The current carriers can have
A. positive charge only
B. negative charge only
C. positive or negative charge
D. neither positive nor negative charge


Find number of terms in \( \left(1+x+x^{4}\right)^{12} \)


if \( \sin \theta=-\frac{4}{5}, \pi<\theta<\frac{3 \pi}{2}, \) then find
1. \( \sin 2 \theta \)
2. \( \cos 2 \theta \)
3. \( \tan 2 \theta \)


When a metal surface is illuminated by
light of wavelengths \( 400 \mathrm{nm} \) and 250 \( \mathrm{nm}, \) the maximum velocities of the
photoelectrons ejected are v and 2v respectively. The work function of the metal is
A \( \cdot 3.972 \times 10^{-19} \mathrm{J} \)
В. \( 1.59 \times 10^{-19} \mathrm{J} \)
D. \( 0.5 \times 10^{-19} \mathrm{J} \)


Carboxylic acids may be prepared by the reaction of Grignard reagents with:
A. \( C O_{2} \)
в. \( C O \)
c. Formaldehyde
D. Formic acid


A hydrogen electrode
\( \left(p_{H_{2}}=1 a t m ; T=298 K\right) \) is placed in
buffer solution of \( C H_{3} C O O N a \) and
\( \boldsymbol{C H}_{3} \boldsymbol{C O O H} \) in the molar ratio \( \boldsymbol{x}: \boldsymbol{y} \)
and then in \( y: x \) has reduction
potential values as \( E_{1} \) and \( E_{2} \) volts
respectively. Then \( p K_{e} \) of \( C H_{3} \) COOH
will be:
A \( \cdot \frac{E_{1}+E_{2}}{0.118} \)
B. \( \frac{E_{1}+E_{2}}{0.059} \)
\( \mathbf{c} \cdot \quad-\frac{E_{1}+E_{2}}{0.118} \)
D. \( \frac{E_{2}-E_{1}}{0.118} \)


Differentiate roasting and calcination
with examples?


Suppose a current carrying wire has a
cross-sectional area that gradually
become smaller along the wire has the
shape of a very long cone as shown in figure.Then:
This question has multiple correct options
A. electric current is different in different portions of wire
B. electric current is same everywhere.
C. drift speed of electrons at point \( A \) is lesser than that of at point B.
D. drift speed of electrons at point \( A \) is same as that of at point B.


If the bond energies of \( \mathrm{H}-\mathrm{H}, \mathrm{Br} \) -Br, and \( \mathrm{H} \) Br are 433,192 and \( 364 \mathrm{kJ} \) mol \( ^{-1} \)
respectively, the \( \triangle H^{0} \) for the reaction
\( \boldsymbol{H}_{2(g)}+\boldsymbol{B} \boldsymbol{r}_{2(g)} \rightarrow 2 \boldsymbol{H} \boldsymbol{B} \boldsymbol{r}_{(g)} \) is:
A . -261 k J)
B. +103 k
\( c .+261 \mathrm{kJ} \)
D. -103 kJ


Assertion: The induced emf and current
will be same in two identical loops of copper and aluminium, when rotated with same speed in the same magnetic field.
Reason: Mutual induction does not depend on the orientation of the coils.
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion and Reason both are false


Equimolar quantities of \( \boldsymbol{H} \boldsymbol{I}, \quad \boldsymbol{H}_{2}, \quad \boldsymbol{I}_{2} \)
are brought to equilibrium. If the total pressure in the vessel is 1.5 at \( m \) and
\( K_{p} \) for the reaction
\( \mathbf{2} \boldsymbol{H} \boldsymbol{I}_{(g)} \rightleftharpoons \boldsymbol{H}_{2(g)}+\boldsymbol{I}_{2(g)} \) is \( \mathbf{4 9} \)
Which of the following is the correct value for the equilibrium partial
pressure of \( I_{2} ? \)
A . 0.4
B. 0.9
\( c .0 .7 \)
D. 0.5


\( \boldsymbol{P b O}+\boldsymbol{H}_{2} \rightarrow \boldsymbol{P b}+\boldsymbol{H}_{2} \boldsymbol{O} \)
Which of the following statements is wrong?
A. \( H_{2} \) is the reducing agent
B. PbO is the oxidizing agent
c. PbO is oxidized to Pb
D. \( H_{2} \) is oxidizes to \( H_{2} O \)


The area of the parallelogram whose adjacent sides are \( 2 \mathrm{i}-3 \mathrm{k} \) and \( 4 \mathrm{j}+2 \mathrm{k} \) is
A \( \cdot 2 \sqrt{(14)} \)
в. \( 4 \sqrt{(14)} \)
C \( .16 \sqrt{(14)} \)
D. \( \sqrt{(14)} \)


Trajectory of two particles projected
from origin with speed \( v_{1} \) and \( v_{2} \) and
angles \( \theta_{1} \) and \( \theta_{2} \) with positive \( x \) - axis
respectively as shown in the figure
given that \( g=-10 m / s^{2}(j) . \) Choose the
correct option related to diagram:
This question has multiple correct options
\( \mathbf{A} \cdot v_{1}-v_{2}=2 v_{1} \)
B . \( \theta_{2}-\theta_{1}=2 \theta_{1} \)
\( \mathbf{c} \cdot 3\left(v_{1}-v_{2}\right)=0 \)
D. \( 3\left(\theta_{1}-\theta_{2}\right)=-\theta_{1} \)


If \( \alpha \) is a real number for which \( f(x)= \)
\( \cos ^{-1} x \) is defined then a possible value
of \( [\alpha] \) is (where \( [.] \) denotes greatest
integer function)
This question has multiple correct options
\( A \cdot 2 \)
B.
\( c \cdot-1 \)
\( D \cdot-2 \)


If a vector \( \vec{A} \) makes angles \( \alpha, \beta \) and \( \gamma \)
with \( X, Y \) and \( Z \) axes respectively then \( \sin ^{2} \alpha+\sin ^{2} \beta+\sin ^{2} \gamma= \)
A .
B.
\( c \cdot 2 \)
D. 3


A battery of \( \boldsymbol{E} \boldsymbol{M} \boldsymbol{F} \) 3 \( \boldsymbol{v} \) and internal
resistance \( r \) connected in series with
the resistor \( 55 \Omega \) through can ammeter
of resistance \( 1 \Omega \) it reads \( 50 m A \)
Calculate \( r \)


A particle moves in the \( x \) -y plane with
velocity \( v_{x}=8 t-2 \) and \( v_{y}=2 . \) If it
passes through the point \( x=14 \) and
\( \boldsymbol{y}=\mathbf{4} \) at \( \boldsymbol{t}=\mathbf{2 s}, \) the equation of the path
is?
A. \( x=y^{2}-y+2 \)
В. \( x=y^{2}-2 \)
c. \( x=y^{2}+y-6 \)
D. None of these


Which of the following processes is responsible for the release of oxygen?
I. Lactic acid fermentation
II. Alcohol fermentation
III. Aerobic respiration
IV. Photosynthesis
A . I and II
B. I and III
c. ॥ only
D. IV only
E . III and IV


Find the area of the region bounded by the ellipse \( \frac{x^{2}}{16}+\frac{y^{2}}{9}=1 \)
A . \( 6 \pi \)
в. \( 12 \pi \)
c. \( 18 \pi \)
D. \( 24 \pi \)


A uniform chain of length \( \pi r \) lies inside
a smooth semicircular tube \( A B \) of
radius \( r . \) Assuming a slightly
disturbance to start the chain in
motion, the velocity with which it will
emerge from the end \( \mathrm{B} \) of tube will be:
\( \sqrt[A \cdot]{g r\left(1+\frac{2}{\pi}\right)} \)
B. \( \sqrt{2 g r\left(\frac{2}{\pi}+\frac{\pi}{2}\right)} \)
c. \( \sqrt{g r(\pi+2)} \)
D. \( \sqrt{\pi g r} \)


Which of the following works on Pascal's law?
A. Sprayer
B. Venturimeter
c. Hydraulic liftt
D. Aneroid barometer


Correct relationship between the two
structure given below is:
A. enantiomers
B. tautormers
c. geometrical isomers
D. constitutional isomers


A ray of light is incident on glass slab making an angle of incidence \( \sin ^{-1}\left(\frac{\sqrt{3}}{2}\right) . \) What will be the angle of
refraction in glass of refractive index
1.5?
\( \mathbf{A} \cdot 40^{\circ} 18 \)
В \( \cdot 24^{\circ} 49^{\prime} \)
c. \( 25^{\circ} \) о \( 7^{\text {। }} \)
\( \mathbf{D} \cdot 35^{\circ} 16^{\prime} \)


A bucket full of hot water is kept in a
room. It cools from \( 75^{\circ} \mathrm{C} \) to \( 70^{\circ} \mathrm{C} \) in \( T_{1} \)
minutes, from \( 70^{\circ} \mathrm{C} \) to \( 65^{\circ} \mathrm{C} \) in \( T_{2} \)
minutes and from \( 65^{\circ} \mathrm{C} \) to \( 69^{\circ} \mathrm{C} \) in \( T_{3} \)
minutes. Which of the following relation
is correct?
A. \( T_{1}>T_{2}>T_{3} \)
в. \( T_{1}<T_{2}<T_{3} \)
c. \( T_{1}<T_{2}>T_{3} \)
D. \( T_{1}=T_{2}=T_{3} \)


A particle moves along positive branch of the curve, \( y=\frac{x}{2}, \) where \( x=\frac{t^{3}}{3}, x \) and
\( y \) are measured in maters and \( t \) in
second, then:
This question has multiple correct options
A ' the velocity of particle at \( t=1 s \) is \( \hat{i}+\frac{1}{2} \hat{j} \)
B \cdot The velocity of particle at \( t=1 s \) is \( \frac{1}{2} \hat{i}+\hat{j} \)
C. The acceleration of particle at \( t=2 s \) is \( 2 \hat{i}+\hat{j} \)
D. The acceleration of particle at \( t=2 s \) is \( \hat{i}+2 \hat{j} \)


The respiratory quotient of carbohydrate is
A. Unity.
B. Greater than unity
c. Less than unity.
D. Equal to five


Morphallaxis is reported in
A. Porifers
B. Coelenterates and flatworms
C. Nemarteans and some ascidians
D. All the above


Compound with antiseptic properties
are:
This question has multiple correct options
A. \( C H C l_{3} \)
в. \( C H I_{3} \)
c. Boric acid
D. 0.3 ppm \( C l_{2} \)


A symmetrical die is thrown four times and getting a multiple of 2 is considered to be a
success.
The mean and variance of success are
A \( \cdot 4,2 \)
в. 2,1
c. 0,2
D. 1,2


Assertion
The metal sulphides and carbonates are
converted to metal oxides in the
process of extraction of metal from
them.
Reason
Easier to obtain metal from its oxide, as
compared from its sulphides and
carbonates.
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


Schlerenchymatous hypodermis is
found in?
A. Dicot root
B. Monocot leaf
c. Dicot stem
D. Monocot stem


(1) Mass of a book is 500 g on thew surface of the earth. what will be its
mass at a height equal to radius of earth
(2) find the weight of the book at the
surface of the earth


How many \( S-O-S \) linkage(s) is/are
present in \( \boldsymbol{H}_{2} \boldsymbol{S}_{3} \boldsymbol{O}_{6} ? \)


Match the columns.
A \( \begin{array}{clcc} & \text { List I } & & \text { List } \\ & & & \text { II } \\ \text { A } & \text { Residual volume } & 1 & 4.6 \mathrm{L} \\ \text { B } & \text { Vital capacity } & 2 & 1.2 \mathrm{L} \\ \text { C } & \begin{array}{l}\text { Inspiratory reserve } \\ \text { volume }\end{array} & 3 & 3.5 \mathrm{L} \\ \text { D } & \text { Inspiratory capacity } & 4 & 3 \mathrm{L}\end{array} \)
A. \( A-2, B-1, C-4, D-3 \)
B. \( A-2, B-1, C-3, D-4 \)
D. \( A-1, B-2, C-3, D-4 \)


\( A \cdot \) Both \( A \) and \( R \) are correct and \( R \) is the correct explanation of the \( A \)
B. Both A and R are correct but \( R \) is not the correct explanation of the \( A \)
C. A is correct, but R is incorrect.
D. A is incorrect, but R is correct.


How do plants get rid of their excretory
products?


In Rutherford's scattering experiment
which of the following does not happen?
A. Most of the \( \alpha \) -rays pass through without deflection
B. A few \( \alpha \) -particles pass through the nucleus
C. A few \( \alpha \) -particles are deflected back
D. \( \alpha \) -particles going near the nucleus are slightly deflected


Find the incorrect answer from the
following?
A. Veins are typically larger in diameter than arteries
B. Because of their small size,capillaries contain blood that is moving more quickly than in other parts of the circulatory system
C. The walls of arteries are elastic,enabling them to stretch and shrink during changes in blood pressure
D. Veins contain more blood than any other part of the circulatory system


The half life, \( T \), of a substance is related
to the decay constant by the equation
\( A \cdot T=\frac{1}{\lambda} \)
в. \( \frac{1}{0.693 \lambda} \)
c. \( \frac{0.693}{\lambda} \)
D. \( \frac{2.303}{\lambda} \)


The equation representing the process by which standard reduction potential
of zinc can be defined
is
\( \mathbf{A} \cdot Z n^{2+}(s)+2 e^{-} \rightarrow Z n \)
\( \mathbf{B} \cdot Z n(g) \rightarrow Z n^{2+}(g)+2 e^{-} \)
\( \mathbf{c} \cdot Z n^{2+}(g)+2 e^{-} \rightarrow Z n \)
D. \( Z n^{2+}(a q .)+2 e^{-} \rightarrow Z n(s) \)


Match Column I with Column II.


