Which of the following monomer in excess makes \( P H B V \) more flexible?
This question has multiple correct options
A. \( \beta \) - hydroxy butanoic acid
B. \( \alpha \) -hydroxy butanoic acid
C. \( \beta- \) hydroxy pentanoic acid
D. \( \alpha \) -hydroxy pentanoic acid


Which is the main constituent of
petroleum gas?
A. Methane
B. Ethane
c. Butane
D. Hexane


In
\( 0.1 \mathrm{M} \) solution, weak electrolyte,
\( C H_{3} C O O H \) is \( 1.3 \% \) dissociated. If 100
molecules of \( \boldsymbol{C H}_{3} \boldsymbol{C O O H} \) are placed originally in the solution, how many acid molecules remain nonionized at
equilibrium?


\( \int \frac{d x}{\sin ^{2} x \cos ^{2} x} \) equals
A \( \cdot \tan x-\cot x+C \)
B. \( \tan x+\cot x+c \)
\( c \cdot \tan x \cot x+c \)
D. \( \tan x-\cot 2 x+c \)


Sum of the maximum and minimum
values of \( 12 \cos ^{2} x-6 \sin x \cos x+ \)
\( 2 \sin ^{2} x \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B. 7
c. 14
D. 15


plates \( A, B \) and \( C \) are placed as shown.
Switches \( S_{1} \) and \( S_{2} \) are open, and can
connect \( A \) and \( C \) to earth when closed.
\( +Q \) charge is given to \( B: \)
This question has multiple correct options
A. If \( S_{1} \) is closed with \( S_{2} \) open, a charge of amount \( Q \) will
pass through \( S_{1} \)
B. If \( S_{2} \) is closed with \( S_{1} \) open, a charge of amount \( Q \) will pass through \( S_{2} \)
c. If \( S_{1} \) and \( S_{2} \) are closed together, a charge of amount
Q/3 will pass through \( S_{1} \), and a charge of amount
\( 2 Q / 3 \) will pass through \( S_{2} \)
D. All the above statements are incorrect


Which isomerism is shown by the given
compound?
A. E-isomer
B. Z-isomer
c. Cis-isomer
D. Trans-isomer


The terms bond enthalpy and bond dissociation enthalpy stand for one and the same thing.If true enter 1 else o
\( A \)


If the points \( \boldsymbol{A}(\mathbf{1}, \mathbf{2}), \boldsymbol{B}(\mathbf{4}, \boldsymbol{6}), \boldsymbol{C}(\boldsymbol{3}, \mathbf{5}) \) are
the vertices of a \( \Delta A B C \), find the
equation of the line passing through the midpoints of \( A B \) and \( B C \)


A body is thrown vertically upwards and rises to a height of \( 10 \mathrm{m} \). The velocity with which the body was thrown
upwards is \( \left(\boldsymbol{g}=\mathbf{9 . 8} \boldsymbol{m} / \boldsymbol{s}^{2}\right) \)
\( A \cdot 16 \mathrm{m} / \mathrm{s} \)
B. \( 15 \mathrm{m} / \mathrm{s} \)
\( c \cdot 14 m / s \)
D. \( 12 \mathrm{m} / \mathrm{s} \)


\( \operatorname{Let} \boldsymbol{S}_{\boldsymbol{n}}=\sum_{\boldsymbol{k}=1}^{n} \frac{\boldsymbol{n}}{\boldsymbol{n}^{2}+\boldsymbol{k} \boldsymbol{n}+\boldsymbol{k}^{2}}, \boldsymbol{T}_{\boldsymbol{n}}= \)
\( \sum_{k=0}^{n-1} \frac{n}{n^{2}+k n+k^{2}} \) for \( n=1,2,3 \dots \) Then
This question has multiple correct options
A \( \cdot S_{n}<\frac{\pi}{3 \sqrt{3}} \)
в. \( s_{n}>\frac{\pi}{3 \sqrt{3}} \)
c. \( T_{n}<\frac{\pi}{3 \sqrt{3}} \)
D. \( T_{n}>\frac{\pi}{3 \sqrt{3}} \)


If \( f(x)=\frac{x}{\sqrt{1-x^{2}}}, g(x)=\frac{x}{\sqrt{1+x^{2}}} \)
\( \operatorname{then}(f o g)(x)= \)
\( A \)
В. \( \frac{x}{\sqrt{1+x^{2}}} \)
c. \( \sqrt{1+x^{2}} \)
D. 2x


Assertion
The presence of vessels is a
characteristic feature of Angiosperms.
Reason
Vessels are spindle primitive conducting elements
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The curve \( y=\frac{x^{2}}{2} \) and the line \( y=\frac{x}{2} \)
intersect at the origin and at the point
\( (a, b), \) as shown in the figure above. Find
the value of \( b \)
\( A \)
\( \overline{8} \)
B. \( \frac{1}{4} \)
\( c \cdot \frac{1}{2} \)
D.
\( E \)


If \( -1.5 \times 10^{x} J \) is the gas exchange
along BC, find the value of \( x \)


State true or false:
Following are the car parking charges near a railway station upto
4 hours Rs 60
8 hours Rs 100
12 hours Rs 140
24 hours Rs 180
Hence, the parking charges are in direct proportion to the parking time.
A. True
B. Fals


Differentiate \( \cot x \)
\( A \cdot \tan x \)
B. \( \cot ^{2} x \)
\( \mathbf{c} \cdot \operatorname{cosec}^{2} x \)
D. \( -\operatorname{cosec}^{2} x \)


To liberate \( 5.4 \mathrm{g} \) of silver (atomic mass 108 amu) from an aqueous solution of sliver nitrate, it is required to pass:
A. 965C of electricity
B. 4825C of electricity
c. \( 9650 \mathrm{c} \) of electricity
D. \( 48250 \mathrm{c} \) of electricity


Assertion
For each ten degree rise of temperature the specific rate constant is nearly doubled.
Reason
Energy-wise distribution of molecules in a gas is an experimental function of temperature
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


Half-life of a radioactive material is 693
yr. Calculate the value of decay constant
of material


The frequency of the visible light of wave length \( 6000 A . U . \) (Angstrom
units) is
A \( \cdot 4 \times 10^{14} \mathrm{Hz} \)
B. 6000
c. \( 5 \times 10^{10} H z \)
D. \( 5 \times 10^{14} \mathrm{Hz} \)


A light ray, going through a prism with
the angle of prism \( 60^{\circ}, \) is found to
deviate by \( 30^{\circ} . \) What limit on the refractive index can be put from these
data ?


A block of mass \( 0.18 k g \) is attached to a
spring of force constant \( 2 N m^{-1} \). The
coefficient of friction between the block
and the floor is \( 0.1 . \) Initially, the block is at rest and the spring is un-stretched. An impulse is given to the block as shown in Fig. The block slides a distance of \( 0.06 m \) and comes to rest for
the first time. The initial velocity of the block in \( m s^{-1} \) is \( V=N / 10 . \) Then N is :
\( A \)
B.
\( c \)
D.


Explain the construction and working of a compound microscope with a neat ray diagram


\( A: \) The area bounded by \( x=3, y^{2}=3 x \)
\( B: \) The area bounded by \( y=1-|x| \) and
X-axis
\( C: \) The area enclosed between the curve
\( y=x^{2} \) and the line \( y=\sqrt{3} x \)
The descending order of \( \boldsymbol{A}, \boldsymbol{B}, \boldsymbol{C} \) is
A. \( A, C, B \)
в. \( C, B, A \)
c. \( A, B, C \)
D. \( C, A, B \)


Derive the equation for the kinetic energy and potential energy of a simple harmonic oscillator and show that the
total energy of a particle in simple harmonic motion constant at any point on its path.


If \( \eta_{2} \) and \( \eta_{2} \) are the coefficients of
viscosity of two liquids, \( d_{1} \) and \( d_{2} \) their
densities and \( t_{1} \) and \( t_{2} \) the flow times in Ostwald viscometer, then
A \( \cdot \frac{\eta_{1}}{\eta_{2}}=\frac{d_{1} t_{2}}{d_{2} t_{1}} \)
В. \( \frac{\eta_{1}}{\eta_{2}}=\frac{d_{2} t_{2}}{d_{1} t_{1}} \)
c. \( \frac{\eta_{1}}{\eta_{2}}=\frac{d_{1} t_{1}}{d_{2} t_{2}} \)
D. \( \frac{\eta_{1}}{\eta_{2}}=\frac{d_{2} t_{1}}{d_{1} t_{2}} \)


A length \( L=15 m \) if flexible tape is
tightly wound. It is then allowed to unwinding as it rolls down a fixed
incline that makes and angle \( \boldsymbol{\theta}=\mathbf{3 0}^{\circ} \)
with the horizontal, the upper end of the
tape being fixed. Find the time taken (in
second) by the tapes to unwind completely. Neglect radius at any time
w.r.t. the length of the rope.


In the compound \( C o C l_{3} .5 N H_{3} \)
A. all the \( C l \) show primary valency only
B. Two \( C l \) show primary valency and one \( C l \) shows secondary valency
C. Two \( C l \) show primary valency and one \( C l \) shows primary valency as well as secondary valency
D. All the \( C l \) show secondary valency


The magnetic field at point \( C \) as shown in
the figure is:
\( A \)
\[
\frac{\mu_{0} M_{0}}{2 \pi r_{0}^{3}}
\]
B. \( \frac{\sqrt{2} \mu_{0} M_{0}}{2 \pi r_{0}^{3}} \)
C. zero
D. \( \frac{\sqrt{2} \mu_{0} M_{0}}{4 \pi r_{0}^{3}} \)


Suppose \( M=\int_{0}^{\pi / 2} \frac{\cos x}{x+2} d x, N= \)
\( \int_{0}^{\pi / 4} \frac{\sin x \cos x}{(x+1)^{2}} d x . \) Then, the value of
\( (M-N) \) equals
A \( \frac{3}{\pi+2} \)
в. \( \frac{2}{\pi-4} \)
c. \( \frac{4}{\pi-2} \)
D. \( \frac{2}{\pi+4} \)


The mass of one amu is approximately:
A . \( 1 g \)
в. \( 0.5 g \)
C. \( 1.67 \times 10^{-24} g \)
D. \( 3.2 \times 10^{-24} g \)


Which scientist came up with the
concept of a periodic table that included all of the known elements?
A. Joseph Priestly
B. Dmitri Mendeleev
c. Antoine Lavoisier
D. Albert Einstein


For the situation shown in the figure below, match the entries of column with the entries of column II


A human zygote has
A. 46 chromosomes
B. 23 chromosomes
C. 47 chromosomes
D. 48 chromosomes


In 5 throws of a die, getting 1 or 2 is a success. The mean number of
successes is
A \( \cdot \frac{5}{3} \)
в. \( \frac{3}{5} \)
\( c \cdot \frac{5}{9} \)
D. \( \frac{9}{5} \)


Name the two nucleic acids present in the cell.
A. (i) RNA (ii) DNA
B. (i) RNA (ii) Mitochondria
c. (i) DNA (ii) Mitochondria
D. (i) DNA (ii) Ribosome


A wire suspended vertically from one of its ends stretched by attaching a
weight of \( 200 N \) to the lower end. The
weight stretches the wire by 1 mm. Then the elastic energy stored in the wire is:
A. 0.25
J \( J \)
в. \( 10 J \)
\( c .20 J \)
D. \( 0.1 J \)


Given lines \( : 4 x+3 y=3 \) and \( 4 x+ \)
\( 3 y=12 \) The other possible equation of
straight line passing through (-2,-7) and making an intercept of length 3 between the given lines.
A. \( 7 x+24 y+182=0 \)
в. \( 5 x-7 y=39 \)
c. \( 3 y-11 x=1 \)
D. \( 7 x+16 y=-126 \)


A sum of money invested at a certain
rate of interest doubles itself in 10
years. In how many years will the money triple itself at the same rate?


An aluminium measuring rod, which is
correct at \( 5^{\circ} \mathrm{C} \) measures the length of a
line as \( 80 \mathrm{cm} \) at \( 45^{\circ} \mathrm{C} \). If thermal
coefficient of linear expansion of aluminium is \( 2.50 \times 10^{-5} \) per \( ^{o} \) C.The
correct length of line is :
A \( .80 .08 \mathrm{cm} \)
B. \( 79.92 \mathrm{cm} \)
c. \( 81.12 \mathrm{cm} \)
D. \( 79.62 \mathrm{cm} \)


The cost of 3 digital cameras and 5 cell phones is Rs. \( 35,290 . \) What is the cost of 9 digital cameras and 15 cell phones?
A . Rs. 1,68,450
B. Rs. 1,79,220
c. Rs. 1,05,870
D. None of these


A filament bulb \( (500 W, 100 V) \) is to be
used in a \( 230 \mathrm{V} \) main supply. When a resistance \( R \) is connected in series, it works perfectly and the bulb consumes \( \mathbf{5 0 0} \boldsymbol{W} \). The value of \( \boldsymbol{R} \) is.
A . \( 13 \Omega \)
B . \( 230 \Omega \)
c. \( 46 \Omega \)
D. 26 \Omega


The equivalent capacitance of three
capacitors of capacitance \( C_{1}, C_{2} \) and \( C_{3} \)
connected in parallel is 12 units and the
product \( C_{1} C_{2} C_{3}=48 . \) When the
capacitors \( C_{1} \) and \( C_{2} \) are connected in
parallel the equivalent capacitance is 6
units. Then the capacitance are:
\( \mathbf{A} \cdot 1.5,2.5,8 \)
B. 2,3,7
\( \mathbf{c} \cdot 4,2,6 \)
D. 1,5,6


The free energy changes for the two reactions given below are:
\( \mathbf{a} . \boldsymbol{S} \boldsymbol{O}_{2}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g}) \longrightarrow \)
\( \boldsymbol{S} \boldsymbol{O}_{2} \boldsymbol{C l}_{2}(\boldsymbol{g}), \boldsymbol{\Delta} \boldsymbol{G}=-\boldsymbol{2} 270 \boldsymbol{c} \boldsymbol{a} \boldsymbol{l} \)
b. \( S(R h o m b)+O_{2}(g)+C l_{2}(g) \longrightarrow \)
\( \boldsymbol{S O}_{2} \boldsymbol{C l}_{2}(\boldsymbol{g}), \boldsymbol{\Delta} \boldsymbol{G}=-\mathbf{7 4 0 6 0 c a l} \)
Find \( \Delta G \) for the reaction \( S(r h o m)+ \)
\( O_{2}(g) \longrightarrow S O_{2}(g) \)
A \( . \Delta G=-71790 c a l \)
в. \( \Delta G=+71790 \) са \( l \)
c. \( \Delta G=-9670 c a l \)
D. None of these


