Sun radiates energy at the rate of \( 3.6 \times \)
\( 10^{26} \) Joule/s. The rate of decrease in
mass of the sun is \( \left(\text { in } \mathrm{kgs}^{-1}\right) \)
A \( .12 \times 10^{10} \)
B . \( 1.3 \times 10^{20} \)
c. \( 4 \times 10^{9} \)
D . \( 3.6 \times 10^{36} \)


If water samples are taken from the sea, rivers, clouds, lakes or snow, they will be
found to contain hydrogen and oxygen in the ration of \( 1: 8 . \) This clearly
demonstrates the law of ?
A. Chemical equilibrium
B. Definite proportions
c. combining volumes
D. The relation of elements in the periodic tables


The substance which has greater ability to raise its temperature has less
capacity to store heat and the substance which has less ability to raise its temperature has more capacity to store heat.
A. True
B. False


A triangular plate of uniform thickness and density is made to rotate about an
axis perpendicular to the plane of the
paper and
(a) passing through \( \boldsymbol{A} \) passing through \( B, \) by the
application of some force \( \boldsymbol{F} \) at \( \boldsymbol{C}(\operatorname{mid}- \)
point of \( A B) \) as shown in fig. In which
case is angular acceleration more
A \( . \) in case \( (a) \)
B. in case (b)
c. both \( (a) \) and \( (b) \)
D. none of these


Which of the following is a fibre? Nylon, Neoprene, PVC


Virion is a/an
A. Virus without protein coat
B. Enucleated virus
c. Prion
D. virus


Net torque on the planet is
A. Constant at all points
B. Zero at all point
c. Maximum at \( A \)
D. Minimum at \( D \)


Assertion
The value of K increases with increase
in temperature in case of endothermic
reaction.
Reason
The increase in temperature shifts the equilibrium in the backward direction in case of exothermic reaction.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


Choose the correct alternate, which the
type of tropism exhibited by plants is correctly matched with the stimulus to which they respond.
Stimulus Tropism 1 Hydrotropism (i) Earth
2 Geotropism
(ii) Light
3 Chemotropism (iii) Water (iii) Chemotropism phototropism chemical (iv)
A. \( 1- \) ii, \( 2-i, \) 3-iv, 4-ii
B. 1-iii, 2-i, 3-iv, 4-i
c. 1 -iv, 2-iii, 3-i, 4-i
D. 1-iii, 2-i, 3-ii, 4-ì


Distinguish between:
(a) Afferent neurons and efferent
neurons
(b) Impulse conduction in a myelinated nerve fibre and unmyelinated nerve fibre
(c) Aqueous humor and vitreous humor
(d) Blind spot and yellow spot
(e) Cranial nerves and spinal nerves


One of the most common applications
of chemical effect of electric current is
A. electroplating
B. chemical etching
c. electric shielding
D. none of these


If the distance of earth from the sun
reduces to one fourth of its present
value then the length of the year will become
A . \( 1 / 6 \) of present year
B. 1/8 of present year
c. \( 1 / 4 \) of present year
D. \( 1 / 2 \) of present year


Which one of the following is not a condensation polymer?
A. Dacron
B. Neoprene
c. Melamine
D. Glyptal


\( \ln H_{2}-O_{2} \) fuel cell, the reaction
occurring at cathode is :
\( \mathbf{A} \cdot 2 H_{2(g)}+O_{2(g)} \rightarrow 2 H_{2} O_{(l)} \)
B. \( O_{2(g)}+2 H_{2} O_{(l)}+4 e^{-} \longrightarrow 4 O H_{(a q)}^{-} \)
\( ^{\mathrm{c}} \cdot H^{+}+e^{-} \rightarrow \frac{1}{2}^{H}_{2} \)
\( \mathbf{D} \cdot H_{(a q)}^{+}+O H_{(a q)}^{-} \longrightarrow H_{2} O_{(l)} \)


Identify the correct statement:
A. For a body in motion, average speed can be zero but average velocity can not be zero
B. For a body in motion, average velocity can be zero but average speed can not be zero
C. For a body in motion, both average velocity and average speed can be zero
D. For a body in motion, both average velocity and average speed can not be zero


If a train is retarding and at same time coin is thrown upwards, then you
will observe that:
A. the coin reaches again in your hand
B. the coin falls behind you
c. the coin falls in front of you
D. the coin follows a circular path


How heat capacity of a body is related to specific heat capacity of its substance
\( ? \)


The magnetic induction at the centre 0
of the arc due to current in portion \( \boldsymbol{A B} \)
will be
A. zero
в. \( \frac{\mu_{0} i}{r} \)
c. \( \frac{\mu_{0} i}{2 r} \)
D. \( \frac{\mu_{0}}{4 r_{0}} \)


A 50 turn circular coil has a radius of 3
\( \mathrm{cm}, \) it is kept in a magnetic field acting normal to the area of the coil. The
magnetic field B is increased from \( 0.10 T \) to \( 0.35 T \) in 2 milli second, the
average induced emf will be
A. \( 177 V \)
B. \( 1.77 V \)
c. \( 0.177 V \)
D. \( 17.7 V \)


Auxin inhibits the growth of
A. Apical bud
B. Lateral axillary buds
C. Roots on stem cutting
D. Parthenocarpic development of fruits


In case of plane mirror, the size of the image is equal to the size of the object, irrespective of the distance of the object from the mirror.
A . True
B. False


The excess presence of which of the following cause the teeth of children mottled and discolored?
A. Hardness
B. calcium
c. salt
D. Fluoride


\( A \) 2kg body and 3kg body are moving along the X-axis. At a particular instant the \( 2 \mathrm{kg} \) body is \( 1 \mathrm{m} \) from the origin and
has the velocity of \( 3 m s^{-1} \) and \( 3 k g \) body is \( 2 \mathrm{m} \) from the origin and has a velocity
of \( -1 m s^{-1} . \) The position of the center of mass of the system is:
\( A \cdot 1 m \)
B. 1.6m
c. \( 2.2 \mathrm{m} \)
D.


The self inductance of two solenoids \( A \)
\( \& \mathrm{B} \) having equal length are same. If the number of turns in two solenoids \( A \& B \)
are 100 and 200 respectively. The ratio
of radii of their cross-section will be
A . 2: 1
B. 1: 2
c. 1: 4
D. 4: 1


Why are red coloured lights are used in traffic signals to stop the vehicles?
A. minimum wavelength and less scatter.
B. maximum wavelength and more scatter.
c. maximum wavelength and less scatter.
D. less wavelength and less scatter.


Imagine a light planet revolving around a very massive star in a circular orbit of
radius R with a period of revolution T. If the gravitational force of attraction between planet and stars is proportion to \( R_{1} / 2, \) there \( T^{2} \) is proportional to.
A \( \cdot R^{2} \)
B . \( R^{1 / 2} \)
c. \( R^{-1 / 2} \)
D. \( R^{1} / 3 \)


In an atom two electrons move around the nucleus in circular orbits of radii
and \( 4 \mathrm{R} \). The ratio of the time taken by them to complete one revolution is:
A .1: 4
B . 4: 1
c. 1: 8
D. 8: 7


The molar concentration of \( 64 \mathrm{g} \) of \( S O_{2} \) in a four litre flask would be:
\( A \cdot 2 \)
B.
\( c \cdot 5 \)
D. 0.25


What amount of heat energy (kJ) is released in the combustion of 12.0 g of
\[
\begin{array}{l}
C_{3} H_{4} ? \\
C_{3} H_{4}(g)+4 O_{2}(g) \rightarrow 3 C O_{2}(g)+
\end{array}
\]
\( \mathbf{2} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l}) \quad \boldsymbol{\Delta} \boldsymbol{H}^{\circ}=-\mathbf{1} \mathbf{9} \mathbf{3} \mathbf{9} . \mathbf{1} \boldsymbol{k} \boldsymbol{J} \)
[Atomic weights: \( C=12.01, H=1.008,0= \)
16.00]
A. 725
B. 504
c. 783
D. 581


Three long, straight and parallel wires are arranged as shown in figure. The
force experienced by \( 10 \mathrm{cm} \) length of
wire \( \boldsymbol{Q} \) is
A \( .1 .4 \times 10^{-4} N \) toward the right
B. \( 1.4 \times 10^{-4} N \) toward the left
c. \( 2.6 \times 10^{-4} N \) toward the right
D. \( 2.6 \times 10^{-4} N \) toward the left


State Blackman's Law of limiting
factors.


Who first proposed that the light exhibits wave nature and explained wave phenomenon?
A. Max Planck
B. James Clerk Maxwell
c. Isaac Newton
D. Christian Huygens


The line \( A B \) divides the line segment
OP in the ratio
A . 1: 1
B. 3: 4
c. 1: 2
\( \mathbf{D} \cdot 9: 16 \)


\( \int 32 x^{3}(\log x)^{2} d x \) is equal to
\( \mathbf{A} \cdot 8 x^{4}(\log x)^{2}+c \)
B . \( x^{4}\left\{8(\log x)^{2}-4 \log x+1\right\}+c \)
C. \( x^{4}\left\{8(\log x)^{2}-4 \log x\right\}+c \)
D. \( x^{3}\left\{(\log x)^{2}+2 \log x\right\}+c \)


Light energy is changed into chemical
energy during the process of
A. respiration
B. transpiration
c. photosynthesis
D. digestion


The differential equation of the family of circles passing through the fixed points \( (a, 0) \) and \( (-a, 0) \) is:
A \( \cdot y_{1}\left(y^{2}-x^{2}\right)+2 x y+a^{2}=0 \)
B . \( y_{1} y^{2}+x y+a^{2} x^{2}=0 \)
C. \( y_{1}\left(y^{2}-x^{2}+a^{2}\right)+2 x y=0 \)
D. none of these


An AC source is connected to a resistive
circuit. Which of the following is true?
A. Current leads ahead of voltage in phase
B. Current lags behind voltage in phase
c. current and voltage are in same phase
D. Any of the above may be true depending upon the value of resistance


Explain the term hysteresis.


Lanthanoid contraction is applicable on which group of the following element
set?
This question has multiple correct options
A \( . Z n, \) Cd, \( H g \)
в. \( T i, Z r, H f \)
c. \( S c, Y, L a \)
D. \( C u, A g, Z n \)
E. \( V, N b, T a \)


toppr
Q Type your question
showing correctly the image of the
object on the screen is:
\( \mathbf{A} \)
\( B \)
\( c \)
D.


A complex is represented as \( \mathrm{CoCl}_{3} \cdot x N H_{3} \) its 0.1 molal solution in
aq. solution shows \( \Delta T_{f}=0.558^{0} C . K_{f} \)
for \( \boldsymbol{H}_{2} \boldsymbol{O} \) is \( 1.86 \boldsymbol{K} \boldsymbol{m o l}^{-1} \boldsymbol{k g} . \) Assuming
\( 100 \% \) ionisation of complex and
coordination no. of \( C o \) is six, calculate
formula of complex.


In the given figure, velocity of the body
at \( A \) is
A. Zero
B. Unity
c. Maximum
D. Infinite


(a) Write two properties of metals.
(b) What is alloy? Give two examples.
(c) What is the nature of oxides of
metals and non-metals?


Displacement of a particle of mass \( 2 \mathrm{kg} \) varies with time as: \( s= \)
\( \left(2 t^{2}-2 t+10\right) m . \) Find total work done
on the particle in a time interval from \( t=0 \) to \( t=2 s \)
A . 16
B. 32 J
c. 48 J
D. 96 J


Electrons of mass \( \mathrm{m} \) and charge e are accelerated through a potential difference V and strike the target. The
maximum speed of these electrons is
A \( \cdot \frac{e V}{m} \)
B. \( \frac{e V^{2}}{m} \)
c. \( \sqrt{\frac{e V}{m}} \)
D. \( \sqrt{\frac{2 e V}{m}} \)


A point dipole is located at the origin in
some orientation. the electric field at
the point \( (10 \mathrm{cm}, 10 \mathrm{cm}) \) on the \( \mathrm{x} \) -y plane is measured to have a magnitude \( 1.0 \times \)
\( 10^{-3} \mathrm{V} / \mathrm{m} . \) What will be the magnitude
of the electric field at the point(20 \( \mathrm{cm} \)
\( 20 \mathrm{cm}) ? \)
A. \( 5.0 \times 10^{-4} \mathrm{V} / \mathrm{m} \)
В. \( 2.5 \times 10^{-4} \mathrm{V} / \mathrm{m} \)
c. It will depend on the orientation at the dipole
D. \( 1.25 \times 10^{-4} \mathrm{V} / \mathrm{m} \)


An experiment consists of tossing a coin and then throwing it second time if
a head occurs. If a tail occurs on the
first toss then a die is rolled once. Find
the sample space


Which of the following is not a state function?
A. Work-done in adiabatic process
B. Work done in isothermal process
c. Heat at constant pressure
D. Heat at constant volume


Which one of the following has the regular tetrahedral structure?
A \( . B F_{4}^{-} \)
в. \( S F_{4} \)
c. \( X e F_{4} \)
D. \( \left[N i(C N)_{4}\right]^{2} \)


The dimensions of self-inductance L are
\( \mathbf{A} \cdot\left[M L^{2} T^{-2} A^{-2}\right] \)
B. \( \left[M L^{2} T^{-1} A^{-2}\right] \)
\( \mathbf{c} \cdot\left[M L^{2} T^{-1} A^{-1}\right] \)
D. \( \left[M L^{-2} T^{-2} A^{-2}\right] \)


The chance of throwing a total of 3 or 5
or 11 with two dice is.
A \( \cdot \frac{5}{36} \)
в. \( \frac{1}{9} \)
\( c \cdot \frac{2}{9} \)
D. \( \frac{19}{36} \)


Government of India has adopted auto fuel policy to effectively cut down
A. Sulphur oxides
B. Carbon monoxide
c. Carbon dioxide
D. Sulphur and nitrogen oxides


What is fluid friction?


