If \( x \% \) of \( a \) is the same as \( y \% \) of \( b \), then
\( z \% \) of \( b \) is
A. \( \frac{y z}{x} \% \) of \( a \)
B. \( \frac{x y}{z} \% \) of \( a \)
c. \( \frac{x z}{y} \% \) of \( a \)
D. \( x y z \% \)


A manometer attached to flask
contains with ammonia gas have no difference in mercury level initially as shown in diagram. After sparking into the flask, ammonia is partially
dissociated as \( 2 N H_{3}(g) \rightarrow N_{2}(g)+ \)
\( 3 H_{2}(g) \) now it have difference of \( 6 \mathrm{cm} \) in
mercury level in two columns, what is
partial pressure of \( \boldsymbol{H}_{2}(\boldsymbol{g}) \) at equilibrium?
\( A \cdot 6 \mathrm{cm} \mathrm{Hg} \)
B. \( 18 \mathrm{cm} \mathrm{Hg} \)
C. \( 27 \mathrm{cm} \mathrm{Hg} \)
D. None of these


List three techniques that have been developed to prevent pregnancy.Which one of these techniques is not meant for males? How does the use of these
techniques have a direct impact on the health and prosperity of a family?


Fungi producing 8 spores in a sac belong to the class
A. Phycomycetes
B. Ascomycetes
c. Basidiomycetes
D. Deuteromycetes


Suppose India had a target of producing by \( 2020 \mathrm{AD}, 200,000 \mathrm{MW} \) of electric
power, ten percent of which was to be obtained from nuclear power plants. Suppose we are given that, on an average, the efficiency of utilization (i.e. conversion to electric energy) of thermal energy produced in a reactor was \( 25 \% . \) How much amount of
fissionable uranium would our country need per year by \( 2020 ? \) Take the
heat energy per fission of \( ^{235} U \) to be
about \( 200 \mathrm{MeV} \)


The roots for \( 3 x^{2}=x+4 \) are
\( ^{A} \cdot \frac{2}{3},-\frac{1}{2} \)
B. \( \frac{4}{3},-\frac{1}{2} \)
\( c \cdot \frac{4}{3},-1 \)
D. \( \frac{2}{3},-1 \)


IUPAC representation of the element of atomic number 115 is Uup. If true enter 1 else enter 0


In an ideal step-up transformer input voltage is \( 110 \mathrm{V} \) and current flowing in the secondary is \( 10 \mathrm{A} \), if transformation
ratio is \( 10, \) calculate output voltage,
current in primary input power and
output power.


If the energy of a ball falling from a
height of 10 meters is reduced by \( 40 \% \) how high will it rebound?


A body cools down from \( 80^{\circ} \mathrm{C} \) to \( 60^{\circ} \mathrm{C} \) in
10 Minutes when the temperature of
surrounding is \( 30^{\circ} \mathrm{C} \). The temperature
of the body after next 10 minutes will be:
A \( \cdot 30^{\circ} \mathrm{C} \)
B . \( 48^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 50^{\circ} C \)
D. \( 52^{\circ} \mathrm{C} \)


A mixture contains 1 mole of helium
\( \left.C_{p}=2.5 R, C_{v}=1.5 R\right) \) and 1 mole of
hydrogen \( \left(C_{p}=3.6 R, C_{v}=2.5 R\right) \)
Calculate the volue of \( C_{p}, C_{v} \) and \( \gamma \) for the mixture.


A beam of \( 16 M e V \) deutrons from a
cyclotron falls on a copper block. The beam is equivalent to a current of \( 15 \mu A \)
At what rate do the deutrons strike the
block?
A \( \cdot 9.4 \times 10^{9} \)
B. \( 9.4 \times 10^{7} \)
c. \( 9.4 \times 10^{11} \)
D. \( 9.4 \times 10^{13} \)


Solve :
\( \frac{x}{2}-\frac{1}{5}=\frac{x}{3}+\frac{1}{4} \)


If \( A=\{1,2,3\} \) and \( B=\{4,5\} \) then the
number of function \( \boldsymbol{f}: \boldsymbol{A} \rightarrow \boldsymbol{B} \) which is
not onto is
\( A \cdot 2 \)
B. 6
c. 8
D. 4


if \( L=2.331 c m, B=2.1 c m, \) then \( L+B= \)
A. \( 4.431 \mathrm{cm} \)
в. \( 4.43 \mathrm{cm} \)
c. \( 4.5 \mathrm{cm} \)
D. \( 4.2 \mathrm{cm} \)


Assertion
High-level waste and spent fuel from a nuclear power plant must be handled
and stored with care.
Reason
Used fuel from a nuclear reactor is no
longer efficient in creating electricity, because its fission process has slowed.
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


Amongst the following compounds (I)
\( \boldsymbol{H}_{5} \boldsymbol{P}_{3} \boldsymbol{O}_{10},(\text { II }) \boldsymbol{H}_{6} \boldsymbol{P}_{4} \boldsymbol{O}_{13},(\| \text { II }) \boldsymbol{H}_{5} \boldsymbol{P}_{5} \boldsymbol{O}_{15} \)
and \( (\mathrm{IV}) \boldsymbol{H}_{7} \boldsymbol{P}_{5} \boldsymbol{O}_{16}, \) the non-cyclic
phosphates are:
A. I and III
B. I, II and III
c. ।, ॥ and IV
D. I, II, II and IV


\( \boldsymbol{H}_{2} \boldsymbol{O}+\boldsymbol{H}_{2} \boldsymbol{O} \rightleftharpoons \boldsymbol{H}_{3} \boldsymbol{O}^{+}+\boldsymbol{O} \boldsymbol{H}^{-} \)
The above reverse reaction is an
exothermic reaction. What will happen if the temperature is lowered?
A. The \( p H \) will decrease
B. The equilibrium will shift to the right
C. The concentration of \( H_{3} O^{+} \) ions will increase
D. The equilibrium will shift to the left.t.
E. Temperature does not affect equilibrium.


If \( n_{t}, \) number of radio atoms are present
at time \( t, \) the following expression will
be a constant
A \( \cdot \frac{n_{t}}{t} \)
в. \( \ln \frac{n_{t}}{t} \)
c. \( \frac{d}{d t}\left(\ln n_{t}\right) \)
D. \( t \cdot n_{t} \)


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


High frequency capacitor offers
A. more resistance
B. less resistance
C. zero resistance
D. None of these


A vessel contains 1 mole of \( \mathrm{O}_{2} \) (molar
\( \operatorname{mass} 32 g m) \) at a temperature \( T . \) The
pressure is \( P . \) An identical vessel
containing 1 mole of He (molar mass
\( 4 g m \) ) at a temperature \( 2 T \) has a
pressure :
A.
в. \( \frac{P}{8} \)
c. \( 2 P \)
D. 8P


The melting of ice is also known as having the property of
A. Latent heat of fusion
B. Latent heat of vaporisation
c. Latent heat of fermentation
D. Latent heat of sublimation


Arrange the following terms regarding process of respiration in chronological order of its decreasing volume of air
I. Expiratory reserve volume
II. Vital capacity
III. Tidal volume
IV. Residual volume
A. \( I I \rightarrow I V \rightarrow I \rightarrow I I I \)
B. \( I I \rightarrow I V \rightarrow I I I \rightarrow I \)
c. \( I \rightarrow I V \rightarrow I I I \rightarrow I I \)
D. \( I V \rightarrow I \rightarrow I I I \rightarrow I \)


What is a glycosidic linkage?


Verify Lagranage's mean value theorem for the \( f(x)=x^{3}-2 x^{2}-x+3 \) in [0,1]


Litharge is a mineral of:
A. Magnesium
B. Lithium
c. Lead
D. zinc


For the equilibrium, an increase of temperature will,
\[
\mathbf{2} N \boldsymbol{O}_{2}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{N}_{2} \boldsymbol{O}_{4}(\boldsymbol{g})+\mathbf{1 4 . 6} \boldsymbol{k} c \boldsymbol{a} \boldsymbol{l}
\]
A . favour the formation of \( N_{2} O_{4} \)
B. favour the decomposition of \( N_{2} O_{4} \)
c. not affect the equilibriumm
D. stop the reaction


All are solid fuels except:
A. Alcohol
B. Wood and Coal
c. coke
D. charcoal


Find the maximum emf induced


Which phase comes in between the G1
and G2 phases of cell cycle?
A. M-phase
B. Go phase
c. s-phase
D. Interphase


Two bodies have thermal capacities in the ratio 3: 4 and the rates of loss of
heat in the ratio \( 3: 5 . \) Their rates of
cooling will be in the ratio of :
\( A \cdot 9: 20 \)
B. 4: 5
\( c \cdot 5: 4 \)
D. 1:


\( 2 \tan ^{-1}\left(\frac{1}{3}\right)+\tan ^{-1}\left(\frac{1}{7}\right) \) is equal to
A. \( \frac{\pi}{6} \)
в. \( \frac{\pi}{4} \)
\( c \cdot \frac{\pi}{3} \)
\( D \cdot \frac{\pi}{2} \)


If a ray of light incident on a plane mirror is such that it makes an angle of
\( 30^{\circ} \) with the mirror, then the angle of
reflection is:
A . \( 30^{\circ} \)
B . \( 4.5^{\circ} \)
\( \mathrm{c} .55^{\circ} \)
D. \( 60^{\circ} \)


Let \( \hat{a}, \hat{b}, \hat{c} \) be unit vectors such that \( \hat{a}+ \) \( \hat{\boldsymbol{b}}+\hat{\boldsymbol{c}}=\hat{\mathbf{0}} \) and \( \mathbf{x}, y, \mathbf{z} \) be distinct integers
then minimum value of \( |\boldsymbol{x} \hat{\boldsymbol{a}}+\boldsymbol{y} \hat{\boldsymbol{b}}+\boldsymbol{z} \hat{\boldsymbol{c}}| \)
is
\( A \cdot 2 \)
B. \( \sqrt{2} \)
\( c \cdot \sqrt{3} \)
D.


The accelerated motion of a body can
occur:
This question has multiple correct options
A. Due to change in its speed only.
B. Due to change in direction of motion only.
C. Due to change in both speed and direction of motion.
D. Due to constancy of velocity.


The equivalent conductance of \( N a C l \) at
concentration \( C \) and at infinite dilution
\( \operatorname{are} \lambda_{C} \) and \( \lambda_{\infty}, \) respectively. The correct
relationship between \( \lambda_{C} \) and \( \lambda_{\infty} \) is
given as:
(here the constant B is positive)
A \( \cdot \lambda_{C}=\lambda_{\infty}-(B) \sqrt{C} \)
B . \( \lambda_{C}=\lambda_{\infty}+(B) \sqrt{C} \)
c. \( \lambda_{C}=\lambda_{\infty}-(B) C \)
D. \( \lambda_{C}=\lambda_{\infty}+(B) C \)


In a triangle, the largest angle is ten times the smallest and the remaining angle is the square of the smallest. The
largest angle of the triangle is
A \( .80^{\circ} \)
B . \( 100^{\circ} \)
\( c \cdot 120^{\circ} \)
D. \( 90^{\circ} \)


A stone is dropped into a quiet lake and
waves move in a circle at a speed of
\( 3.5 c m / \)sec. At the instant when the
radius of the circular wave is \( 7.5 \mathrm{cm} \)
The enclosed area increases as fastly
as.
A \( \cdot 52.5 \pi \mathrm{cm}^{2} / \mathrm{sec} \)
в. \( 50.5 \pi \mathrm{cm}^{2} / \mathrm{sec} \)
\( \mathbf{c} \cdot 57.5 \pi \mathrm{cm}^{2} / \mathrm{sec} \)
D. \( 62.5 \pi \mathrm{cm}^{2} / \mathrm{sec} \)


At some temperature and under a
pressure of 4 atm, \( P C l_{5} \) is \( 10 \% \)
dissociated. Calculate the pressure at
which \( P C l_{5} \) will be \( 20 \% \) dissociated, temperature remaining
same.
A. 0.096 atm
B. 19.2 atm
c. 0.96 atm
D. 0.192 atm


Chlorine was discovered by:
A. Priestley
B. Davy
c. shceele
D. Cavendish


Coloured balls are distributed in 3
bags.
\( \boldsymbol{B}_{1} \rightarrow \mathbf{1} \boldsymbol{B}, \mathbf{2} \boldsymbol{W}, \mathbf{3} \boldsymbol{R} \)
\( B_{2} \rightarrow 2 B, 4 W, 1 R \)
\( \boldsymbol{B}_{3} \rightarrow \mathbf{4} \boldsymbol{B}, \mathbf{5} \boldsymbol{W}, \mathbf{5} \boldsymbol{R} \)
A bag is selected at random and then 2
balls are drawn from the selected bag. They happen to be black and red. What is the probability that the balls come
from bag 1?


Which tissue masses form erectile
tissue in the penis and why do they become rigid during sexual arousal?


