. 40


A cart of mass \( 20 \mathrm{kg} \) at rest is to be
dragged at a speed of \( 18 \mathrm{km} \mathrm{h}^{-1} \). If the co-efficient of friction between the cart
and the ground is \( 0.1, \) what is the minimum force required to drag the cart to a distance of \( 10 \mathrm{m} \) ? (Take \( g= \)
\( \left.10 m s^{-2}\right) \)


Why does the total amount of \( C O_{2} \) in the atmosphere remains constant even
though respiration liberates \( C O_{2} ? \)
\( A \cdot C O_{2} \) acts as a buffer
B. \( C O_{2} \) is converted to carbohydrates in photosynthesis
\( \mathrm{c} \cdot \mathrm{CO}_{2} \) forms carbonic acid
D. \( C O_{2} \) undergoes cleavage during photosynthesis


\( 28 g \) of \( N_{2} \) and \( 6 g \) of \( H_{2} \) were kept at
\( 400^{\circ} \mathrm{C} \) in 1 litre vessel, the equilibrium
mixture contained \( 27.54 g \) of \( N H_{3} . \) The
appropriate value of \( \boldsymbol{K}_{c} \) for the above reaction can be (in mole\( ^{-2} \) litre\( ^{2} \) )
\( \mathbf{A} \cdot 75 \)
B. 50
c. 25
D. 100


Common name of calcium oxychloride
is
(washing/bleaching) powder


The sum of \( n \) terms of three
arithmetical progression are \( S_{1}, S_{2} \) and
\( S_{3} . \) The first term of each is unity and
the common differences are 1,2 and 3
respectively. Prove that \( \left(\boldsymbol{S}_{1}+\boldsymbol{S}_{3}=\boldsymbol{2} \boldsymbol{S}_{2}\right) \)


Sulphuric acid reacts with sodium hydroxide as follows
\( H_{2} S O_{4}+2 N a O H \rightarrow N a_{2} S O_{4}+2 H_{2} O \)
When 1 L of 0.1 M sulphuric acid solution is allowed to react with 1 L of \( 0.1 \mathrm{M} \)
sodium hydroxide solution, the amount of sodium sulphate formed and its molarity in the solution obtained is ?
A. \( 0.1 \mathrm{molL}^{-1} \)
B. \( 7.10 g \)
c. 0.025 mol \( L^{-1} \)
D. \( 3.55 g \)


Which of the following forms a virtual and erect image for all positions of the object?
A. Convex lens
B. Plane mirror
c. Convex mirror
D. Concave mirror


A small candle, \( 2.5 \mathrm{cm} \) in size is placed
at \( 27 \mathrm{cm} \) in front of a concave mirror of
radius of curvature \( 36 \mathrm{cm} . \) At what
distance from the mirror should a
screen be placed in order to obtain a sharp image? Describe the nature and size of the image. If the candle is moved closer to the mirror, how would the
screen have to be moved?


An electric bulb works on the principle
of
A. Archimedes
B. heating effect of current
c. magnetic effect of current
D. none of these


Sapwood is
A. Outer functional part of secondary xylem
B. Inner non functional part of secondary xylem
C. Outer as well as inner part of secondary xylem
D. None of the above


The probability of student \( A \) passing an examination is \( \frac{2}{9} \) and of students, \( B \) passing is \( \frac{5}{9} . \) Assuming the two events:
\( A \) passes'. \( B \) passes' as independent, find the probability of both passing the examination.


What happened when a rubber band is
stretched?


Q Type your question.
projected towards the pulley'P' with an
initial velocity \( u_{0} \) then select incorrect option
A the string would become tight at \( t=\frac{2 u_{0}}{g} \)
3. the distance travelled by 'A' before the string is taut is \( \frac{u_{0}^{2}}{g} \)
c. the distance travelled by 'B' before string is taut is \( \frac{2 u_{0}^{2}}{g} \)
D. the common speed of the blocks just after the string i aut is \( \left[\frac{n+2}{n+1}\right] u_{0} \)


Identify the wrong pair of statements.
I) The number of stamens in 5 flowers of
Allium is equal to those in 5 flowers of Solanum.
Il) The microsporangia of Hibiscus and Asparagus are having 80 pollen grains each. Then the ratio of the number of
pollen grains produced from each stamen of these two plants is 1: 1
III) The ratio of the number of stamens
in the flowers of Pisum and Datura is 2: 1
IV) The number of carpels in a flower of Smilax is equal to the number of carpels in a cyathium inflorescence.
A. ॥I, IV
B . ।, ॥
\( c \cdot 1,1 \)
D. II, III


Find the following in \( 24 \% \) (w/v) of the
solution if the density of the solution is \( 1.06 g m l^{-1} \)
(a) Weight of solute
(b) Weight of solvent


A man rows upstream a distance of
\( 9 k m \) or downstream a distance of
\( 18 k m \) taking 3 hours each time. The
speed of the boat in still water is
A \( \cdot 7 \frac{1}{2} k m / h \)
В \( \cdot 6 \frac{1}{2} k m / h \)
c. \( _{5} \frac{1}{2} k m / h \)
D. \( 4 \frac{1}{2} k m / h \)


On the basis of following features identify the correct option:
I. It is stored in air-tight bags.
II. It is used in surgical bandages for setting fractured bones.
A. Plaster of paris
B. Gypsum
c. Dead burnt plaster
D. Both A and B


Kumaran went to a shop near his house on a bicycle. The bicycle made a lot of noise when he pedalled it. After coming home, he applied some oil on some parts of the bicycle. Then there was no noise, why?


Which one of the following roles is not charcteristic of an essential element?
A. Being a component of biomolecules
B. Changing the chemistry of soil
c. Being a structural component of energy related chemical compounds.
D. Activation or inhibition of enzymes.


Two blocks of steel A and B, A being two
times heavier than \( \mathrm{B} \), are at \( 40^{\circ} \mathrm{C} \). The
ratio of heat content of \( A \) to \( B \) is:
\( A \cdot 1 \)
B. 4
\( c \cdot 2 \)
D.


Which of the following statements are
correct?
This question has multiple correct options
A. Electron density in \( X Y \) plane of \( 3 d_{x^{2}-y^{2}} \) orbital is zero.
B. Electron density in \( X Y \) plane of \( 3 d_{z^{2}} \) orbital is zero.
C. \( 2 s \) orbital has only one spherical node.
D. For \( 2 p_{z} \) orbital \( Y Z \) is the nodal plane.


If
\( \boldsymbol{\theta} \) and \( \phi \) are angles in the 1 st quadrant such that \( \tan \theta=\frac{1}{7} \) and \( \sin \phi=\frac{1}{\sqrt{10}} \)
\( \mathbf{A} \cdot \theta+2 \phi=90^{\circ} \)
B . \( \theta+2 \phi=60^{\circ} \)
c. \( \theta+2 \phi=30^{\circ} \)
D. \( \theta+2 \phi=45^{\circ} \)


A solenoid is
A . an electromagnet
B. a temporary magnet
C. a permanent magnet
D. Both 1 and 2


Super glue or crazy glue is:
A . polymethyl methacrylate
B. polyethyl acrylate
C . polymethyl \( \alpha \) -cyanoacrylate
D. polyethyl methacrylate


Define vital capacity. What is its
significance?


\( \mathbf{1 f} \mathbf{A}=\left[\begin{array}{ccc}\mathbf{1} & \mathbf{5} & \mathbf{- 6} \\ \mathbf{- 8} & \mathbf{0} & \mathbf{4} \\ \mathbf{3} & \mathbf{- 7} & \mathbf{2}\end{array}\right] \) then the
cofactors of the elements 3,-7,2 are
p,q,r respectively their ascending order
is
\( \mathbf{A} \cdot \mathbf{p}, \mathbf{r}, \mathbf{q} \)
B. \( \mathrm{q}, \mathrm{r}, \mathrm{p} \)
\( c \cdot p, q, r \)
\( D \cdot r, p, q \)


Mary says "The number I am thinking is divisible by 2 or it is divisible by \( 3 " \). This statement is false if the number Mary is
thinking of is
\( A \cdot 6 \)
B. 8
\( c \cdot 11 \)
D. 15


A man throws a ball weighing \( 500 g \)
vertically upwards with a speed of \( 10 m / s \)
(i) what will be its initial momentum?
(ii) What would be its momentum at the
highest point of its flight?