Assertion
The reaction of alcohols with \( S O C l_{2} \) is
catalysed by the presence of a tertiary
\( \operatorname{amine}\left(\boldsymbol{R}_{3} \boldsymbol{N}\right) \)
Reason
Tertiary amine promote the reaction by reacting with the by-product \( \boldsymbol{H} \boldsymbol{C l} \)
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


Arrange the following in decreasing order of their basic strength:
\( \boldsymbol{C}_{6} \boldsymbol{H}_{5} \boldsymbol{N} \boldsymbol{H}_{2}, \boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{N} \boldsymbol{H}_{2},\left(\boldsymbol{C}_{2} \boldsymbol{H}_{5}\right)_{2} \boldsymbol{N} \boldsymbol{H}, \boldsymbol{\lambda} \)


If \( \boldsymbol{P}(\boldsymbol{A})=\boldsymbol{P}(\boldsymbol{B}), \) then the two events \( \boldsymbol{A} \)
and \( B \) are -
A. Independent
B. Dependent
c. Equally likely
D. Both (A) and (C)


Only one subject
A \( \cdot \frac{14}{25} \)
в. \( \frac{11}{25} \)
c. \( \frac{13}{25} \)
D. \( \frac{12}{25} \)


Let \( f \) and \( g \) be two real valued functions
and \( S=\{x \mid f(x)=0\} \) and \( T= \)
\( \{x \mid g(x)=0\}, \) then \( S \cap T \) represent the
set of roots of
A \( . f(x) g(x)=0 \)
B \( \cdot(f(x))^{2}+(g(x))^{2}=0 \)
c. \( f(x)+g(x)=0 \)
D. \( \frac{f(x)}{g(x)}=0 \)


When a right triangle of area 3 is
rotated \( 360^{\circ} \) about its shorter leg, the
solid that results has a volume of 30 Calculate the volume of the solid if
the same right triangle is rotated about
its longer leg.
A . 0.99
B. 7.90
c. 8.88
D. 31.42
E . 41.12


Energy equivalent of 10 amu is
A. 93.15 Mev
B. 931.5 Mev
C. 9315 Mev
D. 9315 Joules


If the displacement of a body is proportional to the square of time, then the body is moving with
A. Uniform acceleration
B. Increasing acceleration
c. Decreasing acceleration
D. Uniform velocity


The sum of first three terms of a G.P. is
\( \mathbf{3 9} \)
\( \frac{w}{10} \) and their product is \( 1 . \) Find the common ratio and the terms.


Let a total charge \( 2 Q \) be distributed in a
sphere of radius \( R, \) with the charge
density given by \( \rho(r)=k r, \) where \( r \) is
the distance from the centre. Two
charges \( A \) and \( B, \) of \( -Q \) each, are
placed on diametrically opposite points, at equal distance, a form the centre. If \( \boldsymbol{A} \)
and \( B \) do not experience any force, then:
A \( \cdot a=\frac{3 R}{2^{1 / 4}} \)
B. \( a=\frac{R}{\sqrt{3}} \)
C \( \cdot a=8^{-1 / 4} R \)
D . \( a=2^{-1 / 4} R \)


Momentum of a photon of wavelength \( \lambda \)
is:
\( A \cdot h / \lambda \)
B. Zero
c. \( h \lambda / c^{2} \)
D. \( h \lambda / c \)


A beautiful whorl, which encloses whole of the inflorescence is
A. Bract
B. Spadix
c. spathe
D. Involucre


Two plane mirrors are inclined to each
other at an angle \( \theta . \) A ray of light is reflected first at one mirror and then at
the other. The total deviation of the ray
is
A \( \cdot 360^{\circ}-2 \theta \)
B. \( 240^{\circ}-20 \)
c. 20
D. \( 180^{\circ}-\theta \)


The electric field at any point \( (x, y, z) \) is
\( \mathbf{A} \cdot(8 x-3) \hat{i} \)
B . \( -(8 x-3) \)
c. \( -8 x \hat{i} \)
D. \( 8 x \hat{i} \)


A coin is tossed two times, what is the
probability of getting head at least once


The activity of adrenal cortex is governed by a pituitary hormone, abbreviated as
A . HCG
B. FSH
c. АСТН
D. TSH


An angle is two-thirds of its
supplementary angle. Find the angle.


The diversification of an ancestral
group of organisms into a variety of related forms specialized to fit different environments is known as
A. Convergent evolution
B. Divergent evolution
c. Adaptive radiation
D. Gradualism
E. Directional selection


Evaluate: \( \frac{x\left(8 x^{2}-32\right)}{8 x(x-4)} \)
\( \mathbf{A} \cdot x+2 \)
B. \( x+4 \)
c. \( \frac{x^{2}-4}{x-4} \)
D. \( x^{2}-4 \)


State condition when magnitude of force on a current carrying conductor placed in a magnetic field is zero.
A. When current in conductor is in the direction of magnetic field.
B. When current in conductor is perpendicular to the direction of magnetic field.
c. Always zero
D. None of these


Draw a frequency polygon for the following data using histogram.
Marks
20
an
Number
of
students


\( \left(x^{2}-9 x-10\right) \div(x+1)= \)
A . \( x-10 \)
B. \( x+10 \)
\( \mathbf{c} \cdot x-8 \)
D. \( x+8 \)


A car moving at a certain speed stops on applying brakes within \( 16 \mathrm{m} \). If the speed of the car is doubled, maintaining the same retardation. then at what distance does it stop? Also, calculate the percentage change in this distance.(in percent)
A . 300
B. 3000
\( c \cdot 500 \)
D. 1300


Water in the aquifers can be usually pumped out with the help of:
A. handpumps
B. drilling
c. tubewell
D. both \( A \) and \( C \)


Duchenne muscular dystrophy is
A. Autosomal disorder
B. Dominant autosomal disorder
c. Sex linked disorder
D. Recessive autosomal disorder


Expand
\( \cos \theta+\cos \phi= \)


The minimum heat energy required to emit an electron from the surface of a
metal is called
A. Extracting function
B. Work function
C. Threshold energy
D. None of the above


Determine if the following function is
continuous at \( x=1 \) if \( f(x)=3 x-5 \) if
\( \boldsymbol{x} \neq 1 \) and 2 if \( \boldsymbol{x}=\mathbf{1} \)


In many plants the change over from vegetative to reproductive phase takes place in response to
A. The length of the day
B. Mainly the food material available in the soil
c. The oxygen present in the air
D. The severity of temperature


The diameter of a circle is \( 1 . \) Calculate
the area of the circle.
A \( \cdot \frac{\pi}{8} \)
B.
c.
D. \( \pi \)
E . \( 2 \pi \)


Name and define unit for electric
current


Two planets \( A \) and \( B \) have their radii in
the ratio of 2: 5 and densities in the
ratio of 1: 6 respectively. Which of the
following statements is NOT true regarding the given information?
A. The ratio of acceleration due to gravity on them is 1 :
15
B. For the same volume of planets, mass of planet \( A \) is greater than that of planet \( B \)
c. A body weighs 15 times more on planet \( B \) than on planet \( A \)
D. Planet \( B \) has greater volume than planet \( A \)


The following substances were
all dissolved in 100 grams of water at \( 290 \mathrm{K} \) to produce saturated solutions.lf the solution is
heated to \( 310 \mathrm{K} \), which substance will have a decrease in its solubility:
\( \mathbf{A} \cdot N a C I \)
в. \( K I \)
c. \( \mathrm{CaCl}_{2} \)
D. \( H C I \)
E . \( K N O_{3} \)


When n number identical cell of emf
and internal resistance is connected in
parallel, the net emf of the system will be
\( A \cdot E \)
B. nE
\( c \cdot E / n \)
D. n/E


The Tyndall effect is observed only when
following conditions are satisfied:
(a) The diameter of the dispersed particles is much smaller than the wavelength of the light used.
(b) The diameter of the dispersed particle is not much smaller than the wavelength of the light used.
(c) The refractive indices of the
dispersed phase and dispersion medium are almost similar in
magnitude.
(d) The refractive indices of the
dispersed phase and dispersion medium differ greatly in magnitude.
\( A \cdot(b) \) and \( (c) \)
B. (a) and (c)
\( c \cdot(b) \) and (d)
D. (a) and (d)


The value of current in the above
diagram is (diode assumed to be ideal one)
A. \( 0.1 A \)
B. \( 0.01 A \)
\( c .1 A \)
\( D \)


The measures of length and breadth of a rectangle are \( (30 \pm 3 \%) \) and \( (10 \pm 0.5 \%) \) metre. Calculate the percentage error in
the perimeter.
A . 2.4\%
в. 3.5\%
c. \( 1.9 \% \)
D. 4\%


A photocell is illuminated by a small
bright source placed one metre away. When the same source of light is placed two metres away, the electrons emitted
by the photo cathode
A. Each carries one-quarter of its previous energy
B. Each carries one-quarter of its previous momentum
c. Are half as numerous
D. Are one-quarter as numerous


For making cake, baking powder is taken. If at home your mother uses baking soda instead of baking powder in cake, what is the role of tartaric acid
added to baking soda?
A. Make it more acidic
B. Make it more basic
c. Neutralise it
D. None of these


In a hydrogen-oxygen fuel cell, combustion of hydrogen occurs to:
A. generate heat
B. create potential difference between the two electrodes
c. produce high purity water
D. remove absorbed oxygen from electrode surfaces


If \( [123] \mathrm{B}=[34], \) the order of the matrix B is
\( \mathbf{A} \cdot 3 \times 1 \)
B. \( 1 \times 3 \)
c. \( 2 \times 3 \)
D. \( 3 \times 2 \)


A light ray is incident on a plane mirror
with \( 30^{\circ} \) angle of incidence. What will
be the angle of reflection?


If the following ion(s) is/are coloured
enter \( 1, \) else enter 0
\( \boldsymbol{C} \boldsymbol{a}^{2+} \)


The total radiant energy per unit area, normal to the direction of incidence, received at a distance \( \mathrm{R} \) from the center
of a star of radius \( r, \) whose outer surface
radiates as a black body at a temperature \( T \) Kelvin is given by:
(Where \( \sigma \) is Stefan's Constant)
\( ^{\text {A } \cdot \frac{\sigma r^{2} T^{4}}{R^{2}}} \)
в. \( \frac{\sigma r^{2} T^{4}}{4 \pi r^{2}} \)
c. \( \frac{\sigma r^{4} T^{4}}{r^{4}} \)
D. \( \frac{4 \pi \sigma r^{2} T^{4}}{R^{2}} \)


Evaluate \( 1+i^{2}+i^{4}+i^{6}+\ldots+i^{2 n} \)


Calculate the concentration of nitric
acid in moles per litre in a sample
which has a density. 1.41 g \( m L^{-1} \) and the mass per cent of nitric acid in it being \( 69 \% \)


If true enter 1 , else enter 0 .
\( \boldsymbol{s} \boldsymbol{p}^{2} \) hybrid orbitals have equal \( \boldsymbol{s} \) and \( \boldsymbol{p} \)
character.


The two main differences between RNA
and DNA are:
A. ribose sugar and thymine in RNA
B. deoxyribose sugar and uracil in DNA
c. ribose sugar and uracil in RNA
D. deoxyribose sugar and guanine in DNA


If \( A \) is a \( 3- \) rowed square matrix and
\( |\mathbf{3} \boldsymbol{A}|=\boldsymbol{k}|\boldsymbol{A}| \) then \( \boldsymbol{k}=? \)
\( A \cdot 3 \)
B. 9
\( c \cdot 27 \)
D.


A fly wheel rotating at 600 rev/min is brought under uniform deceleration and
stopped after 2 minutes, then what is angular deceleration in \( r a d / s e c^{2} ? \)


Q Type your question_
expenditure of 200 families of a village.
Find the modal monthly expenditure of
the families. Also, find the mean
monthly expenditure:
\begin{tabular}{ll}
Expenditure (in Rs.) & No. of families \\
\( 1000-1500 \) & 24 \\
\( 1500-2000 \) & 40 \\
\( 2000-2500 \) & 33 \\
\( 2500-3000 \) & 28 \\
\( 3500-4000 \) & 22 \\
\( 4000-4500 \) & 16 \\
\( 4500-5000 \) & 7 \\
\hline
\end{tabular}
A. 2662.5
B . 2642.5
c. 2600.5
D. 2505.5


The value of \( \frac{\sin 50^{\circ}}{\sin 30^{\circ}} \)


Can we dry ethanol by anhydrous \( C a C l_{2} \)
?


Let \( f(x) \) be a real valued function not
identically zero, such that
\( \boldsymbol{f}\left(\boldsymbol{x}+\boldsymbol{y}^{n}\right)=\boldsymbol{f}(\boldsymbol{x})+(\boldsymbol{f}(\boldsymbol{y}))^{n} \quad \forall \boldsymbol{x}, \boldsymbol{y} \in \)
\( \boldsymbol{R} \)
where \( n \in N(n \neq 1) \) and \( f^{\prime}(0) \geq 0 . \) We
may get an explicit form of the function \( \boldsymbol{f}(\boldsymbol{x}) \)
The value of \( \$ \$ f^{\prime}(0) \$ \$ f^{\prime}(0) \) is :
A.
B. \( n \)
c. \( n+1 \)
D. 2


Hard soaps are:
A. calcium salts of higher fatty acids
B. magnesium salts of higher fatty acids
C. potassium salts of higher fatty acids
D. sodium salts of higher fatty acids


Vital morphological and physiological units of mammalian kidney are
A. Ureters
B. Seminiferous tubules
c. Uriniferous tubules
D. Nephridia


A sphere fits exactly inside a right
circular cone with base area \( 154 \mathrm{cm}^{2} \)
as shown.What is the radius of the
sphere if the height and slant height of
the cone are integers?
\( \mathbf{A} \cdot 21 / 4 \mathrm{cm} \)
B. \( 41 / 2 \mathrm{cm} \)
\( \mathbf{c} \cdot 6 \mathrm{cm} \)
D. \( 51 / 4 \mathrm{cm} \)


A \( 20 L \) box contains \( O_{3} \) and \( O_{2} \) at \( t \)
equilibrium at \( 202 K . K_{p}=2 \times 10^{14} \)
for \( 2 O_{3} \rightleftharpoons 3 O_{2} . \) Assume that \( p_{O_{3}}>> \)
\( p_{O_{2}} \) and total pressure is 8 at \( m \), then
the partial pressure of \( \boldsymbol{O}_{3} \) is:
A . exactly \( 1.6 \times 10^{-6} \) at \( m \)
B. sufficiently less than \( 1.6 \times 10^{-6} \) atm
C. slightly more than \( 1.6 \times 10^{-6} \) atm
D. very slightly less than \( 1.6 \times 10^{-6} \) atm


A wire carrying \( 5.0 ~ V \) is applied to a
transformer. The primary coil has 5 turns and the secondary coil has 10 turns.
A . \( 0.50 V \)
B. \( 5.0 V \)
c. \( 10 V \)
D. \( 50 V \)
E . \( 100 V \)


An object approaches a convergent lens from the left of the lens with a
uniform speed \( 5 \mathrm{m} s^{-1} \) and stops at the
focus. The image:
A. moves away from the lens with an uniform speed 5 m
B. moves away from the lens with an uniform acceleration
c. moves away from the lens with a non-uniform acceleration
D. moves towards the lens with a non-uniform acceleration.