In the reaction, \( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{I}_{2}(\boldsymbol{g}) \rightleftharpoons \)
\( 2 H I(g) \) the concentration of \( H_{2}, I_{2} \) and
\( H I \) at equilibrium are 8.0,3.0 and 28 moles per litre respectively. What will be the equilibrium constant?
\( A \cdot 30.61 \)
B. 32.66
c. 29.40
D. 20.90


An accelerated form of dialysis where electrodes are placed in the colloidal solution, an electric field is applied across the semipermeable membrane and the ions are separated, is known as
A. Electro dialysis
B. Electrophoresis
c. Ultracentrifugation
D. None of these


Which one of the following is not a subatomic particle?
A. Proton
B. Neutron
c. Electron
D. Positron


There is no S-S bond in:
\( A \cdot S_{2} O_{4}^{2-} \)
B. \( S_{2} O_{5}^{2-} \)
\( \mathrm{c} \cdot S_{2} \mathrm{O}_{3}^{-2} \)
D. \( S_{2} O_{7}^{-2} \)


The National Physical Laboratory is situated at:
A. Kolkata
B. New Delhi
c. Bombay
D. None of these


Dihydrogen has:
A. two isotopes and no isomers
B. three isotopes and two nuclear isomers
C. three isotopes and two optical isomers
D. two isotopes and two geometrical isomers


Which is the correct in the following?
A \( . \) Radius of \( C l \) is \( 0.99 \AA \), while that of \( C l^{+} \) ion is 1.54 A.
B. Radius of \( C l \) atoms is 0.99 , \( \hat{A} \), while that of \( N a \) atom is 1.54 月.
C. Radius of \( C l \) atoms is 0.99 , a , while that of \( C l^{-} \) ion is \( 0.81 A \)
D. Radius of \( N a \) atoms is 0.95 , \( \dot{A} \), while that of \( N a^{+} \) ion is \( 1.54 \AA \)


(i) Arrange the following compounds in the ascending order of their basic strength and give reasons for your
answer:

Methylamine, Aniline, Ethylamine,
Diethyl ether
(ii) Name the monomers and the type of polymerization in each of the folloiwng
polymers:
(a) Polyester
(b) Bakelite


The center of a circle which passes
through the points (0,0),(1,0) and touches the circles \( x^{2}+y^{2}=9 \)
\( ^{A} \cdot\left(\frac{3}{2}, \frac{1}{2}\right) \)
в. \( \left(\frac{1}{2}, \frac{3}{2}\right) \)
c. \( \left(\frac{1}{2}, \frac{1}{2}\right) \)
D. \( \left(\frac{1}{2}, \sqrt{2}\right) \)


The disodium salt of ethylene diamine tetracetic acid can be used to estimate the following ion(s) in the aqueous solution.
A. \( M g^{2+} \) ion
B. \( C a^{2+} \) ion
c. \( N a^{+} \) ion
D. both \( M g^{2+} \) and \( C a^{2+} \)


Find \( \left|V_{B A}\right| \) if \( 12 J \) of work has to be done
against an electric field to take a
charge of \( 10^{-2} C \) from \( a \) to \( b \)


Match List I with List II and select the
correct answer using the codes given below the lists


A small ball is dropped in a viscous
liquid. Its fall in the liquid is best
described by the figure:
A. Curve A
B. Curve B
c. Curve \( C \)
D. Curve D


In determination of young modulus of elasticity of wire, a force is applied and extension is recorded. Initial length of
wire is \( 1 \mathrm{m} \). The curve between
extension and stress is depicted then young modulus of wire will be:


Three identical capacitors, each of capacitance \( C, \) are connected in series
with a battery of emf \( V \) and get fully charged. Now, the battery is removed and the capacitors are connected in
parallel with positive terminals are one point and negative terminals at other point. Then, the common potential will be :
A. \( V \)
в. \( 3 V \)
c. \( \frac{V}{3} \)
D.


Write short note on hindbrain.


In producing a pure spectrum, the
incident light is passed through a
narrow slit placed in the focal plane of
an achromatic lens because a narrow
slit
A. produce less diffraction
B. increase intensity
C. allows only one colour at a time
D. allows a more parallel beam when it passes through the lens.


Two forces whose magnitudes are in the ratio 3: 5 give a resultant of \( 28 N . \) If the
angle of their inclination is \( 60^{\circ} \), find the magnitude of each force.


Which among the following forms octahedral complex?
A \( \cdot d^{4} \) (low spin)
B. \( d^{8} \) (high spin)
c. \( d^{6} \) (low spin)
D. All of these


The angle between the vectors \( (\hat{i}+\hat{j}+ \)
\( \hat{\boldsymbol{k}}) \) and \( (\hat{\boldsymbol{i}}-\hat{\boldsymbol{j}}-\hat{\boldsymbol{k}}) \) is:
A \( \cdot \sin ^{-1} \frac{\sqrt{8}}{3} \)
в. \( \sin ^{-1} \frac{1}{3} \)
c. \( \cos ^{-1} \frac{\sqrt{8}}{3} \)
D. \( \cos ^{-1} \sqrt{\frac{8}{3}} \)


The bar graph shows the number of
cakes sold at a shop in four days.
What is the difference in number of
cakes between the highest and the
lowest daily sale?
4.20
B. 35
\( c \cdot 30 \)
D. 40


its speed?


Carbon, Silicone, and Germanium al
have the same number of electrons in
an outer most shell. Explain?


What are the speeds of two objects if they move uniformly towards each other, they get \( 4 \mathrm{m} \) closer in each second and if they move uniformly in the same direction with the original speeds they get \( 4 \mathrm{m} \) closer in each \( 10 \mathrm{sec} ? \)
A. \( 2.8 \mathrm{m} / \mathrm{s} \) and \( 1.2 \mathrm{m} / \mathrm{s} \)
B. 5.2 \( \mathrm{m} / \mathrm{s} \) and \( 4.6 \mathrm{m} / \mathrm{s} \)
c. \( 3.2 \mathrm{m} / \mathrm{s} \) and \( 2.1 \mathrm{m} / \mathrm{s} \)
D. 2.2 \( \mathrm{m} / \mathrm{s} \) and \( 1.8 \mathrm{m} / \mathrm{s} \)


If two protons are moving with speed \( \boldsymbol{v}=\mathbf{4 . 5} \times \mathbf{1 0}^{\mathbf{5}} \mathbf{m} / \mathrm{s} \) parallel to each other
then find the ratio of electrostatic and
magnetic force between them?
\( \mathbf{A} \cdot 4.4 \times 10^{5} \)
В. \( 2.2 \times 10^{5} \)
c. \( 3.3 \times 10^{5} \)
D. \( 1.1 \times 10^{5} \)


Which of the following has higher
lattice energy \( -A l_{2} O_{3} \) or \( A l_{2} S e_{3} ? \)
A. \( A l_{2} O_{3}>A l_{2} S e_{3} \)
B . \( A l_{2} O_{3}<A l_{2} S e_{3} \)
c. \( A l_{2} O_{3}=A l_{2} S e_{3} \)
D. None of these


\( \int \frac{x+1}{x\left(1+x e^{x}\right)} d x=0 \)
\( ^{\mathbf{A}} \cdot \log \left|\frac{1+x e^{x}}{x e^{x}}\right|+C \)
\( ^{\mathbf{B}} \cdot \log \left|\frac{x e^{x}}{1+x e^{x}}\right|+C \)
\( \mathbf{c} \cdot \log \left|x e^{x}\left(1+x e^{x}\right)\right|+C \)
\( \mathbf{D} \cdot \log \left(1+x e^{x}\right)+C \)


In the estimation of carbon and
hydrogen, if the substance also
contains nitrogen, then near the exit, it is placed:
A. a roll of silver
B. a bright copper gauge spiral
c. ammonium sulphate
D. a layer of lead chromate


When a ball is thrown up, it reaches a
maximum height \( h \) travelling 5 m in the last second. Find the velocity with which the ball should be thrown up.


In a series L.C.R circuit, the potential drop across \( L, C \) and \( R \) respectively are \( 40 V, 120 V \) and \( 60 V . \) Then the source
voltage is
\( \mathbf{A} \cdot 220 V \)
B. \( 160 V \)
\( \mathbf{c} \cdot 180 V \)
D. \( 100 V \)


The velocity vector \( \mathbf{v} \) and displacement vector \( x \) of a particle executing SHM are related as \( \frac{\boldsymbol{v} \boldsymbol{d} \boldsymbol{v}}{\boldsymbol{d} \boldsymbol{x}}=-\boldsymbol{\omega}^{2} \boldsymbol{x} \) with the initial
condition \( V=v_{0} \) at \( x=0 . \) The velocity
v, when displacement is \( x, \) is?
\( \mathbf{A} \cdot v=\sqrt{v_{0}^{2}+\omega^{2} x^{2}} \)
B . \( v=\sqrt{v_{0}^{2}-\omega^{2} x^{2}} \)
c. \( v=\sqrt[3]{v_{0}^{3}+\omega^{3} x^{3}} \)
D. \( V=v_{0}-\left(\omega^{3} x^{3} e^{x^{3}}\right)^{1 / 3} \)


Arrange the following in the decreasing order of boiling point:
¡) \( C_{2} H_{5} O H \)
ii) \( \left(\boldsymbol{C H}_{3}\right)_{2} \boldsymbol{N H} \)
iii) \( \boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{N} \boldsymbol{H}_{2} \)
A. i > ii > ii
B. ii>i>iii
\( c . \) iii \( >i>i \)
D. iii > ii > i


Which of the following statements
is/are correct?
This question has multiple correct options
\( \mathbf{A} \cdot \) Solid \( P C l_{5} \) exists as tetrahedral \( P C l_{4}^{+} \) and octahedral
\( P C l_{6}^{-} \) ions.
B. Solid \( P B r_{5} \) exists as \( P B r_{4}^{+} B r^{-} \)
C. Solid \( N_{2} O_{5} \) exists as \( N O_{3}^{-} \) and \( N O_{2}^{+} \)
D. Oxides of phosphorus \( P_{2} O_{3} \) and \( P_{2} O_{5} \) exist as
monomers.


When a candle burns, both physcial and chemical changes takle place. Identify these changes. Give another example of a familiar process in which both the
chemical and physical changes take place


Treatment of the dry solid with
a mild oxidizing agent produces a purple solid.
A. \( N_{2} \)
в. \( K I \)
c. \( C C l_{4} \)
D. \( A g N O_{3} \)


Find order and degree (if defined) of the differential equation \( \frac{\boldsymbol{d}^{4} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{4}}+ \)
\( \sin \left(\frac{\boldsymbol{d}^{3} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{3}}\right)=\mathbf{0} \)


The net gain of ATP molecules through glycolysis is
A. 6
B. 4
\( c \cdot 8 \)
D. 36


Alkyl halides develop colour on:
A. addition of water
B. addition of non polar solvent
c. exposure to light
D. exposure to air


Compare the pressure exerted by a sharp needle on a surface and the
pressure exerted by a blunt needle.
A. The pressure exerted by a sharp needle is more
B. The pressure exerted by a blunt needle is more
c. The pressure exerted by both is equal
D. None of these


A lens forms an erect, magnified and virtual image of an object
Draw a labelled ray diagram to show the image formation


Combustion of carbon studies in a
bomb calorimeter to obtain heat of
reaction. Which of the following options
are correct?
This question has multiple correct options
A. The value obtained shows change in heat enthalpy
B. The value obtained shows change in internal energy.
c. The volume remains constant
D. The pressure remains constant


ff \( \Delta=\left|\begin{array}{ccc}\mathbf{3} & \mathbf{5} & \mathbf{7} \\ \mathbf{2} & -\mathbf{3} & \mathbf{1} \\ \mathbf{1} & \mathbf{1} & \mathbf{2}\end{array}\right|, \) find it's value


Find the number of acid(s) which are
having pyro prefix in its name from the
following:
\( \boldsymbol{H}_{4} \boldsymbol{P}_{2} \boldsymbol{O}_{7}, \boldsymbol{H}_{4} \boldsymbol{P}_{2} \boldsymbol{O}_{5}, \boldsymbol{H}_{2} \boldsymbol{S}_{2} \boldsymbol{O}_{7}, \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{5} \)


Obtain a differential equation by eliminating the arbitrary constants \( A, B \) from the following equation. \( \boldsymbol{y}=\boldsymbol{A} \cos \boldsymbol{t}-\boldsymbol{B} \sin \boldsymbol{t} \)


A body is projected vertically upward with speed \( 10 m / s \) and other at same time with same speed in downward
direction form the top of a tower. The
magnitude of acceleration of first body with respect to second is \( \{\text { take } g= \)
\( \left.10 m / s^{2}\right\} \)
A. zero
B . \( 5 m / s^{2} \)
c. \( 10 m / s^{2} \)
D. \( 20 m / s^{2} \)


To know the opinion of the student about the subject statistic, a survey of
200 students was conducted.
The data is recorded in the following table
opinion 1 Like Dislike
No. of Students 65 135
Find the probability that a student chosen at random
\( (i) \) likes statistics,
\( (i i) \) does not like it.
A.
\[
\begin{array}{l}
(i) \frac{13}{40} \\
(i i) \frac{19}{40}
\end{array}
\]
в.
\[
(i) \frac{27}{40}
\]
\( (i i) \frac{13}{40} \)
c.
\[
(i) \frac{17}{40}
\]
\( (i i) \frac{29}{40} \)
D. None of these


In catabolic series of reaction, complex
molecules are broken down into smaller
molecules releasing
A. water
B. Oxygen
c. Energy
D. Nutrients


Which does not represent correct
method?
\( \mathbf{A} \cdot T i C l_{2}+2 M g \rightarrow T i+2 M g C l_{2}: K r o l \)
B. \( N i(C O)_{4} \rightarrow N i+4 C O: \) Mond
c. \( _{A g_{2}} C O_{3} \rightarrow 2 A g+C O_{2}+\frac{1}{2} O_{2}: \) van Arkel
\( \mathbf{D} \cdot Z r l_{4} \rightarrow Z r+2 I_{2}: \) van Arkel


In given figure find \( x \)
\( \mathbf{A} \cdot 110^{0} \)
\( \mathbf{B} \cdot 120^{0} \)
\( \mathbf{c} \cdot 130^{\circ} \)
D. \( 140^{\circ} \)


The velocity of a particle is given by \( v= \)
\( 12+3\left(t+7 t^{2}\right) . \) What is the
acceleration of the particle?
A \( .3+21 t \)
B. \( 3+42 t \)
\( c .42 t \)
D. \( 4 t \)


The bond orders of \( O_{2}^{2-}, O_{2}^{-}, O_{2} \) are
respectively \( x, y \) and \( z \)
Then what is the value of \( 2(x+y+z) ? \)


The area of the triangle whose vertices \( \operatorname{are} A(1,2,3), B(2,-1,1) \) and
\( \boldsymbol{C}(\mathbf{1}, \mathbf{2},-\mathbf{4}) \) is
A . \( 7 \sqrt{10} \) sq units
B. \( \frac{1}{2} \sqrt{10} \) sq units
c. \( \frac{7}{2} \sqrt{10} \) sq units
D. None of these


An ideal gas, of volume \( 189 m L \), is collected over water. The temperature is
\( 27^{\circ} \mathrm{C}, \) and the barometric pressure is
\( 756 m m H g . A t 27^{\circ} C, \) the vapor
pressure of water is 27 mm \( H g \)
Which of the following CORRECTLY gives the mole fraction of water vapor in the
collection vessel?
A \( \cdot \frac{27}{756} \)
в. \( \frac{27}{729} \)
c. \( \frac{729}{756} \)
D. \( \frac{729}{27} \)


If \( \sec \theta=\sqrt{2} \) and \( \theta \) lies in first
quadrant. Find value of \( \frac{1+\tan \theta+\operatorname{cosec} \theta}{1+\cot \theta-\operatorname{cosec} \theta} \)


In which of the following sclerenchyma cells, the secondary cell walls are
present
A. The cells containing cytoplasm only
B. The cells with protoplast
c. cells which are living at maturity
D. cells which are non-living at maturity


In a triangle \( E D C \), what is the angle \( C \) ?
3.19
\( c \cdot 7 \)
D


A card from a pack of 52 cards is lost. from the remaining cards of pack, two cards are drawn and are found to be
both diamonds. Find the probability of the lost card being a diamond.