A liquid of specific heat 0.3 at \( 90^{\circ} \mathrm{C} \) is
mixed with another liquid of specific
heat 0.5 at \( 15^{\circ} \mathrm{C} \). If the final
temperature of the mixture is \( 60^{\circ} \mathrm{C} \)
then find the ratio of masses of the two
liquids mixed.


Find the equation of the circle drawn on the intercept made by the line \( 2 x+ \) \( 3 y=6 \) between the coordinate axes as
diameter.


The correct molecular shape for the
molecule \( X e O F_{4} \)
A . tetrahedral
B. trigonal pyramidal
c. trigonal bipyramidal
D. square pyramidal
E. flat


If \( x^{2}-2 x^{2} y^{2}+5 x+y-5=0 \) and
\( \boldsymbol{y}(1)=1, \) then
This question has multiple correct options
A \( \cdot y^{\prime}(1)=1 \)
в. \( y^{\prime \prime}(1)=-\frac{4}{3} \)
c. \( \quad y^{\prime \prime}(1)=-\frac{22}{3} \)
D. \( y^{\prime}(1)=\frac{2}{3} \)


Find how the normal acceleration of the
balloon varies as a function of the
height of ascent.
\( \mathbf{A} \cdot \omega_{n}=\frac{a v_{0}}{\sqrt{1+\left(\frac{a_{y}}{v_{0}}\right)^{2}}} \)
B. \( \omega_{n}=\frac{2 a v_{0}}{\sqrt{1+\left(\frac{a_{y}}{v_{0}}\right)^{2}}} \)
\( ^{\mathbf{C}} \cdot_{\omega_{n}}=\frac{3 a v_{0}}{2 \sqrt{1+\left(\frac{a_{y}}{v_{0}}\right)^{2}}} \)
D \( \cdot \omega_{n}=\frac{a v_{0}}{2 \sqrt{1+\left(\frac{a_{y}}{v_{0}}\right)^{2}}} \)


The radius of a circle with centre 0 is 5
\( \mathrm{cm} \) (given figure). Two radii OA and \( \mathrm{OB} \)
are drawn at right angles to each other.
Find the areas of the segment made by the chord \( A B \text { (Take } \pi=3.14) \)


If \( A \) is a skew symmetric matrix of order
3, then the value of \( |\boldsymbol{A}| \) is
A . 3
B. 0
\( c .9 \)
D. 27


The electric field in a region is radially outwards and has a magnitude \( \boldsymbol{E}=\boldsymbol{K} \boldsymbol{r} \)
The charge contained in a sphere of radius \( a \) is :
A. \( K 4 \pi \varepsilon_{0} a^{2} \)
В \( \cdot \quad K \frac{4}{3} \pi \varepsilon_{0} a^{3} \)
c. \( K 4 \pi \varepsilon_{0} a^{3} \)
D. none of these


Insulin contains \( 3.4 \% \) sulphur. The
minimum molecular mass of insulin is
A. 940
в. 350
\( c .470 \)
D. 560


Explain with the help of an activity the nature of metallic oxides or hydroxide and non metallic oxide by using metal as sodium and non metal as sulphur.


\( \lim _{x \rightarrow \frac{\pi}{3}} \frac{\sqrt{3} \cos x-\sin x}{1-2 \cos x} \)


The co-efficient of \( x^{53} \) in the expression \( \sum_{m=0}^{100} 100 c_{m}(x-3)^{100-m} 2^{m} \) is
B. \( 98_{c_{53}} \)
\( \mathbf{c} .^{65} \sigma_{53} \)
D. \( 100 c_{65} \)


Choose the correct answer from the
alternatives given The lac operon is transcribed when
A. lactose is needed by the cell
B. lactose is available to the cell
c. lactose is unavailable to the cell
D. lactic acid is available to the cell


A particle of mass \( \mathrm{m} \) is tied to a string of length L. The free end of the string is fixed and the particle is whirled in a circular path. The speed of the particle increases from \( 5 \mathrm{m} / \mathrm{s} \) to \( 10 \mathrm{m} / \mathrm{s} \) for 5
secs. The motion is
A. Uniform circular motion
B. Non-uniform circular motion
c. Non uniformly accelerated motion
D. Non of these


A mixture of \( L i_{2} C O_{3} \) and \( K_{2} C O_{3} \) on
strong heating gave 0.25 mole of \( C O_{2} \)
The mole \( \% \) of \( L i_{2} C O_{3} \) and \( C O_{2} \) in the
mixture is :
\( \begin{array}{lll}\text { A } \cdot L i_{2} C O_{3}: 25 \% & K_{2} C O_{3}: 75 \%\end{array} \)
B . \( L i_{2} C O_{3}: 75 \% \quad K_{2} C O_{3}: 25 \% \)
\( \mathrm{c} \cdot L i_{2} C O_{3}: 60 \% \quad K_{2} C O_{3}: 40 \% \)
D. \( L i_{2} C O_{3}: 40 \% \quad K_{2} C O_{3}: 60 \% \)


The portion of a line intercepted between the coordinate axes is divided by the point (2,-1) in the ration \( 3: 2 . \) The
equation of the line is :
A. \( 5 x-2 y-20=0 \)
В. \( 2 x-y+7=0 \)
c. \( x-3 y-5=0 \)
D. \( 2 x y+y-4=0 \)


The equation \( y=A \sin ^{2}(k x-\omega t) \)
represents a wave with
A. amplitude A frequency \( \omega / 2 \pi \)
B. amplitude A /2 frequency \( \omega / \pi \)
c. amplitude 2A frequency \( \omega / 4 \pi \)
D. It does not represent a wave motion


ff \( 2\left[\begin{array}{ll}3 & 4 \\ 5 & x\end{array}\right]+\left[\begin{array}{ll}1 & y \\ 0 & 1\end{array}\right]=\left[\begin{array}{cc}7 & 0 \\ 10 & 5\end{array}\right] \)
matrices. Find the value of \( x \& y \)


Two cells of emf \( 1.5 v \) and \( 2.0 v \) have
internal resistances \( 0.2 \Omega \) and \( 0.3 \Omega \)
respectively are connected in parallel. Calculate the emf and internal
resistance of the equivalent cell?


Which of the following exhibit minimum number of oxidation states:
A. Mn
B. Np
c. Th
D. cr


A wire is stretched through 1 mm by certain load. The extension produced in the wire of same material with double
the length and radius will be
\( \mathbf{A} \cdot 4 m m \)
B. \( 3 m m \)
\( \mathbf{c} \cdot 1 m m \)
D. \( 0.5 m m \)


A disc of radius \( 0.2 m \) is rolling with
slipping on a flat horizontal surface, as shown in figure. The instantaneous
centre of rotation is: (the lowest contact
point is 0 and centre of disc is \( C \) )
A . zero
B. \( 0.1 m \) above 0 on line 0 C
c. \( 0.2 m \) below o on line oc
D. \( 0.2 m \) above 0 on line 0 c


Can you think of two particles which do
not exert gravitational force on each
other?


The image formed by convex lens in a simple microscope is ...... erect and
A. Virtual, magnified
B. Real, magnified
c. Virtual, diminished
D. Real, diminished


\( N_{2} \) can be obtained by heating
\( \left(N H_{4}\right)_{2} C r_{2} O_{7} \)


An elastic spring is given a force of 1000
N over an area of \( 0.2 m^{2} \)
A. \( 3000 N m^{-2} \)
B. \( 5000 \mathrm{Nm}^{-2} \)
c. \( 500 N m^{-2} \)
D. \( 2500 N m^{-2} \)


The degree and order of the differential equation \( \left[1+\left(\frac{d y}{d x}\right)^{3}\right]^{7 / 3}=7\left(\frac{d^{2} y}{d x^{2}}\right) \)
respectively are:
A. 3 and 7
B. 3 and 2
\( c .7 \) and 3
D. 2 and 3


Simplify \( 2 \frac{2}{7} \div 1 \frac{4}{11} \times 2 \frac{4}{9} \)


Explain the reason which ray of light wil
be transmitted through the face \( A B \) the
refractive index of the prism for red,
green, blue are \( 1.39,1.42,1.47 ? \sin \)
\( \mathbf{7 1}=\mathbf{4 6}^{\circ}, \sin . \mathbf{7 0}=\mathbf{4 4}^{\circ}, \operatorname{sin.67}=\mathbf{4 2}^{\circ} \)