Power loss (in W) in case of dc is


In a cylindrical vessel containing liquid of density \( \rho, \) there are two holes in the
side walls at heights of \( h_{1} \) and \( h_{2} \)
respectively such that the range of efflux at the bottom of the vessel is
same. Find the height of a hole, for which the range of efflux would be maximum
A \( \cdot \frac{h_{2}+h_{1}}{2} \)
B. \( \frac{h_{2}-h_{1}}{2} \)
\( c \cdot \frac{h_{2} h_{1}}{2} \)
D. \( \frac{h_{2}}{h_{1}} \)


If \( 2 \vec{a}+3 \vec{b}+4 \vec{c}=0 \Rightarrow \vec{a} \times \vec{b}+\vec{b} \times \)
\( \vec{c}+\vec{c} \times \vec{a}= \)
\( A \)
B \( \cdot 3 \vec{a} \times \vec{b} \)
c. \( 3 \vec{b} \times \vec{c} \)
D. \( 3 \vec{c} \times \vec{a} \)


The variation of solubility \( (S) \) with temperature for Glauber's salt is gives
as:

Which of the following options correctly explain the above behavior?
A. Dissolution of Glauber salt is exothermic
B. Dissolution of G;auber salt is endothermic
C . At \( 32.28^{\circ} \mathrm{C} \) Glauber salt looses water of crystalization
due to which dissolution above \( 32.28^{\circ} \mathrm{C} \) becomes
exothermic and below \( 32.28^{\circ} \mathrm{C} \) it is endothermic
D. Above \( 32.28^{\circ} \mathrm{C} \) dissolution of Glauber salt is
endothermic and below \( 32.28^{\circ} \mathrm{C} \) it is exothermic


How many \( C_{6} H_{3} C l B r N O_{2} \) isomers may be produced by bromination of meta-chloronitrobenzene?
A
B. 2
\( c \cdot 3 \)
D. 4


Due to lanthanide
contraction
A. Fe, Co, Ni have equal size
B. Zr and Hf have equal size
C. all f-block ions have equal size
D. all isoelectronic ions have equal size


From the given table, which properties of the undetected third particle can we
calculate?
A. Total energy, but not kinetic energy.
B. Kinetic energy, but not total energy.
c. Both total energy and kinetic energy
D. Neither total energy nor kinetic energy.


An exterior angle of a triangle is \( 105^{\circ} \) and its two interior opposite angles are equal. Each of these equal angles is
A. \( _{37} \frac{1^{0}}{2} \)
в. \( _{52} \frac{1^{0}}{2} \)
c. \( _{72} \frac{1^{0}}{2} \)
D. 75


If rth term in the expansion of
\( \left(x^{2}+\frac{1}{x}\right)^{12} \) is independent of \( x, \) then
\( \boldsymbol{r}= \)
\( \mathbf{A} \cdot \mathbf{9} \)
B. 8
c. 10
D. none of these


distance travelled by the ball upto that instant, when lift and ball were of same
height from ground take \( g=10 m / s^{2} \)
A \( \cdot \frac{350}{9} m \)
в. \( \frac{700}{9} \mathrm{m} \)
c. \( \frac{175}{9} m \)
D. None of the above


Find the sum to the series \( 1 . n+2(n- \)
1) \( +3(n-2)+\ldots+n .1 \)


Locus of z if \( \left|z-z_{1}\right|=\left|z-z_{2}\right|, \) where \( z_{1} \)
and \( z_{2} \) are complex numbers with the
greatest and the least moduli, is
A. Line parallel to the real axis
B. Line parallel to the imaginary axis
c. Line having a positive slope
D. Line having a negative slope


Two resistance at \( 0^{\circ} \mathrm{C} \) with
temperature coefficient of resistance
\( \alpha_{1} \) and \( \alpha_{2} \) joined in series act as a single resistance in a circuit. The temperature coefficient of their single resistance will be
A \( \cdot \alpha_{1}+\alpha_{2} \)
В. \( \frac{\alpha_{1} \alpha_{2}}{\alpha_{1}+\alpha_{2}} \)
c. \( \frac{\alpha_{1}-\alpha_{2}}{2} \)
D. \( \frac{\alpha_{1}+\alpha_{2}}{2} \)


Two particles undergo SHM along same line with same time period (T) and same amplitude
(A) At particular instant one particle is \( x=-A \) and the other is at \( x=0 \) If they move in same
direction then they will meet each other
at
A \( \cdot x=\frac{A}{2} \)
в. \( x=\frac{A}{\sqrt{2}} \)
c. \( x=\frac{A}{4} \)
D. \( x=\frac{4}{8} \)


Hydroponics is growing of plants
A. Without soil.
B. Without organic matter.
C. In water.
D. All of the above.


is applied to unwind a screw.
A. single force
B. Couple
c. Parallel force
D. None of these


Sudhir's present age is 5 more than three times the age of Viru, Anil's age is half the age of Sudhir. If the ratio of the
sum of Sudhir's and Viru's age to three
times Anil's age is \( 5: 6, \) then find Viru's
age


Which one of the following is not a constituent of saliva?
A. Bicarbonate
B. Lysozyme
c. Glucose
D. Immunoglobulin


Two block \( A \) and \( B \) are arranged as
shown in the figure. The mass of block \( A \) is 10 kg. The coefficient of friction
between the block \( A \) and the horizontal
plane is \( 0.2 . \) The minimum mass of block \( B \) to start motion will be
A . \( 0.2 \mathrm{kg} \)
в. \( 10 \mathrm{kg} \)
\( c .5 k g \)
D. \( 2 k g \)


The escape velocity for a rocket on the earth is \( 11.2 \mathrm{km} / \mathrm{sec} \). Its value on a planet where acceleration due to gravity
is twice that on the earth and the
diameter of the planet is twice that of the earth, will be (in \( k m / s e c \) ):
A . 11.2
B. 5.6
c. 22.4
D. 33.6


Which of the following structures is not correctly matched?
\( A \)
\( H_{3} \)
\( \alpha \) - Methoxypropionaldehyde \( -H_{3} C-C H-C-H \)
в. 3-Hydroxybutanal - \( C H_{3}-C H-C H_{2} C H O \)
\( c \)
4 - Oxopentanal \( -C H_{3} C H_{2} C H_{2}-C_{-} C H O \)
D. Di-sec. -butylketone - \( C H_{3} C H_{2}-C H-C-C H \)
\( C H_{2} C H_{3} \)


Value of \( \operatorname{lt}_{x \rightarrow 0}\left(\frac{1+\tan x}{1+\sin x}\right)^{\operatorname{cosec} x} \) equals
A . 1
B.
\( c \cdot \frac{1}{e} \)
D. None of these


\( \frac{k}{k} \)


Which of the following is best insulator?
A. Carbon
B. Paper
c. Graphite
D. Ebonite


Given the structural formula for the
following:
Acetone.


"Thêorie élémentaire de la botanique" is
the book of
A. Takhtajan
B. Augustin Pyramus de Candolle
c. Eichler
D. Linnaeus


Liquid is filled in a vessel which is kept
in a room with temperature \( 20^{\circ} \mathrm{C} \). When
the temperature of the liquid is \( 80^{\circ} C \) then it losses heat at the rate of 60
cal/sec.What will be the rate of loss of
heat when the temperature of the liquid
is \( 40^{\circ} \mathrm{C} \)
A . 180 cal / sec
B . 40 cal/sec
c. 30 cal/sec
D. 20 cal/sec


n changing the state of a gas adiabatically from an equilibrium state A to another equilibrium state \( \mathrm{B} \) an amount of work equal to \( 22.3 \mathrm{J} \) is done on the system. If the gas is taken from state \( A \) to \( B \) via a process in which the net heat absorbed by the system is 9.35 cal then net work done by the system in the later case is:
(Take \( 1 \mathrm{cal}=4.2 \mathrm{J} \)
A . 15 J
в. 16
c. 17
D. 18 J


Point \( D \) has coordinates as (3,4,5)
Referring to the given figure, find the
coordinates of point \( \boldsymbol{B} \)
A \( \cdot(3,0,4) \)
\( \mathbf{B} \cdot(4,3,0) \)
C. (4,0,3)
D. (3,4,0)


Write the chemical formulae of four oxy
acids of chlorine.


If \( \boldsymbol{f}(\boldsymbol{x})=|\boldsymbol{x}+\mathbf{1}|(|\boldsymbol{x}|+|\boldsymbol{x}-\mathbf{1}|) \) then at
what points the function is/are not differentiable at in the interval [-2,2] This question has multiple correct options
A . -1
B.
c. 1
D. \( 1 / 2 \)


During estimation of nitrogen present in an organic compound by Kjedhal's method, 0.17 g of \( N H_{3} \) was evolved from 0.28 g of a nitrogenous compound. What is the percentage of nitrogen in the organic compound?
A. 5
B. 30
\( c .50 \)
D. 80


The relation between force ' \( F \) ' and
density ' \( d \) ' is \( F=\frac{x}{\sqrt{d}} . \) The dimensions
of \( x \) are:
\( \mathbf{A} \cdot\left[L^{-1 / 2} M^{3 / 2} T^{-2}\right] \)
B \( \cdot\left[L^{-1 / 2} M^{1 / 2} T^{-2}\right] \)
\( \mathbf{C} \cdot\left[L^{-1} M^{3 / 2} T^{-2}\right] \)
D・ \( \left[L^{-1} M^{1 / 2} T^{-2}\right] \)


Two coils \( X \) and \( Y \) are linked such that
emf \( E \) is induced in \( Y \) when the current
in \( X \) is changing at the rate \( I^{\prime}(=d I / d t) \)
If a current \( I_{0} \) is now made to flow through \( Y \), the flux linked with \( X \) will be
A \( . E I_{0} I^{\prime} \)
в. \( \frac{I_{0} I^{\prime}}{E} \)
\( ^{\mathbf{c}} \cdot\left(\frac{E}{I_{0}}\right) I^{\prime} \)
D. \( \left(\frac{E}{I^{\prime}}\right) I_{0} \)


Which is correct
A. An increase in glomerular blood flow stimulates formation of angiotensin II
B. During summer, when body loses a lot of water by evaporation, the release of ADH is suppressed
C. When someone drinks a lot of water, ADH release is
suppressed
D. Exposure to cold temperature stimulates ADH release


Which of the following isomers is more
volatile: \( o \) -nitrophenol or \( p \) -nitrophenol?


Which of the following statements about benzyl chloride is incorrect?
A. It is less reactive than alkyl halides
B. It can be oxidised to benzaldehyde by boiling with copper nitrate solution
c. It is a lachrymatory liquid and answers Beilstein's test
D. It gives a white precipitate with alcoholic silver nitrate


The \( n^{t h} \) term of an \( A . P \) is \( 7-4 n . \) Find
its common difference.


111.1g of the non-volatile solute, urea needs to be dissolved in 100 g of water, in order to decrease the vapour pressure of water by \( 25 \% \). The molarity of the solution will be:
A. 18.52 м
в. 18.92
c. 19.52 м
D. None of the above


\( \boldsymbol{C}-\boldsymbol{C}-\boldsymbol{C}-\boldsymbol{C}=\boldsymbol{C}-\boldsymbol{C} \)
\( \boldsymbol{S O}_{3} \boldsymbol{H} \)
Draw complete structure of the given compound (using hydrogen-carbon bonds)


At what height from the surface of earth
will the value of \( g \) be reduced by \( 36 \% \)
from the value at the surface? \( \boldsymbol{R}= \)
\( 6400 k m \)
A . \( 400 k m \)
B. \( 800 k m \)
\( c .1600 k m \)
D. 3200km


A metal sphere has a charge of \( -6 \mu C \) When \( 5 \times 10^{12} \) electrons are removed
from the sphere, what would be net
charge on it?
A. \( -6.8 \mu C \)
в. \( 6.8 \mu C \)
c. \( 5.2 \mu C \)
D. - \( 5.2 \mu C \)


When the light is very bright,
A. The iris makes the pupil expand
B. The iris makes the pupil contract
C. The iris and the pupil remain as they are
D. The iris and the pupil damages


The angle of incidence for a ray of light
at a refracting surface of a prism is \( 45^{\circ} \)
The angle of prism is \( 60^{\circ} . \) If the ray suffers minimum deviation through the prism, the angle of minimum deviation and refractive index of the material of
the prism respectively, are
\( ^{\mathrm{A}} \cdot_{45^{\circ} ;} \frac{1}{\sqrt{2}} \)
B . \( 30^{\circ} ; \sqrt{2} \)
c. \( 45^{\circ} ; \sqrt{2} \)
D. \( 30^{\circ} ; \frac{1}{\sqrt{2}} \)


Dalton's atomic theory successfully explained:
(i) Law of conservation of mass
(ii) Law of constant composition
(iii) Law of radioactivity
(iv) Law of multiple proportions
A. (i), (ii) and (iii)
B. (i), (iii) and (iv)
c. (ii), (iii) and (iv)
D. (i), (ii) and (iv)


An aeroplane drops a parachutist. After covering a distance of \( 40 \mathrm{m} \), he opens
the parachute and retards at \( 2 m s^{-1} . \) If he reaches the ground with a speed of
\( 2 m s^{-1}, \) he remains in the air for about
A . \( 16 s \)
B. 3
c. \( 13 s \)
D. 10 \( s \)


The phenomenon of light passing through the object is called:
A. Reflection
B. Refraction
c. Dispersion
D. Total internal reflection


Find the area of a parallelogram having \( \bar{a}=(4,-3,1), \bar{b}=(2,-4,5) \) as
diagonals


A sphere of mass \( \mathrm{M} \) and radius \( \mathrm{R} \) is falling in a viscous fluid. The terminal velocity attained by the falling object will be proportional to:
A \( \cdot R^{2} \)
B.
c. \( \frac{1}{R} \)
D. \( \frac{1}{R^{2}} \)


Assertion \( (A): \) If \( f(x)=|x|, \) then \( f \) has
minimum value at \( x=0 \)
Reason (R): A function f(x) has
minimum value at \( x=a \) if \( f^{\prime}(a)=0 \) and
\( \mathbf{f}^{\prime \prime}(\mathbf{a})>\mathbf{0} \)
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 and R is false
D. A is false and R is true


The configuration of sugars is related to glyceraldehyde and that of amino acids
is related to :
A. serine
B. leucine
c. alanine
D. glycine


If \( a^{2}+\frac{1}{a^{2}}=102, \) find the value of \( a-\frac{1}{a} \)


Mention three applications of total internal reflection of light.