Consider the complex
\( \left[\boldsymbol{C o}(\boldsymbol{e n})_{2} \boldsymbol{C l}\left(\boldsymbol{N O}_{2}\right)\right] \boldsymbol{B r} . \) It can exhibit:
This question has multiple correct options
A. geometrical isomerism
B. optical isomerism
c. ionization isomerism
D. linkage isomerism


Assertion
If a line makes angles \( \boldsymbol{\alpha}, \boldsymbol{\beta}, \boldsymbol{\gamma} \) with
\( O X, O Y, O Z \) respectively, then \( \sin ^{2} \alpha+\sin ^{2} \beta+\sin ^{2} \gamma=2 \)
Reason
If \( l=\cos \alpha, m=\cos \beta, n=\cos \gamma, \) are
direction cosines of a line, then \( l^{2}+ \)
\( \boldsymbol{m}^{2}+\boldsymbol{n}^{2}=\mathbf{1} \)
A. Both Assertion \& Reason are individually true \& Reason is correct explanation of Assertion
B. Both Assertion \& Reason are individually true but Reason is not the ,correct (proper) explanation of Assertion
C. Assertion is true but Reason is false
D. Assertion is false but Reason is true


Find the cosine of \( 8^{\circ} 12 \).
A . 0.84
B. 0.54
c. 0.44
D. 0.98


A train is moving with uniform acceleration. The two ends of the train
pass through a point on the track with
velocity \( V_{1} \) and \( V_{2} . \) With what velocity the middle point of the train would pass through the same point?
A \( \cdot\left[\frac{\left(V_{1}^{2}+V_{2}^{2}\right.}{2}\right] \)
B. \( \frac{\left(V_{1}^{2}-V_{2}^{2}\right)}{2} \)
\( c \cdot \frac{v_{1}+v_{2}}{2} \)
\( D \cdot \frac{V_{1}-V_{2}}{2} \)


The Sl unit of linear momentum is
\( \mathbf{A} \cdot m s^{-1} \)
в. \( k g s^{-1} \)
c. \( k g m s^{-1} \)
D. \( k g m \)


Adding first 100 terms in a sequence is
called
A. term
B. series
c. constant
D. sequence


Most of the alpha particles pass:
A. straight through the gold foil
B. unusual through the gold foil
C . rare through the gold foil
D. none of the above


\( C l_{2} \) is passed into \( N H_{3} . \) When \( C l_{2} \) is in
excess, the products are \( N C l_{3} \) and
\( \boldsymbol{H} \boldsymbol{C l} \)
State whether the given statement is true or false.


A conducting rod of length \( l \) and mass
\( m \) is moving down a smooth inclined plane of inclination \( \theta \) with constant
velocity \( v . A \) current \( i \) is flowing in the conductor in a direction perpendicular to paper inwards, a vertically upwards magnetic field \( B \) exists in space. Then
magnitude of magnetic field \( B \) is :
A. \( \frac{m g}{i l} \sin \theta \)
в. \( \frac{m g}{i l} \tan \theta \)
c. \( \frac{m g \cos \theta}{i l} \)
D. \( \frac{m g}{\text {ilsint}} \)


The denominator of an algebraic fraction should not be
A . 1
B. 0
\( c \cdot 4 \)
\( D \)


If \( \angle A \) and \( \angle B \) are complementary
angles and \( m \angle A \) is \( x^{o}, \) which equation
can be used to find \( m \angle B \) which is
denoted by \( y ? \)
A. \( y=(90+x)^{\circ} \)
в. \( y=(90-x)^{\circ} \)
c. \( y=(180 x)^{\circ} \)
D. \( y=(x+180)^{\circ} \)


A tangent to the hyperbola \( \boldsymbol{y}=\frac{\boldsymbol{x}+\mathbf{9}}{\boldsymbol{x}+\mathbf{5}} \)
passing though the origin is
A . \( x+25 y=0 \)
в. \( 5 x+y=0 \)
c. \( 5 x-y=0 \)
D. \( x-25 y=0 \)


Reproduction is one of the most important characteristics of living
beings. Give three reasons in support of the statement.


Which one of the following statement is
true?
A. According to the modern atomic theory, atoms of the same element may have different atomic weights
B. Reduction is the process of electron loss
C. Acidic oxide are the non-metallic oxides
D. The solubility of all substances decreases with increase in temperature


In the white light of sun, maximum
scattering by the air molecules present in the earth's atmosphere is for:
A. red colour
B. yellow colour
c. green colour
D. blue colour


If \( y=\frac{f(x)}{\phi(x)} \) and \( z=\frac{f^{\prime}(x)}{\phi^{\prime}(x)}, \) then \( \frac{f^{\prime \prime}}{f}- \)
\( \frac{\phi^{\prime \prime}}{\phi}+\frac{2(y-z)}{f \phi}\left(\phi^{\prime}\right)^{2}= \)
A \( \cdot \frac{d^{2} y}{d x^{2}} \)
B. \( \frac{1}{y} \cdot \frac{d^{2} y}{d x^{2}} \)
c. \( y \cdot \frac{d^{2} y}{d x^{2}} \)
D. None of these


Find the ratio of specific charges \( \left(\frac{\boldsymbol{q}}{\boldsymbol{m}}\right) \) of an \( \alpha- \) particle and a deuteron?


Why high temperature is required for Nuclear fusion?
A. All nuclear reactions absorb heat
B. The particles can not come together unless they are moving rapidly
c. The binding energy must be supplied from an external source
D. The mass defect must be supplied


A hemispherical bowl of internal radius \( 15 c m \) contains a liquid. The liquid is to
be filled into cylindrical-shaped bottles
of diameter \( 5 \mathrm{cm} \) and height \( 6 \mathrm{cm} . \) How many bottles are necessary to empty the bowl?


Which of the following is used in making automobile tyres and foot
wear?
A. Vulcanised rubber
B. Neoprene
c. Plexi glass
D. Glyptal


A geostationary satellite is orbiting the earth at a height of \( 5 R \) above the
surface of the earth, R being the radius of the earth. The time period of another satellite in hours at a height of \( 2 \mathrm{R} \) from
the surface of the earth is:
A \( \cdot \frac{6}{\sqrt{2}} \)
B. 5
c. 10
D. \( 6 \sqrt{2} \)


The differential equation of all
parabolas with axis parallel to the axis
of \( \boldsymbol{y} \) is:
A \( \cdot y_{2}=2 y_{1} \)
в. \( y_{3}=2 y_{1} \)
c. \( y_{2}^{3}=y_{1} \)
D. none of these


If \( E \) represents total mechanical energy
of a system while \( U \) represents the
potential energy, then \( \boldsymbol{E}-\boldsymbol{U} \) is:
A. always zero
B. always less than zero
c. always greater than or equal to zero
D. either positive or negative


A certain characteristic in a large population has a distribution that is
symmetric about the mean \( m \). If 68 percent of the distribution lies within
one standard deviation \( d \) of the mean,
what percent of the distribution is less
\( \operatorname{than} \boldsymbol{m}+\boldsymbol{d} ? \)
A . \( 16 \% \)
B. \( 32 \% \)
c. \( 48 \% \)
D. \( 84 \% \)
E \( .92 \% \)


n figure, \( A C=13 \mathrm{cm}, B C=12 \mathrm{cm}, \) then
\( \sec \theta \) equals:
A \( \cdot \frac{13}{12} \)
B. \( \frac{5}{12} \)
c. \( \frac{12}{13} \)
D. \( \frac{5}{13} \)


Find the equation of the circle whose
diameters are along the lines \( 2 x- \)
\( 3 y+12=0 \) and \( x+4 y-5=0 \) and
whose area is 154 sq. units.


How much work is done moving an electron from a potential of \( 2 \mathrm{V} \) to \( 5 \mathrm{V} \) ?
A . 2ev
B. 3ev
c. \( 5 \mathrm{ev} \)
D. 10ev


The coxal of the pelvic girdle is formed
by the fusion by
A. llium, ischium and pubis
B. Scapula and clavicle
c. llium and scapula
D. Ilium, scapula and ischium
E. clavicle and pubis


State whether the given statement is true or false:

Maximum ionization energy stands for He.


Which is correct order in evolutionary
history of man
A. Peking Man Habilus Man \( \rightarrow \)
Neanderthal Man \( \rightarrow \)
Cro-Magnon Man
B. Peking Man \( \rightarrow \)
Heidelberg Man \( \rightarrow \)
Neanderthal Man \( \rightarrow \)
Cro-Magnon Man
c. Peking Man \( \rightarrow \)
Neanderthal Man \( \rightarrow \)
Homo sapiens \( \rightarrow \)
Heidelberg Man
D. Poking. Man \( \rightarrow \)
Homo sapiens \( \rightarrow \)
Neanderthal Man \( \rightarrow \)
Cro-Magnon Man


Which one of the following statement is not applicable to Solanaceae?
A. Adnation
B. Swollen axile placentation
c. Bicarpellary superior ovary
D. Monocarpellary superior ovary


A wire carrying \( 5.0 V \) is applied to a primary coil of the transformer. The
primary coil has 10 turns and the secondary coil has 20 turns. Find out the emf induced in the secondary coil?
\( \mathbf{A} \cdot 0.50 V \)
в. \( 5.0 V \)
c. \( 10 V \)
D. \( 50 V \)
E . \( 100 V \)


A student is unable to see clearly the words written on the black board placed
at a distance of approximately 3 m from him. Name the defect of vision the boy
is suffering from. State the possible causes of this defect and explain the method of correcting it.


Write a note on Botanical Garden?


If the two vectors \( \vec{A}=2 \hat{i}+3 \hat{j}+4 \hat{k} \) and \( \vec{B}=\hat{i}+2 \hat{j}-n \hat{k} \) are perpendicular
then the value of \( n \) is:
A . 1
B . 2
\( c \cdot 3 \)
D. 4


If the function \( f(x)=\frac{t+3 x-x^{2}}{x-4} \)
where \( t \) is a parameter, has a minimum
and a maximum, then the greatest
value of \( t \) is


Write \( \boldsymbol{A}=\left[\begin{array}{cc}\mathbf{3} & \mathbf{5} \\ \mathbf{1} & \mathbf{-} \mathbf{1}\end{array}\right] \) as the sum of \( \mathbf{a} \)
symmetric and a skew-symmetric
matrix.


The values of \( x \epsilon[-2 \pi, 2 \pi] \) such that
\( \frac{\sin x+i \cos x}{1+i}, i=\sqrt{-1}, \) is purely
imaginary, are given by
A \( \cdot n \pi-\frac{\pi}{4} \)
в. \( n \pi+\frac{\pi}{4} \)
\( c \cdot n \pi \)
D. none of these


A beaker full of hot water is kept in a room and it cools from
\( 90^{\circ} \mathrm{C} \) to \( 80^{\circ} \mathrm{C} \) in \( t_{1} \) sec.
II) \( 80^{\circ} \mathrm{C} \) to \( 70^{\circ} \mathrm{C} \) in \( t_{2} \) sec.
III) \( 70^{\circ} \mathrm{C} \) to \( 60^{\circ} \mathrm{C} \) in \( t_{3} \) sec.
\( 1 V) 60^{\circ} \mathrm{C} \) to \( 50^{\circ} \mathrm{C} \) in \( t_{4} \) sec.
f the room temperature is \( 10^{0} \) C. Identify the order in which the time of cooling
increases
A. IV,III,II \& 1
B. ।,॥।,IV \& ॥
c. ।, ॥,॥। \& IV
D. III, I, II \& IV


According to Darwin, diversity as found in Australian marsupials is due to :
A. Convergent evolution
B. Adaptive radiation
c. Parallel radiation
D. Parallel evolution


Evaluate the given integral. \( \int \frac{x^{9}}{\left(4 x^{2}+1\right)^{6}} d x \)
\( ^{\mathrm{A}} \frac{1}{5 x}\left(4+\frac{1}{x^{2}}\right)^{-5}+C \)
в. \( \frac{1}{5}\left(4+\frac{1}{x^{2}}\right)^{-5}+C \)
\( ^{\mathrm{c}} \frac{1}{10 x}\left(\frac{1}{x^{2}}+4\right)^{-5}+C \)
\( ^{\mathrm{D}} \frac{1}{10}\left(\frac{1}{x^{2}}+4\right)^{-5}+C \)


Aryl halides are less reactive towards
nucleophilic substitution reaction as
compared to alkyl halides due to:
A. formation of a less stable carbonium ion in aryl halides
B. resonance stabilisation in aryl halide
C. presence o fdouble bonds in alkyl halides
D. inductive effect in aryl halides


Construct a trapezium \( A B C D \) in which \( \boldsymbol{A B} \| \boldsymbol{C D}, \boldsymbol{A B}=\mathbf{5} \boldsymbol{c m}, \angle \boldsymbol{B}= \)
\( \mathbf{8 0}^{\circ}, \boldsymbol{B C}=\mathbf{4} \boldsymbol{c m} \) and \( \boldsymbol{A D}=\mathbf{4 . 5} \boldsymbol{c m} \)


Suppose that of all used cars of a particular year \( 30 \% \) have bad brakes.
You are considering buying a used car of that year. You take the car to a mechanic to have the brakes checked.
The chance that the mechanic will give you the wrong report is \( 20 \% \). Assuming that the car you take to the mechanic is selected at random from the population
of cars of that year. The chance that the
car's brakes are good, given that the mechanic says its brakes are good, is
A \( \frac{28}{130} \)
в. \( \frac{29}{31} \)
c. \( \frac{37}{62} \)
D. \( \frac{29}{62} \)


A body of mass \( m \) is released from the
top of a rough inclined plane length \( l \). If the frictional force is \( f, \) and the height
of body from ground is \( h \) then the velocity of the body of the bottom in
\( \boldsymbol{m} \boldsymbol{s}^{-1} \) will be :
A \( \cdot \sqrt{\frac{2}{m}(m g h-f l)} \)
в. \( 2 g h-f / l \)
c. \( \sqrt{\frac{2}{m} g h} \)
D. zero


Integrals of sum particular function
prove that \( \int \frac{d x}{x^{2}-a^{2}}=\frac{1}{2 a} \log \left|\frac{x-a}{x+a}\right|+c \)