\( \mathbf{2} N \boldsymbol{a} \boldsymbol{O} \boldsymbol{H}+\boldsymbol{S} \boldsymbol{O}_{2} \rightarrow ? \)
A \( \cdot N a_{2} O+H_{2}+S O_{2} \)
в. \( N a_{2} S O_{3}+H_{2} O \)
c. \( N a_{2} S O_{3}+H_{2} \)
D. \( N a_{2} O+H_{2}+O_{2} \)


\( \left|\begin{array}{ccc}\mathbf{2}^{3} & \mathbf{3}^{3} & \mathbf{3 . 2}^{\mathbf{2}}+\mathbf{3 . 2}+\mathbf{1} \\ \mathbf{3}^{\mathbf{3}} & \mathbf{4}^{\mathbf{3}} & \mathbf{3 . 3}^{\mathbf{2}}+\mathbf{3 . 3}+\mathbf{1} \\ \mathbf{4}^{\mathbf{3}} & \mathbf{5}^{\mathbf{3}} & \mathbf{3 . 4}^{\mathbf{2}}+\mathbf{3 . 4}+\mathbf{1}\end{array}\right| \) is equal to
\( A \)
B.
\( c \cdot 2 \)
D. 3


Consider the reaction of trans-2-butene
with \( B r_{2} \) in \( C H_{2} C l_{2} . \) Which statement
concerning this reaction is correct?
A. The product is optically active because it possesses two chirality centers.
B. The product is optically inactive because it is a racemic mixture of enantiomers.
C. The product is optically inactive because it is meso.
D. The product is optically inactive because it does not possess any chirality centers.


A thin layer of water is transparent but a very thick layer of water is
A. Translucent
в. ०раяче
c. Most transparent
D. None of these


Compare the solubility and thermal stability of alkali metals carbonates with those of the alkaline earth metals
nitrates.


Two hailstones with radii in the ratio of
: 2 fall from a great height through the atmosphere. Then the ratio of their
momentum after they have attained terminal velocity is
A . 1:
B. 1: 4
\( c \cdot 1: 16 \)
D. 1: 32


If \( \vec{r}=3 \vec{i}+2 \vec{j}-5 \vec{k}, \vec{a}=2 \vec{i}-\vec{j}+\vec{k} \)
\( \vec{b}=\vec{i}+3 \vec{j}-2 \vec{k} \) and \( \vec{c}=-2 \vec{i}+\vec{j}-3 \vec{k} \)
such that \( \vec{r}=\lambda \vec{a}+\mu \vec{b}+\nu \vec{c} \) then
A \( \cdot \mu, \frac{\lambda}{2}, \nu \) are in \( A P \)
B. \( \lambda, \mu, \nu \) are in \( A P \)
c. \( \lambda, \mu, \nu \) are in \( H P \)
D. \( \mu, \lambda, \nu \) are in \( G P \)


Define the current sensitivity of a
galvanometer. Write S.I unit
Figure shows two circuits each having a
galvanometer and a battery of \( 3 \mathrm{V} \)
When the galvanometer in each
arrangement do not show any deflection
obtain the ratio \( \boldsymbol{R}_{1} / \boldsymbol{R}_{2} \)


Which group of periodic table contains no metal?
A. IA
в. IIIA
c. VIIA
D. vıl


Number should be added top \( \frac{-5}{7} \) to get \( \frac{-2}{3} \) is \( \frac{1}{x} . \) Find 'x?


\( \mathbf{f} A=\left[\begin{array}{cc}\frac{-\mathbf{1}+i \sqrt{\mathbf{3}}}{\mathbf{2} i} & \frac{-\mathbf{1}-i \sqrt{\mathbf{3}}}{\mathbf{2} i} \\ \frac{\mathbf{1}+i \sqrt{\mathbf{3}}}{\mathbf{2} i} & \frac{\mathbf{1}-i \sqrt{\mathbf{3}}}{\mathbf{2} i}\end{array}\right], i= \)
\( \sqrt{-i} \) and \( f(x)=x^{2}+2, \) then \( f(A) \) is
equal to
\( ^{A} \cdot\left(\frac{5-i \sqrt{3}}{2}\right)\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right] \)
\( ^{\text {В }} \cdot\left(\frac{3-i \sqrt{3}}{2}\right)\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right] \)
c. \( \left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right] \)
D. \( (2+i \sqrt{3})\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right] \)


Assertion
Charge on all the condensers connected in series is the same.
Reason
Charge present on a capacitor is directly proportional to its capacitance
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


If \( f:\left(-\frac{\pi}{2}, \frac{\pi}{2}\right) \rightarrow(-\infty, \infty) \) is defined
by \( f(x)=\tan x, \) then \( f^{-1}(2+\sqrt{3})= \)
\( A \cdot \frac{\pi}{12} \)
в.
c. \( \frac{5 \pi}{12} \)
D.


A object of mass \( 1 \mathrm{kg} \) and radius \( 1 \mathrm{m} \) is falling vertically downward inside liquid in a gravity free space. At t=0 velocity of
the sphere is \( 2 m s^{-1} . \) If the of viscosity
of the liquid is \( \frac{1}{18 \pi} \) Pas, the velocity of
the ball will become \( 0.5 \mathrm{ma}^{-1} \) after a
time (in second)
\( A \cdot \ln 4 \)
B. \( 2 \ln 4 \)
\( c \cdot 3 \ln 4 \)
D. \( 3 \ln 2 \)


Assertion
An AND gate is a universal gate.
Reason
The boolean expression for AND gate is
\( A \cdot B=C \)
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is
not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


State true or false:
In \( \triangle A B C, A D \) is the median and \( D E \)
is parallel to \( B A \), where \( E \) is a point in \( A C \) and Hence \( B E \) is Parallel to BC
A. True
B. False


The concept of displacement current
introduced by Maxwell removes
asymmetry between
A. Gauss's law in electrostatics and Gauss's law in magnetism
B. Faraday's law and Ampere' law
C. Gauss's law and Ampere's law
D. Gauss's law and Faraday's law


Find the greatest value assumed by the function \( \boldsymbol{w}=\left|\boldsymbol{z}-\frac{\boldsymbol{4}}{\boldsymbol{z}}\right|=\mathbf{2} \) where \( \mathbf{z} \) is
a complex variable.


The range of values of p for which the
equation \( \sin \cos ^{-1}\left(\cos \left(\tan ^{-1} x\right)\right)=p \)
has a solution is
\( A \cdot\left(-\frac{1}{\sqrt{2}}, \frac{2}{\sqrt{2}}\right) \)
в. [0,1)
c. \( \left(\frac{1}{\sqrt{21}}\right) \)
D. (-1,1)


Find the largest value of \( x \) for which
\( 2(x-1) \leq 9-x \) and \( x \in W \)


Multiply \( (5-2 x) \) and \( (3+x) \)
A. \( 15-x+2 x^{2} \)
B . \( 15-x-x^{2} \)
c. \( 15-x-2 x^{2} \)
D. \( 15-x+x^{2} \)


A sphere with diameter \( 50 \mathrm{cm} \)
intersects a plane \( 14 \mathrm{cm} \) from the center of the sphere. What is the
number of square centimeters in the area of the circle formed?
A . \( 49 \pi \)
в. \( 196 \pi \)
c. \( 429 \pi \)
D. \( 576 \pi \)
E . \( 2304 \pi \)


In a series circuit, \( \boldsymbol{R}=\mathbf{3 0 0 \Omega}, \boldsymbol{L}= \)
\( \mathbf{0 . 9 H}, \boldsymbol{C}=\mathbf{2 . 0 \mu} \boldsymbol{F} \) and \( \boldsymbol{\omega}=\mathbf{1 0 0 0 r a d} / \boldsymbol{s} \)
The impedance of the circuit is
A . \( 1300 \Omega \)
в. \( 900 \Omega \)
\( \mathbf{c} .500 \Omega \)
D. \( 400 \Omega \)


Choose the incorrect statement related
to the image formed by a plane mirror:
This question has multiple correct options
A. a plane mirror always forms a virtual image
B. the image formed by a plane mirror may be magnified or diminished
C. the image formed by a plane mirror is always unmagnified and laterally inverted
D. the image formed by a plane mirror is always unmagnified and erect


Solve the following equations. \( \sin \frac{x}{2} \cos 2 x+\sin ^{2} x \cos \frac{x}{2}= \)
\( \cos ^{2} x \cos \frac{x}{2} \)


Answer the following questions briefly. Name the different layers of atmosphere.