Find the variance of the following data 6,8,10,12,14,16,18,20,22,24


Which of the following phenomena of light are involved in the formation of a
rainbow?
A. Reflection, refraction and dispersion
B. Refraction, dispersion and total internal reflection
c. Refraction, dispersion and internal reflection
D. Dispersion, scattering and total internal reflection


The average marks of boys in a class is
52 and that of girls is \( 42 . \) The average marks of boys and girls combined is 50 The percentage of boys in the class is
A . \( 40 \% \)
B. 20\%
c. \( 80 \% \)
D. \( 60 \% \)


Which physical quantity is measured in \( k W \)
A. electric energy
B. voltage
c. charge
D. electric power


Fill in the blanks.
The device that detects the induced emf
is called


If normality of a solution \( =3.33 \times 10^{-5} \)
find \( p H \)


\( e-\delta \)
\( x-2 \)


For the reaction equilibrium \( 2 N O B r_{(g)} \leftrightharpoons 2 N O_{(g)}+B r_{2(g)}, \) if
\( P_{B r_{2}}=\frac{P}{9} \) at equilibrium and \( P \) is the initial total pressure, then the ratio \( \frac{\boldsymbol{K}_{\boldsymbol{P}}}{\boldsymbol{P}} \)
is equal to :
A \( \cdot \frac{1}{9} \)
в. \( \frac{4}{441} \)
c. \( \frac{1}{27} \)
D. \( \frac{1}{3} \)


Lycopersicum esculentum belongs to family
A. Brassicaceae
B. Solanaceae
c. Liliaceae
D. Poaceae


The volume of a colloidal particle \( V_{c} \) as
compared to the volume of a solute
particle in atrue solution \( V_{s} \) could be
A \( \cdot \frac{V_{c}}{V_{s}}=1 \)
B. \( \frac{V_{c}}{V_{s}}=10^{23} \)
c. \( \frac{V_{c}}{V_{s}}=10^{-3} \)
D. \( \frac{V_{c}}{V_{s}}=10^{3} \)


Express the following as a rational number i.e. in the form \( \frac{a}{b} ; \) where \( a, b \in I \) and \( \boldsymbol{b} \neq \mathbf{0} \)
\( \mathbf{0 . 7} \overline{\mathbf{1}} \)
A \( \cdot \frac{22}{45} \)
в. \( \frac{32}{45} \)
c. \( \frac{16}{45} \)
D. \( \frac{19}{45} \)


The given distribution shows the
number of runs scored by some top batsmen of the world in one-day
international cricket matches.
Runs scored \( \quad \) Number of batsmen tsmen \( 3000-4000 \) Is \( ^{4000}-5000 \) \( \begin{array}{lll}5000-6000 & 9 \\ 6000-7000 & 7 \\ 7000-8000 & 6 \\ 8000-9000 & 3 \\ 9000-10000 & 1 \\ 10000-11000 & 1\end{array} \) and
Find the mode of the data.


A toy cart is tied to the end of an
unstretched string of length 'L'. When revolved, the toy card moves in
horizontal circle with radius '2 \( l \) ' and
time period \( T . \) If it is speeded until it moves in horizontal circle of radius '3 \( l^{\prime} \)
with period \( T_{1}, \) relation between \( T \) and
\( T_{1} \) is (Hooke's law is obeyed)
\( ^{\mathbf{A}} \cdot_{T_{1}}=\frac{2}{\sqrt{3}} T \)
в. \( T_{1}=\sqrt{\frac{3}{2}} T \)
\( ^{\mathbf{c}} \cdot_{T_{1}}=\sqrt{\frac{2}{3}} T \)
\( T_{1}=\frac{\sqrt{3}}{2} T \)


Which of the following is not included in micronutrients?
\( A \cdot Z n \) and \( M n \)
B. B and Cu
c. \( \mathrm{Cl} \) and \( \mathrm{Ni} \)
D. K and s


The initial velocity of a particle is \( u \)
\( (a t t=0) \) and the acceleration is given
by \( \boldsymbol{f}=\boldsymbol{a t} . \) Which of the following
relations is valid?
A \( \cdot v=u+a t^{2} \)
B. \( v=u+\frac{a t^{2}}{2} \)
\( \mathbf{c} \cdot v=u+a t \)
\( \mathbf{D} \cdot v=u \)


Which of the following is a semisynthetic polymer?
A. Rubber
B. Silk
c. wool
D. Cellulose nitrate


If pressure of a gas contained in a closed vessel is increased by \( 0.4 \% \) when heated by \( 1^{0} C, \) the initial temperature
must be
A. 250K
B \( \cdot 250^{0} C \)
c. 2500k
D \( .25^{\circ} \mathrm{C} \)


Pick out the correct statements
This question has multiple correct options
A. The ratio of vapour pressure over solution phase on mixing two immiscible liquids is equal to ratio of their moles in vapour phase
B. The ratio of vapour pressure over solution phase on mixing two miscible liquids is equal to ratio of their moles in liquid phase
C. The ratio of vapour pressure over solution phase on mixing two miscible liquids is equal to ratio of the product of their vapour pressure and their moles fraction in a liquid phase
D. The ratio of vapour pressure over solution phase on mixing two miscible liquids is equal to ratio of the product of their vapour pressure and their mole fraction in vapour phase


When yeast and sugar solution are left to stand without oxygen for some time they develop a characteristic smell due to the production of new compound, which is
A. Ethanol
B. Ammonia
c. Carbondioxide
D. Sodium carbonate


State whether the following statement
is True or False.

The sum of two odd numbers and one
even number is even.
A. True
B. False


Reaction of which among the following ether with \( H I \) in cold leads to the
formation of methyl alcohol?
A. Ethyl methyl ether
B. Methyl propyl ether
c. Isopropyl methyl ether
D. tert-butyl methyl ether


Find the value of \( x, \) if:
\( \tan ^{-1}\left(\frac{x-2}{x-1}\right)+\tan ^{-1}\left(\frac{x+2}{x+1}\right)=\frac{\pi}{4} \)


The circumference of the base of a
circular cylinder is \( 6 \pi \mathrm{cm} . \) The height of
the cylinder is equal to the diameter of the base. How many litres of water can it hold?
A . \( 0.54 \pi \) litres
B. \( 0.6 \pi \) litres
c. \( 0.5 \pi \) litres
D. \( 0.4 \pi \) litres


According to Maxwell's theory the value of \( \frac{1}{\sqrt{\mu_{0} \epsilon_{0}}} \) for free space represents:
A. Wave length in any medium
B. Frequency of light
c. speed of light in vacuum
D. Dual nature of light


A mixture of \( 1.65 \times 10^{21} \) molecules of \( x \)
and \( 1.85 \times 10^{21} \) molecules of \( Y \) weighs
0.688 g. If molecular mass of Y is 187 what is the molecular mass of \( X ? \)
A .41 .35
B. 42.35
c. 41.65
D. 41.75


(a)Name the chemical that cements
animal cells.
(b)Name two contractile proteins.
(c)What is the difference between RNA
and DNA in their nitrogen bases.


Nuclear-fusion chain initiation reaction
is endothermic and further reaction is
exothermic.
A. True
B. False


Which fungi is harmful to sericulture?
A. Babesia
B. Monocystis
c. Nosema
D. Plasmodium


Choose the correct statements -
This question has multiple correct options
A. A change in one unit in the pH corresponds to a tenfold change in concentration
B. Solution of \( \mathrm{pH} 1 \) or more are considered strongly acidic
C. Solutions with pH less than 7 but greater than 1 are weakly acidic.
D. A solution of \( \mathrm{pH} 6 \) is 100,000 times less acidic than a solution of \( \mathrm{pH} 1 \)


The power of a lens is \( +2.0 D . \) Find its focal length and state the kind of the lens.
A. Convex, \( 50 \mathrm{cm} \)
B. Convex, \( 200 \mathrm{cm} \)
c. concave, \( 50 \mathrm{cm} \)
D. Concave, \( 100 \mathrm{cm} \)


The length of a given cylindrical wire is increased by \( 150 \% \). Due to the consequent decrease in diameter the
change in the resistance of the wire will be
\( \mathbf{A} \cdot 200 \% \)
B. \( 525 \% \)
c. \( 300 \% \)
D. 400\%


One end of a uniform bar of weight \( \boldsymbol{w}_{1} \) is suspended from the roof and a weight
\( \boldsymbol{w}_{2} \) is suspended from the other end, the area of cross-section is A. What is the
stress at the mid point of the rod?
A. \( \frac{w_{1}+w_{2}}{A} \)
в. \( \frac{w_{1}-w_{2}}{A} \)
c. \( \frac{\left(w_{1} / 2\right)+w_{2}}{A} \)
D. \( \frac{w_{2} / 2+w_{1}}{A} \)


A machine, which is 75 percent efficient uses 12 joules of energy in lifting up a 1 kg mass through a certain distance. The mass is then allowed to
fall through that distance. What will its
velocity be at the end of its fall?
A \( \cdot \sqrt{32} \mathrm{m} / \mathrm{s} \)
B. \( \sqrt{24} m / s \)
c. \( \sqrt{18} \mathrm{m} / \mathrm{s} \)
D. \( \sqrt{9} m / s \)


single Correct Answer Type The path of a projectile is given by the
equation \( y=a x-b x^{2}, \) where \( a \) and \( b \)
are constants and \( x \) and \( y \) are
respectively horizontal and vertical distances of projectile from the point of projection. The maximum height attained by the projectile and the angle of projection are respectively:
A \( \cdot \frac{2 a^{2}}{b}, \tan ^{-1}(a) \)
B. \( \frac{b^{2}}{2 a}, \tan ^{-1}(b) \)
c. \( \frac{a^{2}}{b}, \tan ^{-1}(2 b) \)
D \( \cdot \frac{a^{2}}{4 b}, \tan ^{-1}(a) \)


How can quick lime be prepared from
slaked lime?
A. By cooling slaked lime
B. By heating slaked lime
c. By adding water
D. None of these


In the dichromate dianion, the nature of
bonds are:
A. four equivalent \( C r-O \) bonds
B. six equivalent \( C r-O \) bonds and one \( O-O \) bond
C . six equivalent \( C r-O \) bonds and one \( C r-C r \) bond
D. six non-equivalent \( C r-O \) bonds
E. six equivalent \( C r-O \) bonds and one \( C r-O-C r \)
bond


Which of the following metals reacts
with \( \boldsymbol{H}_{2} \boldsymbol{S O}_{4} ? \)
A. \( A u \)
в. \( A g \)
\( c \cdot P t \)
D. \( P b \)


Offspring formed due to sexual reproduction have better chances of survival. Why? Is this statement always true?


An vehicle has a mass of 1500 kg. What must be the force between the vehicle
and the road if the vehicle is to be
stopped with a negative acceleration of \( 1.7 m s^{-2} ? \)
A. \( 2550 N \) in a direction opposite to that of the vehicle
B. \( 2550 N \) in a direction same to that of the vehicle
c. \( 1550 N \) in a direction opposite to that of the vehicle
D. \( 1550 N \) in a same opposite to that of the vehicle


A source of light suspended above a circular table at a height equal to the radius of the table gives an intensity at the centre of the table, the intensity at the edge of the table would be (Assuming illuminance remains the same)
A . 0.251
B. 0.5 ।
c. 0.71
D. 2.81


Find the dimensions of:
(i) Power
(ii) Forces and (iii)
Permittivity of vacuum \( \left(\varepsilon_{o}\right) \)


Mention the role of Methanobacterium
in rumen of cattle


If the unit of velocity is equal to the velocity of light and the unit of
acceleration is \( 10 m s^{-2}, \) then the unit
of time is
\( \mathbf{A} \cdot 3 \times 10^{7} s \)
В. \( 3 \times 10^{-7} s \)
c. \( 3 \times 10^{-5} s \)
D. \( 3 \times 10^{-4} s \)


If \( \mu \) is the permeability and \( \epsilon \) is the permittivity then \( \frac{1}{\sqrt{\mu \epsilon}} \) is equal to
A. speed of sound
B. speed of light in vacuum
c. speed of sound in medium
D. speed of light in medium


The unit of rate and rate constant are
same for a:
A. zero order reaction
B. First order reaction
c. second order reaction
D. Third order reaction


Which of the following is/are nondisposable batteries? This question has multiple correct options
A. Dry cell
B. Mercury cell
c. Lead acid battery
D. \( N i-C d \) battery


Why is steel is more elastic than
rubber?


What is the atomic number of the
element Ununnilium?
A . 199
в. 191
\( c .119 \)
D. 110


Photorespiration is favoured by
A . Low light and high \( O_{2} \)
B. Low \( O_{2} \) and high \( C O_{2} \)
C. Low temperature and high \( O_{2} \)
D. High \( O_{2} \) and low \( C O_{2} \)


An atom has mass number 23 and
atomic number 11. How many protons, electrons and neutrons are present in
the atom?
A. 11,12,13
B. 11,11,12
c. 11,11,13
D. 11,14,15


Which of the following have been arrange in order of decreasing oxidation number of sulphur? This question has multiple correct options
A \( \cdot N a_{2} S_{4} O_{6}>H_{2} S_{2} O_{7}>N a_{2} S_{2} O_{3}>S_{8} \)
в. \( S O_{2}^{+}>S O_{4}^{2-}>S O_{3}^{2-}>H S O_{4} \)
c. \( H_{2} S O_{5}>H_{2} S O_{3}>S C l_{2}>H_{2} S \)
D. \( H_{2} S O_{4}>S O_{2}>H_{2} S>H_{2} S_{2} O_{8} \)


The statement \( \boldsymbol{p} \rightarrow(\boldsymbol{q} \rightarrow \boldsymbol{p}) \) is
equivalent to
A \( \cdot p \rightarrow(p \wedge q) \)
в. \( p \rightarrow(p \leftrightarrow q) \)
c. \( p \rightarrow(p \rightarrow q) \)
D. \( p \rightarrow(p \vee q) \)


The respiratory substrate yielding maximum number of ATP molecules
among the following is
A. Glycogen
B. Amylase
c. Ketogenic amino acid
D. Glucose


The maximum current flowing long time after the switch \( \mathrm{S} \) is moved to \( \mathrm{B} \)
should be
A. 0.707 A
B. 1.0 \( A \)
\( c \cdot 0.5 \mathrm{A} \)
D. 1.414 A


The equilibrium constant \( \boldsymbol{K}_{c} \) for the reaction:
\( \boldsymbol{C u}(\boldsymbol{s})+\boldsymbol{2} \boldsymbol{A} \boldsymbol{g}^{+}(\boldsymbol{a} \boldsymbol{q} \cdot) \rightleftharpoons \boldsymbol{C} \boldsymbol{u}^{2+}(\boldsymbol{a} \boldsymbol{q} \cdot)+ \)
\( \mathbf{2} \boldsymbol{A} \boldsymbol{g}(\boldsymbol{s})\left(\boldsymbol{E}_{c e l l}^{\circ}=\mathbf{0 . 4 6} \boldsymbol{V}\right) \) will be:
A. antilog 15.6
B. antilog 2.5
c. antilog 1.5
D. antilog 12.2


Which of the following is not soluble in
water?
A. \( H_{2} \)
в. \( O_{2} \)
\( c \cdot s O_{2} \)
D. \( C O_{2} \)


A wooden toy in the form of cone surmounted on a hemisphere. The
diameter of the base of the cone is \( 6 \mathrm{cm} \)
and height is \( 4 \mathrm{cm} \). find the cost of painting the toy at the rate of \( R s .5 \) per
\( 1000 \mathrm{cm}^{2} \)


The IUPAC name of succinic acid is


Give equations for the racharging of a
lead storage battery.