\( \int \frac{d x}{x\left(x^{2}+1\right)^{2}}= \)
A. \( \ln \frac{|x|}{\sqrt{x^{2}+1}}+\frac{1}{2\left(x^{2}+1\right)}+K \)
B. \( \ln \frac{|x|}{\sqrt{x^{2}+1}}-\frac{3}{2\left(x^{2}+1\right)}+K \)
C. \( -\ln \frac{|x|}{\sqrt{x^{2}+1}}+\frac{3}{2\left(x^{2}+1\right)}+K \)
D. \( -\ln \frac{|x|}{\sqrt{x^{2}+1}}+\frac{3}{2(x+1)}+K \)


Which of the following is not corretly matched for the organism and its cell wall degrading enzyme?
A. Bacteria - Lysozyme
B. Plant cells - Cellulase
c. Algae - Methylase
D. Fungi - Chitinase


Small liquid droplets dispersed in another liquid is called:
A. suspension
B. emulsion
c. gel
D. true solution


A parenchymatous cell has 20 units of DNA. It starts to divide mitotically How many units of DNA would it have
during very late telophase


Assertion
Bromoacetic acid reacts with conc.
NaOH to form \( \alpha \) -ethoxy acetic acid.
Reason
It is \( S_{N} 1 \) mechanism.
Read the above assertion and reason
and choose the correct statement
regarding it.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


If \( f(x)=x^{4}-2 x^{3}-a x+b \) is a
polynomial such that when it is divided by \( x-1 \) and \( x+1 \),the remainders are
respectively 45 and \( 19 . \) Determine the remainder when \( f(x) \) is divided by \( (x- \)
2


A wheel with 10 metallic spokes each \( 0.5 \mathrm{m} \) long rotated with a speed of 120 rpm in a plane normal to the horizontal
component of earth's magnetic field \( B_{h} \)
at a place. If \( B_{h}=0.4 \mathrm{G} \) at the place. What is the induced emf between the
axle and the rim of the wheel? \( \left(1 \mathrm{G}=10^{4}\right. \)
\( T \)
A. o v
B. 0.628 mV
c. \( 0.628 \mu v \)
D. 62.8 \( \mu \) V


Carry out the following divisions \( 11 x y^{2} z^{3} \) by \( 55 x y z \)


In Mac-Arthur Forrest method, silver is extracted from solution of
\( N a\left[A g(C N)_{2}\right] \) by the use of
A . \( F e \)
в. \( M g \)
c. \( C u \)
D. \( Z n \)


The different spectral absorbencies of a conjugate acid/base pair is a/an:
A. chemical pH indicator
B. acid/base buffer
c. anhydrous solution
D. hypotonic solution
E. supersaturated solution


Use the MO theory to predict the bond order and the number of unpaired
electrons in \( O_{2}^{2-}, O_{2}^{-}, O_{2}, O_{2}^{+}, N O \)
and \( C O \)


An L-shaped glass tube is just
immersed in flowing water such that its
opening is pointing against flowing
water. If the speed of water current is \( \mathbf{v} \)
then :
A the water in the tube rises to height \( \frac{v^{2}}{2 g} \)
B. The water in the tube rises to height \( \frac{g}{2 v^{2}} \)
c. The water in the tube does not rise at all
D. None of these.


In an intrinsic semiconductor, the Fermi
energy level is
A. nearer to valence band than conduction band.
B. equidistant from conduction band and valence band.
C. nearer to conduction band than valence band.
D. bisecting the conduction band


Solve \( \lim _{x \rightarrow a} \frac{x \sqrt{x}-a \sqrt{x}}{x-a} \)


The value of \( x \) is \( m \sqrt{2}, \) so \( m \) is


A long solenoid with 10 turns per \( \mathrm{cm} \)
has a small loop of area \( 3 \mathrm{Cm}^{2} \) placed inside, normal to the axis of the solenoid. If the current carried by the
solenoid changes steadily form \( 2 A \) to \( 4 A \) in \( 0.2 s, \) what is the induced voltage
in the loop, while the currect is changing?
A \( \cdot 4.2 \times 10^{-8} \)
B. \( 2.8 \times 10^{-8} \)
C \( .7 .3 \times 10^{-6} \)
D. \( 3.8 \times 10^{-6} \)


An ideal fluid flows in the pipe as shown
in the figure. The pressure in the fluid at
the bottom \( p_{2} \) is the same as it is at the
top \( p_{1} \). If the velocity of the top \( v_{1}= \)
\( \boldsymbol{m} / \boldsymbol{s} . \) Then the ratio of areas \( \boldsymbol{A}_{1} . \boldsymbol{A}_{2} \) is
A . 2: 1
B . 4: 1
\( c \cdot 8: 1 \)
D. 4: 3


What parameter is used to measure the stability of a nucleus?
A. Average binding energy
B. No. of protons
c. No. of neutrons
D. No. of electrons


Aspartame, an artificial sweetener, is a
peptide and has the given structure.
Which of the following is correct about
the molecule?
This question has multiple correct options
A. It has four functional groups
B. It has three functional groups
c. on hydrolysis, it produces only one amino acid
D. On hydrolysis, it produces a mixture of amino acids


Nucleons is the name given for
and
A. electron, neutron
B. electron, proton
c. nucleus, electron
D. proton, neutron


As the temperature of the medium increases,
A. speed of sound increases
B. speed of sound decreases
c. no effect on speed of sound
D. may increase or decrease


The complex that can show fac- and
mer- isomers is :
A \( \cdot\left[\operatorname{Co}\left(N H_{3}\right)_{3}\left(N O_{2}\right)_{3}\right] \)
B \( \cdot\left[P t\left(N H_{3}\right)_{2} C l_{2}\right] \)
c. \( \left[\operatorname{CoCl}_{2}(e n)_{2}\right] \)
D. \( \left[\operatorname{Co}\left(N H_{3}\right)_{4} C l_{2}\right]^{+} \)


A diatomic ideal gas is compressed adiabatically to \( \frac{1}{32} \) of its initial volume.
If the initial temperature of the gas is \( \mathbf{T}_{\mathbf{i}} \) (in Kelvin) and the final temperature is
\( a T_{i}, \) the value of a is
\( A \cdot 4 \)
B. 5
\( c \cdot 2 \)
D. 3


All monosaccharides containing five or six carbon atoms have:
A. open chain structures
B. pyranose structure
c. furanose structures
D. may have pyranose or furanose structures


Find the coordinates of the point where the line \( \frac{\boldsymbol{x}+\mathbf{1}}{\mathbf{2}}=\frac{\boldsymbol{y}+\boldsymbol{2}}{\mathbf{3}}=\frac{\boldsymbol{z}+\mathbf{3}}{\mathbf{4}} \) meets
the plane \( \boldsymbol{x}+\boldsymbol{y}+\boldsymbol{4} \boldsymbol{z}=\boldsymbol{6} \)


In the give velocity-time graph,
acceleration equals
\( A \cdot 4 m / s^{2} \)
B. \( 5 \mathrm{m} / \mathrm{s}^{2} \)
\( c \cdot 4.5 m / s^{2} \)
\( \mathbf{D} \cdot 3.5 \mathrm{m} / \mathrm{s}^{2} \)


Nongenetic RNA is of
A. Two types
B. Three types
C. Four types
D. One type


The melting point of ice can be given by:
\( \mathbf{A} \cdot 32^{\circ} F \)
B. \( 32^{\circ} \mathrm{C} \)
c. \( 273.15 K \)
D. Both a and c


Explain the purpose of vulcanization of
rubber.


f some charge is given to a solid metallic sphere, the field inside remains zero and by Gauss's law all the charge resides on the surface. Suppose now that Coulomb's force between two
charges varies as \( 1 / r^{3} . \) Then, for a charged solid metallic sphere
A . field inside will be zero and charge density inside will be zero
B. field inside will not be zero and charge density inside will not be zero
c. field inside will not be zero and charge density inside will be zero
D. field inside will be zero and charge density inside will not be zero


Equal volume of two immiscible liquids of densities \( \rho \) and \( 2 \rho \) are filled in a vessel as shown in the figure. Two small \( \boldsymbol{h} \quad \boldsymbol{3 h} \)
holes are punched at depths \( \frac{-}{2} \) and \( \frac{1}{2} \)
from the surface of lighter liquid. If \( v_{1} \)
and \( v_{2} \) are the velocities of efflux at
these two holes, then \( v_{1} / v_{2} \) is
\( ^{A} \cdot \frac{1}{2 \sqrt{2}} \)
B. \( \frac{1}{2} \)
\( c \cdot \frac{1}{4} \)
D. \( \frac{1}{\sqrt{2}} \)


The horizontal ranges described by two
projectiles, projected at angles \( \left(45^{\circ}-\right. \)
\( \theta \) ) and \( \left(45^{\circ}+\theta\right) \) from the same point
and same velocity are in the ratio.
A . 2: 1
B. 1: 1
\( c \cdot 2: 3 \)
D. 1: 2


Some substances are acidic while
others are basic. A scale called the pH
scale is used to measure the extent of
acidity. What will happen to the pH of
the solution if a little acid is added to a
beaker of water (original \( \mathrm{pH}=7 \) )?
A. It will become a little less than 7
B. It will become a little more than 7
c. It will remain 7
D. It will become 0


Three collinear points \( A, B \) and \( C \) ares
such that point \( B \) is between points \( A \) and \( C . \) The distance from \( A \) to \( B \) is 8
more than 4 times the distance from \( B \)
to \( C \) and the distance from \( A \) to \( C \) is 5
times the distance from \( B \) to \( C . \) What is
the distance from \( \boldsymbol{A} \) to \( \boldsymbol{C} \) ?
A .4
B . 20
c. 16
D. 24


Maximum green house gas released by which of the following country?
A. India
B. France
c. china
D. Britain


The value of \( x \) fo which \( \sin (\pi x)+ \)
\( \cos (\pi x)=0 \)


A solution of benzene and toluene is an
example of solution.
A. Ideal
B. non ideal
c. azeotrope
D. none


Solve \( : I_{n}=\int_{0}^{\frac{\pi}{2}} e^{-x} \sin ^{n} x d x \)


Properties of covalent solids can be used to identify a substance.

Which of the following would be the most directly related to the properties of a covalent substance?
A. Molecular structure
B. Elemental composition
c. Substance mass
D. Empirical formula


Stellate hairs are found in
A . Musa
B. Citrus
c. Styrax
D. Hydrilla


\( \mathbf{A} \)
p-n photodiode is fabricted from a semiconductor with a band gap of
2.5eV. It can detect a signal of wavelength
A. 6000
B. 4000
c. \( 4000 \mathrm{nm} \)
D. 6000 nm


The number of \( S \) -S bonds in polythionic
\( \operatorname{acid}\left(\boldsymbol{H}_{2} \boldsymbol{S}_{n} \boldsymbol{O}_{6}\right) \)
\( A \cdot n \)
B. \( n-1 \)
c. \( n-2 \)
D. None of these


One root of the equation \( \cos x-x+ \)
\( \frac{1}{2}=0 \) lies in the interval:
A \( \cdot\left(0, \frac{\pi}{2}\right) \)
B \( \cdot\left(-\frac{\pi}{2}, 0\right) \)
c. \( \left(\frac{\pi}{2}, \pi\right) \)
D. \( \left(\pi, \frac{3 \pi}{2}\right) \)


In the figure, identical capacitors are
connected in the given three
configurations.The ratio of the total capacitancies in (i), (ii) and (iii)
respectively, is :
\( \mathbf{A} \cdot 3: 5: 5 \)
B. 3: 3: 5
\( \mathbf{c} \cdot 5: 4: 4 \)
\( \mathbf{D} \cdot 5: 5: 3 \)


The sum of three numbers in A.P is 27 .
Their product is is \( 405 . \) Find the numbers.


If mean of a series is 40 and variance
\( 1486, \) then coefficient of variation is
A .0 .9021
B. 0.9637
c. 0.8864
D. 0.9853


How many NOR gates are required to
form NAND gate:
A . 1
B. 3
c. 2
\( D \)


A transformer converts \( 200 \mathrm{V} \) ac into
\( 2000 \mathrm{V} \) ac. Calculate the number of
turns in the secondary if the primary
has 10 turns.


Which of the following is/are true regarding international standards of
drinking water?
A. Fluoride deficiency causes tooth decay.
B. Required fluoride concentration is 10 ppm
c. When fluoride concentration exceeds 20 ppm, brown mottling of teeth occurs.
D. Excess fluoride (over 100 ppm ) has serious effect on bones and teeth


In \( Y D S E, d=2 m m, D=2 m \) and \( \lambda=500 \)
nm. If intensity of two slits are \( l_{0} \) and \( 9 l_{0} \)
then find intensity at \( \boldsymbol{y}=\frac{1}{6} \)
A. \( 7 l_{0} \)
B. \( 10 l_{0} \)
c. \( 16 l_{0} \)
D. \( 4 l_{0} \)


At \( 444^{\circ} C, \) the equilibrium constant \( (K) \) for the reaction \( 2 A B \rightleftharpoons A_{2}+B_{2} \) is \( \frac{1}{64} \) The degree of dissociation of \( A B \) is
A . \( 10 \% \)
B. 20\%
c. \( 30 \% \)
D. \( 50 \% \)


\( y^{2}=6 x^{3}+x-8 \) find \( \frac{d y}{d x} \)


Find the degree measure of \( \frac{1^{c}}{4} \)


What is Iymph?


Let \( G=\{x \mid x \text { is boy of your class }\} \) and
\( \boldsymbol{H}=\{\boldsymbol{y} \mid \boldsymbol{y} \text { is a girl of your class }\} . \) What
type of sets \( \mathrm{G} \) and \( \mathrm{H} \) are?
A. Finite sets
B. Infinite sets
c. Cannot be determined
D. None of these


A capillary tube when immersed vertically in a liquid records a rise of \( 3 c m . \) if the tube is immersed in the
liquid at an angle of \( 60^{\circ} \) with the vertical, then length of the liquid
column along the tube will be:
\( A \cdot 2 c m \)
в. 3 ст
c. \( 6 \mathrm{cm} \)
D. 9 cm


The area of a circle is equal to the area
of a rectangle with sides \( 112 \mathrm{m} \) and \( 88 \mathrm{m} \) respectively. Find the circumference of the circle.


