General formula for
diketone
A. \( C_{n} H_{2 n} O \)
в. \( C_{n} H_{2 n} O_{3} \)
\( \mathbf{c} \cdot C_{n} H_{2 n} O_{4} \)
D. \( C_{n} H_{2 n} O_{2} \)


The diameter of the eye ball of a normal
eye is about \( 2.5 \mathrm{cm} . \) The power of the eye lens varies from
\( \mathbf{A} \cdot 9 D \) to \( 8 D \)
B. \( 40 D \) to \( 32 D \)
c. \( 44 D \) to \( 40 D \)
D. None of these


\( \operatorname{Let} f(x)=\left\{\begin{array}{cc}1 /|x| & \text { for }|x| \geq 1 \\ a x^{2}+b & \text { for }|x|<1\end{array} \) The \right.
coefficients a and b so that fis
continuous and differentiable at any
point, are equal to
A. \( a=-1 / 2, b=3 / 2 \)
в. \( a=1 / 2, b=-3 / 2 \)
c. \( a=1, b=-1 \)
D. none of these


Find the principal value of:
\( \sec ^{-1}(-\sqrt{2}) \)


A charge \( +q \) is fixed at each of the
points \( \boldsymbol{x}=\boldsymbol{x}_{0}, \boldsymbol{x}=\mathbf{3} \boldsymbol{x}_{0}, \boldsymbol{x}=\mathbf{5} \boldsymbol{x}_{0} \dots \dots, \infty \)
on the \( x \) -axis and charge \( -q \) is fixed at
each of the points \( \boldsymbol{x}=\mathbf{3} \boldsymbol{x}_{0}, \boldsymbol{x}= \)
\( \mathbf{4} \boldsymbol{x}_{0}, \boldsymbol{x}=\boldsymbol{6} \boldsymbol{x}_{0}, \ldots \ldots, \infty . \) Here, \( \boldsymbol{x}_{0} \) is a
positive quantity. Take the electric potential at a point due to charge \( Q \) at a distance \( r \) from it to be \( \frac{Q}{4 \pi \varepsilon_{0} r} . \) Then the potential at origin due to the above system of charges is:
A . zero
B. infinity
c. \( \frac{q}{8 \pi \varepsilon_{0} x_{0} \text { In2 }} \)
D. \( \frac{q \operatorname{In} 2}{4 \pi \varepsilon_{0} x_{0}} \)


Red \( P \) can be obtained from white \( P \) by
A. Heating it with a catalyst in an inert atmosphere.
B. Distilling it in an inert atmosphere.
c. Dissolving it in carbon disulphide and crystallising.
D. Melting it and pouring liquid in water


If \( F \) is the force required to keep a train
moving at a constant speed \( v, \) the
power required is
A \( \cdot \frac{1}{2} F v^{2} \)
B. \( F v^{2} \)
c. \( \frac{1}{2} F v \)
D. \( F v \)


The acceleration of a body projected upwards with a certain velocity is equal
to
A \( \cdot 9.8 m / s^{2} \)
В. \( -9.8 m / s^{2} \)
c. zero
D. insufficient data


The thermal capacity of calorimeter system is \( 17.7 k J K^{-1} .(R= \)
\( 8.313 m o l^{-1} K^{-1} \) ) (only magnitude in
nearest integer in kJ/mol)


Perpendiculars \( A P, A Q \) and \( A R \) are drawn to the \( x-, y- \) and \( z- \) axes, respectively
from the point \( \boldsymbol{A}(\mathbf{1},-\mathbf{1}, \mathbf{2}) . \) The A.M. of
\( A P^{2}, A Q^{2} \) and \( A R^{2} \) is
A .4
B. 5
\( c .3 \)
D.


A long current carrying conductor of
length \( l \) is placed in a uniform magnetic
field strength \( B \). If current in conductor is \( i A, \) write down the formula of force
exerted on current carrying conductor.
What will be the maximum force? Write
its direction.


By increasing the temperature, the specific resistance of a conductor and a
semiconductor.
A. Increasing for both
B. Decreases for both
c. Increases, decreases
D. Decreases, increases


The energy released during the fission of \( 1 \mathrm{kg} \) of uranium:
A \( .9 \times 10^{20} \) ergs
B. \( 9.0 \times 10^{10} \) ergs
c. \( 9.0 \times 10^{18} \) ergs
D. \( 9.0 \times 10^{8} \) ergs


The magnetic flans associated with a metal ring varies with time all. to \( \phi= \) \( \mathbf{3}\left(\boldsymbol{a} \boldsymbol{t}^{3}-\boldsymbol{b} \boldsymbol{t}^{2}\right) \boldsymbol{T} \boldsymbol{m}^{2}, \boldsymbol{a}=\boldsymbol{2} \boldsymbol{s} \boldsymbol{e} \boldsymbol{c}^{-3}, \boldsymbol{b}= \)
\( 6 \sec ^{-2} . \) If the resistance of the ring is
\( 24 \Omega, \) the current induced in the ring
during the time \( t=2 \sec \) is
A. \( 2 a m p \)
в. \( 4 a m p \)
c. \( 6 a m p \)
D. zero


How long (approximate) should water be electrolysed by passing through 100
amperes current so that the oxygen
released can completely burn \( 27.66 g \) of diborane?
(Atomic weight of \( \boldsymbol{B}=\mathbf{1 0 . 8 u} \) )
A. 3.2 hours
B. 1.6 hours
c. 6.4 hours
D. 0.8 hours


\( f^{n} P_{r}=840,^{n} C_{r}=35, \) then \( n \) is equal
to:
\( A \cdot 6 \)
B.
\( c \cdot 8 \)
D.


Propeller blades in aeroplane are \( 2 m \)
long
(a) When propeller is rotating at 1800rev/min, compute the tangential
velocity of tip of the blade.
(b) What is the tangential velocity at a point on blade midway between tip and
axis?


The mass of a compound is 10 g and the
mass of \( C O_{2} \) formed is 23 g. Estimate the percentage of oxygen.
A . \( 83 \% \)
B . \( 61.2 \% \)
c. \( 71.8 \% \)
D . 25.4\%


State true or false:
The region of the z-plane for which \( \left|\frac{\boldsymbol{z}-\boldsymbol{a}}{\boldsymbol{z}+\overline{\boldsymbol{a}}}\right|=1(\boldsymbol{R} e \boldsymbol{a} \neq 0) \) is \( X \) -axis.


In which of the following pairs, the first atom or ion is not larger than the
second?
A \( \cdot F e^{2+}, F e^{3+} \)
в. \( O, S \)
c. \( N, O \)
D. \( C l^{-}, C l \)


The coordinate of vertices of triangles are given. Identify the types of triangles (3,5)(-1,1)(6,2)


Construct a \( 2 \times 3 \) matrix \( A=\left[a_{i j}\right] \)
whose elements are given by \( a_{i j}= \)
\( \left\{\begin{array}{l}i-j i \geq j \\ i+j i<j\end{array}\right. \)


A point charge of magnitude \( +1 \mu c \) is
fixed at \( (0,0,0) . \) An isolated uncharged spherical conductor is fixed its centre
at \( (4 m, 0,0) . \) The potential and the induced electric field at the centre of
the sphere is
A . \( 1.8 \times 10^{5} V \) and \( -5.625 \times 10^{6} V / m \)
B. \( 0 \mathrm{V} \) and \( 0 \mathrm{V} / \mathrm{m} \)
C . \( 2.25 \times 10^{5} V \) and \( -5.625 \times 10^{6} V / m \)
D. \( 2.25 \times 10^{5} V \) and \( 0 V / m \)


A charge \( +10^{-9} C \) is located at the
origin in free space and another charge
\( Q \) at \( (2,0,0) . \) If the \( X \) -component of the electric field at (3,1,1) is zero. The
value of \( Q \) is
A \( \cdot 2.4 \times 10^{-10} \mathrm{C} \)
В. \( -6.2 \times 10^{-20} C \)
c. \( -4.3 \times 10^{-10} C \)
D. \( -1.2 \times 10^{-20} C \)


\( \boldsymbol{A}^{+} \boldsymbol{B}^{-}+\boldsymbol{C}^{+} \boldsymbol{D}^{-} \longrightarrow \boldsymbol{A}^{+} \boldsymbol{D}^{-}+\boldsymbol{C}^{+} \boldsymbol{B}^{-} \)
Identify the above generalized type of
reaction:
A. Chemical replacement reaction
B. Chemical double decomposition reaction
c. Chemical displacement reaction
D. Chemical combination reaction


Draw any circle and mark a sector


The highest energy band which is filled at zero Kelvin is called
A. conduction band
B. valence band
c. insulation band
D. filled band


The poisson's ratio cannot have the value
A. 0.7
B. 0.2
c. \( 0 . \)
D. 0.3


Which one of the following traits of Garden Pea studied by Mendel was a recessive feature?
A. Axial flower position
B. Green seed colour
c. Green pod colour
D. Round seed shape


Zn-Ag alloy formed in the upper layer of molten lead is skimmed off from the surface of the molten lead by perforated ladles. This alloy contains leed as impurity, This impurity of Pb is removed by :
A. distillation process
B. cupellation
c. liquation
D. Bett's electrolysis


Two small boats are \( 10 m \) apart on a
lake. Each pops up and down with a period of 4.0 seconds due to wave motion on the surface of the water.
When one boat is at its highest point. the other boat is at its lowest point. Both boats are always within a single cycle of the waves. The speed of the waves is
A \( .2 .5 \mathrm{m} / \mathrm{s} \)
B. \( 5.0 \mathrm{m} / \mathrm{s} \)
c. \( 14 \mathrm{m} / \mathrm{s} \)
D. \( 40 \mathrm{m} / \mathrm{s} \)


For the molecule \( \boldsymbol{I} \boldsymbol{F}_{7} \)
(i) State the hybridisation of the central
atom.
(ii) State the geometry of the molecule.


The marks distribution of 30 students
in a mathematics examination are as
follows:
Class-
\[
\begin{array}{lll}
\text { interval } & \mathbf{1 0}- & \mathbf{2 5}- \\
\text { of } & \mathbf{2 5} & \mathbf{4 0}
\end{array}
\]
marks
Number of
students
Find the mean by assume mean method and find also the mode of given data.


Biochemical Oxygen Demand (BOD) may not be a good index for pollution for water bodies receiving effluents from
A. Petroleum industry
B. Sugar industry
c. Domestic sewage
D. Dairy industry


State whether the following statements
are true or false.

A species may be defined as a group of closely resembling organisms that are sexually reproducing and freely interbreed in nature
A. True
B. False


The reflection from a concrete sidewalk
is a diffused reflection.
A. True
B. False


Which of the following sets of real numbers is such that if \( x \) and \( y \) are the
elements of the set, then the sum of \( x \)
and y is also an element of the set:
I. The set of negative integers
II. The set of rational numbers
III. The set of irrational numbers
A. None
B . I only
c. I and II only
D. Il and III only
E . I, II, and III


Solve for \( x \) :
\( \mathbf{3}(\boldsymbol{x}+\mathbf{1})+\mathbf{4} \boldsymbol{x}=\mathbf{2 4} \)


\( \int_{-1}^{1} 5 x^{4} \sqrt{x^{5}+1} d x \)


Two balls are drawn at random from a
bag containing 2 white , 3 red , 5 green and 4 black balls, one by one without, replacement. Find the probability that both the balls are of different colours.


The difference between angular speed
of minute hand and second hand of a
clock is
A \( \cdot \frac{59 \pi}{900} \operatorname{rad} / \mathrm{s}^{-1} \)
в. \( \frac{59 \pi}{1800} \mathrm{rad} / \mathrm{s}^{-1} \)
c. \( \frac{59 \pi}{2400} \mathrm{rad} / \mathrm{s}^{1} \)
D. \( \frac{59 \pi}{3600} \mathrm{rad} / \mathrm{s}^{-1} \)


Water drops present on leaf margins of Tropaeolum, Balsam and grasses in early morning are due to
A. Guttation
B. Dew
c. osmosis
D. Transpiration


As the thickness of the atmosphere increases colour of scattered light is
found in
A. Blue, violet, yellow, red
B. Violet, blue, yellow, red
c. Red, yellow, blue, violet
D. Violet, blue, red, yellow


From a uniform disc of radius \( \mathrm{R} \), a disc of radius \( \frac{\boldsymbol{R}}{\mathbf{2}} \) is scooped out such that they have the common tangent. Find the centre of mass of the length remaining
part


Assertion
Transition of electron between \( \boldsymbol{p}_{\boldsymbol{x}} \) and \( \boldsymbol{p}_{\boldsymbol{y}} \)
would not lead to an spectral line.
Reason
\( p \) -orbitals are degenerate orbitals.
Read the above assertion and reason
and choose the correct option regarding
¡t.
A. Both Assertion and Reason are correct and the Reason is the correct explanation of Assertion
B. Both Assertion and Reason are correct but the Reason is not the correct explanation of the Assertion
c. Assertion is correct but the Reason is incorrect
D. Assertion is incorrect and Reason is correrct


The mixture is compressed adiabatically to \( \frac{1}{5} \) its initial volume \( V \)
Find the change in its adiabatic
compressibility in terms of given quantities?


In which of the following there is some loss of energy in the form of heat
A. Forced vibrations
B. Free vibration
c. Damped vibrations
D. All


Show that \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \begin{array}{ll}\frac{\sin 3 x}{\tan 2 x}, & \text { if } x<0 \\ \frac{3}{2}, \quad \text { if } x=0 & \text { is contint } \\ \frac{\log (1+3 x)}{e^{2 x}-1}, & \text { if } x>0\end{array} \)


A circular beam of light of diameter
\( d=2 c m \) falls on a plane surface of
glass. The angle of incident is \( 60^{\circ} \) and refractive index of glass is \( \mu=3 / 2 . \) The
diameter of the refracted beam is
A \( .2 .00 \mathrm{cm} \)
в. \( 1.50 \mathrm{cm} \)
c. \( 1.63 \mathrm{cm} \)
D. \( 2.52 \mathrm{cm} \)


\( f \) is a function defined as \( \sum_{k=1}^{n} f(a+ \) \( \boldsymbol{k})=\mathbf{1 6}\left(\mathbf{2}^{n}-\mathbf{1}\right) \) and \( \boldsymbol{f}(\boldsymbol{x}+\boldsymbol{y})= \)
\( f(x) \cdot f(y) \) and \( f(1)=2 \) then integral
value of \( \boldsymbol{a} \)
A . 3
B. 0
\( c \cdot 2 \)
D.


The solubility product of \( A g C l \) is \( 1.8 \times \)
\( 10^{-10} . \) Precipitation of \( A g C l \) will occur
only when equal volumes of solutions of
A \( \cdot 10^{-4} M A g^{+} \) and \( 10^{-4} M C l^{-} \) are mixed
B . \( 10^{-7} M A g^{+} \) and \( 10^{-7} M C l^{-} \) are mixed
C \( \cdot 10^{-5} M A g^{+} \) and \( 10^{-5} M C l^{-} \) are mixed
D. \( 10^{-10} M A g^{+} \) and \( 10^{-10} M C l^{-} \) are mixed


Calculate the enthalpy of formation of
\( \operatorname{acetic} \operatorname{acid}\left(C H_{3} C O O H\right) \) if its
enthalpy of combustion is
\( -867 k J m o l^{-1} . \) The enthalpies of
formation of \( \boldsymbol{C O}_{2}(\boldsymbol{g}) \) and \( \boldsymbol{H}_{2} \boldsymbol{O}(l) \) are
-393.5 and \( -285.9 k J m o l^{-1} \)
respectively.