The correct order of radii is:
\( \mathbf{A} \cdot L i<B e<M g \)
B \( \cdot B e^{+2}<L i^{+}<H^{-} \)
\( \mathbf{C} \cdot M n^{3+}<M n^{2+}<M n^{+7} \)
D. \( K^{+}>C l^{-}>S^{2-} \)


Which of the following oxide is most
acidic ?
A \( \cdot P_{2} O_{5} \)
в. \( N_{2} O_{5} \)
\( \mathrm{c} \cdot \operatorname{Sb}_{2} \mathrm{O}_{5} \)
D. \( A s_{2} O_{6} \)


Solve
\( -12-(10 \div 5)+5-(-2 \times 3+5)+ \)
\( \mathbf{6}-\{(-\mathbf{2} \times \mathbf{3}) \times \mathbf{1}+(-\mathbf{3}-\mathbf{5})\} \)


Professor Birbal Sahani discovered 100
million years old fossil plant from fossi forest at Rajmahal Hills, Bihar. This
plant was
A. Rhynia
B. Horneophyton
c. williamsonia
D. Red alga


Estimate the distance for which ray
optics is good approximation for an aperture of 4 mm and wavelength
\( 400 n m \)


The bending of light near the edges of an obstacle and spreading into the region of geometrical shadow is called
A . Interference
B. Diffraction
c. Polarization
D. Doppler effect


Which of the following is the tallest goat breed found in India?
A. Kanni aadu
B. Kodi aadu
c. Black Bengal
D. Jamunapari


Thin film interference happens with
This question has multiple correct options
A. point or spherical source
B. board source
C. film thickness of the order of 10,000 A
D. very thick transparent slabs


Let the line \( \frac{\boldsymbol{x}-\mathbf{2}}{\mathbf{3}}=\frac{\boldsymbol{y}-\mathbf{1}}{-\mathbf{5}}=\frac{\boldsymbol{z}+\mathbf{2}}{\mathbf{2}} \) lie
in the plane \( x+3 y-\alpha z+\beta=0 . \) Then
\( (\alpha, \beta) \) equals:
A \( \cdot(-6,7) \)
B \( \cdot(5,-15) \)
c. (-5,5)
D. (6,-17)


Breathing rate increase during physical exercise because
A. Cells require extra oxygen
B. Cells require extra energy
c. Cells require carbon dioxide
D. Both A and B


Write the degree of the following polynomial:
\( 7 x^{3}+5 x^{2}+2 x-6 \)


\( \boldsymbol{C u} \boldsymbol{S O}_{4} \) is paramagnetic while \( \boldsymbol{Z} \boldsymbol{n} \boldsymbol{S} \boldsymbol{O}_{4} \)
is diamagnetic because:
A. \( C u^{2+} \) ion has \( 3 d^{9} \) configuration while \( Z n^{2+} \) ion has \( 3 d^{10} \) configuration
B. \( C u^{2+} \) ion has \( 3 d^{5} \) configuration while \( Z n^{2+} \) ion has \( 3 d^{6} \) configuration.
\( \mathrm{c} \cdot \mathrm{Cu}^{2+} \) has half filled orbitals while \( Z n^{2+} \) has fully filled orbitals
D. \( C u S O_{4} \) is blue in colour while \( Z n S O_{4} \) is white


If \( S=18+17 \frac{1}{3}+16 \frac{2}{3}+\ldots \ldots .=242 \)
then the number of terms are:
A .22
B . 33
c. Both 22 and 33
D. none of these


If \( |\widehat{a}-\widehat{b}|=\sqrt{3}, \) then \( |\widehat{a}+\widehat{b}| \) may be:
A .
B. \( \frac{\sqrt{3}}{2} \)
c. Either (1) and (2)
D. None of these


What is the cause of Green house
effect?
A. Infrared rays
B. Ultraviolet rays
c. x-rays
D. Radio waves


If \( k \epsilon R^{+} \) and the middle term of \( \left(\frac{k}{2}+\right. \)
2) \( ^{8} \) is \( 1120, \) then value of \( k \) is
\( \mathbf{A} \cdot \mathbf{3} \)
B. 2
c. 1
D.


The colour of \( M n O_{4}^{-} \) ion is due to:
A. unpaired d-electrons
B. \( d \) -d transition
c. d-p transition
D. charge transfer


The resultant intensity for two identical waves of intensity I with a phase difference of \( \pi / 3 \) is
B . \( R=\sqrt{3 I} \)
D. \( R=3 \sqrt{3 I} \)


Fig shows an arrangment of masses hanging from a ceiling. In equilibrium, each rod is horizontal, has negligible
mass and extends three times as far to
the right of the wire supporting it as to
the left. If mass \( m_{4} \) is \( 48 \mathrm{kg} \) then mass
of \( m_{1} \) is equal to
A . \( 1 k g \)
в. \( 2 k g \)
\( c .3 k g \)
D. \( 4 k g \)


What is the degree of the differential eqaution \( : \frac{d^{3} y}{d x^{3}}-6\left(\frac{d y}{d x}\right)^{2}-4 y=0 \)
\( A \)
B. 2
\( c \cdot 3 \)
D. None of these


Which among the following has highest melting point?
A \( \cdot\left(C H_{3} C O\right)_{2} O \)
в. \( C H_{3} C N \)
c. \( C H_{3} C O N H_{2} \)
D. \( C H_{3} C O C l \)


Find the common solution:
\( \boldsymbol{y}=\mathbf{3} \boldsymbol{x}+\mathbf{1} \)
\( \boldsymbol{x}+\boldsymbol{y}=\mathbf{9} \)


A \( 1 \mathrm{kg} \) body slides from the point \( \mathrm{A} \) along a horizontal track with an initial
speed of \( 6 m s^{-1} \) towards a weightless
horizontal spring of length \( 2 \mathrm{m} \) and force constant \( 4 N m^{-1} \).The part \( A B \) of the track is frictionless and the part
BC has the coefficients of static and
dynamic friction 0.22 and 0.2 respectively. Find the total distance through which the block moves before it comes to rest completely \( \left(g=10 m s^{-2}\right. \)
)
if \( A B=4 \mathrm{m} \) and \( B D=4.28 \mathrm{m} \)


For gaseous reaction, the rate is often expressed in terms of dP/dt instead of dc/dt or dn/dt (where c is the
concentration and \( n \) the number of mol)
What is the relation among these three expressions?
A \( \cdot \frac{d c}{d t}=\frac{1}{V}\left(\frac{d n}{d t}\right)=\frac{1}{R T}\left(\frac{d P}{d t}\right) \)
в. \( \frac{d c}{d t}=\left(\frac{d n}{d t}\right)=\left(\frac{d P}{d t}\right) \)
\( ^{\mathbf{c}} \cdot \frac{d c}{d t}=\left(\frac{d n}{d t}\right)=\frac{V}{R T}\left(\frac{d P}{d t}\right) \)
D. None of these


If the functions \( f(x) \) and \( g(x) \) are continuous on \( [a, b] \) and differentiable on \( (a, b), \) then in the interval \( (a, b), \) the
equation \( \left|\begin{array}{ll}\boldsymbol{f}^{\prime}(\boldsymbol{x}) & \boldsymbol{f}(\boldsymbol{a}) \\ \boldsymbol{g}^{\prime}(\boldsymbol{x}) & \boldsymbol{g}(\boldsymbol{a})\end{array}\right|=\frac{1}{\boldsymbol{a}-\boldsymbol{b}}\left|\begin{array}{ll}\boldsymbol{f}(\boldsymbol{a}) & \boldsymbol{f}(\boldsymbol{b}) \\ \boldsymbol{g}(\boldsymbol{a}) & \boldsymbol{g}(\boldsymbol{b})\end{array}\right| \)
A. has at least one root
B. has exactly one root
c. has at most one root
D. no root


character of the
metals give rise to certain characteristic chemical properties of
metals.
A. Electronegative
B. Electropositive
c. Neutral
D. All of the above


The long form of periodic table is nothing but just a graphical representation of principle.
A. Aufbau
B. Hunds
c. Pauli exclusion
D. wave mechanical


Write the examples of animal fiber


Two particles \( A \) and \( B \) are moving with
constant velocities \( v_{1} \) and \( v_{2} \cdot A t t=0, v_{1} \)
makes an angle \( \theta_{1} \) with the line joining
\( A \) and \( B \) and \( v_{2} \) makes an angle \( \theta_{2} \) with
the line joining \( A \) and \( B \). Find their
velocity of approach


(a) What are the defects of eye? How are
these rectified?
(b) Observe the figure and answer the following questions:
(i) What does the given diagram
represent?
(ii) Write the principle of the device
denoted in the given diagram.


\( \tan \left[\frac{\pi}{4}+\frac{1}{2} \cos ^{-1}\left(\frac{5}{7}\right)\right]+ \)
\( \cot \left[\frac{\pi}{4}+\frac{1}{2} \cos ^{-1}\left(\frac{5}{7}\right)\right] \) is equal to
\( A \cdot \frac{5}{7} \)
B. \( \frac{10}{7} \)
c. \( \frac{14}{5} \)
\( D \cdot \frac{7}{5} \)


Chemical kinetics, a branch of physical chemistry, deals with:
A. heat changes in a reaction
B. physical changes in a reaction
c. rate of reactions
D. structure of molecules


The correct order of decreasing acidity
of nitrophenols will be:
A. \( m- \) nitrophenol \( >p- \) nitrophenol \( >o \) - nitrophenol
B. \( o \) - nitrophenol \( >m- \) nitrophenol \( >p- \) nitrophenol
c. \( p- \) nitrophenol \( >m- \) nitrophenol \( >o- \) nitrophenol
D. \( p- \) nitrophenol \( >o \) - nitrophenol \( >m- \) nitrophenol


Hydronium exist even in pure water
A. True
B. False


A system is said to be in
thermodynamic equilibrium with
Surrounding
¡f
A. it is only in thermal equilibrium with surrounding.
B. it is in both thermal and chemical equilibrium with surrounding.
C. it is in thermal, chemical as well as mechanical equilibrium with the surrounding.
D. it is in thermal and mechanical equilibrium, but not in chemical equilibrium with surrounding.


\( \left|\begin{array}{cc}\sin ^{2} \theta & \cos ^{2} \theta \\ -\cos ^{2} \theta & \sin ^{2} \theta\end{array}\right|= \)
\( \mathbf{A} \cdot \cos 2 \theta \)
в. \( \frac{1}{2}\left(1+\cos ^{2} 2 \theta\right) \)
c. \( \frac{1}{2}\left(1-\sin ^{2} 2 \theta\right) \)
D. \( \frac{1}{2} \sin ^{2} 2 \theta \)


Explain Displacement reaction with examples


When huge amount of \( \mathrm{CO}_{2} \) is dumped into a river, the BOD will
A. Increase
B. Slightly decrease
c. Remain unchanged
D. Decrease


If \( \boldsymbol{y}^{2}=\boldsymbol{P}(\boldsymbol{x}) \) is a polynomial of degree
3, then \( 2 \frac{d}{d x}\left(y^{3} \frac{d^{2} y}{d x^{2}}\right) \) is equal to
A \( \cdot P(x)+P^{\prime}(x) \)
в. \( P(x) P^{\prime}(x) \)
c. \( P(x) P^{\prime \prime \prime}(x) \)
D. a constant


State two conditions for sustained
interference of light. Also write the
expression for the fringe width


A ring of mass \( 3 k g \) is rolling without
slipping with linear velocity \( 1 \mathrm{ms}^{-1} \) on a smooth horizontal surface. A rod of
same mass is fitted along its one
diameter. Find total kinetic energy of the system (in \( J \) ).


The sequence \( -6+42-294+2058 \) is
\( a \)
A . finite geometric sequence
B. finite arithmetic sequence
C. infinite geometric sequence
D. infinite harmonic sequence


Breathing rate increases which of the following value?
A. Pulse rate
B. Metabolic rate
c. Exhalation
D. All of the above


A sphere and the base of a cylinder have equal radii. The diameter of the sphere
is equal to the height of the cylinder. The ratio of the curved surface area of
the cylinder and surface area of the sphere is
A . 1: 1
B. 2: 3
c. 3: 2
D. 1: 2


Dyes like cosin and fluorescein are used as indicator in titrating bromide solution with \( Z n S O_{4} \)
A. True
B. False


For a particular reversible reaction at
temperature \( T, \Delta H \) and \( \Delta S \) were found
to be both +ve. If \( T_{e} \) is the temperature at equilibrium, the reaction would be
spontaneous when:
A \( \cdot T_{e}>T \)
в. \( T>T_{e} \)
\( \mathbf{c} \cdot T_{e} \) is 5 times \( T \)
D. \( T=T_{e} \)


If \( y=\sqrt{\frac{1-x}{1+x}}, \) then \( \frac{d y}{d x} \) equals
A \( \cdot \frac{y}{1-x^{2}} \)
в. \( \frac{y}{x^{2}-1} \)
c. \( \frac{y}{1+x^{2}} \)
D. \( \frac{y}{y^{2}-1} \)


An electric dipole of moment p is kept along an electric field E. The work done
in rotating it from an equilibrium
position by an angle \( \boldsymbol{\theta} \) is :
\( A \cdot P E(1-\cos \theta) \)
B. PE(1 - \( \sin \theta \) )
c. \( P E \cos \theta \)
D. PE sin \( \theta \)


\( 2^{\circ} \) halide among the following is:
A. Isopropyl chloride
B. Isobutyl chloride
c. n-propyl chloride
D. n-butyl chloride


Find the sum of interior angles of a
polygon with 8 sides.