Pressure at a certain depth in river
water is \( p_{1} \) and at the same depth in
sea water is \( p_{2} \). Then (Density of sea water is greater than that of river water):
A \( \cdot p_{1}=p_{2} \)
в. \( p_{1}>p_{2} \)
c. \( p_{1}<p_{2} \)
D. \( p_{1}-p_{2}= \) atmospheric pressure


A compound with molecular mass 180 is
acylated. with [image] to get a compound with molecular mass 390 The no. of amino group present per molecule of the former compound is:
\( A \cdot 2 \)
B. 5
\( c \cdot 4 \)
\( D \)


The promoter site and the terminator
site for transcription are located at
\( A \cdot 3 \) (downstream) end and 5 (upstream) end, respectively of the transcription unit
B. 5 (upstream) end and 3 (downstream) end, respectively of the transcription unit
C. the 5 (upstream) end
D. the 3 (downstream) end.


The image formed by a plane mirror is always laterally inverted.
A. True
B. False


Quantity of heat produced by a conductor is directly proportional to in the conductor.
A. The time of current flow
B. The resistance
c. The Square of magnitude of current
D. All


Permanent hardness is caused due to:
A. magnesium bicarbonate
B. magnesium carbonate
C. magnesium sulphate
D. all of the above


When you go far a trek/trip to any high altitude places, you are advised to take
it easy and rest for the first two days. Comment giving reasons.


The following arrangement performs the logic function of \( _{-}-_{-}-_{-}-_{-} \) gate
All the gates present above are NAND
gate
\( A \cdot A N D \)
B. OR
c. NAND
D. EXOR


Two blocks of masses \( 10 \mathrm{kg} \) and \( 30 \mathrm{kg} \) are placed along a vertical line. If the first block is raised through a height of 7 cm by what distance should the second mass be moved to raise the
center of mass by \( 1 \mathrm{cm} \)
A. \( 1 \mathrm{cm} \) up
B. \( 1 \mathrm{cm} \) down
c. \( 2 \mathrm{cm} \) down
D. \( 2 \mathrm{cm} \) up


If \( f(x) \) is a continuous function on [0,1] differentiable in (0,1) such that \( f(1)=0, \) then there exists some
\( c \epsilon(0,1) \) such that
A \( \cdot c f^{\prime}(c)-f(c)=0 \)
B. \( f^{\prime}(c)+c f(c)=0 \)
c. \( f^{\prime}(c)-c f(c)=0 \)
D. \( c f^{\prime}(c)+f(c)=0 \)


A solution of weak acid was titrated
with base \( N a O H . \) The equivalence point was reached when \( 36.12 m L \) of
\( 0.1 M \) NaOH have been added. Now,
\( 18.06 m L \) of \( 0.1 M H C l \) were added to
titrated solution, the \( p H \) was found to
be \( 4.92 . K_{a} \) of acid is
A \( \cdot K_{a}=1.3 \times 10^{-5} \)
В. \( K_{a}=1.0 \times 10^{-5} \)
C \( . K_{a}=1.2 \times 10^{-5} \)
D. \( K_{a}=1.1 \times 10^{-5} \)


A very long straight solenoid carries a
current \( I . \) The cross-sectional area of
the solenoid is equal to \( S \), the number
of turns per unit length is equal to \( n \) The flux of the vector \( \vec{B} \) through the
end plane of the solenoid is \( \frac{\Phi_{0}}{x} . \) Find \( x \)


The substances you start with is called and after the chemical change, what is formed is called the
A . reactants, products
B. reactants, gases
c. element, products
D. element, compounds


For the cell \( Z n(s)\left|Z n^{2+}\right|\left|C u^{2+}\right| C u(s) \)
the standard cell voltage, \( \boldsymbol{E}_{c e l l}^{\ominus} \) is \( 1.10 \mathrm{V} \) When a cell using these reagents was prepared in the lab, the measured cell voltage was \( 0.98 \mathrm{V} \). One possible explanation for the observed voltage is :
A. There were 2.00 mol of \( Z n^{2+} \) but only 1.00 mol of \( C u^{2} \)
B. The Zn electrode had twice the surface of the cu electrode
C. The \( \left[Z n^{2+}\right] \) was larger than the \( \left[C u^{2+}\right] \)
D. The volume of the \( \left[Z n^{2+}\right] \) solution was larger than the volume of the \( C u^{2+} \) solution


Which of the following types of animal are affected the most by temperature changes in the environment?
\( A \). Birds
B. Desert living
c. Poikilothermic
D. Homoiothermic


Identify the different types of coke.
A. Honeycomb coke
B. Needle coke
c. sponge coke
D. All of these


Suppose \( a, b, c \epsilon R \) and \( a b c=1 . \) If \( A= \) \( \left[\begin{array}{ccc}2 a & b & c \\ b & 2 c & a \\ c & a & 2 b\end{array}\right] \) is such that \( |A|\left|A^{\prime}\right|=64 \)
and \( |A|>0, \) then find the value of
\( \left(a^{3}+b^{3}+c^{3}\right)^{4} \)
\( \left(A^{\prime} \text { denotes transpose of a matrix } A .\right) \)
A . 1
B. 2
\( c .3 \)
\( D \)


are the change in the function or structure of a living body which occurs after birth.
A. Inherited traits
B. Dual traits
c. Both A and B
D. Acquired traits


Assertion
If \( \alpha, \beta \) are the roots of the equation
\( 18\left(\tan ^{-1} x\right)^{2}-9 \pi \tan ^{-1} x+\pi^{2}=0 \)
\( \operatorname{then} \boldsymbol{\alpha}+\boldsymbol{\beta}=\frac{\boldsymbol{4}}{\sqrt{\mathbf{3}}} \)
Reason
\( \sec ^{2}\left(\cos ^{-1}\left(\frac{1}{4}\right)\right)+ \)
\( \operatorname{cosec}^{2}\left(\sin ^{-1}\left(\frac{1}{5}\right)\right)=41 \)
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


Based on the above Ellingham diagram,
the formation of carbon monoxide from
carbon can reduce the metal oxide to
metal at a temperature the
point of intersection of the two lines.
1. Equal to
2. Higher than
3. Lower than
4. None


Standard enthalpies of formation of \( \boldsymbol{O}_{3} \)
\( C O_{2}, N H_{3} \) and \( H I \) are 142.2,-393.2
-46.2 and +25.9 kJ \( m o l^{-1} \) respectively
The order of their increasing stabilities will be:
A. \( O_{3}, C O_{2}, N H_{3}, H I \)
в. \( C O_{2}, N H_{3}, H I, O_{3} \)
c. \( O_{3}, H I, N H_{3}, C O_{2} \)
D. \( N H_{3}, H I, C O_{2}, O_{3} \)


In five kingdom classification, Euglena is placed in
A. Monera
B. Protista
c. Fungi
D. Animalia


If a gas has n degrees of freedom ratio of specific heats of gas is?
A \( \cdot \frac{1+n}{2} \)
в. \( _{1+\frac{1}{n}} \)
\( c \cdot 1+\frac{n}{2} \)
D. \( _{1+\frac{2}{n}} \)


The differential equation \( \frac{d y}{d x}= \)
\( \sqrt{1-y^{2}} \) determines a family of circles \( \boldsymbol{y} \)
with:
A . variable radii and a fixed centre (0,1)
B. variable radii and a fixed centre (0,-1)
C. fixed radius 1 and variable centres along the \( x \) -axis
D. fixed radius 1 and variable centres along the \( y \) -axis


Given figure shows the vertical section
of a frictionless surface. A block of
mass \( 2 \mathrm{kg} \) is released from the position
A, its kinetic energy as it reaches the position C is
A \( .180 \mathrm{J} \)
В. 140
c. \( 40 \mathrm{J} \)
D. 280


Two circularly shaped linear polarisers are placed coaxially. The transmission
axis of the first polarizer is at \( 30^{\circ} \) from
the vertical while the second one is at
\( 60^{\circ}, \) both in the clockwise sense. If an
unpolarised beam of light of intensity \( I=20 W / m^{2} \) is incident on this pair of
polarisers, then the intensities \( I_{1} \) and \( I_{2} \)
transmitted by the first and the second polarisers, respectively, will be close to.
A \( \cdot I_{1}=10.0 W / m^{2} \) and \( I_{2}=7.5 W / m^{2} \)
B . \( I_{1}=20 W / m^{2} \) and \( I_{2}=15 W / m^{2} \)
C \( . I_{1}=10.0 W / m^{2} \) and \( I_{2}=8.6 W / m^{2} \)
D. \( I_{1}=15.0 W / m^{2} \) and \( I_{2}=0.0 W / m^{2} \)


Release of phosphates and nitrates in water bodies (rivers and lakes) leads to
A. Increased algae growth
B. Increased growth of decomposers
c. Decreased nutrient content
D. Reduced algae growth


Which of the following are correct?
This question has multiple correct options
A. 0.0304 can be rounded off to 0.030 (to two significant figures)
B. The less the number of significant figures, the greater the reliability of the measurement the number represents.
C. A result can be made more significant by a mathematical operation.
D. 487.56 can be rounded off to 490 (to two significant figures)


Three concurrent coplanar forces \( 1 \mathrm{N}, 2 \) N and 3 N acting along different directions on a body:
A. Can keep the body in equilibrium if 2 N and 3 N act at right angle
B. Can keep the body in equilibrium if \( 1 \mathrm{N} \) and \( 2 \mathrm{N} \) act at right angle
c. cannot keep the body in equilibrium
D. Can keep the body in equilibrium in \( 1 \mathrm{N} \) and \( 3 \mathrm{N} \) act at an acute angle


rest on a inclined plane and are separated by a distance of 6.0 m as
shown in figure. The coefficient of
friction between each of the blocks and
the inclined plane is \( 0.25 . \) The \( 2 k g \) block
is given a velocity of \( 10.0 \mathrm{m} / \mathrm{s} \) up the
inclined plane. It collides with \( \boldsymbol{M} \)
comes back and has a velocity of \( 1.0 m / s \) when it reaches its initial
position. The other block \( M \) after the
collision moves \( 0.5 m \) up comes to rest.
calculated the coefficient [Take \( \sin \theta= \)
\( \left.\tan \theta=0.05 \text { and } g=10 m / s^{2}\right] \)
\( \mathbf{A} \cdot e=0.84, M=15 k g \)
в. \( e=4, M=5 k g \)
c. \( e=9, M=15 k g \)
D. \( e=84, M=17 k g \)


The diagram given below is a representation of a certain phenomenon pertaining to the nervous system. Study the diagram and answer the following questions.
(i) Name the phenomenon that is being depicted.
(ii) Give the technical term for the point
of contact between the two nerve cells.
(iii) Name the parts 1,2,3 and 4
(iv) Write the functions of parts 5 and 6
(v) How does the arrangement of neurons in the spinal cord differ from
that of the brain?


A progressive wave is given by the equation, \( \boldsymbol{y}=\boldsymbol{A} \sin (\boldsymbol{\omega} \boldsymbol{t}-\boldsymbol{k} \boldsymbol{x}) . \) The wave
velocity
A. increases with time
B. fluctuates with time
c. decreases with time
D. remains constant


Red blood cells
A. Divide by mitotic division
B. Divide by meiotic division
C . Divide amitotically
D. Do not divide


Find the area of the closed figure bounded by the following curve
\( \boldsymbol{y}=\boldsymbol{x}^{2}-\boldsymbol{2} \boldsymbol{x}+\boldsymbol{2}, \boldsymbol{y}=\boldsymbol{2}+\boldsymbol{4} \boldsymbol{x}-\boldsymbol{x}^{2} \)


The \( p^{t h} \) term of an arithmetic
progression is \( \boldsymbol{q}, \) and the \( \boldsymbol{q}^{t h} \) term is \( \boldsymbol{p} \)
then the \( m^{t h} \) term is:
A. \( p+q-m \)
в. \( p-q-m \)
c. \( p+q+m \)
D. None of these


Mark the correct alternative of the
following.

If the measures of the angles of a triangle are \( (2 x-5)^{o},\left(3 x-\frac{1}{2}\right) \) and \( \left(30-\frac{x}{2}\right), \) then \( x=? \)
A \( \cdot \frac{311}{9} \)
в. \( \frac{309}{11} \)
c. \( \frac{310}{9} \)
D. \( \frac{301}{9} \)


Find out which of the following equations have \( x=2, y=1 \) as a
solution:
\( 2 x-3 y=1 \)


A student takes about \( 4 \mathrm{ml} \) of distilled
water in four test tubes marked \( P, Q, R \)
and \( S . \) He then dissolves in each test
tube, an equal amount of various salts,
viz. sodium sulphate in \( P, \) potassium
sulphate in \( Q, \) calcium sulphate in \( R \)
and magnesium sulphate in \( S \). After that, he adds an equal amount of soap solution in each test tube. On shaking each of these test tubes well, he
observes a good amount of lather
(foam) in the test tube marked:
A. \( P \) and \( Q \)
B. \( Q \) and \( R \)
c. \( P, Q \) and \( S \)
D. \( P, R \) and \( S \)


Which of the following functions is/are
constant?
A \( \cdot f(x)=x^{2}+2 \)
в. \( f(x)=x+\frac{1}{x} \)
\( \mathbf{c} \cdot f(x)=7 \)
D. \( f(x)=6+x \)


Which of the following is incorrect
statement?
A. A dimensionally correct equation may be correct
B. A dimensionally correct equation may be incorrect
C. A dimensionally incorrect equation may be correct
D. A dimensionally incorrect equation is incorrect


An element with electronic
arrangement as 2,8,18,1 will exhibit which of the following stable oxidation states?
A. +2 and +4
B. +1 and +2
\( \mathbf{c} \cdot+2 \operatorname{to}+7 \)
D. +1 only


Find: \( \int \frac{e^{x} d x}{\left(e^{x}-1\right)^{2}\left(e^{x}+2\right)} \)


Which of the following do/does not
reduce to unity?
This question has multiple correct options
A \( \frac{\sin \left(180^{0}+A\right)}{\tan \left(180^{0}+A\right)} \frac{\cot \left(90^{0}+A\right)}{\tan \left(90^{0}+A\right)} \frac{\cos \left(360^{0}-A\right) \operatorname{cosec} A}{\sin (-A)} \)
B. \( \frac{\sin (-A)}{\sin \left(180^{0}+A\right)}-\frac{\tan \left(90^{0}+A\right)}{\cot A}+\frac{\cos A}{\sin \left(90^{0}+A\right)} \)
C. \( \frac{\sin 24^{0} \cos 6^{0}-\sin 6^{0} \cos 24^{0}}{\sin 51^{0} \cos 69^{0}-\cos 51^{0} \sin 69^{0}} \)
D. \( \frac{\cos \left(90^{0}+A\right) \sec (-A) \tan \left(180^{0}-A\right)}{\sec \left(360^{0}+A\right) \sin \left(180^{0}+A\right) \cot \left(90^{0}-A\right)} \)


If \( \lim _{x \rightarrow 0} \frac{x^{a} \sin ^{b} x}{\left(\sin ^{c} x\right)}, \) where \( a, b, c \in R-\{0\} \)
exists \& has non zero value then \( a+ \)
\( \boldsymbol{b}=\boldsymbol{c} \)
If true enter 1 else enter 0


The average of six number is 12 and The
average of 4 numbers is 15 what is the
average of these 10 number?