Large energy released in atomic bomb
explosion is mainly due to:
A. conversion of heavier to lighter atoms
B. products having lesser mass than initial substance
c. release of neutrons
D. release of electrons


Fill in the blanks:
Animals make use of
carry out their physical activities and other tasks.
A. contact force
B. non-contact force
c. force of friction
D. muscular force


A sum of money becomes to 6000 in 3 years and 9000 in 6 years at C.I. Find
the sum.


Sea Anemone is characterised by
A. A whorl of several tentacles
B. Many whorls of tentacles
c. Irregularly placed tentacles
D. Absence of tentacles


Mention factors which determine the
extent of damage due to an earthquake?


The principle of column chromatography is:
A. capillary action
B. gravitational force
c. differential adsorption of the substance on the solid phase
D. differential absorption of the substance on the phase


The value of
1) \( \sin \left(4 \theta+\frac{\pi}{2}\right) \)
2) \( \tan \theta+\sec \theta \)


Two balls are moving on the same smooth horizontal plane. Their velocity components along one edge of the square plane are \( 10 \sqrt{3} m / s \) and \( 20 m / s \) respectively. Their velocity components along a perpendicular edge are \( 30 m / s \) and \( 20 m / s \) respectively Find the angle between their directions of motion.
A . 15
в. \( 30^{\circ} \)
\( c \cdot 60 \)
D. 45


The maximum and minimum values of
the function \( y=x^{3}-3 x^{2}+6 \) are
A .2,0
в. 6,0
\( c \cdot 6,2 \)
D. 4,2


Choose the photosynthethic protozoa from the following.
A. Euglena
B. Plasmodium
c. Paramecium
D. Amoeba


Which one of the following contains either aldehyde or ketones in it? This question has multiple correct options
A. vanillin
B. Acetone
c. Camphor
D. Formalin


Write the differences between DNA and
RNA.


If \( \left(\begin{array}{c}3 x+7 \\ y+1 & 2-3 x\end{array}\right)=\left(\begin{array}{cc}1 & y-2 \\ 8 & 8\end{array}\right) \) then the values
of \( x \) and \( y \) respectively are
A. -2,7
B. \( -\frac{1}{3}, 7 \)
\( c \cdot-\frac{1}{3},-\frac{2}{3} \)
D. 2,-7


A property that must decrease when a
gas condense into a liquid:
A. Standard voltaic potential
B. Entropy
c. Enthalpy
D. Reaction rate
E. Gibbs free energy


Adsorption of a gas follows Freundlich
adsorption isotherm \( x \) is the mass of
the gas adsorbed on mass \( m \) of the adsorbent. The plot of \( \log \frac{x}{m} \) versus log \( p \) is shown in the given graph. \( \frac{x}{m} \) is
proportional to :
\( A \cdot p^{3 / 2} \)
В \( \cdot p^{3} \)
\( c \cdot p^{2 / 3} \)
D. \( p^{2} \)


which of the following numbers are the cubes of following numbers:
(i) 216
(ii) 729
(iii) 512
\( (i v) 3375 \)
(v) 1000


Solve the following inequalities graphically in two-dimensional plane:
\( \boldsymbol{y}<-\mathbf{2} \)


Solve the following inequalities graphically in two-dimensional plane:
\( -3 x+2 y \geq-6 \)


A metal wire of circular cross-section
has a resistance \( \boldsymbol{R}_{1} \). The wire is now stretched without breaking so that its length is doubled and density is assumed to remain same. If the
resistance of the wire now becomes \( \boldsymbol{R}_{2} \)
then \( R_{2}: R_{1} \) is:
A .1:
B. 1: 2
\( c \cdot 4: \)
D. 1: 4


Who demonstrated that green plants purify the foul air produced by breathing animals and burning
candles?
A. Priestley
B. Ingenhousz
c. sachs
D. Engelmann


Coordination number of aluminium is:
\( A \cdot 8 \)
B. 6
\( c \cdot 12 \)
D. 4


An ideal monatomic gas expands to twice its volume. If the process is isothermal, the magnitude of work done
by the gas is \( W_{i} . \) If the process is adiabatic, the magnitude of work done
by the gas is \( W_{a} . \) Which of the following
is true?
A \( . W_{i}=W_{a}>0 \)
в. \( W_{i}>W_{a}=0 \)
c. \( W_{i}>W_{a}>0 \)
D. \( W_{a}=W_{i}=0 \)


\( \boldsymbol{X} \stackrel{\text {StepI}}{\longrightarrow} \boldsymbol{Y} \stackrel{\text {StepII}}{\longrightarrow} \boldsymbol{Z} \) is a complex
reaction. Total order of reaction is 2 and
step II is slow step. What is molecularity of step II?
\( A \cdot 2 \)
B. 1
\( c \cdot 3 \)
D. 4


The heat needed to turn 1 kg of solid into liquid at its melting point is known as
A . Latent heat
B. Specific latent heat of vaporisation
c. specific latent heat of fusion
D. specific latent heat of substance


Two waves of intensities \( I \) and \( 4 I \)
produce interference. Then the
intensity of constructive and destructive interferences respectively
are
A. \( 3 I, 5 I \)
B. \( 5 I, 3 I \)
c. \( I, 9 I \)
D. \( 9 I, I \)


Find the principal value of \( \operatorname{cosec}^{-1}(2) \)


Which of the following is not a mineral acid?
A. Hydrochloric acid
B. Citric acid
c. Sulphuric acid
D. Nitric acid


Write the first five terms of the
sequence and obtain the corresponding
series:
\( \boldsymbol{a}_{1}=\boldsymbol{a}_{2}=\boldsymbol{2}, \boldsymbol{a}_{n}=\boldsymbol{a}_{n-1}-\mathbf{1}, \boldsymbol{n}>\mathbf{2} \)


A mixture of ethanol and water contains
\( 54 \% \) water by mass. Calculate the mole
fraction of alcohol in this solution. If
your answer is \( x, \) write the value of \( 100 x \)


Acetone \( \left(C H_{3} C O C H_{3}\right) \) is the major product in:
\( \boldsymbol{I} . \boldsymbol{C H}_{2}=\boldsymbol{C}=\boldsymbol{C H}_{2} \stackrel{\boldsymbol{H}_{3} \boldsymbol{O}^{+}}{\longrightarrow} \)
\( \boldsymbol{I I} \cdot \boldsymbol{C H}_{3} \boldsymbol{C} \equiv \boldsymbol{C H} \frac{\boldsymbol{H}_{2} \boldsymbol{S O}_{4} / \boldsymbol{H} \boldsymbol{g} \boldsymbol{S O}_{4} / \boldsymbol{H}_{2} \boldsymbol{O}}{\longrightarrow} \)
IIII. \( C H_{3} C \equiv C H \frac{B H_{3} . T H F}{H_{2} O_{2} / O H^{-}} \)
This question has multiple correct options
A . \( I \)
в. \( I I \)
c. \( I I I \)
D. none of the above


\( H_{2} \) is more reactive than \( D_{2} \) because:
A. \( H_{2} \) is lighter than \( D_{2} \).
B. \( H_{2} \) has low bond dissociation energy than \( D_{2} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \) is non radioactive while \( D_{2} \) is radioactive
D. \( D_{2} \) has two neutrons.


Draw the pattern of magnetic field lines
for a bar magnet.


Four identical plates each of area \( a \) are
separated by a distance \( d \). The
connection is shown below. What is the
capacitance between \( P \) and \( Q ? \)
A \( \cdot \frac{2 a \varepsilon_{0}}{d} \)
B. \( \frac{a \varepsilon_{0}}{2 d} \)
c. \( \frac{\varepsilon_{0}}{d} \)
D. \( \frac{4 a \varepsilon_{0}}{d} \)


If \( A B C D \) is a parallelogram, \( A E \perp \)
DC and \( \boldsymbol{C F} \perp \boldsymbol{A D} \). If \( \boldsymbol{A B}=\mathbf{1 6 c m} \)
\( A E=8 c m \) and \( C F=10 \mathrm{cm}, \) find
\( A D \)


\( \boldsymbol{F}=\frac{9}{5} \boldsymbol{C}+\mathbf{3 2} ; \) make 'C' the subject of
formula.
A \( \cdot C=\frac{5}{9}(F-32) \)
B. \( C=\frac{9}{5}(F-32) \)
c. \( c=\frac{5}{9}(F+32) \)
D. none of the above


1: Method of dimensions cannot be used
for deriving formulae containing trigonometrical ratios.
2: Trigonometrical ratios are dimensionless.
A. 1 and 2 are correct and 2 is correct explanation of
B. 1 and 2 are correct and 2 is not correct explanation of
\( c .1 \) is true and 2 is false
D. 1 is false and 2 is true


If \( a, b \notin R, \) then \( \left|e^{a+i b}\right| \) is equal to
A \( \cdot e^{a} \)
в. \( e^{b} \)
c. 1
D. None of these


A spherical metal shell \( A \) of radius \( R_{A} \)
and a solid metal sphere \( B \) of radius
\( R_{8}\left(<R_{A}\right) \) are kept far apart and each
is given charge \( +Q . \) Now they are connected by a thin metal wire. Then This question has multiple correct options
\( \mathbf{A} \cdot E_{A}^{i n s i d e}=0 \)
в. \( \quad Q_{A}>Q_{B} \)
c. \( \frac{\sigma_{A}}{\sigma_{B}}=\frac{R_{B}}{R_{A}} \)
D. \( E_{A}^{\text {on surface}}<E_{B^{\text {B }}}^{\text {snj }} \)


Suppose a current carrying wire has a cross-sectional area that gradually
become smaller along the wire has the shape of a very long cone as shown in
figure:
A. Electric current is different in different portions of wire
B. Electric field at point \( A \) is same as that of point \( B \)
C. Drift speed of electrons at point \( A \) is lesser than that of at point \( B \)
D. Drift speed of electrons at point \( A \) is same as that of at point \( B \)


By adding the same constant to each of
20,50,100 a geometric progression results. The common ratio is
A \( \cdot \frac{5}{3} \)
B. \( \frac{4}{3} \)
\( c \cdot \frac{3}{2} \)
D.
E \( \cdot \frac{1}{3} \)


In a closed circuit drawing current from cell, the emf of a cell is always
A. Less than potential difference
B. More than potential difference
c. Half of the potential difference
D. Double of the potential difference


Arrange the following steps in the proper order to explain how a sea breeze occurs, near coastal regions.
(a) The temperature of land rises rapidly as compared to sea, because the specific heat capacity of land is five times less than that of water.
(b) Due to the low pressure over the land mass, the cool air over the sea starts
blowing towards the land.
(c) The sun shines equally on the land mass and sea, giving equal amount of heat energy to both.
(d) The air above the land becomes hot
and light, rises up and hence creates
the low pressure over the land.
\( A \cdot a d c b \)
B. \( \operatorname{cd} a b \)
\( c \cdot c a b d \)
D. \( c \) a d b


If the angles made by a straight line with the coordinate axes are \( \alpha, \frac{\pi}{2}- \) \( \boldsymbol{\alpha}, \boldsymbol{\beta} \) then \( \boldsymbol{\beta}= \)
A . 0
в. \( \frac{\pi}{6} \)
c. \( \frac{\pi}{2} \)
\( D \)


Pick the correct statements.
A. Synapsis of homologous chromosomes takes place during prophase I of meiosis.
B. Division of centromeres takes place
during anaphase I of meiosis.
C. Spindle fibres disappear completely in telophase of mitosis.
D. Nucleoli reappear at telophase I of meiosis.
A. A only
B. C only
C. \( A \) and \( B \) only
D. A, C and Donly
E. A and C only


What is nitogen fixation and name two microbes which bring about the same.


A block is gently placed on a conveyor belt moving horizontally with constant
speed. After \( t=4 s, \) the velocity of the
block becomes equal to the velocity of the belt. If the coefficient of friction
between the block and the belt is \( \mu= \)
\( 0.2, \) then the velocity of the conveyor
belt is
\( \mathbf{A} \cdot 8 m s^{-1} \)
B. \( 4 m s^{-1} \)
\( \mathbf{c} \cdot 6 m s^{-1} \)
D. \( 18 \mathrm{ms}^{-1} \)


Explain, why an organic liquid vaporises at a temperature below its boiling point in its steam distillation?