Which of the following when stretched, break into pieces?
A. Calcium
B. Phosphorus
c. Iron
D. Radium


Bacterial infection on eye surface is
protected by the enzyme:
A . urease
B. carbonic anhydrase
c. lysozyme
D. xymase


How many of the following letters have rotational symmetry of order more than
1?
\( \mathrm{R}, \mathrm{B}, \mathrm{F}, \mathrm{H}, \mathrm{O}, \mathrm{P}, \mathrm{S}, \mathrm{W}, \mathrm{X}, \mathrm{Z}, \mathrm{N} \)
A .4
B. 9
\( c .5 \)
\( D \)


An element A has atomic number 7. It
will have properties similar to the element with the atomic number:
A. 85
B. 57
\( c \cdot 26 \)
D. 51


Solve the differential equation: \( \boldsymbol{y} \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}= \)
\( \frac{\boldsymbol{x}}{\boldsymbol{e}^{\boldsymbol{y}}} \)


Two rain drops reach the earth with
different terminal velocities having
ratio \( 9: 4 . \) Then the ratio of their volume
is:
A .3: 2
B . 4: 9
c. 9: 4
D. 27: 8


Which of the following planets takes
minimum time to take one revolution
around the Sun?
A. Mercury
B. Jupiter
c. saturn
D. Pluto


The variable which takes some specific values is called
A. discrete random variable
B. continuous random variable
c. both A and B
D. none


toppr I
Q Type your question
a. \( \boldsymbol{C H}_{\mathbf{3}}-\boldsymbol{S}-\boldsymbol{C H}_{\mathbf{3}} \)
b. \( \boldsymbol{C H}_{\mathbf{3}}-\boldsymbol{C N} \)
c. \( \boldsymbol{C H}_{\mathbf{3}}-\boldsymbol{C u} \)
\( \mathbf{A} \cdot \) a. \( C H_{3}-\tilde{S}-C H_{3} \rightarrow \stackrel{\oplus}{C} H_{3}+\stackrel{\ominus}{S} C H_{3} \)
b. \( C H_{3}-\tilde{C} N \rightarrow C H_{3}+\stackrel{\ominus}{C} N \)
c. \( C \hat{H}_{3}-C u \rightarrow \stackrel{\ominus}{C} H_{3}+C u \)
\( (C u \text { is more electropositive than } C) \)
B \( \cdot \) a. \( C H_{3}-S-C H_{3} \rightarrow \stackrel{\ominus}{C} H_{3}+\stackrel{\oplus}{S} C H_{3} \)
\( \mathrm{b} . \mathrm{CH}_{3}-\widetilde{\mathrm{C}} \mathrm{N} \rightarrow^{\oplus} \mathrm{CH}_{3}+^{\ominus} \mathrm{C} N \)
c. \( C \stackrel{\hat{H}_{3}}{-C u} \rightarrow \stackrel{\oplus}{C H_{3}}+C u \)
\( (C u \text { is more electropositive than } C) \)
\( \mathbf{c} \cdot \) а. \( C H_{3}-\tilde{S}-C H_{3} \rightarrow \stackrel{\oplus}{C} H_{3}+\stackrel{\ominus}{S} C H_{3} \)
\( \mathrm{b} . \mathrm{CH}_{3}-\widetilde{\mathrm{C}} \mathrm{N} \rightarrow \stackrel{\oplus}{\mathrm{C}} \mathrm{H}_{3}+^{\ominus} \mathrm{C} N \)
c. \( C \hat{H}_{3}-C u \rightarrow \stackrel{\ominus}{C} H_{3}+C u \)
\( (C u \text { is more electropositive than } C) \)
D. a. \( C H_{3}-S-C H_{3} \rightarrow C H_{3}+S C H_{3} \)
b. \( C H_{3}-\tilde{C} N \rightarrow C H_{3}+\stackrel{\ominus}{C} N \)
c. \( C \stackrel{\Omega}{H}_{3}-C u \rightarrow \stackrel{\oplus}{C} H_{3}+C u \)
\( (C u \text { is more electronegative than } C) \)


Choose the correct alternative:
The tax on goods and services purchased and is usually a certain percentage added to buyer's cost.
A. vat
B. Sales tax
c. Property tax
D. None


A shopkeeper buys an article at a discount of \( 30 \% \) from the wholesaler
(the printed price of the article being \( R s .2,000) \) and paid sales-tax at the
rate of \( 8 \% \). The shopkeeper sells the article to a buyer at the printed price
and charges tax at the same rate. Find the VAT (Value Added Tax) paid by the shopkeeper


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


Which term of the sequence
\( 114,109,104 \dots \dots \) is the first negative
term


If \( \boldsymbol{f}: \boldsymbol{Z} \rightarrow \boldsymbol{Z} \) is defined by \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{ll}\frac{x}{2} & \text { if } x \text { is even } \\ 0 & \text { if } x \text { is odd }\end{array} \text { then } f \) is \right.
A. onto but not one to one
B. One to one but not onto
c. one to one and onto
D. Neither one to one nor onto


Dominant producers of neritic zone of
sea are the
A. Phytoplankton
B. Zooplankton
c. Microorganisms
D. Diatoms


Write two demerits of arithmetic mean.


Why the elements of group 17 are coloured?


The local maximum value of \( x(1-x)^{2}, 0 \leq x \leq 2 \) is
\( A \cdot 2 \)
в. \( \frac{4}{27} \)
\( c .5 \)
D. \( 2, \frac{4}{27} \)


State whether true or false:
The particle is moving simple harmonically
A. True
B. False


A molecule having three differential chiral carbon atoms, how many stereoisomers it will have?
\( A \cdot 8 \)
B. 3
\( c .9 \)
D. 6


Find the circumference of a circle
whose area is \( 301.84 \mathrm{cm}^{2} \)


In which period of the periodic table,will an element, be found whose
differentiating electron is a \( 4 \mathrm{d} \) electron?


A particle moves in the \( x \) -y plane with the velocity \( \overrightarrow{\boldsymbol{v}}=\boldsymbol{a} \hat{\boldsymbol{i}}+\boldsymbol{b} \boldsymbol{t} \hat{j} . \) AT the instant
\( \mathrm{t}=a \sqrt{3} / b \) the magnitude of tangential normal and total acceleration are


Evaluate:
\( \int \frac{5 x+3}{\sqrt{x^{2}+4 x+10}} d x \)


Closing cells are found in
A. Stomata
B. Sieve
C. Lenticels
D. wounded areas


A vessel of uniform cross-section of
length \( 500 \mathrm{cm} \) as shown in figure is
divided in two parts by a weightless \( \& \) frictionless piston. One part contains 5
mole of \( N_{2}(g) \) and other part contains 2
moles of \( \boldsymbol{H}_{2}(\boldsymbol{g}) \& 1 \) mole of \( \boldsymbol{H} \boldsymbol{e}(\boldsymbol{g}) \)
gaseous mixture at the same
temperature and pressure.
What is the length of \( N_{2} \) compartment? (Assume volume of piston to be engligible)
A. \( 187.5 \mathrm{cm} \)
B. 300 \( c m \)
c. \( 312.5 \mathrm{cm} \)
D. none of these


Sum of first 14 terms of an \( A P \) is 1505
and it first term is \( 10 . \) Find its \( 25^{t h} \) term


Which of the following is used in automobile battery casings?
A. HDPE
B. PP
c. PVC
D. Polyester


In the figure shown the radius of
curvature of the left \( \& \) right surface of
the concave lens is \( 10 \mathrm{cm} \& 15 \mathrm{cm} \)
respectively. The radius of curvature of
the mirror is \( 15 \mathrm{cm} \)
A. Equivalent focal length of the combination is \( 18 \mathrm{cm} \)
B. Equivalent focal length of the combination is \( +36 \mathrm{cm} \)
c. The system behaves like a concave mirror
D. The system behaves like a convex mirror


A \( 1 \mathrm{cm} \) height needle is placed at a
distance of \( 0.1 ~ m \) from a convex mirror
of focal length 0.05 m, then size of the
image is
A. \( 1 \mathrm{cm} \)
в. \( 0.66 \mathrm{cm} \)
\( \mathrm{c} .0 .33 \mathrm{cm} \)
D. \( 0.5 \mathrm{cm} \)


