Calculate the electronegativity time) of fluorine on Pauling scale form the following data:
\( \boldsymbol{E}_{\boldsymbol{H}-\boldsymbol{H}}=\mathbf{1 0 4 . 2 k c a l} \boldsymbol{m o l}^{-1} \)
\( \boldsymbol{E}_{\boldsymbol{F}-\boldsymbol{F}}=\boldsymbol{3 6 . 6 k c a l} \boldsymbol{m o l}^{-1} \)
\( \boldsymbol{E}_{\boldsymbol{H}-\boldsymbol{F}}=\mathbf{1 3 4 . 6 k c a l} \boldsymbol{m o l}^{-1} \)
Given \( =\boldsymbol{X}_{\boldsymbol{H}}=\mathbf{2 . 1} \)


The electronic configuration of the two
outermost shells of an atom is
\( 3 s^{2} 3 p^{6} 3 d^{5} 4 s^{2} . \) What is this atom?
A. Manganese
B. Phosphorus
c. strontium
D. Vanadium


What is the phase angle of the source voltage with respect to the current? Does the source voltage lag or lead the current?


A stationary ball weighing \( 0.25 \mathrm{kg} \) acquire a speed of \( 10 \mathrm{m} / \mathrm{s} \) when hit by a hockey stick. The impulse imparted to the ball is:
A. \( 0.25 N \times s \)
B. \( 2.5 N \times s \)
\( \mathbf{c} \cdot 2 N \times s \)
D. \( 0.5 N \times s \)


If \( A \) and \( B \) are square matrices of order 3 such that \( |\boldsymbol{A}|=-\mathbf{1},|\boldsymbol{B}|=\mathbf{3}, \) then the
determinant of \( 3 A B \) is equal to
A . -9
B. -27
c. -81
D. 81


Why is the Wheatstone bridge better than the other methods of measuring resistances?
A. It does not involve Ohm's law
B. It is based on Kirchoff's law
c. It has four resistor arms
D. It is a null method


Solve by cross multiplication method:
\( 6 x+7 y-11=0 \)
\( 5 x+2 y=13 \)


Chlorine gas is passed in a medium which has \( p H=12 . \) Two products \( A \)
and \( B \) are formed with water. Now \( p H \) of
medium is changed to 1 by acidifying it.Again a product \( C \) is formed with
water. It is found that \( A \) is strong
oxidising agent Answer the following questions carefully: Oxidation state of \( C l \) in compound \( A \) is:
A. -1
B. +1
\( c .+3 \)
D. +5


If edible oil is allowed to stand for a
long time in an iron or tin container, the oil becomes rancid.
A. True
B. False


For \( \boldsymbol{m}, \boldsymbol{n} \in \boldsymbol{N}, \) if \( \lim _{x \rightarrow 0} \frac{\boldsymbol{x}^{n}-(\sin \boldsymbol{x})^{m}}{\boldsymbol{x}^{m}}=\boldsymbol{L} \)
where \( L=\frac{n}{6}, \) then \( m-n= \)
A .2
B. -
\( c \cdot 0 \)
D. -


If the \( K E \) of a free electron doubles then
its de-Broglie wavelength changes by a
factor
A \( \cdot \frac{1}{2} \)
в. \( \frac{1}{\sqrt{2}} \)
\( c \cdot 2 \)
D. \( \sqrt{2} \)


The number of cubic polynomials \( \boldsymbol{P}(\boldsymbol{x}) \) satisfying \( P(1)=2, P(2)=4, P(3)=6 \)
\( P(4)=8 \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B.
c. more than one but finitely manyt
D. infinitely many


In the Bohr model of a \( \pi- \) mesic atom,
a \( \pi- \) meson of mass \( m_{\pi} \) and of the
same charge as the electron is in a
circular orbit of radius ' \( r^{\prime} \) about the
nucleus with an orbital angular momentum \( h / 2 \pi . \) If the radius of a
nucleus of atomic number \( Z \) is given by \( \boldsymbol{R}=\mathbf{1 . 6} \times \mathbf{1 0}^{-15} \boldsymbol{Z}^{\frac{1}{3}} \boldsymbol{m}, \) then the limit
on \( Z \) for which \( \left(\epsilon_{0} h^{2} / \pi m e^{2}=\right. \) \( \left.0.53 A \text { and } m_{\pi} / m_{e}=264\right) \pi- \) mesic
atoms might exist is
\( \mathbf{A} \cdot<105 \)
B \( .>105 \)
\( \mathbf{c} .<37 \)
\( \mathbf{D} \cdot>37 \)


In electro-refining of copper, some gold is deposited as:
A. cathode mud
B. electrolyte
c. anode mud
D. none of these


The process of converting hydrated alumina into anhydrous alumina is
called
1. Roasting
2. Calcination


The general solution of the equation \( \frac{d y}{d x}=\frac{y^{2}-x}{2 y(x+1)} \) is
\( \mathbf{A} \cdot y^{2}=(1+x) \log (1+x)-c \)
B. \( _{y^{2}}=(1+x) \log \frac{c}{(1-x)}-1 \)
c. \( y^{2}=(1-x) \log \frac{c}{(1+x)}-1 \)
D. \( y^{2}=(1+x) \log \frac{c}{(1+x)}-1 \)


If the refractive indices of crown glass for red, yellow and violet colours are
1.5140,1.5170 and 1.6434,1.6499 and
1.6852 respectively, then the dispersive power for crown and flint glass are respectively-


Deforestation, intensive cultivation, mismanagement of cultivated soils and intensive urbanization are major factors triggering the
A. soil erosion
B. water eroding
c. air pollution
D. soil pollution


Globular protein which masks active sites on F-actin is
A. Troponin
B. Tropomyosin
c. Myosin
D. Light meromyosin
E. Heavy meromyosin


is a flammable gaseous fuel made from coal and supplied to the user via a piped distribution system.
A. Coal tar
B. Coal gas
c. Petroleum
D. carbon monooxide


A block slides down on an inclined plane
of slope angle \( \theta \) with constant velocity. It is then projected up on the same
plane with initial velocity \( V_{0} . \) How far up the incline will it move before coming to
rest
A \( \cdot \frac{V_{0}^{2}}{g \sin \theta} \)
в. \( \frac{V_{0}^{2}}{2 g \sin \theta} \)
c. \( \frac{V_{0}^{2}}{4 g \sin \theta} \)
D. \( \frac{V_{0}^{2}}{8 g \sin \theta} \)


Which of the following is smallest in
size?
A \( \cdot O^{2} \)
B. \( C^{4} \)
\( c \cdot F^{-} \)
D. \( N^{3} \)


\( \alpha-1 \) antitrypsin is used to treat
A. Metasema
B. Polysma
c. Emphysema
D. colysema


Write chemical reactions to show the
amphoteric nature of water


Find the critical points of the function \( f(x)=(x-2)^{2 / 3}(2 x+1) \)
\( A .-1 \) and 2
B.
c. 1 and -2
D. 1 and 2


A single resistor is connected in circuit. \( A 2 A \) of current is flowing through circuit and potential difference across resistor is 12 Volts. The power
dissipated in the resistor is :
A. 6 watts
B . 10 watts
c. 14 watts
D. 24 watts
E . 144 watts


The reactant which is entirely consumed in reaction is known as
limiting reagent. In the reaction \( 2 A+ \) \( 4 B \longrightarrow 3 C+4 D, \) if 5 moles of \( A \) reacts
with 6 moles of \( \mathrm{B} \) then, which is the limiting reagent?
A. \( A \)
в. \( B \)
\( c . c \)
D. \( D \)


What is DNA Packaging? Describe the importance of it.


Choose the correct option from the following:
A. In the electrophilic substitution of toluene with \( B r_{2} \) iron (III) bromide acts as a Lewis acid.
B. In the reaction of toluene with \( C l_{2} / F e C l_{3} \), ortho and para isomers are easily separated.
C. Similar reaction with iodine is reversible in nature
D. All of these


If \( e^{y}+x y=e \) then at \( x=0, \frac{d^{2} y}{d x^{2}}=e^{-\lambda} \)
then numerical quantity \( -\lambda \) should be
equal to
A .2
B. 3
\( c \cdot 4 \)
D. 5


Solve: \( \lim _{x \rightarrow 0} \frac{\sin x^{o}}{x} \)


Assertion
The density of \( _{6}^{12} \mathrm{C} \) nuclide is about
\( 1.8 \times 10^{17} k g m^{-3} \) to that of water.
Reason
The ratio of density of \( \frac{12}{6} \) C nuclide and
water is about \( 1.8 \times 10^{14} k g m^{-3} \)
A. Assertionis correct but Reasson is wrong
B. Assertion is wrong but Reasson is correct
C. Both Assertion and Reason are correct and Reason is the correct explanation of Assertion
D. Both Assertion and Reason are correct but Reason is not the correct explanation of Assertion


The resistance of the series comb of two
resistance is S. When they are joined in parallel the total resistance is P. If \( \mathrm{S}=\mathrm{nP} \) then the minimum possible value of \( n \) is:
\( A \cdot 4 \)
B. 3
\( c \cdot 2 \)
\( D \)


Which is not correct order for the
properties specified?
\( \mathbf{A} \cdot I>B r>C l>F \) (oxidising character)
B . \( K>M g>A l>B \) (metallic character)
C \( . L i<B<B e<C<O<N<F<N e \) (first
ionisation enthalpy)
D. None of these


Which of the following is used for lowering blood pressure?
A. Reserpine
B. Morphine
c. Diethyl ether
D. cocaine


For the reaction \( A \rightarrow B \) it has been found
that the order of the reaction is zero with respect to A. Which of the following
expressions correctly describes the reaction?
A \( \cdot K=\frac{2.303}{t} \log \frac{\left[A_{0}\right]}{[A]} \)
B \( \cdot\left[A_{0}\right]-[A]=K t \)
\( \mathbf{c} \cdot_{t_{1 / 2}}=\frac{0.693}{K} \)
D. \( t_{1 / 2} \propto \frac{1}{\left[A_{0}\right]} \)


The initial pressure of the reactant at \( 500 K, \) in the reaction \( C a C O_{3}=C a O+ \)
\( C O_{2} \) is \( 200 m m . \) After \( 20 m \) ins the
pressure is reduced to \( 150 \mathrm{mm} \). Find the
average rate of the reaction?
A . \( 0.33 \times 10^{-6} \) molL \( ^{-1} \) sec \( ^{-1} \)
B . \( 2.33 \times 10^{-6} \) molL \( ^{-1} \) sec \( ^{-1} \)
\( \mathbf{c} \cdot 1.33 \times 10^{-6} \mathrm{molL}^{-1} \mathrm{sec}^{-1} \)
D. \( 3.33 \times 10^{-6} \) molL \( ^{-1} \) sec \( ^{-1} \)


Points on the line \( y=x \) whose
perpendicular distance from the line
\( 3 x+4 y=12 \) is 4 have the coordinates
\( ^{A} \cdot\left(-\frac{8}{7},-\frac{8}{7}\right),\left(-\frac{32}{7},-\frac{32}{7}\right) \)
в. \( \left(\frac{8}{7}, \frac{8}{7}\right),\left(\frac{32}{7}, \frac{32}{7}\right) \)
\( ^{\mathbf{c}} \cdot\left(-\frac{8}{7},-\frac{8}{7}\right),\left(\frac{32}{7}, \frac{32}{7}\right) \)
D. None of these


Assertion
Threshold frequency is a characteristic
for a metal.
Reason
Threshold frequency is a maximum frequency required for the ejection of electron from the metal surface.
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


Vetebral column is derived from
A. Dorsal nerve cord
B. Ventral nerve cord
C. Outgrowth of cranium
D. Notochord


The given figure represents locations in human female reproductive system that are affected by different birth control measures. Identify them and
select the correct option
A. P-Copper T, Q - Birth control pills, R Tubectomy, S condom
B. P - Birth control pills, Q Copper T, R Tubectomy, S -
C. P- Birth control pills, Q Diaphragm, R Ovariectomy, copper \( T \)
D. P Copper T, Q - Birth control pills, R Ovariectomy, S -


Define the term chemotherapy.


The solution set of the equation \( \mid x- \) \( \mathbf{3} \mid=\boldsymbol{x}-\mathbf{3} \) is?
B. [3,0]
\( c \cdot \phi \)
D. The set R of all real numbers


The anomalous pairs in Mendeleev's periodic table is/are
\( A \cdot C o, N i \)
в. Te,
c. Ar, \( k \)
D. All the above


For the reaction, \( N_{2}+3 H_{2} \rightarrow 2 N H_{3} \)
The rate of change of concentration for
hydrogen is \( 0.3 \times 10^{-4} M s^{-1} . \) The rate
of change of concentration ammonia is:
A . \( -0.2 \times 10^{-4} \)
В. \( 0.2 \times 10^{-4} \)
c. \( 1 \times 10^{-4} \)
D. \( 0.3 \times 10^{-4} \)


Name a device which is commonly used to convert an electric signal into a visual signal
A. Cathode ray tube
B. Transducer
c. RMS converter
D. None of the above


The population of a town in 2009 was \( 125000 . \) It increase \( 10 \% \) per year. What
is the population after 3 years?
A . 166375
в. 170000
c. 125000
D. 10000


What is MCB? Why is MCB preferred to electric fuse?


Complete the reaction:
\( \boldsymbol{S} \boldsymbol{O}_{3}+\boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \)


Integrate the rational function
\( \frac{x}{(x-1)(x-2)(x-3)} \)


Which of the following is an insulator?
A. copper
B. Iron
c. sulphur
D. Graphite


The value of \( C_{v} \) for 1 mol of polyatomic
gas is \( (\mathrm{F}= \) number of degrees of freedom) :
A \( \cdot \frac{f R}{2 T} \)
в. \( \frac{f R}{2} \)
c. \( \frac{f R T}{2} \)
D. \( 2 f R T \)


Assertion
Aeroplanes always fly at low altitudes.
Reason
According to Newton's third law of
motion, for every action there is an
equal and opposite 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. Both Assertion and Reason are incorrect


Assertion
Time taken by the bomb to reach the ground from a moving aeroplane depends on height of aeroplane only.
Reason
Horizontal component of velocity of the bomb remains constant and vertical
component of bomb changes due to gravity.
A. Both Assertion and Reason are true and the Reason is correct explanation of the Assertion.
B. Both Assertion and Reason are true, but Reason is not correct explanation of the Assertion.
C. Assertion is true, but the Reason is false
D. Assertion is false, but the Reason is true.