Consider a long conductor, the middle of
which is earthed. If the potential
difference across the two ends of the
conductor is \( 220 \mathrm{V} \), then what is the
potential at the ends and the middle
point?
A. \( 220 V \) all over the conductor
B. \( 110 V \) and \( -110 V \) at ends and \( 0 V \) at the mid point
C. \( 0 V \) at ends and \( 220 V \) at midpoint
D. \( -220 \mathrm{V} \) all over the conductor


The number of coulombs necessary to deposit \( 1 ~ g \) of potassium metal (molar mass \( 39 g m o l^{-1} \) ) from \( K^{+} \) ions is:
A \( \cdot 96500^{\circ} \mathrm{C} \)
B . \( 1.93 \times 10^{50} C \)
\( \mathbf{c} \cdot 1237^{\circ} \mathrm{C} \)
D. 2474 \( ^{\circ} \mathrm{C} \)


A ball is thrown upwards from the top of
a tower \( 40 m \) high with a velocity of 10 \( m / s \). Find the time when it strikes
the ground. Take \( \boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{\mathbf{2}} \)
A. \( 4 s \)
B. \( 6 s \)
\( c \cdot 3 s \)
D. \( 7 s \)


The multiplicative inverse of -1 is \( p \)
then \( -p \) is equal to


Without expanding, show that the value of each of the following determinants is
zero:
\( \left|\begin{array}{ccc}a & b & c \\ a+2 x & b+2 y & c+2 z \\ x & y & z\end{array}\right| \)


In normal healthy female, the number of
\( \mathrm{RBC} / \mathrm{mm}^{3} \) of blood is
A. \( 6.5-7.0 \) million
B. 5.5 - 6.0 million
c. \( 4.5-5.0 \) million
D. 3.5 - 4.0 million


The diagram shows a uniformly charged
hemisphere of radius \( R \). It has volume
charge density \( \rho . \) If the electric field at a
point \( 2 R \) distance above its center is \( E \)
then what is the electric field at the
point which is \( 2 R \) below its center?
A \( \cdot \rho R / 6 \epsilon_{0}+E \)
В . \( \rho R / 12 \epsilon_{0}-E \)
c. \( -\rho R / 6 \epsilon_{0}+E \)
D. \( \rho R / 24 \epsilon_{0}+E \)


State True or False.
Real gases consists of atoms or molecules with intermolecular
attractions and repulsions.
A. True
B. False


A photon of energy \( \mathrm{E}_{1} \) incident on a surface liberates electrons whose
energy is equal to the work function \( \mathbf{W} \) of the metal. When a photon of energy
2
is incident on the same surface, energy of the emitted electrons is \( 3 \mathrm{W} \)
The ratio \( \mathrm{E}_{1}: \mathrm{E}_{2} \) is
A . 1: 2
B. 2:
c. 1: 3
D. 3:


A hydrocarbon is:
A. a compound containing carbon, hydrogen and oxygen
B. is sodium hydrogen carbonate
C. a compound containing carbon and hydrogen only
D. a derivative of benzene


A plane wave \( \boldsymbol{y}=\boldsymbol{a} \sin (\boldsymbol{\omega} \boldsymbol{t}-\boldsymbol{k} \boldsymbol{x}) \)
propagates through a stretched string. The particle velocity versus \( x \) graph at \( \boldsymbol{t}=\mathbf{0} \) is :
\( A \)
\( B \)
\( c \)
\( D \)


Maximum covalent character is in:
A . Nal
в. \( M g I_{2} \)
c. \( A l C l_{3} \)
D. \( A l I_{3} \)


Homologous series
is
A. A series of compounds in which the same functional group substitutes for hydrogen in a carbon chain
B. A series of compounds in which different functional group substitutes for hydrogen in a carbon chain.
C. A series of compounds with same molecular formula and different structural formulas.
D. A series of compounds with same molecular formula but different functional groups


Which of the following statement is
false regarding sodium?
A. It takes the oxidation state +1
B. It reacts with water to form a basic solution
C. It forms metallic bonds in its solid uncombined form
D. It is found in nature as a diatomic gas
E. It reacts with a halogen to form an ionic salt


Match the column I (polymer) with column II (its type)


A police cruiser, approaching a rightangled intersection from the north, is chasing a speeding car that has turned the corner and is now moving straight
east. When the cruiser is \( 0.6 \mathrm{km} \) north
of the intersection and the car is \( 0.8 \mathrm{km} \)
to the east, the police determine with radar that the distance of the car is
increasing at \( 20 \mathrm{km} / \mathrm{h} \). Suppose that the cruiser is moving at \( 60 \mathrm{km} / \mathrm{h} \) at the instant of measurement.
The speed of the car is (in \( \mathrm{km} / \mathrm{h}) \)
A . 70
B. 80
c. 75
D. 60


The potential energy of a particle executing SHM varies sinusoidally with frequency f. The frequency of oscillation of the particle will be:
\( A \cdot \frac{f}{2} \)
в. \( \frac{f}{\sqrt{2}} \)
\( c \cdot f \)
D. \( 2 f \)


The focal length of a convex lens is 10 cm. The magnifying powers when it is used as a magnifying glass to form the image at (i) near point and (ii) far point
are :
A \( .2 .5,3.5 \)
B. 3.5, 4.
c. 4.5,3.5
D. 3.5, 2.5


For periodic motion of small amplitude
\( A, \) the time period \( T \) of this particle is
proportional to
\( \mathbf{A} \cdot A \sqrt{\frac{m}{\alpha}} \)
B. \( \frac{1}{A} \sqrt{\frac{m}{\alpha}} \)
c. \( A \sqrt{\frac{\alpha}{m}} \)
D. \( A \sqrt{\frac{2 \alpha}{m}} \)


Find the value of \( \sin 765^{\circ} \)


How many isomers of \( C_{5} H_{11} O H \) will
be primary alcohol?
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. 5


Total energy of an electron in the ground state of hydrogen atom is \( -13.6 e V \). Its
total energy, when hydrogen atom is in the first excited state, is:
\( \mathbf{A} \cdot+13.6 \mathrm{eV} \)
B. \( +3.4 e V \)
c. \( -3.4 e V \)
D. \( -54.4 e V \)


Two identical discs of mass M and
radius \( R \) are connected by a light rod The assembly rests at a corner, the
vertical wall is smooth and there is
sufficient friction on the floor to ensure
pure rolling of disc B. The system starts
from position \( \boldsymbol{\theta}=\mathbf{0} . \) Find the velocity of
the midpoint of the rod when \( \boldsymbol{\theta}=\mathbf{6 0}^{\circ} \)


In a catalytic conversion of \( N_{2} \) to \( N H_{3} \)
by Haber's process, the rate of reaction was expressed as change in the concentration of ammonia per time is
\( 40 \times 10^{-3} \mathrm{mol} \mathrm{L}^{-1} \mathrm{s}^{-1} . \) If there is no
side reaction, the rate of the reaction as expressed in terms of hydrogen is :
\( \left(\text { in } \operatorname{mol} L^{-1} s^{-1}\right) \)
A \( \cdot 60 \times 10^{-3} \)
B . \( 20 \times 10^{-3} \)
c. 1.200
D. \( 10.3 \times 10^{-3} \)


In the given figure, what percent of the circle is occupied by sector \( C \).
\( 33 \frac{1}{3} \% \)
\( 22 \frac{2}{9} \% \)
\( 16 \frac{2}{3} \% \)


Q Type your question-
length \( 4.9 \mathrm{m} \). The other end of the spring (see the figure) is fixed. The system lies on a horizontal frictionless surface. The
block is stretched by \( 0.2 \mathrm{m} \) and released from rest at \( t=0 . \) It then executes simple
harmonic motion with angular
frequency \( \omega=\frac{\pi}{3} r a d / s \)
Simultaneously at \( t=0, \) a small pebble is projected with speed v from point \( \mathrm{P} \) at an angle of 45 as shown in the figure. Point \( P \) is at a horizontal distance of 10
\( \mathrm{m} \) from \( 0 . \) If the pebble hits the block at \( t=1 \mathrm{s}, \) the value of \( \mathrm{v} \) is
\( \left(\operatorname{take} g=10 m / s^{2}\right) \)
\( \mathbf{A} \cdot \sqrt{50} m / s \)
B. \( \sqrt{51} \mathrm{m} / \mathrm{s} \)
c. \( \sqrt{52} \mathrm{m} / \mathrm{s} \)
D. \( \sqrt{53} \mathrm{m} / \mathrm{s} \)


In stationary wave, the distance between a node and its adjacent antinode is
\( A \cdot \lambda \)
B. \( \frac{\lambda}{4} \)
\( c \cdot \frac{\lambda}{2} \)
D. \( 2 \lambda \)


The most electronegative element of period-3 is :
A . \( A r \)
B. \( S \)
\( c \cdot s i \)
D. \( C l \)


Check whether the following form an AP:
The amount of money in the account of
Varun at the end of every year when
Rs.1000 is deposited at simple interest
of \( 10 \% \) per annum.
A. True
B. False


A dice is manufactured in such a way
that probability of getting an even number is twice likely to occur as an odd number. If the dice is tossed twice,
find the probability distribution of the
random variable representing the perfect square in the both tosses.


The graph \( A B \) shown in the figure is
plot of the temperature of a body in degree Celsius and degree Fahrenheit Then
A. Slope of line \( A B \) is \( 9 / 5 \)
3. Slope of line \( A B \) is \( 5 / 9 \)
C. Slope of line \( A B \) is \( 1 / 9 \)
Slope of line \( A B \) is \( 3 / 9 \)


Two particles move in the same straight
line starting at the same moment from
the same point in the same
direction. The first moves with constant
velocity u and the second starts from
rest with constant acceleration \( f . \) Then
This question has multiple correct options
A. They will be at the greatest distance at the end of time Idfrac \( \{\mathrm{u}\}\{2 \mathrm{f}\} \$ \$ \) from the start
B. They will be at the greatest distance at the end of time Idfrac \( \{\mathrm{u}\}\{\mathrm{f}\} \$ \$ \) from the start
C their greatest distance is \( \frac{u^{2}}{2 f} \)
D. Their greatest distance is \( \frac{u^{2}}{f} \)


The reagent commonly used to determine hardness of water
titrimetrically is:
A . oxalic acid
B. sodium citrate
c. disodium salt of EDTA
D. sodium carbonate


Fill in the blank:
The last digit in the measurement gives
the first
A. certain
B. significant
c. uncertain
D. insignificant


The proof of oxidizing action of hydrogen peroxide in acid solution is in the formation of
\( A \cdot O_{2} \)
в. \( H_{2} \) о
c. both \( H_{2} O \) and \( O_{2} \)
D. both \( H_{3} O^{+} \) and \( O_{2} \)


Solve : \( \int \sin ^{-1} x \cdot \frac{1}{x^{2}} d x \)


An object, \( 1 m \) tall, is put in front of a
plane mirror at a distance of 0.2 m.The
size of the image formed is:
A. \( 0.2 m \)
в. \( 0.5 m \)
\( \mathrm{c} .0 .1 \mathrm{m} \)
D. \( 1 m \)


Cold solution of barium nitrite on
mixing with sulphuric acid produces
A \( \cdot \) BaSO \( _{4}+H N O_{2} \)
в. \( B a S O_{4}+H N O_{3} \)
c. \( B a S O_{4}+N O_{2} \)
D. \( B a S O_{4+} N_{2}+O_{2} \)


If a lanthanide element with \( \boldsymbol{x} \boldsymbol{f} \)
electrons has a pink colour, then the lanthanide with \( (14-x) f \) electrons will
have colour.
A. blue
B. red
c. green
D. pink


Permanent hardness is due to \( C l^{\ominus} \) and
\( \boldsymbol{S O}_{4}^{2-} \) of \( \boldsymbol{M} \boldsymbol{g}^{2+} \) and \( \boldsymbol{C} \boldsymbol{a}^{2+} \) and is
removed by adding \( N a_{2} C O_{3} \)
\( \boldsymbol{C a} \boldsymbol{S O}_{4}+\boldsymbol{N a}_{2} \boldsymbol{C O}_{3} \rightarrow \boldsymbol{C a} \boldsymbol{C O}_{3}+ \)
\( N a_{2} S O_{4} \)
\( \boldsymbol{C a C l}_{2}+\boldsymbol{N a}_{2} \boldsymbol{C O}_{3} \rightarrow \boldsymbol{C a C O}_{3}+ \)
\( 2 N a C l \)
Which of the following statements is/are correct?
This question has multiple correct options
\( A \cdot \) If hardness is 100 ppm \( C a C O_{3} \), the amount of \( N a_{2} C O_{3} \) required to soften 10 L of hard water is 1.06 g.
B. If hardness is 100 ppm \( C a C O_{3} \), the amount of \( N a_{2} C O_{3} \) required to soften 10 L of hard water is 10.6 g.
C. If hardness is 420 ppm \( M g C O_{3} \), the amount of \( N a_{2} C O_{3} \) required to soften 10 L of hard water is \( 53.0 \mathrm{g} \)
D. If hardness is 420 ppm \( M g C O_{3} \), the amount of \( N a_{2} C O_{3} \) required to soften 10 L of hard water is \( 5.3 \mathrm{g} \)


Prove that the median to the base of an
isosceles triangle is perpendicular to
the base.


Which of the following given statements
is/are not correct?
This question has multiple correct options
A \( \cdot \frac{d}{d x}(\operatorname{cosec} x)=\operatorname{cosec} x \cdot \cot x \)
B. \( \frac{d}{d x}(\sec x)=\sec x . \tan x \)
C \( \cdot \frac{d}{d x}(3 \cot x)=-3 \operatorname{cosec}^{2} x \)
D \( \cdot \frac{d}{d x}(2 \tan x)=-2 \sec ^{2} x \)


Show that the product of perpendiculars on the line \( \frac{x}{a} \cos \theta+ \) \( \frac{y}{b} \sin \theta=1 \) from the points
\( (\pm \sqrt{a^{2}-b^{2}}, 0) \) is \( b^{2} \)


Show that the points \( \boldsymbol{A}(-\mathbf{3}, \mathbf{3}), \boldsymbol{B}(\mathbf{0}, \mathbf{0}) \)
\( C(3,-3) \) are collinear


In manufacture of sodium carbonate
from Solvay (or ammonia soda) process
the raw material used is:
A . \( N a O H \)
в. \( N a_{2} S O_{4} \)
c. \( N a C l \)
D. \( \operatorname{NaH} \mathrm{CO}_{3} \)


Plastics are:
A. salts
B. acids
c. polymers
D. solvents


The refractive through the prisms are as shown. Pick out the WRONG statement
from the following. Path of the light ray
in
A \( \cdot \) A is correct if \( n_{2}>n_{1} \) and \( n_{2}>n_{3} \)
B. B is correct if \( n_{1}=n_{2} \) and \( n_{2}>n_{3} \)
c. \( c \) is correct if \( n_{2}<n_{1} \) and \( n_{2}=n_{3} \)
D. D is correct if \( n_{1}>n_{2} \) and \( n_{2}<n_{3} \)


Show that the function given by \( f(x)= \) \( 3 x+17 \) is strictly increasing on \( R \)


NaCl does not hydrolysis at \( P_{H} \)
(Natural) at \( 25^{\circ} \mathrm{C} \)
Explain.