The element used by Rutherford in his famous scattering experiment was
A. Gold
B. Tin
c. Silver
D. Leadd


The number of nodal planes '5d' orbital
is:
A . zero
B. one
c. two
D. three


Work-energy theorem is valid in the
presence of
A. External forces only
B. Internal forces onlhy
c. conservative forces only
D. All type of forces


The focal length of a convex lens is \( 5 \mathrm{cm} \) where should the object be placed to get a real image with same size as that
of object:
\( \mathbf{A} \cdot 10 \mathrm{cm} \)
B. \( 15 \mathrm{cm} \)
c. \( 60 \mathrm{cm} \)
D. None of these


Assertion: Electrode potential for the
electrode \( M^{n+} \mid M \) with concentration
is given by the expression under STP conditions; \( \boldsymbol{E}=\boldsymbol{E}^{\ominus}+\frac{\mathbf{0 . 0 5 9}}{\boldsymbol{n}} \log \left[\boldsymbol{M}^{\boldsymbol{n}+}\right] \)
Reason: STP conditions require the
temperature to be \( 273 \mathrm{K} \)
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
E. Both Assertion and Reason are false


The velocity of the particle at any time \( t \)
is given by \( \boldsymbol{v}=\mathbf{2} \boldsymbol{t}(\boldsymbol{3}-\boldsymbol{t}) \mathbf{m} \boldsymbol{s}^{-1} . \) At what
time is its velocity maximum?
A . 2 s
B. 6s
c. \( 1.5 \mathrm{s} \)
D. 1s


A travelling of frequency \( 30 \mathrm{Hz} \) and velocity \( 300 \mathrm{m} / \mathrm{s} \) enters a water surface
and the speed of the wave becomes 400 \( \mathrm{m} / \mathrm{s} . \) What is the new frequency of the
wave
\( A \cdot 40 \mathrm{Hz} \)
B. 30 Нz
c. 22.5 нz
D. 10 Hz


The unit of susceptance is
\( A \cdot \) ohm
B. ohm \( ^{-1} \)
c. ohm/cm
D. ohm/m


The proper IUPAC name of the
compound is :
A. trimethylcyclohexanecarboxylate
B. methylethylcyclohexanecarboxylate
c. ethylmethylcyclohexanecarboxylate
D. None of these


The first element of actinide series is :
A. thorium
B. cerium
c. lanthanum
D. actinium


For a body moving with an initial
velocity \( u \) and uniform acceleration \( a \)
Find the displacement of the body in time t.
A \( \cdot s=u t+\frac{1}{2} a t^{2} \)
B. \( s=u+a t \)
c. \( s=u t-\frac{1}{2} a t^{2} \)
D. \( s=u t+a t^{2} \)


The given electrical network is
equivalent to:
A. NOT gate
B. AND gate
c. or gate
D. NOR gate


A gas which exists in three allotropic from \( \alpha, \beta \) and \( \gamma \) is:
\( A \cdot S O_{2} \)
в. \( S O_{3} \)
\( c \cdot C O_{2} \)
D. \( N H_{3} \)


\( \int \frac{\sin 2 x}{\sin ^{2} x+2 \cos ^{2} x} d x= \)
A \( \cdot \log \left(1+\cos ^{2} x\right)+C \)
В \( \cdot \log \left(1+\tan ^{2} x\right)+C \)
\( \mathbf{c} \cdot-\log \left(1+\sin ^{2} x\right)+C \)
\( \mathbf{D} \cdot-\log \left(1+\cos ^{2} x\right)+C \)


What is correct order of size in each
pair given below?
\( N b^{3+} \) and \( T a^{3+} \)
A. \( N b^{3+}=T a^{3+} \)
B . \( N b^{3+}<T a^{3+} \)
\( \mathbf{c} \cdot N b^{3+}>T a^{3} \)
D. None of these


The stopping potential in an experiment
of photon is \( 2 \mathrm{eV} \). What is the maximum
kinetic energy of photoelectrons emitted ?


A magnetic field is directed normally
downwards through a magnetic frame
as shown in the figure. On increasing
the magnetic field:
\begin{tabular}{r|rrrrr}
\( \times \) & \( \times \) & \( \times \) & \( \times \) & \( \times \) & \( \times \) \\
\( \times \) & \( \times \) & \( \times \) & \( \times \) & \( \times \) & \( \times \) \\
\( \times \) & \( \times \) & \( \times \) & \( \times \) & \( \times \) & \( \times \) \\
\( \times \) & \( \times \) & \( \times \) & \( \times \) & \( \times \) & \( \times \) \\
\( \times \) & \( \times \) & \( \times \) & \( \times \) & \( \times \) & \( \times \) \\
\( \times \) & \( \times \) & \( \times \) & \( \times \) & \( \times \) & \( \times \) \\
\( \times \) & \( \times \) & \( \times \) & \( \times \) & \( \times \) & \( \times \) \\
\hline
\end{tabular}
\[
\times \times \times \times \times \times
\]
A. plate B will be positively charged
B. plate A will be positively charged
C. none of the plates will be positively charged
D. all of the above


When potassium iodide solution is treated with ozone, the products formed
are:
This question has multiple correct options
A \( \cdot I_{2} \)
в. \( H_{2} \)
\( c \cdot O_{2} \)
D. all of these


The area of pistons in a hydraulic machine are \( 5 c m^{2} \) and \( 625 c m^{2} . \) The
force on the smaller piston so that a
load of \( 1250 N \) on the larger piston can be supported, is \( X \) N. Find \( \frac{X}{2} \) N.
A. 5
B. 10
c. 1250
D. None of the above


A closed system containing \( 10^{-2} \mathrm{M} H_{2} \)
and \( 2 \times 10^{-2} \mathrm{M} I_{2} \) at \( 450^{\circ} \mathrm{C} \) is allowed to
reach equilibrium and at equilibrium the \( H I \) concentration is \( 1.8 \times 10^{-2} \mathrm{M} \)
Calculate \( K_{C} \) at \( 450^{\circ} \mathrm{C} \) for \( H_{2}(g)+ \) \( \boldsymbol{I}_{2}(\boldsymbol{g}) \rightleftharpoons 2 \boldsymbol{H} \boldsymbol{I}(\boldsymbol{g}) \)


Which of the following joints would
allow no movement?
A. Ball and socket joint
B. Fibrous joint
c. cartilaginous joint
D. synovial joint


What is mass or bulk flow system?


Find the largest number which divides
853 and 385 leaving remainder 7 in each case.


Organic compounds are numerous since:
A. carbon has high catenation ability
B. tetravalency of carbon
c. isomerism of organic compounds
D. All of these


The chemical formula of the oxide of
Eka - aluminium is:
A. \( G a O \)
в. \( G a O_{2} \)
c. \( G a_{2} O_{2} \)
D. \( G e_{2} O_{3} \)


What is the nature of chemical bonding
between \( C s \) and \( F ? \)
A. Ionic
B. Covalent
c. coordinate
D. Metallic


Degree measure of \( \left(\frac{1}{4}\right)^{c} \) is
A \( \cdot 15^{\circ} 19^{\prime} 5^{\prime \prime} \)
B . \( 14^{\circ} 19^{\prime} 5^{\prime \prime} \)
\( \mathbf{c} \cdot 15^{\circ} 18^{\circ} 6 " \)
D. \( 14^{\circ} 18^{\circ} 6 " \)


Monocots and dicots which are the two
subgroups of flowering plants cannot be differentiated significantly on the basis
of
A. Seed structure
B. Floral parts
c. Leaf venation
D. Stomata structure
E. Vascular organization


If \( \mathbf{f}:[\mathbf{0}, \infty) \rightarrow[\mathbf{0}, \infty), \) and \( \mathbf{f}(\mathbf{x})=\frac{\mathbf{x}}{\mathbf{1}+\mathbf{x}} \)
then \( \boldsymbol{f} \) is
A. one - one and onto
B. one - one but not onto
c. onto but not one - one
D. neither one - one nor onto


Differentiate between corm and bulb.


If \( \cos \alpha+2 \cos \beta+3 \cos \gamma=\sin \alpha+ \)
\( 2 \sin \beta+3 \sin \gamma=0, \) then the value of
\( \sin 3 \alpha+8 \sin 3 \beta+27 \sin 3 \gamma \) is
\( A \cdot \sin (a+b+\gamma) \)
B. \( 3 \sin (\alpha+\beta+\gamma) \)
c. \( 18 \sin (\alpha+\beta+\gamma) \)
D. \( \sin (\alpha+2 \beta+3) \)


Conductivity of a solution is affected
by:
A. addition of water
B. process of heating
c. addition of acetic acid
D. all of the above


Which of the following alcohols will dehydrate most rapidly when treated
with conc. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} ? \)
\( \mathbf{A} \cdot C H_{3} C H(O H) C\left(C H_{3}\right) \)
в. \( C H_{3} C\left(C H_{3}\right)(O H) C H\left(C H_{3}\right)_{2} \)
c. \( \left(C H_{3}\right)_{2} C H C H(O H) C H_{3} \)
D. \( C H_{3} C H_{2} C H_{2} C H_{2} O H \)


The plane \( a x+b y+c z+d=0 \) divides
the line joining the points \( \left(x_{1}, y_{1}, z_{1}\right) \)
and \( \left(x_{2}, y_{2}, z_{2}\right) \) in the ratio
A \( \cdot \frac{-\left(a x_{1}+b y_{1}+c z_{1}+d\right)}{\left(a x_{2}+b y_{2}+c z_{2}+d\right)} \)
B. \( \frac{\left(a x_{1}+b y_{1}+c z_{1}+d\right)}{\left(a x_{2}+b y_{2}+c z_{2}+d\right)} \)
c. \( \frac{a x_{1} x_{2}+b y_{1} y_{2}+c z_{1} z_{2}}{d^{2}} \)
D. None of these


(a) A rod of length \( l \) is moved
horizontally with a uniform velocity' \( v \) ' in a direction perpendicular to its length through a region in which a uniform magnetic field is acting vertically downward. Derive the expression for the emf induced across the ends of the rod.
(b) How does one understand this
motional emf by invoking the Lorentz force acting on the free charge carriers
of the conductor? Explain.


An animal cell when placed in a \( 0.9 \% \)
solute solution, the cell will
A. Remain unchanged.
B. Swell and burst.
c. Shrivel
D. Swell and divide
E. Release solute by exocytosis


A freely falling body acquires a velocity
\( v m s^{-1} \) in falling through a distance of
\( 80 m . \) How much further distance
should it fall, so as to acquire a velocity of \( 2 v m s^{-1} ?\left(\text { Take } g=10 m s^{-2}\right) \)


What is the momentum versus velocity graph is like, when mass is fixed?
A. Straight line
B. Exponential curve
c. Parabola
D. circle


Solve: \( a x+b y-c=0 \)
\( b x+a y=1+c \)


Water is running into an underground right circular conical reservoir, which is 10 \( m \) deep and radius of its base is 5 m.
If the rate of change in the volume of water in the reservoir is \( \frac{3}{2} \pi m^{3} / m i n \quad, \) then the rate \( ( \) in \( \mathrm{m} / \mathrm{min} \) ) at which water rises in it, when
the water level is \( 4 \boldsymbol{m}, \) is:
\( A \cdot \frac{3}{8} \)
в. \( \frac{1}{8} \)
c. \( \frac{1}{4} \)
D. \( \frac{3}{2} \)


Calculate the e.m.f of the cell in \( \mathbf{V} \)
\( \boldsymbol{P t}\left|\boldsymbol{H}_{2}\right|(\mathbf{1} . \mathbf{0} \boldsymbol{a} \boldsymbol{t m}) \mid \boldsymbol{C H}_{3} \boldsymbol{C O O H}(\mathbf{0 . 1} \boldsymbol{M}) \)
\( \boldsymbol{K}_{\boldsymbol{a}}\left(\boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{C O O H}\right)=\mathbf{1 . 8} \times \)
\( \mathbf{1 0}^{-\mathbf{5}}, \boldsymbol{K}_{\boldsymbol{B}^{\prime}}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)=\mathbf{1 . 8} \times \mathbf{1 0}^{-\mathbf{5}} . \) if the
value is \( -46 \times 10^{-x}, \) then what is the
value of \( x ? \)


As shown in the figure, force of \( 105 N \)
each are applied in opposite directions,
on the upper and lower force of a cube of
side \( 10 \mathrm{cm}, \) shifting the upper face
parallel to itself by \( 0.5 \mathrm{cm} . \) If the side of
another cube of the same material is
\( 20 \mathrm{cm}, \) then under similar condition as
shown as above, the displacement will
be:
\( \mathbf{A} \cdot 0.25 \mathrm{cm} \)
B. \( 0.37 \mathrm{cm} \)
c. \( 0.75 \mathrm{cm} \)
D. \( 1.00 \mathrm{cm} \)


A beam of light of wavelength 600 nm from a distinct source falls on a single
slit \( 1.0 \mathrm{mm} \) wide and the resulting diffraction pattern is observed on a
screen \( 2 \mathrm{m} \) away. The distance between
the first dark fringes on either side of the central bright fringe is?


In order to excite an electron from \( n= \)
2 to \( n=4 \) the atom needs to
A. release heat
B. release a photon.
c. maintain a constant energy.
D. release energy.
E. absorb energy.


EM waves are
A. deflected by electric and magnetic waves
B. not deflected by electric and magnetic waves
C. sometimes deflected sometimes not deflected
D. none of the above


The method used for the concentration
of sulphide ores is:
A. froth floatation
B. smelting
c. magnetic separatio
D. gravity separation


You tend to slip when step on a banana peel lying on a smooth surface. This is due to:
A. increased friction
B. reduced friction
c. gravity
D. characteristics of the banana peel


If aq. NaCl is electrolysed using graphite as anode and Hg as cathode than products are:
A. \( C l_{2} \) gas at anode and Na at cathode
B. \( C l_{2} \) gas at anode and \( H_{2} \) gas at cathode
c. \( O_{2} \) gas at anode and \( H_{2} \) gas at cathode
D. \( C l_{2} \) gas at anode and \( O_{2} \) gas at cathode


By applying a force \( \boldsymbol{F}=(\mathbf{3} \boldsymbol{x} \boldsymbol{y}-\mathbf{5} \boldsymbol{z}) \boldsymbol{j}+ \)
\( 4 z k \) a particle is moved along the path
\( \boldsymbol{y}=\boldsymbol{x}^{2} \) from point \( (\boldsymbol{0}, \boldsymbol{0}, \boldsymbol{0}) \) to the point
\( (2,4,0) . \) The work done by the \( F \) on the particle is (all values are in SI units)
\( A \)
в. \( \frac{140}{5} J \)
c. \( \frac{232}{5} J \)
D.