The oxidation state of phoshorus varies
from
A. -1 to +1
B . -3 to +3
\( \mathbf{c} \cdot-3 \) to +5
D. -5 to +1


Fill in the blanks with approriate words. Inflammation in the outer covering of lungs is known as


If \( \omega \) is a non-real cube root of unity and
n is not a multiple of \( 3, \) then \( \Delta= \) \( \left|\begin{array}{ccc}\mathbf{1} & \boldsymbol{\omega}^{n} & \boldsymbol{\omega}^{2 n} \\ \boldsymbol{\omega}^{2 \boldsymbol{n}} & \boldsymbol{1} & \boldsymbol{\omega}^{n} \\ \boldsymbol{\omega}^{\boldsymbol{n}} & \boldsymbol{\omega}^{2 \boldsymbol{n}} & \boldsymbol{1}\end{array}\right| \) is equal to
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( \omega \)
\( c \cdot \omega^{2} \)
D.


If \( \boldsymbol{P}(\boldsymbol{A})=\frac{4}{5} \) and \( \boldsymbol{P}(\boldsymbol{B} / \boldsymbol{A})=\frac{2}{5}, \) find
\( \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B}) \)


Assertion
A piece of paper wrapped tightly around a wooden rod gets charred quickly when
held over a flame compared to a piece of
paper wrapped around a brass rod.
Reason
Thermal conductivity of wood is smaller than the conductivity of brass
A. Assertion is false and Reason is True
B. Reason is false and assertion is True.
C. Both Assertion and Reason are True and reason correctly explains assertion
D. Both Assertion and Reason are True but assertion does not correctly explain reason


The sides of safety matches contains:
A. red phosphorus + sand powder
в. \( P_{4} S_{3} \)
c. \( C a_{3}\left(P O_{4}\right)+ \) glass pieces
D. \( K C l O_{3}, K N O_{3} \), sulphur \( + \) antimony


A \( 1500 k g \) car is initially moving with
speed \( 30 m / s . \) Suddenly, a rock falls
onto the road ahead.

The maximum coefficient of friction
between the car tires and the roads is
\( \mu=0.7 \)
Approximately how much distance will the car need to stop to avoid hitting the rock?
\( \mathbf{A} \cdot 22 m \)
B. \( 46 m \)
c. \( 66 m \)
D. \( 87 m \)
E . \( 131 m \)


Which of the following statement is
correct?
A. At sunset or sunrise, the suns rays have to pass through a small distance in the atmosphere.
B. At sunset or sunrise the suns rays have to pass through a larger distance in the atmosphere.
C. Rayleigh scattering which is proportional to \( (l / \lambda)^{2} \)
D. Most of the blue and other shorter wavelengths are not removed by scattering.


A particle of mass \( \mathrm{M} \) at rest decays into
particles of masses \( m_{1} \) and \( m_{2} \) having non -zero velocities. The ratio of the de
broglie wavelengths of the particles
\( \lambda_{1} / \lambda_{2} \) is :
\( \mathbf{A} \cdot m_{1} / m_{2} \)
в. \( m_{2} / m_{1} \)
\( c \)
D. m1.m2


A cell of emf \( 1.5 \% \) and internal
resistance \( 0.5 \Omega \) is connected to a
conductor whose \( V-I \) graph is an
shown in the figure. Then, the terminal
voltage of the cell is
\( \mathbf{A} \cdot 0.75 V \)
в. \( 1.0 V \)
c. \( 1.25 V \)
D. \( 1.5 V \)


If \( \boldsymbol{A}=\left[\begin{array}{cc}\mathbf{2} & -\mathbf{3} \\ \mathbf{4} & \mathbf{1}\end{array}\right], \boldsymbol{B}=\left[\begin{array}{cc}\mathbf{2} & \mathbf{3} \\ \mathbf{5} & \mathbf{0}\end{array}\right] \) and
\( \boldsymbol{C}=\left[\begin{array}{cc}-\mathbf{1} & \mathbf{2} \\ \mathbf{0} & \mathbf{5}\end{array}\right], \) then find \( \boldsymbol{A}(\boldsymbol{B}+\boldsymbol{C}) \)


An open pipe of length \( 33 \mathrm{cm} \) resonates with frequency of \( 1000 H z \). If the speed
of sound is \( 330 m s^{-1}, \) then this
frequency is
A. The fundamental frequency of the pipe
B. The first harmonic of the pipe
c. The second harmonic of the pipe
D. The forth harmonic of the pipe


An element M has the electron
configuration \( [A r] 3 d^{5} 4 s^{2} . \) So, which of the following oxide cannot exist for element
M?
A. \( M O_{2} \)
B. \( M_{2} O_{3} \)
c. \( M O_{4} \)
D. \( M_{2} O_{7} \)


Anthers dehisce by terminal pores in
A. Pea
B. Petunia
c. Datura
D. Solanum


Heat is also called thermal energy
A. True
B. False


If \( \boldsymbol{A}=(-2,3,4), B=(1,2,3) \) are two
points and \( P \) is the point of intersection
of \( A B \) and \( z x \) -plane, then \( P_{x}+P_{y}+ \)
\( \boldsymbol{P}_{z}= \)
\( \mathbf{A} \cdot \mathbf{6} \)
B. -8
c. 8
D.


For a cell, the cell reaction is \( M g(s)+ \) \( C u^{2+}(a q) \rightarrow M g^{2+}(a q)+C u(s) . \) If the
S.R.P. values of \( M g \) and \( C u \) are \( -2.37 V \)
and \( +0.34 V \) respectively, the EMF of the
cell is:
A \( .+2.03 V \)
B . \( -2.03 \mathrm{V} \)
\( \mathrm{c} \ldots+2.71 \mathrm{V} \)
D. \( -2.71 V \)


Using the formula for squaring a
binomial the value of \( (999)^{2} \) is:
A. 98009
B. 998005
c. 998001
D. 998002


The human eye forms the image of an
object at its
A. cornea
B. iriss
c. pupil
D. retina


Hydrolysis of 1 mol of peroxodisulphuric
acid produces:
A. 2 mol of sulphuric acid.
B. 2 mol of peroxomono sulphuric acid.
C. 1 mol of sulphuric acid and 1 mol of peroxomono sulphuric acid.
D. 1 mol of sulphuric acid, 1 mol of peroxomono sulphuric acid, and 1 mol of hydrogen peroxide.


Solve the differential equation, \( \frac{d y}{d x}- \) \( \frac{2 x y}{1+x^{2}}=x^{2}+1 \)


If \( O(0,0), A(4,13) \) and \( B(8,9) \) are vertices of a \( \Delta O A B \) and a line \( y=k x \)
bisects the area of the triangle. If the intercept of \( y=k x \) between the
triangle is taken as a diameter of the circle, then the centre of this circle is:
\( ^{\mathrm{A}} \cdot\left(5, \frac{11}{2}\right) \)
в. \( \left(4, \frac{22}{3}\right) \)
\( ^{c} \cdot\left(3, \frac{11}{2}\right) \)
D. \( \left(3, \frac{22}{3}\right) \)


Calculate the surface area of a sphere
with radius \( 3.2 \mathrm{cm} \)
A \( \cdot 110.6 \mathrm{cm}^{2} \)
B . \( 128.6 \mathrm{cm}^{2} \)
c. \( 131.5 \mathrm{cm}^{2} \)
D. None of these


In organic compounds, phosphorus is estimated as:
A. \( M g_{2} P_{2} O_{7} \)
в. \( M g\left(N H_{4}\right) P O_{4} \)
c. \( M g_{3}\left(P O_{4}\right)_{2} \)
D. \( H_{3} P O_{4} \)


\( (\sqrt{2}+1)^{6}+(\sqrt{2}-1)^{6}= \)
A . 99
B. 98
c. 196
D. 198


Which of the following choices will favor the melting of ice in a closed container
if all other parameters are kept constant?
A. Adding water with a temperature of \( 0^{\circ} \mathrm{C} \)
B. Lowering the temperature below \( 0^{\circ} \mathrm{C} \)
c. Lowering the pressure
D. Raising the pressure
E. Decreasing the amount of ice


Statement - 1: During secondary growth in dicot stem the wood formed in winter
is called late wood.
Statement - 2: In spring season cambium becomes inactive therefore it
does not produce xylary elements. Which of the following option is true for
the above given statements?
A. Only statement 1 is correct
B. Only statement 2 is correct
c. Both the statements are correct
D. Both the statements are incorrect


n the given figure, what are the
substances labelled as \( P, Q, R \) and \( S ? \)
A . P-PGA, Q-Glyoxylate, \( R-N H_{3} \), S-serine
3. P-Glycolate, Q-Glyoxylate, \( R-N H_{3} \), S-serin
c. P-Glycolate, Q-Glyoxylate, \( R-C O_{2} \), S-serin
'. P-RuBP, Q-Glycerate, \( R-C O_{2} \), S-Serine


In the parallelogram ABCD, the angles A
and \( C \) are obtuse. Points \( X \) and \( Y \) are
taken on the diagonal BD such that the angles \( \mathrm{XAD} \) and \( \mathrm{YCB} \) are right angles.
Prove that: \( X A=Y C \).
State whether the above statement is
true or false.
A. True
B. False


Action spectrum of photosynthesis was discovered by
A. Calvin
B. Engelman
c. Blackman
D. Hill


Statement I: The entropy of a solid decreases when it is dissolved
Because
Statement II : It becomes less ordered
A. Statement 1 and Statement 2 are correct and
Statement 2 is the correct explanation of Statement 1
B. Both the Statement 1 and Statement 2 are correct and
Statement 2 is not the correct explanation of Statement 1.
C. Statement 1 is correct but Statement 2 is not correct.
D. Statement 1 is not correct but Statement 2 is correct.
E. Both the Statement 1 and Statement 2 are not correct.


In a common-base mode of a transistor,
the collector current is 5.488 mA for an
emitter current of 5.60 mA. The value of
the base current amplification factor \( (\boldsymbol{\beta} \)
will be
A .49
B. 50
\( c \cdot 51 \)
D. 48


The potential energy of an object of
mass \( m \) moving in \( x y \) plane in a
conservative field is given by \( \boldsymbol{u}=\boldsymbol{a} \boldsymbol{x}+ \)
\( b y, \) where \( x \) and \( y \) are position
coordinates of the object. Find magnitude of its acceleration.


The commercial name of poly(methyl methacrylate) is:
A . Lucite
B. Plexiglas
c. Perspex
D. All the above


Find the equation of the ellipse whose
foci are (0,±5) and length of the minor
axis is 24


Write the principal value of \( \sin ^{-1}\left(-\frac{1}{2}\right) \) \( ? \)


Number of Faradays (F) required to reduce 3 mol of \( M n O_{4}^{\ominus} \) to \( M n^{2+} \) is:


Derive the relation between elevation of
boiling point and molar mass of solute.


Which of the following shows maximum molar conductance?
A \( \cdot\left[\operatorname{Co}\left(N H_{3}\right)_{6}\right] C l_{3} \)
В \( \cdot\left[\operatorname{Co}\left(N H_{3}\right)_{3} C l_{3}\right] \)
c. \( \left[\operatorname{Co}\left(N H_{3}\right)_{4} C l_{2}\right] C l \)
D \( \cdot\left[\operatorname{Co}\left(N H_{3}\right)_{5} C l\right] C l_{2} \)


A house is fitted with 4 lamps 60 w each, 2 fans rated 100 w each, an electric kettle rated 2KW. If the energy
\( \operatorname{costs} \) Rs. 5.50 per \( \mathrm{KWh} \), calculate the monthly bill (of 30 days) for running the appliances for 5 hours a day.


The function \( \boldsymbol{f}:(-\infty,-1] \rightarrow\left(0, e^{5}\right) \)
defined by \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{e}^{\boldsymbol{x}^{3}-\mathbf{3} \boldsymbol{x}+\mathbf{2}}, \) is
A. many-one and onto
B. many-one and into
c. one-one and onto
D. one-one and into


An electron is taken from point \( A \) to
point \( B \) along the path \( A B \) in a uniform
electric field of intensity \( \boldsymbol{E}=\mathbf{1 0} \boldsymbol{V m}^{-1} \)
Side \( A B=5 m, \) and side \( B C=3 m \)
Then, the amount of work done on the
electron by us is :
A. 50 ev
B. 40 ev
c. - -50 ev
D. -40 eV


Let \( A B C \) be a right triangle in which
\( A B=3 c m, B C=4 c m \) and \( \angle B= \)
\( 90^{\circ} . B D \) is the perpendicular from \( B \) on
\( A C . \) The circle through \( B, C, D \) is drawn. Construct the tangents from \( \boldsymbol{A} \) to this circle.


An object is moving along a straight
line whose velocity-time graph is given below:

What will be the ratio of the distance
travelled to the displacement of object
from \( t=0 \) and \( t=5 \) sec?
1: 3
B . 2: 1
\( c \cdot 3: 1 \)
6


According to which law current \( \boldsymbol{I} \) flowing in the rod must vary for the rod to rotate at a constant angular speed. Begin to measure the time from the instant when the rod is in its right-hand horizontal position. Consider the current to be positive when it flows from the axis of rotation toward the ring.


Describe the steps of procedure of
Mendel's experiments with suitable example.


The motion of second's hand in a clock
is an example of
A. uniform motion
B. non-uniform motion
c. a combination of uniform and non-uniform motion
D. neither uniform nor non-uniform motion


A steel rod of length \( 0.5 \mathrm{km} \) is used in
the construction of a bridge. It has to
withstand a temperature change of
\( 40^{\circ} \mathrm{C} . \) The gap that is allowed for its
expansion is :
\( \left(\boldsymbol{\alpha}=\mathbf{1 0}^{-\mathbf{6}} /^{\circ} \boldsymbol{C}\right) \)
A. \( 0.02 \mathrm{cm} \)
B. 0.02mm
\( c .2 m \)
D. 20 mm


\( \lim _{x \rightarrow 2} \frac{x^{10}-1024}{x-2} \)
evaluate above limit.
At \( x=2 \) final value is


\( 4.5 g \) of aluminium (At. mass \( =27 \) atm
is deposited at cathode from \( \boldsymbol{A} \boldsymbol{l}^{\mathbf{3}+} \)
solution by a certain quantity of electric charge. The volume of hydrogen
produced at STP from \( \boldsymbol{H}^{+} \) ions in solution by the same quantity of electric charge will be
A . \( 44.8 L \)
B. 22.4 L
c. \( 11.2 L \)
D. \( 5.6 L \)


Which of the following causes delaying
of senescence?
A. Cytokinins
B. Auxins
\( c \cdot \) ।АА
D. Ascorbic acid


Pencil lead is formed from:
A. graphite and clay
B. lead oxide
c. bone black
D. lead peroxide


Which of the following is an example of super octet molecule?
A. \( S F_{6} \)
в. \( P C l_{5} \)
c. \( I F_{7} \)
D. All the three


Assertion
Cyclotron is a device which is used to
accelerate the positive ions.
Reason
Cyclotron frequency depends upon the velocity
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


The value of integral \( \int_{\pi / 4}^{\pi / 2} \cos x d x \) is?