The relative permeability of a material is
\( 0.9 . \) The material is
A. diamagnetic
B. para magnetic
c. ferro magnetic
D. non-magnetic


If \( x=\sqrt{2}-1, y=1-\sqrt{3} \) and \( z= \)
\( \sqrt{3}-\sqrt{2}, \) find \( x^{3}+y^{3}+z^{3}-x y z \)


Prove that the ratio of slope of adiabatic
curve to slope of isothermal is \( \gamma \)


Find the wavelength associated with an electron which has mass \( 9.1 \times 10^{-28} g \)
and is moving with a velocity of \( 10^{5} \mathrm{cm} \) \( \sec ^{-1} .\left(\text {Given: } h=6.625 \times 10^{-27} \) erg \right.
\( \sec \)
A \( . \lambda=5.28 \times 10^{-5} m \)
в. \( \lambda=7.28 \times 10^{-5} \mathrm{cm} \)
c. \( \lambda=7.28 \times 10^{-5} m \)
D. \( \lambda=5.28 \times 10^{-5} \mathrm{cm} \)


The objective function \( z=x_{1}+x_{2} \)
subject to \( \boldsymbol{x}_{1}+\boldsymbol{x}_{2} \leq \mathbf{1 0},-\mathbf{2} \boldsymbol{x}_{\mathbf{1}}+\mathbf{3} \boldsymbol{x}_{2} \leq \)
\( \mathbf{1 5}, \boldsymbol{x}_{1} \leq \mathbf{6}, \boldsymbol{x}_{1}, \boldsymbol{x}_{2} \geq \mathbf{0} \) has maximum
value \( \ldots \ldots . . . . . . . . . \) of the feasible region.
A. at only one point
B. at only two points
c. at every point of the segment joining two points
D. at every point of the line joining two points


The displacement \( x \) of a particle moving in one dimension under constant acceleration is related to the
time \( t \) as \( t=\sqrt{x}+3 . \) The displacement of the particle when its velocity is zero is
A . zero
B. 3 units
c. \( \sqrt{3} \) units
D. 9 units


If the distance travelled by an object is zero, then the displacement of the object is
A. zero
B. not zero
c. negative
D. may or may not be zero


With increase in pressure
This question has multiple correct options
A. solubility of solids in liquids is unaffected
B. solubility of solids decreases
C . solubility of gases decreases in liquids
D. solubility of gases in liquids increases


For adiabatic expansion of a monoatomic perfect gas, the volume increases by \( 2.4 \% . \) What is the percentage decreases in pressure?
A . \( 2.4 \% \)
в. \( 4.0 \% \)
c. \( 4.8 \% \)
D. \( 7.1 \% \)


A drop of water of radius \( r \) is falling
through the air of coefficient of viscosity \( \eta \) with a constant velocity of \( v \)
The resultant force on the drop is:
A \( \cdot \frac{1}{6 \pi \eta r v} \)
в. \( 6 \pi \eta r v \)
c. \( \sqrt{6 \pi \eta r v} \)
D. zero


A charged spherical conductor has a
surface charge density of \( 0.07 C / m^{2} \)
When its charge is increased by \( 0.44 C \) the charge density changes by 0.14 \( C / m^{2} . \) The radius of the sphere is :
A . \( 5 \mathrm{cm} \)
в. \( 10 m \)
c. \( 0.5 m \)
D. \( 5 m \)


A parallel plate capacitor contains a mica sheet \( \left(\text { thickness } 10^{-3} m\right) \) and \( a \)
sheet of fiber (thickness \( 0.5 \times 10^{-3} m \) ).
The dielectric constant of mica is 8 and
that of the fiber is \( 2.5 . \) Assuming that the fiber breaks down when subjected to an electric field of \( 6.4 \times 10^{6} V m^{-1} \)
find the maximum safe voltage (in
kV) that can be applied to the capacitor.


A ball placed on a table starts rolling when table is tilted. Which is the force
which causes this motion?
A. friction
B. push by table
c. rolling force
D. gravitational pull by earth


Elements having a single electron in their outermost shell is :
A. \( L \)
B.
c. Na
D. all of these


Three balls are drawn at random from a
collection of 7 white, 12 green and 4 red balls. The probability that each is different colour is
A \( \cdot \frac{48}{253} \)
в. \( \frac{64}{253} \)
c. \( \frac{23}{253} \)
D. \( \frac{56}{253} \)


Let \( A \) be a square matrix all of whose
entries are integers. Then, which one of
the following is true?
\( \mathbf{A} \cdot \) If \( \operatorname{det} A=\pm 1, \) then \( A^{-1} \) exists and all its entries are
integers
B. If \( \operatorname{det} A=\pm 1, \) then \( A^{-1} \) need not exist
C. If \( \operatorname{det} A=\pm 1, \) then \( A^{-1} \) exists but all its entries are
not necessarily integers
D. If det \( A \neq\pm 1 \), then \( A^{-1} \) exists and all its entries are non-integers


The lengths of the sides of a triangle are proportional to the numbers 5,12 and \( 13 . \) The largest side of the triangle exceeds the smallest side by \( 1.6 \mathrm{m} \) Find the perimeter and the area of the triangle.


\( 40 g \) of ice at \( 0^{\circ} C \) is used to bring down
the temperature of certain mass of
water at \( 60^{\circ} \mathrm{C} \) to \( 10^{\circ} \mathrm{C} \). Find the mass
of water used.
[Specific heat capacity of water \( = \) \( 4200 J K g^{-1} C^{-1} \)
[Specific latent heat of fusion of ice \( = \)
\( \left.336 \times 10^{3} J k g^{-1}\right] \)


If \( y=e^{m \sin ^{-1} x} \) then show that \( (1- \)
\( \left.\boldsymbol{x}^{2}\right) \boldsymbol{y}_{\boldsymbol{n}+\mathbf{2}}-(\boldsymbol{2} \boldsymbol{n}+\mathbf{1}) \boldsymbol{x} \boldsymbol{y}_{\boldsymbol{n}+\mathbf{1}}-\left(\boldsymbol{n}^{2}+\right. \)
\( \left.\boldsymbol{m}^{2}\right) \boldsymbol{y}_{n}=\mathbf{0} \)


Choose the correct answers from the
alternatives given. Mycologists are specialists in the study
of:
A . plants
B. fungi
c. algae
D. protists


The lewis acid nature is maximum in:
A. \( A l C l_{3} \)
в. \( B C l_{3} \)
c. \( G a C l_{3} \)
D. \( \operatorname{InCl}_{3} \)


Area enclosed between the curves \( y= \)
\( 8-x^{2} \) and \( y=x^{2}, \) is:
A . \( 32 / 3 \)
B. \( 64 / 3 \)
c. \( 30 / 4 \)
D.


The distance between the sun and the
earth is -
A. 200 million kilometres
B. 150 million kilometres
c. 1.4 light years
D. 3 billion kilometres


\( e+C H_{3} O H^{H C l(g)} \)
(1)Mannose Glucose 9)
\( \begin{array}{ll}\text {Sucrose }+H_{3} O^{+} \rightarrow & \text { (2) Galactose } \\ \text {Fructose} \stackrel{\text {Base}}{\rightarrow} & \text { (3) Glucose } \\ \text {Lactose}+H_{3} O^{+} \rightarrow & \text { (4) Fructose } \\ & \text { (5) Glucoside }\end{array} \)
\( \begin{array}{llll}\text { A. } A-5 ; & \text { B-3, 4; } & \text { C-1,3; } & \text { D-2,3 }\end{array} \) What is ; \( \quad \mathrm{C}-1,2 ; \)
B. A-4; B-4,5; ; \( \quad D-1,3 \) , an \( D-1,3 \)
C \( . A-5 ; \quad B-3,4 ; \)
4; \( \quad \) C-2,3; \( \quad D-1,2 \) ; \( \quad D-1,2 \) \( c-3.5 \) ; ; \( \quad \mathrm{B}-4,1 \)
D. \( A-3 \)


What kind of changes is undergone
when an electric bulb glows?
A. A physical change
B. A chemical change
c. Both a physical and a chemical change
D. A permanent change


A conductor has a non-uniform section
as shown in the figure. A steady current is flowing through it. Then the drift speed of the electrons:
A. varies unpredictably
B. increases from P to Q
c. decreases from P to Q
D. is constant throughout the wire


If a women is using a copper-T, will it
help in protecting her from sexually transmitted disease?