The function \( f(x)=x^{3}-3 x^{2}+6 \) is an
increasing function for:
A. \( 0<x<2 \)
B. \( x<2 \)
c. \( x>2 \) or \( x<0 \)
D. all \( x \)


In an insulator, the forbidden energy gap between the valence band
and conduction band is of the order of
A. \( 1 \mathrm{MeV} \)
B. \( 0.1 \mathrm{MeV} \)
c. \( 1 e V \)
D. \( 5 e V \)


When the angle of reflection is \( 60^{0} \)
what will be the angle between the incident ray and the mirror?
A \( .30^{\circ} \)
В. \( 60^{\circ} \)
\( c \cdot 90^{\circ} \)
D. \( 45^{\circ} \)


To get maximum current through a resistance of \( 2.5 \Omega \), one can use \( \mathrm{m} \) rows
of cells, each row having n cells. The internal resistance of each cell is \( 0.5 \Omega \)
What are the value of \( n \) and \( m \), if the
total number of cells is \( 45 ? \)
A \( . m=3, n=15 \)
в. \( m=5, n=9 \)
c. \( m=9, n=5 \)
D. \( m=15, n=3 \)


Deoxygenated blood from wall of heart is carried by
A. Coronary sinus
B. Inferior vena cava
c. Superior vena cava
D. Pulmonary artery


Benzoin is:
A. compound containing an aldehyde and a ketonic
group
B. \( \alpha, \beta- \) unsaturated acid
c. \( \alpha- \)hydroxy aldehyde
D. \( \alpha- \)hydroxy ketone


A dental disease characterised by
mottling of teeth is due to the presence of an ingredient in drinking water, namely
A. Flourine
B. Mercury
c. Boron
D. Chlorine


The area of the triangle whose vertices
are represented by \( 0, z, z^{i \alpha}(0<\alpha<\pi) \)
equals
\( \mathbf{A} \cdot \frac{1}{2}|z|^{2} \cos \alpha \)
B . \( \frac{1}{2}|z|^{2} \sin \alpha \)
C \( \cdot \frac{1}{2}|z|^{2} \sin \alpha \cos \alpha \)
D \cdot \( \frac{1}{2}|z|^{2} \)


If the roots of the equation \( x^{3}-a x^{2}+ \)
\( 4 x-8=0 \) are real and positive, then
the minimum value of \( a \) is


The urinary bladder is muscular and is under - ............ control
A. Muscular
B. Mechanical
c. Nervous
D. Hormonal


The degree of the polynomial \( x^{2}- \) \( 5 x^{4}+\frac{3}{4} x^{7}-73 x+5 \) is
A. 7
B. \( \frac{3}{4} \)
\( c \cdot 4 \)
D. -73


What is the refractive index of material
of a plano-convex lens, if the radius of curvature of the convex surface is \( 10 \mathrm{cm} \) and focal length of the lens is \( 30 \mathrm{cm} ? \)
A \( \cdot \frac{6}{5} \)
B. \( \frac{7}{4} \)
\( c \cdot \frac{2}{3} \)
D. \( \frac{4}{3} \)


Apples growing on tree can have larger than normal size by
A. Thinning of blossoms
B. Defoliation
c. Decapitation of stem apex
D. Applying of hormones


The correct order according to size is
A \( \cdot O>O^{-}>O^{2-} \)
В. \( O^{-}>O^{2-}>O \)
c. \( O^{2-}>O^{-}>O \)
D. \( O>O^{2-}>O^{-} \)


The first scientist to find out the role of
light in photosynthesis was
A. Ingenhousz
B. Senebier
c. Priestley
D. sachs


\( N a C l \) is doped with \( 10^{-6} \) mol \( \% S r C l_{2} \)
the concentration of cation vacancies
is:
[Heat concentration of vacancies \( = \) \( \left.\frac{10^{-4}}{100} N_{A}\right] \)
A \( \cdot 6.02 \times 10^{15} \mathrm{mol}^{-1} \)
В. \( 6.02 \times 10^{16} \mathrm{mol}^{-1} \)
c. \( 6.02 \times 10^{17} \mathrm{mol}^{-1} \)
D. \( 6.02 \times 10^{14} \mathrm{mol}^{-1} \)


In the adjacent circuit a resistance \( \mathrm{R} \) is
used. Initially with 'wire \( A B^{\prime} \) not in the
circuit, the galvanometer shows a deflection of d divisions. Now, the 'wire
\( A B^{\prime} \) is connected parallel to the
galvanometer and the galvanometer shows a deflection nearly \( \boldsymbol{d} / 2 \) division. Therefore current sensitivity of the galvanometer is about:


The area of a square of side 16


Rear view mirrors in vehicles forms:
A . Real Image
B. Virtual Image
c. Both A and B
D. Neither A nor B


Let \( X \) denote the number of hours you
study during a randomly selected school day. The probability that \( X \) can
take the value 'x' has the following from, where 'k' is some unknown constant.
\( p=(X=X)= \)
\( \left\{\begin{array}{ll}\mathbf{0 . 1}, & \boldsymbol{i f} \boldsymbol{x}=\mathbf{0} \\ \boldsymbol{k} \boldsymbol{x}, & \boldsymbol{x}=\mathbf{1} \boldsymbol{o r} \mathbf{2} \\ \boldsymbol{k}(\mathbf{5}-\boldsymbol{x}), & \boldsymbol{i f} \boldsymbol{x}=\mathbf{3} \boldsymbol{o r} \mathbf{4} \\ \mathbf{0}, & \text { otherwise }\end{array}\right. \)
(a) find the value of 'k'
(b) what is the probability that you study :
(i) at least two hours?
(ii) exactly two hours??
(iii) at most 2 hours?


Which of the following polymer is not an addition polymer?
A. Teflon
B. BUNA-N
c. PAN
D. Propylene


\( \int_{0}^{4} x+e^{x} d x \)


Which of the following metal is found in
our body?
A. Iron
B. Calcium
c. Potassium
D. All of the above


The compound obtained when acetaldehyde reacts with dilute aqueous sodium hydroxide exhibits:
A. geometrical isomerism
B. optical isomerism
c. neither optical nor geometrical isomerism
D. both optical and geometrical isomerism


Use Rolle's theorem to prove that equation \( a x^{2}+b x=\frac{a}{3}+\frac{b}{2} \) has a root
between 0 and 1


Express each of the following without using decimals:
\( \mathbf{1 2 . 0 5} \boldsymbol{m} \)


Which one of the following is NOT
correct?
A. Dimensional formula of thermal conductivity (K) is \( M^{1} L^{1} T^{-3} K^{-1} \)
B. Dimensional formula of potential (V) is \( M^{1} L^{2} T^{-3} A^{-1} \)
C. Dimensional formula of permeability of free space \( \left(\mu_{0}\right) \) is \( M^{1} L^{1} T^{-2} A^{-2} \)
D. Dimensional formula of RC is \( M^{0} L^{0} T^{-1} \)


The gas that usually causes explosion
in coal mines is
A. methane
B. carbon monoxide
c. carbon dioxide
D. hydrogen


The plot of \( \log \left(\frac{x}{m}\right) \) vs \( \log P \) showing a straight line parallel to X-axis reveals that:
\( \mathbf{A} \cdot n=0 \)
B. \( \frac{1}{n}=0 \)
c. \( P=0 \)
D. \( \log P= \) constant


A horizontal magnetic field B is produced across a narrow gap between the two square iron pole pieces.
closed square loop of side a, mass \( \mathrm{m} \)
and resistance \( R \) is allowed to fall with
the top of the loop in the field. The loop
attains a terminal velocity equal to:
A \( \cdot \frac{R m g}{B^{2} a^{2}} \)
B. \( \frac{\mu_{0}}{4 \pi} \frac{R m g}{B a^{2}} \)
c. \( \frac{m g B}{R a^{2}} \)
D. \( \frac{\mu_{0}}{4 \pi} \frac{R m B}{B a^{2}} \)


Suppose a new planet is discovered between Uranus and Neptune. Its time period would be
A. less than that of Neptune.
B. more than that of Neptune.
c. equal to that of Neptune or Uranus.
D. less than that of Uranus


The geometric sequence is also called
as
A. geometric progression
B. arithmetic sequence
c. harmonic sequence
D. geometric series


Solve: \( \left(i^{25}\right)^{3} \times i \)


Three rings each of mass \( m \) and radius
are so placed that they touch each
other. The radius or gyration of the
system about the axis as shown in the
figure is:
A \( \cdot \sqrt{\frac{6}{5}} \)
B. \( \sqrt{\frac{5}{6}} \)
c. \( \sqrt{\frac{6}{7}} \)
D. \( \sqrt{\frac{7}{6}} \)


Faraday's second law of electrolysis is
related to the:
A. molecular mass of the electrolyte
B. Equivalent weight of the cation /anion
C. Atomic weight of the electrolyte
D. Atomic number of the cation/anion


A coin is tossed If it shows a tail we
draw a ball from a box which contains 2
red and 3 black balls If it shows head we
throw a die Find the sample space for this experiment


Silk is obtained from
the silk moth.
A. pupa
B. larva
c. cocoon
D. caterpillar


Vapour pressure of a liquid increases with :
A. decrease in temperature
B. increase in temperature
c. increase in surface area
D. increase in volume


Two long parallel wires are at a distance
of \( 1 \mathrm{m} \). If both of them carry one ampere of current in same direction, then the
force of attraction on unit length of the wires will be
A \( \cdot 2 \times 10^{-7} N / m \)
B . \( 4 \times 10^{-7} N / m \)
c. \( 8 \times 10^{-7} N / m \)
D. \( 10^{-7} N / m \)


Define refraction of light waves.
Draw a ray diagram for refraction at a spherical separating two media. For refraction at a spherical surface, derive
the relation \( \frac{\boldsymbol{n}_{2}}{\boldsymbol{v}}-\frac{\boldsymbol{n}_{1}}{\boldsymbol{u}}=\frac{\boldsymbol{n}_{2}-\boldsymbol{n}_{1}}{\boldsymbol{R}} \) in
object distance \( (u), \) image distance \( (v) \)
refractive index of media \( \left(n_{1}, n_{2}\right) \) and radius of curvature \( (\boldsymbol{R}) \)


Which condition favors guttation?
A. High humidity
B. Low humidity
c. More transpiration
D. Bright sunlight


What is the geometric mean of 6 and 24
\( ? \)
A . 10
B. 12
c. 14
D. 16


A bead of mass \( m \) slides on a
hemispherical surface with a velocity \( \boldsymbol{v} \)
at an angular position \( \theta \). If the coefficient of friction between the bead
and hemispherical surface is \( \mu, \) Find
the magnitude of Angular momentum of the bead about \( O \) in the position
shown.


Find the equation of the line passing
through the point (-6,10) and perpendicular to the straight line \( 7 x+ \)
\( 8 y=5 \)


Which of the following statements is
not correct?
A. Primary amines show intermolecular hydrogen bonding.
B. Secondary amines show intermolecular hydrogen bonding
C. Tertiary amines show intermolecular hydrogen bonding.
D. Amines have lower boiling points as compared to those of alcohols and carboxylic acids of comparable molar masses.


The equilibrium constant of the following reactions are:
(।) \( \boldsymbol{C} \boldsymbol{H}_{4}(\boldsymbol{g})+\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{C} \boldsymbol{O}(\boldsymbol{g})+ \)
\( \mathbf{3} \boldsymbol{H}_{\mathbf{2}}(\boldsymbol{g}) \boldsymbol{K}_{\mathbf{1}} \)
(II) \( \boldsymbol{C O}(\boldsymbol{g})+\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g})+ \)
\( \boldsymbol{H}_{2}(\boldsymbol{g}) \boldsymbol{K}_{2} \)
\( (\| I) C O_{2}(g)+4 H_{2}(g) \rightleftharpoons C H_{4}(g)+ \)
\( \mathbf{2} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \boldsymbol{K}_{3} \)
Which of the following is true?


The position vectors of the points \( A, B, C \) \( \operatorname{are} \bar{i}+2 \bar{j}-\bar{k}, \bar{i}+\bar{j}+\bar{k}, 2 \bar{i}+3 \bar{j}+2 \bar{k} \)
respectively. If \( A \) is chosen as the origin then the position vectors of \( \mathrm{B} \) and \( \mathrm{C} \) are
\( \mathbf{A} \cdot \bar{i}+2 \bar{k}, \bar{i}+\bar{j}+3 \bar{k} \)
B. \( \bar{j}+2 \bar{k}, \vec{i}+\bar{j}+3 \bar{k} \)
c. \( -\bar{j}+2 \bar{k}, \vec{i}-\bar{j}+3 \bar{k} \)


For a gaseous reaction \( \boldsymbol{A} \rightarrow \boldsymbol{B}+\mathbf{2} \boldsymbol{C} \)
at \( 250^{\circ} \mathrm{C}, \) following data were observed.
The partial pressure of the gases at 100th min will be (in 100x mm)
Time
20 \( \quad 40 \)
\[
(\min )
\]
Total pressure
\( (\mathrm{mm} \mathrm{Hg}) \) 587.6


Glucose and amino acids are absorbed
in intestine by
A. Osmosis
B. Passive transport
c. Active transport
D. Selective absorption


Find the number of ways in which the letters of the word 'MUNMUN' can be
arranged so that no two alike letters are together?
A . 30
B. 40
\( c \cdot 60 \)
D. 20


Grass stem elongates after initia
growth due to
A . Lateral meristem
B. Secondary meristerm
c. Intercalary meristem
D. Apical meristem


The magnetising field required to be applied in opposite direction to reduce residual magnetism to zero is called
A. coercivity
B. retentivity
c. hysteresis
D. none of these


The given figure depicts the change in
concentration of species \( X \) and \( Y \) as a
function of time. The point of
ntersection of the two curves
represents:
\( A \cdot t_{1 / 2} \)
в. \( t_{3 / 4} \)
\( c \cdot t_{2 / 3} \)
D. data insufficient to predict


Show that the function \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \)
defined as \( f(x)=x^{2}, \) is not one-one.


The compound that is not a Lewis acid
is:
A. \( B a C l_{2} \)
в. \( A l C l_{3} \)
c. \( B C l_{3} \)
D. \( \operatorname{SnCl}_{4} \)


\( 15.9 g \) of copper sulphate and \( 10.6 g \) of sodium carbonate react together to give
\( 14.2 g \) of sodium sulphate and \( 12.3 g \) of copper carbonate. Which law of chemical combination is obeyed? How?


Match list I (atomic number of the
elements) with list II (position in the periodic table) and select the correct
answer using the codes given below the
lists.
\begin{tabular}{c|cc|c}
& List I & & List II \\
A. & 52 & 1. & s-block \\
B & 56 & 2. & p-block \\
c. & 57 & 3. & d-block \\
D. & 60 & 4. & f-block
\end{tabular}
A. \( A-2, B-1, C-3, D-4 \)
B. \( A-2, B-1, C-4, D-3 \)
\( c \)
\( A-1, B-2, C-3, D-4 \)
D. \( A-1, B-2, C-4, D-3 \)


In which circuit can the lamps be
switched on and off independently?
\( A \)
B.
\( c \)
\( D \)


The fastest acting enzyme, in the biological kingdom, is
A . Lipase
B. Amylase
c. Peptidase
D. Carbonic anhydrase


What is \( a_{4} \) when \( a_{1}=2, r=-3 ? \)
A .27
в. -27
\( c .-54 \)
D. 54


A body weighs \( 8 g \) when placed in one
pan and \( 18 g \) when placed on the other pan of a false balance. If the beam is
horizontal when both the pans are
empty, the true weight of the body is:
A \( \cdot 13 g \)
в. \( 12 g \)
c. \( 15.5 g \)
D. \( 15 g \)


Two plane mirrors are parallel to each other and spaced \( 20 \mathrm{cm} \) apart. \( \mathrm{A} \) luminous point is placed between them
at a distance \( 5 \mathrm{cm} \) from one mirror.
Determine the distances of the first
nearest images from each other


Time period depends on Gravitational constant (G),plank constant, (h) and speed of light (c), then \( \mathrm{T} \) is proportional
to
\( ^{\mathrm{A}} \cdot \frac{G^{1 / 2} h^{1 / 2}}{C^{3 / 2}} \)
B. \( \frac{G^{1 / 2} h}{C^{5 / 2}} \)
\( ^{\mathrm{C}} \cdot \frac{G h^{1 / 2}}{C^{5 / 2}} \)
\( ^{\mathrm{D} \cdot \frac{G^{1 / 2} h^{1 / 2}}{C^{5 / 2}}} \)