Identify the wrong statements from the following.
(i) Branches of limited growth in
Asparagus perform photosynthesis.
(ii) Petiole of Australian Acacia helps in
climbing.
(iii) Floral buds of Agave store food materials.
(iv) Aerial roots of taeniophyllum help in
vegetative propagation.
A. i, iv
B. i, i i
C . iii, iv
D. ii, iv


How carbon dioxide is stored in the
house to extinguish fire?
A. It can store in the bottles
B. It can store in the cylinders under high pressure
c. It can store in canes
D. It can not store in any form


The cell constant of a conductivity cell:
A. changes with change of electrolyte
B. changed with change of concentration of electrolyte
C. changes with temperature of electrolyte
D. remains constant for a cell


In YDSE using monochromatic visible light, the distance between the plane of slits and the screen is \( 1.7 m . \) At point \( P \)
on the screen which is directly in front of the upper slit, maximum path is observed. Now, the screen is moved
\( 50 c m \) closer to the plane of slits. Point
\( P \) now lies between third and fourth
minima above the central maxima and
the intensity at \( P \) is one-fourth of the maximum intensity on the screen. Find the wavelength of light if the separation of slits is \( 2 m m \)
A. \( 2.9 \times 10^{-7} \mathrm{m} \)
В. \( 3.9 \times 10^{-7} \mathrm{m} \)
c. \( 5.9 \times 10^{-7} m \)
D. \( 6.9 \times 10^{-7} \) т


A solution contains \( A g^{+} \) ion of
concentration \( 2 \times 10^{-18} M . \) What is the
concentration of \( N a_{2} S \) solution to be used in order to just start precipitation? \( \left(\boldsymbol{K}_{s p}\left(\boldsymbol{A} \boldsymbol{g}_{2} \boldsymbol{S}\right)=\boldsymbol{4} \times \mathbf{1 0}^{-48}\right) \)
A \( \cdot 1 \times 10^{-30} M \)
В. \( 1 \times 10^{-24} M \)
c. \( 1 \times 10^{-18} \mathrm{M} \)
D. \( 1 \times 10^{-12} M \)


Distinguish between pectoral and pelvic girdle.


A Cathode ray tube emits \( 1.875 \times 10^{3} \)
electrons per second when heated. When \( 600 \mathrm{V} \) is applied to the anode all the electrons emitted reach the anode.
The maximum electron current will be
A. \( 3 A \)
в. \( 3 \mu A \)
\( c .3 m A \)
D. None of these


Followings are some of the characteristics of animals:
(i) Diets heavy on fruits,
(ii) White fur
(iii) Need to migrate
(iv) Loud voice (v)
Sticky pads on feet (vi) Layer of fat under skin (vii) Wide and large paws
(viii) Bright colors (ix) Strong tails \( (x) \) Long and large beak. For each characteristic indicate
whether it is adaptation for tropical
rainforests or polar regions. Do you think that some of these
characteristics can be adapted for both regions?


A person travelled a distance of \( 100 m \)
in 10 seconds. What is the speed of the
person?
A. \( 10 \mathrm{m} / \mathrm{s} \)
в. \( 12 m / s \)
\( \mathbf{c} \cdot 15 m / s \)
D. \( 5 m / s \)


You are thrown outside when your car
suddenly takes a turn. Which law of Newton is involved in this?
A. First Law
B. Second Law
c. Third law
D. Can't say


\( \frac{1}{3}+\frac{1}{3}\left(\frac{1}{3}\right)^{3}+\frac{1}{5}\left(\frac{1}{3}\right)^{5}+\dots= \)
A \( \cdot \frac{1}{2} \log _{e} 2 \)
B \( \cdot 2 \log _{e} 2 \)
\( \mathbf{c} \cdot \log _{e} 2 \)
D. \( \log _{e} 3 \)


In a simultaneous throw of a pair of dice, find the probability of getting a
total more than 7 .


A field of \( 100 \mathrm{Vm}^{-1} \) is directed at \( 30^{\circ} \mathrm{to} \)
positive x-axis. Find \( \left(V_{A}-V_{B}\right) \) if
\( O A=2 m \) and \( O B=4 m \)
A \( \cdot 100(\sqrt{3}-2) V \)
B . \( -100(2+\sqrt{3}) V \)
c. \( 100(2-\sqrt{3}) v \)
D \( \cdot 200(2+\sqrt{3}) v \)


The hybridisation of central and terminal carbon atoms is
are respectively
\( \mathbf{A} \cdot s p \) and \( s p \)
B. \( s p^{2} \) and \( s p^{2} \)
c. \( s p \) and \( s p^{2} \)
D. \( s p^{2} \) and \( s p \)


In a flask colourless \( N_{2} O_{4} \) is in
equilibrium with brown coloured \( N O_{2} \) At equilibrium, when the flask is heated
to \( 100^{\circ} C \) the brown colour deepens and
on cooling, the brown colour became
less coloured. The change in enthalpy
\( \Delta H \) of the system is:
A. negative
B. positive
c. zero
D. not defined


A coin is tossed. Find the total number
of elementary events and also the total number events associated with the
random experiment.


Range of values of the function \( y= \) \( \log _{3}\left[\frac{3 \sin x+4 \cos x+10}{3 \sin x+4 \cos x}\right] \) is equal to
\( A \cdot(-\infty, 1] \)
B . \( [1, \infty) \)
\( c \cdot[3, \infty) \)
D・ [0,1]


The inequality \( |z-4|<|z-2| \)
represents the following region.
\( \mathbf{A} \cdot \operatorname{Re}(z)>0 \)
B \( \cdot \operatorname{Re}(z)<0 \)
\( \mathbf{c} \cdot \operatorname{Re}(z)>2 \)
D. None of these


\( \ln H_{2} O, \) the bond angle \( \mathrm{HOH} \) is \( 104^{\circ} 28^{\prime} \)
but in \( H_{2} S, H_{2} S e \) and \( H_{2} T e \) the bond
angles are pretty close to \( 90^{\circ} . \) This
suggests that:
A . oxygen uses \( s p^{2} \) -hybrid orbitals while \( S, \) Se and Te use \( s p^{3} \) -hybrid orbitals for bonding with the hydrogen atoms
B. oxygen uses \( s p^{3} \) -hybrid orbitals to bond with the two hydrogen atoms while \( S, \) Se and Te use almost pure \( \mathrm{p} \) orbitals
c. oxygen uses \( s p^{3} \) -hybrid orbitals while \( S, \) Se and \( T e \) utilize d orbitals for bonding with the hydrogen atoms
D. all the atoms use pure p orbitals to bond with the hydrogen atoms


Which of the following represents the isopolyacid of phosphorus?


For the given parabola find the coordinates of focus, axis, the equation of the directrix and the length of the
latus rectum.
\( \boldsymbol{x}^{2}=-\mathbf{9} \boldsymbol{y} \)


Tendency of abortion in ladies is caused by
A. Cyanobacteria
B. Bacteria
c. Mycoplasma
D. None of the above


Two resistances are connected in the
two gaps of a metre bridge. The balance point is \( 20 \mathrm{cm} \) from the zero end. When a resistance \( 15 \Omega \) is connected in series with the smaller of two resistances, the
null point shifts to \( 40 \mathrm{cm} . \) The smaller of
the two resistances has the value.
\( A \cdot 8 \Omega \)
B. \( 9 \Omega \)
\( c .10 \Omega \)
D. 12\Omega


When electron jumps from \( \mathrm{N} \) shell to shell, the energy is:
A. emitted
B. absorbed
c. reflected
D. cannot be predicted


Two lithium nuclei in a lithium vapour
at room temperature do not combine to
form a carbon nucleus- because:
A. a lithium nucleus is more tightly bound than a carbon nucleus
B. carbon nucleus is unstable particle
c. it is not energetically favourable
D. coulomb repulsion does not allow the nuclei to come very close


After two or three years of the secondary growth, the cortex in dicot root
A. Remains intact
B. Is completely sloughed away
c. Is largely lost.
D. Is converted into cork.


Motion of charges is nothing but:
A. electric current
B. magnetic effect
c. heating effect
D. all of the above


A mass \( m \) is moving with constant
velocity parallel to the \( x \) axis. Its
angular momentum w.r.t the origin
A. Is zero
B. Remains constant
c. Goes on increasing
D. Goes on decreasing


On the occasion of Dipawali festival each student of a class sends greeting cards to one another. If the postmen
deliver 1640 greeting cards to the students of this class, then the number
of students in the class is
A . 39
B. 41
\( c \cdot 5 \)
D. 53


The correct statement in respect of
structure of hypo phosphorous acid is:
A. 2 -OH groups, 2 -H atoms are attached directly
to \( P \)
B. One OH group and 2-H atoms are directly
attached to \( \mathrm{P} \)
C. One OH group and 3 - H atoms are directly
attached to \( \mathrm{P} \)
D. Three OH groups are attached directly to P


A voltmeter of a very high resistance is joined in the circuit as shown in figure.
The voltage shown by this voltmeter will
be
\( A \cdot 5 V \)
B. \( 6 V \)
c. \( 2.5 V \)
D. \( 3 V \)


The mean value of the function \( f(x)= \)
\( \frac{2}{e^{x}+1} \) on the interval [0,2] is
A \( \cdot \log \frac{2}{e^{2}+1} \)
B. \( 1+\log \frac{2}{e^{2}+1} \)
c. \( _{2+\log _{e^{2}+1}} \frac{2}{e} \)
D. \( 2+\log \left(e^{2}+1\right) \)


In acidic medium, \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) changes
\( C r_{2} O_{7}^{-2} \) to \( C r O_{5} \) which has two \( (-O- \)
\( O-) \) bonds oxidation state of \( C r \) in
\( \boldsymbol{C r} \boldsymbol{O}_{5} \) is:
\( A \cdot+5 \)
\( B \cdot+3 \)
\( c \cdot+6 \)
D. -10


Which of the following is a true statement about aromatic aldehydes
and ketones?
A. They are insoluble in water
B. They are water soluble
c. They are insoluble in organic solvents.
D. None of these


If a charged particle goes unaccelerated in a region containing electric and magnetic fields:
A . \( \vec{E} \) must be parallel to \( \vec{B} \)
B. \( \bar{V} \) must be perpendicular to Electric field
c. \( \vec{V} \) must be parallel to \( \vec{B} \)
D. \( E \) must be equal to \( v B \)


Show that the points with position vectors \( \vec{a}+\vec{b}, \vec{a}-\vec{b} \) and \( \vec{a}+k \vec{b} \) are
collinear for all values of \( k \)


\( x=\frac{\sin ^{3} p}{\cos ^{2} p}, y=\frac{\cos ^{3} p}{\sin ^{2} p} \) and \( \sin p+\cos p \)
\( =\frac{1}{2} \) then \( x+y= \)
A \( \cdot \frac{75}{18} \)
в. \( \frac{44}{9} \)
c. \( \frac{79}{18} \)
D. \( \frac{48}{9} \)


The compound that neither forms semicarbazone nor oxime is:
A. \( H C H O \)
в. \( C H_{3} \)СОСН\( _{3} \)
с. \( C H_{3} C H O \)
D. \( C H_{3} C H_{2} C H_{2} N H_{2} \)
E \( \cdot\left(C H_{3}\right)_{2} C H C H O \)


The common immediate source of
energy for cellular activity is
A. NAD
B. ATP
\( c . \) DNA
D. RNA


"Of the alkali metals, only Na forms
nitrides."
Answer whether the above statement is
true or false.
If true enter 1 , else enter 0


Assertion
When KI solution is added to \( A g N O_{3} \)
solution, negatively charged sol results.
Reason
Negative charge of sol is due to preferential adsorption of iodide ions from the dispersion medium.
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


Identify the compounds \( A, B \) and \( C \)
(i) \( \boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{O} \boldsymbol{H} \quad \boldsymbol{P C l}_{5} \quad \boldsymbol{A} \quad \boldsymbol{K} \boldsymbol{C} \boldsymbol{N} \)
(ii) \( \boldsymbol{C}_{6} \boldsymbol{H}_{5} \boldsymbol{C O O H} \quad \boldsymbol{S O C l}_{2}, \boldsymbol{A} \quad \boldsymbol{N H}_{3} \)


How many terms are need in the A.P.
\( 24,20,16 \ldots . . \) to make the sum \( 72 ? \)


The seeds in gymnosperms are
A. Naked
B. Enclosed within the ovule
C. Present in fruits
D. Partly naked and partly enclosed within the ovules


An automobile engine absorbs \( 1600 J \) of heat from a hot reservoir and expel
\( 1000 J \) to a cold reservoir in each
cycle.Find the efficiency of the cycle?
A . \( 37.5 \% \)
B . \( 47.5 \% \) \%
c. \( 40 \% \)
D. 30 \%


If \( A \) is \( 2 \times 2 \) matrix such that \( A^{2}=0 \)
then \( t r(A) \) is
A
B.
\( c \cdot-1 \)
D. none of these


Which of the following reacts most slowly with nitric acid?
A. Phosphorus
B. Chlorine
c. sulphur
D. lodine


The two main parts of nephron are
A. Bowman's capsule and renal tubule
B. Glomerulus and renal tubule
C. Bowman's capsule and glomerulus
D. Glomerulus and malpighian body


A person travelling towards east at the rate of \( 2 \mathrm{m} / \mathrm{sec} \) finds that the wind
seems to blow directly from the north, on doubling his speed it appears to come from the north east. Find the
magnitude and direction of the wind.


In acid medium, the standard reduction
potential of \( N O \) converted to \( N_{2} O \) is
\( \mathbf{1 . 5 9} \boldsymbol{V} \). Its standard potential in alkaline
medium would be:
A. \( -1.59 V \)
В. \( -0.764 V \)
c. \( 0.764 V \)
D. \( 0.062 V \)


An electric dipole placed in a nonuniform electric field may experiences:
A. a force but no torque
B. a torque but no force
c. a force as well as a torque
D. neither a force nor a torque


What is refraction? Give its two
examples.


A solid sphere falls with a terminal velocity of \( 10 \mathrm{m} / \mathrm{s} \) in air. If it is allowed to
fall in vacuum:
A. terminal velocity will be more than \( 10 \mathrm{m} / \mathrm{s} \)
c. terminal velocity will be \( 10 \mathrm{m} / \mathrm{s} \)
D. there will be no terminal velocity


The set of values of ' \( x^{\prime} \) for which the
formula \( 2 \sin ^{-1} x=\sin ^{-1}(2 x \sqrt{1-x^{2}}) \)
is true, is
A. (-1,0)
B. [0,1]
c. \( \left[-\frac{\sqrt{3}}{2}, \frac{\sqrt{3}}{2}\right] \)
D. \( \left[-\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right] \)


Simplify :
\( 3 x(2+5 x)-6(1-2 x) \)


Evaluate : \( \int \frac{d x}{a+b e^{c x}} \)


\( \frac{d y}{d x} \) for \( y=\tan ^{-1}\{\sqrt{\frac{1+\cos x}{1-\cos x}}\}, \) where
\( \mathbf{0}<\boldsymbol{x}<\boldsymbol{\pi}, \) is?
\( A \cdot \frac{-1}{2} \)
B.
\( c \cdot 1 \)
D.