Electrolysis of fused \( N a C l \) will give:
A. \( N a \)
в. \( N a O H \)
c. NaClO
D. \( N a C l O_{3} \)
E . \( N a C l O_{4} \)


The value of \( \Delta=\left|\begin{array}{llll}1^{2} & 2^{2} & 3^{2} & 4^{2} \\ 2^{2} & 3^{2} & 4^{2} & 5^{2} \\ 3^{2} & 4^{2} & 5^{2} & 6^{2} \\ 4^{2} & 5^{2} & 6^{2} & 7^{2}\end{array}\right| \)
equals to
\( \mathbf{A} \cdot \mathbf{0} \)
B \( \cdot 1^{2}+2^{2}+3^{2}+4^{2}+\ldots+7^{2} \)
\( c \cdot 1 \)
D. -


A driver is driving his car along a road is
shown in Fig. The driver makes sure
that the speedometer reads exactly 40 km/h. What happens to the speed of the
car from \( P \) to \( Q ? \)
A. Speed remains constant
B. Speed first increases then decreases
c. Speed first decreases then increases
D. Nothing can be decided


Which of the following is an example of electroplating?
A. coating of chromium on many objects such as bath taps, car parts, etc.
B. Coating of gold or silver on less expensive metals
c. coating of zinc on tin to make cans
D. All of the above


The conversion of \( -\operatorname{coch}_{2}-t o- \)
\( \boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}- \) using Hg/ Zn and HCl is
known as
A. Clemmensen reduction
B. Birch reduction
c. Wolf kishner reduction
D. Rosenmund reduction


A meter bridge is set-up as shown, to
determine an unknown resistance. \( \boldsymbol{X} \)
using a standard 10 ohm resistor. The
galvanometer shows null point when
tapping key is a \( 52 \mathrm{cm} \) mark. The end-
corrections are \( 1 \mathrm{cm} \) and \( 2 \mathrm{cm} \)
respectively for the ends \( A \) and \( B \). The
determined value of \( X \) is:
\( \mathbf{A} \cdot 10.2 \mathrm{ohm} \)
B. 10.6 ohm
c. 10.8 ohm
D. 11.1 ohm


When zinc oxide is reacted with carbon
mono oxide, the product formed is :
A. zinc carbonate
B. carbon
c. zinc
D. none of these


If the temperature of hot body is raised by \( 5 \% \) then the heat energy radiated would increase by
A . \( 18 \% \)
B . 24\%
c. \( 16 \% \)
D . 21\%


The hybridization of Chlorine atom in \( C l F_{3} \) molecule is:
\( A \cdot s p \)
B . sp \( ^{2} \)
\( c \cdot s p^{3} \)
\( \mathbf{D} \cdot \mathbf{s p}^{3} \mathrm{d} \)


1 \( g \) mole of an ideal gas at \( S T P \) is subjected to a reversible adiabatic
expansion to double its volume. Find the change in internal energy \( (\gamma=1.4) \)
A. \( 11.695 .5 J \)
в. \( 769.5 J \)
c. \( 1369.5 J \)
D. \( 969.5 J \)


How many \( C l \) atoms can you ionize in the process \( C l \rightarrow C l^{+}+e \) by the
energy liberated for the process \( C l+ \)
\( e \rightarrow C l^{-} \) for one Avogadro number of
atms. Given \( I P=13.0 e V \) and \( E A= \)
\( 3.60 e V . \) Avogadro number \( =6 \times 10^{23} \)


A small source of light is \( 4 \mathrm{m} \) below the surface of a liquid of refractive index
\( 5 / 3 . \) In order to cut off all the light coming out of liquid surface, minimum diameter of the disc placed on the surface of liquid is
A. 3 m
B. \( 4 \mathrm{m} \)
\( c \cdot 6 m \)
\( D \cdot \infty \)


For what value of \( k \) the point \( (k, 2-2 k) \)
\( (1-k, 2 k) \) and \( (-4-k, 6-2 k) \) are
collinear
A \( .1,-1 / 2 \)
в. \( 1,1 / 2 \)
c. \( -1,1 / 2 \)
D. \( -1,-1 / 2 \)


Following reaction is used to remove temporary hardness which is due to
dissolved bicarbonates of \( C a^{2+} \) and
\( M g^{2+} \)
\( \boldsymbol{C a}\left(\boldsymbol{H} \boldsymbol{C O}_{3}\right)_{2}+\boldsymbol{C a}(\boldsymbol{O H})_{2} \rightarrow \)
\( 2 C a C O_{3} \downarrow+2 H_{2} O \)
Actually lime ( \( C a O \) ) is added which in
\( H_{2} O \) forms \( C a(O H)_{2} \) and precipitates
\( \boldsymbol{C a} \boldsymbol{C O}_{3} \boldsymbol{C a O}+\boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \boldsymbol{C a}(\boldsymbol{O H})_{2} \)
If \( 10 \mathrm{L} \) of hard water requires \( 0.56 \mathrm{g} \) of Ca 0 , temporary hardness of \( C a C O_{3} \) is
\( x \times 10^{2} \) ppm. Find \( x \)


Which of the following has aromatic ring in complex?
A. DMG in dimethyl glyoximate
B. Cyclopentadienyl anion in ferrocene
c. Both \( (A) \) and \( (B) \)
D. None of the above


adjacent circuit. With the resistors
\( P=50 \Omega \) and \( Q=100 \Omega, \) the null point
is obtained at \( C \) where \( A C=33 \mathrm{cm} \)
When the resistors are interchanged, the null point is found at \( C \) with \( A C= \)
\( 67 \mathrm{cm} . \) The systematic error in this
experiment seems to be due to non-
coincidence of \( A \) and \( B \) with 0 cm mark
and \( 100 \mathrm{cm} \) mark respectively. If these
and errors are equivalent to \( ^{\prime} a^{\prime} c m \) and
\( b^{\prime} c m \) respectively, then they are.
A. 0 and 1
B. 1 and 0
c. 0.33 and 0.33
D. 1 and 1


Assertion
On adding \( H_{2} S O_{4} \) to water, the
resulting aqueous solution get corrosive.
Reason
Hydronium ions are responsible for
corrosive action.
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


Which among the following is the smallest gymnosperm?
A. Cycas
B. Pinus
c. zamia
D. Gnetum


When epidermal peeling of Tradescantia is placed in a strong sugar solution and the cell
content contract away from the cell wall This phenomenon is called as
A. Hydrolysis
B. Plasmolysis
c. Deplasmolysis
D. None of the above


The length, breadth and height of a room are \( 5 m, 4 m \) and \( 3 m \) respectively Find the cost of white washing the walls of the rooms and the ceiling at the rate
of \( R s .7 .50 \) per \( m^{2} \)
A . Rs.355
в. \( R s .505 \)
c. \( R s .455 \)
D. Rs.555


Biotic factors are
A. Chemical factors of soil which affect life.
B. Physical factors of soil which affect life.
C. All living organisms which influence other organisms.
D. Factors of atmosphere which affect life.


Arteries carry oxygenated blood,except
A. Coronary artery
B. Hepatic artery
c. Aorta
D. Pulmonary artery


Identify A and B in the following:


An aluminium rod has a breaking strain \( 0.2 \% . \) The minimum cross-sectional
area of the rod in \( m^{2} \) in order to support
a load of \( 10^{4} N \) is if (Young's modulus is
\( \mathbf{7} \times \mathbf{1 0}^{\mathbf{9}} \mathbf{N m}^{-\mathbf{2}} \mathbf{)} \)
\( \mathbf{A} \cdot 1.7 \times 10^{-4} \)
В. \( 1.7 \times 10^{-3} \)
c. \( 7.1 \times 10^{-4} \)
D. \( 1.4 \times 10^{-4} \)


The length of \( D E= \)
1
B
\( c \cdot 13 \)
D


How much energy is released when a \( \mathrm{s} \mathrm{O}^{16} \) nucleus is completely converted
into energy?

The binding energy per nucleon of \( _{8} O^{16} \)
is \( 7.97 M e V \) and \( m_{p}=1.0078 u \) and
\( \boldsymbol{m}_{\boldsymbol{n}}=\mathbf{1 . 0 0 8 7 u} \)
A . \( 14899.438 \mathrm{MeV} \)
в. 148.99 Ме \( V \)
c. 4489.73 Ме \( V \)
D. 448.973 MeV


Triple point temperature for water is nearly:
A . \( 273.16 K \)
в. \( 373.16 K \)
\( \mathbf{c} \cdot 100^{\circ} \mathrm{C} \)
D. \( 444.6^{\circ} \mathrm{C} \)


A particle performs SHM with amplitude \( 25 \mathrm{cm} \) and period 3s. The minimum time required for it to move between two mean positions is :
A . 0.6 s
в. 0.5 s
\( c \cdot 0.4 \mathrm{s} \)
D. 0.2 s


Which of the following molecule/ion has a triangular pyramidal shape?
A. \( B F_{3} \)
в. \( H_{3} O^{+} \)
\( \mathbf{c} \cdot N O_{3}^{-} \)
D. \( C O_{3}^{2} \)


The equation \( (x-n)^{m}+\left(x-n^{2}\right)^{m}+ \)
\( \left(x-n^{3}\right)^{m}+\ldots+\left(x-n^{m}\right)^{m}=0(m \) is
odd positive integer), has
A. all real roots
B. one real and \( (n-1) \) imaginary roots
C . one real and \( (m-1) \) imaginary roots
D. No real roots


A neutron moving with a speed \( v \) makes
a head on collision with a hydrogen atom in ground state kept at rest. The minimum kinetic energy of neutron for which inelastic collision will take place
is
A . \( 10.2 e V \)
B. 20.4eV
c. \( 12.1 e V \)
D. \( 16.8 e V \)


The potential at a distance R/2 from the centre of a conducting sphere will be:-
A. 0
В. \( \frac{Q}{8 \pi \epsilon_{E} R} \)
c. \( \frac{Q}{4 \pi \epsilon_{c} R} \)
D. none of these


Which of the following is a way to
protect your eye, if chemical splatters
into your eye?
A. By slow addition of concentrated acid to water.
B. By slow addition of water to the concentrated acid.
C. By proper replacement of unused or excess chemicals into their properly labelled containers from where they have come.
D. Dispose of chemicals in the proper places following posted procedures. Do not return them to their original containers.
E. Flush eyes with water at the eyewash fountain for at least 15 minutes and then report the accident for further help


The mutual inductance \( M_{12} \) of a coil 1
with respect to coil 2
A. increases when they are brought nearer
B. depends on the current passing through the coilss
c. increases when one of them is rotated about an axis
D. both (a) and
(b) are correct


A bomb at rest explodes into three fragments of equal masses. Two fragments fly off at right angles to each other with velocities \( 9 m s^{-1} \) and
\( 12 m s^{-1} \) respectively. Calculate the
speed of the third fragment.


In a factory, the cost of manufacturing \( x \)
article is \( R s 20+2 x \) and the selling
price of \( x \) articles is \( R s(2.5) x . \) Draw the graph and determine.
(i) Number of articles to be
manufactured and sold to reach break-
even point (no profit and no loss situation);
(ii) The profit made when 60 articles are manufactured and sold


Domain of the function is \( \boldsymbol{y}= \)
\( \frac{\sqrt{\cos x-1 / 2}}{\sqrt{6+35 x-6 x^{2}}} \)
\( \mathbf{A} \cdot \therefore D_{1} \cap D_{2}=[0, \pi / 6] \cup[5 \pi / 3,6] \)
B \( \ldots D_{1} \cap D_{2}=[0, \pi / 3] \cup[5 \pi / 3,6] \)
\( \mathrm{c} \cdot \therefore D_{1} \cap D_{2}=[0, \pi / 3] \cup[5 \pi / 6,6] \)
D. \( \therefore D_{1} \cap D_{2}=[0, \pi / 2] \cup[5 \pi / 3,6] \)


The reaction for \( N_{2}+3 H_{2} \rightarrow 2 N H_{3} \) at
\( 27^{\circ} \mathrm{C} \) is \( -91.94 k J . \) What will be its
value at \( 50^{\circ} \mathrm{C} \) ? (The molar heat
capacities at constant \( \boldsymbol{P} \) and \( 27^{\circ} \mathrm{C} \) for
\( N_{2}, H_{2} \) and \( N H_{3} \) are 28.45,28.32 and
\( 37.07 k J \) respectively
\( \mathbf{A} \cdot-92.843 k J \)
в. \( -47.7723 k J \)
c. \( -132.5 k J \)
D. \( -176,11 k J \)


Choose the correct statement of the
following.
A. Conversion of solid into vapours without passing through the liquid state is called vapourisation.
B. Conversion of solid into vapours without passing through the liquid state is called sublimation.
C. Conversion of vapours into solid without passing through the liquid state is called freezing
D. Conversion of solid into liquid is called sublimation.


Which of the following factors does not
favour \( \boldsymbol{S}_{N} \mathbf{1} \) mechanism?
A. Strong nucleophile
B. Polar solvent
c. Low conc. of nucleophile
D. \( 3^{0} \) halide


Which is non-metal (excluding noble
gas)?
A.
B. \( Q \)
\( c \cdot R \)
\( D \)


Evaluate \( : \int_{0}^{1} \frac{2 x+3}{5 x^{2}+1} d x \)


A wave pulse traveling on a two piece string, gets partially reflected and partially transmitted at the junction. The reflected wave is inverted in shape as compared to incident one. If the
incident wave has wavelength \( \lambda \) and
transmitted wave has \( \lambda^{\prime}, \) then
\( A \cdot \lambda^{\prime}>\lambda \)
B . \( \lambda^{\prime}=\lambda \)
c. \( \lambda^{\prime}<\lambda \)
D. none


Out of \( B e^{2+}, M g^{+} \) and \( C a, B e^{2+} \) has
maximum IE.
If true enter 1 , else enter 0 .


Do you think there is any limitation in a detritus food chain?