Calculate the Number of \( 3^{\circ} \) -free radical
formed by homolysis of C-H bonds of alkanes having molecular formula
\( \mathbf{C}_{6} \boldsymbol{H}_{14} \)


\( 1+3+6+10+\ldots \) upto \( n \) terms is equal to
A \( \cdot \frac{1}{3} n(n+1)(n+2) \)
B \( \cdot \frac{1}{6} n(n+1)(n+2) \)
c. \( \frac{1}{12} n(n+2)(n+3) \)
D \( \cdot \frac{1}{12} n(n+1)(n+2) \)


Two rods of different materials having coefficients of thermal expansion and
Young's moduli \( Y_{1}, Y_{2}, \) respectively are
fixed between two rigid massive walls. The rods are heated such that undergo the same increase in temperature.
There is no bending of the rods. If \( \boldsymbol{\alpha}_{1}: \)
\( \boldsymbol{\alpha}_{2}=\boldsymbol{2}: \boldsymbol{3}, \) the thermal stresses
developed in the two rods are equal
provided \( Y_{1}: Y_{2} \) is equal to:
A .2: 3
B. 1: 1
c. 3: 2
D. 4: 9


Which of the following numbers has the terminal decimal representation?
A \( \cdot \frac{1}{7} \)
B. \( \frac{1}{3} \)
\( c \cdot \frac{3}{5} \)
D. \( \frac{17}{3} \)


n \( \triangle \boldsymbol{P Q R}, \boldsymbol{P Q}=\boldsymbol{P R}, \angle \boldsymbol{Q}=\mathbf{6 5}^{\circ} \) then
find \( \angle P \)


Reflected sound waves are called


toppr \( t \)
Q Type your question
This question has multiple correct options
\( A \)
B.
\( c \)
D


The zone refining process of metals is
based on the principle of :
A. excess noble character of the liquid metal than that of impurity
B. lower melting point of the impurity than that of pure metal
c. greater solubility of impure metal than that of impurity
D. greater solubility of the impurities in the molten state than in the solid


At a harbour, a boat is standing and wind is blowing at a speed of \( \sqrt{2} \mathrm{m} / \mathrm{sec} \) due to which, the flag on the boat flutters along northeast. Now the boat enters in to river, which is flowing with a velocity of \( 2 \mathrm{m} / \mathrm{sec} \). due north. The boat
starts with zero velocity relative to the river and its constant acceleration
relative to the river is \( 0.2 m / s e c^{2} \) due east. In which direction will the flag
flutter at 10 seconds?
A. south-east
B. south-west
c. \( 30^{\circ} \) south of west
D. west


Pressure exerted by a sharp needle on a
surface is :
A. More than the pressure exerted by a blunt needle.
B. Less than the pressure exerted by a blunt needle.
C. Equal to the pressure exerted by a blunt needle.
D. None of these.


A horizontal force of \( 500 N \) pulls two
masses \( 10 k g \) and \( 20 k g \) connected by a light string and placed on a frictionless horizontal table. What is the tension in
the string if the force is applied on the \( 20 k g \) mass?
A. \( 333.3 N \)
N
в. \( 166.7 N \)
c. \( 233.3 N \)
D. \( 217 N \)


Soap removes grease by:
A. adsorption
B. emulsification
C . coagulation
D. none of these


If relation \( \mathrm{R}= \)
\( \{(x, x+2): x \in N, 1 \leq x<4\} \) then \( R \)
is
в. \{(2,3),(4,2),(5,3)\}
c. \{(1,3),(2,4),(3,5),(4,6)\}
D. none of these


Find the median class of the following
distribution.
\( \begin{array}{ll} \text { Weight }\operatorname{(in} k g) & \text { Number of students } \\ 45-47 & 7 \\ 47-49 & 5 \\ 49-51 & 8 \\ 51-53 & 12 \\ 55-57 & 2 \\ 57-59 & 10\end{array} \)


Who is the father of microscopy and microbiology?
A. Theophrastus
B. Janssen
c. Leeuwenhoek
D. Hooker


When force \( F \) acts on side of hexagonal
body for what range of coefficient of friction will body topple?
A \( \cdot \mu>\frac{1}{2 \sqrt{3}} \)
В. \( _{\mu}<\frac{1}{2 \sqrt{3}} \)
c. \( \mu>\frac{\sqrt{3}}{2} \)
D. \( _{\mu}<\frac{\sqrt{3}}{2} \)


Convert \( \frac{\mathbf{4 6}}{\mathbf{5}} \) into percentage.
A . \( 92 \% \)
B. \( 920 \% \)
c. \( 9.2 \% \)
D. \( 0.92 \% \)


A body of weight \( 50 \mathrm{N} \) is placed on a smooth surface. If the force required to move the body on the surface is 30 N
the coefficient of friction is
A . 0.60
B. 1.2
\( c \cdot 0.3 \)
D. 1.67


Change the following radian measure to degree measure:
\( \frac{3 \pi}{2} \)
A \( \cdot 120^{\circ} \)
\( ^{\circ} \)
B \( .240^{\circ} \)
\( c .270^{\circ} \)
D. \( 300^{\circ} \)


Find the area of the sector whose arc
length and radius are \( 14 \mathrm{cm} \) and \( 6 \mathrm{cm} \) respectively


Is the use of contraceptives justified?
Give reasons.


\( P \) and \( Q \) are the foci of the ellipse \( \frac{x^{2}}{a^{2}}+ \) \( \frac{y^{2}}{b^{2}}=1 \) and \( B \) is an end of the minor
axis. If \( \triangle P B Q \) is an equilateral triangle, the eccentricity of the ellipse is:
A \( \cdot \frac{1}{\sqrt{2}} \)
в. \( \frac{1}{3} \)
\( c \cdot \frac{1}{2} \)
D. \( \frac{\sqrt{3}}{2} \)


How many ions \( 1.75 \mathrm{cm} \) in diameter
and 2 mm thick must be melted to
form a cuboid \( 11 \mathrm{cm} \times 10 \mathrm{cm} \times 7 \mathrm{cm} ? \)


Which of the following is a bactericidal antibiotic?
A. Ofloxacin
B. Tetracycline
c. chloramphenicol
D. Erythromycin


In the following Ellingham diagram, \( x, Y \) and \( z \) represent graphs for metal
oxides. Select the correct option.
A. Y will reduce oxide of
3. Y will reduce oxide of \( x \)
c. z will reduce oxide of \( x \)
D. z will reduce oxide of \( Y \)


If \( f(x)=(12 x)^{3 / 2}, \) and \( n=f(3), \) what
is the value of 2 n?


Show that the following system of linear equations is consistent and also find their solution:
\( \mathbf{5} \boldsymbol{x}+\mathbf{3} \boldsymbol{y}+\mathbf{7} \boldsymbol{z}=\mathbf{4} \)
\( \mathbf{3} \boldsymbol{x}+\mathbf{2 6} \boldsymbol{y}+\mathbf{2} \boldsymbol{z}=\mathbf{9} \)
\( \mathbf{7} \boldsymbol{x}+\mathbf{2} \boldsymbol{y}+\mathbf{1 0} \boldsymbol{z}=\mathbf{5} \)


Pick out the wrong statement about the
properties of covalent compounds.
A. They posses high melting and boiling points
B. They have poor thermal and electrical conductivity
C. They are generally soft or brittle
D. they have low enthalpies of fusion and vaporization


We have seen that a gamma-ray does of 3Gy is lethal to half the people exposed to it. If the equivalent energy were absorbed as heat, what rise in body temperature would result?
A. 600
B. 500
c. 700
D. 900


Which of the following practices will
come under green chemistry?
A. If possible, making use of soap made of vegetable oils instead of using synthetic detergents
B. Using \( H_{2} O \) for bleaching purpose instead of using chlorine based bleaching agents
C. Using bicycle for travelling small distances instead of using petrol/diesel based vehicles
D. All of these


A perfect gas at \( 27^{0} C \) is heated at constant pressure so as to double its
volume. The increase in temperature of the gas will be
\( \mathbf{A} \cdot 300^{0} C \)
B . \( 54^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 327^{0} C \)
D. \( 600^{\circ} \mathrm{C} \)


What are electromagnetic waves? Write
its nature.


\( I_{1} \) is moment of inertia of a thin circular
ring about its own axis. The ring is cut at a point then it is unfolded into a
straight rod. If \( I_{2} \) is moment of inertia of
the rod about an axis perpendicular to the length of rod and passing through
its centre, then the ratio of \( I_{1} \) to \( I_{2} \) is:
A . \( 3: \pi \)
B. \( 3: \pi^{2} \)
c. \( 4: \pi \)
D. \( 4: \pi^{2} \)


The mean of the following data is 50 Find the value of a and hence the
frequencies of 30 and 70
\[
\begin{array}{cccccc}
\boldsymbol{X} & \mathbf{1 0} & \mathbf{3 0} & \mathbf{5 0} & \mathbf{7 0} & \mathbf{9 0} \\
\boldsymbol{F} & \mathbf{1 7} & \mathbf{5 a + 3} & \mathbf{3 2} & \mathbf{7 a - 1 1} & \mathbf{1 9}
\end{array}
\]
A .28 and 34
B. 68 and 24
c. 28 and 24
D. None of these


A uniform disc of mass \( m \) is fitted
(pivoted smoothly) with a rod of mass
\( m / 2 . \) If the bottom of the rod is pulled
with a velocity \( v, \) it moves without changing its angle of orientation and the disc rolls without sliding. Find the
kinetic energy of the system \( (r o d+ \)
\( \operatorname{disc} \)


A metallic spherical shell has an inner
radius \( \boldsymbol{R}_{1} \) and outer radius \( \boldsymbol{R}_{2} . \) A charge
is placed at the centre of the spherical cavity. The surface charge density on
the outer surface is
A \( \cdot \frac{-q}{4 \pi R_{1}^{2}} \)
В. \( \frac{q}{4 \pi R_{2}^{2}} \)
c. \( \frac{q^{2}}{4 \pi R_{1}^{2}} \)
D. \( \frac{2 q}{4 \pi R_{2}^{2}} \)


A capacitor of capacitance \( C \) has initial
charge \( Q_{0} \) and connected to an
inductance \( L . \) At \( t=0 \) switch \( S \) is
closed. The current through the inductor when energy in the capacitor is three times the energy of the inductor is :
A \( \cdot \frac{Q_{0}}{2 \sqrt{L C}} \)
в. \( \frac{Q_{0}}{\sqrt{L C}} \)
c. \( \frac{2 Q_{0}}{\sqrt{L C}} \)
D. \( \frac{4 Q_{0}}{\sqrt{L C}} \)


For a wave propagating in a medium, identity the property that is independent of the others
A. Velocity
B. Wavelength
c. Frequency
D. All these depend on each other


A toroid is
A. a finite
B. an endless
C . straight
D. either A or B


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


Degeneration of a genetic code is attributed to the
A. First member of a codon
B. Second member of a codon
c. Entire codon
D. Third member of a codon


What is different for isotopes of uranium?
A. Number of protons
B. Numbers of planetary electrons
c. Atomic masses
D. Atomic numbers


One litre of water contains \( 1.0 \times 10^{-7} \)
moles of \( \boldsymbol{H}^{+} \) ions. The degree of
ionization of water is:
A \( \cdot 1.8 \times 10^{-9} \% \)
В. \( 0.8 \times 10^{-9} \% \)
c. \( 3.6 \times 10^{-9} \% \)
D. \( 3.6 \times 10^{-7} \% \)


Differentiate Lanthanides and
Actinides.


Proconsul is the other name of
A. Dryopithecus
B. Parapithecus
C. Aegyptopithecua
D. Ramapithecus


Thomas slag is:
A \( \cdot C a_{3}\left(P O_{4}\right)_{2} \cdot 2 H_{2} O \)
в. \( C a_{3}\left(P O_{4}\right)_{2} \cdot \) Са \( \operatorname{Si} O_{3} \)
\( \mathbf{c} \cdot M g S i O_{3} \)
D. \( \operatorname{casi} O_{3} \)


When harmful substances such as
sewage, toxic chemicals get mixed with
water, then:
A. the water becomes more pure
B. the water get polluted
c. the water becomes clean and clear
D. none of these


Metamerism is shown by:
This question has multiple correct options
A. diethylether
B. diethylketone
C . diethylamine
D. dimethylether


Evaluate the following limits. \( \lim _{x \rightarrow 1} \frac{x-1}{\sqrt{x^{2}+3}-2} \)


\( \ln \) a point \( v=-5 x+3 y+\sqrt{15} z \) in that point. Find the value of E?


In how much time will a certain sum be
1.5 times the principal at \( 10 \% \) per annum?
A. 1 year
B. 2 year
c. 4 year
D. 5 year


Which of the following character was not selected by Mendel in his experiment?
A. Plant height
B. Plant colour
c. Pod shape
D. Pod colour


A stress - strain relationship shows a straight line that is making an angle of 10 degrees with the strain axis, the material has
A. High Young's modulus of elasticity
B. Low Young's modulus of elasticity
c. Young's modulus of elasticity as zero
D. Young's modulus of elasticity = 1


The compound which does not show
simple ratio of atoms, is


\( \int \frac{2 x}{\sqrt{1-x^{2}-x^{4}}} d x \)


\( \boldsymbol{H}^{+}, \boldsymbol{D}^{+} \) and \( \boldsymbol{T}^{+} \) differ in all except in:
A. number of electrons
B. number of neutrons
c. ionic mass
D. all are correct


COD is a measure of:
A. organic substance in water
B. oxides of sulphur, phophorus,nitrogen in water
C. inorganic pollutants in water
D. salinity of water


Write any five salient features of
International Code of Botanical
Nomenclature (ICBN)


If the line \( 2 x-y+1=0 \) touches the
circle at the point (2,5) and the centre
of the circle on the line \( \boldsymbol{x}+\boldsymbol{y}-\boldsymbol{9}=\mathbf{0} \)
Find the equation of the circle.


Flow of current though electrolyte solution is due to migration of :
A. Ions
B. Electrons
c. Protons
D. Nucle


Solve:
\( \int \sin ^{3} x \cdot \cos ^{2} x d x \)


Find the product in the given reaction.