Assertion: The clouds in sky generally appear to be whitish.

Reason: Diffraction due to clouds is
efficient in equal measure at all wavelengths.
A. If both assertion and reason are true but the reason is the correct explanation of assertion
B. If both assertion and reason are true but the reason is not the correct explanation of assertion
c. If assertion is true but reason is false
D. If both the assertion and reason are false
E. If reason is true but assertion is false


The area of a rhombus is 2016 sq \( \mathrm{cm} \)
and its side is \( 65 \mathrm{cm} . \) The lengths of the diagonals (in cm) respectively are
A . 125,35
B. 126,32
c. 132,26
D. 135,25


Find the value of \( k \) if the pts \( A \equiv \)
\( (1,2,-1), B \equiv(4,-2,4) \) and \( C \equiv \)
\( (0,0, k) \) form a triangle right angled at
\( \boldsymbol{C} \)


In the electrolytic reduction of alumina, the electrolyte is covered with coke powder because, it
A. prevents oxidation of aluminium formed
B. reacts with aluminium forming aluminium carbide
C. prevents heat loss from the electrolyte
D. none of the above


How many milli moles of sucrose should
be dissolved in 500 gms of water so that the difference between the boiling point and freezing point of the solution
becomes \( 103.57^{\circ} \mathrm{C} ?\left(K_{f}=\right. \)
\( \mathbf{1} . \mathbf{8 6}^{\circ} \boldsymbol{C} / \boldsymbol{m}, \boldsymbol{K}_{\boldsymbol{b}}=\mathbf{0 . 5} \mathbf{2}^{\boldsymbol{o}} \boldsymbol{C} / \boldsymbol{m} \)
A. 500 moles
B. 90 mmoles
c. 1330 mmoles
D. 1330 moles


Assertion
Solubility on n-alcohols in water decreases with increase in molecular
weight.
Reason
The relative proportion of the hydrocarbon part in alcohols increases with increasing molecular weight which permits enhanced hydrogen bond with
water.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


In the given figure, \( O \) is the centre of a
circle. If \( A B \) and \( A C \) are chords of the
circle such that \( A B=A C \) and \( O P \perp \)
\( A B, O Q \perp A C, \) prove that \( P B=Q C \)


The particle used by Rutherford in \( \alpha \) -ray scattering experiment was:
A. neutron
B. electron
c. helium nuclei
D. x-rays


Which of the following is not a characteristic of alcohol?
A. They are lighter than water.
B. Their boiling points rise fairly uniformly with rising molecular weight
C. Lower members are insoluble in water and organic solvents but the solubility regularly increases with molecular mass.
D. Lower members have a pleasant smell and burning taste, higher members are colourless and tasteless.
E. Higher members have a pleasant smell and burning taste, lower members are colourless and tasteless.


Magnetic field at a point on the line of current carrying conductor is
A. maximum
B. infinity
c. zero
D. finite value


In the second period, Li to Ne identify the element
(a) Most reactive element
(b) Most non-reactive non-metal
(c) Largest atomic radius
(d) With valency equal to 4


vurich ol trie ronowing is/are a rneso
compound?
This question has multiple correct options
\( A \)
B.
\( c \)
D.


Number of carbon atoms in the longest
chain is \( 3 . \) A methyl group is present at carbon number 2. So, IUPAC name is
A. 2-ethyl propane
B. butane
c. 2-methyl propane
D. 2-methyl butane


The coefficient of friction between two
blocks of masses \( 1 \mathrm{kg} \) and \( 4 \mathrm{kg} \) as
shown in figure is \( \mu \) and the horizontal
plane is smooth. If the system is slightly displaced and released it will execute
S.H.M. The maximum amplitude if the
upper block does not slip relative to lower block will be (k is spring constant)
\( A \cdot \frac{5 \mu g}{k} \)
в. \( \frac{\mu g}{k} \)
\( c \cdot \frac{3 \mu g}{k} \)
D. \( \frac{2 \mu g}{k} \)


Let \( \boldsymbol{f}(\boldsymbol{x})=(\boldsymbol{x}-\mathbf{1})^{4} \cdot(\boldsymbol{x}-\boldsymbol{2})^{n}, \boldsymbol{n} \boldsymbol{\epsilon} \boldsymbol{N} \)
Then \( f(x) \) has
This question has multiple correct options
A. a maximum at \( x=1 \) if \( n \) is odd
B. a maximum at \( x=1 \) if \( n \) is even
c. a minimum at \( x=2 \) if \( n \) is even
D. a maximum at \( x=2 \) if \( n \) is odd


Differentiate the function \( \tan ^{-1} \frac{2 x}{1-x^{2}} \) w.r.to \( \cos ^{-1}\left(\frac{1-x^{2}}{1+x^{2}}\right) \)


How many \( S-S \) linkage present in
\( \boldsymbol{H}_{2} \boldsymbol{S}_{\boldsymbol{n}} \boldsymbol{O}_{\boldsymbol{6}} ? \)
A . n-
B. n- -
\( c \cdot n \)
D.


\( y= \)
\( x \)
0


A boiled egg show a/an in
entropy
A. increase
B. decrease
c. no chnage
D. none of these


The shaded region in the given figure is
\( \mathbf{A} \cdot A \cap(B \cup C) \)
в. \( A \cup(B \cap C) \)
\( \mathbf{c} \cdot A \cap(B-C) \)
D . \( A-(B \cup C) \)


A man \( 160 \mathrm{cm} \) tall, walks away from a source of light situated at the top of a
pole \( 6 \mathrm{m} \) high, at the rate of \( 1.1 \mathrm{m} / \mathrm{sec} \)
How fast is the length of his shadow increasing when he is \( 1 \mathrm{m} \) away from the pole?


Select one of the following pairs of important features distinguishing Gnetum from Cycas and Pinus and showing affinities with angiosperms.
A. Perianth and no integuments
B. Embryo development and apical meristem
c. Absence of resin duct and leaf venation
D. Presence of vessel elements and absence of archegonia


FSH (follicle stimulating hormone) is
produced by
A. Adrenal cortex
B. Anterior pituitary lobe
c. Middle pituitary lobe
D. Posterior pituitary lobe


If a wire is stretched to make it \( 0.1 \% \)
Ionger, its resistance will
A. increase by \( 0.05 \% \)
B. increase by \( 0.2 \% \)
c. decrease by \( 0.2 \% \)
D. decrease by \( 0.05 \% \)


If \( \left(\boldsymbol{x}+\frac{\mathbf{1}}{\boldsymbol{x}}+\mathbf{1}\right)^{\boldsymbol{6}}=\boldsymbol{a}_{\boldsymbol{0}}+\left(\boldsymbol{a}_{\boldsymbol{1}} \boldsymbol{x}+\frac{\boldsymbol{b}_{\boldsymbol{1}}}{\boldsymbol{x}}\right)+ \)
\( \left(a_{2} x^{2}+\frac{b_{2}}{x^{2}}\right)+\ldots+\left(a_{6} x^{6}+\frac{b_{6}}{x^{6}}\right) \) the
find the value of \( a_{0} \)


The branch of chemistry in which the study of the mathematical description of the motion and interaction of
subatomic particles and also incorporates quantization of energy, wave-particle duality, the uncertainty principle, and their relationship to chemical processes is called:
A. Quantum chemistry
B. Analytical chemistry
c. spectroscopy
D. Physical chemistry


A \( 10 \Omega \) resistance, \( 5 m H \) coil and \( 10 \mu F \)
capacitor are joined in series. When a suitable frequency alternating current source is joined to this combination, the circuit resonates. If the resistance
is halved, the resonance frequency:
\( A \). is halved
B. is doubled
c. remains unchanged
D. is quadrupled


Some magnetic flux is changed in a coil
of resistance 10 ohm. As a result an
induced current is developed in it,
which varies with time as shown in
figure. The magnitude of change in flux
through the coil in Webers is (Neglect
self inductance of the coil)
\( A \cdot 2 \)
\( B .4 \)
\( c \cdot 6 \)
\( D \)


Which of the following sequence contains atomic number of only
representative elements?
A. 55,12,48,53
в. 13,33,54,80
c. 3,33,53,87
D. 22,33,55,66


To make a benzene soluble cement, 60 g rosin is melted in an iron pot and 68 g beeswax and 12 g shellac are added. How much of shellac should be taken to
make 35 g cement?


X-ray beam can be deflected:
A. by an electric field
B. by a magnetic field
C . by electric \&magnetic fields both
D. neither by an electric field nor by a magnetic field


If \( \frac{\pi}{5} \) and \( \frac{\pi}{3} \) are respectively the
arguments of \( \bar{z}_{1} \) and \( z_{2}, \) what is the
value of \( \left(a r g z_{1}+a r g z_{2}\right) ? \)


Global warming is a direct result of:
A. an increased imbalance of gases in the atmosphere.
B. a decreased imbalance of gases in the atmosphere.
C. an increased balance of gases in the atmosphere.
D. none of these


Mass of thin long metal rod is \( 2 \mathrm{kg} \) and its moment of inertia about an axis
perpendicular to the length of rod and
passing through its one end is \( 0.5 k g m^{2} \) Its radius of gyration is:
\( \mathbf{A} \cdot 20 \mathrm{cm} \)
B. \( 40 \mathrm{cm} \)
c. \( 50 \mathrm{cm} \)
D. \( 1 m \)


In the following compound, the
favourable site/s for protonation is/are:
\( A \cdot(b),(c) \) and \( (d) \)
\( B \). \( (a) \)
\( c \cdot(a) \) and \( (e) \)
D. (a) and (d)


Assertion If \( n>1 \) then \( \int_{0}^{\infty} \frac{d x}{1+x^{n}}= \)
\( \int_{0}^{1} \frac{d x}{\left(1-x^{n}\right)^{1 / n}} \)
Reason \( \int_{a}^{b} f(x) d x=\int_{a}^{b} f(a+b-x) d x \)
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


Evaluate the given definite integrals as
limit of sums:
\( \int_{0}^{4}\left(x+e^{2 x}\right) d x \)


In an alternating circuit applied voltage
is \( 220 V . \) If \( R=8 \Omega, X_{L}=X_{C}=6 \Omega \)
then write the values of the following:
(a) Root mean square value of voltage.
(b) Impedance of circuit.


An observer moves towards a stationary source of sound with a speed \( 1 / 5^{t h} \) of the speed of sound. The wavelength and frequency of the source emitted are \( \lambda \)
and \( f \) respectively. The apparent frequency and wavelength recorded by the observer are respectively:
A. \( 1.2 f, 1.2 \lambda \)
B. \( 1.2 f, \lambda \)
c. \( f, 1.2 \lambda \)
D. \( 0.8 f, 0.8 \lambda \)


State whether given statement is True or False
You find your mass to be \( 42 \mathrm{kg} \) on a weighing machine. Is your mass more
or less than \( 42 \mathrm{kg} ? \)
A. True
B. False


Let \( z=x+i y \) then prove that \( \left|e^{z}\right|=e^{x} \)


The least area of a circle
circumscribing any right triangle of area S is:
A . \( \pi S \)
в. \( 2 \pi S \)
c. \( \sqrt{2} \pi S \)
D. \( 4 \pi S \)


Anterior lobe of pituitary secretes
A. \( \mathrm{TSH} \), ADH and prolactin
B. \( L H, F S H \) and a growth hormone
C. ACTH, TSH and oxytocin
D. STH, GH and antidiuretic hormone


In a right triangle having angles of \( 30^{\circ} \)
and \( 60^{\circ}, \) the \( 60^{\circ} \) angle is bisected. What
is the ratio of the segments into which the angle bisector divides the opposite leg?
A . 2: 3
B. 3:
\( c \cdot 1: 2 \)
D. 3:
E. 2: 5


topp
тре уои
ollowing graph best represents th ne variation of relative position o
cond stone with respect to the first
Assume stones do not rebound afte
itting the ground and neglect air esistance, take \( g=10 m / s^{2} \)
The figures are schematic and no frawn to scale.


Haemoglobin is
A. An oxygen carrier in human blood
B. A protein used as food supplement
C. An oxygen scavenger in root nodules
D. A plant protein with high lysine content


Find the value of \( x \) if \( x^{3}=\left(\frac{6}{5}\right)^{-3} x \) \( \left(\frac{6}{5}\right)^{6} \)


Draw the diagram of a Helium-Neon laser tube and label the parts.


Suppose \( E F G H \) is a trapezium in
which \( \boldsymbol{E F} \) is parallel to \( \boldsymbol{H} \boldsymbol{G} \). Through \( \boldsymbol{X} \) the mid-point of \( E H, X Y \) is drawn
parallel to \( E F \) meeting \( F G \) at \( Y \). Prove that \( X Y \) bisects \( F G \)


On the bases of Le-Chatelier's principle predict which of the following conditions would be unfavourable for
the formation of \( S O_{3} ? \) Given that
\( 2 S O_{2}+O_{2} \rightleftharpoons 2 S O_{3} ; \Delta H=42 K C a l \)
A. Low pressure and low temperature
B. High pressure and low temperature
c. Low temperature and low pressure
D. High concentration of \( S O_{2} \).