In the experiment of potentiometer, at balance point, there is no current in the
A. main circuitt
c. potentiometer circuit
D. both main and galvanometer circuits


\( \lim _{x \rightarrow 0^{-}}(\ln (\{x\}+|[x]|))^{\{x\}}, \) where \( \{\cdot\} \)
denotes fractional part function and \( [\cdot \) denotes greatest integer function, is
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot \ln 2 \)
D. \( \ln \frac{1}{2} \)


Moon is visible to us because:
A. it reflects light
B. it refracts light
c. it emits light
D. it absorbs light


Lewis acid character is maximum for
\( \mathbf{A} \cdot \operatorname{Se} C l_{4} \)
в. \( S C l \)
c \( \cdot T e C l_{4} \)
D. \( T e B r_{4} \)


Electric potential can be calculated in a
A. static electric field
B. dynamic electric field
c. both static and dynamic electric field
D. neither static nor dynamic electric field


Switching from air to pure oxygen eliminates the NO production. This is an
application of:
A. Green chemistry
B. waste management
c. Green revolution
D. none of above


\( \mathbf{2} z \boldsymbol{n}+\boldsymbol{O}_{2} \rightarrow \mathbf{2} \boldsymbol{Z} \boldsymbol{n} \boldsymbol{O} \quad \boldsymbol{\nabla} \boldsymbol{G}^{o}=-\boldsymbol{6} \mathbf{1 6} \boldsymbol{J} \)
\( \mathbf{2} z \boldsymbol{n}+\boldsymbol{S}_{2} \rightarrow \mathbf{2} \boldsymbol{Z} \boldsymbol{n} \boldsymbol{S} \quad \boldsymbol{\nabla} \boldsymbol{G}^{\boldsymbol{o}}=-\boldsymbol{2} \boldsymbol{9} \boldsymbol{3} \boldsymbol{J} \)
\( \boldsymbol{S}_{2}+\mathbf{2 0}_{2} \rightarrow \mathbf{2 S O}_{2} \quad \boldsymbol{\nabla} \boldsymbol{G}^{\boldsymbol{o}}=-\boldsymbol{4 0 8} \boldsymbol{J} \)
\( \nabla G^{o} \) for the following reaction is :
\( 2 Z n s+3 O_{2} \rightarrow 2 Z n O+2 S O_{2} \)
B. 1317 J
c. 501
D. + 731 J


Select the correct statement(s).
This question has multiple correct options
A. Transition metals and many of their compounds show paramagnetic behaviour.
B. The enthalpies of atomisation of the transition metals are low.
C. The transition metals generally form coloured compounds.
D. Transition metals and their many compounds act as good catalyst.


The internal energy of an isolated
system:
A. remains constant
B. keeps on changing
c. zero
D. may change depending on gas


Which of the following taxonomist described the classification of the plant kingdom in the book 'Families of flowering plants'?
A. cronquist
B. Takhtajan
c. Benson
D. Hutchinson


\( |\mathfrak{f}| \overline{\boldsymbol{a}}|=\mathbf{2},| \overline{\boldsymbol{b}} \mid=\mathbf{5} \) and \( |\overline{\boldsymbol{a}} \times \overline{\boldsymbol{b}}|=\mathbf{8}, \) then
\( |\bar{a} \cdot \bar{b}| \) is equal to


Which of the following pteridophytes that inhabit desert regions are popularly known as 'resurrection plants'?
A. Horneophyton
B. Asteroxylon
c. selaginella
D. Rhynia


Explain the following named reactions:
(i) Sandmeyer reaction
(ii) Gattermann reaction


What is the molecular weight of water?
A . 2
B. 18
c. 20
D. 16


Assertion
The ratio of specific conductivity to the observed conductance does not depend upon the concentration of the solution
taken in the conductivity cell.
Reason
The specific conductivity decreases with dilution whereas observed
conductance increases with the
dilution.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


When chloroform reacts with
ethylamine in presence of alc. \( \boldsymbol{K O H} \) the compound formed is:
A . ethyl cyanide
B. ethyl isocyanide
c. formic acid
D. phosgene


Five identical conducting plates 1, 2, 3, 4 and 5 are fixed parallel to and equidistant from each other (see figure). Plates \( 2 \& 5 \) are connected by a conductor while \( 1 \& 3 \) are joined by another conductor. The junction of \( 1 \& 3 \)
and the plate 4 are connected to a
source of constant e.m.f. \( V_{0} . \) Find:
(i) The effective capacity of the system between the terminals of the source.
(ii) the charges on plates \( 3 \& 5 \)
Given \( \boldsymbol{d}= \) distance between any
successive plates \( \& \boldsymbol{A}= \) area of either face of each plate


If \( \frac{x}{(x-3)(x-2)}=\frac{3}{x-3}+\frac{A}{x-2} \)
then \( A= \)
A . 1
B . 2
\( c \cdot-1 \)
D. - 2


Which is true in case of catalyst?
This question has multiple correct options
A. A catalyst always initiate a reaction
B. A catalyst does not alter the position of equilibrium in a reversible reaction
C. A catalyst remains unchanged in quality and composition at the end of the reaction
D. Catalysts are sometimes very specific in respect of a reaction


Two identical vehicles are moving with
same velocity \( v \) towards an intersection
as shown in the figure. If the collision is completely inelastic, then:
A. The velocity of separation is zero
C. The common velocity after collision is \( v \cos \frac{\theta}{2} \frac{\theta}{2} \) common vition
D. All of the above


\( \boldsymbol{n}_{1} \sin \boldsymbol{i}=\boldsymbol{n}_{2} \sin \boldsymbol{r}, \) is called
(Newton's, Snell's) law.


In Van Arkel method for refining zirconium or titanium, the halogen
used is
A. fluorine
B. chlorine
c. bromine
D. iodine


In the given figure, \( \overline{P L} \perp \overline{O B} \) and \( \boldsymbol{P M} \perp \overline{\boldsymbol{O} \boldsymbol{A}} \) such that \( \overline{\boldsymbol{P} \boldsymbol{L}}=\overline{\boldsymbol{P} \boldsymbol{M}} . \) Is
\( \triangle P L O \cong \triangle P M O ? \) Give reasons in
support of your answer


Which of the following is correct representation of reaction of acidified permanganate solution with sulphur dioxide?
A \( \cdot 2 M n O_{4}+5 S O_{2}+2 H_{2} O \rightarrow 5 S O_{4}^{2-}+2 M n^{2+}+4 H^{+} \)
B. \( M n O+S O_{2}+2 H_{2} O \rightarrow S+M n^{2+} \)
c. \( 2 M n O_{4}+5 S O_{2}+2 H_{2} O \rightarrow 4 S O_{2}+S+2 M n^{2+}+4 H^{+} \)
D. \( 3 M n O_{4}+2 S O_{2}+2 H_{2} O \rightarrow 2 S+3 M n^{2+}+4 H^{+} \)


Life cycle of gymnosperm is
A. Haplontic
B. Haplodiplontic
c. Diplontic
D. Diplohaplontic


A bullet of mass 50 g moving with velocity \( 200 \mathrm{m} / \mathrm{s} \) penetrates a wooden block of mass 5 kg suspended through a string from rigid support and comes to rest inside it. If length of the string is
\( 10 \mathrm{m} \) find the angular deflection of the string.


The osmotic pressure of \( 400 \mathrm{ml} \) urea and \( 600 \mathrm{ml} \) glucose solutions are respectively 0.3 atm and 0.4 atm. The osmotic pressure of the solution obtained by mixing them will be?
A. 0.24 atm
B. 0.36 atm
c. 0.48 atm
D. 0.52 atm


Identify the correct order of appearance of the following organisms on the
surface of earth.
I. Eukaryotes
II. Heterotrophic organisms
III. Metazoa
IV. Photosynthetic organisms
\( \mathbf{A} \cdot\|, 1,1 V,\| 1 \)
В. ॥, ।, ॥I, IV
c. ॥, IV, ।, ॥ा
D. IV, I, II, III
E . \( \mathrm{IV}, \) ।।, ।, ॥ा


How many minimum number of
carbons are needed for an optically
active ether?
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. 5


Find the sum of deviations of all
observations of the data 5,8,10,15,22 from their mean


Evaluate the given integral.
\( \int(x+1) e^{x} \log \left(x e^{x}\right) d x \)


State whether given statement is True or False
Doping of pure \( S i \) with trivalent impurities, gives p-type semiconductors
A. True
B. False


During succession(from pioneer to climax community) NCP(Net Community Productivity)
A. Decrease
B. Increase
c. First increase then decrease
D. constant


A waste management technique that involves the use of organisms to remove or neutralize pollutants from a contaminated site is known as
A. Biomagnification
B. Bioremediation
c. waste degradation
D. Bioreduction


Two plane mirrors are placed perpendicular to each other. A ray strikes one mirror and, after reflection,
falls on the second mirror. The ray, after reflection from the second mirror, will
emerge:
A. perpendicular to the original ray
B. parallel to the original ray
c. at \( 45^{\circ} \) to the original ray
D. at any angle to the original ray


State true or false:
In triangle \( A B C, \) angle \( B \) is obtuse. \( D \)
and \( E \) are mid-points of sides \( A B \) and \( B C \) respectively and \( F \) is a point in
side \( A C \) such that \( E F \) is parallel to \( A B \)
Then, \( B E F D \) is a parallelogram.
A. True
B. False


During the electrolysis of carnallite, \( M g C l_{2} \) is decomposed and not \( K C l \)
This is because of :
A . Lower decomposition voltage of \( M g C l_{2} \) than that of \( K C l \)
B. Reverse reaction \( M g C l_{2}+2 K \rightarrow M g+2 K C l \) if \( K C l \) is decomposed under other experimental condition
c. Both (A) and (B)
D. None of the above


Hedge Hog resembles porcupine in being
A. Herbivorous
B. Covered on back by spines
c. Insectivorous
D. Both B and C


Assertion
A biconvex lens of focal length \( 10 \mathrm{cm} \) is split into two equal parts by a plane parallel to its principle axis.The focal length of each part will be \( 20 \mathrm{cm} \)
Reason

Focal length depends on the radii of curvature of two surfaces.
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


Prove that 1,1,1 cannot be direction cosines of a straight line


Which one is the most powerful oxidizing
agent?
\( \mathbf{A} \cdot C l_{2}+2 e^{-} \rightarrow 2 C l^{-}, \quad E^{o}=1.36 V \)
B. \( N a^{+}+e^{-} \rightarrow N a, \quad E^{o}=-2.71 V \)
\( \mathbf{c} \cdot M n O_{4}^{-}+2 H_{2} O+3 e^{-} \rightarrow M n O_{2}+4 O H^{-}, \quad E^{o}= \)
\( 0.6 V \)
\( \mathbf{D} \cdot H_{2} O_{2}+2 H^{+}+2 e^{-} \rightarrow 2 H_{2} O, \quad E^{o}=1.78 V \)


A sound wave is a pressure wave; regions of high (compressions) and low pressure (rarefactions) are established
as the result of the vibrations of the
sound source. These compressions and
rarefactions result because sound:
A. is more dense than air and thus has more inertia causing the bunching up of sound
B. waves have a speed which is dependent only upon the properties of the medium.
C. is like all waves; it is able to bend into the regions of space behind obstacles
D. is able to reflect off fixed ends and interfere with incident wavesvibrates longitudinally; the longitudinal movement of air produces pressure fluctuations.


Explain excretion in human beings.


\( 0.73 \mathrm{g} \) of an organic compound on oxidation gave \( 1.32 \mathrm{g} \) of carbon dioxide. The percentage of
carbon in the given compound will be?
A . 49.32
B. 59.32
c. 29.32
D. 98.64


Solubility of \( M X_{2} \) -type electrolytes is
\( 0.5 \times 10^{-4} \) mol/L. Then find out \( K_{s p} \) of
electrolyte :
A . \( 5 \times 10^{-12} \)
В. \( 25 \times 10^{-10} \)
c. \( 1 \times 10^{-13} \)
D. \( 5 \times 10^{-13} \)


\( K_{2} H g I_{4} \) is \( 40 \% \) ionised in aqueous solution. The value of its van't Hoff
factor (i) is:
A. 1.8
B. 2.
c. 2.0
D. 1.


Analgesics is a/an:
A. pain killer
B. bacteria
c. organic compound
D. none of the above


\( \ln \) a parallel \( L-C-R \) circuit as
shown in figure if \( I_{R}, I_{L}, I_{C} \) and \( I \)
represents the rms values of current
flowing through resistor, inductor, capacitor and the source, then choose the appropriate correct answer
\( \mathbf{A} \cdot I=I_{R}+I_{L}+I_{C} \)
В . \( I=I_{R}+I_{L}-I_{C} \)
c. \( I_{L} \) or \( I_{C} \) may be greater than \( I \)
D. None of the above


A car is travelling at the average speed of \( 50 \mathrm{km} / \mathrm{hr} \). How much distance would
it travel in 12 minutes?


List six specific characteristic of sexual reproduction


Which of the following choices both show the correct order of elements by
increasing atomic radius AND by increasing ionization energy?
A. \( A l, S, C l \) and \( A l, S, C l \)
в. \( A l, S, C l \) and \( C l, S, A l \)
c. \( C l, S, A l \) and \( C l, S, A l \)
D. \( C l, S, A l \) and \( A l, S, C l \)


\( 4 P+5 O_{2} \rightarrow \)
A. POS
B. 2P205
\( c \cdot 4 P O 4 \)
D. 2P305


By using only one of the two strands of DNA, mRNA is produced this process is called as
A. Transcription
B. Translation
c. Translocation
D. Replacement


Which of the following weak electrolytes would give aqueous solution having \( 3 C \alpha \) anion concentration?
A \( . A_{3} B \)
B. \( A_{3} B_{2} \)
\( \mathrm{c} \cdot A B_{3} \)
D. \( A_{3} B_{4} \)


A variable can take
numeric value
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D. infinite


In the equilibrium
\( \boldsymbol{C H}_{3} \boldsymbol{C O O H}+\boldsymbol{H} \boldsymbol{F} \rightleftharpoons \)
\( \boldsymbol{C H}_{3} \boldsymbol{C O O H}_{2}^{+}+\boldsymbol{F}^{-} \)
A \( \cdot F^{-} \) is the conjugate acid of \( C H_{3} C O O H \)
B. \( F^{-} \) is the conjugate base of \( H F \)
C. \( C H_{3} C O O H \) is the conjugate acid of \( C H_{3} C O O H_{2}^{+} \)
D. \( C H_{3} C O O H_{2}^{+} \) is the conjugate base of \( C H_{3} C O O H \)


is present in traces in air.
A. Nitrogen
B. Oxygen
c. Hydrogen
D. None of these


State whether the given statement is True or False :

Waste products emitted from nuclear power plants are very harmful.
A. True
B. False


A reaction has both \( \Delta \boldsymbol{H} \) and \( \boldsymbol{\Delta} \boldsymbol{S} \)
negative. The rate of reaction:
A. Increases with increase of temperature
B. Increases with decrease of temperature
c. Remains unaffected by change of temperature
D. Cannot be predicted for change in temperature


The adjacent figure shows the crosssection of a long rod with its constant perpendicular to the plane of the paper It carries a constant current flowing
along its length \( B_{1}, B_{2}, B_{3} \) and \( B_{4} \)
respectively represent the length magnetic fields due to the current in the rod at point \( 1,2,3, \) and 4 lying at different separations from the centre 0 as shown in the figure. Which of the
following shall hold true.
A. \( B_{1}>B_{2} \neq 0 \)
В. \( B_{2}>B_{3} \neq 0 \)
c. \( B_{1}=B_{2}=B_{3}=0 \)
D. \( B_{3}>B_{4} \neq 0 \)


Two parallel wires each of length \( 5 m \) are
placed at a distance of \( 10 \mathrm{cm} \) apart in
air. They carry equal currents along the same direction and experience a mutually attractive force of \( 3.6 \times \)
\( 10^{-4} N . \) Find the current through the
conductors.