An electric current runs
counterclockwise in a rectangular loop around the outside edge of the page which lies flat on your table. A uniform magnetic field is then turned on directed parallel to the page from the top to bottom. The magnetic force on the page will cause:
A. the left edge to lift up
B. the right edge to lift up
c. the top edge to lift up
D. the bottom edge to lift up


End product formed in the above reaction is :
\[
\equiv \sim_{\mathrm{CH}_{3}} \widehat{\mathrm{oH}} \frac{\mathrm{H}_{2}}{\mathrm{O}}
\]
A. Optically active
B. Racemic
c. Meso
D. Diastereomer


The IUPAC name of the given compound
is:


Which of the following is the lens
maker's formula
\( \mathbf{A} \cdot 1 / f=(n-1)\left(1 / R_{1}+1 / R_{2}\right) \)
B . \( 1 / f=(n+1)\left(1 / R_{1}-1 / R_{2}\right) \)
\( \mathbf{c} \cdot 1 / f=(n-1)\left(1 / R_{1}-1 / R_{2}\right) \)
D. \( 1 / f=(n+1)\left(1 / R_{1}+1 / R_{2}\right) \)


Find the rational number which is not equal to \( \frac{2}{3} \)
\( A \cdot \frac{-2}{-3} \)
B. \( \frac{-4}{+6} \)
\( c \cdot \frac{8}{12} \)
D. \( \frac{6}{9} \)


Assertion
The unpaired electrons in a subshell
possess same spin.
Reason
Symmetric distribution of electrons
gives stability to an atom.
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


Let \( t \) be a positive integer and \( \Delta_{t}= \) \( \left|\begin{array}{lll}\mathbf{2} t-1 & \boldsymbol{m}^{2}-\mathbf{1} & \cos ^{2}\left(\boldsymbol{m}^{2}\right) \\ \boldsymbol{m}_{C_{t}} & \mathbf{2}^{m} & \cos ^{2}(\boldsymbol{m}) \\ \mathbf{1} & \boldsymbol{m}+\mathbf{1} & \cos \left(\boldsymbol{m}^{2}\right)\end{array}\right| \) then the
value of \( \sum_{t=0}^{m} \Delta_{t} \) is equal to:
\( A \cdot 2^{m} \)
B.
\( \mathbf{c} \cdot 2^{m} \cos ^{2}\left(2^{m}\right) \)
D. \( m^{2} \)


\( \int_{0}^{1} \frac{e^{x}}{1+e^{2 x}} d x \)
\( \mathbf{A} \cdot \tan ^{-1} e-\frac{\pi}{4} \)
B \( \cdot \tan ^{-1} e+\frac{\pi}{4} \)
\( \mathrm{C} \cdot \tan e-\frac{\pi}{4} \)
D. None of these


Internal resistance of a battery cell
increases with:
A. increase in concentration of electrolyte
B. increase in distance between two electrodes
C. increase in area of the plates inside the electrolyte
D. increase in size of the electrodes


The mass of carbon anode consumed
(giving of carbon dioxide) in the production of \( 270 \mathrm{kg} \) aluminium metal bum bauxite by Hall process is: (Atomic
\( \operatorname{mass} A l=27) \)
A. \( 180 \mathrm{kg} \)
в. \( 270 \mathrm{kg} \)
c. \( 540 \mathrm{kg} \)
D. \( 90 \mathrm{kg} \)


A five-digit number divisible by 3 is to be formed using the digits 0,1,2,3 and 4 without repetition of digits. What is
the number of ways this can be done?
\( \mathbf{A} \cdot 96 \)
B. 48
\( c \cdot 32 \)
D. No number can be formed


Define watt. Write down an equation linking watts, volts and amperes.


Plaster of Paris has the formula:
A. \( \operatorname{CaSO}_{4} \cdot(1 / 2) \mathrm{H}_{2} \mathrm{O} \)
в. \( \operatorname{CaSO}_{4} . \mathrm{H}_{2} \mathrm{O} \)
\( \mathrm{c} \cdot \operatorname{CaSO}_{4} \cdot 2 \mathrm{H}_{2} \mathrm{O} \)
D. none of the above


In the estimation of sulphur by Carius method, 0.468 gm of an organic sulphur compound afforded 0.668 gm of barium sulphate. Find out the percentage(in nearest integer) of sulphur in the given compound.


Define chemiosmosis.


The amount of \( N a \) produced by the passage of 2 moles of electrons through the fused \( N a C l \) is \( _{-}-----8 \)
A . 23
B. 46
c. 11.5
D. 34.5


How high does a mercury barometer
stand on a day when atmospheric pressure is \( 98.6 k P a \)


The leaves are modified into pitcher in
A. Drosera
B. Aldrovendra
c. sarracenia
D. Utricularia


Number of R.B.C. is more in persons
living at hills because
A. There is less oxygen
B. Air is more purified
c. Heat is required to warm the body
D. None of these


Two angles are adjacent and form an
angle of \( 100^{\circ} . \) The larger is \( 20^{\circ} \) less than five times the smaller. The larger angle
is
\( \mathbf{A} \cdot 90 \)
B. 70
\( c \cdot 80^{\circ} \)
D. 75


Evaluate :
\( \int \sqrt{\frac{1-\cos 2 x}{1+\cos 2 x}} d x \)


Anthrax can be used as:
A . Pesticides
B. Insecticides
c. Germ bombs
D. All


A certain metal sulphide, \( M S_{2} \), is used
extensively as a high temperature lubricant. If \( M S_{2} \) is \( 40.06 \% \) by mass of
sulphur, metal \( M \) has atomic mass:
\( \mathbf{A} \cdot 160 \) amu
B. 64 amu
c. 40 amu
D. 96 amu


The structure of DNA and RNA are
similar in that
A. Both molecules are made of the same 5 carbon sugar.
B. Both molecules are composed of the same four nitrogenous bases.
C. The nucleotides of both molecules contain a
phosphate group.
D. Both molecules are double stranded which are antiparallel in directionality.


The heat of combustion of ethanol
determined in a bomb calorimeter is
\( -670.48 k c a l m o l^{-1} \) at \( 298 K . \) What is
the \( \Delta U \) at \( 298 K \) for the reaction?
A. -760 kcal \( m o l^{-1} \)
B. -670.48 k cal mol\( ^{-1} \)
c. +760 kcal \( m o l^{-1} \)
D. +670.48 k cal mol\( ^{-1} \)


Check the wrong statement:
A. Line spectrum is characteristic of the element
B. Absorption line spectrum is characteristic of the element
C. Continuous spectrum is characteristic of the source of light
D. There are two prominent yellow lines in the spectrum of sodium


Two blocks \( A \) and \( B \) of masses \( M_{A} \) and
\( M_{B} \) respectively, are located \( 1.0 m \) apart on a horizontal surface. The
coefficient of static friction \( \mu_{s} \) between
the block and the surface is \( 0.50 . \) Block
\( A \) is secured to the surface and cannot
move, what is the minimum mass of
Block \( A \) that provides enough gravitational attraction to move Block
B? The universal gravitation constant is \( 6.67 \times 10^{-11} N m^{2} / k g^{2} .(g= \)
\( 9.8 m s^{-2} \)
A \( \cdot 7.5 \times 10^{9} k g \)
в. \( 7.3 \times 10^{16} k g \)
c. \( 14.7 \times 10^{11} k g \)
D. The problem cannot be solved without knowing the mass of Block \( B \)


The reaction \( \boldsymbol{C H}_{\mathbf{3}}-\boldsymbol{C H}_{\mathbf{2}}-\boldsymbol{N O}_{\mathbf{2}}+ \)
\( \boldsymbol{O H}^{-} \rightarrow \boldsymbol{C H}_{3}-\boldsymbol{C H}-\boldsymbol{N O}_{2}+\boldsymbol{H}_{2} \boldsymbol{O} \)
obeys the rate law for pseudo first order
kinetics in the presence of a large
excess of hydroxide ion. If 1 percent of
nitro ethane undergoes reaction in half a minute when the reactant
concentration is \( 0.002 M, \) the pseudo
first order rate constant is :
A \( \cdot 2 \times 10^{-2} \min ^{-1} \)
B . \( 3 \times 10^{-2} \) min \( ^{-1} \)
c. \( 5 \times 10^{-2} \) min \( ^{-1} \)
D. \( 7 \times 10^{-2} \) min \( ^{-1} \)


For a first order reaction, time required
for \( 99.0 \% \) completion is \( x \) times for the first time required for the completion of
\( 90 \% \) of the reaction \( x \) is:


Renal calculi is made up of
A. Uric, acid, cholestrol
B. Calcium oxalate, cystine
c. cholesterol, calcium
D. Calcium phosphate \& cholesterol


Elements \( A, B \) and \( C \) have respectively
1, 3 and 5 electrons in valence shell.
lonic compound is not formed from :
A. \( A \) and \( C \)
B. \( A \) and \( B \)
\( \mathbf{c} \cdot B \) and \( B \)
D. \( B \) and \( C \)


Which of the following statements
is/are correct?
This question has multiple correct options
A. The freezing point of water is depressed by the addition of glucose.
B. The degree of dissociation of a weak electrolye decrease as its concentration decreases
C. Energy is released when a substance dissolves in water provided that the hydration energy of the substance is more than its lattice energy.
D. If two liquids that form an ideal solution are mixed,the change in entropy is positive.


If \( x^{2}+x-12 \) divides \( P(x)=x^{3}+ \) \( a x^{2}+b x-84 \) exactly, find \( a \) and \( b \).


Two straight lines passing through the point \( A(3,2) \) cut the line \( 2 y=x+3 \) and
x-axis perpendicularly at \( P \) and \( Q \) respectively. The equation of the line PQ
is
A. \( 7 x+y-21=0 \)
B. \( x+7 y+21=0 \)
\( \mathbf{c} \cdot 2 x+y-8=0 \)
D. \( x+2 y+8=0 \)


Add the following rational numbers:
\( \frac{31}{-4} \) and \( \frac{-5}{8} \)


In a compound microscope, the image produced by the objective lens is:
A. real, enlarged and erect
B. real, enlarged and inverted
c. virtual, enlarged and erect
D. virtual, enlarged and inverted


Assertion
Relative atomic mass of chlorine is
35.5
Reason
Chlorine gas is diatomic element.
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


Two coils have a mutual inductance
\( 0.005 H . \) The current changes in the first coil according to the equation \( i= \)
\( i_{m} \sin \omega t \) where \( i_{m}=10 A \) and \( \omega= \)
\( 100 \pi \) rad \( s^{-1} . \) The maximum value of
the emf induced in the second coil is
A \( .2 \pi \)
в. \( 5 \pi \)
c. \( \pi \)
D. \( 4 \pi \)


Ganong's respiroscope is enployed for demonstrating
A. Heat during respiration
B. Evolution of oxygen during respiration
C. Production of CO2 during fermentation
D. Production of CO2 during aerobic respiration


A cylinder is filled with a gaseous mixture containing equal masses of
\( C O \) and \( N_{2} . \) The ratio of their partial
pressure is:
\( \mathbf{A} \cdot P_{N_{2}}=P_{C O} \)
B . \( P_{C O}=0.875 P_{N_{2}} \)
c. \( P_{C O}=2 P_{N_{2}} \)
D. \( P_{C O}=\frac{1}{2} P_{N_{2}} \)


If mercury is used as cathode in the
electrolysis of aqueous NaCl solution, the ions discharged at cathode are:
\( \mathbf{A} \cdot \mathbf{H}^{\mathbf{t}} \)
B. Nat
c. он
D. cᅵ


Compound \( A\left(C_{7} H_{13} B r\right) \) is a tertiary
bromide. On treatment with sodium
ethoxide in ethanol, \( A \) is convert into \( B \)
\( \left(C_{7} H_{12}\right) . \) Ozonolysis of \( B \) gives \( C \) as the
only product. A and B are:
A . A: 1-bromo 1-methylcyclohexane; B:1-methy cyclohexene
B. A: 1-bromo 2-methylcyclohexane; B: 3-methyl cyclohexene
c. A: 1-bromo 1-methylcyclohexane; B methylenecyclohexane
D. None of these


Arrange the following in increasing
lattice energy:
\( \boldsymbol{L} \boldsymbol{i}_{2} \boldsymbol{C} \boldsymbol{O}_{3}, \boldsymbol{N} \boldsymbol{a}_{2} \boldsymbol{C} \boldsymbol{O}_{3}, \boldsymbol{K}_{2} \boldsymbol{C} \boldsymbol{O}_{3} \)


Which of the following is a physical
mean for concentration of ore?
A. Using sodium hydroxide
B. Using electrolysis
c. Froth flotation method
D. None of above


Figure gives a speed-time graph of a particle in motion along a constant direction. Three equal
intervals of time are shown. In which
interval is the average acceleration greatest in magnitude ? In which
interval is the average speed greatest? Choosing the positive direction as the constant direction of motion, give the
signs of \( \mathbf{v} \) and a in the three intervals.
What are the accelerations at the points \( A, B, C \) and \( D ? \)


Assertion
Ionic compounds are bad conductors of electricity.
Reason
In ionic compounds mobile ions exists.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is
not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect and the Reason is correct


The number of sigma and pi bonds in peroxydisulphuric acid is/are: [lf ans is \( 13 \text { and } 6, \text { represent as } 136] \)


(a) How are eddy currently generated in a conductor which is subjected to \( n \) magnetic field?
(b) Write two examples of their useful applications.
(c) How can the disadvantages of eddy currents be minimized?


A charged particle is in the electric field experiences a electric force. All particles which are given below are kept in the electric field of same strength. Which of the following particles would experience the greatest electric force?
A. proton
B. electron
c. alpha particle
D. neutron
E. photon


The maximum oxidation state
exhibited by actinide ions is:
\( A \cdot+5 \)
B. +4
\( c \cdot+7 \)
D. +8


The wave function (in S.I. units) for an
electromagnetic wave is given as-
\( \psi(x, t)=10^{3} \sin \pi\left(3 \times 10^{6} x-9 x\right. \)
\( \left.10^{14} t\right) \) The speed of the wave is:
A \( \cdot 9 \times 10^{14} \mathrm{m} / \mathrm{s} \)
В. \( 3 \times 10^{8} \mathrm{m} / \mathrm{s} \)
c. \( 3 \times 10^{6} m / s \)
D. \( 3 \times 10^{7} m / s \)


When in going east at \( 10 \mathrm{km} / \mathrm{h} \) a train moving with constant velocity appears to be moving exactly north - east. when my velocity is increased to \( 30 \mathrm{km} / \mathrm{h} \)
east it appears to be moving north. At what speed (in Kmph) should I move North so that train appears to be moving exactly South-East?
\( A \cdot 30 \mathrm{km} / \mathrm{h} \)
B. 20 km/h
\( c .50 \mathrm{km} / \mathrm{h} \)
D. \( 10 \mathrm{km} / \mathrm{h} \)


Endorphins reduce the perception of
pain through
A. Sedation
B. Blocking nerve transmission
c. opposing encephalins
D. All of the above


An electrolyte is:
A. a cell
B. a metal
C. a liquid that conducts electricity
D. sugar


Define electric current. What is its \( S I \)
unit?