A potentiometer wire of length \( L \) and
resistance \( 10 \Omega \) is connected in series
with a battery of e.m.f. \( 2.5 \% \) and a
resistance in its primary circuit. The null point corresponding to a cell of
e.m.f. \( 1 V \) is obtained at a distance \( L / 2 \)
If the resistance in the primary circuit is doubled then the position of new null
point will be
\( \mathbf{A} \cdot 0.4 L \)
B. \( 0.5 L \)
c. \( 0.6 L \)
\( \mathbf{D} \cdot 0.8 L \)


If three mutually perpendicular lines have direction cosines
\( \left(\ell_{1}, \mathbf{m}_{1}, \mathbf{n}_{1}\right),\left(\ell_{2}, \mathbf{m}_{2}, \mathbf{n}_{2}\right) \) and
\( \left(\ell_{3}, \boldsymbol{m}_{3}, \boldsymbol{n}_{3}\right), \) then the line having
direction cosines \( \ell_{1}+\ell_{2}+\ell_{3}, \boldsymbol{m}_{1}+ \)
\( \boldsymbol{m}_{2}+\boldsymbol{m}_{3} \) and \( \boldsymbol{n}_{1}+\boldsymbol{n}_{2}+\boldsymbol{n}_{3} \) make an
angle of \( \ldots \ldots \) with each other.
A . 0
B. 30
\( c \cdot 60^{\circ} \)
D. \( 90^{\circ} \)


In fructose and glucose the possible optical isomers are:
A. 12,12
B. 8, 16
\( c \cdot 16,8 \)
D. 4, 12


The surface of water in a water tank on
the top of a house is \( 4 \mathrm{m} \) above the tap level. Find the pressure of water at the tap when the tap is closed. Is it necessary to specify that the tap is closed? Takeg \( =10 m s^{-2} \)


\( A(0,0) \) and \( B(8,2) \) are fixed points on the curve \( y^{3}=|x| . \) A point \( C \) starts
moving from origin along the curve for \( x<0 \) such that rate of change in the
ordinate is \( 2 \mathrm{cm} / \mathrm{s} \). After \( t_{0} \) seconds
triangle \( A B C \) become a right
triangle. After \( t_{0} \) seconds, tangent is
drawn to the curve at point \( C \) to
intersect it again at \( (\boldsymbol{\alpha}, \boldsymbol{\beta}) \) then \( \mathbf{4} \boldsymbol{\alpha}+ \)
\( \mathbf{3} \boldsymbol{\beta} \) is
A \( \cdot \frac{4}{3} \)
B. \( \frac{3}{4} \)
\( c \cdot 2 \)
\( D \)


A coin is tossed for 50 times and get a
head 10 times, this action is called
A. space
B. experiment
c. sample
D. event


Which of the following is correct pair of pyrimidine bases?
A. Adenine and Thymine
B. Adenine and Guanine
c. Thymine and Cytosine
D. Guanine and Cytosine


A radioactive substance is being
consumed at a rate constant of \( 1 s^{-1} \)
After what time will the number of
radioactive nuclei become 100. Initially, there were 200 nuclei present
A . \( 1 s \)
B. \( \frac{1}{\ln (2)} s \)
c. \( \ln (2) \) s
D. \( 2 s \)


Two sides of a triangle are of lengths 5 \( \mathrm{cm} \) and \( 1.5 \mathrm{cm}, \) then the length of the third side of the triangle cannot be
\( \mathbf{A} \cdot 3.6 \mathrm{cm} \)
B. \( 4.1 \mathrm{cm} \)
c. \( 3.8 \mathrm{cm} \)
D. \( 3.4 \mathrm{cm} \)


Cancer is a disease where body cells grow unchecked. A protein found in the body interferes with the growth of
cancer cells. It is used for the treatment
of cancer. Identify it
A. Haemoglobin
B. casein
c. Keratin
D. Interferon


The number of values of k for which the
system of linear equations, \( (2 k+ \)
1) \( x+5 k y=k+2 \) and \( k x+(k+ \)
2) \( y=2 \) has no solution, is:
A. Infinitely many
B. 3
\( c .1 \)
D. 2


Two person \( A \) and \( B \), each carrying a source of frequency \( 300 \mathrm{Hz} \), are standing a few metre apart. A starts moving towards B with velocity \( 30 \mathrm{m} / \mathrm{s} \) If the speed of sound is \( 300 \mathrm{m} / \mathrm{s} \), which of the following is true?
A. number of beats by A is higher than that heard by E
B. the number of beats by B are 30 Hz
c. both (a) and (b) are correct
D. both (a) and (b) are wrong


A stream of water (density \( \rho \) ) flowing horizontally with a speed v emerges from a tube of cross-sectional area \( A \)
and hits on adjacent vertical wall. The
force of impact on the wall when the
water does not rebound is:
A \( \cdot \rho A v^{2} \)
B. \( \rho A v \)
c. \( \frac{\rho A}{v} \)
D. none of these


With regard to an astronomical telescope for refracting type, state how you will increase its:
(i) magnifying power.
(ii) resolving power


Assertion
Transition metals are good catalysts.
Reason
Transition metals have variable
oxidation state.
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


Poisonous fangs of a snake are modified
A. Mandible
B. Maxillary teeth
c. canines
D. Nasals


Give one word for the following. The colour shown by a neutral substance on a \( p H \) scale.


Two waves represented by \( y_{1}= \)
\( 10 \sin (2000 \pi t) \) and \( y_{2}= \)
\( 10 \sin (2000 \pi t+\pi / 2) \) are
superimposed at any point at a particular instant. The resultant amplitude is?
A. 10 units
B. 20 units
c. 14.1 units
D. zero


The relation between frequency (n) and wavelength \( (\lambda) \) is given by (v is velocity, n is frequency and \( T \) is time-period)
в. \( n=\frac{\lambda}{v} \)
c. \( v=\frac{n}{\lambda^{2}} \)
D. \( n=\frac{T}{\lambda} \)


A converging lens of focal length \( f \) is
used as simple microscope. If the least distance of distinct version of the
observer is \( D \) and the lens is held close
to the eye, the magnifying power of the lens is
A. \( D / 2 f \)
B. \( f / D \)
c. \( \frac{D}{f}-1 \)
D. \( D / f \)


A steel rod has a radius of \( 10 \mathrm{mm} \) and a
length of \( 1.0 \mathrm{m} . \) A force stretches it along its length and produces a strain of \( 0.16 \% . \) Young's modulus of the steel is \( 2.0 \times 10^{11} N / m^{2} . \) What is the
magnitude of the force stretching the rod?
A . \( 100 \mathrm{kN} \)
B. 314 k
c. \( 31.4 \mathrm{kN} \)
D. 200kN


When a p-njunction diode is connected
in forward bias its barrier potential
A. decreases and less current flows in the circuit
B. decreases and more current flows in the circuit
C. increases and more current flows in the circuit
D. decreases and no current flows in the circuit


Rolling friction is sliding friction, if all other factors are the same.
A. greater than
B. less than
c. same as
D. none


A particle is moving in a straight line at
\( \boldsymbol{t}=\mathbf{0}, \boldsymbol{x}=\mathbf{0}, \) velocity is \( \mathbf{9} \boldsymbol{m} \boldsymbol{s}^{-1} . \) If graph
shows the variation of acceleration \( (\boldsymbol{a}) \)
with time ( \( t \) ) of a moving particle then:
A. Its velocity can become zero
C. Minimum velocity possible is \( 5 \mathrm{ms}^{-1} \)
D. Minimum velocity possible is \( 6 \mathrm{ms}^{-1} \)


In a healthy human eye, the focussing is
done by the
A. To and fro movement of the eye-lens
B. Changing the curvature of the retina
C. Change in the convexity of the lens through ciliary tubes
D. Change in the refractive index of the eye fluid


Seven capacitors, each of capacitance \( 2 \mu F \) are to be connected to obtain a
capacitance of \( 10 / 11 \mu F \).Which of the following combinations is possible?
A. 5 in parallel 2 in series
B. 4 in parallel 3 in series
c. 3 in parallel 4 in series
D. 2 in parallel 5 in series


Find \( \int \frac{e^{x}(x-3)}{(x-1)^{3}} d x \)


Solve the following equations by substitution method.
\( \boldsymbol{x}=\mathbf{2} \boldsymbol{y}-\mathbf{1} ; \boldsymbol{y}=\mathbf{2} \boldsymbol{x}-\mathbf{7} \)
A. \( x=8, y=3 \)
в. \( x=2, y=3 \)
c. \( x=5, y=3 \)
D. \( x=1, y=3 \)


Among the following options, which molecule contains both ionic and
covalent bonds?
A. \( C_{6} H_{14} \)
в. \( M g C l_{2} \)
\( \mathrm{c} \cdot\left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{4} \)
D. \( H_{2} O \)
E \( \cdot C_{2} H_{4} \)


Assertion
The equation \( x^{2}+2 \lambda x y+y^{2}-2 x- \)
\( 2 y+2=0 \) represent an ellipse if \( \lambda \in \)
(-1,1)
Reason
The general equation of second degree \( \operatorname{given} \operatorname{by} a x^{2}+2 h x y+b y^{2}+2 g x+ \)
\( 2 f y+c=0 \) represent an ellipse if
\( a b c+2 f g h-a f^{2}-b g^{2}-c h^{2} \neq 0 \& \)
\( h^{2}<a b \)
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 particle moves parallel to \( x \) -axis with
constant velocity \( v \) as shown in the figure. The angular velocity of the particle about the origin \( \boldsymbol{O} \)
A. remains constant
B. continuously increases
c. continuously decreases
D. oscillates


A gas occupies volume of \( 0.35 d m^{3} \) at
\( 290 \mathrm{K} \) and \( 92.458 \mathrm{K} \mathrm{Nm}^{-2} \) pressure.
Calculate the volume of gas at STP (Ans
\( \left.0.3 d m^{3}\right) \)


A charged oil drop is suspended in
uniform field of \( 3 \times 10^{4} V / m \) so that it
neither falls nor rises. The charge on the drop will be:
(Take the mass of the charge \( =\mathbf{9 . 9} \times \)
\( \left.10^{-15} \mathrm{kg} \text { and } g=10 m / s^{2}\right) \)
A . \( 3.3 \times 10^{-18} \mathrm{C} \)
B. \( 3.2 \times 10^{-18} \mathrm{C} \)
c. \( 1.6 \times 10^{-18} \mathrm{C} \)
D. \( 4.8 \times 10^{-18} \mathrm{C} \)


Find the slope and \( y \) -intercept of line
\( \boldsymbol{y}-\mathbf{3} \boldsymbol{x}=\mathbf{5} \)


At what velocity ratio \( \frac{v_{e}}{v_{p}} \) are the wavelengths of an electron and a proton
equal?
\( \left(\boldsymbol{m}_{e}=\mathbf{9 . 1} \times \mathbf{1 0}^{-\mathbf{2 8}} \boldsymbol{g} \quad \boldsymbol{\text {and}} \quad \boldsymbol{m}_{\boldsymbol{p}}=\mathbf{1 . 6 7}\right. \)
A. \( 1.2 \times 10^{3} \)
В. \( 1.8 \times 10^{3} \)
c. \( 2.4 \times 10^{3} \)
D. \( 1.6 \times 10^{3} \)


Living fossil is
A . Latimeria
B. Uromastix
c. Archaeopteryx
D. All of the above


Number of sides of equation in simple equation is/ are
A. Two
B. One
c. Three
D. None of these


If the angle between the lines \( k x-y+ \) \( 6=0,3 x-5 y+7=0 \) is \( \frac{\pi}{4}, \) then one
of the value of \( k= \)
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c \cdot 3 \)
D.


The force that water exert on the base of
a house tank of base area \( 1.5 \mathrm{m}^{2} \) when it
is filled with water up to a height of \( 1 \mathrm{m} \)
if \( \left(g=10 \mathrm{m} / \mathrm{s}^{2}\right) \)
A. 1200 kgwt
B. 1500 kgwt
c. 1700 kgwt
D. 2000 kgwt


The sum of the digits of a two digit number is \( 15 . \) If 9 is added to the
number, the digit are reversed. Find the number.


If \( x \% \) of 200 is \( 10, \) then the value of \( x \) is
A . 10
B. 2
\( c .5 \)
D. none of the above.


Which one is not a source of
carbohydrate?
A. Rice
B. Millets
c. sorghum
D. Gram


Which of the following statement(s) is/are correct?

As the s-character of a hybrid orbital decreases,
(1) the bond angle decreases
(II) the bond strength increases
(III) the bond length increases
(IV) the size of orbital increases
\( A \cdot(1),(11) \) and (IV)
B. (I), (III) and (IV)
c. (।) and (II)
D. (I), (II), (III) and (IV)


\( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{1} & \mathbf{8} \\ \mathbf{9} & \mathbf{4}\end{array}\right] \boldsymbol{B}=\left[\begin{array}{ll}\mathbf{6} & \mathbf{7} \\ \mathbf{3} & \mathbf{5}\end{array}\right] \) Find \( \boldsymbol{A}+\boldsymbol{B} \)


Van Arkel method of purification of metals involves converting the metal to
\( a: \)
A. volatile unstable compound
B. volatile stable compound
c. non-volatile stable compound
D. None of the above


Assertion
When a salt such as NaCl dissolves, the
\( N a^{+} \) and \( C l^{-} \) ions leaving the crystal
lattice acquire far greater freedom.
Reason
In thermodyanamic terms, the formation of solution occurs with a
favourable change in free energy, i.e.
\( \triangle H \) has a high positive value and \( T \triangle S \)
a low negative vaiue.
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


In the atmosphere of industrial smog, copper corrodes to form:
This question has multiple correct options
A. Basic copper carbonate
B. Copper sulphide
c. Basic copper sulphate
D. copper oxide


If the square of an odd positive integer
can be of the form \( 6 q+1 \) or \( 6 q+3 \) for
some \( q \) then \( q \) belongs to:
This question has multiple correct options
A. integers
B. rational
c. real
D. none of these


The initial velocity of the particle is 10 \( m \) sec and its retardation is \( 2 m / s^{2} . \) The distance moved by the particle is 5 th second of its motion is :
A. \( 1 m \)
в. \( 19 m \)
\( c .50 m \)
D. \( 75 m \)


A ray of light is incident on a medium
with angle of incidence i and refracted
into a second medium with angle of
refraction \( r . \) The graph of \( \sin (i) \vee s \) \( \sin (r) \) is as shown in the figure. Then
the velocity of light in the first medium
is \( \ldots \ldots . . . . . . . . . \) times the velocity of light in
the second medium.
\( A \cdot \sqrt{3} \)
B. \( 1 / \sqrt{3} \)
c. \( \sqrt{3} / 2 \)
D. \( 2 / \sqrt{3} \)


ff \( 5(1-2 x)=15 ; \) evaluate \( x^{2}-3 x+ \)
2
\( A \cdot 1 \)
B. 4
\( c .3 \)
D. 6


If (1,-1,0),(-2,1,8) and (-1,2,7) are three consecutive vertices of a
parallelogram then the fourth vertex is
A. (2,0,-1)
В. (1,0,-1)
c. (1,-2,0)
a 5
D. (0,-2,1)


A maglev train is gradually taking a \( 45^{\circ} \) turn while moving with constant-speed
of \( \pi m s^{-1} . \) For a special compartment
of train, turning process takes \( 220 m \) length on the track. Magnitude of centripetal acceleration of the train is:
A \cdot Is constant and \( \frac{\pi}{88} m s^{-2} \) (approximately)
B. Is variable
c. zero, as speed is constant
D. Either (2) or (3)


In a number without decimal, what is the significance of zeros on the right of non-zero digits?