Which of the following alcohol has highest solubility in water?
A. Tertiary butyl alcohol
B. Secondary butyl alcohol
c. Ethylene glycol
D. Glycerol


Because of lanthanoid contraction, which of the following pairs of elements have nearly same atomic radii? (Numbers in the brackets are atomic
numbers)
A \( . \quad Z r(40) \) and \( N b(41) \)
B. \( Z r(40) \) and \( H f(72) \)
c. \( Z r(40) \) and \( T a(73) \)
D. \( T i(22) \) and \( Z r(40) \)


The potential energy (in joules) of a
particle of mass \( 1 \mathrm{kg} \) moving in a plane
is given by \( U=3 x+4 y, \) the position
coordinates of the point being \( x \) and \( y \) measured in metres. If the particle is at rest at \( (\mathbf{6}, \mathbf{4}), \) then
This question has multiple correct options
A . Its acceleration is of magnitude \( 5 \mathrm{m} / \mathrm{s}^{2} \)
B. its speed when it crosses the y-axis is \( 10 \mathrm{m} / \mathrm{s} \)
c. co-ordinates of particle at \( t=1 \) sec are (4.5,2)
D. the particle has zero acceleration


Name the following compound
according to IUPAC system:
A. Octamine- \( \mu \) -chloro- \( \mu \) -nitrodicobalt(III) sulphate
B. Octaammine- \( \mu \) -chloro- \( \mu \) -nitrodicobalt(III) sulphate
C. Octaammine- \( \mu \) -nitro- \( \mu \) -chlorodicobalt(III) sulphate
D. None of the above


Identify the best graph which
represents the relationship between the
average kinetic energy of the molecules
of a gas and its temperature?
\( A \)
B.
\( c \)
D.
E .


A bomb at rest explodes in air in two equal fragments. If one of the fragments starts moving vertically upwards with
velocity \( v_{0}, \) then the other fragment will
move:
A. vertically up with velocity \( v_{0} \)
B. vertically downwards with velocity \( v_{0} \)
c. in any arbitrary direction
D. none of these


Solve:
\( \left(1+\frac{1}{x+1}\right)\left(1+\frac{1}{x-1}\right)=\frac{7}{8} \)


Match List I with List II and select the
correct answer using the codes given
below the lists-
List List II
(1) Muscle contraction
(i) Zinc
(2) Blue-green algae
(ii) Cobalt
(3) Carboxypeptidase
(iii) Calcium
(4) Cyanocobalamine
(iv) Molybdenum
A. (1)-iv; (2)-iii; (3)-i; (4)-ii
B. (1)-iii; (2)-iv; (3)-ii; (4)-
c. (1)-iv; (2)-iii; (3)-ii; (4)-ii
D. (1)-iii; (2)-iv; (3)-i; (4)- -


fig a polynomial satisfying \( \boldsymbol{g}(\boldsymbol{x}) \boldsymbol{g}(\boldsymbol{y})=\boldsymbol{g}(\boldsymbol{x})+\boldsymbol{g}(\boldsymbol{y})+\boldsymbol{g}(\boldsymbol{x} \boldsymbol{y})-\boldsymbol{2} \)
for all real \( x \) and \( y \) and \( g(2)=5 \) then
\( \lim _{x \rightarrow 3} g(x) \) is
\( A \cdot 9 \)
B. 25
c. 10
D. none of these


Can you draw a triangle having: no line
of symmetry.


Petroleum is soluble in water.
A. True
B. False


The - COOH group in a carboxylic acid canbe replaced by H by heating the acid with :
A. zn with HCI
B. \( H_{2} \) in presence of nickel
c. soda lime
D. bromine and concentrated aqueous alkal


Arrange oxides \( \left(M_{2} O_{3}\right) \) of nitrogen family in increasing acidic nature:
A \( \cdot S b_{2} O_{3}<A s_{2} O_{3}<B i_{2} S_{3}<P_{2} O_{3}<N_{2} O_{3} \)
B. \( S b_{2} O_{3}>B i_{2} S_{3}>A s_{2} O_{3}>P_{2} O_{3}>N_{2} O_{3} \)
c. \( B i_{2} S_{3}<S b_{2} O_{3}<A s_{2} O_{3}<P_{2} O_{3}<N_{2} O_{3} \)
D. \( B i_{2} S_{3}>S b_{2} O_{3}>A s_{2} O_{3}>P_{2} O_{3}>N_{2} O_{3} \)


In which of the following cases will there
be no dispersion when sunlight passes
\( \mathbf{A} \)
B.
\( c \)
D.


A charged body possesses
A. a positive charge
B. a negative charge
C. either a positive or a negative charge
D. no charge


The number of structural isomers of
\( C_{3} H_{5} B r_{3} \) is :
\( A \cdot 4 \)
B. 5
\( c \cdot 6 \)
D. 7


The ion with pyramidal shape is:
\( A \cdot S_{2} O_{3}^{2} \)
B. \( S O_{3}^{-2} \)
\( \mathrm{c} \cdot \mathrm{SO}_{4}^{2-} \)
D. \( S_{2} O_{8}^{2-} \)


One \( k g \) of a diatomic gas is at a
pressure of \( 8 \times 10^{4} \mathrm{N} / \mathrm{m}^{2} . \) The density
of the \( \operatorname{gas} \) is \( 4 \mathrm{kg} / \mathrm{m}^{3} . \) What is the energy of the gas due to its thermal
motion?
A. \( 3 \times 10^{4} \mathrm{J} \)
B . \( 5 \times 10^{4} \mathrm{J} \)
c \( \cdot 6 \times 10^{4} \mathrm{J} \)
D. \( 7 \times 10^{4} \mathrm{J} \)


In which of the following pairs, both members liberate methane gas on reaction with water?
A. \( M g_{2} C_{3} \) and \( C a C_{2} \)
B. \( M g_{2} C_{3} \) and \( A l_{4} C_{3} \)
c. \( B e_{2} C \) and \( C a C_{2} \)
D. \( B e_{2} C \) and \( A l_{4} C_{3} \)


In DDT:
A. total 5 chlorine atoms are present
B. two chlorine atoms are attached to two phenyl rings each
C. three chlorine atoms are attached to the secondary carbon atom
D. All the above


The greenhouse effect is possible if the
percentage of \( \boldsymbol{C O}_{2} \) is :
A . 0.01 \%
B. 0.03 \%
c. \( 0.15 \% \)
D. 0.02 \%


During the decomposition of hydrogen peroxide glycerine acts as positive
catalyst. If this is true enter 1 and if false enter 0


In a given arrangement. Find out
velocity of water coming out of 'C'
\( \sqrt{\frac{2 g h_{3}}{1-\frac{a^{2}}{A^{2}}}} \)
\( \mathrm{B} \cdot \sqrt{\frac{3 g h_{3}}{1-\frac{a^{2}}{A^{2}}}} \)
\( \mathrm{c} \cdot \sqrt{\frac{2 g h_{3}}{1-\frac{a^{3}}{A^{2}}}} \)
\( D \)


Cyanocobalamin is rich in:
A. sewage sludge
B. liver of pig
\( c \cdot \operatorname{egg} \)
D. all of these


Which of the following table helps in representing the previous and next of the sequential circuit prior to and after the clock pulse respectively?
A. Truth table
B. Characteristic table
c. Excitation table
D. None of the above


Find the zeroes of the polynomial \( \frac{1}{7} x- \) \( \frac{2}{7} \)


Assertion
Sodium metal is stored under Kerosene.
Reason

Metallic sodium melts when exposed to
air.
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


Answer the following question in one
word or one sentence or as per exact
requirement of the question. Find the least value of \( f(x)=a x+\frac{b}{x} \)
where \( a>0, b>0 \) and \( x>0 \)


Consider the two gaseous equilibrium
involving \( S O_{2} \) and the corresponding equilibrium constants at \( 299 \mathrm{K} \)
\( \boldsymbol{S} \boldsymbol{O}_{2}(\boldsymbol{g})+\mathbf{1} / \boldsymbol{2} \boldsymbol{O}_{2}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{S} \boldsymbol{O}_{3}(\boldsymbol{g}) ; \boldsymbol{K}_{1} \)
\( \mathbf{4} \boldsymbol{S} \boldsymbol{O}_{3}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{4} \boldsymbol{S} \boldsymbol{O}_{2}(\boldsymbol{g})+\boldsymbol{2} \boldsymbol{O}_{2}(\boldsymbol{g}) ; \boldsymbol{K}_{2} \)
The value of the equilibrium constant are related by :-
A \( \cdot_{K_{2}}=\frac{1}{\left(K_{1}\right)^{4}} \)
B. \( K_{2}=K_{1}^{4} \)
c. \( _{K_{2}}=\left(\frac{1}{K_{1}}\right)^{1 / 4} \)
D. \( _{K_{2}}=\frac{1}{K_{1}} \)


Let \( * \) be binary operation on the set of all non-zero real numbers, given by \( a * \) \( b=\frac{a b}{5} \) for all \( a, b, \in R-\{0\} . \) Find the
value of \( x, \) given that \( 2 *(x * 5)=10 \)


A body is thrown up with an initial velocity u and it covers a maximum height of \( h, \) then h is equal to
\( ^{\mathrm{A}} \cdot \frac{u^{2}}{2 g} \)
в. \( \frac{u}{2 g_{g}} \)
c. \( 2 u g \)
D. None of these


Evaluate :
\( \int \frac{\sec ^{2} x}{\tan x} d x \)


\( \operatorname{Det}\left\{\begin{array}{ccc}1^{2} & 2^{2} & 3^{2} \\ 2^{2} & 3^{2} & 4^{2} \\ 3^{2} & 4^{2} & 5^{2}\end{array}\right\}=\dots \)
A . -8
B. -7
\( c .-6 \)
D. \( -21 / 4 \)


\( A B C D \) is a trapezium in which \( A B|| D C \) and its diagonals intersect
each other at point \( ^{\prime} \boldsymbol{O}^{\prime} \). Show that \( \frac{A O}{B O}=\frac{C O}{D O} \)


Find the domain of definition and the
range of the following function:
\( \boldsymbol{y}=\frac{\boldsymbol{x}}{|\boldsymbol{x}|} \)


Resonance structures of a molecule do
not have.
A. Identical arrangement of atoms
B. Nearly the same energy content
C. The same number of paired electrons
D. Identical bonding
E. All of the above


the ground state energy of hydrogen atom is \( -13.6 \mathrm{eV} \). the energy of second
excited state of \( H e^{+} \) ion in eV is :
\( \mathbf{A} \cdot-27.2 \)
в. -3.4
c. -54.4
D . -6.04


Our earth as well as the sun belongs to the galaxy which has a spiral shape called the
A. Milky way
B. Galaxy
c. Light Year
D. Universe


In a crossword puzzle, 20 words are to be guessed of which 8 words have each
an alternative solution also. The number
of possible solutions will be
A. \( 20 P_{8} \)
в. \( 20 \mathrm{C}_{8} \)
c. 512
D. 256


In domestic electric circuit,appliances are connected in parallel. Why?
A. because it consumes less power
B. because if one appliance stops working,other appliances keep on working
c. because it is longer than series supply so can be distributed to the whole house
D. it is comparatively easier to create.


A metal \( M \) forms a sulphate which is
isomorphous with \( M g S O_{4} .7 H_{2} O . \) If
\( 0.6538 \mathrm{g} \) of metal \( M \) displaced 2.16 g of silver from silver nitrate solution, then
the atomic weight of the metal \( M \) is:
A . 32.61
B. 56.82
c. 65.38
D. 74.58


Fill in the blanks with approriate words. Growth of female secondary sex organs is stimulated at puberty by .......... while
growth of male secondary sex organs is stimulated by


Which of the following proteins is globular?
A. Collagen
B. Albumin
c. Myosin
D. Fibroin


Photochemical smog always contains
A. aluminium ions
B. methane
c. ozone
D. phosphorus


A \( 250 g \) block slides on a rough horizontal table. Find the work done by
the frictional force in bringing the block to rest if it is initially moving at a speed of \( 40 \mathrm{cm} / \mathrm{s} \). If the friction coefficient between the table and the block is 0.1
how far does the block move before
coming to rest?


Assertion
Mixture is agitated in a washing machine. Agitation is necessary to get clean clothes.
Reason
To wash away the loosened dirt particle in form of micelles from the surface of
cloth, agitation is necessary.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A covalent chloride is :
A \( \cdot B e C l_{2} \)
B. \( N a C l \)
c. \( M g C l_{2} \)
D. \( C a C l_{2} \)


What is the unit digit in the product \( \left(3^{65} \times 6^{59} \times 7^{71}\right) ? \)
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c \cdot 4 \)
D. 6


For the inversion of cane sugar
\( \left(C_{12} H_{22} O_{11}\right) \) obeying I order following
data were obtained.
Time (min.) \( \mathbf{0} \)
rotation of Angle of +20 2.5 solution(degree)
What will be rate constant in \( m i n^{-1} ? \)
\[
(\ln 2=0.7)
\]
A. 0.7
B. 0.14
c. 0.21
D. 0.07


State a reason for each of the following
situations :

CO is a stronger complexing reagent
than \( \boldsymbol{N} \boldsymbol{H}_{3} \)


Iron glows in red colour when it is
heated to very high temperature. The reason for this is :
A. Heat we supply consumes red colour at high temperature
B. Mechanical energy is being converted into heat energy
c. All metals glow in red colour when heated
D. Heat energy is being converted into light energy


The composition of aqua-regia is :
A . Dil.HCl : Conc.H NO \( _{3}=3: 1 \)
в. Сопс.НСl: Dil. \( H N O_{3}=3: 1 \)
c. Conc.HCl: Conc.H \( \mathrm{NO}_{3}=3: 1 \)
D. Dil.HCl: Dil. \( \mathrm{H} \mathrm{NO}_{3}=3: 1 \)


Identify the organic compound:
HOOC \( -\left(\boldsymbol{C H}_{2}\right)_{2}-\boldsymbol{C O O H} \)


Short / Long answer type questions. Write briefly about the endocrine gland
which helps combat stress.