Buna-N synthetic rubber is a copolymer
of:
\( \mathbf{A} \cdot \mathrm{H}_{2} \mathrm{C}=\mathrm{CH}-\mathrm{C}=C H_{2} \) and \( \mathrm{H}_{2} \mathrm{C}=\mathrm{CH}-C H=\mathrm{CH}_{2} \)
B. \( \mathrm{H}_{2} \mathrm{C}=\mathrm{CH}-C H=\mathrm{CH}_{2} \) and \( \mathrm{H}_{5} \mathrm{C}_{6}-C H=\mathrm{CH}_{2} \)
\( \mathbf{C} \cdot \mathrm{H}_{2} \mathrm{C}=\mathrm{CH}-C N \) and \( \mathrm{H}_{2} \mathrm{C}=\mathrm{CH}-C H=\mathrm{CH}_{2} \)
\( \mathbf{D} \cdot \mathrm{H}_{2} \mathrm{C}=\mathrm{CH}-C N \) and \( \mathrm{H}_{2} \mathrm{C}=\mathrm{CH}-\mathrm{C}\left(\mathrm{CH}_{3}\right)=C H_{2} \)


Fossilised fuel obtained from bog is
A. Tar
B. Peat
c. Bio-gas
D. Petrol


A metallic rod of length 'L' and crosssection 'A' has Young's modulus 'Y' and coefficient of linear expansion \( \alpha \). If the
rod is heated to a temperature 'T', then the energy stored per unit volume is:
A \( \cdot \frac{1}{2} Y \alpha^{2} T^{2} \)
B. \( \frac{1}{2} Y A \alpha^{2} T^{2} \)
c. \( \frac{1}{2} Y A \alpha T \)
D. \( \frac{1}{2} Y A^{2} \alpha^{2} T^{2} \)


Na is obtained by the electrolysis of aqueous NaCl solution.
1. True
2. False


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


The apparent weight of a body is :
This question has multiple correct options
A. may be positive
B. may be negative
c. may be zero
D. is always positive


Metal oxides are reduced to metal by:
A. electrolytic reduction
B. liquation
c. distillation
D. none of the above


Find inverse proportionaly constant if \( x \) and \( y \) are in inverse proportion.
\[
\boldsymbol{x} \quad \mathbf{9} \quad \boldsymbol{6} \quad \boldsymbol{3} \quad \boldsymbol{1}
\]
\begin{tabular}{l}
6 \\
\hline
\end{tabular} \( y \quad 2 \quad 3 \)
\( \mathbf{A} \cdot \mathbf{9} \)
B. 18
c. 27
D. 30


Which planet has atmosphere up to \( 1 \% \) of the atmosphere of the Earth?
A. Mars
B. Venus
c. Jupiter
D. Saturn


The electric potential at point \( X \) is 20 V and at point Y is - 40 V. Then, the work done by an external force in moving an electron from \( X \) to \( Y \) is:
\( \mathbf{A} \cdot 13 \times 10^{-8} J \)
В. \( 9.6 \times 10^{-18} \mathrm{J} \)
c. \( 3.2 \times 10^{-8} J \)
D. \( 30 \times 10^{-15} \mathrm{J} \)


The radius of the balloon is variable.
Find the rate of change of its volume, when the radius is \( 5 \mathrm{cm} \) ?


The plant embryo is formed by the
structure
\( A \cdot A, B \)
\( B \cdot A, D \)
\( c \cdot B, C \)
D. \( A, B, E \)
E. B, C, D


State whether given statement is True or False

The heat coming from the sun travels by
convection
A. True
B. False


No. of Solutions for:
\( \frac{4}{3} x+2 y=8 \)
\[
2 x+3 y=12
\]


Which of the following is a defect in the Mendleev's periodic table?
A. Prediction of new elements
B. Doubtful atomic weights
c. Anomalous position of hydrogen
D. Non-systematic study of elements


Find \( \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}} \quad \) If \( \boldsymbol{x}=\boldsymbol{a}(\boldsymbol{\theta}-\sin \boldsymbol{\theta}), \boldsymbol{y}= \)
\( \boldsymbol{a}(1+\cos \boldsymbol{\theta}) \)


If the figure shows a part of an electric
circuit, then the current \( I \) is
A . \( 1 A \)
в. \( 3 A \)
\( c .2 A \)
D. 4.4


How much pressure should be applied on a litre of water if it is to be
compressed by \( 0.1 \% ? \) (Bulk moduls of water \( =2100 M P a) \)
A \( .2100 k P a \)
в. \( 210 k P a \)
c. \( 2100 M P a \)
D. \( 210 M P a \)


What is "Tailing of Mercury"


Calculate the energy associated with the following nuclear reaction:
\[
\begin{array}{cc}
\begin{array}{c}
27 A l \\
26.9815 a m u
\end{array}+\underbrace{2}_{2.0141 a m u}^{2} H \\
_{12}^{25} M g & _{2}^{4} H e \\
24.9858 a m u^{+} 4.0026 a m u &
\end{array}
\]


Find \( x \) in the following nuclear reaction
\( _{12} M g^{24}+_{2} H e^{4} \rightarrow_{14} S i^{x}+_{0} n^{1} \)
A . 17
B. 27
c. 37
D. 24


Evaluate: \( \int \frac{\boldsymbol{d t}}{\left(1-t^{2}\right)\left(1-2 t^{2}\right)} \)


A synthetic material used for washing clothes, even when water is hard is:
A. detergent
B. soap
c. shampoo
D. facewash


\( A=\{x: x \) is a letter of the word 'paper'
\} and \( A=\operatorname{set} \) of digists in the number
\( \mathbf{5 9 6 7 8} \)
Sets \( A \) and \( B \) are equal
A. True
B. False


Write IUPAC name of the following \( N o_{2} \)
\( C H_{3}-C H-C H-C_{1} H-C H_{3} \)
\( C l \)


Two planets are revolving around a star in circular orbits. If the ratio of radii of
orbit is \( 1: 4, \) then ratio of their time
period will be
A . 1: 1
B. 1: 4
c. 1: 8
D. 1: 16


How will the resistance of a wire change when : Its length is doubled.


Which metal is protected by a layer of its own oxide?
A . \( A l \)
в. \( A g \)
c. \( A u \)
D. \( F e \)


If \( a^{2}-4 a-1=0, a \neq 0, \) then the value of \( a^{2}+3 a+\frac{1}{a^{2}}-\frac{3}{a} \) is
A .24
B . 26
c. 28
D. 30


Two identical air filled parallel plate
capacitors are charged to the same
potential in the manner shown by closing the switch S. If now the switch is opened and the space between the plates is filled with a dielectric of
relative permittivity \( \varepsilon_{r}, \) then :
A. The potential difference as well as charge on each capacitor goes up by a factor \( \varepsilon_{r} \)
B. The potential difference as well as charge on each capacitor goes down by a factor \( \varepsilon_{r} \)
c. The potential difference across A remains constant and the charge on B remains unchanged
D. The potential difference across B remains constant while the charge on A remains unchanged


A person \( A B \) of height \( 170 c m \) is standing in front of a plane mirror. His eyes are at height \( 164 \mathrm{cm} \). At what
distance from P should a hole be made
in the mirror so that he cannot see the
top of his head


Which of the following is not a thermodynamic property of a system?
\( \mathbf{A} \cdot H \)
в. \( P \)
\( c . E \)
D. \( W \)


Sunken stomata are characteristic of
A . Cycas
B. Pinus
c. taxus
D. All of the above


When a tension \( F \) is applied, the
elongation produced in uniform wire of length \( L, \) radius \( r \) is \( e . \) When tension \( 2 F \)
is applied, the elongation produced in another uniform wire of length \( 2 L \) and
radius \( 2 r \) made of same material is:
A . \( 0.5 e \)
B. \( 1.0 e \)
c. \( 1.5 e \)
D. \( 2.0 e \)


When \( n \) is an odd natural number other
than \( 1, \) then the value of \( x \) is
This question has multiple correct options
A. \( -\pi / 2 \)
B.
\( c . \pi \)
D. \( 3 \pi \)


Factorise:
\( \boldsymbol{x}^{3}+\mathbf{3} \boldsymbol{x}^{2} \boldsymbol{y}+\mathbf{3} \boldsymbol{x} \boldsymbol{y}^{2}+\boldsymbol{y}^{3}-\mathbf{1 2 5}=\mathbf{0} \)


Two Resistor \( 2 \Omega \) and \( 4 \Omega \) are connected
in parallel. Two more Resistor \( 3 \Omega \) and
\( 6 \Omega \) are connected in parallel. These two combinations are in series with a
battery of emf \( 5 V \) and internal
Resistance \( 0.7 \Omega \). Calculate the current
through \( 6 \Omega \) Resistors.


A racing car is travelling along a track
at a constant speed of \( 60 m s^{-1} . \) A
television cameraman is recording the event from a distance of \( 30 m \) directly away from the track as shown in the
figure. In order to keep the car under view at the situation shown in the
figure, find the angular speed at which
the camera should be rotated?
A \( \cdot \operatorname{lrads}^{-} \)
B. \( \frac{1}{2} \) rads \( ^{-1} \)
\( c \cdot 2 r a d s^{-1} \)
\( D \)


A \( 10.0 \mu F \) parallel-plate capacitor with
circular plates is connected to a \( 12.0 V \)
battery. How much charge \( (\text { in } \mu C) \) would be on the plates if the capacitor were connected to the \( 12.0 V \) battery
after the radius of each plate was
doubled without changing their separation?


Short Answer Type Questions:
Give an account of the composition of atmosphere. Also discuss the importance of the components.


Find the slope of the line which make the following angle with the positive direction of \( x- \) axis :
\( \frac{2 \pi}{3} \)


Assertion
A rigid body can be elastic.
Reason
If a force is applied on the rigid body, its
dimensions may change.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


is a phenomenon that occurs when two objects naturally vibrate at the
same frequency and the sound
produced by one object causes the other object to vibrate.


If \( \sqrt{\frac{1-\sin A}{1+\sin A}}+\frac{\sin A}{\cos A}=\frac{1}{\cos A}, \) for all
permissible values of \( A, \) then \( A \) belongs
to
This question has multiple correct options
A. First Quadrant
B. Second Quadrant
c. Third Quadrant
D. Fourth Quadrant


Look at the ray diagram shown, what
will be the focal length of the 1 st and the
2nd lens, if the incident light ray passes
without any deviation?
\( A .-5 \mathrm{cm} \) and \( -10 \mathrm{cm} \)
B. \( +5 \mathrm{cm} \) and \( +10 \mathrm{cm} \)
\( c .-5 \mathrm{cm} \) and \( +5 \mathrm{cm} \)
D. \( +5 \mathrm{cm} \) and \( +5 \mathrm{cm} \)


The value closest to the thermal velocity of a Helium atom at room temperature
\( (300 \mathrm{K}) \) in \( m s^{-1} \) is \( :\left[k_{B}=1.4 \times\right. \)
\( \left.\mathbf{1 0}^{-\mathbf{2 3}} \boldsymbol{J} / \boldsymbol{K} ; \boldsymbol{m}_{\boldsymbol{H} e}=\mathbf{7} \times \mathbf{1 0}^{-\mathbf{2 7}} \boldsymbol{k} \boldsymbol{g}\right] \)
A \( \cdot 1.3 \times 10^{4} \)
B . \( 1.3 \times 10^{3} \)
c. \( 1.3 \times 10^{5} \)
D. \( 1.3 \times 10^{2} \)


Select the correct option:
Match column I with column II and
select the correct option from the codes
given below:
Column I (Parts of alimentary canal of earthworm)
(A) Buccal cavity
(i) \( 1-3 \)
(B) Pharynx
(ii) \( 3-4 \)
(C) Oesophagus
(iii) 5-7
(D) Gizzard
(iv) \( 8-9 \)
(E) Stomach
\( (v) 9-14 \)
(F) Intestine
(vi) 15 to last
(G) Typhlosole
(vii) \( 26-35 \)
A \( \cdot \) A- (i); B- (ii); C- (iii);
D- (iv); E- (v); F- (vi); G- (vii)
B. \( A-(i) ; B-(i i) ; C-(i i i) ; D-(v) ; E-(i v) ; F-(v i) ; G-(v i i) \)
C. \( A-(i) ; B-(i i i) ; C-(i i) ; D-(i v) ; E-(v) ; F-(v i i) ; G-(v i) \)
D. A- (i); B- (iii); C\( (v) ; E-(i v) ; F-(v i i) ; G-(v i) \)


Four identical charges are placed at the points (1,0,0),(0,1,0),(-1,0,0) and
\( (0 .-1,0) \)
A. The potential at the origin is zero
B. The field at the origin is zero
c. The potential at all points on the z-axis, other than the origin, is zero
D. The potential at all points on the z-axis, other than the origin acts along the z-axis


A liquid is in equilibrium with its vapour in a sealed container at a fixed
temperature. The volume of the container is suddenly increased. What is the initial effect of the change
on vapour pressure?