In the circuit shown here,cells \( A \) and \( B \)
have emf \( 10 V \) each and the internal
resistance is \( 5 \Omega \) for \( A \) and \( 3 \Omega \) for \( B \). For
what value of \( R \) will the potential difference across the cell A will be zero?
A . 0
B. 1 ohm
c. 2 ohm
D. 3 ohm


If \( y \) is second entry and \( x \) is first entry then its ordered pair will be
A. \( (x, y) \)
(i) \( x \)
в. \( (y, y) \)
c. \( (y, x) \)
D. None of the above


A solid hemisphere is just pressed
below the liquid, the value of \( \frac{F_{1}}{F_{2}} \) is
(where \( F_{1} \) and \( F_{2} \) ) are the hydrostatic
force acting on the curved and flat
surfaces of the hemisphere)(Neglect atmospheric pressure)
A \( \cdot \frac{1}{2} \)
B. 2 3
\( c \cdot \frac{1}{3} \)
D. None of these


A gas is expanded from volume \( V_{0} \) to
\( 2 V_{0} \) under three different processes.
Process 1 is isobaric process, process 2 is isothermal and process 3 is
adiabatic. Let \( \Delta U_{1}, \Delta U_{2} \) and \( \Delta U_{3} \) be
the change in internal energy of the gas in these three process. Then
A \( \cdot \Delta U_{1}>\Delta U_{2}>\Delta U_{3} \)
в. \( \Delta U_{1}<\Delta U_{2}<\Delta U_{3} \)
c. \( \Delta U_{2}<\Delta U_{1}<\Delta U_{3} \)
D. \( \Delta U_{2}<\Delta U_{3}<\Delta U_{1} \)


If \( \mathbf{A}=\left\{x \mid \frac{\pi}{6} \leq x \leq \frac{\pi}{3}\right\} \) and \( f(x)= \)
\( \cos x-x(1+x), \) then \( f(A) \) is equal to
\( \mathbf{A} \cdot\left[\frac{\pi}{6}, \frac{\pi}{3}\right] \)
\( \mathbf{B} \cdot\left[-\frac{\pi}{3},-\frac{\pi}{6}\right] \)
\( \mathbf{C} \cdot\left[\frac{1}{2}-\frac{\pi}{3}\left(1+\frac{\pi}{3}\right), \frac{\sqrt{3}}{2}-\frac{\pi}{6}\left(1+\frac{\pi}{6}\right)\right] \)
\( \mathrm{D} \cdot\left[\frac{1}{2}+\frac{\pi}{3}\left(1-\frac{\pi}{3}\right), \frac{\sqrt{3}}{2}+\frac{\pi}{6}\left(1-\frac{\pi}{6}\right)\right] \)


Longitudinal strain is possible in:
A . Gases
B. Liquids
c. Solids
D. All of these


Material used in heating coils is:
A. Nichrome
B. Copper
c. Silver
D. Gold


\( N a H_{2} P O_{4} \stackrel{230^{\circ} C}{\rightarrow} N a_{3}\left(P_{3} O_{9}\right) \stackrel{638^{\circ} C}{\rightarrow}(D) \)
Compound (D) contains \( 200\left(P O_{4}\right) \) units and called:
A. Bunsen's salt
B. Graham's salt
c. Reimann's salt
D. werner's salt


The vector perpendicular to \( \hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}} \) is
\( \mathbf{A} \cdot \hat{i}-\hat{j}+\hat{k} \)
B. \( \hat{i}-\hat{j}-\hat{k} \)
c. \( -\hat{i}-\hat{j}-\hat{k} \)
D. \( 3 \hat{i}+2 \hat{j}-5 \hat{k} \)


Consider the chemical reaction:
\( N_{2}(g)+3 H_{2}(g) \rightarrow 2 N H_{3}(g) \)
The rate of this reaction can be
expressed; in terms of time and of
concentration of \( N_{2}(g), H_{2}(g) N H_{3}(g) \)
Identify the correct relationship
amongst the rate expressions.
A \( \cdot \operatorname{Rate}=-\frac{d\left[N_{2}\right]}{d t}=-\frac{1}{3} \frac{d\left[H_{2}\right]}{d t}=+\frac{1}{2} \frac{d\left[N H_{3}\right]}{d t} \)
B. \( \operatorname{Rate}=-\frac{d\left[N_{2}\right]}{d t}=-\frac{3 d\left[H_{2}\right]}{d t}=\frac{2 d\left[N H_{3}\right]}{d t} \)
c. \( \operatorname{Rate}=-\frac{d\left[N_{2}\right]}{d t}=-\frac{1}{3} \frac{d\left[H_{2}\right]}{d t}=\frac{d\left[N H_{3}\right]}{d t} \)
D. \( \operatorname{Rate}=-\frac{d\left[N_{2}\right]}{d t}=\frac{d\left[H_{2}\right]}{d t}=\frac{d\left[N H_{3}\right]}{d t} \)


A spherical mirror and a thin spherical lens have each a focal length of \( -15 \mathrm{cm} \) The mirror and lens are likely to be:
A. both concave
B. both Convex
c. the mirror is concave and lens is convex
D. the mirror is convex but lens is concave


Among the compound \( 1-1 V \), the compound having the lowest boiling point is
\( A \)
B. II
c. III
D. IV


A conducting circular loop is placed in a uniform magnetic field \( \mathrm{B}=0.025 \mathrm{T} \) with its plane perpendicular to the magnetic field. The radius of the loop starts
shrinking at \( 1 \mathrm{mm} \mathrm{s}^{-1} \). The induced emf
in the loop when the radius is \( 2 \mathrm{cm} \) is:
A. \( 2 \pi \mu V \)
в. \( \pi \mu V \)
c. \( \frac{\pi}{2} \mu V \)
D. \( 3.2 \pi \mu V \)


\( \ln \) an A.C. circuit in 1 second current
reduces to zero value 120 times. Hence
the frequency of A.c. current is
\( \mathrm{Hz} \)
A . 50
в. 100
c. 60
D. 120


A sinusoidal voltage \( V=200 \sin 314 t \) is
applied to a \( 10 \Omega \) resistor. Find rms
current
A . \( 14.14 A \)
B. \( 28.28 A \)
c. \( 56.56 A \)
D. \( 100 A \)


Solve: \( \frac{2}{x}+\frac{3}{y}=13, \frac{5}{x}+\frac{7}{y}=31 \)


An electrical device which offers a low
resistance to the current in one
direction but a high resistance to the
current in opposite direction is:
A. Current Amplifier
B. Oscillator
c. Power Amplifier
D. Rectifier


Soft metals which can be cut with a
knife is/are:
A. lithium
B. potassium
c. gold
D. both A and B


Due to the capacity to absorb water, which among the following is used to replace cotton and also used as a fuel?
A. Marchantia
B. Riccia
c. sphagnum
D. Funaria


Find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \) for \( \boldsymbol{y}=\boldsymbol{e}^{\sin \sqrt{\tan \boldsymbol{x}}} \)


Solve \( \int \frac{\cos ^{2} \theta d \theta}{\cos ^{2} \theta+4 \sin ^{2} \theta} \)


A parallel plate capacitor consists of two circular plates each of radius \( 12 \mathrm{cm} \)
and separated by \( 5.0 m m . \) The capacitor
is being charged by an external source. The charging current is constant and is
equal to \( 0.15 A \)
The displacement current is:
\( \mathbf{A} \cdot 15 A \)
в. \( 1.5 A \)
c. \( 0.15 A \)
D. \( 0.015 A \)


Even though it is a non-metal, graphite conducts electricity. It is due to the presence of :
A. free electrons
B. bonded electrons
c. its bond length
D. none of these


Figure shows two long wires carrying
equal currents \( I_{1} \) and \( I_{2} \) flowing in
opposite directions.Which of the arrows
labeled \( A, B, C \) and \( D \) correctly
represents the direction of the
magnetic field due to the wires at a
point located at an equal distance \( d \)
from each wire?
A . \( A \)
B. \( B \)
c. \( C \)
\( D . D \)


\( 4 x-3=0 \) is a line parallel to
A . \( y \) axis
B. \( x \) axis
\( \mathbf{c} \cdot y=x \)
D. \( y=2 x \)