Equilibrium constant \( \left(\boldsymbol{K}_{C}\right) \) of
\( \mathbf{2} \boldsymbol{H} \boldsymbol{I}_{(\boldsymbol{g})} \rightleftharpoons \boldsymbol{H}_{2(\boldsymbol{g})}+\boldsymbol{I}_{2(\boldsymbol{g})} \) is \( \boldsymbol{2} \times \mathbf{1 0}^{-4} \)
What is the equilibrium concentration
of \( \boldsymbol{H} \boldsymbol{I}, \) if concentration of \( \boldsymbol{H}_{2(\boldsymbol{g})} \) and \( \boldsymbol{I}_{2}(\boldsymbol{g}) \)
respectively are \( 2.2 \times 10^{-2} M \) and
\( \mathbf{2} . \mathbf{2} \times \mathbf{1 0}^{-\mathbf{4}} \mathbf{M} ? \)
A \( \cdot 1.55 \times 10^{-1} M \)
В. \( 2.22 \times 10^{-5} \) М
c. \( 3.11 \times 10^{-5} M \)
D. \( 6.66 \times 10^{-5} M \)


Lectotype is
A. Duplicate of holotype.
B. Specimen described along with holotype.
C. Specimen cited by author without making one hlotype.
D. Specimen cited by author from original material for nomenclature type when there is no holotype.


The statement pattern \( (\boldsymbol{p} \wedge \boldsymbol{q}) \wedge[\sim \boldsymbol{r} \vee \)
\( (p \wedge q)] \vee(\sim p \wedge q) \) is equivalent to
\( A \)
B. 9
\( c \cdot p \wedge q \)
D.


The solution of \( \frac{d y}{d x}+\frac{2 x}{1+x^{2}} y= \)
given that \( \boldsymbol{x}=\mathbf{1}, \boldsymbol{y}=\mathbf{0} \) is
\( \left(1+x^{2}\right)^{2} \)
A \( \cdot y\left(1+x^{2}\right)=\tan ^{-1} x-\frac{\pi}{4} \)
В \( \cdot y\left(1-x^{2}\right)=\tan ^{-1} x-\pi / 4 \)
c. \( y\left(1+x^{2}\right)=\tan ^{-1} x+\frac{\pi}{4} \)
D. \( y\left(1-x^{2}\right)=\tan ^{-1} x+\pi / 4 \)


Velocity of a viscous liquid in long
cylinder of radius \( R \) at a distance \( R_{1} \)
from centre is \( V_{1} \) Find the velocity of the
liquid as a function of the distance from the axis of the cylinder,


Which of the following statements
is/are incorrect?
A. A nucleic acid is a molecule made up of a nitrogenous base, a phosphate group and a 5-carbon sugar
B. A nucleic acid is a molecule made up of a nitrogenous base, a phosphate group and a ribose sugar
C. A nucleic acid is a molecule made up of a nitrogenous base, a phosphate group and a deoxyribose sugar
D. None of the above


The radius of a sphere increased by 50 percent. By how many per cent did the surface area of the sphere increase?


An organic compound contains carbon, hydrogen and oxygen. Its elemental analysis gave \( C, 38.71 \% \) and \( \mathrm{H}, 9.67 \% \) The empirical formula of the compound would be?
A. \( C H_{4} O \)
в. \( C H_{3} O \)
\( \mathrm{c} \cdot \mathrm{CH}_{2} \mathrm{O} \)
D. \( C H O \)


Obtain relation when object distance
varies in a convex lens of focal length \( \mathrm{f} \)


Xavier, Yvonne, and Zelda each try
independently to solve a problem. If their individual probabilities for success are \( \frac{1}{4}, \frac{1}{2} \) and \( \frac{5}{8} \) respectively, what is the probability that Xavier and Yvonne, but not Zelda,
will solve the problem?
A \( \cdot \frac{11}{8} \)
в. \( \frac{7}{8} \)
c. \( \frac{9}{64} \)
D. \( \frac{5}{64} \)
E \( \cdot \frac{3}{64} \)


A rigid ball of mass m strikes a rigid
wall at \( 60^{\circ} \) and gets reflected without
loss of speed as shown in the figure
below. The value of impulse imparted by
the wall on the ball will be :
A \( \cdot \frac{m V}{3} \)
B. \( m V \)
\( \mathbf{c} \cdot 2 m V \)
D. \( \frac{m V}{2} \)


The van't Hoff factor (i) for a dilute
aqueous solution of the strong electrolyte barium hydroxide is :
\( A \cdot 2 \)
B. 3
\( c \cdot 0 \)
D.


If \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) and \( \boldsymbol{g}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) defined by
\( \boldsymbol{f}(\boldsymbol{x})=|\boldsymbol{x}| \) and \( \boldsymbol{g}(\boldsymbol{x})=[\boldsymbol{x}-\boldsymbol{3}] \) for \( \boldsymbol{x} \in \boldsymbol{R} \)
[.] denotes greatest integer function, \( \operatorname{then}\left\{\boldsymbol{g}(\boldsymbol{f}(\boldsymbol{x})): \frac{-\boldsymbol{8}}{\boldsymbol{5}}<\boldsymbol{x}<\frac{\boldsymbol{8}}{\boldsymbol{5}}\right\}= \)
A \( \cdot\{0,1\} \)
в. \{-1,-2\}
\( \mathbf{c} \cdot\{-3,-2\} \)
D. \{2,3\}


Plastics are generally good conductors of electricity.
A . True
B. False


As shown in fig. if a charge \( +q \) is
carried from a point \( \boldsymbol{A}\left(\boldsymbol{r}, \mathbf{1} \mathbf{3 5}^{\circ}\right) \) to point
\( B\left(r, 45^{\circ}\right) . \) If dipole moment is \( p \) then the
work done by the external agent is then
going to be
A . 0
В. \( \frac{q p}{4 \pi \epsilon_{0} r^{2}} \)
\( c \cdot \frac{1}{4 \pi \epsilon_{0}} \frac{\sqrt{2} q p}{r^{2}} \)
D. \( \frac{1}{4 \pi \epsilon} \frac{q p}{r^{2}} \)


Imagine that a reactor converts all
given mass into energy and that it
operates at a power level of \( 10^{9} W \). The
mass of the fuel consumed per hour in
the reactor will be (velocity of light, c is
\( \left.3 \times 10^{8} m / s\right) \)
\( \mathbf{A} \cdot 0.8 g m \)
в. 0.96 gm
c. \( 4 \times 10^{-2} g m \)
D. \( 6.6 \times 10^{-5} g m \)


toppr
Q Type your question
voltage with time in the coil?
\( A \)
B.
\( c \)
D.


Keystone species deserve protection
because they
A. Are capable of surviving in harsh environmental conditions.
B. Indicate presence of certain minerals in the soil.
C. Have become rare due to overexploitation.
D. Play an important role in supporting other species.


Which of the following arrangements of electrons is mostly likely to be stable?
\( A \)
\begin{tabular}{|c|c|c|c|c|c|}
\hline\( \uparrow \) & \( \uparrow \) & \( \uparrow d \) & \( \uparrow \) & \( \uparrow \) & \( ^{4 s} \) \\
\hline
\end{tabular}
в. \begin{tabular}{|c|c|c|c|c|c|}
\hline\( \uparrow \downarrow \) & \( \uparrow \) & \( \uparrow \) & \( \uparrow \) & \( \uparrow \) & \( \uparrow \) \\
\hline
\end{tabular}
\( c \)
\begin{tabular}{|c|c|c|c|c|}
\hline\( \uparrow \) & \( \uparrow \) & \( \uparrow \) & \( \uparrow \) & \( \uparrow \) \\
\hline
\end{tabular} \( \frac{4}{\downarrow} \)
D. \begin{tabular}{r}
\( 4 s \) \\
\hline\( \uparrow \uparrow \)
\end{tabular} \begin{tabular}{|c|c|c|c|c|c|}
\hline\( \uparrow \) & \( \uparrow \) & \( \uparrow \) & \( \uparrow \) & \( \uparrow \) \\
\hline
\end{tabular}


\( f(x)=x^{2}+5, \) Find \( f(5) \)


Which of the following plant tissues is not a simple permanent tissue?
A. Xylem
B. Collenchyma
c. sclerenchyma
D. Parenchyma


In the Duma's method for the
estimation of nitrogen in an organic compound, nitrogen is determined in the form of:
A. gaseous nitrogen
B. gaseous ammonia
c. ammonium sulphate
D. sodium cyanide


If the distance of Earth from the Sun
were half the present value, how many days will make one year?


In LCR series circuit, an alternating emf
\( e \) and current \( i \) are given by the
equations \( e=100 \sin (100 t) \) volt
\[
\boldsymbol{i}=\mathbf{1 0 0} \sin \left(\mathbf{1 0 0 t}+\frac{\boldsymbol{\pi}}{\mathbf{3}}\right) \boldsymbol{m} \boldsymbol{A}
\]
The average power dissipated in the circuit will be
\( \mathbf{A} \cdot 100 W \)
в. \( 10 W \)
\( \mathrm{c} \cdot 5 \mathrm{W} \)
D. \( 2.5 W \)


Iron can be prevented from rusting by:
This question has multiple correct options
A. connecting iron to more electropositive metal a case of cathodic protection.
B. connecting iron to more electropositive metal a case of anodic protection.
c. connecting iron to less electropositive metal a case of anodic protection
D. connecting iron to less electropositive metal a case of cathodic protection.


If there was no \( C O_{2} \) in the earth's
atmosphere, the temperature of the earth's surface would be
A. Same as the present level
B. More than the present level
C. Less than the present level
D. Dependent on \( O_{2} \) content of atmosphere


A hollow spherical conductor of radius
\( R \) is given a charge \( Q . \) Work done in
moving a charge \( q \) from its centre to surface is :
A \( \cdot \frac{Q q}{4 \pi \varepsilon_{0} R} \)
в. \( \frac{Q q}{2 \pi \varepsilon_{0} R} \)
c. \( \frac{Q q}{\pi \varepsilon_{0} R} \)
D. zero


Scientist credited with development of
formula for balanced solution of
mineral elements is?
\( A . \quad \) Knop
B. went
c. нill
D. Emerson


A cricket ball of mass \( 150 g \) moving with a speed of \( 126 k m / h \) hits at the
middle of the bat, held firmly at its position by the batsman. The ball moves straight back to the bowler after hitting the bat. Assuming that collision between ball and bat is completely elastic and the two remain in constant
for \( 0.001 s, \) the force that the batsman
had to apply to hold the bat firmly at its place would be:
A . \( 10.5 N \)
B. \( 21 N \)
c. \( 1.05 \times 10^{4} N \)
D. \( 2.1 \times 10^{4} N \)


Two particles \( A \) and \( B \) initially at rest, move towards each other under a
mutual force of attraction. At the
instant when the speed of A is v and speed of \( \mathrm{B} \) is \( 2 \mathrm{v} \), the speed of centre of
mass of the system is :
A. zero
в.
\( c \cdot 1.5 v \)
D. 3


If \( (1+x)^{n}=\sum_{i=0}^{n} C_{i} x^{i}, \) then the sum of
the products of \( C_{i} \) 's taken two at a time is represented by \( \sum_{0 \leq i \leq j \leq n} C_{i} C_{j} \)
A \( \cdot 2^{n}-\frac{(2 n) !}{2(n !)^{2}} \)
B. \( 2^{n}+\frac{(2 n) !}{2(n !)^{2}} \)
c. \( \frac{1}{2}\left(2^{2 n}+\frac{(2 n) !}{(n !)^{2}}\right) \)
D. \( \frac{2^{2 n}}{2(n !)^{2}} \)


The value of \( \int \frac{d x}{\sqrt{2 x-x^{2}}} \) is
\( A \cdot \sin ^{-1}(x)+c \)
B \( \cdot \sin ^{-1}(x-1)+c \)
\( \mathbf{c} \cdot \sin ^{-1}(1+x)+c \)
D. \( -\sqrt{2 x-x^{2}}+c \)


The time by a photo-electron to come out after the photon strikes is approximately
\( \mathbf{A} \cdot 10^{-1} s \)
B. \( 10^{-4} s \)
\( \mathbf{c} \cdot 10^{-10} s \)
D. \( 10^{-16} s \)


Which of the following statements
is/are correct?
This question has multiple correct options
A. The nitration of phenol is faster than phenyl acetate
B. The reaction of \( P h O^{\ominus} \) is faster than \( p-N C- \)
\( C_{6} H_{4} O^{\ominus} \) with \( P h C H_{2} C l \)
C. Base-catalysed hydrolysis of p-nitrophenyl acetate is faster than phenyl acetate
D. Acid-catalysed esterification of PhOH is faster than \( p \) nitrophenol with MeCOOH


Name the processes from which
chlorine is obtained as a by-product What will happen if an aqueous solution of \( N a C l \) is subjected to electrolysis?


An atom has electronic configuration of
2,8,18,7
What is the atomic number the of
atom?
A. 7
B. 35
c. 70
D. 17


What is the degree of the given
monomial \( -x y^{2} ? \)
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. none


If \( I_{n}=\int x^{n} e^{a x} d x, \) then \( I_{n}-\frac{x^{n} e^{a x}}{a}= \)
A. \( \frac{n}{a} I_{n-2} \)
B. \( -\frac{n}{a} I_{n-2} \)
c. \( \frac{n}{a} I_{n-1} \)
D. \( -\frac{n}{a} I_{n-1} \)


Give any two real-life examples of
congruent shapes.


Four reactions that take place in the blast furnace to produce iron are shown. Which reaction is used to keep the furnace hot?
A. \( C+O_{2} \rightarrow C O_{2} \)
в. \( C O_{2}+C \rightarrow 2 C O \)
c. \( F e_{2} O_{3}+3 C \rightarrow 2 F e+3 C O \)
D. \( F e_{2} O_{3}+3 C O \rightarrow 2 F e+3 C O_{2} \)


a diverging lens of focal length - 10 \( \mathrm{cm} \) is moving towards right with a velocity \( 5 \mathrm{m} / \mathrm{s} \). An object, placed on Principal axis is moving towards left with a velocity \( 3 \mathrm{m} / \mathrm{s} \). The velocity of the image at the instant when the lateral magnification produced is \( 1 / 2 \) is: \( (\mathrm{All} \) velocities are with respect to ground)
A. \( 3 \mathrm{m} / \mathrm{s} \) towards right
B. \( 3 \mathrm{m} / \mathrm{s} \) towards left
c. \( 7 \mathrm{m} / \mathrm{s} \) towards right
D. \( 7 \mathrm{m} / \mathrm{s} \) towards left


We can use soap to check the hardness
of water.
A . True
B. False


Solve the following inequality and show
it graphically:
\( |\boldsymbol{x}+\mathbf{3}|<\mathbf{4}, \boldsymbol{x} \in \boldsymbol{Z} \)
\( A \)
B.
\( c \)
D.