An object falls from a height of \( 15 \mathrm{m} \) in 0.5 sec. What is the average speed of the object?
A. \( 1.85 \mathrm{m} / \mathrm{s} \)
B. 20 \( \mathrm{m} / \mathrm{s} \)
c. \( 2.45 \mathrm{m} / \mathrm{s} \)
D. 2.86 \( \mathrm{m} / \mathrm{s} \)


Between the number 1 and \( 31, m \)
means are inserted so that the ratio of
\( 7^{t h} \) and \( (m-1)^{t h} \) means is \( 5: 9, \) then
the value of \( m \) is
A . 14
B. 10
\( c \cdot 7 \)
D. 3


\( \int_{0}^{\pi / 2} \frac{d x}{3+4 \sin x} d x= \)
\( \frac{1}{\sqrt{(k)}} \log \left(\frac{4+\sqrt{7}}{3}\right) \) then find the
value of \( k \)


The mass of the rocket is \( 500 \mathrm{Kg} \) and relative velocity of gas ejected out is \( 950 \mathrm{m} / \mathrm{s} \) with respect to rocket. determine the rate burning of the fuel in order to given the acceleration of the
rocket is \( 20 m / s^{2} ? \)


The area of a triangle formed with sides \( \mathbf{5} \hat{\mathbf{i}}+\mathbf{3} \hat{\mathbf{j}}-\hat{\boldsymbol{k}} \) and \( \mathbf{3} \hat{\mathbf{i}}+\mathbf{2} \hat{\mathbf{j}}-\hat{\boldsymbol{k}} \) is:
A \( \cdot \sqrt{6} \)
B. \( \sqrt{3} \)
\( c \cdot \sqrt{\frac{3}{2}} \)
D. \( \sqrt{\frac{5}{2}} \)


Draw diagrams illustrating each of the following situation:
(a) Three straight lines which do not pass through a fixed point.
(b) A point and rays emanating from that point such that the angle between any two adjacent rays is an acute angle.
(c) Two angles which are not adjacent angles, but still supplementary.
(d) Three points in the plane which are equidistant from each other


Find the measure of each angle of an
equilateral triangle.


A man is suffering from myopia can not see clearly objects kept distance away from 10.0 metre. What type of lens is used in spectacles to see objects at infinity and also find focal length and
power of the lens?


Wind blows with a velocity \( x \) in the direction shown in Fig. Two aeroplanes start out from point \( A \) and fly with a
constant speed \( y . \) The first flies from \( \boldsymbol{A} \)
to \( B \) and the other along \( A \) to \( C . \) Both of
them return back to \( \boldsymbol{A} \). If \( \boldsymbol{A B}=\boldsymbol{A C} \)
then which plane will return to point \( \boldsymbol{A} \)
first, and what will be the ratio of the
times of flight of the two planes?


A small hole is made at a height of \( \boldsymbol{h}= \)
\( \boldsymbol{m} \) from the bottom of a cylindrical
water tank and at a depth of \( \boldsymbol{h}=\mathbf{2 m} \)
from the upper level of water in the tank. The distance, where the water emerging from the hole strikes the ground, is:
A \( .22 m \)
в. \( 1 m \)
\( c .2 m \)
D. None of these


If \( r>1, \) then \( \frac{n P_{r}}{n C_{r}} \) is
This question has multiple correct options
A. is an integer
B. may be fraction
c. is an odd number
D. an even number


In the figure, line \( A B \) is a tangent to
both the circles touching at \( A \) and \( B \)
\( \boldsymbol{O} \boldsymbol{A}=\mathbf{2 9}, \boldsymbol{B P}=\mathbf{1 8}, \) and \( \boldsymbol{O P}=\boldsymbol{6 1 .} \) The
length of \( \boldsymbol{A B} \) is
\( A \cdot 61 c m \)
B. \( 60 \mathrm{cm} \)
c. \( 47 \mathrm{cm} \)
D. \( 11 c m \)


For a weak acid \( p K_{a} \) is \( 4.8, \) what will be the ratio of concentration of acid and
salt in pH 5.8 solution?
A . 10
B. 3
c. 9
D. 0.1


The equation of line bisecting perpendicularly the segment joining the points (-4,6) and (8,8) is
\( \mathbf{A} \cdot y=7 \)
в. \( 6 x+y-19=0 \)
c. \( x+2 y-7=0 \)
D. \( 6 x+2 y-19=0 \)


Write the degree of the following polynomial:
\( \mathbf{7} p^{2} \boldsymbol{q}^{3} \boldsymbol{t}-\mathbf{1} \mathbf{1} \boldsymbol{p}^{4} \boldsymbol{t}+\mathbf{2} \boldsymbol{p}^{8} \)
\( A \cdot 3 \)
B. 5
\( c \cdot 7 \)
\( D \)


A circular disc of radius R and
thickness R/6 has moment of inertia I
about an axis passing through its center and perpendicular to its plane. It is melt and recast into a solid sphere.
The moment of inertia of the sphere
about its diameter as axis of rotation is:
A \( \cdot \frac{1}{5} \)
в. \( \frac{2 I}{5} \)
c. \( \frac{4 I}{5} \)
D. \( \frac{I}{10} \)


For the equilibrium, \( N_{2} O_{4}(g) \rightleftharpoons \) \( 2 N O_{2}(g) ; \) if percentage dissociation of
\( N_{2} O_{4} \) are \( 25 \%, 50 \%, 75 \% \) and \( 100 \% \) then
the sequence of observed vapour densities will be:
A \( \cdot d_{1}>d_{2}>d_{3}>d_{4} \)
в. \( d_{4}>d_{3}>d_{2}>d_{1} \)
c. \( d_{1}=d_{2}=d_{3}=d_{4} \)
\( \mathbf{D} \cdot\left(d_{1}=d_{2}\right)>\left(d_{3}=d_{4}\right) \)


\( A B \) and \( C D \) are two parallel chords of a circle such that \( A B=10 \mathrm{cm} \) and
\( C D=24 \mathrm{cm} . \) If the chords are on
opposite sides of the centre and the distance between them is \( 17 \mathrm{cm} . \) The
radius of the circle is
\( \mathbf{A} \cdot 26 \mathrm{cm} \)
B. \( 39 \mathrm{cm} \)
c. \( 6.5 \mathrm{cm} \)
D. \( 13 \mathrm{cm} \)


A stone is dropped into a well of depth
\( h " . \) The splash is heard after time " \( \boldsymbol{t} " \) If " \( C " \) be the velocity of sound, then -
A \( \cdot t=\sqrt{\frac{g c}{2 h}} \)
B. \( t=c+g h \)
c. \( t=c-v \)
D. \( t=\frac{h}{c}+\sqrt{\frac{2 h}{g}} \)


A pool that is being drained contains \( 300-6 t \) gallons of water after \( t \)
minutes of draining. Calculate the gallons of water the pool contains after 15 minutes of draining.
A . 210
B. 250
c. 260
D. 230


Two monochromatic rays of light are
incident normally on the face \( A B \) of an isosceles right-angled prism ABC. The refractive indices of the glass prism for
the two rays '1' and '2' are respectively
1.38 and \( 1.52 . \) Trace the path of these
rays after entering through the prism.


Let \( * \) be an operation such that \( \boldsymbol{a} * \boldsymbol{b}= \)
LCM of \( a \) and \( b \) defined on the \( \operatorname{set} A= \)
\( \{1,2,3,4,5\} . \) Is \( * \) a binary operation?
Justify your answer.


Which one of the following is lyophillic colloid?
A. Milk
B. Gum
\( c \cdot \) Fog
D. Bloodd


Sugarcane is
A. Saccharum arundinaceum
B. Saccharum officinarum
c. saccharum spontaneum
D. Saccharum procerum


Substances used in two different
projects done by the members of a science club are given in the table.
Project - 1

Project - 2
Ethanoic acid
Ethanol
concentrated sulphuric acid
water
(a) In which project (Project 1 or Project
2) a compound with pleasant fruity smell is formed?
(b) How will you distinguish between distilled water and hard water by using the precipitate formed in Project 2 ?


A table lamp of power 60 W consumed 9 (commercial) units of electricity in the month of April. For how many hours per day, on an average, was the lamp in
use?
\( A \cdot 1 h \)
в. \( 3 h \)
\( c .5 h \)
D. \( 6 h \)


Name the instrument used to control
the current in an electric circuit.
A. Rheostat
B. Voltmeter
c. Ammeter
D. Galvanometer


The total number of cyclic structural
isomers of \( C_{6} H_{12} \) is \( x . \) Find the sum of
digits of \( x ? \)
(in case of single digit take another number as \( 0) \)


Left hand derivative and right hand
derivative of a function \( f(x) \) at a point \( x=a \) are defined as
\( f^{\prime}\left(a^{-}\right)=\lim _{h \rightarrow 0^{+}} \frac{f(a)-f(a-h)}{h}= \)
\( \lim _{h \rightarrow 0^{-}} \frac{f(a)-f(a-h)}{h}= \)
\( \lim _{x \rightarrow a^{+}} \frac{f(a)-f(x)}{a-x} \) respectively
Let \( f \) be a twice differentiable function.
We also know that derivative of an even
function is odd function and derivative
of an odd function is even function.
If \( f \) is even, which of the following is
Right hand derivative of \( \boldsymbol{f}^{\prime} \) at \( \boldsymbol{x}=\boldsymbol{a} \)
A. \( \lim _{h \rightarrow 0^{-}} \frac{f^{\prime}(a)+f^{\prime}(-a+h)}{h} \)
B. \( \lim _{h \rightarrow+} \frac{f^{\prime}(a)+f^{\prime}(-a-h)}{h} \)
c. \( \lim _{h \rightarrow 0} \frac{-f^{\prime}(a)+f^{\prime}(-a+h)}{-h} \)
D. \( \lim _{h \rightarrow 0^{+}} \frac{f^{\prime}(a)+f^{\prime}(-a+h)}{h} \)


Solve the following inequalities.
\( \log _{1 / 2}(x+4)<2 \)


Write the balanced reaction of
ammonia with excess chlorine?


Which roots amongst the following grow against gravitational force?
A. Prop roots
B. Stilt roots
c. Buttress roots
D. Pneumatophores


What is reverberation? How can it be
reduced?


Examine the figure given and select the
correct options giving all the four parts \( (a, b, c, d) \) correctly identified.
A. A - Seta, B - Sporophyte, C - Protonema, D - Rhizoids
B. A - Antheridio-phore, B - Male thallus, C - Globule, D Roots
C. A - Archegonio-phore, B - Female thallus, C - Bud, D Foot
D. A - Archegonio-phore, B - Female thallus, C - Gemma cup, D - Rhizoids


From a uniform circular disc of mass
\( M \) and radius \( R \) a small disc of radius
\( R / 2 \) is removed is such away that both have a common tangent. Find the distance of center of mass of remaining
part from the center of original disc.
\( \mathbf{A} \cdot R / 20 \)
в. \( R / 16 \)
c. \( R / 6 \)
D. \( \frac{3}{4} R \)


13824 is a perfect cube
Find the units digit of the cube root of
the following numbers:


The numbering in alkenyl groups is started from the carbon with double
bond.
A. True
B. False


Solubility of salt \( X \) in water is 32 at \( 30^{\circ} \)
C. Calculate the amount of solvent
present in 500 g of saturated solution of \( X \)
A. \( 160 \mathrm{g} \)
в. 379 g
c. \( 460 \mathrm{g} \)
\( D \cdot 68 g \)


The gravitational potential energy of a body at a distance \( r \) from the centre of
earth is \( U . \) Its weight at a distance \( 2 r \)
from the centre of earth is
A \( \cdot \frac{U}{r} \)
в. \( \frac{U}{2 r} \)
c. \( \frac{U}{4 r} \)
D. \( \frac{U}{\sqrt{2} r} \)


Solids have infinite free surfaces while
liquids have only one upper free surface.


It is known that \( \sum_{r=1}^{\infty} \frac{1}{(2 r-1)^{2}}=\frac{\pi^{2}}{8} \)
Then \( \sum_{r=1}^{\infty} \frac{1}{r^{2}} \) is equal to
A \( \cdot \frac{\pi^{2}}{24} \)
в. \( \frac{\pi^{2}}{3} \)
c. \( \frac{\pi^{2}}{6} \)
D. none of these


For an ideal solution with \( \boldsymbol{p}_{\boldsymbol{A}}>\boldsymbol{p}_{\boldsymbol{B}} \)
which of the following is true?
\( \mathbf{A} \cdot\left(x_{A}\right)_{l i q}=\left(x_{B}\right)_{v a p} \)
B . \( \left(x_{A}\right)_{l i q}>\left(x_{B}\right)_{v a p} \)
C . \( \left(x_{A}\right)_{l i q}<\left(x_{B}\right)_{v a p} \)
D. \( \left(x_{A}\right) \) liqand \( \left(x_{B}\right)_{v a p} \) do not bear any ralationship with each other


Which one of the following is a cartilaginous fish?
A. Wallago
B. Anguilla
c. Notopterous
D. Torpedo


The ratio of the slopes of adiabatic and isothermal curves is
A \( \cdot \frac{1}{\gamma} \)
в. \( \frac{1}{\gamma^{3}} \)
\( c \cdot \gamma^{3} \)
D.


Which of the following socio-economic factor tend to keep birth rate in India at a high level?
A. Urbanisation
c. Poverty
D. None of the above


Expected number of heads when we toss \( n \) unbiased coins is
\( \mathbf{A} \cdot 2 n \)
в. \( n \)
\( c \cdot \frac{n}{2} \)
D. \( \frac{n}{4} \)


\( \int \frac{x^{2}}{\left(x^{2}+2\right)\left(x^{2}+3\right)} d x= \)
\( \mathbf{A} \cdot-\sqrt{2} \tan ^{-1} x+\sqrt{3} \tan ^{1} x+c \)
B \( \cdot-\sqrt{2} \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)+\sqrt{3} \tan ^{-1}\left(\frac{x}{\sqrt{3}}\right)+c \)
C \( \cdot \sqrt{2} \tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)+\sqrt{3} \tan ^{-1}\left(\frac{x}{\sqrt{3}}\right)+c \)
D. None of these


Let \( y=\left(1+x^{2}\right) \tan ^{-1}(x-x) \) and
\( f(x)=\frac{1}{2 x} \frac{d y}{d x}, \) then \( f(x)+\cot ^{-1} x \) is
equal to
\( \mathbf{A} \cdot \mathbf{0} \)
в. \( \frac{\pi}{2} \)
c. \( -\frac{\pi}{2} \)
D.