Which of the following is less than zero during adsorption?
A. \( \Delta \) G
в. \( \Delta \) s
c. \( \Delta \) н
D. All of these


If \( \boldsymbol{A}=\left[\begin{array}{cc}1 & \tan x \\ -\tan x & 1\end{array}\right], \) then \( A^{T} A^{-1} \) is
\( \mathbf{A} \cdot\left[\begin{array}{ll}-\cos 2 x & \sin 2 x \\ -\sin 2 x & \cos 2 x\end{array}\right] \)
В. \( \left[\begin{array}{cc}\cos 2 x & -\sin 2 x \\ \sin 2 x & \cos 2 x\end{array}\right] \)
c. \( \left[\begin{array}{cc}\cos 2 x & \cos 2 x \\ \cos 2 x & \sin 2 x\end{array}\right] \)
D. none of these


The possible hazards of air pollution are
due to :
A) acid rains
B) photo chemical reactions taking place at stratosphere
C) an increase in the \( C O_{2} \) level in
the atmosphere
\( A \cdot A \& B \)
B. B \& \( c \)
\( c \cdot c \& A \)
D. \( A, B \& C \)


Nitrogen can be prepared by the action of ammonia on:
A. Oxygen
B. Chlorine
c. Phosphorus
D. Sulphur


What will be the melting point of KCl if enthalpy change for the reaction is 7.25
mol \( ^{-1} \) and entropy change is 0.007 \( K^{-1} m o l^{-1} ? \)
\( \mathbf{A} \cdot 1835.2 \mathrm{K} \)
B. 173 К
c. \( 1035.7 \mathrm{K} \)
D. 1285.2 K


If the \( 10^{t h} \) term of an A.P. is 52 and the
\( 17^{t h} \) term is 20 more than the \( 13^{t h} \) term,
find the A.P.


Let \( A \) be an invertible matrix then which
of the following is/are true
This question has multiple correct options
A \( \cdot\left|A^{-1}\right|=|A|^{-1} \)
- \( \left.^{-1}|A|^{-1}|=| A\right|^{-1} \)
B. \( \left(A^{2}\right)^{-1}=\left(A^{-1}\right)^{2} \)
C \( \cdot\left(A^{T}\right)^{-1}=\left(A^{-1}\right)^{T} \)
D. none of these


At low frequency a condenser offers:
A. high impedance
B. low impedance
C. zero impedance
D. impedance of condenser is independent of frequency


If \( \frac{(1+i)^{2}}{2-i}=x+i y, \) find \( x+y \)
A \( \cdot \frac{-2}{5} \)
B. \( \frac{2}{7} \)
\( c \cdot \frac{2}{5} \)
D. \( \frac{-2}{7} \)


Two point charges \( (+e) \) and \( (-e) \) are
kept inside a large metallic cube without touching its sides. Electric flux emerging out of the cube is?
A \( \cdot e / \varepsilon_{0} \)
В. - \( -e / \varepsilon_{0} \)
c. zero
D. \( 2 e / \varepsilon_{0} \)


Solve:
\( \lim _{x \rightarrow 8} \frac{\sqrt{1+\sqrt{1+x}}-2}{x-8} \)


Which of the following types of metals form the most efficient catalysts?
A. Alkali metalss
B. Alkaline earth metals
c. Transition metals
D. All of the above


Q Type your question
mass-less thread in vertical plane.
When a beam of light of intenisty
\( 1 W m^{-2} \) is made an incident normally
on the mirror, it gets displaced so that
the thread makes angle \( \theta \) with the
vertical. Assuming the mirror is
perfectly reflecting, the value of \( \boldsymbol{\theta} \)
(Consider it very small) is
\( ^{A} \cdot \frac{2 I m}{c a q} \)
в. \( \frac{2 I c}{m a} \)
c. \( \frac{2 I g}{c a m} \)
D. \( \frac{2 I a}{c m q} \)


Which is correct statement?
A. Starch is polymer of \( \alpha \) -glucose.
B. Amylose is a component of cellulose.
C. Proteins are composed of only one type of amino acid.
D. In cyclic structure of fructose, there are four carbons and one oxygen atom.


Choose the correct order of bond
strength:
\( \mathbf{A} \cdot C H_{3} F>C R_{3} C l>C R_{3} B r>C H_{3} I \)
B \( \cdot C H_{3} F<C R_{3} C l<C R_{3} B r<C H_{3} I \)
\( \mathbf{c} \cdot C H_{3} F>C R_{3} C l>C R_{3} B r<C H_{3} I \)
D. \( C H_{3} F>C R_{3} C l<C R_{3} B r<C H_{3} I \)


In Thomsons method, electric field of
intensity \( \boldsymbol{E}, \) magnetic field of induction
\( B \) and velocity \( V \) of the electrons were in mutually perpendicular directions. The condition for velocity is
A. \( V=E / B \)
в. \( V=B / E \)
c. \( V=B E \)
D. \( V=\sqrt{B / E} \)


A body of mass \( 2 k g \) is on an inclined
plane inclined at \( 30^{0} \) to the horizontal.
The force applied on it parallel to the plane so that it moves up that slope with the acceleration of \( 2 m s^{-2} \) against
a frictional force of \( 5 N \) is:
A . \( 5 N \)
B. \( 9.8 N \)
c. \( 14.2 N \)
D. 18.81N


Shape of P-Orbital is:
A. spherical
B. dumb-Bell
c. double dumb bell
D. none of these


Let \( A_{0}, A_{1}, A_{2}, A_{3}, A_{4}, A_{5} \) be a regular hexagon inscribed in a circle of unit radius. Then the product of the lengths
of the line segments \( A_{0} A_{1}, A_{0} A_{2} \) and
\( \boldsymbol{A}_{0} \boldsymbol{A}_{4} \) is:
A \( \cdot \frac{3}{4} \)
B. \( 3 \sqrt{3} \)
\( c \cdot 3 \)
D. \( \frac{3 \sqrt{3}}{2} \)


Assertion
In the formation of water molecule, both hydrogen and oxygen atoms attain octet of electrons.
Reason
Oxygen atom forms two ionic or electrovalent bonds with two hydrogen
atoms.
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


What is the direction and magnitude of
the force on the positive charge \( +Q_{0} \) in
terms of the given quantities?
A \( \cdot \frac{-2 Q_{0}^{2}}{4 \pi \epsilon_{0} d^{2}} \)
B. \( \frac{-\sqrt{3} Q_{0}^{2}}{4 \pi \epsilon_{0} d^{2}} \)
\( c \)
\( D \)


If
\( a, b, c \) all are non-zero and unequal and \( \left|\begin{array}{ccc}\mathbf{1}+\boldsymbol{a} & \mathbf{1} & \mathbf{1} \\ \mathbf{1} & \mathbf{1}+\boldsymbol{b} & \mathbf{1} \\ \mathbf{1} & \mathbf{1} & \mathbf{1}+\boldsymbol{c}\end{array}\right|=\mathbf{0}, \) then
\( 1+\frac{1}{a}+\frac{1}{b}+\frac{1}{c} \) is equal to?


\( \int \frac{x}{\sqrt{\left(4-x^{4}\right)}} d x \)
A \( \cdot \sin ^{-1}\left(\frac{1}{2} x^{2}\right) \)
B \( \cdot \frac{1}{2} \sin ^{-1}\left(x^{2}\right) \)
C \( \cdot \frac{1}{2} \sin ^{-1}\left(\frac{1}{2} x^{2}\right) \)
D. \( \frac{1}{2} \cos ^{-1}\left(\frac{1}{2} x^{2}\right) \)


Which of the following has lowest boiling point?
A. \( p \) -nitrophenol
B. \( m \) -nitrophenol
c. \( o \) -nitropheno
D. phenol


In the figure given below, \( \angle \boldsymbol{P}=\angle \boldsymbol{R} \boldsymbol{T} \boldsymbol{S} \)
Prove that \( \triangle R P Q \sin \triangle R T S \)


The capacity between the adjacent plates of a parallel plate capacitor is \( 10 \mu F . \) If we want a capacity of \( 50 \mu F \) the number of plates to be used is
A. 5
B. 50
\( c \cdot 6 \)
\( D \)


Noradrenaline is a:
A. enzyme
B. anti-depressant drug
c. hormone
D. None of the above


Which of the following can form image?
A. Diffused reflection
B. Irregular reflection
c. Regular reflection
D. All of these


The area of the quadrilaterial formed by the two tangents from (4,5) to the circle
\( x^{2}+y^{2}-4 x-2 y-11=0 \) and a pair
of radii is
A .2
B. 4
\( c \cdot 8 \)
D. 16


A parallel narrow beam of light travelling through water in a container incident on an air bubble of radius 8
mm. What be the distance of image obtained due to refraction of beam on
first face of air bubble from the centre of bubble? \( \quad\left(\text { take } \mu_{w a t e r}=\frac{4}{3}\right) \)
\( \mathbf{A} \cdot 17.2 \mathrm{mm} \)
B. 32 mm
c. \( 41.5 \mathrm{mm} \)
D. 25.75 mm


Law of octaves stated:
A. every eighth element had properties similar to the first element
B. every third element had properties similar to the first element
C. the properties of the middle element were in between the other two members
D. the properties of the elements were repeated after regular intervals of 3,4 or 8 elements


A portal system is one in which
\( A \cdot A \) vein starts from an organ and ends up in heart.
B. A vein starts from an organ and ends up in another
organ
C. A vein starts from heart and ends up in lungs.
D. None of the above


For a radioactive element, the correct
representation of number of nuclei (N)
decayed after time (t) is represented by
A.
B.
\( c \)
D.


Calculate mode for the following data
shows the number of colour pencils the
students have in a class.
\( \begin{array}{lllll}\text { Colour } & \mathbf{0}- & \mathbf{5}- & \mathbf{1 0}- & \mathbf{1 5}- \\ \text { Pencils } & \mathbf{5} & \mathbf{1 0} & \mathbf{1 5} & \mathbf{2 0}\end{array} \)
Number
of
students 17 13
\( \mathbf{A} \cdot 11 \)
B. 15
\( \mathbf{c} \cdot 19 \)
D. 16


Orion and Acrilan are fibres of well-
known textile materials of the same
name. They are copolymers of:
A. styrene and butadiene
B. alcohol and ester
c. acrylonitrile and 2-vinylpyridine
D. methane and acetone


In a test there were \( n \) questions. In the
test \( 2^{n-i} \) students gave wrong answers
to at least \( i \) questions \( i=1,2,3 \dots . n . \) If
the total number of wrong answers
given is \( 2047, \) then \( n \) is
A . 12
B. 11
c. 10
D. 13


The vander waals constants for \( \boldsymbol{H} \boldsymbol{C l} \) are
a \( 371.843 K P a \) and \( b=40.8 \mathrm{cm}^{3} m o l^{-1} \)
Choose the correct options:
A. The critical pressure is \( 8.273 \mathrm{MPa} \)
B. The critical temperature is \( 224.8 K \)
C. The critical volume is \( 122.4 \mathrm{cm}^{3} \)
D. The critical temperature is \( 324.8 K \)


Bakane disease in paddy is caused by
A. Abscissic acid
B. Gibberellic acid
c. Phenyl acetic acid
D. Naphthalene acetic acid


Assertion
The voltage of mercury cell remains
constant for longer period of time.
Reason
It is because net cell reaction does not
involve ions.
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 body dropped freely from a height \( h \) onto a horizontal plane, bounces up and down and finally comes to rest. The
coefficient of restitution is \( e \), the ratio
of times of two consecutive rebounds:
A \( .1: e \)
B . \( e: 1 \)
c. \( 1: e^{2} \)
D. \( e^{2}: 1 \)


The letters of the work "Questions" are arranged in a row at random.The probability that there are exactly two letters between \( Q \) and \( S \) is.
A \( \cdot \frac{1}{14} \)
B. \( \frac{5}{7} \)
\( c \cdot \frac{1}{7} \)
D. \( \frac{5}{28} \)


Electric field outside a long wire carrying charge q is proportional to:
A \( \cdot \frac{1}{r} \)
в. \( \frac{1}{r^{2}} \)
c. \( \frac{1}{r^{\frac{1}{35}}} \)
D. \( \frac{1}{r^{\frac{1}{32}}} \)


A metallic sphere is placed in a uniform
electric field. Which one of paths \( a, b, c \)
and \( d \) shown in the figure will be followed by the field lines and why?


The highest electrical conductivity of the following aqueous solutions is of
A. \( 0.1 M \) acetic acid
B. \( 0.1 M \) chloroacetic acid
c. \( 0.1 M \) fluoroacetic acid
D. \( 0.1 M \) difluoroacetic acid


A constant power is supplied to a rotating disc. The relationship between the angular velocity \( (\omega) \) of the disc and
number of rotations \( n \) made by the disc
is governed by:
A. \( \quad_{\omega} \propto n^{\frac{1}{3}} \)
в. \( \quad_{\omega} \propto n^{\frac{2}{3}} \)
c. \( \quad_{\omega} \propto n^{\frac{3}{2}} \)
D. \( \omega \propto n^{2} \)


A block of mass \( 0.2 \mathrm{kg} \) is suspended
from the ceiling by a light string. \( \mathbf{A} \) second block of mass \( 0.3 \mathrm{kg} \) is
suspended from the first block through another string. Find the tensions in the
two strings. Take \( g=10 m / s^{2} \)


What is the nature of the following
reaction?
\( \boldsymbol{C u}+\boldsymbol{H} \boldsymbol{C l} \rightarrow \)
A. Reacts vigorously
B. No reaction
c. Reacts modestly
D. Reacts slowly


If \( A \) and \( B \) are events such that \( P(A)= \) \( \frac{3}{8}, P(B)=\frac{5}{8} \) and \( P(A \cup B)=\frac{3}{4}, \) then
\( P\left(\frac{A}{B}\right)= \)
\( A \cdot \frac{2}{3} \)
B. \( \frac{2}{5} \)
\( c \cdot \frac{1}{3} \)
D.