Ortho and para hydrogen differ:
A. in the number of protons
B. in the molecular mass
C. in the nature of spins of protons
D. in the nature of spins of electrons


Q Type your question_
organs and select the right option.
Name of Organism Class
Rhodoplayceae \( \begin{array}{ll}(1) & \text { Acetabularia } \\
(2) & \text { Chlamydomonas } \\
(3) & \text { Chara } \\
(4) & \text { Chara }\end{array} \) as Chlorophyceae
Chlorophyceae
\( \mathrm{F} \) Phaeophyceae
\( \mathbf{A} \)
\( B \cdot 2 \)
\( c \cdot 3 \)
\( D \)


Which of the following statement is not true for the reaction given below?
\( \left.\mathbf{9} \boldsymbol{C u}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{4}\right]^{2+}+\boldsymbol{4} \boldsymbol{N} \boldsymbol{H}_{3} \rightleftharpoons \)
\( \left[\boldsymbol{C u}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4}\right]^{2+}+\boldsymbol{4} \boldsymbol{H}_{2} \boldsymbol{O} \)
A. It is a ligand substitution reaction
B. \( N H_{3} \) is a relatively strong field ligand while \( H_{2} O \) is a weak field ligand
c. During the reaction, there is a change in colour from light blue to dark blue
D \cdot \( \left[C u\left(N H_{3}\right)_{4}\right]^{2+} \), has a tetrahedral structure and is paramagnetic


Given below are the steps of protein synthesis. Arrange them in. correct sequence and select the correct option.
(j) Codon-anticodon reaction between mRNA and aminoacyl tRNA complex.
(ii) Attachment of mRNA and smaller
sub-unit of ribosome.
(iii) Charging or aminoacylation of tRNA.
(iv) Attachment of larger sub unit of ribosome to the mRNA-tRNAMet
complex.
(v) Linking of adjacent amino acids.
(vi) Formation of polypeptide chain.
A \( \cdot(\text { ii }) \rightarrow(i) \rightarrow(\text { iii }) \rightarrow(v) \rightarrow(\text { iv }) \rightarrow(v \) i)
B. (v) \( \rightarrow \) (ii) \( \rightarrow(\text { i) } \rightarrow \text { (iii) } \rightarrow \text { (iv) } \rightarrow \) (vi)
\( c \cdot(\text { iii) } \rightarrow(\text { ii) } \rightarrow(\text { iv }) \rightarrow(i) \rightarrow(v) \rightarrow(v i) \)
D. (iii) \( \rightarrow(\text { ii }) \rightarrow(i) \rightarrow(\text { iv } v \rightarrow(v) \rightarrow(v i) \)


toppr
Q Type your question
Chloroplasts
No
No
The rate of growth of the three cell types
was measured by growing them in
separate cultures in a plenty of oxygen and nutrient conditions. There was no
oxygen available to the cells at time 1
According to the table, cell type A is
A. Fungi
B. Plant
c. Bacteria
D. Animal
E . Protist


Which of the following acids is a strong electrolyte?
A. \( H C l \)
в. \( H B r \)
c. \( H I \)
D. All of the above


Three identical bars \( A, B \) and \( C \) are
made of different magnetic materials. When kept in a uniform magnetic field, the field lines around them look as
given in the figure. Make the
correspondence of these bars with their material being diamagnetic (D), ferromagnetic (F) and paramagnetic (P)
A. \( A \leftrightarrow F, B \leftrightarrow D, C \leftrightarrow P \)
в. \( A \leftrightarrow D, B \leftrightarrow P, C \leftrightarrow F \)
c. \( A \leftrightarrow F, B \leftrightarrow P, C \leftrightarrow D \)
D. \( A \leftrightarrow P, B \leftrightarrow F, C \leftrightarrow D \)


Stem of few dicot plants are getting mechanical strength mainly because of tissue, before secondary growth.
A. Sclerenchyma
B. Collenchyma
c. Parenchyma
D. None of the above


In a series RLC circuit, the r.m.s. the
voltage across the resistor and the
inductor are respectively \( 400 \mathrm{V} \) and
\( 700 V . \) If the equation for the applied voltage is \( \varepsilon=500 \sqrt{2} \sin \omega t, \) then the
peak voltage across the capacitor is
B. \( 400 \sqrt{2} V \)
c. \( 400 V \)
D. \( 1200 \sqrt{2} \mathrm{V} \)


When only light of wavelength beyond \( 680 \mathrm{nm} \) are available then which of the
following is not occur:-
A. Absorption of light
B. Formation of ATP
c. Release of \( C O_{2} \)
D. Excitetion of electron


Which of the following correctly presents the sequence of operations of isolator circuit breaker and earthing switch while closing a circuit :
A. Ensure circuit breaker is closed - close isolator - open earthing switch
B. Ensure circuit breaker is open - close isolator - open earthing switch if any close circuit breaker
C. Ensure circuit breaker is open - open isolator - open earthing switch if any close circuit breaker
D. None of the above


Evaluate the following limits. \( \lim _{x \rightarrow-5} \frac{2 x^{2}+9 x-5}{x+5} \)


A physical quantity \( x \) is calculated from the relation \( x=\frac{a^{2} b^{3}}{c \sqrt{d}} . \) If the percentage
error in \( a, b, c \) and \( d \) are \( 2 \%, 1 \%, 3 \% \) and \( 4 \% \), respectively, what is the percentage
error in \( x \) ?


State whether true or false.
When a short-circuit takes place, the fuse wire melts and breaks the electric
circuit.
A. True
B. False


Which of the following pairs is correctly
matched?
A. amino acid alanine ; opticallt active
B.
optically active
\( \mathbf{C} \)
D.
optically inactive


If the van der Waals parameters of two
gases are given as:
\( a / d m^{6} b a r m o l^{-2} \) \( b / d m^{3} b a r m \)
Gas \( 6.5 \quad \) 0.056
Gas 18.0 0.01
Then which of the above statements
is/are correct?
This question has multiple correct options
A. Critical volume of A <Critical volume of B
B. Critical pressure of A <Critical pressure of B
c. critical temperature of A ccritical temperature of B
D. None of the above


The property of metals which allows them to be drawn into wires is known as
A. ductility
B. malleability
c. elasticity
D. compressibility


Calculate the value of \( \boldsymbol{x} \)


Who is given credit for coming up with the "plum pudding" model of the atom?
A. Niels Bohr
B. Earnest Rutherford
c. J.J. Thompson
D. James chadwick
E. Max Planck


\( Q \) туре уоит question
в \( \frac{\mathrm{CH}_{3} \mathrm{OH}}{\mathrm{CH}_{3} \mathrm{ONa}} \mathrm{CH}_{3}-\underbrace{\mathrm{I}}_{\mathrm{C}-\mathrm{CH}_{2}}^{\mathrm{CH}_{3}} \frac{\mathrm{H}_{2} \mathrm{O}^{18}}{\mathrm{H}^{+}} \)
\( \begin{array}{cc}\mathbf{C H}_{3} & \mathbf{C H}_{3} \\ \mathbf{C H}_{3}-\mathbf{C}-\mathbf{C H}_{2}, \mathbf{C H}_{3}-\mathbf{C}-\mathbf{C H}_{2} \\ \mid & \mid \\ \mathbf{O H}_{\mathbf{1 8}} \mathbf{O} \mathbf{H} & \mathbf{O H}\end{array} \)
\( \mathrm{CH}_{3}-\frac{\mathrm{CH}_{3}}{\mathrm{C}-\mathrm{CH}_{2}, \mathrm{CH}_{3}-\mathrm{C}-\mathrm{CH}_{2}} \underbrace{\mathrm{CH}_{3}}_{\mathrm{Is}} \mathrm{OH}_{18} \mathrm{OH}_{\mathrm{OH}}^{1 \mathrm{d}} \)


\( \boldsymbol{C}_{\boldsymbol{6}} \boldsymbol{H}_{\boldsymbol{5}}\left(\boldsymbol{C} \boldsymbol{H}_{2}\right)_{\boldsymbol{2}} \boldsymbol{C} \boldsymbol{d}+ \)
\( \boldsymbol{2} \boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{C o C l} \stackrel{d r y}{\operatorname{ether}} \)


The distribution given below shows the number of wickets taken by bowlers in one-day cricket matches. Find the mean number of wickets by choosing a suitable method.
\( \begin{array}{llll}\text { No. of } & \mathbf{2 0}- & \mathbf{6 0 -} & \mathbf{1 0 0 -} \\ \text { wickets } & \mathbf{6 0} & \mathbf{1 0 0} & \mathbf{1 5 0}\end{array} \)
Bowl No. of
owlers
16


Let \( Q \) denote the charge on the plate of a
capacitor of capacitance \( C . \) The dimensional formula for \( \frac{Q^{2}}{C} \) is
\( \mathbf{B} \cdot\left[L M T^{2}\right] \)
\( \mathbf{c} \cdot\left[L^{2} M T^{-2}\right] \)
D \( \cdot\left[L^{2} M^{2} T^{2}\right] \)


Calculate the total number of protons in
10 gms of Calcium Carbonate \( \left(C a C O_{3}\right) \)


Cutting of trees decreases:
A. pollution level
B. temperature
C. fertility of soil
D. carbon dioxide level


\( N H_{4} C l(s)+H_{2} O \rightarrow N H_{4} C l(a q) ; \Delta H= \)
\( 16.3 k J \)
In the above reaction, \( \Delta H \) represents:
A. heat of solution
B. integral heat of solution
c. heat of dilution
D. heat of ionization


Appropriate material to be used in the construction of resistance boxes out of
the following is
A. copper
B. iron
c. manganin
D. aluminium


Which hydrogen-like species will have the same radius as that of Bohr's orbit
of the hydrogen atom?
A \( \cdot n=2, L i^{2+} \)
B . \( n=2, B e^{3+} \)
c. \( n=2, H e^{+} \)
D . \( n=3, L i^{3+} \)


If \( \Delta G^{\circ}>0 \) for a reaction, then:
A \( \cdot K_{p}>1 \)
в. \( K_{p}<1 \)
c. The products predominate in the equilibrium mixture
D. None of the above


Animal nutrition does not include which
of the following?
A. Mode of intake
B. Cooking of food
c. Nutrient requirement
D. Utilization in the body


Draw the histogram and use it to find the mode for the following frequency distribution.
House -
\[
\begin{array}{llll}
\text { Rent in } & \mathbf{4 0 0 0}- & \mathbf{6 0 0 0}- & \mathbf{8 0 0 0}- \\
\text { Rs. per } & \mathbf{6 0 0 0} & \mathbf{8 0 0 0} & \mathbf{1 0 0 0 0}
\end{array}
\]
month
Number
of
\[
200
\]
families
A . Rs. 8000
B. Rs. 8350
c. Rs. 8500
D. Rs. 8750


What is the structure of \( \boldsymbol{E} \) ?


If Henles loop were absent from
mammalian nephron which of the following is to be expected
A. There will be no urine formation
B. There will be hardly any change in the quality and quantity of urine formed
c. The urine will be more concentrated
D. The urine will be more dilute


\( Z r I_{4} \) converted to \( Z r \) by the
process
1. Monds
2. van Arkel
3. Hall
4. Kroll


Heterophylly found in Eucalytus is
A. Habitual
B. Developmental
C . Adaptive
D. Environmental


Which material should be chosen to
make the concave mirrors of a high resolution telescope so that it can also withstand temperature variations?
A. Quartz
B. Flint glass
c. crown glass
D. combination of Flint and Silica


In a copper wire, current is the flow of :
A. positive charge
B. negative charge
c. both a and b
D. none of above


How will two parallel beams of electron behave while moving in the same direction?
A. repel each other
B. attract each other
c. not interact with each other
D. annihilate each other


64 small drops of mercury each of radius \( r \) and change \( q \) coalesce to from a big drop. The ratio of the surface charge density of each small drop with that of big drop is:
A . 4: 1
B. 1: 4
\( \mathbf{c} \cdot 1: 64 \)
D. 64: 1


Brass scale of a Barometer gives
correct reading at \( 0^{\circ} \mathrm{C} \). coefficient of
linear expansion of brass is \( 18 \times \) \( 10^{-6} /^{-6} \mathrm{C} . \) If the barometer reads
\( 76 \mathrm{cm} \) at \( 20^{\circ} \mathrm{C}, \) the correct reading is
\( \left(\gamma_{\mathrm{Hg}}=18 \times 10^{-5} / 0 \mathrm{C}\right) \)
A. \( 76.426 \mathrm{cm} \)
B. \( 75.7 \mathrm{cm} \)
c. \( 76.2736 \mathrm{cm} \)
D. \( 76.264 \mathrm{cm} \)


If two forces of equal magnitudes act simultaneously on a body in the east and the north directions then
A. The body will displace in the north direction
B. The body will displace in the east direction
c. The body will displace in the north-east direction
D. The body will remain at the rest


Area bounded by the curve \( \mathbf{y}=\mathbf{x}+\sin \mathbf{x} \)
and its inverse function between the
ordinates \( \mathbf{x}=\mathbf{0} \) and \( \mathbf{x}=\mathbf{2} \pi \) is
A. \( 8 \pi \) sqp. units
B. 4 \( \pi \) sq. units
c. 8 sq. units
D. 3 \( \pi \) sq. units


The process by which solid \( C O_{2} \) is
directly converted to its gaseous form is
called:
A. Evaporation
B. Decomposition
c. Sublimation
D. None of the above


A power transmission line feeds input
power at \( 2400 \mathrm{V} \) to a step down transformer with its primary winding having 4000 turns. What should be the
number of turns in the secondary winding in order to get output power at \( 240 \vee ? \)
A . 400
B. 420
\( c \cdot 424 \)
D. 436


Which property of an object cannot be changed by applying forces?
A. Mass
B. Shape
c. speed
D. volume


Order of heat of combustion is:
A. \( 1>3>2>4>5 \)
В. \( 4>1>5>3>2 \)
c. \( 1>4>2>3>5 \)


In myopia, the image of distant object
is formed :
A. Before the retina
B. on the retina
c. Behind the retina
D. Above the retina


Universal zygomorphy occurs in
A. Malvaceae
B. Mimosoideae
c. Papilionaceae
D. Solanaceae


If a line makes angles \( 90^{\circ} \) and \( 60^{\circ} \)
respectively with the positive directions of \( x \) and \( y \) axes, find the angle which it
makes with the positive direction of \( z- \)
axis.