As per observation (iii) LiH is more
stable than NaH, because:
A. Due to small size of \( L i^{+} \), the lattice energy of LiH is
greater
B. Due to greater size of \( H^{-} \), the lattice energy of LiH is greater
C. LiH is more covalent than NaH
D. Due to greater size of \( N a^{+} \), the lattice energy of NaH is greater


The element which gives explosive
halides is:
A. phosphorus
B. nitrogen
c. arsenic
D. bismuth


An object is placed
(i) Asymmetrically
\( (i i) \) Symmetrically, between two plane
mirrors inclined at an angle of \( 50^{\circ} . \) Find
the number of images formed.
A \( \cdot(1) 7,(i i) 7 \)
B. (1) 6, ( ii)6
c. \( (1) 6,(i i) 7 \)
D. \( (1) 7,(i i) 6 \)


Torr is the physical quantity for atmospheric pressure. Type 1 for true
and 0 for false


Which of the following has maximum complex forming ability with a given metal ion?
A \( \cdot \mathrm{PH}_{3} \)
в. ВіНз
c. \( \mathrm{NH}_{3} \)
D. \( \operatorname{sb} \mathrm{H}_{3} \)


The angle between vectors \( \vec{A}=\hat{i}-5 \hat{j} \) and \( \vec{B}=2 \hat{i}-10 \hat{j} \) is:
A \( .90^{\circ} \)
B . \( 180^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 0^{\circ} \)


The nearest point up to which an eye
can see objects clearly is called the far point of the eye.
A. True
B. False


\( \boldsymbol{n}(\boldsymbol{E}) / \boldsymbol{n}(\boldsymbol{S}) \) is the formula of calcilating
the:
A . Mean
B. Median
c. Mode
D. Probability


Which of the following corresponds to the configuration?
\( 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} \)
A. не
B. Na a
c. мg
\( D \cdot A \)


Where should be a uniform rod of length
\( 10 m \) and weight \( 100 N \) and with a
weight of \( 100 N \) at an extreme point be
balanced?
A. \( 5 \mathrm{m} \) from that extreme
B. \( 2.5 \mathrm{m} \) from that extreme
\( \mathrm{c} .2 .5 \mathrm{m} \) from the other extreme
D. \( 5 m \) from the other extreme


ATP binding site is located
on/associated with
A. Troponin
B. Tropomyosin
c. Head part of meromyosin
D. Tail part of myosin


Consider a chemical species in which a carbon atom forms single bonds to three hydrogen atoms in which the
carbon atom possesses no other
valence electrons.
(a) What formal charge would the
carbon atoms have?
(b) What shape would you expect this species to have?
(c) What is the hybridization of carbon atom?


A cuboidal block of side \( 10 \mathrm{cm} \) is
surmounted by a hemisphere. What is the largest diameter the hemisphere can have? Find the cost of polishing the total surface area of the side so formed
at the rate of 5 per square \( c m \)


Construct \( \triangle A B C \) such that \( A B= \)
\( 2.5 c m, B C=6 c m \) and \( A C=6.5 c m \)
Measure \( \angle B \)


In a plane mirror the image formed is
real.
A . True
B. False


White fibrous tissue is
A. Nerve
B. Muscle
c. Ligaments
D. Tendons


When the number of turns per unit length in a solenoid is doubled then its
coefficient of self induction will become
A . half
B. double
c. four times
D. unchanged


The final acid obtained during the
manufacture of \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4}, \) by contact
process is:
A \( \cdot H_{2} S O_{4} \) (conc.)
B . \( H_{2} S O_{4} \) (dil)
c. \( H C I \)
D. \( H_{2} S_{2} O_{7} \)


The angular frequency of an AC source is 10 radian/sec. The reactance of \( 1 \mu F \) capacitor will be
A \( \cdot 10^{4} \Omega \)
B . \( 10^{2} \Omega \)
\( \mathbf{c} \cdot 10^{1} \Omega \)
D. \( 10^{5} \Omega \)


Identify the unsaturated compounds from the following:
(i) Propane
(ii) Propene
(iii) Propyne
(iv) Chloropropane
\( A \cdot \) (i) and (ii)
B. (ii) and (iv)
c. (iii) and (iv)
D. (ii) and (iii)


(a)Draw a schematic sketch of a
cyclotron. Explain clearly the role of crossed electric and magnetic field in accelerating the charge. Hence derive the expression for the kinetic energy
acquired by the particles.
(b) An \( \alpha \) - particle and a photon are released from the centre of the cyclotron
and made to accelerate:
(i) Can both be accelerated at the same
cyclotron frequency? Give reason to justify your answer
(ii) When they are accelerated in turn,
which of the two will have higher velocity at the exit slit.


Do the following addition with the help
of numberline:
\( (-3)+8 \)


\( N A D^{+} \) is reduced in photorespiration
inside
A. Mitochondria
B. Mitochondria and peroxisome
c. Mitochondria and chloroplasts
D. chloroplasts and peroxisomes


The set of values of \( x \) for which the
inequality \( [\boldsymbol{x}]^{2}-\mathbf{5}[\boldsymbol{x}]+\boldsymbol{6} \leq \mathbf{0} \) (where [
denote the greatest integral function) holds good are
A \( .2 \leq[x]<3 \)
в. \( 2 \leq x<4 \)
c. \( 2 \leq[x] \leq 3 \)
D. \( (b) \) and \( (c) \) both


The number of unpaired electrons present in the first excited state of
chlorine atom is:
A . 1
B. 3
\( c .5 \)
D.


Solve the following inequalities:
\( \frac{2 x-3}{4}+8 \geq 2+\frac{4 x}{3} \)
A . \( x \leq 6.3 \)
в. \( x \leq 7 \)
c. \( x \leq 7.3 \)
D. \( x \leq 8.3 \)


Explain with neat diagram the principle, construction and working of a cyclotron.


\( \int_{0}^{1} \frac{2 \sin ^{-1} \frac{x}{2}}{x} d x \) is equal to
\( ^{\mathrm{A}} \cdot \int_{0}^{\pi / 6} \frac{x}{\tan x} d x \)
в. \( \int_{0}^{\pi / 6} \frac{2 x}{\tan x} d x \)
\( ^{\mathrm{C}} \int_{0}^{\pi / 2} \frac{2 x}{\tan x} d x \)
D. None of these


Find friction force acting on block of
mass \( =1 k g \) where \( \mu=0.8 \)
A . \( 6.8 N \)
B. \( 7 N \)
\( c .6 N \)
D. \( 0 N \)


Assertion
Ammonia can be liquefied by applying high pressure.
Reason
Ammonia is highly soluble in water
A. Both assertion and reason are CORRECT and reason is the CORRECT explanation of the assertion
B. Both assertion and reason are CORRECT, but reason is NOT THE CORRECT explanation of the assertion
C. Assertion is CORRECT, but reason is INCORRECT
D. Assertion is INCORRECT, but reason is CORRECT


If a gas at constant temperature and pressure expands, then its:
A. internal energy increases
B. internal energy remains same
c. internal energy decreases
D. entropy increases and then decreases


If \( y=\left(5 x^{3}-4 x^{2}-8 x\right)^{9}, \) find \( \frac{d y}{d x} \)


The probability of getting number 10 in a throw of a dice is
A. 0
B.
\( c \cdot 0.5 \)
D. 0.75


Which of these statements is true for
the following molecule?
A. The bromine and methyl group are cis to one another
B. The bromine and methyl group are trans to one another
c. The bromine and methyl group are both axial
D. The bromine and methyl group are both equatorial


Calculate \( \Delta S_{r}^{o} \) at \( 298 K \) of
(a) \( N a(s)+\frac{1}{2} C l_{2}(g) \rightarrow N a C l(s) \)
\( \frac{1}{2} N_{2}(g)+2 H_{2}(g)+\frac{1}{2} C l_{2}(g) \rightarrow \)
\( N H_{4} C l(s) \)
(iii) \( C(\text { graphite }) \rightarrow C \) (Diamond)
The values of \( S^{o} \) of
\( N a, C l_{2}, N a C l, N H_{4} C l, N_{2}, H_{2} \)
diamond and graphite are
\( \mathbf{5 1}, \mathbf{2 2 3}, \mathbf{7 2}, \mathbf{9 5}, \mathbf{1 9 2}, \mathbf{1 3 1}, \mathbf{2 . 4 3}, \mathbf{5}, \mathbf{6 9} \mathbf{J K} \)
and \( m o l^{-1} \) respectively:


A \( 120 \mathrm{V}, 60 \mathrm{W} \) lamp is to be operated on 220 \( \mathrm{V}, 50 \mathrm{Hz} \) supply mains Calculate what value of pure inductance which
would be required so that the lamp runs on correct value of power
A \( \cdot 1.174 \)
B. 2.348
c. 3.522
D. 4.696


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


If \( \boldsymbol{f}(\boldsymbol{y})=\boldsymbol{e}^{\boldsymbol{y}}, \boldsymbol{g}(\boldsymbol{y})=\boldsymbol{y} ; \boldsymbol{y}>\mathbf{0} \) and
\( \boldsymbol{F}(\boldsymbol{t})=\int_{0}^{t} \boldsymbol{f}(\boldsymbol{t}-\boldsymbol{y}) \boldsymbol{g}(\boldsymbol{y}) \boldsymbol{d} \boldsymbol{y}, \) then which
of the following is true?
A \( \cdot F(t)=e^{t}-(1+t) \)
B \( \cdot F(t)=t e^{t} \)
c. \( F(t)=t e^{-t} \)
D. \( F(t)=1-e^{-t}(1+t) \)


A triangle \( A B C \) in which DE \( \| B C \), and
intersects \( A B \) in \( D \) and \( A C \) in \( E \)
Hence, \( \frac{A B}{D B}=\frac{A C}{E C} \)
A. True
B. False


The glancing angle of incidence is \( 10^{\circ} \) What will be the glancing angle of reflection?
A \( \cdot 10^{\circ} \)
в. \( 80^{\circ} \)
c. \( 170^{\circ} \)
D. \( 60^{\circ} \)


Chordates have
A. Dorsal nerve cord
B. Dorsal hollow nerve cord
C. Brain
D. Ventral nerve cord


If \( \int \frac{d x}{\left(x^{2}+1\right)\left(x^{2}+4\right)}=k \tan ^{-1} x+ \)
\( l \tan ^{-1} \frac{x}{2}+C, \) then
A \( \cdot \quad k=\frac{1}{3} \)
B \( \cdot l=\frac{2}{3} \)
c. \( \quad k=-\frac{1}{3} \)
D \( \cdot l=-\frac{1}{6} \)


A dishonest milkman a buys 100 liters of milk from another dishonest
milkman \( B \) for onward distribution. He
retains 10 liter of milk for personal use, adds water to make up the shortfall and sells the mixture at Rs. 15 /liter, there
by making a profit of Rs. 2.75 /liter on
the quantity sold. If \( B \) had already
diluted the milk with water in the ratio
of milk : water 9: 1 and he makes a
profit of Rs. \( 1, \) the price per liter of pure milk purchased by \( B \) is closest to?


If \( f \) and \( g \) are two increasing function such that \( f o g \) is defined, then fog will
be
A. increasing function
B. decreasing function
c. neither increasing nor decreasing
D. None of these


Number of measurements required to
construct a square are
A.
B. 2
\( c \cdot 3 \)
\( D \)


If \( \angle B_{1} O A_{1}=60^{\circ} \& \) radius of biggest
circle is r. According to figure trapezium
\( \boldsymbol{A}_{1} \boldsymbol{B}_{1} \boldsymbol{D}_{1} \boldsymbol{C}_{1}, \boldsymbol{C}_{1} \boldsymbol{D}_{1} \boldsymbol{D}_{2} \boldsymbol{C}_{2}, \boldsymbol{C}_{2} \boldsymbol{D}_{2} \boldsymbol{D}_{3} \boldsymbol{C}_{3} \ldots \)
and so on are obtained. Sum of areas of
all the trapezium is -
A \( \cdot \frac{r^{2}}{2 \sqrt{3}} \)
B. \( \frac{9 r^{2}}{2 \sqrt{3}} \)
\( \mathrm{c} \cdot \frac{9 r^{2}}{\sqrt{3} r^{2}} \)
D. \( \frac{r^{2}}{9 \sqrt{3}} \)


Energy of \( 1000 \mathrm{J} \) is spent to increase the angular speed of a wheel from 20 \( r a d / s \) to 30 rad/s. Calculate the moment of inertia of the wheel.


\( N H_{2} C N_{(s)}+\frac{3}{2} O_{2(g)} \rightarrow N_{2(g)}+ \)
\( \boldsymbol{C O}_{2(g)}+\boldsymbol{H}_{2} \boldsymbol{O}_{(l)} \)
This reaction is carried out in a bomb
calorie-meter. The heat released was
\( 743 K J \) mol \( ^{-1} \). The value of \( \Delta H_{300} \) for
this reaction would be:
A. \( -740 \mathrm{KJ} \mathrm{mol}^{-1} \)
В. -741.75 КJ mol\( ^{-1} \)
c. \( -743.0 K J \) mol\( ^{-1} \)
D. \( -744.25 \mathrm{KJ} \mathrm{mol}^{-1} \)


Which of the following is correct IUPAC name of compound? \( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{C H}=\boldsymbol{C H}-\boldsymbol{C H}_{3} \)
A. Pent-2-ene
B. Prop-1-en-2-yne
c. 1-Methylpropane
D. Pen-4-ene


BHNS is abbreviation of :
A. Banaras Natural History Society.
B. Bombay Natural History Society
C. Botanical North Himalayan Survey.
D. Biological Natural History Society.


A convex lens forms 19 times magnified image of an object on a screen placed 10 \( \mathrm{m} \) from the lens. What is the focal
length of the lens?


What is the magnitude of atmosphere
pressure.


State True or False.
Carbon-14 dating is used to determine the age of once living material
A. True
B. False


Which step is the chain propagation step in the following mechanism?
\[
\begin{array}{ll}
\text { 1. } \mathrm{Cl}_{2} \stackrel{\mathrm{hv}}{\longrightarrow} \mathrm{Cl}^{*}+\mathrm{Cl}^{\prime} & 2 . \mathrm{Cl}^{*}+\mathrm{CH}_{4} \longrightarrow \mathrm{CH}_{3}^{\circ}+\mathrm{HCl} \\
\text { 3. } \mathrm{Cl}^{*}+\mathrm{Cl}^{*} \longrightarrow \mathrm{Cl}_{2} & \text { 4. } \mathrm{CH}_{3}+\mathrm{Cl}^{*} \longrightarrow \mathrm{CH}_{3} \mathrm{Cl}
\end{array}
\]
\( A \). (i)
B. (ii)
c. (iii)
D. (iv)


What is biodegradable polymer? Give
one example


The smallest value of an angle whose
sine is \( -\frac{\sqrt{\mathbf{3}}}{\mathbf{2}} \) is
\( A \cdot 30^{\circ} \)
B . \( 60^{\circ} \)
\( c \cdot 120^{\circ} \)
D. \( 240^{\circ} \)


The point which lies in the perpendicular bisector of the line segment joining the points \( A(-2,-5) \) and \( B(2,5) \) is
\( A \cdot(0,0) \)
B. (0, 2)
c. (2, 0)
\( D \cdot(-2,0) \)


In the diagram given below, label the
incident, refracted and emergent rays
Also, indicate the angle of deviation


Show that \( f, \) given by \( f(x)= \) \( \frac{\boldsymbol{x}-|\boldsymbol{x}|}{\boldsymbol{x}}(\boldsymbol{x} \neq \mathbf{0}), \) is continuous on \( \mathrm{R}[\mathbf{0}] \)


Using elementary tansormations, find
the inverse of each of the matrices, if it
exists in \( \left[\begin{array}{ll}2 & 5 \\ 1 & 3\end{array}\right] \)


When we burn wool why do we get the smell of hair burn?


Alloys of ferromagnetic
materials
A. are always ferromagnetic in nature
B. need not be ferromagnetic in nature
C . are always diamagnetic in nature
D. are always antiferromagnetic in nature


Solubility of KCl is maximum in:
A \( \cdot C H_{3} C H_{2} O H \)
в. \( C H_{3} O C H_{3} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{O} \)
D. \( C H_{3} \) COOH


Maximum no. of electrons that can be
present in \( \mathrm{M} \& \mathrm{N} \) shells respectively are
\( \mathbf{A} \cdot 18,32 \)
B. 8,18
c. 32,50
D. 32,48