A ball is allowed to fall from a height of
\( 10 \mathrm{m} . \) If there is \( 40 \% \) loss of energy due to impact, then after one impact ball will go upto:
A. \( 10 m \)
B. \( 8 m \)
\( c .4 m \)
D. \( 6 m \)


A tube one metre long is filled with liquid of mass \( 1 k g \). The tube is closed at both the ends and is revolved about
one end in a horizontal plane at 2 rev / \( s \)
The force experienced by the lid at the other lid is
A \( \cdot 4 \pi^{2} N \)
B. \( 8 \pi^{2} N \)
\( \mathbf{c} \cdot 16 \pi^{2} N \)
D. \( 9.8 N \)


An exterior angle of regular polygon is \( 12^{\circ} \) the sum of all the interior angles is
A \( \cdot 4040^{\circ} \)
B . \( 5040^{\circ} \)
c. \( 6040^{\circ} \)
D. \( 7040^{\circ} \)


Write the negation of the following
statements:
(i) \( p: \) For every positive real number \( x \) the number \( x-1 \) is also positive
(ii) \( q: A \| \) cats scratch
(iii) \( r: \) For every real number \( x, \) either
\( x>1 \) or \( x<1 \)
(iv) \( s: \) There exist a number \( x \) such that
\( \mathbf{0}<\boldsymbol{x}<\mathbf{1} \)


The reaction at hydrogen and iodine monochloride is represented by the equation is \( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{2} \boldsymbol{I} \boldsymbol{C l}(\boldsymbol{g}) \rightarrow \boldsymbol{2} \boldsymbol{H} \boldsymbol{C l}(\boldsymbol{g})+\boldsymbol{I}_{2}(\boldsymbol{g}) \)
This reaction is first order in \( \boldsymbol{H}_{2}(\boldsymbol{g}) \) and also first - order in ICI(g). which of these proposed mechanism can be consistent with the given information about this reaction ?
Mechanism I \( : \boldsymbol{H}_{2}(\boldsymbol{g})+2 \boldsymbol{I} \boldsymbol{C l}(\boldsymbol{g}) \rightarrow \)
\( 2 H C l(g)+I_{2}(g) \)
\( \|: \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{I} \boldsymbol{C l}(\boldsymbol{g}) \stackrel{s l o w}{\rightarrow} \)
Mechanism
\( \boldsymbol{H} \boldsymbol{C l}(\boldsymbol{g})+\boldsymbol{H} \boldsymbol{I}(\boldsymbol{g}) \)
\( \boldsymbol{H I}(\boldsymbol{g})+\boldsymbol{I} C l(\boldsymbol{g}) \stackrel{f a s t}{\rightarrow} \boldsymbol{H} C l(\boldsymbol{g})+\boldsymbol{I}_{2}(\boldsymbol{g}) \)
A . I only
в. ॥ only
c. Both I and II
D. Neither I nor I


The variation of magnitude field \( (B) \)
due to circular coil as the distance \( \boldsymbol{X} \)
varies is shown in the graph.
Which of the following is false?
A. Point \( A \) and \( A^{\prime} \) are known as point of zero curvature.
B. \( B \) varies linearly with \( X \) at point \( A \) and \( A^{\prime} \)
\( \frac{d B}{d t}=0 \) at point \( A \) and \( A^{\prime} \)
\( \frac{d^{2} B}{d t^{2}}=0 \) at point \( A \) and \( A^{\prime} \)


If \( \sqrt{9^{x}}=\sqrt[3]{9^{2}}, \) then \( x= \)
A \( \cdot \frac{2}{3} \)
B. \( \frac{4}{3} \)
\( c \cdot \frac{1}{3} \)
D.


The energy emitted per second by sun is approximately
A . \( 3.8 \times 10^{26} \) Joule
B. \( 3.8 \times 10^{14} \) Joule
c. \( 3.8 \times 10^{12} \) Joule
D. \( 3.8 \times 10^{-26} \) Joule


Let \( R \) be a relation from a set \( A \) to a set \( B \)
then
\( \mathbf{A} \cdot R=A \cup B \)
в. \( R=A \cap B \)
c. \( R \subseteq A \times B \)
D. \( R \subseteq B \times A \)


Convection cannot take place in


If water contains dissolved calcium
hydrogencarbonate, out of soaps and synthetic detergents which one will you use for cleaning clothes?


If \( \boldsymbol{P}(\boldsymbol{A})=\frac{\mathbf{3}}{\boldsymbol{4}}, \boldsymbol{P}\left(\boldsymbol{B}^{\prime}\right)=\frac{1}{3} \boldsymbol{a} \boldsymbol{n} \boldsymbol{d} \boldsymbol{P}(\boldsymbol{A} \cap \)
\( B)=\frac{1}{2} \) then find \( P(A \cup B) \)
A \( \cdot \frac{5}{12} \)
в. \( \frac{6}{12} \)
c. \( \frac{7}{12} \)
D. \( \frac{11}{12} \)


The sum of the intercepts on the coordinate axes of the plane passing
through the point (-2,-2,2) and
containing the line joining the points
(1,-1,2) and \( (1,1,1), \) is
A . 4
B. -4
c. 12
D. -8


The area of the region bounded by the curve \( y=x^{2} \) and the line \( y=16 \) is
A \( \cdot \frac{128}{3} \) sq.units
в. \( \frac{64}{3} \) sq.units
c. \( \frac{32}{3} \) sq.units
D. \( \frac{256}{3} \) sq.units


Valency of \( C r \) in \( C r P O_{4} \) is:
\( A \cdot 4 \)
B. 3
\( c \cdot 2 \)
D.


Let \( X \) be the set consisting of the first 2018 terms of the arithmetic
progression \( 1,6,11,_{-} \) \( -, \) and \( Y b e \)
the set consisting of the first 2018 terms of the arithmetic progression
\( \mathbf{9}, \mathbf{1 6}, \mathbf{2 3} \)
. Then, the
number of elements in the set XUY is
\( ? \)


When 1-pentyne \( (A) \) is treated with \( 4 N \)
alcoholic \( K O H \) at \( 175^{\circ} C, \) it is slowly
converted into an equilibrium mixture of \( 1.3 \% \) of 1 -pentyne \( (A), 95.2 \% \) 2-pentyne
\( (B) \) and \( 3.5 \% \) of 1,2 -pentadiene \( (C) . \) The
equilibrium was maintained at \( 174^{\circ} \mathrm{C} \)
Calculate \( \Delta G^{o} \) for the following
equilibria:
\( \boldsymbol{B} \rightleftharpoons \boldsymbol{A} ; \boldsymbol{\Delta} \boldsymbol{G}_{1}^{o}=? \)
\( \boldsymbol{B} \rightleftharpoons \boldsymbol{C} ; \boldsymbol{\Delta} \boldsymbol{G}_{2}^{o}=? \)
From the calculated values of \( \Delta G_{1}^{o} \) and
\( \Delta G_{2}^{o} \) indicate the order of stability of \( (A),(B) \) and \( (C) . \) Write a reasonable reaction mechanism showing all intermediates leading to \( (A),(B) \) and
\( (C) \)


The mean and variance of \( n \)
observations \( x_{1}, x_{2}, x_{3}, \dots \dots \dots \dots . . x_{n} \) are 5
and 0 respectively. If \( \sum_{i=1}^{n} x_{i}^{2}=400, \) then \( n \) is
A . 10
B. 20
c. 25
D. 36


Alcoholic beverages contain:
A. Glycerol
B. Ethyl alcohol
c. Methyl alcohol
D. Isopropyl alcohol


\( \frac{=}{\frac{i}{L}} \)


In going from \( O_{2} \) to \( O_{2}^{+}, \) the bond
dissociation energy increases and bond length decreases. Do we expect the same behavior for the change \( N_{2} \) and
\( N_{2}^{+} ? \)


(a) Why are the connections between the resistor in a meter bridge made of thick copper strips?
(b) Why is it generally preferred to obtain the balance point in the middle of the meter bride wire?
(c) Which material is used for the meter
bridge wire and why?


The zigzag development of axis is an example of
A. Umbel
B. Nelicoid cyme
c. scorpioid cyme
D. Verticillaster


Based on the compounds of group 15 elements, the correct statement(s)
is/are:
This question has multiple correct options
\( \mathbf{A} \cdot B i_{2} O_{5} \) is more basic than \( N_{2} O_{5} \)
B. \( N F_{3} \) is more covalent than \( B i F_{3} \)
\( \mathrm{C} \cdot P H_{3} \) boils at lower temperature than \( N H_{3} \)
D. The \( N-N \) single bond is stronger than the \( P-P \)
single bond.


Write the process of making curd from
milk. Explain the changes that take place in the milk?


An iron block of sides \( 5 \mathrm{cm} \times 8 \mathrm{cm} \times \)
\( 15 c m \) has to be pushed along the floor. The force required will be minimum when the surface in contact with the
ground is
\( \mathbf{A} \cdot 8 \mathrm{cm} \times 15 \mathrm{cm} \) surface
B. \( 5 \mathrm{cm} \times 15 \mathrm{cm} \) surface
c. \( 8 \mathrm{cm} \times 5 \mathrm{cm} \) surface
D. force is same for all surfaces


Which of the following option are
related with the second law of
thermodynamics (law of entropy)?
A. The heat lost by one object must be gained by another object
B. Heat flow naturally from a hotter body to a cooler body
C. Celsius degrees and Kelvin degrees are equivalent
D. Heat can be transformed into work
E. The average kinetic energy of molecules is proportional to temperature


Nucleoside is
A. Nitrogenous base + sugar
B. Nitrogenous base + sugar + phosphate
c. sugar + phosphate
D. Nitrogenous base + phosphate


A smooth wire is bent into a vertical
circle of radius \( a \). A bead \( P \) can slide
smoothly on the wire. The circle is
rotated about vertical diameter \( A B \) as
axis with a constant speed as shown in
figure. The bead \( P \) is at rest w.r.t the
wire in the position shown. Then \( \omega^{2} \) is
equal to:


Choose the correct answers from the
alternatives given :
In a typical cell cycle, cytokinesis generally overlaps in time with which stage?
A. Metaphase
B. Anaphase
c. Telophase
D. Prophase


If the position vector \( \vec{a} \) of a point \( (12, n) \) is such that \( |\vec{a}|=13, \) find the value of
\( n \)


Pentane has a molecular formula
\( C_{5} H_{12} . \) It has:
A. 5 covalent bonds
B. 12 covalent bonds
c. 16 covalent bonds
D. 17 covalent bonds


The process of 'eutrophication' is due to
A. increase in concentration of insecticide in water
B. increase in concentration of fluoride iron in water
C. the reduction in concentration of the dissolved oxygen in water due to phosphate in water
D. attack of younger leaves by peroxyacetyl nitrate


Which row describes the nature of \( \alpha \) -
particles and of \( \gamma- \) rays
A. \( \alpha \) - particles : helium nuclei ; rays - electromagnetic radiation
B. \( \alpha \) - particles : helium nuclei ; \gamma rays - electrons
c. \( \alpha \) - particles: protons; \( \gamma \) rays - electromagnetic radiation
D. \( \alpha \) - particles: protons; \( \gamma \) rays - electrons


\( \operatorname{Let} f(x)=\left\{\begin{array}{l}x+1, x>0 \\ 2-x, x \leq 0\end{array} \text { and } g(x)=\right. \)
\( \left\{\begin{array}{c}x+1, x<1 \\ x^{2}-2 x-2,1 \leq x<2 \\ x-5, x \geq 2\end{array}\right. \)
Find the LHL and RHLof \( g(f(x)) \) at \( x=0 \) lim
and, hence, find \( _{\boldsymbol{x} \rightarrow 0} g(f(x)) \)


Prove that \( \sqrt{5}+\sqrt{3} \) is irrational


A stone is thrown upwards with a
velocity \( 50 m g^{-1} \). Another stone is
simultaneously thrown downwards from the same location with a velocity
\( 50 m s^{-1} . \) When the first stone is at the
highest point, the relative velocity of the
second stone w.r.t. the first stone is:
A. Zero
B. \( 50 m s^{-1} \)
c. \( 100 \mathrm{ms}^{-1} \)
D. \( 150 \mathrm{ms}^{-1} \)


For the vectors \( \overline{\boldsymbol{x}}=(\mathbf{1}, \mathbf{2}, \mathbf{1}) ; \overline{\boldsymbol{y}}= \)
(2,-3,-1) Component of \( \bar{y} \) along \( \bar{x}= \)
A \( \frac{5}{\sqrt{14}} \)
в. \( -\frac{5}{14} \)
c. \( \frac{5}{14} \)
D. \( -\frac{5}{\sqrt{14}} \)


Coefficient of thermal conductivity:
A. depends upon nature of the material of the body
B. is independent of dimensions of the body
c. both 1 and 2
D. only 1


The incomplete breakdown of sugars in anaerobic respiration results in the formation of
A. Fructose and water
B. Glucose and \( C O_{2} \)
c. Alcohol and \( C O_{2} \)
D. water and \( C O_{2} \)


In corrosion of iron,
A. electrons flow from anode to cathode through the metal, while ions flow through the water droplets
B. an electrochemical (galvanic) cell is formed in which \( F e \) acts as anode and \( O_{2} \) is reduced at cathode
C \( . \) dissolved \( O_{2} \) oxidizes \( F e^{2+} \) to \( F e^{3+} \) before it is
deposited as rust \( \left(F e_{2} O_{3} \cdot x H_{2} O\right) \)
D. All of the above takes place


Magnification produced is \( +\frac{1}{3}, \) then
what kind of mirror it is?
A. concave mirror
B. convex mirror
c. opaque mirror
D. plane mirror


\( x=\frac{(n+1)^{n}}{(n+2)} \)
\( \frac{d x}{d n}=? \)


Solve-
\( \cos x^{3} \cdot \sin ^{2}\left(x^{5}\right) \)


Which one is the oxidising agent in the reaction given below? \( \mathbf{2} \boldsymbol{C r} \boldsymbol{O}_{\mathbf{4}}^{2-}+\mathbf{2} \boldsymbol{H}^{+} \rightarrow \boldsymbol{C r}_{2} \boldsymbol{O}_{\mathbf{7}}^{2-}+\boldsymbol{H}_{2} \boldsymbol{O} \)
A . \( H^{+} \)
в. \( C r_{2} O_{7}^{-2} \)
\( c \cdot C r^{2} \)
D. None


Rising and setting sun appears to be
reddish because:
A. The sun is colder at sunrise or at sunset
B. Diffraction sends red rays to the earth at these times
C. Refraction is responsible for it
D. Scattering due to dust particles and air molecules is responsible for it


In an L-C-R series circuit, at resonance
A. the current and voltage are in phase
B. the impedance is maximum
c. the current is minimum
D. the quality factor is Independent of R
E \( \cdot \) the current leads the voltage by \( \frac{\pi}{2} \)


A toroid with mean radius \( r_{0} \) and
diameter \( 2 a \) has \( N \) turns carrying current I. What is the magnetic field B inside the toroid?
A \( \cdot \frac{\mu_{0} N I}{2 \pi r_{0}} \)
В. \( \frac{\mu_{0} N I}{2 \pi\left(r_{0}+a\right)} \)
c. \( \frac{\mu_{0} N I}{\pi\left(r_{0}+a\right)} \)
D. zero


Consider the following processes
(i) Electrical oscillation
(ii) Rapid deceleration of fast electrons
(iii) Atomic transition
Which of these are likely to produce visible light?
A. (iii) only
B. (ii) and (iii)
c. (i) and (iii)
D. (i), (ii) and (iii)


Which of the following statement
regarding a catalyst in an equilibrium process is correct?
A. It increases the rate of forward reaction only
B. It hastens the easy attainment of equilibrium
C. It increases the activation energy of both the forward and backward process
D. It decreases the rate of backward process
E. It decreases the activation energy of direct process It increases the activation energy of backward process


The ratio between the \( \boldsymbol{R} \boldsymbol{M} \boldsymbol{S} \) velocity of
\( H_{2} \) at \( 50 K \) and \( R M S \) velocity of \( O_{2} \) at
\( 800 K \) will be:
A . 4:
B. 2:
c. 1:
D. 1:


If the differential equation of a body falling from rest under gravity is given by \( v \frac{d v}{d x}+\frac{n^{2}}{g} v^{2}=g, \) then the velocity of
the body is given by \( v^{2}=\frac{g^{2}}{n^{2}}(1- \)
\( \left.e^{-2 n^{2} x / g}\right) \)
A. True
B. False


The distance of the centre of mass of
the T-shaped plate from O is
\( A \cdot 7 m \)
B. 2.7 \( m \)
\( c \cdot 4 m \)
D. \( 1.7 \mathrm{m} \)


Arrange the \( p H \) values of \( 0.1 M \)
solution of \( (\boldsymbol{I}) \boldsymbol{H} \boldsymbol{C O O} \boldsymbol{N} \boldsymbol{a} \)
\( (I I) H C O O H,(I I I) C H_{3} C O O N H_{4} \)
\( (I V) N a O H,(V) H C l \) in decreasing order.
\( \mathbf{A} \cdot I V>I I I>I>I I>V \)
в. \( I V>I>I I I>I I>V \)
с. \( I I>I I I>I>I V>V \)
D. \( V>I I>I I I>I>I V \)


In uniform circular motion, the factor
that remains constant is :
A. acceleration
B. momentum
c. kinetic energy
D. linear velocity


A bag contains 3 red and 2 black balls. One ball is drawn from it at random.
Find the probability of drawing red ball.
A \( \cdot \frac{2}{5} \)
B. \( \frac{3}{5} \)
\( c \cdot \frac{4}{5} \)
D.