Two identical wires are suspended from a roof, but one is of copper and other is of iron. Young's modulus of iron is thrice that of copper. The weights to be added on copper and iron wires so that the ends are on the same level
must be in the ratio of
A .1: 3
B. 2:
c. 3: 1
D. 4: 1


About how many nephrons are there in each kidney of a human?
A . 16
B. 200
\( c \cdot 1000 \)
D. 1,000,000


Find the angle of evelation of the sun
when the shadow of a pole \( h \) meter high is \( \sqrt{3} h \) meters long


The charge is moving along the direction of magnetic field. Then force acting on it is
A. Maximum
B. qvB
c. zero
D. Bil


Evaluate: \( \int \frac{2 x}{\left(x^{2}+4\right)} d x \)


A rectangular coil is rotated in a uniform magnetic field about an axis passing through its centre and perpendicular to the direction of the field, then the induced voltage in the coil is directly proportional to the:
A. Number of turns in the coil
B. Area of the coil
c. Angular speed of the coil
D. All of these


1250 persons went to see a circus-show
Each adult paid Rs. 75 and each child
paid Rs. 25 for the admission ticket Find the number of adults and number
of children, if the total collection from them amounts to Rs. 61,250
A. Adults \( =600 \) and children \( =650 \)
B. Adults = 300 and children = 450
c. Adults \( =800 \) and children \( =700 \)
D. Adults \( =640 \) and children \( =800 \)


The exact equation of motion of the
bead along the thread is
\( ^{\mathbf{A}} \cdot_{m} \frac{d^{2} x}{d t^{2}}=--\frac{k 2 Q q x}{\left(x_{0}^{2}+R^{2}\right)^{3 / 2}} \)
B. \( \quad m \frac{d^{2} x}{d t^{2}}=--\frac{k Q q x}{\left(x_{0}^{2}+R^{2}\right)^{3 / 2}} \)
\( ^{\mathbf{C}} \cdot \quad m \frac{d^{2} x}{d t^{2}}=--\frac{k 2 Q q x}{\left(x_{0}^{2}-R^{2}\right)^{3 / 2}} \)
\( ^{\mathrm{D}} \cdot \quad m \frac{d^{2} x}{d t^{2}}=--\frac{k Q q x}{\left(x_{0}^{2}-R^{2}\right)^{3 / 2}} \)


Atoms of the same two elements can
combine in different ratios to form
different compounds. This is:
A. law of constant composition
B. law of multiple proportion
c. law of reciprocal proportion
D. law of conservation of mass


The \( _{\text {一一一一一一一 }} \) provides easy route for the transfer of \( _{-}-_{-}-_{-}- \) charges to the ground.
A. metallic rod, only positive
B. plastic rod, only negative
c. metallic rod, electric
D. plastic rod, electriç


One mole of an ideal gas \( \left(C_{v, m}=\frac{5}{2} R\right) \) at \( 300 \mathrm{K} \) and 5 atm is expanded adiabatically to a final
pressure of 2 atm against a
constant pressure of 2 atm. Final temperature of the gas is:
\( \mathbf{A} \cdot 270 \mathrm{K} \)
B. 273 к
c. \( 248.5 \mathrm{k} \)
D. 200 к


Sulphur molecule exists as:
\( A \cdot S_{2} \)
в. \( S \)
c. \( S_{6} \)
D. \( S_{8} \)


in fig consists of two horizontal
conducting plates of equal area A. The
bottom plate rests on a fixed support and the top plate is suspended by four springs with spring constant \( \mathrm{k} \)
positioned at each of the four corners of
the plate as shown in Fig. When uncharged, the plates are separated by
a distance \( z_{0} . \) A battery is connected to the plates and produces a potential difference V between them. This causes
the plate separation to decrease to z.
Neglect any fringing effects. Find the condition of stable equilibrium:
A. z shall have positive root
B. z shall negative root
c. no dependence on value of \( z \)
D. none of these


If the projections of the line segment \( A B \) on the coordinate axes are 2,3,6
then the square of the sine of the angle made by \( \boldsymbol{A B} \) with \( \boldsymbol{x}=\mathbf{0}, \) is
A \( \cdot \frac{3}{7} \)
B. \( \frac{3}{49} \)
\( c \cdot \frac{4}{7} \)
D. \( \frac{40}{49} \)


In a circle of radius \( 21 \mathrm{cm}, \) an arc
subtends and angle of \( 60^{\circ} \) at the centre.
Find:
(i) The length of the arc
(ii) Area of the
sector formed by the arc (iii) Area of the segment formed by the corresponding chord


Which of the following is highly unstable and has tetrahedral structure?
A. \( X e O_{3} \)
в. \( X e O_{4} \)
c. \( X e F_{4} \)
D. \( X e F_{2} \)


The magnetic moment of
\( \left[\boldsymbol{C u}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4}\right]^{2+} \) was found to be 1.73 B.M.
The number of unpaired electrons in the complex is:
\( A \cdot O \)
B.
\( c \cdot 2 \)
\( D \cdot 3 \)


If \( \boldsymbol{P}(\boldsymbol{A})=\mathbf{0 . 8}, \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 5} \) and
\( P\left(\frac{B}{A}\right)=0.4 \) then \( P\left(\frac{A}{B}\right)=? \)
A .0 .32
B. 0.64
c. 0.16
D. 0.25


Let \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) be a function such that \( \boldsymbol{f}\left(\frac{\boldsymbol{x}+\boldsymbol{y}}{\mathbf{2}}\right)=\frac{\boldsymbol{f}(\boldsymbol{x})+\boldsymbol{f}(\boldsymbol{y})}{2} \) for all \( \mathbf{x}, \mathbf{y} \)
and \( f(0)=3 \) and \( f^{\prime}(0)=3 . \) Then
A . \( f(x) / x \) is continuous on \( \mathbb{R} \)
B. \( f(x) \) is continuous on \( R \)
c. \( f(x) \) is bounded on \( R \)
D. none of these


The homeostatic regulation of an animal requires three basic components, \( \dots . . \) to detect changes, to evaluate the changes and to adjust the changes respectively.
A. Receptor, affectors, effectors
B. Brain, spinal cord, effectors
c. Receptors, integrators, effectors
D. Receptors, integrator, effectors


Evaluate: \( \int_{0}^{1}\left(8 x^{2}+16\right) d x \)


Divide the polynomial \( 39 y^{3}\left(50 y^{2}-98\right) \)
by \( 36 y^{2}(5 y+7) \)


The gravitational potential difference between the surface of a planet and a
point \( 20 m \) above the surface is
2Joule/Kg. If the gravitational field is uniform then the work done in carrying a \( 5 K g \) body to a height of \( 4 m \) above the
surface is
A . 2 Joule
в. 20Joule
c. 40 Joule
D. 10 Joule


A hollow cylinder has a charge \( q \)
coulomb within it. If \( \phi \) is the electric flux in units of voltmeter associated
with the curved surface \( B \), the flux
linked with the plane surface \( A \) in units
of voltmeter will be
A \( \cdot \frac{q}{\epsilon_{0}}-\phi \)
B \( \cdot \frac{1}{2}\left(\frac{q}{\epsilon_{0}}-\phi\right) \)
c. \( \frac{q}{2 \epsilon_{0}} \)
D. \( \frac{\phi}{3} \)


\( \frac{d x}{d} \)
\( d_{j}^{d} \)


A uniform beam of \( 2 m \) is fixed to a wall
and loaded by the forces shown above. Given that the beam is at equilibrium,
calculate force \( F \)
A \( .2 N \)
B. \( 4 N \)
\( c \cdot 7 N \)
D. \( 8 N \)


\( N_{2}+O_{2} \rightleftharpoons \quad 2 N O-Q c a l s \)
In the above reaction which is the
essential condition for the higher
production of \( N O \)
A. High temperature
B. High pressure
c. Low temperature
D. Low pressure


The capacitance of a parallel-plate
capacitor is \( C_{0} \) when the region
between the plates has air. This region
is now filled with a dielectric slab of
dielectric constant K. The capacitor is
connected to a cell emf \( \varepsilon_{1} \) and the slab
is taken out.
This question has multiple correct options
A. Charge \( \varepsilon C_{0}(K-1) \) flows through the cell
B. Energy \( \varepsilon^{2} C_{0}(K-1) \) is absorbed by the cell.
C. The energy stored in the capacitor is reduced by \( \varepsilon^{2} C_{0}(K-1) \)
D. The external agent has to do \( \frac{1}{2} \varepsilon^{2} C_{0}(K-1) \) amount of work to take the slab out.


\( A B C \) is an isosceles triangle in which
the altitudes \( B E \) and \( C F \) are drawn to
the equal sides \( A C \) and \( A B \)
respectively. Then
\( \mathbf{A} \cdot B E=C F \)
B. \( B E=A B \)
c. \( A B=B C \)
D. \( A C=B C \)


Two point charges \( Q \) and \( -Q / 4 \) are separated by


Which one of the following is responsible for causing skin cancer and mutation?
A. Ozone depletion
B. Smog formation
c. snowfall
D. Smoke from aeroplane


Which three dimensional
representation is commonly used for cyclic sugars?
A. Haworth Projection
B. Newman Projection
c. Fischer Projection
D. Sawhorse Projection


Consider the chemical reaction,
\( N_{2}(g)+3 H_{2}(g) \longrightarrow 2 N H_{3}(g) \)
The rate of reaction can be expressed in terms of time derivative of
concentration of \( \boldsymbol{N}_{2}(\boldsymbol{g}), \boldsymbol{H}_{2}(\boldsymbol{g}) \) or
\( N H_{3}(g) . \) Identify the correct
relationship amongst the rate expressions.
A \( \cdot \operatorname{Rate}=-\frac{d\left[N_{2}\right]}{d t}=-\frac{1}{3} \frac{d\left[H_{2}\right]}{d t}=+\frac{1}{2} \frac{d\left[N H_{3}\right]}{d t} \)
B. Rate \( =-\frac{d\left[N_{2}\right]}{d t}=-3 \frac{d\left[H_{2}\right]}{d t}=+2 \frac{d\left[N H_{3}\right]}{d t} \)
\( ^{\mathbf{c}} \cdot_{\mathrm{Rate}}=\frac{d\left[N_{2}\right]}{d t}=\frac{1}{3} \frac{d\left[H_{2}\right]}{d t}=\frac{1}{2} \frac{d\left[N H_{3}\right]}{d t} \)
D. \( \operatorname{Rate}=-\frac{d\left[N_{2}\right]}{d t}=-\frac{d\left[H_{2}\right]}{d t}=\frac{d\left[N H_{3}\right]}{d t} \)


Which of the following factors may be
regarded as the main cause of
lanthanide contraction?
A. Poor shielding of one of \( 4 f \) electron by another in the subshell
B. Effective shielding of one of 4 f electrons by another in the subshell
C. Poorer shielding of 5d electrons by 4f electrons
D. Greater shielding of 5d electrons by 4f electrons


The value of
\( \left\{s i n^{-1}\left[x^{2}+\frac{1}{2}\right]+\cos ^{-1}\left[x^{2}-\frac{1}{2}\right]\right\} \)
where \{\} and \( [.] \) denote fractional part
function and greatest integer function respectively
\( \mathbf{A} \cdot \pi-3 \)
B. \( 4-\pi \)
\( c \cdot 2-\frac{\pi}{2} \)
D. o


The heat evolved in the combustion of
benzene is given by
\( C_{6} H_{6}(l)+7 \frac{1}{2} O_{2}(g) \rightarrow 3 H_{2} O(l)+ \)
\( \mathbf{6} C O_{2}(\boldsymbol{g}), \boldsymbol{\Delta} \boldsymbol{H}=-\mathbf{7} \mathbf{8} \mathbf{1} . \mathbf{0} \boldsymbol{K} \boldsymbol{c} \boldsymbol{a} \boldsymbol{l} \boldsymbol{m} \boldsymbol{o} \boldsymbol{l}^{-1} \)
When 156 g of \( C_{6} H_{6} \) is burnt in an open container, the amount of heat energy released will be
This question has multiple correct options
A. \( 150.2 \mathrm{kcalmol}^{-1} \)
B . 1562.0 kcalmol-
\( \mathbf{c} \cdot 6528.2 \mathrm{kJmol}^{-1} \)
D. 2448.5 kJmol-


If \( |y|=5 x-2 y, \) then which of the
following is incorrect?
A. \( y(x) \) is discontinuous at \( x=0 \)
B. \( y(x) \) is continuous \( \forall x \in R \)
c. \( y(x) \) is strictly increasing \( \forall x \epsilon R \)
D. domain of \( y(x) \) is set of all real values


A truck and a car are moving on a smooth, level road such that the kinetic energy associated with them is same. Brakes are applied simultaneously in both of them such that equal retarding forces are produced in them. Which one will cover a greater distance before it stops?
A . car
B. Truck
c. Both will cover the same distance
D. Nothing can be decided


For the reaction, \( 2 S O_{2}(g)+O_{2}(g) \rightleftharpoons \)
\( 2 S O_{3}(g) \) at \( 300 K, \) the value of \( \Delta G^{o} \) is
\( -690.9 R \)
The equilibrium constant value for the reaction at that temperature is (R is gas constant)
A. \( 10 a t m^{-1} \)
B. 10 atm
c. 10
D.


Find the measure of all the angles of a
parallelogram, if one angle is \( 24^{\circ} \) less than twice the smallest angle.
A \( \cdot 68^{\circ}, 112^{\circ}, 68^{\circ}, 112^{\circ} \)
B . \( 48^{\circ}, 72^{\circ}, 48^{\circ}, 72^{\circ} \)
c. Insufficient data
D. None of these


For the reaction \( R \rightarrow P \). the
concentration ofa reactant changes frotn \( 0.03 M \) to \( 0.02 M \) in 25 minutes.
Calculate the average rate of reaction using units of time both in minutes and seconds.


Arrange the process of image formation in proper order
a. Brain processes the signal so that we see the objects as they are.
b. Light sensitive cells activate upon illumination and generate electric signals.
c. Optical nerves carry the signals to the brain.
d. Light falls on the retina.
A \( \cdot \) c, \( d, b, a \)
в. b, d, c.
\( c \cdot d, c, b, a \)
D. \( d, b, c, a \)


How would you rewrite Euclid's fifth postulate so that it would be easier to understand?


A satellite of the earth is revolving in circular orbit with a uniform velocity \( V \)
If the gravitational force suddenly disappears, the satellite will
A. continue to move with the same velocity in the same orbitt
B. move tangentially to the original orbit with velocity \( v \).
c. fall down with increasing velocity.
D. come to a stop somewhere in its original orbit.


Give the chemical name \( \& \) formula of
chloride of lime. what happens when it is exposed to air. Write Chemical equation.


Calcium of the lime stone added in the
metallurgy of iron comes out at the end
as:
A \( \cdot C a C O_{3} \)
в. \( C a O \)
c. \( \operatorname{casio}_{3} \)
D. None of these


A reaction attains equilibrium, when the free energy change is
A .
B.
\( c \cdot 3 \)
\( D \)


Compute \( \boldsymbol{P}(\boldsymbol{A} \mid \boldsymbol{B}) \) if \( \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 5} \) and
\( \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B})=\mathbf{0 . 3 2} \)


Assertion
Coaxial cables make use of a dielectric
between the two conducting lines.
Reason
dielectrics are good insulators.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A wire loop formed by joining two semi-
circular wires of radii \( \boldsymbol{R}_{1} \) and \( \boldsymbol{R}_{2} \) carries
a current as shown in the adjoining
diagram. The magnetic induction at
the center \( \boldsymbol{O} \) is
A \( \cdot \frac{\mu_{0} I}{4 R_{1}} \)
B. \( \frac{\mu_{0} I}{4 R} \)
c. \( \frac{\mu_{0} I}{4}\left(\frac{1}{R_{1}}-\frac{1}{R_{2}}\right) \)
D. \( \frac{\mu_{0} I}{4}\left(\frac{1}{R_{1}}+\frac{1}{R_{2}}\right) \)


Steam engines of Indian railways are
replaced with diesel engine. Justify this move with two scientific reasons.