If the cube equation \( x^{3}-p x+q \) has
three distinct real roots, where \( p>0 \)
and \( \boldsymbol{q}>\mathbf{0} \)
Then, which one of the following is
correct?
A \( \cdot \) the cubic has maxima at both \( \sqrt{\frac{p}{3}} \) and \( -\sqrt{\frac{p}{3}} \)
B. The cubic has minima at \( \sqrt{\frac{p}{3}} \) and maxima at \( -\sqrt{\frac{p}{3}} \)
c. The cubic has minima at \( -\sqrt{\frac{p}{3}} \) and maxima at \( \sqrt{\frac{p}{3}} \)
D. The cubic has minima at both \( \sqrt{\frac{p}{3}} \) and \( -\sqrt{\frac{p}{3}} \)


The angular momentum of an electron
in the first orbit of an \( L i^{+} \) ion is
A \( \cdot \frac{3 h}{2 \pi} \)
в. \( \frac{9 h}{2 \pi} \)
c. \( \frac{h}{2 \pi} \)
D. \( \frac{h}{6 \pi} \)


(a) What is the slope of the line joining the points \( A(2,-3) \) and \( B(6,3) ? \) Find the equation of this line.
(b) Find the co-ordinates of the point \( C \) at which the line cuts the \( x \) -axis.
(c) Show that \( C \) is the mid-point of the
line \( \boldsymbol{A B} \)


If the mean deviation about the median
of the numbers a, \( 2 a, \ldots, 50 a \) is 50
then |a| is equal
A .2
B. 3
\( c \cdot 4 \)
D. 5


Which of the following allotropes of carbon is isomorphous with crystalline silicon?
A. coke
B. Diamond
c. Graphite
D. coal


Find a vector of magnitude 6 perpendicular to each of the vectors \( \rightarrow \)
\( +\vec{b} \) and \( \vec{a}-\vec{b} \)
where \( \underset{a}{\rightarrow}=\hat{i}+\hat{j}+ \)
\( \hat{\boldsymbol{k}} \) and \( \overrightarrow{\boldsymbol{b}}=\hat{\boldsymbol{i}}+\boldsymbol{2} \hat{\boldsymbol{j}}+\boldsymbol{3} \hat{\boldsymbol{k}} \)


The sum of first three terms of a geometric sequence is \( \frac{13}{12} \) and their product is \( -1 . \) Find the common ratio and the terms


In Millikan's experiment, the slope of \( v \)
versus \( V_{o} \) graph was found to be
\( 4.125 \times 10^{-15} V s . \) Given \( e=1.6 \times \)
\( 10^{-19} C, \) the value of Planck's constant
is
B. \( 6.4 \times 10^{-34} J s \)
C \( .4 .125 \times 10^{-34} \mathrm{Js} \)
D. \( 6.6 \times 10^{-34} J s \)


A steel cable with a radius \( 2 c m \)
supports a chairlift at a ski area. If the
maximum stress is not to exceed
\( 10^{8} N \quad m^{-2}, \) the maximum load the
cable can support is
A \( \cdot 4 \pi \times 10^{5} N \)
B \( \cdot 4 \pi \times 10^{4} N \)
C \( .2 \pi \times 10^{5} N \)
D. \( 2 \pi \times 10^{4} N \)


The difference between \( U^{235} \) and \( U^{238} \)
atoms is that \( U^{238} \) contains
A. 3 more protons
B. 3 more protons and 3 more electrons
c. 3 more neutrons and 3 more electrons
D. 3 more neutrons


In the expansion of \( (1+x)^{n}, \) the
binomial coefficients of 3 consecutive
terms are respectively 220,495 and 792
then \( n= \)
A .4
B. 8
\( c \cdot 12 \)
D. 16


Which of the following is not a
characteristic of XX-rays?
A. The radiation can ionize gas
B. It causes \( Z n S \) to fluorescence
C. Deflected by electric and magnetic fields
D. Have wavelength shorter then ultraviolet rays


A point moving with constant
acceleration from \( \boldsymbol{A} \) to \( \boldsymbol{B} \) in the straight
line \( A B \) has velocities \( v_{o} \) and \( v \) at \( A \) and
\( B \) respectively. Find the velocity at \( C \)
the mid point of \( A B . \) Also show that if the time from \( A \) to \( C \) is twice that from
\( C \) to \( B \) then \( v=7 v_{o} \)


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


If \( \boldsymbol{y}=\boldsymbol{x} \log |\boldsymbol{x}+\sqrt{\left(\mathbf{1}+\boldsymbol{x}^{2}\right)}|-\sqrt{\mathbf{1}+\boldsymbol{x}^{2}} \)
then \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}= \)


Calculate energy needed for moving a mass of \( 4 k g \) from the centre of the earth
to its surface (in joule). If radius of the
earth is \( 6400 \mathrm{km} \) and acceleration due
to gravity at the surface of the earth is
\( \boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s e c ^ { 2 }} \)
A \( \cdot 1.28 \times 10^{8} J \)
в. \( 1.28 \times 10^{6} J \)
c. \( 2.56 \times 10^{8} J \)
D. \( 2.56 \times 10^{1} 0 J \)


Kinetic energy of 1 mole of an ideal gas is:
\( ^{\mathbf{A}} \cdot \frac{3}{2}^{R T} \)
в. \( \frac{3}{2}^{K T} \)
c. \( \frac{R T}{2} \)
D. \( \frac{2 R}{3} \)


Coordinates of a square are:
\( (2,2),(-2,2),(-2,-2) . \) Find the length of the side of square
A .4
B . 2
\( c \cdot 6 \)
D. None of these


Cards numbered from 11 to 60 are kept in a box. If a card is drawn at random
from the box, find the probability that the number on the drawn card is
(i) an odd number
(ii) a perfect square
number
(iii) divisible by 5
(iv) a prime number less than 20


Two uniform rods of equal length but
different masses are rigidly joined to form an L-shaped body, which is then pivoted about 0 as shown in the figure. If the system is in equilibrium in the
shown configuration. Then the ratio M/m will be:
\( A \)
B.
\( c \cdot \sqrt{2} \)
D. \( \sqrt{3} \)


In faraday's experiment current in not
produced in
A. the coil is moved and magnetic is stationary
B. the magnetic is moved the coil is stationary
C. both coil and magnetic are moved in same direction with same speed
D. both coil and magnet stationary


Which is in the decreasing order of boiling points of Vth group hydrides?
A. \( N H_{3}>P H_{3}>A s H_{3}>S b H_{3} \)
B. \( S b H_{3}>A s H_{3}>P H_{3}>N H_{3} \)
c. \( P H_{3}>N H_{3}>A s H_{3}>S b H_{3} \)
D. \( S b H_{3}>N H_{3}>A s H_{3}>P H_{3} \)


Explain with neat circuit diagram how will you determine unknown resistance by using meterbridge experiment.


The \% of Copper and Oxygen in samples of Cu0 obtained by different methods were found to be the same.
This proves the law of:
A. constant proportions
B. reciprocal proportions
C. multiple proportions
D. conservation of mass


toppr
-०६ा॥
Q Type your question
Point \( P \) is located on the right side of the
sphere; and point \( \mathrm{T} \) is located somewhere on the inside of the sphere,
not necessarily in the center.

What happens to the charge density on
the hollow sphere at point \( P \) and to the
electric field at point \( T \) as the point
charge, \( +q, \) is brought closer to the
hollow sphere?
A. The charge density at P decreases. The electric field at T remains zero.
B. The charge density at P remains zero. The electric field at T remains zero
C. The charge density at P increases. The electric field at increases in magnitude and always points to the right
D. The charge density at P increases. The electric field at T remains zero
E. The charge density at P remains constant but nonzero. The electric field at T remains constant and points to the left.


Dalton's claim that atoms of different
elements are different in all respects
has been proved wrong because of :
A. isotopes
B. allotrope
c. isobars
D. all of the above


Acetylene polymerizes to give:
A. benzene
B. polyacetylene
c. butane
D. octane


A man getting down from a running bus
falls forward:
A. as the forward movement of bus tries to pull the man forward
B. due to inertia of upper part of the body moves in the forward direction while feet come to the rest as soon
as they touch the road
C. as he leans forward as a matter of habit
D. due to the combination effect of all the three factors stated in \( (A),(B) \) and \( (C) \)


The height up to which water will rise in a capillary tube will be
A. Minimum when water temperature is \( 4^{\circ} \mathrm{C} \)
B. Maximum when water temperature is \( 4^{\circ} \mathrm{C} \)
c. Maximum when water temperature is \( 0^{\circ} \mathrm{C} \)
D. Minimum when water temperature is \( 0^{\circ} \mathrm{C} \)


Earth's atmosphere is transparent for
A. only the visible light
B. only the X-rays
c. only the \( \gamma \) - rays
D. visible light and microwaves


The cost of an article including the sales tax is \( R s .616 . \) The rate of sales
\( \operatorname{tax} \) is \( 10 \%, \) if the shopkeeper has made a profit of \( 12 \%, \) then the cost price of the article is?
A. Rs .350
в. \( R s .400 \)
c. \( R s .500 \)
D. Rs .800


The manometer shown below is used to
measure the difference between water
level of the two tanks. Calculate this
difference for the conditions indicated
\( A \cdot 4 \mathrm{cm} \)
B. \( 40 \mathrm{cm} \)
\( c .100 \mathrm{cm} \)
D. \( 12 \mathrm{cm} \)


A current i, indicated by the crosses in
figure, is established in a strip of
copper of height \( h \) and width \( w . A \)
uniform field of magnetic induction B is
applied at right angle to the strip.

Calculate voltage V necessary between
two sides of the conductor in order to
create this field E. Between which sides
of the conductor would this voltage have
to be applied?
A \( \cdot 5 \times 10^{-6} \) Top and Bottom, with top +ve charge and
bottom -ve charge
B. \( 5 \times 10^{-6} \) Top and Bottom, with top -ve charge and
bottom +ve charge
\( \mathbf{c} \cdot 5 \times 10^{-6} \) Any
D. None of the above


Assertion
Podzol is a highly leached soil and acidic in reaction.
Reason
Excessive moisture content of
podzolized soils promotes leaching of the soil
A. If \( A \) and \( R \) both are true and \( R \) is correct explanation of
\( A \)
B. If A and R both are true but R is not correct explanation of A.
C. If A is correct and R is wrong.
D. If A is wrong and R is true


When an eraser presses on a paper with a force of \( 1 \mathrm{N} \) the paper experiences a pressure of 10,000 Pa Find the area of
contact between the eraser and the
paper
A \( \cdot 1 c m^{3} \)
в. \( 10 \mathrm{cm}^{2} \)
\( c \cdot 1 c m^{6} \)
D. \( 1 c m^{2} \)


Find the direction cosines of the
line passing through the two points (-2,4,-5) and (1,2,3)


For the reaction, \( C_{2} H_{5} O H+H X \stackrel{Z n X_{2}}{\longrightarrow} \)
\( C_{2} H_{5} X, \) the order of reactivity is:
A. \( H I>H C l>H B r \)
в. \( H I>H B r>H C l \)
c. \( H C l>H B r>H I \)
D. \( H B r>H I>H C l \)


Non-metals are electronegative in
nature which means:
A. they gain electrons more easily
B. they lose electrons more easily
C. they form bonds by losing electrons
D. they are negatively charged


n \( 0.32 g \) of methane, the number of
moles is:
\( \mathbf{A} \cdot 0.002 \)
B. 0.20
\( c \cdot 2 \)
D. 0.02


A line makes an angle \( \alpha, \beta, \gamma \) with the
\( X, Y, Z \) axes. Then \( \sin ^{2} \alpha+\sin ^{2} \beta+ \)
\( \sin ^{2} \gamma= \)
A .
B. 2
\( c \cdot \frac{3}{2} \)
D.


If \( a_{1}, a_{2}, a_{3}, a_{4}, a_{5} \) are in A.P.with
common difference \( \neq 0, \) then find the value of \( \sum_{i=1}^{5} a_{i} \) when \( a_{3}=2 \)


Test whether \( x^{5}+5 x^{3}+3 x \) is divisible
by \( (x-1) \)


An object covers \( 1 / 4 \) of the circular path, what will be the ratio of the distance
and displacement of the object?


Draw Lewis structure of
tetracyanothylene and point the total number of sigma and pi bonds.


\( 0.0008 m=8 \times 10^{-x} m . \) Find \( x \)


A body rests on a rough horizontal
plane. A force is applied to the body
directly towards the plane at an angle \( \theta \) with the vertical. The body can be moved along the plane only if the value of angle
\( \boldsymbol{\theta} \) is:
A \( .45^{\circ} \)
\( \mathbf{B} \cdot>45^{\circ} \)
C. \( > \) limiting angle of friction
D. < limiting angle of friction


Find sum of the vectors \( 3 \hat{i}+7 \hat{j}-4 \hat{k} \) and \( \hat{i}-5 \hat{j}-8 \hat{k} \hat{i}-5 \hat{j}-8 \hat{k} \) and hence
find the unit vector along the sum of these vectors.


The indicates
the multiplier telling you the power of ten to which the two significant digits in color coding of the resistor must be
multiplied (or how many zeros to add)
A. 2nd band
B. 3rd band
c. 4 th band
D. last band


The electronic configuration of \( \mathrm{Cu}^{+2} \) is:
A \( \cdot(A r) 4 s^{3} 3 d^{10} \)
B . \( (A r) 4 s^{3} 3 d^{10} \)
c. \( (A r) 3 d^{9} \)
D \cdot \( (A r) 4 s^{2} 3 d^{7} \)


Wave functions of electrons in atom and
molecules are called:
A. orbitals
B. azimuthal quantum number
c. orbits
D. degenerate orbitals


If \( m \) denotes the number of 5 digit numbers if each successive digits are in their descending order of magnitude and \( n \) is the corresponding figure. When the digits and in their ascending order of magnitude then \( (\boldsymbol{m}-\boldsymbol{n}) \) has the
value
A \( \cdot^{9} C_{4} \)
B . \( ^{9} C_{5} \)
\( \mathrm{c} \cdot^{10} \mathrm{C}_{3} \)
D. \( ^{9} C_{3} \)


If Hydra is broken into pieces
A. Hydra will die.
B. Every fragment will grow into complete Hydra.
C. Some fragments will form complete Hydra.
D. Hydra will undergo sexual reproduction.


If the slope of a line through \( (-2,3),(4, a) \) is \( \frac{-5}{3} \)
then equation of the line is.
A. \( 5 x-3 y-1=0 \)
B. \( 5 x+3 y+1=0 \)
c. \( 3 x-5 y+1=0 \)
D. \( 5 x+3 y=0 \)


A ray of monochromatic light is incident on the refracting face of a prism (angle
\( 75^{\circ} \) It passes through the prism and is incident on the other face at the critical angle. If the refractive index of the prism is \( \sqrt{2}, \) then the angle of incidence on the first face of the prism is
A . 15
B. \( 30^{\circ} \)
\( c \cdot 45 \)
D. \( 60^{\circ} \)


A child inserted a needle in a man's
ear.the man became deaf. Why?
A. The needle damaged the oval window
B. The needle damaged the stirrup
C. The needle damaged the ear drum
D. All of the above


Which group of plantae includes atracheophytic embryophytes?
A. Thallophyta
B. Bryophyta
c. Pteridophyta
D. More than one option is correct


A circular disc of radius \( 3 \mathrm{cm} \) is being
heated. Due to expansion, its radius increases at the rate of \( 0.05 \mathrm{cm} / \mathrm{s} \). Find
the rate at which its area is increasing when radius is \( 3.2 \mathrm{cms} \)


An organic compound used as a thermometric liquid is :
A. ethene
B. acetic acid
c. ethyne
D. ethanol


If the acceleration due to gravity, \( g \), is \( 10 m / s^{2} \) at the surface of the earth
(radius \( 6400 k m \) ), then at a height of
1600 km the value of \( g \) will be? \( \operatorname{lin} m / s^{2} \)
A . 4
B. 5
\( c .7 .5 \)
D. 2.5


\( M \) and \( N \) are the midpoints of the diagonals \( A C \) and \( B D \) respectively of quadrilateral \( \boldsymbol{A B C D} \), then \( \overline{\boldsymbol{A B}}+ \) \( A D+\overline{C B}+\overline{C D}= \)
\( \mathbf{A} \cdot 2 \overline{M N} \)
в. \( 2 \overline{N M} \)
\( c .4 \overline{M N} \)
D. \( 4 \overline{N M} \)


"Solving the problem of pollution is an effective way of environmental management" Justify the statement


If \( n>1, x>-1, x \neq 0, \) then the
statement \( (1+x)^{n}>1+n x \) is true for
\( \mathbf{A} \cdot n \epsilon N \)
в. \( \forall n>1 \)
c. \( x>-1 \) and \( x \neq 0 \)
D. None of these


Two sides of a triangle are given. If the area of the triangle is maximum then the angle between the given sides is
A \( \cdot 45^{\circ} \)
B. \( 30^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 90^{\circ} \)


The term periodicity is the properties of elements, which are arranged in the increasing order of their atomic numbers. Then the elements
with similar properties:
A. reoccur after a fixed interval
B. reoccur after certain regular interval
c. form vertical groups
D. form horizontal rows


An object and a screen are mounted on an optical bench and a converging lens is placed between them so that a sharp
image is received on the screen. The linear magnification of the image is 2.5 The lens is now moved \( 30 \mathrm{cm} \) nearer
to the screen and a sharp image is again formed on the screen. The focal length of the lens is:
A . \( 14.0 \mathrm{cm} \)
в. \( 14.3 \mathrm{cm} \)
c. \( 14.6 \mathrm{cm} \)
D. \( 14.9 \mathrm{cm} \)


The density of a gaseous element is 5 times that of oxygen under similar
conditions. If the molecule of the
element is triatomic, what will be its
atomic mass?