The worm used in vermi-processing
toilet is
A. Redworm.
B. Roundworm.
c. Flatworm.
D. None of the above


\( \int_{0}^{\pi / 4} \sec ^{2} x d x \)


f \( S_{1}, S_{2}, S_{3}, \dots . . S_{r} \) are the sums of \( n \) terms of arithmetic series whose first
terms are \( 1,2,3,4, \dots ; \) and whose common differences are \( 1,3,5,7, \dots \)
find the value of \( \boldsymbol{S}_{\mathbf{1}}+\boldsymbol{S}_{\mathbf{2}}+\boldsymbol{S}_{\mathbf{3}}+\ldots+ \)
\( \boldsymbol{S}_{\boldsymbol{r}} \)


Select the correct statement from the
following.
A. polyester is obtained from plant stem
B. jute is the outer covering of coconut
c. spinning is a process of making fibers
D. the yarn is made from fibers


The rate of certain hypothetical reaction \( A \) \( +\mathrm{B}+\mathrm{C} \rightarrow \) Products, is given by \( r= \) \( -\frac{d A}{d t}=k[A]^{1 / 2}[B]^{1 / 3}[C]^{1 / 4} \) The order of a
reaction is given by:
A . 1
B. \( \frac{1}{2} \)
\( c \cdot 2 \)
D. \( \frac{13}{12} \)


If \( z \) is unimodular complex number then \( \mathbf{z}=\left(\frac{\mathbf{1}+\mathbf{i} a}{\mathbf{1}-\mathbf{i} \mathbf{a}}\right)^{\mathbf{4}} \) has
A. 2 real 2 imaginary roots
B. 4 real roots
c. 4 imaginary roots
D. 3 real and imaginary roots


\( \boldsymbol{x}=\boldsymbol{e}^{\boldsymbol{\theta}}(\sin \boldsymbol{\theta}+\cos \boldsymbol{\theta}), \boldsymbol{y}=\boldsymbol{e}^{\boldsymbol{\theta}}(\sin \boldsymbol{\theta}-\boldsymbol{1}) \)
\( \cos \boldsymbol{\theta}) \)
Fine \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \)


A hollow conducting sphere is placed in
an electric field produced by a point
charge placed at point \( A, B \) and \( C \)
respectively, then:
A. \( V_{C}>V_{B} \)
B . \( V_{A}>V_{B} \)
с. \( V_{B}>V_{c} \)
\( \mathbf{D} \cdot V_{C}=V_{B} \)


\( \boldsymbol{V}=\boldsymbol{\pi}\left(\boldsymbol{R}^{2}-\boldsymbol{r}^{2}\right) \boldsymbol{h} ; \) make 'r' the subject
of formula.
A \( \cdot r=\sqrt{R^{2}+\frac{V}{\pi h}} \)
в. \( _{r}=\sqrt{R-\frac{V}{\pi h}} \)
\( \mathbf{c} \cdot_{r}=\sqrt{R^{2}-\frac{V}{\pi h}} \)
D. \( r=\sqrt{R^{2}-\frac{V}{\pi h^{2}}} \)


A thin uniform metallic rod of mass \( M \)
and length \( L \) is rotated with a angular
velocity \( \omega \) in a horizontal plane about a
vertical axis passing through one of its ends. The tension in the middle of the
rod is :
A \( \cdot \frac{1}{2} M L \omega^{2} \)
B \( \cdot \frac{1}{4} M L \omega^{2} \)
c. \( \frac{1}{8} M L \omega^{2} \)
D. \( \frac{3}{8} M L \omega^{2} \)


Match List I with List II and select the
answer from the given codes.
List I
List II
A. \( C(s)+O_{2}(g) \longrightarrow C O_{2}(g) \)
\( \mathbf{1} \mathbf{\Delta} \boldsymbol{H}=\mathbf{\Delta} \boldsymbol{U}+\boldsymbol{R} \boldsymbol{T} \)
B. \( N_{2}(g)+3 H_{2}(g) \longrightarrow 2 N H_{3}(g) \)
2. \( \Delta \boldsymbol{H}=\boldsymbol{\Delta} \boldsymbol{U} \)
C. \( \boldsymbol{N} \boldsymbol{H}_{4} \boldsymbol{H} \boldsymbol{S}(\boldsymbol{s}) \longrightarrow \boldsymbol{N} \boldsymbol{H}_{3}(\boldsymbol{g})+\boldsymbol{H}_{2} \boldsymbol{S}(\boldsymbol{g}) \)
3. \( \Delta \boldsymbol{H}=\boldsymbol{\Delta} \boldsymbol{U}-\boldsymbol{2} \boldsymbol{R} \boldsymbol{T} \)
D. \( \boldsymbol{P C l}_{5}(\boldsymbol{g}) \longrightarrow \boldsymbol{P C l}_{3}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g}) \)
4. \( \Delta \boldsymbol{H}=\boldsymbol{\Delta} \boldsymbol{U}+\boldsymbol{2} \boldsymbol{R} \boldsymbol{T} \)
E. \( 2 S O_{2}(g)+O_{2}(g) \longrightarrow 2 S O_{3}(g) \)
5. \( \Delta \boldsymbol{H}=\boldsymbol{\Delta} \boldsymbol{U}-\boldsymbol{R} \boldsymbol{T} \)
A. \( A-1, B-2, C-3, D-4, E-5 \)
B. \( A-5, B-2, C-3, D-4, E-1 \)
c. \( A-1, B-3, C-4, D-2, D-5 \)
D. \( A-2, B-3, C-4, D-1, E-5 \)


Assertion
Potentiometer is used only to compare
potential differences.
Reason
The potentiometer draws current from the voltage source being measured.
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


Zoological name of common Indian
Krait is
A. Bungarus caeruleus
B. Naja naja
c. viper russelli
D. Ophiophagus hannah


The temperature at 12 noon was \( 10^{\circ} \mathrm{C} \)
above zero. If it decreases at the rate of
\( 2^{o} C \) per hour until midnight, at what
time would the temperature be \( 8^{\circ} C \)
below zero? What would be the
temperature at midnight?
A \( \cdot 14^{\circ} \mathrm{C} \)
B. \( -14^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 16^{\circ} C \)
D. \( -16^{\circ} \mathrm{C} \)


During a cyclone, air moves from:
A. Region of high pressure to low pressure
B. Region of high pressure to high pressure
C. Region of low velocity to high velocity
D. Region of high pressure to low velocity


It is required to construct a \( 10 \mu F \)
capacitor which can be connected
\( \operatorname{across} \) a \( 200 V \) battery. Capacitors of
capacitance \( 10 \mu F \) are available but
they can withstand only \( 50 V \) Design a
combination which can yield the
desired result


Best method of preparing alkyl chloride
is:
A. \( R O H+S O C l_{2} \rightarrow \)
в. \( R O H+P C l_{5} \rightarrow \)
c. \( R O H+P C l_{3} \rightarrow \)
D. \( R O H+H C l \) Anhy ZnCla


At what height above the earth's
surface, the value of \( g \) is same as that
at a depth of \( 100 k m ? \)
Hint: Take \( g_{h}=g_{d} \)


Which one of the following is paramagnetic ?
A. \( N_{2} \)
B. \( N O \)
\( c \cdot c o \)
D. \( O_{3} \)


Assertion
In series \( \boldsymbol{L}-\boldsymbol{C}-\boldsymbol{R} \boldsymbol{A} \boldsymbol{C} \) circuit, current
and voltage are in same phase at
resonance.
Reason
In series \( \boldsymbol{L}-\boldsymbol{C}-\boldsymbol{R} \boldsymbol{A} \boldsymbol{C} \) circuit,
resonant frequency does not depend on the value of resistance. Hence current,
at resonance, does not depend on
resistance.
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


彥光 \( (\infty) \)
\( \frac{x+14}{x+1} \)
\( \frac{x}{10} \)


A letter is chosen at random from the
letters of the English alphabet The
probability that it is not a vowel is
A . 5/26
B. 21/26
c. \( 15 / 26 \)
D. \( 1 / 2 \)


If the plane has an eastward heading, and a \( 20 m / s \) wind blow towards the
southwest, then the plane's speed is-
\( \mathbf{A} \cdot 80 m / s \)
B. more than \( 80 \mathrm{m} / \mathrm{s} \) but less than \( 100 \mathrm{m} / \mathrm{s} \)
\( \mathrm{c} \cdot 100 \mathrm{m} / \mathrm{s} \)
D. more than \( 100 \mathrm{m} / \mathrm{s} \)


Plane electromagnetic wave of intensity
S are incident normally on a flat
surface.Only a fraction \( f \) of the incident energy is absorbed.What is the
radiation pressure?


\( A 20 \mathrm{kg} \) block is in motion on a rough horizontal surface. A horizontal force of
\( 60 \mathrm{N} \) is required to keep the body moving with constant speed. Then find coefficient of kinetic friction? \( (\mathrm{g}=10 \mathrm{m} \)
\( \left.s^{-2}\right) \)
A. 0.4
B. 0.3
\( c \cdot 0.8 \)
D. 0.6


Find the area of the shaded region in the
figure shown.


The IUPAC name of the following
compound is:
A. 3-cyclohexylpentan-3-ol
B. 3-cyclohexyl,3-hydroxypentane
C. 3-hydroxypentyl cyclohexane
D. none of the above


A particle executing SHM with an amplitude A. The displacement of the particle when its potential energy is half
of its total energy is
A \( \cdot \frac{A}{\sqrt{2}} \)
в. \( \frac{A}{2} \)
c. \( \frac{A}{4} \)
D. \( \frac{A}{3} \)


The value of \( \left[2-3(2-3)^{-1}\right]^{-1} \) is
A \( \cdot \frac{-1}{5} \)
B.
c. -5
D. 5


Laws of planetary motion were given by
A. Issac Newton
B. Archimedes
c. James Maxwell
D. Johannes Kepler


If \( N_{2} \) gas is bubbled through water at
\( 293 K \), Calculate solubility of \( N_{2} \) gas?
Assume that \( N_{2} \) exerts a partial pressure of 0.987 bar. Given that
Henry's law constant for \( N_{2} \) at \( 293 K \) is \( \mathbf{7 6 . 4 8} \frac{\boldsymbol{k} \text { bar }}{\text { mole } / \text { litre }} \)
A \( \cdot 1.29 \times 10^{-5} \) litree
В. \( _{1.29} \times 10^{-4} \frac{\text { тоде }}{\text { litre }} \)
с. \( _{2.9} \times 10^{-3} \) mole
D. \( 2.9 \times 10^{-5} \) mole


The lowest category in taxonomic hierarchy is
A. Phylum
B. Subspecies
c. species
D. Variety


The elements undergoing reduction and oxidation during the reaction,
\( \left(N H_{4}\right)_{2} C r_{2} O_{7} \rightarrow N_{2}+C r_{2} O_{3}+ \)
\( 4 H_{2} O \) are respectively:
\( A \cdot N \) and \( C r \)
B. Crand N
c. \( \mathrm{N} \) and 0
D. Crand 0


A block of mass 2 kg is free to move along the \( x \) -axis. It is at rest and from
\( t=0 \) onwards it is subjected to a time-
dependent force \( F(t) \) in the \( x \) direction.
The force \( F(t) \) varies with \( t \) as shown in
the figure. The kinetic energy of the block after 4.5 seconds is:
в. 7.50 J
\( c .5 .06 \)
D. \( 14.06 \mathrm{J} \)


When metal foundry products are cleaned by shot blasting, heat is generated by friction. Nitrogen is used
for:
A. providing an inert atmosphere
B. cooling the blast chamber
c. reducing friction
D. displacing hot air


Find the value of \( p \) when the parabola
\( y^{2}=4 p x \) goes through the point \( (i)(3,- \)
2) and (ii) (9,-12)


An object is placed at the centre of
curvature of a concave mirror of radius
of curvature \( 20 \mathrm{cm} . \) The nature and
position of the image shall be.
A. Virtual and \( 15 \mathrm{cm} \) from the mirror
B. Real and \( 20 \mathrm{cm} \) from the mirror
c. virtual and \( 20 \mathrm{cm} \) from the mirror
D. Real and \( 10 \mathrm{cm} \) from the mirror


Differentiate the following functions
with respect to \( x \) \( \frac{\sqrt{x^{2}+1}+\sqrt{x^{2}-1}}{\sqrt{x^{2}+1}-\sqrt{x^{2}-1}} \)


If \( (2 \bar{i}+4 \bar{j}+2 \bar{k}) \times(2 \bar{i}-x \bar{j}+5 \bar{k})= \)
\( 16 \bar{i}-6 \bar{j}+2 x \bar{k}, \) then the value of \( x \) is
\( A \cdot 2 \)
B. -2
\( c . \)
D. 3


State True or False.
\( \mathrm{p}_{z} \) orbital is symmetrical about y-axis :
A. True
B. False


Which one of the following is the correct description of a certain part of a normal
human skeleton?
A. Parietal bone and the temporal bone and the skull are joined by fibrous joint
B. First vertebrae is axis, which articulates with the occipital condyles.
c. The sth and 10 th pairs of ribs are called the floating ribs
D. Glenoid cavity is a depression to which the thigh bone articulates


Transit of work takes place when any
property other than differs
A. Temperature
B. Pressure
c. volume
D. All the above


The length of a rectangle is twice its width. If its perimeter is \( 54 \mathrm{cm}, \) find its length.
\( \mathbf{A} \cdot 18 \mathrm{cm} \)
B. \( 10 \mathrm{cm} \)
\( \mathrm{c} \cdot 19 \mathrm{cm} \)
D. \( 15 \mathrm{cm} \)


The element that does NOT form acidic
oxide is :
A. carbon
B. phosphorus
c. chlorine
D. barium


Find the set of values of \( a \) for which
\( f(x)=x+\cos x+a x+b \) is
increasing on \( \boldsymbol{R} \)


What is known as Astronomical Unit
\( (A \cup) ? \)
A. Average distance between Earth and Sun
B. Average distance between Sun and Moon
C. Average distance between Moon and Earth
D. Average distance between Earth and Star


f a line makes \( \alpha, \beta, \gamma, \delta \) angles with 4
diagonals of a cube, then \( \cos ^{2} \alpha+ \)
\( \cos ^{2} \beta+\cos ^{2} \gamma+\cos ^{2} \delta=? \)
\( \mathbf{A} \cdot \mathbf{1} \)
B.
\( c \cdot \frac{4}{3} \)
D.


Draw the circuit diagram of AND gate using diodes.


Match the following and choose the
correct answer.
\begin{tabular}{lll|l}
& Table \( \mathbf{A} \) & & Table \( \mathbf{B} \) \\
a. & conductor & 1. & plastic \\
b. & charge at rest & 2. & current electricity \\
c. & moving charge & 3. & electrostatic \\
d. & insulator & 4. & copper
\end{tabular}
\( \mathbf{A} \)
\( c-1, d-2, b-3, a-4 \)
B . \( d-1, c-2, a-3, b-4 \)
c. \( c-4, d-2, b-3, a-1 \)
D. \( d-1, c-2, b-3, a-4 \)


Give examples which indicate that nylon fibres are very strong.


Vascular bundle is known as ..........., when
the xylem completely surrounds phloem
A. Bicollateral
B. Amphivasal
c. conjoint and open
D. Amphicribral


Identify correct order of reactivity for electrophilic substitution reaction of the following compounds:
\( A \)
в.
\( c \)
D.