Assertion
Magnetic field lines are continuous and closed.
Reason Magnification of a convex mirror is
always positive, but that of a concave
mirror may be both positive or negative.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The fluid present between the blood
capillaries and the cell membrane through which gasses, nutrients, and metabolic wastes are exchanged between the blood and the cell is called
as
A. Lymph
B. Plasma
c. Serum
D. Normal saline


If a body executes motion with uniform acceleration, the velocity-time graph
A. is a straight line inclined to the time axis
B. is a straight line parallel to the time axis
c. is a straight line perpendicular to the time axis
D. cannot be plotted


Identify the solution set for \( -(x-3)+ \)
\( 4<5-2 x \)
\( A \cdot(-\infty, 0) \)
в. \( (-\infty,-1) \)
c. \( (-\infty,-2) \)
D. \( (-\infty,-5) \)


In \( \triangle P Q R, P D \perp Q R \) such that \( D \) lies
on \( Q R \). If \( P Q=a, P R=b, Q D=c \) and
\( D R=d, \) then
A \( \cdot(a-d)(a+d)=(b-c)(b+c) \)
B . \( (a-c)(b-d)=(a+c)(b+d) \)
C \( \cdot(a-b)(a+b)=(c+d)(c-d) \)
D \( \cdot(a-b)(c-d)=(a+b)(c+d) \)


the density of cooking oil is \( 0.6 g / c m^{3} \)
What is the mass of \( 18 \mathrm{cm}^{3} \) of the
cooking oil?
A . \( 0.5 g \)
в. \( 10.8 g \)
c. \( 18.9 g \)
D. \( 20.0 g \)


A small ball of mass \( m \) and charge \( +q \)
tied with a string of length \( l \) is rotating in a vertical circle under gravity and a
uniform horizontal electric field \( \boldsymbol{E} \) as
shown. The tension in the string will be
minimum for:
A \( \cdot \quad \theta=\tan ^{-1}\left(\frac{q E}{m g}\right) \)
B . \( \theta=\pi \)
\( ^{\mathbf{c}} \cdot_{\theta}=\pi-\tan ^{-1}\left(\frac{q E}{m g}\right) \)
D.


A galvanometer gives full scale deflection of 1 volt when acting like a voltmeter when connected in series
with \( 2 k \Omega \) resistance. The same
galvanometer gives \( 500 \mathrm{mA} \). Full scale deflection when acting like a ammeter
when connected with shunt resistance
of value \( 0.2 \Omega \) in parallel. Find out the resistance of galvanometer


Which among the following is the best conductor of electricity?
A. Oxygen
B. Aluminium
c. carbon
D. woodd


Find the square of 125
A .84113
B . 48000
c. 15625
D. 84920


Solid phosphorus melts and evaporates at high temperature Gaseous phosphorus effuses at a rate that is
0.567 times that of Ne in the same
apparatus under the same conditions.
How many atoms are in a molecule of gaseous phosphorus.


Which process of purification is represented by the following scheme? \( \underset{i m p u r e}{\boldsymbol{T} \boldsymbol{i}}+\boldsymbol{2} \boldsymbol{I}_{2} \stackrel{250^{\circ} C}{\longrightarrow} \boldsymbol{T} \boldsymbol{i} \boldsymbol{I}_{4} \frac{1400^{\circ} \boldsymbol{C}}{\longrightarrow} \boldsymbol{T} \boldsymbol{i}+ \)
\( 2 I_{2} \)
A. Cupellation
B. zone refiningg
c. van-Arkel process
D. Poling


(A) pH of \( 10^{-7} \) M NaOH solution exists
between 7 to 7.3 at \( 25^{\circ} C \)
(R) Due to common ion effect ionization
of water is suppressed.
A. Both (R) and (A) are true and reason is the correct explanation of assertion
B. Both (R) and (A) are true but reason is not correct explanation of assertion
c. Assertion
(A) is true but reason
(R) is false
D. Assertion
(A) and reason
(R) both are false
E. Assertion (A) is false but reason (R) is true


The mean of 30 scores is 18 and their
standard deviation is \( 3 . \) Find the sum of
all the scores and also the sum of the
squares of all the scores


On a two-component solid-liquid phase
diagram, an isopleth indicates which of
the following?
A. A region where the composition of the system is constant
B. An area above which only the liquid phase exists
C. A region where the pressure is constant
D. An area below which only the solid phase exists


Who is responsible for development of chemical nomenclature?
A. Jons Berzelius
B. Antoine Lavoisier
c. otto Hahn
D. Gilbert Lewis


Arrange the following data according to the increasing order of Radius of
curvature of the given plano convex lenses
a) plano convex lens of \( f=40 \mathrm{cm} \) and
\( \mu=1.5 \)
b) plano convex lens of \( f=20 \mathrm{cm} \) and
\( \mu=1.6 \)
c) plano convex lens of \( f=20 \mathrm{cm} \) and
\( \mu=1.5 \)
d) plano convex lens of \( f=25 \mathrm{cm} \) and
\( \mu=1.5 \)
\( \mathbf{A} \cdot \mathbf{b}, \mathbf{a}, \mathrm{d}, \mathrm{c} \)
B. \( a, b, c, d \)
\( c \cdot c, b, d, a \)
D. \( c, b, a, d \)


The product \( ^{\prime} \boldsymbol{A}^{\prime} \) is:
A \( \cdot C_{6} H_{5} C O C H_{3} \)
В \( \cdot C_{6} H_{5} \) СС
\( \mathbf{c} \cdot C_{6} H_{5} C H O \)
D. \( C_{6} H_{5} O H \)


A student burns \( 2.0 g \) magnesium metal over a flame which reacts with excess
oxygen. A white cyrstalline solid begins to form on the piece of magnesium.
\( \mathbf{2} \boldsymbol{M} \boldsymbol{g}_{(s)}+\boldsymbol{O}_{2(\boldsymbol{g})} \rightarrow \mathbf{2} \boldsymbol{M} \boldsymbol{g} \boldsymbol{O}_{(s)} \)
How could you determine the reaction
obeyed the law of conservation of mass?
A. Mass the sample after the reaction is complete and compare it to the mass before the reaction begins
B. Mass the sample as the reaction is run
C. Run the reaction by filtration
D. Run the reaction in an open system


The resistance of a conductivity cell
containing \( 0.001 M K C l \) solution at
\( 298 K \) is \( 1500 \Omega \). What is the cell
constant if conductivity of
\( 0.001 M K C l \) solution at \( 298 K \) is
\( 0.146 \times 10^{-3} S c m^{-1} ? \)


Of the following, the equation of plane progressive wave is:
A. \( y=r \sin \omega t \)
в. \( y=r \sin (\omega t-k x) \)
c. \( y=\frac{a}{\sqrt{r}} \sin (\omega t-k x) \)
D. \( y=\frac{a}{r} \sin (\omega t-k t) \)


What is the basicity of orthophosphorus
acid?
A. one
B. Two
c. Three
D. Four


White phosphorus on reaction with concentrated \( N a O H \) solution in an
inert atmosphere of \( C O_{2} \) gives phosphine and compound \( (X) .(X) \) on acidification with \( H C l \) gives compound
\( (Y) . \) The basicity of compound \( (Y) \) is :
A .4
B. 3
c. 1
D.


Gametophyte embeded in sporophyte in
A. Bryophyta
B. Pteridophyta
c. cryptogams
D. spermatophyta


Current of \( 2 A \) passing through a coil of
100 turns gives rise to a magnetic flux of \( 5 \times 10^{-3} W b \) per turn. The magnetic energy associated with coil is
\( \mathbf{A} \cdot 5 \times 10^{-3} J \)
B. 5.5
c. \( 0.5 \times 10^{-3} J \)
D. \( 0.5 J \)


A body projected vertically up with a
velocity of \( 10 \mathrm{m} \mathrm{s}^{-1} \) reaches a height of \( 20 \mathrm{m} . \) If it is projected with a velocity of \( 20 \mathrm{m} \mathrm{s}^{-1}, \) then the maximum height reached by the body is :
A . 20
B. 10 \( m \)
c. \( 80 \mathrm{m} \)
D. \( 40 \mathrm{m} \)


If the line \( 2 x+5 y=k \) passes through
origin then \( k= \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
c. -1
D.


Compare between metaphase I and metaphase II of meiosis?


Which of the following rules regarding the significant figures and calculations
involving them is not correct?
A. The result of an addition or subtraction is reported to the same number of decimal places as present in number with least decimal places.
B. Result of multiplication or division should have same number of significant figures as present in most precise figure
C. The result of multiplication or division should be rounded off to same number of significant figures as present in least precise figure.
D. The non-significant figures in the measurements are rounded off.


The weight of silver (At. Wt. = 108) displaced by a quantity of electricity
which displaces \( 5600 \mathrm{ml} \) of \( O_{2} \) at STP will be
A. \( 5.4 \mathrm{g} \)
B. \( 10.8 \mathrm{g} \)
c. \( 54.0 \mathrm{g} \)
D. \( 108.0 \mathrm{g} \)


The work done in which of the following process is equal to the internal energy of the system?
A. Adiabatic process
B. isothermal process
c. Isochoric process
D. None of these


Evaluate: \( \tan ^{-1}\left(\frac{3 a^{2} x-x^{3}}{a^{3}-3 a x^{2}}\right) \)


What is NOT an example of an insulator in the kitchen?
A. An oven mitt
B. A wooden spoon
c. Pots and pans
D. A plastic measuring cup


\( \sin 11^{\circ} 19 \cos 18^{\circ} 41+ \)
\( \cos 11^{\circ} 19 \sin 18^{\circ} 41= \)
A .
B. \( \frac{\sqrt{3}}{2} \)
\( c \cdot \frac{1}{2} \)
D. 0


The material which is commonly used for making kitchen containers is :
A. PVC
B. Acrylicc
c. Teflon
D. PET


The mean square deviation of set of \( n \)
observations \( x_{1}, x_{2}, \ldots . . x_{n} \) about a point \( c \) is defined as \( \frac{1}{n} \sum_{i=1}^{n}\left(x_{i}-c\right)^{2} \)
The mean square deviation about -2 and 2 are 18 and 10 respectively, then standard deviation of this set of
observations is
A . 3
B. 2
c. 1
D. none of these


Assertion
The largest term in the sequence \( a_{n}= \) \( \frac{n^{2}}{n^{3}+200}, n \in N \) is the \( 7^{t h} \) term
Reason
The function \( f(x)=\frac{x^{2}}{x^{3}+200} \) attains
local maxima at \( x=7 \)
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


An iron ball has a mass of 35 gms and a speed of \( 50 \mathrm{m} / \mathrm{s} \). If the speed can be measured with in accuracy of \( 2 \% \) then the uncertainty in the position is :
A. \( 1.507 \times 10^{-34} m \)
В. \( 1.507 \times 10^{-31} m \)
c. \( 1.507 \times 10^{-33} m \)
D. \( 1.507 \times 10^{-12} m \)


Sl unit of \( G \) is \( N m^{2} k g^{-2} . \) Which of the
following can also be used as the Sl unit
of G?
A \( \cdot m^{3} k g^{-1} s^{-2} \)
B . \( m^{2} k g^{-2} s^{-1} \)
\( \mathbf{c} \cdot m k g^{-3} s^{-1} \)
D. \( m^{2} k g^{-3} s^{-2} \)


Find the volume of metal used to
construct a hollow metallic sphere of
internal and external diameters as 10
\( \mathrm{cm} \) and \( 13 \mathrm{cm} \) respectively.


The de-Broglie wavelength of a neutron
\( \operatorname{at} 927^{0} \mathrm{C} \) is \( \lambda . \) Its wavelength at \( 27^{0} \mathrm{C} \) is:
\( A \cdot \frac{\lambda}{2} \)
B. \( \lambda \)
\( c \cdot 2 \lambda \)
D. \( 4 \lambda \)


Bentonite, a clay of alumina-silica, is
dropped from aeroplanes in the form of a slurry with water for the purpose of:
A. cooling the soil
B. fertilizing the soil
c. fumigation of plants
D. spreading water over fires


Which of the following is not the component of heat pump?
A. Condenser
B. Compressor
c. cooler
D. Expansion valve


The dissociation constant of uric acid is
\( \boldsymbol{K}_{\boldsymbol{a}}=\mathbf{4 . 0} \times \mathbf{1 0}^{-\mathbf{6}} \boldsymbol{M} . \) The \( \boldsymbol{p} \boldsymbol{H} \) of a
sample is \( 6.0 . \) What is the ratio of urate
ion to uric acid in the urine??


The value of 1 amu is equal to:
A \( \cdot 1.66 \times 10^{-8} g \)
в. \( 1.66 \times 10^{-4} g \)
c. \( 1.66 \times 10^{-16} g \)
D. \( 1.66 \times 10^{-24} g \)


For the elementary reaction \( \mathrm{M} \rightarrow \mathrm{N} \), the rate of disappearance of M increases by factor of 8 upon doubling the concentration of M. The order of the
reaction with respect to M is
\( A \cdot 4 \)
B. 3
\( c \cdot 2 \)
\( D \)


The sensitivity of moving coil galvanometer can be increased by increasing
A. Number of turns of the coil
B. Magnetic field
c. Area of the coil
D. Couple per unit twist of suspension


Two concentric coils each of radius
equal to \( 2 \pi c m \) are placed at right
angles to each other. 3 Ampere and 4
ampere are the currents flowing in each coil respectively. The magnetic induction in \( W \) eber \( / m^{2} \) at the centre of
the coils will be \( \left(\mu_{0}=4 \pi x\right. \)
\( \left.\mathbf{1 0}^{-\mathbf{7}} \boldsymbol{W} \boldsymbol{b} / \boldsymbol{A}-\boldsymbol{m}\right) \)
A \( \cdot 12 \times 10^{-5} \)
B. \( 10^{-5} \)
\( c \cdot 5 \times 10^{-5} \)
D. \( 7 \times 10^{-5} \)


With increase of temperature, the frictional force acting between two surfaces:
A . increases
B. decreases
c. remains same
D. may increases or decreases


The standard deviation of variate \( \boldsymbol{x}_{\boldsymbol{i}} \) is \( \boldsymbol{\sigma} \)
Then standard deviation of the variate \( \frac{a x_{i}+b}{c}, \) where \( a, b, c \) are constants is
A \( \cdot\left(\frac{a}{c}\right)^{\sigma} \)
в. \( \left|\frac{a}{c}\right| \sigma \)
\( ^{\mathrm{c}} \cdot\left(\frac{a^{2}}{c^{2}}\right) \sigma \)
D. none of these


Give an example of bio-degradable
polymer.