\( \mathbf{A} \)
C.D. player is sold for Rs. 3,240 at a loss of \( 10 \% \). The C.P. of the C.D. player


Light with energy flux of 18 w \( / \mathrm{cm}^{2} \) falls
on a non reflecting surface of area 20
\( \mathrm{cm}^{2} \) at normal incidence the
momentum delivered in 30 minutes ise
A \( \cdot 1.2 \times 10^{-6} \mathrm{kgms}^{-1} \)
B . \( 2.16 \times 10^{-3} \mathrm{kgms}^{-1} \)
C. \( 1.8 \times 10^{-3} \mathrm{kgms}^{-1} \)
D. \( 3.2 \times 10^{-3} \mathrm{kgms}^{-1} \)


Which of the following shape of the crown is common in plants of cold
areas?
A. Conical
B. Round
c. Broad
D. None of the above


Sodium nitroprusside when added to an alkaline solution of sulphide ions produces a colouration which is:
A . red
B. blue
c. brown
D. purple


The amplitude of a particle executing SHM is \( 2 \mathrm{cm} \) and its frequency is 50 cycles/s.lts maximum acceleration will be
\( \mathbf{A} \cdot 1972 m s^{-2} \)
B. \( 19.72 m s^{-2} \)
c. \( 1.972 m s^{-2} \)
D. zero


The Orbit of a planet moving around the
sun
Refer image.
Observe the given figure showing the orbit of a planet moving around the Sun
and write the three laws related to it:


A parallel-plate capacitor has
capacitance of \( 1.0 \mathrm{F} \). If the plates are 1.0 \( \mathrm{mm} \) apart, what is the area of the
plates?


Some animals get disturbed and start running here and there just before the earthquakes occur because they can
hear
A. infrasonic sounds
B. ultrasonic sounds
c. audible sounds
D. none of these


Show that \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \frac{x}{1+x \tan x}, x \epsilon\left(0, \frac{\pi}{2}\right) \) is maximum
when \( \boldsymbol{x}=\cos \boldsymbol{x} \)


What is the value of magnetic potential,
at a distance of \( 1 \mathrm{cm} \) from the pole, of
pole strength 60 A-m?
A. \( 600 \mathrm{m} \) J/Am
B. 600 \( \mu \) /Ат
c. 600 MJ/Am
D. 600 KJ/Am


An object \( 2 \mathrm{cm} \) high is placed at a distance of \( 16 \mathrm{cm} \) from a concave
mirror, which produces a real image 3 cm high. What is the focal length of the mirror?
A . \( -48 c m \)
B. \( -36 c m \)
\( \mathrm{c} .-63 \mathrm{cm} \)
D. -83 cm


If the \( A . M \) is twice the \( G . M . \) of the
numbers \( a \) and \( b \), then \( a: b \) will be
This question has multiple correct options
A \( \cdot \frac{2-\sqrt{3}}{2+\sqrt{3}} \)
B. \( \frac{2+\sqrt{3}}{2-\sqrt{3}} \)
c. \( \frac{\sqrt{3}-2}{\sqrt{3}+2} \)
D. \( \frac{\sqrt{3}+2}{\sqrt{3}-2} \)


Which type of bond are there between
atoms of potassium and chloride when they form a crystal of potassium
chloride?
A. Hydrogen bond
B. lonic bond
c. Polar covalent bond
D. Nonpolar covalent bond
E. Metallic bond


A plane electromagnetic wave of frequency \( 25 ~ M H z \) travels in free
space along the \( x \) -direction. At a particular point in space and time, \( \vec{E}=6.3 \hat{j} V / m . \) What is \( \vec{B} \) at this point?


Three convex lenses are available
having focal lengths of \( 4 \mathrm{cm}, 40 \mathrm{cm} \) and \( 4 \mathrm{cm} \) respectively. Which one would you choose as a magnifying glass and why?


At a place on Earth, the vertical
component of Earth's magnetic field is \( \sqrt{3} \) times its horizontal component. The angle of dip at this place is
A \( .30^{\circ} \)
В. \( 60^{\circ} \)
\( c \cdot 45^{\circ} \)
D. \( 0^{\circ} \)


When different metals like zinc, iron or tin were dropped in dilute sulphuric acid, it was found that the same gas
was evolved, which burned explosively
in the air. This gas was:
A. oxygen
B. ammonia
c. chlorine
D. hydrogen


The values of he equation afor which
both the roots of the equation \( (a- \)
6)\( x^{2}=a(x-3) \) are positive are given
by
в. \( \left(0, \frac{72}{11}\right) \)
c. \( \left(6, \frac{72}{11}\right) \)
D. \( \left(\frac{72}{13}, 6\right) \)


What are isotopes? Give an example
also.


A mass of \( 1 \mathrm{kg} \) is suspended from a
spring of force constant \( 400 \mathrm{N} \) executing SHM total energy of the body is \( 2 \mathrm{J} \), then maximum acceleration of
the spring will be
\( \mathbf{A} \cdot 4 m / s^{2} \)
в. \( 40 m / s^{2} \)
c. \( 200 m / s^{2} \)
D. \( 400 \mathrm{m} / \mathrm{s}^{2} \)


Give reasons why respiration is called slow combustion?


Phases of the moon occur because:
A. We can see only that part of the moon which reflects light towards us
B. Our distance from the moon keeps changing
C. The shadow of the Earth covers only a part of moon's surface
D. The thickness of the moon's atmosphere is not constant


What is soil erosion?
A. It is the process by which soil is formed
B. A harmful process that involves the removal and transport of soil by wind and water
C. A natural method of filtering harmful pollutants
D. A process often referred to as the greenhouse effect


A gas expands against a constant external pressure of 2.00 atm, increasing its volume by \( 3.40 L \) Simultaneously, the system absorbs \( 400 J \) of heat from its surroundings.
What is \( \Delta E, \) injoules, for this gas?
\( \mathbf{A} \cdot-689 \)
в. -289
c. +400
D . +289


The distance between a convex lens and
a plane mirror is \( 10 \mathrm{cm} . \) The paralle rays incident on the convex lens, after
reflection from the mirror, form image at the optical centre of the lens. Draw ray-diagram and find out the focal length of the lens.


Which of the following represents the
relative penetrating power of the three types of radioactive emission in
decreasing order?
\( \mathbf{A} \cdot \beta>\alpha>\gamma \)
В \( \cdot \beta>\gamma>\alpha \)
\( \mathbf{c} \cdot \gamma>\alpha>\beta \)
D \( \cdot \gamma>\beta>\alpha \)


Square root of \( \sqrt{13-4 \sqrt{3}} \)


Given: \( \cos A=0.6 ; \) find all other
trigonometrical ratios for angle \( \boldsymbol{A} \)


What is chord?


In solving LP problem : minimize \( \boldsymbol{z}= \) \( 6 x+10 y, \) subject to \( x \geq 6, y \geq 2,2 x+ \)
\( \boldsymbol{y} \geq \mathbf{1 0}, \boldsymbol{x} \geq \mathbf{0}, \boldsymbol{y} \geq \mathbf{0}, \) which constraints
are reduntant?


The pressure exerted by a mixture of atmospheric gases on its surroundings and on the surface of the earth is known
as


Which of the following is responsible to
rule out the existance of defence of
definite paths or trajectories of
electrons?
A. Pauli's exclusion principle
B. Heisenberg's uncertainty principle
c. Hund's rule of maximum multiplicity
D. Aufbau principle


For a particular heat engine, 3,000 J of energy goes in at \( 700 \mathrm{K} \) and \( 2000 \mathrm{J} \) comes out at \( 200 \mathrm{K} \). The rest of the
energy is used work.

What is the actual efficiency of this engine?
A . 0.71
B. 0.33
c. 0.67
D. 0.29
E . 1.5


An object 0 is placed at a point
distance \( x \) from the focus \( F_{1} \) of a
convex lens of focal length \( f \) (both side
medium being same) and its image lis
formed at a distance \( x^{\prime} \) from \( F_{2} \) as
shown in the figure. the magnification is
A \( \cdot \frac{f}{x+x^{\prime}} \)
B. \( \frac{x^{\prime}}{x} \)
\( c \cdot \frac{f}{x} \)
D. none of these


What gases are produced in anaerobic sludge digesters?
A. Methane and \( C O_{2} \)
B. Methane, Hydrogen Sulphide and \( C O_{2} \)
C. Methane, Hydrogen Sulphide and \( O_{2} \)
D. Hydrogen Sulphide and \( C O_{2} \)


In Section \( A, \) defects of eye are given, in Section B, effects arising due to defects
are given and in section \( \mathrm{C} \), remedies are
given using lenses. Find the correct pair.
section \( A \) Section so \( B \)
Focal length
increases Bifocal . Myopia \( \quad \) increases
Hypermetropia Focal length
decreases
8. Presbyopia Power of
accommodation
decreases convex
3
lens
\( A \cdot(1-y-b),(2-x-c),(3-z-a) \)
B. \( (1-z-b),(2-z-b),(3-y-b) \)
C. \( (1-x-a),(2-y-c),(3-x-a) \)
D. \( (1-y-a),(2-x-a),(3-z-c) \)


The concentration of a solution is \( 8 \% \)
\( (w / w) \) and \( 10 \%(w / v) . \) Calculate density \( (\text { in } g / m l) \) of solution.


Prove that \( : \int \frac{1}{a^{2}-x^{2}} d x= \)
\( \frac{1}{2 a} \ln \left|\frac{a+x}{a-x}\right|+c \)


The lengths of the sides of some triangles are given, which of them is not a right angled triangle?
\( A \cdot 5 \mathrm{cm}, 12 \mathrm{cm}, 13 \mathrm{cm} \)
B. \( 7 \mathrm{cm}, 24 \mathrm{cm}, 25 \mathrm{cm} \)
\( \mathrm{c} .5 \mathrm{cm}, 8 \mathrm{cm}, 10 \mathrm{cm} \)
D. \( 3 \mathrm{cm}, 4 \mathrm{cm}, 5 \mathrm{cm} \)


Which of the following is an energy consuming process?
A \( \cdot O(g)+e^{-} \rightarrow O^{-}(g) \)
B . \( N a^{+}(g)+e^{-} \rightarrow N a(g) \)
\( \mathrm{c} \cdot O^{-}+e^{-} \rightarrow O^{2-}(g) \)
D. \( O^{2-}(g) \rightarrow O^{-}(g)+e^{-} \)


Assertion (A): Ozone can not act as a bleaching agent Reason (R): Ozone is an oxidising agent
A. Both A and R are true and R is the correct
explanation of A
B. Both A and R are true and R is not the correct
explanation of A
c. A is true but R is false
D. A is false but R is true


The area of the region bounded by the curves \( \mathbf{y}=\sqrt{\boldsymbol{x}} \) and \( \boldsymbol{y}=\sqrt{\mathbf{4}-\mathbf{3} \boldsymbol{x}} \) and
\( \mathbf{y}=\mathbf{0} \) is:
A . \( 4 / 9 \)
B. 16/9
\( c \cdot 8 / 9 \)
D. 9/2


Explain the trends in the following properties, with reference to group-16? Atomic radii and ionic radii.


Identify the correct complementary base pairing among the following.
A. Adenine - Thymine and Guanine - Cytosine
B. Adenine - Guanine and Thymine - Cytosine
c. Adenine - cytosine and Thymine - Guanine
D. Guanine - Adenine and Cytosine - Adenine


Say true or false:
\( A=\{x: x \in N \text { and } 5<x \leq 6\} \) is an
empty set.
A. True
B. False


\( \boldsymbol{\alpha}- \) rays are composed of:
A. fast moving protons
B. fast moving electrons
C. the same particles that constitute positive rays
D. particles with four mass units and two positive charges


Find the total number of stereoisomer
for each compound.
\( A \)
B.
\( c \)
D. none of these


From one corner A of a rectangular
billiard table ABCD placed on a
horizontal surface, a ball of mass and
negligible dimension is projected in the
direction making \( \theta \) with side \( A B \) it strikes in other sides \( \mathrm{BC}, \mathrm{AD}, \mathrm{DC} \) and \( \mathrm{BC} \)
and then return to same point A. Then
the value of coefficient of restitution is:
\( A \)
в. \( \sqrt{\frac{a \sin \theta}{b \cos \theta+a \sin \theta}} \)
c. \( \sqrt{\frac{a \sin \theta}{b \sin \theta-a \cos \theta}} \)
D. \( \sqrt{\frac{a \sin \theta}{b \sin \theta+a \cos \theta}} \)


An ac circuit consist of a series
combination of circuit elements \( X \) and
\( Y . \) The Current is ahead of the voltage in phanse by \( \frac{\pi}{4} . \) If element \( X \) is a pure resistor of \( 100 \Omega \)
(a) name the circuit element \( Y \)
(b) calculate the rms value of current, if
rms value of voltage is \( 141 V \)
(c) what will happen if the ac source is replaced by a dc source?