A parallel-plate capacitor with an air
gap has magnitude of charge \( Q \) applied
on each plate. The plates have area \( \boldsymbol{A} \) and are separated by a distance dd.
(The distance \( d \) is very small compared to the side lengths of the plates.) The capacitor is then isolated from the voltage source. How much work will be required by an outside force to separate the plates to a
distance \( 3 d ? \)
\( ^{\mathbf{A}} \cdot \frac{Q^{2}}{4 \pi \epsilon_{0} d} \)
В. \( \frac{Q^{2}}{2 \pi \epsilon_{0} d} \)
\( ^{\mathbf{c}} \cdot \frac{Q^{2} d}{2 \epsilon_{0} A} \)
D. \( \frac{Q^{2} d}{\epsilon_{0} A} \)
E \( \cdot \frac{3 Q^{2} d}{\epsilon_{0} A} \)


What are petals? Why are they generally coloured?


The colourless species is
A. \( V C l_{3} \)
в. \( \operatorname{VOSO}_{4} \)
c. \( N a_{3} V O_{4} \)
\( \mathrm{D} \cdot\left[V\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right] \mathrm{SO}_{4} \cdot \mathrm{H}_{2} \mathrm{O} \)


It is better to use a sharp tipped nail than a blunt nail because:
A. the tip with the smallest area will produce a higher pressure when a small force is applied
B. a sharp tipped nail needs a larger force to drive it into wooden surface
C. the sharp tip saves cost as less raw materials are required to make such nails
D. the sharp tip has a spiralling effect when the nail is hit on the head


Find the direction of electric field at
point \( \boldsymbol{P} \) for the charge distribution as
shown in the figure.
A. Along positive \( y \) -axis
B. Along negative \( y \) -axis
c. Along positive \( x \) -axis
D. Along negative \( x \) -axis


Which of the following information is
true for structure of \( H_{2} O_{2} \) in solid
phase?
\( A \)
в.
\( c \)
D.


Root pressure can be measured by
A. Attaching a barometer to the cut end of the stem
B. Attaching a manometer to the cut end of the stem
C. Attaching a thermometer to the cut end of the stem
D. Attaching a potometer to the cut end of the stem.


To the equilibrium system \( \boldsymbol{P} \boldsymbol{C l}_{5}(\boldsymbol{g}) \rightleftharpoons \)
\( \boldsymbol{P C l}_{3}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g}), \) gaseous \( \boldsymbol{C l}_{2} \) is
added, increasing the volume at the same time in such a manner so that
\( P C l_{3} \) in the system remains unchanged temperature remains constant what
happens to the equilibrium?
A. Shifted backward
B. Remains unaffected
c. Shifted forward
D. Depends on the magnitude of \( P C l_{3} \)


Number of rational terms in the
expansion of \( (\sqrt{\mathbf{2}}+\sqrt[4]{\mathbf{3}})^{100} \) is
A . 25
B . 26
c. 27
D . 28


The \( x \) and \( y \) intercepts of the line \( 2 x- \)
\( \mathbf{3} \boldsymbol{y}+\mathbf{6}=\mathbf{0}, \) respectively are :
A .2,3
B. 3,2
c. -3,2
D. 3,-2


A sample of drinking was found to be severely contaminated with chloroform,
\( C H C l_{3}, \) supposed to be a carcinogen
The level of contamination was 15 ppm
(by mass). Express this in percent by
mass.
A. \( 1.5 \times 10^{-3} \)
В. \( 4.0 \times 10^{-3} \)
c. \( 6 \times 10^{-3} \)
D. \( 0.75 \times 10^{-3} \)


Multiple Choice Questions Depletion of which gas in the atmosphere can lead to an increased incidence of skin cancers.
A. Methane
B. Nitrous oxide
c. Ozone
D. Ammonia


Solve for \( x \) in \( \frac{2-(3 x-8)}{5-(4 x-9)}=\frac{1}{2} \)


The process of taking out threads from the cocoon is known as:
A. rearing
B. sorting
c. scouring
D. reeling


The lower chambers of the heart are
called
A. Auricles
B. Ventricles
c. spiracles
D. Tentacles


Lot \( A \) consists of \( 3 G \) and \( 2 D \) articles.
Lot \( B \) consists of \( 4 G 1 D \) article. A new
lot \( C \) is formed by taking 3 articles from \( A \) articles from \( A \) and 2 form \( B \). The
probability that an article chosen at random from \( C \) is
A . \( 1 / 3 \)
в. 2 /
c. \( 8 / 25 \)
D. none


Character not shared by monotremes
and reptiles is
A. Body covered by hair and four chambered heart
B. A median T-shaped interclavicle present
C. Presence of cloaca
D. Thoracic ribs are single headed


The baleen plate of whale is
A. Modified tooth
B. Modified sebaceous gland
c. Modified integument
D. Modified tongue


A superconductor has \( T_{C}(0)=100 K \)
When a magnetic field of 7.5 Tesla is
applied, its \( T_{c} \) decreases to 75 K. For this material one can definitely say that
when
A \( \cdot B=5 \) Tesla, \( T_{c}(B)=80 K \)
B. \( B=5 \) Tesla, \( 75 K<T_{c}(B)<100 K \)
c. \( B=10 \) Tesla, \( 75 K<T_{c}<100 K \)
D. \( B=10 \) Tesla, \( T_{c}=70 K \)


Refining of aluminium is done by
A. electrolysis
B. distillation
c. sedimentation
D. oxidation


Potassium dichromate in alkaline
solution, with \( 30 \% \mathrm{H}_{2} \mathrm{O}_{2} \) produces:
A \( \cdot K_{3} C r O_{8} \)
в. \( \operatorname{Cr} \mathrm{O}\left(\mathrm{O}_{2}\right)_{2} \)
\( \mathrm{c} \cdot \mathrm{CrO}_{3} \)
D. \( L_{2} \) Cr \( O_{4} \)


Two discs of equal mass but different diameter are connected with an axle
system that allows them to roll down an
incline together. Both discs start and
finish at the same time. Find out which
of the following statement is true?
A. Their tangential velocity is the same
B. Their tangential acceleration is the same
c. Their angular velocity is the same
D. Their angular displacement is the same
E. Their angular acceleration is the same


Assertion
The magnetic force on the closed loop in fig is zero
Reason
Force (magnetic) on the wire is \( \int d F= \) \( \int i d \vec{l} \times \vec{B} \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is
not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


A cat running with constant acceleration in one direction is at rest
initially and has velocity \( v(t)= \)
\( 1.00 m / s \) at 2.00 seconds later.
At \( t=4.00 \) seconds, how far away from
the starting point will the cat be?
\( \mathbf{A} \cdot 0.00 m \)
в. \( 1.00 m \)
c. \( 2.00 m \)
D. \( 4.00 m \)
E. \( 8.00 m \)


The pair of amphoteric oxides is:
A. \( V O, C r_{2} O_{3} \)
в. \( V_{2} O_{5}, C r_{2} O_{3} \)
\( \mathrm{c} \cdot \mathrm{V} \mathrm{O}_{2}, \mathrm{Cr}_{2} \mathrm{O}_{3} \)
D. \( V_{2} O_{5}, C r O_{3} \)


How can a convex lens behave like a
diverging lens.


Study the statements about chordates
and identify correct ones:
(a) Columella auris present in the middle year of amphibians is modified hyomandibula of fishes.
(b) Reptiles lay cleidoic eggs.
(c) Sphenodon is connecting link between amphibians and reptiles.
(d) Panthera tigris is an extinct animal of India.
\( A \cdot(a),(c) \)
B. \( (b),(d) \)
\( c \cdot(a),(b) \) and \( (c) \)
D. (b), (c) aand (d)


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


If \( A \) and \( B \) are mutually exclusive such
that \( \boldsymbol{P}(\boldsymbol{A})=\mathbf{0 . 3 5} \) and \( \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 4 5} \)
find
\( \boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B}) \)


What do \( C \) and \( D \) represent on the
curve?


Nidhi has two bulbs connected across
two cells in a simple circuit as shown.
How can she make the bulbs glow
dimmer?
A. Replace one cell with a piece of chalk.
B. Replace one cell with a piece of wire.
C. Replace one bulb with a piece of wire.
D. Replace one bulb with another cell.


Find the \( (p+2) \) th term from the end in \( \left(x-\frac{1}{x}\right)^{2 n+1} \)


Fringing reefs, barrier reefs and atolls
are the types of
A. Algae
B. Bryophytes
c. Pteridophytes
D. coral reefs


The diagram represents a magnetic
field. What causes this field?
\( A . \) A bar magnet
B. A solenoid carrying a current
C. A straight wire carrying a current
D. Two north poles close together


In a triangle \( A B C, D \) and \( E \) are points
on \( B C \) and \( A C \) respectively, such that
\( B D=2 D C, A E=3 E C, \) Let \( P \) be the
point of intersection of \( A D \) and \( B E \) Then \( \frac{\boldsymbol{B} \boldsymbol{E}}{\boldsymbol{P} \boldsymbol{E}}= \)
A .2: 3
B. 3: 8
c. 8: 3
D. 1: 2


Choose the correct answer from the
alternatives given.
A couple has six daughters, What is the possibility of their having a girl next time?
A . 10\%
B. 50\%
c. \( 90 \% \)
D. 100\%


Write the charecteristics of an ideal
drug?


B-DNA which is right-handed double helix contains \( _{-1-} \) base pairs per
turn of the helix and each turn is
long.
A. \( 10,3.4 \AA \)
B. 10,34 ,
c. \( 11,20 \dot{A} \)
D. 11,34 , \( \dot{A} \)


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


For the reaction shown, which best
describes the elementary reaction?
\( \mathbf{2} N_{2} \boldsymbol{O}_{\mathbf{5}} \leftrightarrow \mathbf{4} \boldsymbol{N} \boldsymbol{O}_{\mathbf{2}}+\boldsymbol{O}_{\mathbf{2}} \)
A. First order unimolecular
B. Second order unimolecular
c. Second order bimolecular
D. First order bimolecular


The same mass of copper is drawn into two wires \( A \) and \( B \) or radii \( r \) and \( 3 r \)
respectively. They are connected in series, and electric current is passed. The ratio of the heat produced in \( A \) and \( \mathrm{Bis} \)
A .1: 9
в. 1: 81
\( c .81: \)
D. 9:


The decay constant of radioactive
substance is \( 4.33 \times 10^{-4} \) per year
Calculate its half life period.


Boron cannot form which one of the
following anions?
A \( \cdot \) BF \( _{6}^{3} \)
B. BH \( _{4}^{-} \)
\( c \cdot B(O H) \)
D. BO


\( x \) \( \begin{array}{ccccc}\mathbf{2} & \mathbf{3} & \mathbf{5} & \mathbf{6} & \mathbf{1 0} \\ 15 & 10 & b & 5 & 3\end{array} \) \( y \)
Identify the inverse proportional
quantities.
\( \mathbf{A} \cdot 4 \)
B. 5
\( \mathbf{c} \cdot \mathbf{6} \)
D. 10


Find the value of \( \sin 60^{\circ} \) geometrically.


ABCD is a rectangle in which \( A B=10 \) \( \mathrm{cms}, \mathrm{BC}=8 \mathrm{cms} . \) A point \( \mathrm{P} \) is taken on
AB such that \( P A=x \). Then the minimum
value of \( P C^{2}+P D^{2} \) is obtained when \( x \)
\( = \)
A . 10
B. 5
\( c \cdot 8 \)
D. 4


Difference between sample space and
subset of sample space is considered
as
A. numerical complementary events.
B. equal compulsory events
c. complementary events.
D. compulsory events


The sulphide ores are generally roasted to oxide for the extraction of metals
instead of being directly
A. reduced
B. oxidized
c. both1 and 2
D. no option


All the reactions in glycolysis are
reversible except
A. 3 -Phosphoglycerate to 1,3 -Biphosphoglycerate.
B. Glucose 6-phosphate to fructose - 6-phosphate.
C. 1,3 -Biphosphoglycerate to glyceraldehyde 3 -P.
D. Fructose - 6 -phosphate to fructose- 1,6 -diphosphate.


Which of the following oxidation states
is the most common among the lanthanoids?
\( A \cdot 4 \)
B. 2
\( c \cdot 5 \)
D.


The colloidal system in which the disperse phase and dispersion medium are both liquids is known as:
A. an emulsion
B. an aerosol
\( c \cdot \) a ge
D. a foam


If each row of a determinant of third
order of value \( \Delta \) is multipled by \( 3, \) then the value of new determinant is
A. \( \Delta \)
B. \( 27 \Delta \)
c. \( 21 \Delta \)
D. \( 54 \Delta \)


If \( A \) is a \( 3 \times 3 \) skew-symmetric matrix,
then trace of \( A \) is equal to
\( A \cdot 1 \)
в. \( |A| \)
\( c \cdot-1 \)
D. none of these


The area bounded by the curve \( y= \) \( (x+1)^{2}, y=(x-1)^{2} \) and the line \( y= \)
0 is
A \( \cdot \frac{1}{6} \)
в. \( \frac{2}{3} \)
\( c \cdot \frac{1}{4} \)
D.


Give a demonstration for total internal
reflection. What are the technological applications of total internal reflection
in nature? Briefly explain it.


Doping of silicon with indium leads to
which type of semiconductors?


\( 10 g \) of lce at \( -20^{0} C \) is added to \( 10 g \) of
water at \( 50^{0} C . \) The amount of ice and
water, present at equilibrium, are respectively
A . \( 0,20 g \)
в. \( 5 g, 15 g \)
c. \( 5 g, 10 g \)
D. \( 10 g, 10 g \)


For the travelling harmonic wave \( \boldsymbol{y}(\boldsymbol{x}, \boldsymbol{t})=2.0 \cos 2 \pi(10 \mathrm{t}-0.0080 \mathrm{x}+0.35) \)
where \( x \) and \( y \) are in \( c m \) and \( t \) in \( s \) Calculate the phase difference between oscillatory motion of two points separated by a distance of \( x \)
A. \( x=4 m, \quad \Delta \phi=6.4 \pi r a d \)
в. \( 0.5 m, \quad \Delta \phi=0.6 \pi \) rad
\( \begin{array}{ll}\text { c. } \lambda / 2, & \Delta \phi=.6 \pi r a d\end{array} \)
D. 3\lambda/4, \( \quad \Delta \phi=2.5 \pi r a d \)