If the resultant of two forces \( P \) and \( Q \) be
equal in magnitude to one of the
components \( \boldsymbol{P} \) and perpendicular to it
in direction, then the value of \( Q \) is
A. \( P \)
в. \( \frac{1}{\sqrt{2}} P \)
\( c \cdot \sqrt{2} P \)
D. \( \sqrt{3} P \)


Out of \( F e O_{4}^{2-}, F e C l_{3}, F e C l_{2} \) and \( F e \)
This question has multiple correct options
A. best reducing agent is \( F e \)
B. best oxidising agent is \( F e O_{4}^{2} \)
c. best oxidising agent is \( F e C l_{3} \)
D. best reducing agent is \( F e O_{4}^{2} \)


What does the series \( 1+3^{\frac{-1}{2}}+3+ \)
\( \frac{1}{3 \sqrt{3}}+\ldots . \) represent?
\( A \cdot A P \)
в. GP
c. нр
D. None of the above series


Assertion
Prothrombin is essential for blood
clotting
Reason
Prothrombin is synthesised in the liver
in the presence of \( C a^{++} \)
A. Both statements 1 and 2 are correct
B. Statement 1 is correct but statement 2 is incorrect
c. statement 1 is incorrect but statement 2 is correct
D. Both statements 1 and 2 are incorrect


In the figure, \( A B C D \) is a rectangle,
\( \triangle C E F \) is an equilateral triangle. Find \( x \)
A \( \cdot 25^{\circ} \)
B. \( 30^{\circ} \)
\( c \cdot 20^{\circ} \)
0.50


When 1 coulomb of charge flows
through any cross-section of a
conductor in 1 second, the electric current through it is said to be 1
ampere.
A. True
B. False


along a straight line with constant
acceleration. The variation of velocity \( \boldsymbol{v} \)
with displacement \( S \) is:
\( A \)
B.
\( c \)
D.


Fermentation invariably leads to the
formation of :
A. ethyl alcohol
B. methyl alcohol
c. carbon dioxide
D. acetic acid


The marks in the science of 80 students
of class \( X \) are given below: Find the mode of the marks obtained by the students in science.
\( \begin{array}{lllll}\text { Marks: } & \begin{array}{l}0- \\ 10\end{array} & \begin{array}{l}10- \\ 20\end{array} & \begin{array}{l}\text { 20- } \\ \text { 30 }\end{array} & \begin{array}{l}\text { 30- } \\ 40\end{array}\end{array} \)
Frequency: \( \quad 3 \quad 5 \) 16 12


A wire of resistance \( X \) is cut into four
equal pieces. These four pieces are connected in parallel. The resultant resistance of this combination is \( Y \)
The ratio \( X: Y \) is
A . 20: 1
B. 16:
\( c \cdot 1: 4 \)
D. 4:


A gas behaves most like an ideal gas
under conditions of:
A. high pressure and low temperature
B. high temperature and high pressure
c. low pressure and high temperature
D. low pressure and low temperature


Final speed of the platform in situation
(ii), i.e.just after \( B \) have jumped will be
nearly
A. \( 7.5 m / s \)
B. \( 5.5 m / s \)
c. \( 4.5 m / s \)
D. \( 2.5 m / s \)


The fusion of gametes is called as
A. Embryo
B. Zygote
c. Ovum
D. Pollen grain


Let \( \boldsymbol{f}:(-1,1) \rightarrow(-1,1) \) be continuous
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{f}\left(\boldsymbol{x}^{2}\right) \) for all \( \boldsymbol{x} \in(-1,1) \) and
\( f(0)=\frac{1}{2}, \) then the value of \( 4 f\left(\frac{1}{4}\right) \) is
A . 1
B. 2
\( c \cdot 3 \)
D. 4
E . 5


\( A B \) and \( C D \) are two equal chords of a
circle with centre \( \boldsymbol{O} \) which intersect
each other at right angle at point \( P . \) If \( O M \perp A B \) and \( O N \perp C D ; \) show that
OMPN is a square


Assertion
When the unshared pairs house in the
hybrid orbitals, its consideration
becomes accountable and it is referred
to as hybrid lone pair moment.
Reason
The hybrid orbital concentrated the electron cloud in some particular directions and the electron cloud
remains under the control of a single nucleus.

Read the above assertion and reason
and choose the correct option regarding
¡t.
A. Assertion is true, Reason is true and Reason is correct explanation for Assertion
B. Assertion is true, Reason is true and Reason is not the correct explanation for Assertion
C. Assertion is true, Reason is false
D. Assertion is false, Reason is true


A mass is performing vertical circular motion(see figure).lf The average velocity of theparticle is increased, then
at which point thestring will break:
\( A \cdot A \)
B. B
\( c \cdot c \)
D.


The type of hybridisation present in
chlorine atom of \( C l O_{2}^{-} \) ion is:
\( \mathbf{A} \cdot s p \)
B . \( s p^{2} \)
\( c \cdot s p^{3} \)
D. \( d s p^{2} \)


The area bounded by \( y=\frac{3 x^{2}}{4} \) and the
line \( 3 x-2 y+12=0 \) is:
\( \mathbf{A} \cdot \mathbf{9} \)
B. 18
c. 27
D. None of these


Q Type your question
Leagur Iuuchan a vaic, yuu unotive someone who is clearly supporting
Manchester United in the game. What is the probability that they were actually born within 25 miles of Manchester?
Assume that:
\( \Longrightarrow \) the probability that a randomly selected person in a typical local bar environment is born within 25 miles of Manchester is \( \frac{1}{20}, \) and
\( \Longrightarrow \) the chance that a person born within 25 miles of Manchester
actually supports United is \( \frac{7}{10} \)
\( \Longrightarrow \) the probability that a person not born within 25 miles of
Manchester supports United with probability \( \frac{1}{10} \)
A \( \cdot \frac{7}{26} \)
в. \( \frac{8}{26} \)
c. \( \frac{9}{26} \)
D. \( \frac{10}{26} \)


Solve for \( x: \sqrt{7 x^{2}}-6 x-13 \sqrt{7}=0 \)


\( A B \) and \( C D \) are two vertical poles of
height \( 6 m \) and \( 11 m \) respectively. If the
distance between their feet is \( 12 m, \) find
the distance between their tops.
\( \mathbf{A} \cdot 13 m \)
B. \( 5 m \)
\( c .11 m \)
D. \( 12 m \)


Ortho and para hydrogen differ in
A. atomic number
B. mass number
c. electron spin in two atoms
D. nuclear spin of two atoms


A block is moving on an inclined plane
making an angle \( 45^{\circ} \) with the horizontal
and the coefficient of friction is \( \mu . \) The
force required to just push it up the inclined plane is 3 times the force required to just prevent it from sliding
down. If we define \( N=10 \mu, \) then \( N \) is
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. 5


A gas at pressure \( p \) has volume \( V \). It is adiabatically compressed to volume \( V / 32 . \) If \( (32)^{1.4}=128, \) what is the
current pressure of the gas?
A . \( 128 p \)
B. \( 63 p \)
c. \( 32 p \)
D. \( 16 p \)


Radius of first Bohr orbit is \( r . \) The
radius of 2nd Bohr orbit is
\( A \cdot 8 r \)
B. \( 2 r \)
\( c \cdot 4 r \)
D. \( 2 \sqrt{2} r \)


toppr \( E \)
Q Type your question
3
\( c \)
2


\( \operatorname{Let} \boldsymbol{R}= \)
\( \left\{\left(a, a^{3}\right): a \) is a prime number less than \right.
be a relation. Find the range of \( \boldsymbol{R} \)


The unit 'hertz' is same as.
A. second
B. Second\( ^{-1} \)
c. Metre
D. metre \( ^{-1} \)


Watson and Crick shared the Nobel
Prize for DNA structure with
A. Franklin
B. Paulingg
c. wilkins
D. Tatum


A graph is plotted with PV/T on y-axis and mass of the gas along x-axis for different gases. The graph is
A. a straight line parallel to x-axis for all the gases
B. a straight line passing through origin with a slope having a constant value for all the gases
c. a straight line passing through origin with a slope having different values for different gases
D. a straight line parallel to y-axis for all the gases


In a vertical plane \( p_{1} \) making angle \( 30^{\circ} \) with magnetic meridian, apparent
angle of dip in vertical plane \( p_{2} \) is \( 60^{\circ} \)
which is perpendicular to plane \( p_{1} \) is:
A \( .30^{\circ} \)
B . \( 45^{\circ} \)
\( \mathbf{c} \cdot \tan ^{-1}(3) \)
D. \( \tan ^{-1}\left(\frac{2}{3}\right) \)


A given charge \( q \) is situated at a certain distance from a small electric dipole in the end on position experiences a force
F. If the distance of the charge is doubled, the force acting on the charge
will become:
A \( .2 F \)
B. \( F / 2 \)
c. \( F / 4 \)
D. \( F / 8 \)


Balance the following equations in acidic medium by both oxidation number and ion electron methods and
identify the oxidants and the
reductants :
\( M n O_{4}^{-}(a q)+C_{2} H_{2} O_{4}(a q) \rightarrow \)
\( M n^{2+}(a q)+C O_{2}(g)+H_{2} O(l) \)


A spherical surface of radius of curvature \( R \) separates air (refractive
index 1.0 from glass (refractive index
1.5). The center of curvature is in the
glass.A point object \( \boldsymbol{P} \) placed in air is found to have a real image \( Q \) in the
glass. The line \( P Q \) cuts the surface at a point \( O, \) and \( P O=O Q . \) The distance
\( P Q \) is equal to
A . \( 5 R \)
в. \( 3 R \)
\( c .2 R \)
D. \( 1.5 R \)


The probability distribution function of a random variable \( \boldsymbol{X} \) is given by
\( \boldsymbol{x}_{i}: \quad 0 \quad 1 \quad 2 \)
\( c / 2 \quad c \quad 2 c \)
where \( c>0 . \) Find \( c \)


Simplify \( 3 \frac{4}{7} \times 2 \frac{2}{5} \times 1 \frac{3}{4} \)


What does the sign of magnification indicates \( \left(\boldsymbol{m}=\frac{-\boldsymbol{v}}{\boldsymbol{u}}\right) ? \)
a) Negative sign indicates image is real and inverted.
b) Positive sign indicates image is erect and virtual.
c) Positive sign indicates image is virtual.
\( A \cdot a, b \)
в. b,
\( c . \) a,
D. a, b, c


Find the value of \( y, \) if \( \left[\begin{array}{cc}x-y & 2 \\ x & 5\end{array}\right]= \)
\( \left[\begin{array}{ll}2 & 2 \\ 3 & 5\end{array}\right] \)


Which one of the following reactions is called Rosenmund reaction?
A. Aldehydes are reduced to alcohols.
B. Acids are converted to acid chlorides.
c. Alcohols are reduced to hydrocarbons.
D. Acid chlorides are reduced to aldehydes.


A box has four dice in it. Three of them
are fair dice but the fourth one has the
number five on all of its faces. A die is
chosen at random from the box and is
rolled three times and shows up the
face five on all the three occasions. The
chance that the die chosen was a rigged
die, is
\( \mathbf{A} \cdot \frac{216}{217} \)
В. \( \frac{215}{219} \)
C. \( \frac{216}{219} \)
D. none


What is the value of \( a-b \)
A \( \cdot 180^{\circ} \)
B \( .60^{\circ} \)
\( c \cdot 70^{\circ} \)
\( D \cdot 120 \)


The molecular weight of \( 2.6 \mathrm{gm} \) of a gas which occupies 2.24 litres at \( 0^{\circ} C \& 760 \)
mm pressure is :
A . \( 2.6 \mathrm{gm} \)
B. 26 gm
c. \( 22.4 \mathrm{gm} \)
D. 2.24 gm


Which one of the following mammalian cells is not capable of metabolizing glucose to carbondioxide aerobically?
A. Red blood cells
B. White blood cells
c. Unstriated muscle cells
D. Liver cells


A random survey of the number of
children of various age group playing in
a park was found as follows:

Draw a histogram to represent the data
above
\begin{tabular}{|c|c|}
\hline Age (in years) & Number of children \\
\hline \( 1-2 \) & 5 \\
\( 2-3 \) & 3 \\
\( 3-5 \) & 6 \\
\( 5-7 \) & 12 \\
\( 7-10 \) & 9 \\
\( 10-15 \) & 10 \\
\( 15-17 \) & 4 \\
\hline
\end{tabular}


The standard quantity used for comparison is called a
A. unit
B. quality
c. pick
D. coin


Match Column - I with Column-II and
select the correct option from the codes
given below.
Column - I
P. Brown algae
(i) Anabaena
Q. Blue-green algae
(ii) Gelidilum
R. Green algae
(iii) Sargassum
S. Red algae
(iv) Chlamydomonas
A. P- (ii), Q- (i), R- (iii), S- (iv)
B. P- (iii), Q- (iv), R- (ii), S- (i)
c. P- (ii), Q- (iii), R- (iv), s- - (i)
D. P-(iii), Q- (i), R- (iv), S- (ii)


\( \ln a \)
G. P. of even number of terms the
sum of all terms is 5 times the sum of
the odd term. Find the common ratio of
the G.P.
A .2
B. 3
\( c \cdot 4 \)
D. 5


Which of the following complex/ion has lowest C-O bond order?
\( \mathbf{A} \cdot\left[V(C O)_{6}\right]^{-} \)
в. \( F e(C O)_{5} \)
c. \( N i(C O)_{4} \)
D. \( \left[M n(C O)_{6}\right]^{+} \)


Consider the following reaction:
\( \mathbf{2} \boldsymbol{A}_{(\boldsymbol{g})}+\boldsymbol{B}_{(\boldsymbol{g})} \longrightarrow \boldsymbol{C}_{(\boldsymbol{g})}+\boldsymbol{D}_{(\boldsymbol{g})}+\boldsymbol{q} \)
If \( q \) is \( -v e, \) then which of the following
is correct?
A. Reaction is possible only at low temperature
B. Reaction is possible only at high temperature
c. Reaction is never possible
D. Reaction is possible at all temperatures