The dimensions of electromotive force
in terms of current A are
\( \mathbf{A} \cdot\left[M T^{-2} A^{-2}\right] \)
B . \( \left[M L^{2} T^{-2} A^{2}\right] \)
\( \mathrm{c} \cdot\left[M L^{2} T^{-2} A^{-2}\right. \)
D \( \cdot\left[M L^{2} T^{-3} A^{-1}\right] \)


Which of the following is considered to
be a breath
A. 2 inhalation +2 exhalation
B. 1 inhalation +2 exhalation
c. 2 inhalation +1 exhalation
D. 1 inhalation +1 exhalation


The time needed for two complete cycles of vibration is called time period
A. True
B. False


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


A reversible process changes the state
of a system in such a way that the net change in the combined entropy of the system and its surroundings is :
A. zero
B. Unity
c. Notequal
D. More than zero


Of 30 applicants for a job, 14 had at least 4 years'experience, 18 had degrees, and 3 had less than 4 years experience and did not have a degree. How many of the applicants had at least
4 years' experience and a degree?
A . 14
B. 13
c. 9
\( D .7 \)
E. 5


\( \int \frac{x}{\sqrt{x^{2}+2}} d x \)
\( ^{\mathbf{A}} \cdot \frac{x^{2}+2}{2}+C \)
B . \( x^{2}+2+C \)
c. \( \frac{1}{2} \sqrt{x^{2}+2}+C \)
D. \( \sqrt{x^{2}+2}+C \)


Which of the following will have lowest
value of \( \boldsymbol{K}_{s p} \) at room temperature?
A. \( B e(O H)_{2} \)
B. \( M g(O H)_{2} \)
\( \mathbf{c} \cdot \operatorname{Ca}(O H)_{2} \)
D. \( B a(O H)_{2} \)


Which of the following are done to
increase friction?
A. Making groove in the shoes
B. polishing rough surface
c. using ball bearing in wheels
D. Creating an air cushion


In the figure, resistivities of two
conductors of same material are \( \rho_{1} \Omega \)
\( m \) and \( \rho_{2} \Omega-m \) respectively. Write the
value of ratio of \( \rho_{1} \) and \( \rho_{2} \)


The following data were obtained during the first order thermal decomposition of
\( S O_{2} C l_{2} \) at constant volume
\[
\boldsymbol{S} \boldsymbol{O}_{2} \boldsymbol{C l}_{2(\boldsymbol{g})} \rightarrow \boldsymbol{S} \boldsymbol{O}_{2(\boldsymbol{g})}+\boldsymbol{C l}_{2(\boldsymbol{g})}
\]
Expt Time / \( S^{-1} \quad \) Total pressure/ atm
0.5
\( 0 . \)
when the total pressure is 0.65 atm then the rate constant of reaction is
if \( a=p i, \) and \( a-x=2 p i-P t \)
A. 2.0 \( \times 10^{-3} \mathrm{S}^{-1} \)
в. 2.12 \( \times 10^{-3} S^{-1} \)
c. \( 2.23 \times 10^{-3} S^{-1} \)
D. 2.34 \( \times 10^{-3} S^{-1} \)


The value of \( f(0) \) so that the function \( f(x)=\frac{2 x-\sin ^{-1} x}{2 x+\tan ^{-1} x} \) is continuous at
each point in its domain, is equal to
A . 2
в. \( \frac{1}{3} \)
c. \( \frac{2}{3} \)
D. \( \frac{-1}{3} \)


If an object moves along a straight path
it is said to be
motion. Fill in the blank.
A. Linear
B. one dimensional
c. two dimensional
D. both A and B


If in a \( \Delta A B C, \cos A . \cos B+ \)
\( \sin A \cdot \sin B \cdot \sin C=1, \) then triangle
\( A B C \) is
A. isosceles
B. right angled
c. equilateral
D. right angle isosceles


Several spherical drops of a liquid of radius r coalesce to form single drop of radius \( R . \) If \( T \) is surface tension and \( V \) is
volume under consideration, then the release of energy is:
A \( \cdot \) a \( V T\left(\frac{1}{r}+\frac{1}{R}\right) \)
В \( \cdot \) s \( \operatorname{VT}\left(\frac{1}{r}-\frac{1}{R}\right) \)
c. \( v T\left(\frac{1}{r}-\frac{1}{R}\right) \)
D. \( V T\left(\frac{1}{r^{2}}-\frac{1}{R^{2}}\right) \)


Same quantity of ice is filled in each of the two metal containers P and Q
having the same size, shape and wall thickness but made of different
materials. The containers are kept in
identical surroundings. The ice in \( \mathrm{P} \)
melts completely in time \( t_{1} \) whereas
that in \( Q \) takes a time \( t_{2} . \) The ratio of
thermal conductivities of the materials
of \( P \) and \( Q \) is
\( \mathbf{A} \cdot t_{2}: t_{1} \)
B . \( t_{1}: t_{2} \)
\( \mathbf{c} \cdot t_{1}^{2}: t_{2}^{2} \)
D. \( t_{2}^{2}: t_{1}^{2} \)


A transformer used to reduce the
alternating voltage is :
A. Step-up transformer
B. Step-down transformer
c. Both step-up and step-down transformers
D. None of these


Solve \( \int_{0}^{h} x(h-x) d x \)
\( ^{A} \cdot_{I}=\frac{h^{3}}{3} \)
в. \( _{I=} \frac{h^{3}}{6} \)
\( ^{\mathrm{C}} \cdot_{I}=-\frac{h^{3}}{6} \)
D. None of these


Which of the following represents
saponification reaction?
\( \mathbf{A} \cdot C H_{3} C O O N a+N a O H \stackrel{C a O}{\longrightarrow} C H_{4}+N a_{2} C O_{3} \)
B \( \cdot C H_{3} C O O H+C_{2} H_{5} O H \frac{H_{2} S O_{4}}{\longrightarrow} C H_{3} C O O C_{2} H_{5}+ \)
\( H_{2} O \)
\( \mathbf{c} \cdot 2 C H_{3} C O O H+2 N a \rightarrow C H_{3} C O O N a+H_{2} \)
D. \( C H_{3} C O O C_{2} H_{5}+N a O H \rightarrow C H_{3} C O O N a+C_{2} H_{5} O H \)


\( \frac{\boldsymbol{x}+\boldsymbol{4}}{\boldsymbol{2}}+\frac{\boldsymbol{x}-\boldsymbol{3}}{\boldsymbol{3}}=\frac{\boldsymbol{x}+\boldsymbol{2}}{\boldsymbol{4}}+\frac{\boldsymbol{x}+\boldsymbol{3}}{\boldsymbol{5}}, \) find
the value of \( x \)


A random variable \( X \) has the
probability distribution \( X=x: \)
\( \begin{array}{llllllll}1 & , 2 & , 3 & , 4 & , 5 & , 6 & , 7 & , 8\end{array} \)
\( \boldsymbol{P}(\boldsymbol{X}) \)
\( \mathbf{0 . 1 5}, \mathbf{0 . 2 3}, \mathbf{0 . 1 2}, \mathbf{0 . 1}, \mathbf{0 . 2}, \mathbf{0 . 0 8}, \mathbf{0 . 0 7}, \mathbf{0 . 0 5} \)
Events \( \boldsymbol{E}=\{\mathrm{X} \text { is a prime number }\} \) and
\( \boldsymbol{F}=\boldsymbol{X} / \boldsymbol{X}<\mathbf{4} \)
\( \boldsymbol{i}: \boldsymbol{p}(\boldsymbol{E} \cup \boldsymbol{F})=\mathbf{0 . 2 3} \)
\( \boldsymbol{i} \boldsymbol{i}: \boldsymbol{p}(\overline{\boldsymbol{E}} \cup \overline{\boldsymbol{F}})=\mathbf{0 . 6 5} \)
Which of \( I, I I \) is (are) true?
A. I only
B. II only
c. both \( I \) and \( I I \)
D. neither I nor \( I I \)


Find the differential equation of the family of curves given by \( x^{2}+y^{2}=2 a y \)


If \( y=\tan ^{-1}\left(\frac{2^{x^{\prime}}}{1+2^{2 x+1}}\right) \) then \( \frac{d y}{d x} \) at
\( \boldsymbol{x}=\mathbf{0} \) is?
A \( \cdot \frac{1}{10} \log 2 \)
в. \( \frac{1}{5} \log 2 \)
c. \( -\frac{1}{10} \log 2 \)
D. \( \log 2 \)


What is the De-Broglie wavelength associated with the hydrogen electron in its third orbit :
A \( .9 .96 \times 10^{-10} \mathrm{cm} \)
В. \( 9.96 \times 10^{-8} \mathrm{cm} \)
\( \mathrm{c} \cdot 9.96 \times 10^{4} \mathrm{cm} \)
D. \( 9.96 \times 10^{8} \mathrm{cm} \)


In an examination, a student needs to
\( \operatorname{get} 45 \% \) to secure passing marks. student got 138 marks and failed by \( 15 \% \) What were the maximum marks?
A . 400
B. 450
\( c \cdot 460 \)
D. 500


If the inclination of a line is \( 45^{\circ}, \) then
the slope of the line is?
A . 0
B. -
\( c \cdot 1 \)
D. 2


If \( 2 x-y=4 \) and \( x+y=5, \) then the
value of \( x y \) is
A . 4
B. 6
c. 8
D.


The amount of VAT paid by the retailer
A. \( R s .11 .50 \)
B . \( R s .12 .50 \)
c. \( R s .13 .50 \)
D. \( R s .14 .50 \)


Which of the following is a
characteristic of turbulent flow?
A. velocity more than critical velocity
B. irregular flow
C . molecules crossing from one layer to the other
D. All of the above


In which of the following reactions \( \Delta S \)
is negative? This question has multiple correct options
\( \mathbf{A} \cdot H_{2} O_{(l)} \rightarrow H_{2} O_{(s)} \)
B. \( 3 O_{2(g)} \rightarrow 2 O_{3(g)} \)
c. \( H_{2} O_{(l)} \rightarrow H_{2} O_{(g)} \)
D. \( N_{2(g)}+3 H_{2(g)} \rightarrow 2 N H_{3(g)} \)


\( C O_{2} \) transported as bicarbonate form is
about:
A . \( 0.9 \mathrm{mL} \)
B. 3.8 mL
c. \( 0.27 \mathrm{mL} \)
D. 2.7 mL


Pollution is mainly caused by:
A. increase in population and decrease in natural
resources
B. industrialisation
C. urbanization and deforestation
D. all the above


Two short magnets with pole strengths of
\( 900 A m \) and \( 100 A m \) are placed with their
axes in the same vertical line, with
similar poles facing each other. Each magnet has a length of \( 1 \mathrm{cm} \). When
separation between the nearer poles is
\( 1 \mathrm{cm}, \) the weight of the upper magnet is
supported by the repulsive force between the magnets. If \( g=10 m s^{-2} \), then the
mass of upper magnet is \( \left(x \times 10^{-4}\right) \)
A. \( 1.6 k g \)
в. \( 2.4 k g \)
c. \( 5.5 k g \)
D. \( 4.8 k g \)


Assertion
\( \operatorname{Let} f(x)=\left\{\begin{array}{ll}1 & \text { if } 2 \leq x \leq 3 \\ 3 & \text { if } 3 \leq x \leq 5\end{array}\right. \)
The mean value of \( \boldsymbol{f} \) is attained
Reason
\( f \) is a bounded function but not
continuous on \( [\mathbf{2}, \mathbf{5}] \)
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


One \( \mathrm{Kg} \) of a diatomic gas is at a pressure of \( 8 \times 10^{4} \mathrm{N} / \mathrm{m}^{2} . \) The density
of the gas is \( 4 \mathrm{kg} / \mathrm{m}^{3} . \) The energy of the gas due to its thermal motion will be
B . \( 5 \times 10^{4} \) 」
c. \( 6 \times 10^{4} \) 」
D. \( 7 \times 10^{4} \) 」


Consider following complexes:
I: \( \left[\boldsymbol{F e}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{6}\right]^{2+} \)
\( \|:\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{\boldsymbol{6}}\right]^{4-} \)
\( \| I:\left[N i(C O)_{4}\right] \)
\( \mid V:\left[N i\left(H_{2} O\right)_{4}\right]^{2+} \)
\( \mathbf{V}:\left[\boldsymbol{N} \boldsymbol{i}(\boldsymbol{C} \boldsymbol{N})_{4}\right]^{2-} \)
Out of this, select the complex with equal number of unpaired electrons:
\( \mathbf{A} \cdot\left[F e\left(H_{2} O\right)_{6}\right]^{2+} \)
B \( \cdot\left[N i(C O)_{4}\right] \)
c. \( \left[N i\left(H_{2} O\right)_{4}\right]^{2+} \)
D. None of these


If \( \vec{a}=-\hat{i}-\hat{j}+\hat{k} \) and \( \vec{b}=-\hat{i}+\hat{j}-\hat{k} \)
then find the value of \( |\vec{a} \cdot \vec{b}| \)


Particles of masses \( m_{1} \) and \( m_{2} \) are at a
fixed distance apart. If the gravitational field strength at \( m_{1} \) and \( m_{2} \) are \( \vec{I}_{1} \) and
\( \vec{I}_{2} \) respectively. Then
\( \mathbf{A} \cdot m_{1} \vec{I}_{1}-m_{2} \vec{I}_{2}=0 \)
В . \( m_{1} \vec{I}_{2}+m_{1} \vec{I}_{2}=0 \)
C \( \cdot m_{2} \vec{I}_{2}-m_{2} \vec{I}_{2}=0 \)
D . \( m_{1} \vec{I}_{2}-m_{2} \vec{I}_{1}=0 \)


Among the halogens, the one which is oxidised by nitric acid is:
A. fluorine
B. iodine
c. chlorine
D. bromine


n the given diagram, the boys who are athletic and disciplined are indicated by which number?
\( A \)
3. 2
\( c_{1} \)
\( D \)


If the coefficient of 4 consecutive terms
in the expansion of \( (1+x)^{n} \) are
\( a_{1}, a_{2}, a_{3}, a_{4} \) respectively, then show
that:
\( \frac{\boldsymbol{a}_{\mathbf{1}}}{\boldsymbol{a}_{\mathbf{1}}+\boldsymbol{a}_{\mathbf{2}}}+\frac{\boldsymbol{a}_{\mathbf{3}}}{\boldsymbol{a}_{\mathbf{3}}+\boldsymbol{a}_{\boldsymbol{4}}}=\frac{\mathbf{2} \boldsymbol{a}_{\boldsymbol{3}}}{\boldsymbol{a}_{\mathbf{2}}+\boldsymbol{a}_{\boldsymbol{3}}} \)


Two infinitely long parallel conducting plates having surface charge densities \( +\sigma \) and \( -\sigma \) respectively, are separated
by a small distance. The medium
between the plates is vacuum. If \( \varepsilon_{0} \) is
the dielectric permittivity of vacuum
then the electric field in the region between the plates is:
A. 0 volt \( / m \)
в. \( \sigma / 2 \varepsilon_{0} \) volt \( / \mathrm{m} \)
c. \( \sigma / \varepsilon_{0} \) volt \( / \mathrm{m} \)
D. \( 2 \sigma / \varepsilon_{0} \) volt \( / \mathrm{m} \)


iF \( \boldsymbol{A}=\left[\begin{array}{cc}1 & -1 \\ -1 & 1\end{array}\right], \) then the expression
\( A^{3}-2 A^{2} \) is
A . a null matrix
B. an identity matrix
c. equal to A
D. equal to -A


BOD stands for:
A. Biochemical Oxygen Demand
B. Biological Oxygen Demand
C. Bacterial Oxidation Demand
D. Biochemical Oxidation Demand


Which of the following inhibits protein synthesis by binding to 50S ribosome?
A. Tetracycline
B. Streptomycin
c. Erythromycin
D. Penicillin