A Sound wave with an amplitude of \( 3 \mathrm{cm} \)
starts towards right from origin and
gets reflected at a rigid wall after a
second. If the velocity of the wave is
\( 340 m s^{-1} \) and it has a wavelength of \( 2 m \)
the equations of incident and reflected
waves respectively could be
\( \mathbf{A} . \quad y=3 \times 10^{-2} \sin \pi(340 t-x) \)
\[
y=-3 \times 10^{-2} \sin \pi(340 t+x) \text { towards left }
\]
B. \( \quad y=3 \times 10^{-2} \sin \pi(340 t+x) \)
\[
y=-3 \times 10^{-2} \sin \pi(340 t+x) \text { towards left }
\]
c. \( y=3 \times 10^{-2} \sin \pi(340 t-x) \)
\[
y=-3 \times 10^{-2} \sin \pi(340 t-x) \text { towards left }
\]
D. \( y=3 \times 10^{2} \sin \pi(340 t-x) \)
\[
I=3 \times 10^{-2} \sin \pi(340 t+x) \text { towards left }
\]


Solve for \( \boldsymbol{x}: \frac{\boldsymbol{x}^{2}-|\boldsymbol{x}|-\mathbf{1 2}}{\boldsymbol{x}-\mathbf{3}} \geq \mathbf{2} \boldsymbol{x} \)


Most transition metals-
I: forms sets of compounds that display
different oxidation states of the metal.
Il: form colored ions in solution
III: burn vigorously in oxygen
IV: replace \( H_{2} \) from dilute acids of these
A. I, II, III are correct
B. II, III, Iv and correct
C. I, II are correct
D. all are correct


Consider the following reaction \( ^{1} \boldsymbol{H}_{2}+^{1} \)
\( \boldsymbol{H}_{2} \rightarrow_{2} \boldsymbol{H} \boldsymbol{e}^{4}+\boldsymbol{Q} \)
If \( \boldsymbol{m}\left(_{1} \boldsymbol{H}^{2}\right)=\mathbf{2 . 0 1 4 1} \boldsymbol{u}, \boldsymbol{m}\left(_{2} \boldsymbol{H} \boldsymbol{e}^{4}\right)= \)
\( 4.0024 u, \) then the energy \( Q \) released (in
MeV) in this fusion reaction is
A . 12
B. 6
c. 24
D. 48


On the basis of composition of matter, milk is considered to be:
A . a pure substance
B. an impure substance
c. an element
D. a compound


True or False.
Non metals are sonorous.


Two capacitors of capacity \( C_{1} \) and \( C_{2} \)
are connected in parallel, then the
equivalent capacity is:
A \( \cdot C_{1}+C_{2} \)
в. \( C_{1} C_{2} /\left(C_{1}+C_{2}\right) \)
c. \( C_{1} / C_{2} \)
D. \( C_{2} / C_{1} \)


If a plane has \( X \) -intercept \( l, Y \) -intercept
\( m \) and \( z \) -intercept \( n, \) and perpendicular
distance of plane from origin is \( k, \) then \( ? \)
A \( \cdot l^{2}+m^{2}+n^{2}=\frac{1}{k^{2}} \)
B. \( \frac{1}{l^{2}}+\frac{1}{m^{2}}+\frac{1}{n^{2}}=\frac{1}{k^{2}} \)
c. \( l^{2}+m^{2}+n^{2}=k^{2} \)
D. \( \frac{1}{l^{2}}+\frac{1}{m^{2}}+\frac{1}{n^{2}}=k^{2} \)


Which of the following acids is a weak
electrolyte?
A. \( H_{2} C O_{3} \)
в. \( C H_{3} \) СООН
c. Both A and B
D. None of the above


The gravitational potential energy is the
A. work done in bringing an object from infinity to radius
\( r \)
B. work done in moving an object around the earth
C. work done by an object in attaining an object's acceleration equal to \( 9.8 m / s^{2} \)
D. work done in moving an object between two points horizontally


A large, massive man and a small boy of small mass are held far apart on an icy surface where friction is negligible. The man and the boy hold opposite ends of a bungee cord that is stretched. When the boy and the man are released,
they are each pulled by the bungee cord so that they approach one another. When they get close to each other, how will their momenta, velocity, and kinetic energies compare?
A. Magnitude of Momenta - man's greater then boy's Magnitude of Velocity - boy's greater than man's, Kinetic Energy - man's greater than boy's
B. Magnitude of Momenta - same for both, Magnitude of Velocity - boy's greater than man's, Kinetic Energy same for both
c. Magnitude of Momenta - same for both, Magnitude of Velocity - same for both, Kinetic Energy - same for both
D. Magnitude of Momenta - boy's greater then man's Magnitude of Velocity - boy's greater than man's, Kinetic Energy - same for both
E. Magnitude of Momenta - same for both, Magnitude of Velocity - boy's greater than man's, Kinetic Energy boy's greater than man's


Which of the following are examples of non-uniform motion along a straight line?
A. horse pulling a carttrt
B. brakes applied on a fast moving car
c. train on a straight bridge
D. all of the above


Consider a satellite going round the
earth in a circular orbit. Which of the
following statements is wrong?
A. It is a freely falling body
B. It is a moving with constant speed.
c. It is acted upon by a force directed away from the centre of the earth which counter- balances the gravitational pull.
D. Its angular momentum remains constant


The ratio of slope of man K.E vs
frequency and sloping potential vs frequency is:


What particle was emitted?
A . Alpha
B. Beta
\( c . \) Gamma
D. None of the above


Justify the position of hydrogen in the periodic table on the basis of its electronic configuration.


Q Type your question
figure. The arcs \( B C \) (radius \( =b \) ) and \( D A \)
(radius \( =a \) ) of the loop are joined by
two straight wires \( A B \) and \( C D . A \)
steady current \( I \) is flowing in the loop.
Angle made by \( A B \) and \( C D \) at the
origin \( O \) is \( 30^{\circ} . \) Another straight thin
wire with steady current \( I_{1} \) flowing out of the plane of the paper is kept at the origin. The magnitude of the magnetic field due to the loop \( A B C D \) at the
origin \( (O) \) is:
A . zero
B. \( \frac{\mu_{0} \mathrm{I}(\mathrm{b}-\mathrm{a})}{24 \mathrm{ab}} \)
c. \( \frac{\mu_{0} \mathrm{I}}{4 \pi}\left[\frac{\mathrm{b}-\mathrm{a}}{\mathrm{ab}}\right] \)
D. \( \frac{\mu_{0} I}{4 \pi}\left[2(b-a)+\frac{\pi}{3}(a+b)\right] \)


\( \left[\boldsymbol{P t}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)\left(\boldsymbol{N} \boldsymbol{H}_{2} \boldsymbol{O H}\right)(\boldsymbol{p} \boldsymbol{y})\left(\boldsymbol{N} \boldsymbol{O}_{2}\right)\right] \boldsymbol{N} \boldsymbol{O} \)
has square planar shape and has three geometrical isomer
A. True
B. False


Let \( \boldsymbol{F}(\boldsymbol{x})=\boldsymbol{x}^{3}-\boldsymbol{3} \boldsymbol{x}+\mathbf{1} \)
find no. of real soln, of \( \boldsymbol{F}(\boldsymbol{F}(\boldsymbol{x}))=\mathbf{0} \)


f \( \int_{1}^{a}\left(3 x^{2}+2 x+1\right) d x=11, \) find real
values of a.


A positively charged particle of charge 1
C and mass 40 g, is revolving along a circle of radius \( 40 \mathrm{cm} \) with velocity
\( 5 \mathrm{m} / \mathrm{s} \) in a uniform magnetic field with centre at origin 0 in \( x \) -y plane \( . A t t=0 \) the particle was at \( (0,0.4 \mathrm{m}, 0) \) and velocity was directed along positive \( x \) direction.Another particle having charge \( 1 \mathrm{C} \) and mass \( 10 \mathrm{g} \) moving uniformly parallel to z-direction with velocity \( \frac{40}{\pi} m / s \) collides with revolving particle at \( t=0 \) and gets stuck with it. Neglecting gravitational force and coulombian force,calculate \( x, y \) and \( z \) coordinates of the combined particle at \( t=\frac{\pi}{40} \sec \)


The dimensional formula for electric
flux is
\( \mathbf{A} \cdot\left[M L^{3} T^{-3} A^{-1}\right] \)
B \( \cdot\left[M L^{3} T^{-2} A^{-1}\right. \)
\( \mathrm{c} \cdot\left[M L^{1} T^{-1} A^{-1}\right. \)
D \( \cdot\left[M L^{4} T^{-2} A^{-1}\right] \)


Consider the polynomial \( \frac{x^{3}+2 x+1}{5}-\frac{7}{2} x^{2}-x^{6} \)
Write the degree of the above polynomial
\( \mathbf{A} \cdot \mathbf{6} \)
B. 3
c. 1
D.


Name the disorder which can be
considered both inherited and acquired.
A. Thyroid
B. Heart attack
c. Huntingtons
D. All of the above


Find the degree of :
a) \( x^{3}-3 x^{3} y^{6}+8 y^{3} \)
b) \( 6 x^{4}-9 x^{3} y^{2}-6 y^{6} \)


A plastic box \( 1.5 \mathrm{m} \) long, \( 1.25 \mathrm{m} \) wide, and \( 65 \mathrm{cm} \) deep is to be made. It is to be opened at the top. Ignoring the thickness of the plastic, the cost of the sheet for covering it, if a sheet measuring \( 1 m^{2} \) costs Rs. 20 is:
A . Rs. 100
B. Rs. 109
c. Rs. 115
D. Rs. 110


Assertion
Use of chitinase enzyme, is necessary for isolation of DNA from yeast cells but
not in case of Spirogyra.
Reason
Fungal cell wall is made up of fungal cellulose or chitin.
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


Direction of electric field in P-N junction
diode is
A. from P-side to N-side
B. from N-side to P-side
c. randomly oriented
D. electric field does not exist


Aerobic respiratory pathway is appropriately called as
A. Anabolic
B. Catbolic
c. Amphibolic
D. Parabolic


Given \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{ll}3-\left[\cot ^{-1}\left(\frac{2 x^{3}-3}{x^{2}}\right)\right] & \text { for } x>0 \\ \left\{x^{2}\right\} \cos \left(e^{1 / x}\right) & \text { for } x<0\end{array}\right. \)
where
\{\}\( \&[] \) denotes the fractional part and
the integral part functions respectively,
then which of the following statement
does not hold good -
This question has multiple correct options
\( \mathbf{A} \cdot f\left(0^{-}\right)=0 \)
B . \( f\left(0^{+}\right)=3 \)
C \( . f(0)=0 \Rightarrow \) continuity of \( f \) at \( x=0 \)
D. irremovable discontinuity of \( f \) at \( x=0 \)


(a) Why Transition elements become
paramagnetic?
(b) Explain oxidization properties of potassium permanganate in acidic medium. (any four only)


What do you mean by the audible range of frequency?


If \( \boldsymbol{y}=\mathbf{1}+\boldsymbol{x}+\frac{\boldsymbol{x}^{2}}{\mathbf{2 !}}+\frac{\boldsymbol{x}^{\mathbf{3}}}{\mathbf{3 !}}+\ldots+\frac{\boldsymbol{x}^{\boldsymbol{n}}}{\boldsymbol{n} !} \)
then \( \frac{d y}{d x} \) is equal to
\( \mathbf{A} \cdot \underline{y} \)
B. \( y+\frac{x^{n}}{n !} \)
c. \( y-\frac{x^{n}}{n !} \)
D. \( y-1-\frac{x^{n}}{n !} \)


X number of electrons would have about
the same mass as proton or a neutron?
Identify \( \mathbf{X} \)
A . 200
B. 500
c. 2000
D. 5000


What is essentially the difference between \( \alpha \) - glucose and \( \beta \) - glucose? What is meant by pyranose structure of glucose?


Find \( x \) and \( y, \) if \( (x+3,5)=(6,2 x+y) \)
A. \( x=3, y=-1 \)
B . \( x=6, y=2 \)
c. \( x=2, y=3 \)
D. none of these


Which of the following is not the application of nitrogen?
A. Refrigerant
B. Metallurgy
c. Match sticks
D. Electric bulbs


Two sources of light of wavelengths \( 2500 A \) and \( 3500 A \) are used in Young's
double slit experiment simultaneously. Which orders of fringes of two wavelength patterns coincide?
A. 3 rd order of 1 st source and 5 th of the 2 nd
B. 7th order of 1st and 5th order of 2nd
c. 5 th order of 1 st and 3 rd order of 2 nd
D. 5 th order of 1 st and 7 th order of 2 nd


At a turn of track is banked for
optimum speed of \( 40 k m / h \). At the
instant shown in the figure a car is
travelling out of the plane of the figure. If the car travels at \( 60 k m / h, \) the net
frictional force acting on the wheels
must be :
A. static in nature and point downward along the bank of the track for safe driving
B. static in nature and point upward along the bank of the track for safe driving
c. kinetic in nature and points upward along the bank of the track for safe driving
D. kinetic in nature and points downwards along the bank of the track for safe driving


Solve \( : \frac{3}{x+y}+\frac{2}{x-y}=2 \) and
\( \frac{9}{x+y}-\frac{4}{x-y}=1 \)
A. \( x=\frac{2}{5} ; y=\frac{7}{2} \)
B. \( x=\frac{5}{2} ; y=\frac{1}{2} \)
c. \( x=\frac{6}{7} ; y=\frac{4}{3} \)
D. \( x=\frac{7}{3} ; y=\frac{1}{2} \)


If \( y=2 \sin x-3 x^{4}+8, \) then \( \frac{d y}{d x} \) is
B . \( 2 \cos x-12 x^{3} \)
\( \mathbf{c} \cdot 2 \cos x+12 x^{3} \)
D. \( 2 \sin x+12 x^{3} \)


A disc of mass \( m \) and radius \( R \) rolls
down an inclined plane of height \( h \) without slipping. Find out the velocity of the disc when it reaches the bottom
of the incline? The moment of inertia for
a disk is \( (1 / 2) m R^{2} \)
A \( \cdot \sqrt{g h} \)
в. \( \sqrt{\frac{4}{3} g h} \)
c. \( \sqrt{2 g h} \)
D. \( 2 \sqrt{g h} \)
E \( .2 \sqrt{2 g h} \)