In a constant volume calorimeter, 5 g of
a gas with molecular weight 40 was
burnt in excess of oxygen at \( 298 \mathrm{K} \). The temperature of the calorimeter was
found to increase from \( 298 \mathrm{K} \) to \( 298.75 \mathrm{K} \)
due to combustion process. Given that the heat capacity of the calorimeter is
\( 2.5 \mathrm{kJ} K^{-1} \), the numerical value for the
\( \Delta U \) of combustion of the gas in \( \mathrm{kJ} \)
\( m o l^{-1} \) is:
A . 15
B. 12
c. 90
D. 8


Evaluate \( \int e^{x}(\tan x-\log \cos x) d x \)


If \( \frac{\pi}{2}<\theta<\frac{3 \pi}{2}, \) then the value of \( \sqrt{\frac{1-\sin \theta}{1+\sin \theta}} \) is equal to
\( \mathbf{A} \cdot-\sec \theta+\tan \theta \)
B. \( \sec \theta+\tan \theta \)
\( \mathbf{c} \cdot \sec \theta-\tan \theta \)
D. None of these


Correct arrangement of the following
acids in correct \( \boldsymbol{K}_{3} \) order is :
\( (\boldsymbol{I}) \boldsymbol{H} \mathbf{3} \boldsymbol{N} \oplus \boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{C O O H}(\boldsymbol{I I}) \boldsymbol{N C C H} \mathbf{2 C} \)
A \( .|>||>|||>|V| \)
\( V \)
B. || >|>॥|> |V
c. \( |>|||>||>\mid V \)
D. IV>||| > || > |


\( R \) is a relation on \( N \) given by \( R= \)
\( \{(x, y) \mid 4 x+3 y=20\} . \) Which of the
following doesnot belong to \( R \) ?
A \( .(-4,12) \)
B . (5,0)
c. (3,4)
(年. \( (3,4)) \)
D. (2,4)


Write note on Wurtz reaction and
mention any 2 uses of iodoform


If both the distinct roots of the equation
\( |\sin x|^{2}+|\sin x|+b=0 \) in \( [0, \pi] \) are
real, then the value of \( b \) is
\( \mathbf{A} \cdot[-2,0] \)
B . (-2,0)
\( c \cdot[-2,0) \)
D. None of these


Which of the following statements is
false?
A. The x-coordinates of all points to the right of the y-axis are positive
B. The y- coordinates of all points above the x-axis are positive
C. The \( y \) - coordinates of all points below the x-axis are positive
D. The x-coordinates of all points to the left of the y-axis are negative


Mur man indower


Assertion
\( N_{2} \) molecule is highly unreactive.
Reason
\( \therefore N \ddot{:} N_{0}^{\circ}, N_{2} \) is unreactive since, bond
energy is very high.
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


Find odd one out:
Falling stone, a child sliding down a slope, firing of a bullet from a gun, a girl swinging in a swing
A . a girl swinging in a swing
B. falling stone
c. a child sliding down a slope
D. firing of a bullet from a gun


The number of \( \sigma \) bonds and \( \pi \) bonds in
1, 3-butadiene are respectively:
A. 9 and 2
B. 6 and 2
\( c .9 \) and 6
D. none of these


The reaction of Krebs cycle take place
A. In cytoplasm
B. In endoplasmic reticulum
C. In matrix of mitochondria
D. On the surface of mitochondrion


Find the range of each of the following
functions \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2}-\boldsymbol{6} \boldsymbol{x}+\mathbf{1 1}, \) all \( \boldsymbol{x} \in \)
\( \boldsymbol{R} \)


A car is moving along a straight level road with constant speed. Then
A. The work done on the car is infinite
B. The work done on the car is zero
c. The work done on the car is a measure of the gravitational potential energy
D. The work done on the car cannot be found


Q Type your question
are true?
a. In phase 3 , some bacteria may be
dividing.
b. Phase 2 is called as the lag phase and phase 1 is called as the log phase.
c. Phase 4 could be caused by the buildup of metabolic toxins.
d. Growth in phase 2 follows an exponential progression.
e. The fastest rate of growth is seen at
the plateau, i.e., phase 3
\( A \cdot a, b \) and \( c \)
B. b and e
\( c . a, c \) and \( d \)
D. a and d
三


In a gravity free space, a man of mass \( M \) standing at a height \( h \) above the floor throws a stone of mass \( \boldsymbol{m} \)
downwards with a speed \( u . \) When the stone reaches the floor, distance of the
man above the floor will be :
\( A \cdot h \)
B. \( 2 h \)
c. \( _{h}-\frac{2 m h}{M} \)
D. \( \frac{m h}{M}+h \)


How water act both as on oxidising and reducing agent? Give examples.


Which among the following will be
named as dibromidobis
(ethylenediamine) chromium(III) bromide?
\( \mathbf{A} \cdot\left[\operatorname{Cr}(e n)_{3}\right] B r_{3} \)
в. \( \left[\operatorname{Cr}(e n)_{2} B r_{2}\right] B r \)
c. \( \left.\operatorname{Cr}(e n) B r_{4}\right] \)
D. \( \left[C r(e n) B r_{2}\right] B r \)


Match the pairs.


A point charge q of mass \( \mathrm{m} \) is located at the center of a ring having radius \( \mathrm{R} \) and charge Q.When it is displaced slightly, the point charge accelerates along the x-axis to infinity, the ultimate speed of
the point charge:-
A \( \cdot \sqrt{\frac{2 K Q q}{m R}} \)
в. \( \sqrt{\frac{K Q q}{m R}} \)
c. \( \sqrt{\frac{K Q q}{2 m R}} \)
D. zero


Bonding pairs of electrons in each carbon atom:
A . repel
B. attract
c. remain intact
D. centrifuge


Based on the following reaction and rate data:
\( \boldsymbol{A}(\boldsymbol{g})+\boldsymbol{B}(\boldsymbol{g}) \rightarrow \) products
Experiment \( \quad \begin{array}{ll}{[\boldsymbol{A}]} & {[\boldsymbol{B}]} & \text { Initial } \\ \mathrm{mol} / \mathrm{L} & \mathrm{mol} / \mathrm{L}\end{array} \) 0.040 \( \begin{array}{ccc}1 & 0.060 & 0.010 \\ 2 & 0.030 & 0.010\end{array} \) an 0.040 3 A \( 0.030 \quad 0.020 \) 0.080
What is the order of the reaction with
respect to \( \boldsymbol{A} ? \)
\( A \cdot O \)
B.
\( c \cdot 2 \)
D. 3
\( E \cdot 4 \)


Eukaryotic, achlorophyllous and heterotrophic organisms are grouped under which of the following kingdoms?
A. Monera
B. Protistata
c. Fungi
D. Plantae


Which one value is required for better enzymatic action?
A . High \( \mathrm{K} \)
B . Low k
c. Low \( \kappa_{m} \)
D. High \( \mathrm{K}_{m} \)


The enthalpy change of a reaction does not depend on:
A. state of reactants and products
B. nature of reactants and products
c. different intermediate reactions
D. initial and final enthalpy change of reaction


Which of the following amino acid has
pH greater than \( 7 ? \)
A. Glutamic acid
B. Lysine
c. Glycine
D. Alanine


toppr
Q Type your question-
a. The angle between the edge along
the \( z \) -axis (line ab) and the diagonal
from the origin to the opposite corner
(line ad).
b. The angle between line \( a c \) (the
diagonal of a face) and line \( a d \)
A \( \cdot \) a. \( \cos ^{-1} \frac{1}{\sqrt{2}} \)
b. \( \cos ^{-1} \frac{\sqrt{2}}{\sqrt{3}} \)
B. a. \( \cos ^{-1} \frac{1}{\sqrt{3}} \)
c. a \( \cos ^{-1} \frac{1}{\sqrt{3}} \)
b. \( \cos ^{-1} \frac{\sqrt{3}}{\sqrt{3}} \)
D. a. \( \cos ^{-1} \frac{2}{\sqrt{3}} \)


In a first-order reaction the
concentration of the reactant is
decreased from \( 1.0 M \) to \( 0.25 M \) in
20 min. The rate constant of the
reaction would be:
A .10 min \( ^{-1} \)
B. 6.931 min \( ^{-1} \)
\( \mathbf{c} \cdot 0.6931 \mathrm{min}^{-1} \)
D. 0.06931 min\( ^{-1} \)


\( \frac{a^{2}-b^{2}-2 b c-c^{2}}{a^{2}+b^{2}+2 a b-c^{2}} \) is equivalent to
A \( \cdot \frac{a+b+c}{a-b+c} \)
в. \( \frac{a-b-c}{a+b-c} \)
c. \( \frac{a-b-c}{a-b+c} \)
D. \( \frac{a-b+c}{a+b+c} \)


Select the correct matching in the following pairs.
A. Rough ER - Synthesis of glycogen
B. Rough ER - Oxidation of fatty acids
c. Smooth ER - - Oxidation of phospholipids
D. smooth ER - synthesis of lipids


\( \operatorname{Let} \boldsymbol{S}_{\boldsymbol{n}}=\frac{\boldsymbol{n}}{(\boldsymbol{n}+\mathbf{1})(\boldsymbol{n}+\mathbf{2})}+ \)
\( \frac{n}{(n+2)(n+4)}+\frac{n}{(n+3)(n+6)}+ \)
\( \ldots .+\frac{1}{6 n}, \) then \( \lim _{n \rightarrow \infty} S_{n} \) is
This question has multiple correct options
A \( \cdot \ln \frac{3}{2} \)
B. \( \ln \frac{9}{2} \)
\( c \cdot>1 \)
D . < 2


Find the cube root of 64 by prime factorisation method.


State whether the statement is
ture/false.
\( \int_{-\pi / 2}^{\pi / 2}\left(\frac{\sin x}{1-\cos x}\right) d x=0 \)
A. True
B. False


The concentration of matter in a
material is:
A. volume
B. mass
c. density
D. none of these


A battery is delivering same power to
resistance \( R_{1} \) and \( R_{2} . \) Then find the internal resistance of battery :
A. \( \frac{R_{1}-R_{2}}{2} \)
В. \( R_{1}+R_{2} \)
c. \( \sqrt{R_{1}+R_{2}} \)
D. \( \sqrt{R_{1}+R_{2} / 2} \)


Which side of the heart pumps only deoxygenated blood?
A. Right
B. Left
c. Both right and left
D. None of the above


By the definition of the definite integral, the value of
\( \lim _{n \rightarrow \infty}\left(\frac{1^{4}}{1^{5}+n^{5}}+\frac{2^{4}}{2^{5}+n^{5}}+\frac{3^{4}}{3^{5}+n^{5}}+\right. \)
is
\( A \cdot \log 2 \)
B \cdot \( \frac{1}{5} \log 2 \)
c. \( \frac{1}{4} \log 2 \)
D. \( \frac{1}{3} \log 2 \)


A rational number \( -2 / 3 \)
A. Lies to the left side of 0 on the number line.
B. Lies to the right side of 0 on the number line.
C. It is not possible to represent on the number line.
D. Cannot be determined on which side the number lies.


Distance \( \boldsymbol{x}_{3} \) is given by
A. \( \sqrt{3} a \)
В. \( \sqrt{2} a \)
c. \( \frac{1}{2} \sqrt{3} a \)
\( 2.2 \sqrt{3} a \)


A small village, having a population of \( 5000, \) requires 75 litres of water per head per day. The village has got an
overhead tank of measurement \( 40 \mathrm{m} \)
\( \times 25 \mathrm{m} \times 15 \mathrm{m} . \) For how many days will the water of this tank last?


\( 16.8 \mathrm{g} \) of metal carbonate on thermal decomposition gave 8 g of metallic oxide and \( 8.8 \mathrm{g} \) of carbon dioxide. They follow:
A. Law of constant proportion
B. Law of multiple proportion
c. Law of conservation of mass
D. None of the above


Which of the following is a statement?
\( A \). I am Lion.
B. Logic is an interesting subject
C. A triangle is a circle and 10 is a prime number
D. None of these.


Mention two applications of infrared
radiation.


For the reaction:
\( \boldsymbol{F} \boldsymbol{e}^{2+}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{A} \boldsymbol{g}^{+}(\boldsymbol{a} \boldsymbol{q}) \longrightarrow \boldsymbol{A} \boldsymbol{g}(\boldsymbol{s})+ \)
\( \boldsymbol{F} \boldsymbol{e}^{+\boldsymbol{3}}(\boldsymbol{a} \boldsymbol{q}) \)
Predict which change will decrease the cell voltage?
A. Increase the amount of Agg
B. Decrease the concentration of \( A g^{+} \)
C. Increase the concentration of \( F e^{+3} \)
D. Both \( B \) and \( C \)


Interchange of left and right sides of an object in a plane mirror is known as:
A. reflection
B. refraction
c. lateral inversion
D. all


Which has the smallest bond \( (\boldsymbol{X}-\boldsymbol{S}- \)
\( X) \) in the given molecules?
A. \( O s F_{2} \)
в. \( O s C l_{2} \)
\( \mathrm{c} \cdot O s B r_{2} \)
D. \( O s I_{2} \)


Which of the following factor(s) affect bond length?
This question has multiple correct options
A. Size of atoms making the bond.
B. Bond order.
C. Oxidation number of central atom.
D. Percentage s-character in the orbitals used in making the bond.


Osmoregulation is control over the
A. \( \mathrm{pH} \) of the blood and other tissues
B. removal of nitrogen from the body
C . osmotic properties of cell membranes
D. concentrations of salt and water in the body


Which of the following is not the unit of atmosperhic pressure?
A . Pascal
в. \( N / m^{2} \)
c. \( N / m \)
D. 76 cm of \( H g \)


The correct order of \( A_{e q}^{\infty} \) at infinite dilution is:
A . \( \operatorname{LiC} \mid> \) NaCI \( > \) KCI
B. KCI> NaCI> LiCI
C . NaCI> KCI > LiCI
D. LiCI>KCI> Nacl


Which of the following factors are involve in left shifting of oxygen dissociation curve?
A. High \( P O_{2} \) and low pH
B. High \( P C O_{2} \) and high \( H^{+} \) concentration
c. Low \( P O_{2} \) and low temperature
D. High \( P O_{2} \) and low temperature


How many multiple of 9 lie between 10
and \( 300 ? \)


In Basidiomycotina, well-developed sex organs are present.
A. True
B. False


Two capacitors \( C_{1} \) and \( C_{2} \) are
connected in series, assume that \( C_{1}< \)
\( C_{2} . \) The equivalent capacitance of this
arrangement is \( C, \) where
A. \( C<C_{1} / 2 \)
B. \( C_{1} / 2<C<C_{1} \)
c. \( C_{1}<C<C_{2} \)


Which of the following represents a chelating ligand?
A \( \cdot H_{2} O \)
в. \( C l \)
c. \( O H^{-} \)
D. \( D M G \)


Water which gives good lather readily
with soap is known as hard water.
If this is true enter 1 , if false enter 0 .


a) What are plant hormones?
b) write two functions of auxin.


Which of the following is a co-polymer?
A. Polytetrafluoroethylene
B. Polyvinyl chloride
C . Polyethylene
D. Nylon - 6,6
E. Natural rubber


In the given disproportionation reaction in aqueus solution at room tempearature
\( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{2} \leftrightharpoons \boldsymbol{A}+\boldsymbol{B} \)
\( A \) and \( B \) cannot be:
This question has multiple correct options
A . nitric acid
B. nitrogen dioxide
c. nitrogen pentaoxide
D. nitrous oxide


Find the inverse of the matrix
\( \left[\begin{array}{ccc}1 & 2 & 1 \\ -1 & 0 & 2 \\ 2 & 1 & -3\end{array}\right] \) by elementary row
transformation. Hence solve the system
of equations \( \boldsymbol{x}+\mathbf{2} \boldsymbol{y}+\boldsymbol{z}=\mathbf{4},-\boldsymbol{x}+ \)
\( \mathbf{2} z=\mathbf{0}, \mathbf{2} \boldsymbol{x}+\boldsymbol{y}-\mathbf{3} \boldsymbol{z}=\mathbf{0} \)


The slope of a line perpendicular to \( \mathbf{5} \boldsymbol{x}+\mathbf{3} \boldsymbol{y}+\mathbf{1}=\mathbf{0} \) is
A \( -\frac{5}{3} \)
в. \( \frac{5}{3} \)
c. \( -\frac{3}{5} \)
D.