Two complex numbers are represented
by ordered pairs \( z_{1}:(2,4) \& z_{2}:(-4,5) \)
which of the following is
imaginary part of \( z_{1} \times z_{2}=? \)
A . -28
B. 6
\( c .-6 \)
D. None of these


Find the value of \( \operatorname{cosec}^{2} 45^{\circ}-\cot ^{2} 45^{\circ} \)


In double slit experiment, fringes are obtained using light of wavelength
\( 4800 A^{\circ} . \) One slit is covered with a thin
glass film of refractive index 1.4 and
another slit is covered by a film of same thickness but refractive index \( 1.7 . \) By
doing so, the central fringe is shifted to fifth bright fringe in the original pattern The thickness of glass film is :
A \( \cdot 2 \times 10^{-3} m m \)
B. \( 4 \times 10^{-3} \mathrm{mm} \)
c. \( 6 \times 10^{-3} m m \)
D. \( 8 \times 10^{-3} \mathrm{mm} \)


If the binding energy of the electron in a hydrogen atom is \( 13.6 e V \), the energy
required to remove the electron from the first excited state of \( L i^{2+} \) is:
A. 30.6 eV
в. 13.6 eV
c. \( 3.4 e V \)
D. \( 122.4 \mathrm{eV} \)


Calculate the mean deviation for the
following data about median.
\( \begin{array}{lcc}\text { Class } & & \\ \text { interval } & & 2 & 7\end{array} \)
\[
\mathbf{1 7}
\]
12
\( 11 \quad 12 \) Frequency 17 12
A . 5.12
в. 2.12
c. 7.21
D. 7.54


A peptide hormone is:
A. estrone
B. testosterone
c. insulin
D. corticoid


The median of the following data is 525
Find the values of \( x \) and \( y \) if the total
frequency is 100
\begin{tabular}{|c|c|}
\hline Class Interval & Frequency \\
\hline \( 0-100 \) & 2 \\
\hline \( 100-200 \) & 5 \\
\hline \( 200-300 \) & \( x \) \\
\hline \( 300-400 \) & 12 \\
\hline \( 400-500 \) & 17 \\
\hline \( 500-600 \) & 20 \\
\hline \( 600-700 \) & \( \mathrm{Y} \) \\
\hline \( 700-800 \) & 9 \\
\hline \( 800-900 \) & 7 \\
\hline \( 900-1000 \) & 4 \\
\hline
\end{tabular}


For a linear programming equations, convex set of equations is included in
region of
A . feasible solutions
B. disposed solutions
C. profit solutions
D. loss solutions


\( V=k\left(\frac{P}{T}\right)^{0.33} \) where \( k \) is constant. It is
an:
A. isothermal process
B. adiabatic process
c. isochoric process
D. isobaric process


For the Paschen series the values of \( n_{1} \)
and \( n_{2} \) in the expression \( \Delta E= \) \( \boldsymbol{R h c}\left(\frac{1}{\boldsymbol{n}_{1}^{2}}-\frac{1}{\boldsymbol{n}_{2}^{2}}\right) \) are
\( \mathbf{A} \cdot n_{1}=1, n_{2}=2,3,4, \ldots \)
B \( \cdot n_{1}=2, n_{2}=3,4,5, \ldots \)
c \( \cdot n_{1}=3, n_{2}=4,5,6, \dots \)
D. \( n_{1}=4, n_{2}=5,6,7, \ldots \)


Construct a \( \triangle A B C, \) when \( B C= \)
\( \mathbf{6 . 2} c \boldsymbol{m}, \boldsymbol{C A}=\mathbf{9 . 0} \boldsymbol{c m} \) and \( \angle \boldsymbol{B}=\mathbf{9 0}^{\circ} \)


Crystals of \( 100 \% H_{2} O_{2} \) is obtained
treating \( 90 \% \quad H_{2} O_{2} \) with:
A . solid \( C O_{2} \) and ether
B. dil. \( H_{2} S O_{4} \)
c. quick lime
D. \( N a O H+C a O \)


Assertion
Compound shown in image is named as tetrakis (ethylenediamine) \( \mu \)
\( -h y d r o x o-\mu \) -imido dicobalt(III) ion.
Reason

In naming polynuclear complexes i.e. containing two or more metal atoms joined by bridging ligands, the word \( \mu \) is
added with hyphen before the name of
such ligands.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Find the currents \( I_{1} \) and \( I_{2} \) for the
circuit shown in given figure.
A \( \cdot I_{1}=-6 A \) and \( I_{2}=9 A \)
B . \( I_{1}=6 A \) and \( I_{2}=9 A \)
\( \mathbf{c} \cdot I_{1}=-6 A \) and \( I_{2}=-9 A \)
\( \mathrm{D} \cdot I_{1}=-9 A \) and \( I_{2}=6 A \)


The area of circle centred at (1,2) and
passing through (4,6) is
A . \( 5 \pi \)
В. \( 10 \pi \)
\( c .25 \pi \)
D. None of these


toppr loGıl
Q Type your question_
11
cycle at stage \( --A_{-}- \)
(ii) Hydrogen from reduced hydrogen
acceptor is used at stage \( --B_{-} \)
(iii) Energy from ATP is used to drive
stage \( --\mathrm{C}_{-} \)
(iv) The substance formed at position \( \mathbf{Y} \) Y
is \( -n \)
(v) If one molecule of substance Y is
released per cycle, the cycle must turn
\( \mathrm{E}_{--} \) times for one molecule of
sucrose \( \left(C_{12} H_{22} O_{11}\right) \) to be built up at
position Z.
\( \mathbf{A} \cdot A-4 ; B-2 ; C-2 \) and \( 3 ; D-3 \) carbon sugar; \( E-4 \)
B . \( A-3 ; B-3 ; C-1 \) and \( 2 ; D- \) pyruvicacid; \( E-2 \)
\( \mathbf{c} \cdot A-2 ; B-4 ; C-3 \) and \( 4 ; D-g l u \operatorname{cose}-1- \)
phosphate, \( E-8 \)
D. \( A-1 ; B-1 ; C-2 \) and \( 4, D- \) citricacid \( E-12 \)


Two organ (open) pipes of lengths 50 \( \mathrm{cm} \) and \( 51 \mathrm{cm} \) produce 6 beats/s. Then the speed of sound is nearly
\( A \cdot 300 \mathrm{ms}^{-1} \)
B. 306 \( \mathrm{ms}^{-1} \)
c. \( 303 \mathrm{ms}^{-1} \)
D. 350 \( \mathrm{ms}^{-1} \)


The rectangular fence is enclosed with an area \( 16 \mathrm{cm}^{2} . \) The width of the field is
\( 6 \mathrm{cm} \) longer than the length of the fields.
What are the dimensions of the field?
A. length \( =2 \mathrm{cm}, \) width \( =6 \mathrm{cm} \)
B. length \( =1 \mathrm{cm}, \) width \( =8 \mathrm{cm} \)
c. length \( =2 \mathrm{cm}, \) width \( =8 \mathrm{cm} \)
D. length \( =3 \mathrm{cm}, \) width \( =8 \mathrm{cm} \)


The equilibrium constant for the reaction, \( \boldsymbol{A} \boldsymbol{g} \boldsymbol{C l}_{(s)} \rightleftharpoons \boldsymbol{A} \boldsymbol{g}_{(a q)}^{+}+\boldsymbol{C l}_{(a q)}^{-} \) is:
(Given that \( : \Delta G_{f A g C l}^{0}=-109.7 k J \)
\( \Delta G_{f A g^{+}}^{0}=77.1 k J ; \Delta G_{f C l^{-}}^{0}= \)
\( -131.2 k J) \)
A \( \cdot 2 \times 10^{-10} \)
B . \( 6 \times 10^{-10} \)
c. \( 8 \times 10^{-10} \)
D. \( 2 \times 10^{-8} \)


A shell of mass \( 200 g m \) is ejected from a gun of mass \( 4 k g \) by an explosion that
generates \( 1.05 k J \) of energy. The initial velocity of the shell is:
A \( \cdot 40 \mathrm{ms}^{-1} \)
B . \( 120 \mathrm{ms}^{-1} \)
c. \( 100 \mathrm{ms}^{-1} \)
D. \( 80 \mathrm{ms}^{-1} \)


Lis a circular ring made of a uniform
wire. Current enters and leaves the rind
through straight conductors which, if
produced, would have passed through
the centre \( C \) of the ring. The magnetic
field at \( C: \)
This question has multiple correct options
A. due to the straight conductors is zero
B. due to the loop is zero
C. due to the loop is proportional to \( \theta \)
D. due to the loop is proportional to \( (\pi-\theta) \)


The diagram shows three infinitely long uniform line charges placed on the \( x, Y \) and \( Y \), axis. The work done in moving a unit positive charge from (1,1,1) to \( (0,1, \)
1) is equal to
\( ^{A} \cdot \frac{(\lambda \ln 2)}{2 \pi \varepsilon_{0}} \)
B. \( \frac{(\lambda \ln 2)}{\pi \varepsilon_{0}} \)
c. \( \frac{(3 \lambda \ln 2)}{2 \pi \varepsilon_{0}} \)
D. None


The phenomenon of scattering of light by fine particles is called
A. Snell's law
B. Dispersion effect
c. Law of refraction
D. Tyndall effect


Assertion: Diamond glitters brilliantly.
Reason: Diamond does not absorb
sunlight.
A. Both assertion and reason are true but the reason is the correct explanation of assertion
B. Both assertion and reason are true but the reason is
not the correct explanation of assertion
C. Assertion is true but reason is false
D. Both the assertion and reason are false
E. Reason is true but assertion is false


Which of the following orbitals are associated with angular nodes?
This question has multiple correct options
\( A \cdot f \)
B. \( d \)
\( c \cdot p \)
D.


Which of the following will give a neutral pH solution when dissolved in
water?
A. \( N a O H \)
B. \( C s C l \)
\( \mathbf{c} \cdot H B r \)
D. \( C H_{3} \) СООН
E. \( O_{2} \)


Based on the equation, \( \boldsymbol{E}=-\mathbf{2 . 0} \times \)
\( 10^{-18} \frac{Z^{2}}{n^{2}} J, \) the wavelength of the light
that must be absorbed to excite
hydrogen electron from level \( n=1 \) to
level \( n=2 \) will be: \( (h=6.625 \times \) \( \left.\mathbf{1 0}^{-\mathbf{3 4}} \boldsymbol{J} s, \boldsymbol{C}=\mathbf{3} \times \mathbf{1 0}^{\mathbf{4}} \boldsymbol{m} \boldsymbol{s}^{-1}\right) \)
A . \( 1.2 \times 10^{-7} \mathrm{m} \)
В . \( 1.325 \times 10^{-7} \mathrm{m} \)
c. \( 5.300 \times 10^{-10} \mathrm{m} \)
D. \( 1.325 \times 10^{-10} m \)


Determine de-Broglie wavelength of an
electron having kinetic energy of \( 1.6 \times \) \( 10^{-6} \) erg.
A \( .12 .42 A^{\circ} \)
B. \( 12.42 \mathrm{cm} \)
c. \( 12.42 m \)
D. none of these


The area of response in phototropism and geotropism is
A. Apical meristem
B. Subapical meristem
c. Region of elongation
D. Area of differentiation


Binding energy of a nucleus is of the order of.
A. Electron volt (ev)
B. Kilo electron volt (KeV)
c. Mega electron volt (MeV)
D. A joule (J)


Short day plant is
A. Xanthium
B. Pisum
c. Cucumis
D. Avena


\( \boldsymbol{y}=\cos ^{-1}\left\{\frac{2 \boldsymbol{x}-\boldsymbol{3} \sqrt{1-\boldsymbol{x}^{2}}}{\sqrt{\mathbf{1 3}}}\right\}, \) find \( \frac{\boldsymbol{d} \boldsymbol{2}}{\boldsymbol{d}} \)


The force between two electrons when
placedair is equal to 0.5 times the weight of an electrons find the distance between two electrons (masselectron
\( \left.=\mathbf{9 . 1} \times \mathbf{1 0}^{-\mathbf{3 1}} \mathbf{k g}\right) \)
A . 7.2 m
B. 72cm
c. 72 m
D. 720m


Match the following:
List - I List - II
A. Vitamin B \( _{1} \)
1. Riboflavin
B. Vitamin B
2. Pantothenic
acid
C. Vitamin B \( _{3} \)
3. Niacin
D. Vitamin B \( _{5} \)
4. Thiamine
B. A - 4, B -1, C - 2, D - 3
c. \( A-3, B-4, C-2, D-1 \)
D. A - \( 4, \) B- \( 3, \) C-1, D-2


The pH value of a solution in which a
polar amino acid does not migrate under the influence of electric field is
called:
A. isoelectronic point
B. isoelectric point
c. neutralization point
D. all of the above


The average lung capacity is
A. 7 litres
B. 6 litres
c. 9 litres
D. 5 litres


Is friction necessary to walk on the moon?
A. Yes
B. No
c. мау be
D. Ambiguous


The substance \( A \), when dissolved in
solvent \( \mathrm{B} \), shows the molecular mass
corresponding to \( A_{3} . \) The van"t Hoffs factor will be:
A.
B. 2
\( c \cdot 3 \)
\( D \cdot 1 / 3 \)


\( x \) is \( 40 \% \) of \( y .50 \% \) of \( y \) is 40 Then 16 is what percent of \( x ? \)
A . 40
B. 60
c. 50
D. 45


Four identical thin rods each of mass \( \mathrm{M} \)
and length I, form a square frame. Moment of inertia of this frame about
an axis through the centre of the square and perpendicular to its plane is?
A \( \cdot \frac{1}{3} M l^{2} \)
в. \( \frac{8}{3} M l^{2} \)
c. \( \frac{2}{3} M l^{2} \)
D. \( \frac{13}{3} M l^{2} \)


A road roller takes 750 complete revolutions to move once over to level a
road. Find the area of road if the
diameter of a road roller is \( 84 \mathrm{cm} \) and
length is \( 1 \mathrm{m} \)


The mode of transfer of heat which
requires no medium, is called as:
A. Radiation
B. Conduction
c. combusion
D. convection


\( 2 H I(g) \leftrightharpoons H_{2}(g)+I_{2}(g) \)
What is the equilibrium constant expression for the above reaction?
\( \mathbf{A} \cdot\left[H_{2}\right]^{2}\left[I_{2}\right] \)
B . \( \left[\mathrm{H}_{2}\right] \)
c. \( \frac{\left[H_{2}\right]\left[I_{2}\right]}{[H I]^{2}} \)
D・ \( \left[H_{2}\right]\left[I_{2}\right]^{2} \)
E \( \cdot\left[H_{2}\right]^{2}\left[I_{2}\right]^{2} \)


Assertion The value of \( \left(\begin{array}{c}51 \\ 3\end{array}\right)+\left(\begin{array}{c}50 \\ 3\end{array}\right)+\left(\begin{array}{c}49 \\ 3\end{array}\right)+ \)
\( \left(\begin{array}{c}48 \\ 3\end{array}\right)+\left(\begin{array}{c}47 \\ 3\end{array}\right)+\left(\begin{array}{c}47 \\ 4\end{array}\right) \) is equal to
\( \left(\begin{array}{c}52 \\ 4\end{array}\right) \)
Reason
\( ^{n-1} C_{r}+^{n} C_{r+1}=^{n+1} C_{r+1} \)
A. Both (A) \& (R) are individually true \&
(R) is the correct explanation of (A),
B. Both (A) \& (R) are individually true but (R) is not the correct (proper) explanation of (A).
C. (A) is true but (R) is false,
D. (A) is false but (R) is true.