A soild sphere of radius \( \boldsymbol{R}_{1} \) and volume
charge density \( \rho=\frac{\rho_{0} o}{r} \) is enclosed by a
hollow sphere of radius \( R_{2} \) with
negative surface charge density \( \sigma \), such
that the total charge in the system is
zero. \( \rho_{0} \) is a positive constant and \( r \) is the distance from the center of the
sphere.Then the ratio \( \boldsymbol{R}_{2} / \boldsymbol{R}_{1} \) is
\( A \cdot \sigma / \rho_{o} \)
B. \( \sqrt{2 \sigma} / \rho_{o} \)
c. \( \sqrt{\rho_{-} o} / \quad 2 \sigma \)
D. \( \rho_{o} / \sigma \)


Determine the domain and the range of the relation \( R \) defined by \( R= \)
\( \{(x+1, \quad x+5): x \in \)
\( \{0, \quad 1, \quad 2, \quad 3, \quad 4, \quad 5\}\} \)


Salt \( A \) commonly used in bakery products, on heating, gets converted into another salt \( B \) which itself is used
for removal of hardness of water and a
\( \operatorname{gas} C \) is evolved. The gas \( C \) when
passed through lime water turns it
milky. Identify \( A, B \) and \( C \).
A. Salt \( A \), which is sodium bicarbonate; Salt \( B \) is sodium carbonate; \( C \) is \( C O_{2} \) gas
B. Salt A, which is sodium carbonate; Salt \( B \) is sodium bicarbonate; \( C \) is \( H_{2} \) gas
c. salt \( A, \) which is sodium bicarbonate; Salt \( B \) is sodium carbonate; \( C \) is \( H_{2} \) gas
D. None of these


An organic compound has a triple bond and double bond. It can be tested by :
A. Bromine water
B. Beyer's reagents
c. Fehling's solution
D. Ammonical \( A g N O_{3} \)


Which of the following phylum do not possess true coelom?
A. Aschelminthes
B. Annelida
c. ctenophora
D. Platyhelminthes


If an LED has to emit 662 nm wavelength
of light them what should be the band gap energy of its semiconductor? \( \boldsymbol{h}= \)
\( 6.62 \times 10^{-34} \mathrm{Js} \)


Differentiate with respect to \( x \) :
\( \sin ^{2}(\log (2 x+3)) \)


How many minutes will it takes to plate
out \( 5.2 \mathrm{g} \) of \( \mathrm{Cr} \) from a \( \boldsymbol{C r}_{2}\left(\boldsymbol{S O}_{4}\right)_{3} \)
solution using a current of 9.65 A? (Atomic weight of \( \mathrm{Cr}=52.0 \) )
A . 200
B. 50
\( c \cdot 100 \)
\( D \cdot 103 \)


If \( \int \frac{\operatorname{cosec}^{2} x-2010}{\cos ^{2010 x}} d x= \)
\( -\frac{\boldsymbol{f}(\boldsymbol{x})}{(\boldsymbol{g}(\boldsymbol{x}))^{2010}}+C ; \) then the number of
solutions where equation \( \frac{f(x)}{g(x)}=\{x\} \)
in \( [\mathbf{0}, \mathbf{2} \boldsymbol{\pi}] \) is / are:
\( A \cdot 0 \)
B. 1
c. 2
D. 3


Match the functional activity of the following parts,


Which of the following is the cause of deforestation?
A. Urbanization
B. Agricultural activities
c. Forest fires
D. All of the above


Energy released in a nuclear reaction is given by


Which of the following form the three angles of a triangle.
\( \boldsymbol{a})\left\{\boldsymbol{9} \boldsymbol{0}^{\boldsymbol{o}}, \boldsymbol{3} \boldsymbol{0}^{\boldsymbol{o}}, \boldsymbol{5} \boldsymbol{0}^{\boldsymbol{o}}\right\} \)
\( b)\left\{40^{\circ}, 40^{\circ}, 100^{\circ}\right\} \)
(5)\( \left\{50^{\circ}, 60^{\circ}, 70^{\circ}\right\} \)
\( \boldsymbol{d})\left\{20^{\circ}, 30^{\circ}, 40^{\circ}\right\} \)
A \( . d \) and \( c \)
B. \( b \) and \( c \)
c. \( a \) and \( c \)
D. \( a \) and \( d \)


Which one of the following sources of
energy you recommend to use?
A source of energy having an input
energy Jand an output energy
J.
A . 1000,2000
B. 2000, 2500
c. 100.12500
D. 5000, 5250


\( \int \frac{d x}{x^{2} \sqrt{4-x^{2}}} \) is equal to
\( \mathbf{A} \cdot \frac{1}{4}\left(\frac{\sqrt{4-x^{2}}}{x}\right)+C \)
\( \mathbf{B} \cdot \frac{1}{2}\left(\frac{\sqrt{4-x^{2}}}{x}\right)+C \)
\( \mathbf{C} \cdot-\frac{1}{4}\left(\frac{\sqrt{4-x^{2}}}{x}\right)+C \)
D \( -\frac{1}{2}\left(\frac{\sqrt{4-x^{2}}}{x}\right)+C \)


What happens when phosphorus is heated with strong sodium hydroxide solution?
A. Oxidation takes place
B. Hydroxide is formed
c. An inflammable gas evolves
D. No reaction takes place


Construct a \( \triangle A B C \) in which:
\( \boldsymbol{A B}+\boldsymbol{B C}+\boldsymbol{A C}=\mathbf{1 1 . 8 c m}, \angle \boldsymbol{B}= \)
\( 60^{\circ} \) and \( \angle C=45^{\circ} \)


The correct order of the second
ionisation potential of carbon, nitrogen, oxygen and fluorine is :
A. \( C>N>O>F \)
в. \( O>N>F>C \)
с. \( O>F>N>C \)


Write the name of the lenses used in a
compound microscope near object and
eye.


Find the HCF of 26 and 455
A . 11
B. 12
c. 13
D. none of the above


The amino acid
\( \boldsymbol{H}_{2} \boldsymbol{N} \boldsymbol{C H}(\boldsymbol{C O O H})\left(\boldsymbol{C H}_{2}\right)_{4} \boldsymbol{N} \boldsymbol{H}_{2} \) at low
\( p H \) exits as:
A \( \cdot H_{2} N C H(C O O H)\left(C H_{2}\right)_{4} N H_{2} \)
в. \( H_{3} \stackrel{+}{N} C H(C O O H)\left(C H_{2}\right)_{4} N H_{2} \)
c. \( H_{3} \stackrel{+}{N} C H(C O O H)\left(C H_{2}\right)_{4} \stackrel{+}{N} H_{3} \)
D. \( H_{2} N C H(C O O H)\left(C H_{2}\right)_{4} \stackrel{+}{N} H_{3} \)


If three consecuting vertices of a
parallelogram are \( \boldsymbol{A}(\mathbf{4}, \mathbf{3}, \mathbf{5}), \boldsymbol{B}(\mathbf{0}, \mathbf{6}, \mathbf{0}), \boldsymbol{C}(-\mathbf{8}, \mathbf{1}, \mathbf{4}) \) and \( \boldsymbol{D} \)
is the fourth vertex then the anlge between \( \overline{A C} \) and \( \overline{B D} \) is
\( ^{\mathbf{A}} \cdot \cos ^{-1}\left[\frac{55}{\sqrt{149} \sqrt{161}}\right] \)
\( ^{\mathbf{B}} \cdot \cos ^{-1}\left[\frac{65}{\sqrt{149} \sqrt{161}}\right] \)
\( ^{\mathbf{c}} \cdot \cos ^{-1}\left[\frac{15}{\sqrt{149} \sqrt{161}}\right] \)
D. \( \cos ^{-1}\left[\frac{3}{\sqrt{149} \sqrt{161}}\right] \)


Sketch the emergent wavefront


Dipositive helium ions are called
particles.
A. \( \alpha \) -particle
B. \( \beta \) -particle
c. proton
D. \( \gamma \) -particle


Two equat ions \( \vec{r} . \vec{n}_{1}=q_{1} \) and \( \vec{r} . \vec{n}_{2}=q_{2} \)
represent two perpendicular planes, where \( \vec{n}_{1} \) and \( \vec{n}_{2} \) are two unit vectors.
One of these plane is rotated through an angle 45 about line of intersection of
two given planes then equation of plane in new position can be This question has multiple correct options
A \( \cdot \vec{r} \cdot\left(\vec{n}_{1}+\vec{n}_{2}\right)=q_{1}-q_{2} \)
В \( \cdot \vec{r} \cdot(\overrightarrow{n_{1}}+\overrightarrow{n_{2}})=q_{1}+q_{2} \)
c. \( \vec{r} .\left(\vec{n}_{1}-\vec{n}_{2}\right)=q_{1}+q_{2} \)
D \( \cdot \vec{r} \cdot(\overrightarrow{n_{1}}-\overrightarrow{n_{2}})=q_{1}-q_{2} \)


(i) \( \underset{\boldsymbol{a} \boldsymbol{q} \cdot \boldsymbol{s u s p e n s i o n}}{\boldsymbol{B} \boldsymbol{a} \boldsymbol{C O}_{3}}+\boldsymbol{N} \boldsymbol{a}_{2} \boldsymbol{C r} \boldsymbol{O}_{4}+ \)
\( \boldsymbol{A c O H} \rightarrow \underset{p p t}{\boldsymbol{H}} \)
(ii) \( \boldsymbol{B a C O}_{3}+\boldsymbol{N a}_{2} \boldsymbol{C r} \boldsymbol{O}_{4}+ \)
aq.suspension
\( \boldsymbol{H} \boldsymbol{C} \boldsymbol{N} \rightarrow \underset{p p t}{\boldsymbol{N}} \)
Which is the correct option regarding the given reactions?
A. \( \mathrm{M} \) and \( \mathrm{N} \) are the same and characterized as \( B a C r O_{4} \)
B. \( \mathrm{M} \) is \( \mathrm{BaCrO}_{4} \) and \( \mathrm{N} \) stands for no precipitate
c. \( \mathrm{M} \) is \( \mathrm{BaCrO}_{4} \) and \( \mathrm{N} \) is \( \mathrm{BaCO}_{3} \)
D. M stands for no precipitate and \( \mathrm{N} \) is \( \mathrm{BaCrO}_{4} \)


Use the given Venn-diagram to find the
number of elements in \( A \cup B \)


Which of the following units is not equivalent to Farad?
A \( . C V^{2} \)
в. \( J / V^{2} \)
c. \( Q^{2} / J \)
D. \( Q / V \)


Dirty water contains germs and can be harmful. Swimming pools are disinfected by bubbling through water a controlled amount of:
A . air
B. oxygen
c. bromine
D. chlorine


A circular disc of M.I. \( 10 \mathrm{kg}-\mathrm{m}^{2} \) rotates
about its own axis at a constant speed of 60 r.p.m. under the action of an
electric motor of power 31.4 W. If the motor is switched off, how many
rotations will it cover before coming to rest?
A . 3.14
в. 31.4
c. 314
D. 6.28


Ringer's solution contains
A. lodine and salt
B. Acetic acid and wax
c. sodium and potassium ions
D. water and acid fuchsin


The internal energy of a piece of lead when beaten by a hammer will
A. increase
B. decrease
c. remain constant
D. sometimes increases and sometimes decreases


\( a^{12}-1 \) can be factorised as:
\( \mathbf{A} \cdot(a-1)(a-2)(a-3)(a-4) \)
B \( \cdot(a-1)\left(a^{2}+a+1\right)(a+1)\left(a^{2}+a+1\right) \)
C \( \cdot\left(a^{2}+a+1\right)\left(a^{2}-a+1\right) \)
D \( \cdot(a-1)\left(a^{2}+a+1\right)(a+1)\left(a^{2}-a+1\right)\left[\left(a^{2}+1\right)\left(a^{4}-\right.\right. \)
\( \left.a^{2}+1\right) \)


Why is it easy to walk on sand with flat shoes, then with high heel shoes?


Bring about the following conversion 1-propanol \( \rightarrow \) Acetone


The substance oxidized and the
oxidizing agent in the following reaction are respectively:
\( Z n+H_{2} S O_{4} \rightarrow Z n S O_{4}+H_{2} \)
A. zinc atoms and hydrogen ions
B. zinc ions and hydrogen atoms
c. hydrogen ions and zinc atoms
D. hydrogen atoms and zinc ions


Consider the geometric progression \( \boldsymbol{S}=\mathbf{1}+\boldsymbol{2} \sin ^{2} \boldsymbol{\theta}+\boldsymbol{4} \sin ^{4} \boldsymbol{\theta}+\boldsymbol{8} \sin ^{6} \boldsymbol{\theta}+ \)
\( \ldots . \) up to infinite terms, where \( \mathrm{S} \) is a finite number and \( \boldsymbol{\theta} \neq \frac{\boldsymbol{n} \boldsymbol{\pi}}{\mathbf{2}} \) where \( \mathbf{n} \varepsilon \mathbf{I} \)
Then Values of \( \theta \) always lies in the
interval?
A \( \cdot\left(-\frac{\pi}{6}, \frac{\pi}{6}\right) \)
в. \( \left(0, \frac{\pi}{3}\right) \)
c. \( \left(-\frac{\pi}{3}, 0\right) \)
D. \( \left(-\frac{\pi}{4}, \frac{\pi}{4}\right)-\{0\} \)


At \( 100^{\circ} \mathrm{C} \), benzene \( \& \) toluene have
vapour pressure of \( 1375 \& 558 \) Torr
respectively. Assuming these two form an ideal binary solution, calculate the composition of Ithe solution that boils
at 1 atm \( \& 100^{\circ} \mathrm{C} \). What is the
composition of vapour issuing at these conditions?
A . \( x_{b}=0.2472, Y_{b}=0.4473 \)
B. \( x_{b}=0.4473, Y_{b}=0.2472 \)
c. \( x_{b}=0.362, Y_{b}=0.321 \)
D. None of these


The structure present in all adult
vertebrates is
A. Notochord
B. Dorsal tubular nerve cord
C. Pharyngeal gill slits
D. All of these


A dense sphere of mass \( M \) is placed at
the centre of a circle of radius \( R \). Find
the work done, when a particle of mass
\( m \) is brought from \( A \) to \( B \) along a circle
as shown in the figure.
A . zer
в. \( \frac{G M m}{R} \)
c. \( -\frac{G M m}{R} \)
D. \( \frac{2 G M m}{B} \)


A thin circular ring of area \( A \) is held perpendicular to a uniform magnetic field of induction B. A small cut is made
in the ring and a galvanometer is
connected across the ends such that
the total resistance of the circuit is \( \mathrm{R} \).
When the ring is suddenly squeezed to
zero area, the charge flowing through
the galvanometer is
A. \( \frac{B R}{A} \)
в. \( \frac{B A}{R} \)
c. ABR
D. \( \frac{B^{2} A}{R^{2}} \)