If \( f(x)=5 \log _{5} x \) then \( f^{-1}(\alpha-\beta) \) where
\( \boldsymbol{\alpha}, \boldsymbol{\beta} \in \boldsymbol{R} \) is equal to
A \( \cdot f^{-1}(\alpha)-f^{-1}(\beta) \)
B. \( \frac{f^{-1}(\alpha)}{f^{-1}(\beta)} \)
c. \( \frac{1}{f(\alpha-\beta)} \)
D. \( \frac{1}{f(\alpha)-f(\beta)} \)


A voltmeter of 998 ohm resistance is
connected to a cell of emf 2 volt, having internal resistance of 2 ohms The
error in measuring emf will b
A \( \cdot 4 \times 10^{-1} \mathrm{V} \)
B. \( 2 \times 10^{-3} \mathrm{V} \)
c. \( 4 \times 10^{-3} \mathrm{V} \)
D. \( 2 \times 10^{-1} \mathrm{V} \)


Find the order of rotational symmetry
Refer above image.


The gas oil fraction of petroleum has the highest boiling point?
A. True
B. False


If \( \bar{x} \cdot \bar{y}=\bar{x} \cdot \bar{z} \) and \( \bar{x} \times \bar{y}=\bar{x} \times \bar{z} \) and
\( \bar{x} \neq \overline{0}, \) then prove that \( \bar{y}=\bar{z} \)


A hollow metal sphere of radius \( 5 \mathrm{cm} \) is charged such that the potential on its
surface is \( 10 V . \) The potential at a
distance of \( 2 \mathrm{cm} \) from the centre of the
sphere is:
A. zero
B. \( 10 V \)
\( c .4 V \)
D. \( 10 / 3 V \)


Find the area bounded by the ellipse \( \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 \) and the ordinates \( x=0 \)
and \( x=a e, \) where \( b^{2}=a^{2}\left(1-e^{2}\right) \) and
\( e<1 \)


\( f \cot \left(\cos ^{-1} \frac{3}{5}+\sin ^{-1} x\right)=0, \) find the
value of \( \boldsymbol{x} \)


The process in which carbonate ores are
changed into oxides by heating strongly in limited air is known as


In ray diagrams, what is the least number of rays needed to find the position of an image formed by a lens?
\( A \cdot 4 \)
B. 3
\( c \cdot 2 \)
D.


\( (n-1) \) equal point masses each of
mass \( m \) are placed at the vertices of a regular n-polygon. The vacant vertex has a position vector a with respect to the centre of the polygon. Find the position vector of centre of mass
A \( \cdot-\frac{a}{n-1} \)
в. \( -\frac{a^{2}}{n-1} \)
c. \( -\frac{a}{(n-1)^{2}} \)
D. \( -\frac{3 a}{2 n-1} \)


Evaluate :
\( \int x^{2} \tan ^{-1} \frac{x}{2} d x \)


The angle between the lines \( 2 x+ \)
\( 11 y-7=0 \)
and \( x+3 y+5=0 \) is equal to
A \( \cdot \tan ^{-1}\left(\frac{17}{31}\right) \)
B. \( \tan ^{-1}\left(\frac{11}{35}\right) \)
\( ^{\mathbf{c}} \cdot \tan ^{-1}\left(\frac{1}{7}\right) \)
D \( \cdot \tan ^{-1}\left(\frac{33}{35}\right) \)
E \( \cdot \tan ^{-1}\left(\frac{7}{33}\right) \)


works on the Pascal's law and is
used in automobiles.
A. Hydraulic press
B. Hydraulic lift
c. Hydraulic jack
D. All


Estimate the average drift speed of
conduction electrons in a copper wire of
cross-sectional area \( 2.5 \times 10^{-7} m^{2} \)
carrying a current of 2.7 A. Assume the density of conduction electrons to be
\( 9 \times 10^{28} m^{-3} \)


The distance between the lines \( 3 x+ \)
\( \mathbf{4} \boldsymbol{y}=\mathbf{9} \) and \( \mathbf{6} \boldsymbol{x}+\mathbf{8} \boldsymbol{y}+\mathbf{1 5}=\mathbf{0} \) is:
\( A \cdot \frac{3}{10} \)
в. \( \frac{33}{10} \)
\( c \cdot \frac{33}{5} \)
D. None of these


In organic homologous series, the higher members show the higher melting and boiling point due to the :
A. dipole-dipole interaction
B. ion-dipole interaction
c. London dispersion forces
D. dipole-induced dipole interaction


When two waves of almost equal
frequency \( n_{1} \) and \( n_{2} \) are produced simultaneously, then the times interval between successive maxima is
A \( \cdot \frac{1}{n_{1}+n_{2}} \)
в. \( \frac{1}{n_{1}}+\frac{1}{n_{2}} \)
c. \( \frac{1}{n_{1}}-\frac{1}{n_{2}} \)
D. \( \frac{1}{n_{1}-n_{2}} \)


The integrating factor of the differential equation \( 3 x \log _{e} x \frac{d y}{d x}+y=2 \log _{e} x \) is
given by:
A \( \cdot\left(\log _{e} x\right)^{2} \)
B. \( \log _{e}\left(\log _{e} x\right) \)
\( \mathbf{c} \cdot \log _{e} x \)
D. \( \quad\left(\log _{e} x\right)^{\frac{1}{3}} \)


Show that the points whose position vectors are as given below are collinear:
\( \mathbf{3} \hat{\mathbf{i}}-\mathbf{2} \hat{\mathbf{j}}+\mathbf{4} \hat{\boldsymbol{k}}, \hat{\mathbf{i}}+\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} \) and \( -\hat{\mathbf{i}}+\mathbf{4} \hat{\mathbf{j}}- \)
\( \mathbf{2} \hat{\boldsymbol{k}} \)


In a car race, car A takes a time of ts, less than car \( \mathrm{B} \) at the finish and passes the finishing point with a velocity more than car B. Assuming that the cars start from rest and travel with
constant accelerations \( a_{1} \) and \( a_{2} \)
respectively, show that \( v=\sqrt{a_{1} a_{2} t} \)


If the foetus is \( \mathrm{Rh}^{+} \) and mother is \( \mathrm{Rh}^{-} \)
then which of the following situation is likely to happen?
A. Foetus might transmit antigen to mother's blood
B. Foetus might transmit antibody to mother's blood
c. Foetus is attacked by the antibodies of mother's blood
D. Foetus is attacked by the antigen of mother's blood


A block slips along an incline of a
wedge. Due to the reaction of the block
on the wedge, it slips, backwards. An
observer on the wedge will see the block
moving straight down the incline.
Discuss how to find the absolute
velocity of the block w.r.t wedge.


Find Mean Deviation from Median for
the given data
\( \boldsymbol{x} \quad \mathbf{1 0} \) \( \mathbf{3 0} \) 5 \( \mathbf{2 0} \) 40
\( f \) 18 25 27
A. 18.45
в. 16.65
c. 10.5
D. 11.36


For each of the given solid, the two views
are given. Match for each solid the
corresponding top and front views. The first one is done for you.
\( (d) \)
(e)
\( (v) \)
\( (v) \)


An aeroplane is moving with horizontal velocity u at height h. The velocity of a packet dropped from it on the earth's surface will be (g is acceleration due to gravity
A \( \cdot \sqrt{u^{2}+h^{2}} \)
B . \( \sqrt{u^{2}+2 g h} \)
c. \( \sqrt{u^{2}-h^{2}} \)
D. Data Insufficient


The artificial process of eliminating waste or solute particles by the process of diffusion and eliminating unwanted water by the process of ultrafiltration from blood is known as:
A. diffusion
B. filtration
c. electrophoresis
D. dialysis


Spectrometer is used to measure:
A. angle of prism.
B. refractive index of material of a prism.
C . dispersion.
D. All of the above


Write down the Born-Land equation and define the terms in it. Use the equation to show why some crystalsm which according to the radius ratio concept should adopt a coordination number of
\( 8, \) in fact have a coordination number of
6


Mark the correct statements:
This question has multiple correct options
A. The nuclear force between two protons is always greater than the electromagnetic force between them
B. The electromagnetic force between two protons is always greater than the gravitational force between them
C. The gravitational force between two protons may be greater than the nuclear force between them
D. Electromagnetic force between two protons may be greater than the nuclear acting between them.


Find the intervals in which the following functions are increasing or decreasing \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2}+\boldsymbol{2} \boldsymbol{x}-\mathbf{5} \)


\( \alpha- \) amino acid when heated with
NaOH/CaO forms:
A. \( \alpha, \beta \) -unsaturated acid
B. \( \alpha, \beta \) -unsaturated amine
c. carboxylic acid
D. Amine


If the enthalpy of formation o \( f \boldsymbol{H} \boldsymbol{C l}(\boldsymbol{g}) \)
and \( C l^{-}(a q) \) are \( -92 k J / \) mole and
\( -167.44 k J / m o l, \) find the enthalpy of solution of hydrogen chloride gas.
\( \mathbf{A} \cdot-75.14 k J / m o l \)
B. \( +75.14 k J / \) mol
c. \( -260.7 k J / \) mol
D. None of these


Number of disubstituted benzene is:
\( A \)
B. 2
\( c \cdot 3 \)
D.


Which one of the following is a correct
set?
A \( \cdot H_{2} O, s p^{3}, \) angular
B. \( H_{2} O, s p^{2} \), linear
c. \( N H_{4}^{+}, d s p^{2} \), square planar
D. \( C H_{4}, d s p^{2} \), tetrahedral


Assertion: \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) is more powerful oxidant in alkali medium.
Reason: \( E_{o, p}^{o} H_{2} O_{2}=-1.77 \mathrm{V} \) (in acid)
and \( E_{o, p}^{o} H_{2} O_{2}=-0.87 \mathrm{V} \) (in alkali).
A. Both Assertion and Reason are correct and Reason is correct explanation of Assertion
B. Both Assertion and Reason are correct but Reason is not correct explanation of Assertion
C . Assertion is correct but Reason is wrong
D. Assertion is wrong but Reason is correct


Given that both \( x \) and \( y \) are positive
integers. Solve the following systems of equations. \( \boldsymbol{x}^{2}+\boldsymbol{x} \boldsymbol{y}=\mathbf{1 5}, \boldsymbol{y}^{2}+\boldsymbol{x} \boldsymbol{y}=\mathbf{1 0} \)


\( \boldsymbol{A}(\mathbf{3}, \mathbf{4}) \) and \( \boldsymbol{B}(\mathbf{5},-\mathbf{2}) \) are two given
points. If \( \boldsymbol{A P}=\boldsymbol{P B} \) and area of
\( \triangle P A B=10, \) then \( P \) is
A. (7,1)
()
B. (7,2)
c. (-7,2)
D. (-7,-1)


Given above are four logic gate symbols.
Those for OR, NOR and NAND are
respectively
\( A \cdot a, d, c \)
B. \( d, a, b \)
\( c \cdot a, c, d \)
\( D \cdot d, b, a \)


Mass of atom expressed in atomic mass unit is :
A. atomic mass
B. molecular mass
c. atomic number mass
D. None of the above


Half-life of a radioactive substance A is
two times the half-life of another
radioactive substance
B. Initially, the
number of \( A \) and \( B \) are \( N_{A} \) and \( N_{B} \)
respectively. After three half-lives of \( A \) number of nuclei of both are equal
Then, the ratio \( N_{A} / N_{B} \) is
A . \( 1 / 4 \)
в. \( 1 / 8 \)
c. \( 1 / 3 \)
D. \( 1 / 6 \)


What is molecular formula of oleum?
A. \( H_{2} S O_{3} \)
в. \( H_{2} S O_{4} \)
c. \( H_{2} S_{2} O_{7} \)
D. \( H_{2} S_{2} O_{8} \)


\( \boldsymbol{A}=(\mathbf{2}, \mathbf{4}, \mathbf{5}) \) and \( \boldsymbol{B}=(\mathbf{3}, \mathbf{5},-\mathbf{4}) \) are two
points. If the \( X Y \) -plane, \( Y Z \) -plane divide \( A B \) in the ratio \( a: b \) and \( p: q \)
respectively, then \( \frac{a}{b}+\frac{p}{q}= \)
A \( \cdot \frac{23}{12} \)
B. \( \frac{-7}{12} \)
c. \( \frac{7}{12} \)
D. \( \frac{-22}{15} \)


In throwing of a die, let \( A \) be the event
'an odd humber turns up', \( B \) be the
event 'a number divisible by 3 turns up' and \( C \) be the event 'a number \( \leq 4 \) turns
up', Then find the probability that exactly two of \( A, B \) and \( C \) occur.
A \( \cdot \frac{2}{3} \)
B. \( \frac{1}{6} \)
\( c \cdot \frac{1}{3} \)
D.


Let \( z=\cos \theta+i \sin \theta . \) Then the value of
\( \sum_{m=1}^{1} 5 \operatorname{Im}\left(z^{2 m-1}\right) \operatorname{at} \theta=2^{0} \) is
A \( \cdot \frac{1}{\sin 2^{0}} \)
в. \( \frac{1}{3 \sin 2^{\circ}} \)
c. \( \frac{1}{2 \sin 2^{\circ}} \)
D. \( \frac{1}{4 \sin 2^{\circ}} \)


Which of the following statements is/are correct?
a) In the decomposition of an oxide into
oxygen and metal vapour, entropy
increases.
b) Decomposition of an oxide is an endothermic change.
c) To make \( \Delta G^{0} \) negative, temperature
should be high enough so that \( T \Delta S^{0}> \)
\( \Delta \boldsymbol{H}^{0} \)
A. (a), (b) only are correct
B. (b), (c) only are correct
C. (a), (c) only are correct
D. \( (a),(b),(c) \) are correct


Find the product when monochloro ethane is hydrolysed with aqueous
KOH?
A. \( C H_{3} O H \)
в. \( C H_{3} \) СООН
c \( \cdot C_{2} H_{5} O H \)
D. \( C_{2} H_{6} \)


Three ships \( A . B \& C \) are in motion. Ship A moves relative to B is with speed \( \mathbf{v} \)
towards North east Ship B moves relative to \( C \) with speed \( v \) towards the North-West. Then relative to A. C will be
moving towards:-
A. North
B. South
c. East
D. west