Find the distance between the lines \( 3 x+ \)
\( y-12=0 \) and \( 3 x+y-4=0 \)
A \( \cdot \frac{16}{\sqrt{10}} \)
в. \( \frac{12}{\sqrt{10}} \)
c. \( \frac{4}{\sqrt{10}} \)
D. \( \frac{8}{\sqrt{10}} \)
E. Answer Required


A ball collides with a smooth and fixed
inclined plane of inclination \( \boldsymbol{\theta} \) after falling vertically through a distance h. If it moves horizontally just after impact, the coefficient of restitution is
\( \mathbf{A} \cdot \tan ^{2} \theta \)
B \( \cdot \cot ^{2} \theta \)
\( c . \tan \theta \)
D. \( \cot \theta \)


The value of \( \int_{0}^{\frac{\pi}{2}} \frac{2^{\sin x}}{2^{\sin x}+2^{\cos x}} d x \) is
A.
B.
\( c \cdot 0 \)
D. none of these


A rider on horse falls back when horse
starts running, all of a sudden because:
A. rider is taken back
B. rider is suddenly afraid of falling
c. inertia of rest keeps the upper part of body at rest while lower part of the body moves forward with the horse
D. none of the above


\( \ln \) an A.C circuit, the resistance \( \boldsymbol{R}= \)
\( 0.2 \Omega . \) At a certain instant, \( V_{A}-V_{B}= \)
\( 0.5 V, I=0.5 A, \) and the current is
increasing at the rate of \( \frac{\Delta I}{\Delta t}=8 A / s \) The inductance of the coil is:
A . \( 0.05 H \)
в. \( 0.1 \mathrm{H} \)
\( c .0 .2 H \)
D. none of these


Llama and Alpaca are found in
A. India
B. South America
c. Pakistan
D. None of these


In CGS system water equivalent is
expressed in thermal
capacity is expressed in


The power of a biconcave lens having a focal length of \( 25 \mathrm{cm} \) is:
A. - 40
B. -8D
c. \( -0.25 D \)
D. None of the above


The displacement of a particle moving
along \( \boldsymbol{x} \) axis is given by \( \boldsymbol{X}=\left(\mathbf{4} \boldsymbol{t}^{2}+\right. \)
\( 3 t+7) \mu . \) Calculate instantaneous
velocity and instantaneous acceleration at \( t=2 S \)


If true enter 1 , else enter 0 .
\( H B r \) is stronger acid than \( H I \) due to
\( \boldsymbol{H} \) -bonding.


In the given figure you find two
triangles. Indicate whether the triangles
are similar. Give reasons in support of
your answer.


Which of the following gas absorb to a maximum amount by an activated charcoal?
A. \( N_{2} \)
в. \( O_{2} \)
\( c \cdot C l_{3} \)
D. \( C O_{2} \)


How much momentum will a dumb-bel
of mass \( 10 \mathrm{kg} \) transfer to the floor if it
falls from a height of \( 80 \mathrm{cm} \) ? Take its
downward acceleration to be \( 10 \mathrm{ms}^{-2} \)


\( -7 p-4(-3 p+2)= \)
A. \( -19 p+8 \)
B. \( 5 p+8 \)
\( \mathbf{c} \cdot-19 p-8 \)
D. \( 5 p-8 \)


The formation of acetyl coenzyme-A from pyruvic acid is the result of
A. Reduction
B. Dehydration
c. Dephosphorylation
D. Oxidative decarboxylation


If a gas is expanded at constant
temperature:
A. the pressure increases
B. the kinetic energy of the molecules remains the same
C. the kinetic energy of the molecules decreases
D. the number of molecules of the gas increases


An urn A contains 4 white and 6 redd
balls. Three balls are drawn at random the expected number of white balls drawn is
A . 3.0
B. 1.8
c. 1.2
D. 1.


If 3 numbers are selected from the first
15 natural numbers, then the probability that the numbers are in A.P is
A \( \cdot \frac{7}{65} \)
в. \( \frac{9}{65} \)
\( c \cdot \frac{8}{65} \)
D. \( \frac{6}{65} \)


To get an output \( y=1 \) from the circuit
shown, the inputs \( A, B \) and \( C \) must be respectively
A. 0,1,0
B. 1,0,0
c. 1,0,1
D. 1,1


Prove that:
\[
\begin{array}{c}
\frac{\tan \theta-\cot \theta}{\sin \theta \cos \theta}=\sec ^{2} \theta-\operatorname{cosec}^{2} \theta= \\
\tan ^{2} \theta-\cot ^{2} \theta
\end{array}
\]


Which enzyme plays important role in
transcription?
A. DNA dependent RNA polymerase
B. DNA dependent DNA polymerase
C. RNA dependent DNA polymerase
D. RNA dependent RNA polyrnerase


Select the correct statement(s):
This question has multiple correct options
A. Sodium can be prepared by the electrolysing aqueous solution of \( \mathrm{NaCl} \)
B. Sodium can be prepared by the electrolysing fused NaCl
C. Sodium is a strong oxidising agent
D. Sodium is soluble in liquid ammonia


On shaking \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) with acidified
potassium dichromate and ether, etheral layer becomes:
A. green
B. red
c. blue
D. brown


When \( N_{2} \) combines \( O_{2} \) at \( 3300 K \) the
obtained product is:
A . \( N O \)
в. \( N_{2} \),
\( c \cdot N O_{2} \)
D. \( N_{2} O_{5} \)


Angle strain in cyclopropane is :
\( \mathbf{A} \cdot 24^{\circ} 44^{\prime} \)
в. \( 9^{\circ} 44^{\prime} \)
\( c \cdot 44^{\prime} \)
D. \( -5^{\circ} 16^{\prime} \)


Three sides \( A B, B C \) and \( C A \) of a
triangle \( A B C \) are \( 5 x-3 y+2=0, x- \)
\( 3 y-2=0 \) and \( x+y-6=0 \)
respectively. Find the equation of the
altitude through the vertex \( \boldsymbol{A} \)


Molality of a solution in aqueous medium is \( 0.8 . \) Calculate its mole
fraction and the percentage by mass of solute if molar mass of solute is 60 .
A. \( 0.014,4.8 \% \)
В. \( 0.014,5 \% \)
c. \( 0.1,4.8 \% \)
D. \( 0.4,8 \% \)


One mapping is selected at random from all the mappings of the set \( A= \) \( \mathbf{1}, \mathbf{2}, \mathbf{3}, \dots, \boldsymbol{n} \) into itself. The probability
that the mapping selected is one to one, is given by
A \( \cdot \frac{1}{n^{n}} \)
в. \( \frac{1}{n !} \)
c. \( \frac{(n-1) !}{n^{n-1}} \)
D. None of these


A Zener diode
A. has a high forward voltage rating
B. has a sharp breakdown at low reverse voltage
C. has a negative resistance
D. none of the above


A small generator is called a
A. AC generator
B. DC generator
c. Dynamo
D. All


What do you expect the nature of hydrides is, if formed by elements of atomic numbers 15,19,23 and 44 with dihydrogen? Compare their behaviour towards water


Among the following, the number of elements that do not show malleability
is:

Zinc, Iron, Sulphur, Copper, Aluminium, Nickel, Chlorine, lodine


Crown of teeth is covered by
A. Dentine
B. Enamel
C. Both A and B
D. None of the above


The chemical messengers produced in ductless glands are:
A . vitamins
B. lipids
c. antibiotics
D. hormones


Thalloid body of a slime mould (myxomycetes) is known as
A. Mycelium
B. Protonema
c. Plasmodium
D. Fruiting body


A swimmer is capable of swimming
\( 1.65 m s^{-1} \) in still water. If she swims
directly across a \( 180 \mathrm{m} \) wide river whose current is \( 0.85 \mathrm{m} / \mathrm{s} \), how far downstream(from a point opposite her standing point) will she reach?
\( \mathbf{A} .92 .7 \mathrm{m} \)
в. \( 40 \mathrm{m} \)
c. 48 m
D. 20


In which of the following compounds the oxidation state of nitrogen is most
negative?
A \( . N_{2} \)
в. \( N_{2} \) О
c. \( N H_{3} \)
D. \( N O_{2} \)
E. \( N O_{3} \)


The factor responsible for depletion of ozone layer is
A. Excessive use of automobiles
B. Excessive industrial units
C. Excessive use of man made compounds containing chlorine and fluorine
D. Excessive deforestation


\( \left|\begin{array}{ccc}\boldsymbol{x} & \boldsymbol{y} & \boldsymbol{z} \\ \boldsymbol{x}^{2} & \boldsymbol{y}^{2} & \boldsymbol{z}^{2} \\ \boldsymbol{x}^{\boldsymbol{3}} & \boldsymbol{y}^{\boldsymbol{3}} & \boldsymbol{z}^{\boldsymbol{3}}\end{array}\right|=\boldsymbol{x} \boldsymbol{y} \boldsymbol{z}(\boldsymbol{x}-\boldsymbol{y})(\boldsymbol{y}-\boldsymbol{z})(\boldsymbol{z} \)
\( \boldsymbol{x}) \)
A. True
B. Falss


A neutral particle is at rest in a uniform magnetic field \( \vec{B} \). At time \( t=0 \) it decays into two charged particles,each of mass
m.The two particles move off in seperate paths,both of them lie in the plane perpendicular to \( \vec{B} \). At a later time the
particles collide.Express the time from decay until collison in terms of \( \mathrm{m}, \mathrm{B} \) and
\( \mathbf{q} \)


\( \ln \) an \( A . P 17^{t h} \) term is 7 more then is
\( 10^{t h} \) term. Find the common difference?


\( \mathbf{f} \boldsymbol{A}=\left[\begin{array}{lll}\mathbf{1} & \mathbf{2} & \mathbf{3} \\ \mathbf{0} & \mathbf{5} & \mathbf{7} \\ \mathbf{6} & \mathbf{8} & \mathbf{9}\end{array}\right] \) and \( \boldsymbol{B}=\left[\begin{array}{lll}\mathbf{2} & \mathbf{0} & \mathbf{3} \\ \mathbf{3} & \mathbf{0} & \mathbf{5} \\ \mathbf{5} & \mathbf{7} & \mathbf{0}\end{array}\right] \)
then find the value of \( 3 A-2 B \)


\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}\left(\tan ^{-1} \boldsymbol{x}\right) \)
A \( \cdot \frac{1}{1+x^{2}} \)
B \( \cdot \frac{-1}{1+x^{2}} \)
c. \( \frac{-1}{1-x^{2}} \)
D. \( \frac{1}{1-x^{2}} \)


An air bubble of radius \( 5 \times 10^{-4} \mathrm{m} \) rises
in a liquid of viscosity 0.1 Pas \( (g= \)
\( 10 m s^{-2} \) ) and density \( 900 \mathrm{kgm}^{-3} \). The
terminal velocity of the bubble is:
A \( \cdot 0.005 \mathrm{ms}^{-1} \)
B. \( 0.01 \mathrm{ms}^{-1} \)
c. \( 0.5 \mathrm{ms}^{-1} \)
D. \( 0.4 \mathrm{ms}^{-1} \)


Mendius reaction involves the:
A. Reduction of aldehydes to give alcohols
B. Reduction of nitriles with sodium and ethanol
C. Oxidation of nitriles
D. Hydrolysis of cyanides


Write converse of statement. In \( \Delta A B C \)
if \( A B=A C \) then \( C=B \)


The plot of velocity vs time of a moving
particle is given above. How do the acceleration and
displacement of the particle at point \( \boldsymbol{B} \) compare to the acceleration and
displacement of the particle at point \( A ? \)
A. Acceleration is less, displacement is less
B. Acceleration is less, displacement is the same
C. Acceleration is less, displacement is greater
D. Acceleration is greater, displacement is less
E. Acceleration is greater, displacement is greater


Cotton cloth requires to
decompose.
A. more than 15 years
B. 10-15 years
c. 100 years
D. 2-5 months


If the voltmeter reads \( 0.21 \mathrm{V} \) and the
ammeter reads \( 0.1 A \), the resistance of
the ammeter is (in ohm)
A. 0.0
в. 0.15
\( c \cdot 0 . \)
D. o.


Draw and label the mechanism of reflex
arc.


What are may happen if a building does
not have earthing?
A. Lightning may strike a building due to opposite charge causing fir or damage to the building
B. In the rainy season water increases the chances of lightning striking a building causing damage
C. Both A \& B
D. None of the above


The equivalent quantity of mass in electricity is :
A. current
B. self inductance
c. potential
D. charge


What property of hydrogen chloride is demonstrated when it is collected by downward delivery. upward displacement].
A. Hydrogen chloride is highly reactive in nature and it has great affinity for water
B. Hydrogen chloride is less reactive in nature and it has great affinity for water
c. Hydrogen chloride is highly reactive in nature and it has low affinity for water
D. Hydrogen chloride is less reactive in nature and it has low affinity for water


If \( D=\left|\begin{array}{ccc}a^{2}+1 & a b & a c \\ b a & b^{2}+1 & b c \\ c a & c b & c^{2}+1\end{array}\right| \) then
\( D= \)


Factorize \( 27 m^{3}-216 n^{3} \)


State True or False.
All metals are solids.
A . True
B. False


If \( \left[\begin{array}{ccc}3 & 2 & -1 \\ 4 & 9 & 2 \\ 5 & 0 & -2\end{array}\right]\left[\begin{array}{l}x \\ y \\ z\end{array}\right]=\left[\begin{array}{l}0 \\ 7 \\ 2\end{array}\right], \) then
\( (x, y, z)= \)
В. (2,-1,-4)
c. (3,0,6)
\( \mathbf{D} \cdot(2,-1,4) \)


Name the rays or waves of highest frequency.
A. X-rays
B. UV rays
c. IR rays
D. Gamma rays


State one relevant observation for the
following. Anhydrous calcium chloride is exposed to air for some time.


The value of \( \sqrt{-36} \) is
\( A \cdot 6 \)
в. -6
\( c \cdot 6 i \)
D. None of these


Which of the following best describe the spacing of the field lines?
A. Indicates the strength of the magnetic field
B. Is greatest near the poles
c. Is smallest far away from the poles
D. Indicates the direction of the magnetic field
E. Is the same everywhere around the magnet


Chromatography is a useful method for purification of elements which are:
A. very reactive
B. available in minute quantities
c. present in abundance
D. highly electropositive


State the following statement is True or
False

Range can be calculated as the addition of largest value and smallest value
A. True
B. False