Elements found in native state are
\( \mathbb{P} \)
Chlorides Silicates Carbonates Phosphates Oxides
\( A \cdot P b \) and \( B i \) as they are in \( p \) -block
B. \( \mathrm{Hg} \) and \( 0 \mathrm{s} \) as they are in liquid state
C. \( C \) and \( s i \) as they are non-metals
D. Pt and Au as they are at the bottom of the electrochemical series


Three candidates solve a question. Odds
in favour of the correct answer are 5 :
2,4: 3 and 3: 4 respectively for the three candidates. What is the
probability that at least two of them solve the question correctly?
A \( \cdot \frac{209}{343} \)
в. \( \frac{134}{343} \)
c. \( \frac{149}{343} \)
D. \( \frac{60}{343} \)


An element \( X \) combines with oxygen to
form an oxide \( X_{2} O . \) To which group of
the periodic table does the element \( \boldsymbol{X} \)
belong?
A. group 1
B. group 3
c. group 5
D. group 7


The slope of Kinetic Energy displacement curve of a particle in motion is:
A. equal to the acceleration of the particle
B. inversely proportional to the acceleration
c. directly proportional to the acceleration
D. none of these


Find the value of \( \theta \) such that the
acceleration of \( \boldsymbol{A} \) is \( \boldsymbol{g} / \boldsymbol{6} \) downward
along the incline plane. (All surfaces are
smooth)
A \( \cdot \theta=10^{\circ} \)
B . \( \theta=60^{\circ} \)
\( \mathbf{c} \cdot \theta=45^{\circ} \)
D. \( \theta=53^{\circ} \)


Largest amount of phosphate bound energy is produced in the process of respiration during
A. Anaerobic respiration
B. Glycolysis
c. Krebs cycle
D. None of the above


Which is correct?
\( A \). Birds have \( Z Z \) -ZW sex determination
B. Diosophilla has \( X X \) -XY sex determination
C. Henking discovered Y-ch
D. Grasshoppers show X-XY sex determination


The value of \( \tan ^{-1}\left(\frac{1}{2} \tan 2 A\right)+ \)
\( \tan ^{-1}(\cot A)+\tan ^{-1}\left(\cot ^{3} A\right) \) for \( 0< \)
\( \boldsymbol{A}<\frac{\boldsymbol{\pi}}{\boldsymbol{4}} \) is?
\( \mathbf{A} \cdot 4 \tan ^{-1} 1 \)
B. \( 2 \tan ^{-1} 2 \)
\( c \cdot 0 \)
D. None


Copper wire is used in Beilstein test.
A. True
B. False


Primary producers of deep sea hydrothermal vent ecosystem are
A . Coral reels
B. Green algae
c. chemosynthetic bacteria
D. Blue-green algae


If the position vectors of three consecutive vertex of any parallelogram \( \operatorname{are} \) respectively \( \hat{i}+\hat{j}+\hat{k}, \hat{i}+3 \hat{j}+ \)
\( \mathbf{5} \hat{\boldsymbol{k}}, \mathbf{7} \hat{\boldsymbol{i}}+\mathbf{9} \hat{\boldsymbol{j}}+\mathbf{1 1} \hat{\boldsymbol{k}} \) then the position
vector of its fourth vertex is:
A \( \cdot 6(\hat{i}+\hat{j}+\hat{k}) \)
в. \( 7(\hat{i}+\hat{j}+\hat{k}) \)
c. \( 2 \hat{j}-4 \hat{k} \)
D. \( 6 \hat{i}+8 \hat{j}+1 \hat{0} k \)


Thermal pollution causes a decrease in
dissolved oxygen.
A. True
B. False


If the particle was to start at the extreme position i.e \( x=+A \), then what will be the equation of SHM:
\( \mathbf{A} \cdot A \cos (\omega t) \)
B. \( \operatorname{Asin}(\omega t) \)
c. \( \operatorname{Acot}(\omega t) \)
D. \( \operatorname{Atan}(\omega t) \)


Which of the following structures are responsible for breathing process?
A. The trachea and alveol
B. Larynx and bronchi
c. Ribs and intercostal muscles
D. Intercostal muscles and diaphragm


The reaction \( Z n O+C \rightarrow Z n+C O \) is
an example of a
A. Combination reaction
B. Reduction-oxidation reaction
c. Displacement reaction
D. Decomposition Reaction


The system is said to be in equilibrium when
A \( \cdot \stackrel{F_{1}}{\longrightarrow}-\stackrel{F_{2}}{\longrightarrow}=0 \)
B. \( \stackrel{F_{1}}{\longrightarrow}-\stackrel{F_{2}}{\longrightarrow}=+v e \)
c. \( \stackrel{F_{1}}{\longrightarrow}-\stackrel{F_{2}}{\longrightarrow}=-v e \)
D. All


Who recorded first mineral elements in
plant cell?
A. Liebig
B. Woodward
c. van Helmont
D. None of the above


Water is often treated with chlorine to:
A. cause sedimentation
B. remove insoluble impurities
c. increase oxygen content
D. kill Germs


Assertion
The solubility of a solid in a liquid increases with increase of pressure.
Reason

Solubility of gas in a liquid is directly proportional to the pressure of the gas.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


If the circumference (in \( c m \) ) and the
\( \operatorname{area}\left(\operatorname{in} c m^{2}\right) \) of a circle are equal then
find the radius of the circle
A . \( 1 c m \)
в. 2 ст
\( c .3 c m \)
D. \( 4 c m \)


Who developed law of conservation of
mass?
A. Antoine Lavosier
B. Robert Boyle
c. Rutherford
D. Willard Gibbs


initial speed (in \( \mathrm{m} / \mathrm{s} \) ) with which the
water flows from the orifice.


Assertion
Two equipotential surfaces cannot cut
each other.
Reason
Two equipotential surfaces are paralle
to each other.
A. If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
B. If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
C. If Assertion is correct but Reason is incorrect.
D. If Assertion is incorrect but Reason is correct.


In given figure, \( P \) and \( Q \) are points on
the sides \( A B \) and \( A C \) respectively of
\( \triangle A B C \) such that \( A P=3.5 \mathrm{cm}, P B= \)
\( \mathbf{7} \boldsymbol{c m}, \boldsymbol{A} \boldsymbol{Q}=\mathbf{3} \boldsymbol{c m} \) and \( \boldsymbol{Q} \boldsymbol{C}=\boldsymbol{6} \boldsymbol{c m} \)
\( \boldsymbol{P Q}=\mathbf{4 . 5} \boldsymbol{c m}, \) find \( \boldsymbol{B C} \)


The oxidation potential of hydrogen
half-cell will be negative if:
This question has multiple correct options
\( \mathbf{A} \cdot p\left(H_{2}\right)=1 \) atm and \( \left[H^{+}\right]=1 M \)
B \( \cdot p\left(H_{2}\right)=1 \) atm and \( \left[H^{+}\right]=12 M \)
\( \mathbf{c} \cdot p\left(H_{2}\right)=0.2 \) atm and \( \left[H^{+}\right]=1 M \)
D \( \cdot p\left(H_{2}\right)=0.2 \) atm and \( \left[H^{+}\right]=0.2 M \)


The following charged particles accelerated from rest, through the same potential difference, are projected towards gold nucleus in different experiments. The distance of closest
approach will be maximum for
A. \( \alpha \) -particles
B. proton
c. deuteron
D. neutron


With an increase in the concentration of
the products of photosynthesis in mesophyll cells there is
A. Increase in rate of photosynthesis
B. Decrease in rate of photosynthesis
c. No change in the rate of photosynthesis
D. None of the above


Integrate \( \int_{0}^{1}\left(3 x^{2}+2 x\right) d x \)


\( \frac{\sqrt{2}}{\frac{k}{k}} \)


Cloud seeding is a technique used to
induce rain that was first used by USA
in \( 1946 . \) It has also been done in
Karnataka and other places in India.
What is it?
A. An agricultural practice that depends on clouds
B. Introduction of particles in clouds to decrease condensation
C. Making clouds and placing them in the sky
D. Trimming the clouds into seed like structures
E. An process of spreading dry ice on upper part of cloud to simulate precipitation process and cause rain


State the oxidation number of carbonyl carbon in methanal and methanoic acid
respectively:
A. 0 and 0
B. 0 and +2
\( c \cdot+1 \) and +2
D. +1 and +3


Vitamin C must be supplied regularly in
diet because?
A. it is water soluble hence excreted in urine and can't be
stored in the body
B. it is fat soluble hence stored in the body and cannot be used on regular basis
C. it is required in a large amount by the body hence supplied regularly
D. it is water soluble hence used by the body on daily basis and is to be suppled regularly


An ice cube of mass \( 0.1 \mathrm{Kg} \) at \( 0^{\circ} \mathrm{C} \) is placed in an isolated container which is
\( \operatorname{at} 227^{\circ} \mathrm{C} . \) The specific heat \( s \) of the
container varies with temperature \( \boldsymbol{T} \) according to the empirical relation \( s= \) \( \boldsymbol{A}+\boldsymbol{B} \boldsymbol{T}, \) where \( \boldsymbol{A}=\mathbf{1 0 0} \boldsymbol{c a l} \boldsymbol{k} \boldsymbol{g}^{-1} \boldsymbol{K}^{-1} \)
and \( B=2 \times 10^{-2} \) cal \( k g^{-1} \)
If the final temperature of the container
is \( 27^{\circ} \mathrm{C} \), the mass of the container is
(Latent heat of fusion of water \( =8 x \)
\( 10^{4} \) cal \( k g-1, \) Specific heat of water \( = \)
\( \mathbf{1 0}^{\mathbf{3}} \) cal \( \boldsymbol{k} \boldsymbol{g}^{-1} \boldsymbol{K}^{-1} \)
A . \( 0.495 \mathrm{kg} \)
в. \( 0.595 \mathrm{kg} \)
\( c .0 .695 k g \)
D. \( 0.795 \mathrm{kg} \)


The area of the shaded region in the following figure is
A \( .51 .33 \mathrm{cm}^{2} \)
В. \( 102.67 \mathrm{cm}^{2} \)
c. \( 205.34 \mathrm{cm}^{2} \)
D. can not be determined


Why is the flow of signals in a synapse from axonal end of one neuron to
dendritic end of another neuron but not
the reverse?
A. Axons do not have receptors for neurotransmitters
B. Dendritic ends have receptors for neurotransmitters
c. No synthesis of neurotransmitter takes place at the dendritic end
D. All of the above


A parallel plate capacitor is made by placing n equally spaced plates connected alternatively. If the
capacitance between any two adjacent plates is \( C \) then the resultant capacitance is:
A . nc
в. \( \frac{C}{n} \)
\( c \cdot(n+1) c \)
D. \( (n-1) C \)


The ratio of the wavelengths of a photon and that of an electron of same energy \( \boldsymbol{E} \) will be \( [\boldsymbol{m} \text { is mass of electron }] \)
A \( \cdot \sqrt{\frac{2 m}{E}} \)
в. \( \sqrt{\frac{E}{2 m}} \)
\( c \cdot c \sqrt{\frac{2 m}{E}} \)
D. \( \sqrt{\frac{E c}{2 m}} \)


Block A is hanging from a vertical spring and is at rest. Block B strikes the block A with velocity v and sticks to it. Then the value of \( v \) for which the spring just attains natural length is :
\( A \)
\[
\sqrt{\frac{60 m g^{2}}{k}}
\]
в.
\[
\sqrt{\frac{6 m g^{2}}{k}}
\]
c. \( \sqrt{\frac{10 m g^{2}}{k}} \)
D. none of these


To a man walking at the rate of \( 3 k m / h \) the rain appears to fall vertically. When he increases his speed to \( 6 k m / h \) it
appears to meet him at an angle of \( 45^{\circ} \)
with vertical. The speed of rain is
\( \mathbf{A} \cdot 2 \sqrt{2} k m / h \)
B. \( 3 \sqrt{2} \mathrm{km} / \mathrm{h} \)
\( \mathrm{c} \cdot 2 \sqrt{3} \mathrm{km} / \mathrm{h} \)
D. \( 3 \sqrt{3} \mathrm{km} / \mathrm{h} \)


The placement of elements in the Newlands' table was compared to:
A. weeks of a month
B. notes of music
c. months of a year
D. days of a month


Water in lakes and ponds in cold countries does not freeze all at once


What is the solution of the differential
equation \( \frac{y d x-x d y}{y^{2}}=0 ? \)
where \( c \) is an arbitrary constant.
A \( . x y=c \)
в. \( y=c x \)
c. \( x+y=c \)
D. \( x-y=c \)


Number of atoms in one molecule of
sulphur:
\( A \cdot 8 \)
B. 4
\( c \cdot 3 \)
\( D \)


In spite of having less electron affinity than chlorine, fluorine is the strongest
oxidizing agent among the halogens. The most important reason for this phenomenon is :
A. lower bond dissociation energy of \( F_{2} \) than \( C l_{2} \)
B. much lower heat of hydration of \( F^{-} \) than \( C l \)
C. much greater heat of hydration of \( F^{-} \) than \( C l \)
D. greater electronegativity of \( F \) than \( C l \)


8640 is not a perfect cube
A. True
B. False
c. Ambiguous
D. Insufficient information


Is \( C r_{2} O_{3} \) an amphoteric oxide? If yes
enter \( 1, \) else enter 0


Two wires, one of copper and other of
iron, are of the same length and same radius. Choose correct one.
A. Iron wire has less resistance than copper wire
B. both wires have same resistance
c. Iron wire has more resistance than copper wire
D. none of these


Wheatstones's bridge cannot be used for measurement of very resistances.
A . high
B. low
c. low(or) high
D. zero


Explain why a body with large reflectivity is a poor emitter.


What will be the nature of charge on the metal paper clip of electroscope when a positively charged body is brought in contact with it?
A. Positive
B. Negative
c. Partially negative
D. None of the above


The chloride that cannot get hydrolysed
is :
A. \( \operatorname{SiCl}_{4} \)
в. \( \operatorname{Sn} C l_{4} \)
c. \( P b C l_{4} \)
D. \( C C l_{4} \)


Identify the side view of the given solid
\( A \)
B.
\( c \)
D.


Which of the following is not a sugar?
A. Sucrose
B. Glucose
C. Fructose
D. cellulose


Sequence the following steps involved generally in the extraction of a metal in pure form from its ore
(a) The metal obtained from its oxide require further purification for end use
(b) The ore should be converted to its
oxide form.
(c) The ore is beneficial to us if it is
handpicked then metal crushed and ground, and later subjected to pulverization as per the requirement
(d) The ore in the form of oxide is required to be reduced.
(e) Dressed ore is required for it to be concentrated.
A \( \cdot \operatorname{ecbd} \)
B. cebda
\( c \cdot \operatorname{cob} a d \)
D. ced b a


Find the value of \( 2 \sin 3 \theta \cos \theta- \)
\( \sin 4 \theta-\sin 2 \theta \)