Let \( \boldsymbol{f}(\boldsymbol{x}+\boldsymbol{y})=\boldsymbol{f}(\boldsymbol{x}) \boldsymbol{f}(\boldsymbol{y}) \) for all \( \boldsymbol{x}, \boldsymbol{y} \boldsymbol{\epsilon} \boldsymbol{R} \)
and suppose that \( f \) is differentiable at
0 and \( f^{\prime}(0)=4 . \) If \( f\left(x_{0}\right)=8 \) then
\( f^{\prime}\left(x_{0}\right) \) is equal to


An electric dipole of moment 'p' is placed in an electric field of intensity 'E'. The dipole acquires a position such that the axis of the dipole makes an angle 0 with the direction of the field. Assuming that the potential energy of the dipole to be zero when \( \theta=90^{0} \), the torque and
the potential energy of the dipole will respectively be:
A. \( p E \sin \theta, 2 p E \cos \theta \)
B. \( p E \cos \theta,-p E \sin \theta \)
c. \( p E \sin \theta,-p E \cos \theta \)
D. \( p E \sin \theta,-2 p E \cos \theta \)


Evaluate the following definite integral:
\( \int_{0}^{4} 4 x-x^{2} d x \)


The action and reaction forces referred
to in Newton's third law of motion
A. must act on same body
B. must act on different bodies
c. need not be equal in magnitude but must have the same line of action
D. must be equal in magnitude but need not have the same line of action


Galvanisation is a method of protecting iron from rusting, by coating with a thin layer of:
A . galliummmmmmmmmmmaliuunmmmmmm
B. aluminium
c. zinc
D. silver


Fall in blood pressure, due to loss of
blood is soon restored because
A. Blood vessels dilate
B. Blood cells decrease in number
c. Heart beat is increased
D. Heart beat is decreased


If \( f \) and \( g \) are two functions such that
\( (f g)(x)=(g f)(x) \) for all \( x . \) Then \( f \) and
\( g \) may be defined as
A \( \cdot f(x)=\sqrt{x}, g(x)=\cos x \)
B . \( f(x)=x^{3}, g(x)=x+1 \)
\( \mathbf{c} \cdot f(x)=x-1, g(x)=x^{2}+1 \)
D. \( f(x)=x^{m}, g(x)=x^{n} \) where \( m, n \) are unequal integers


If \( \boldsymbol{A}=\left(\begin{array}{cc}\mathbf{7} & \mathbf{2} \\ \mathbf{1} & \mathbf{3}\end{array}\right) \) and \( \boldsymbol{A}+\boldsymbol{B}= \)
\( \left(\begin{array}{cc}\mathbf{- 1} & \mathbf{0} \\ \mathbf{2} & \mathbf{- 4}\end{array}\right) \) then matrix \( \boldsymbol{B}=\mathbf{?} \)
\( \mathbf{A} \cdot\left(\begin{array}{cc}1 & 0 \\ 1 & 1\end{array}\right) \)
B. \( \left(\begin{array}{cc}6 & 2 \\ 3 & -1\end{array}\right) \)
c. \( \left(\begin{array}{cc}-8 & -2 \\ 1 & -7\end{array}\right) \)
D. \( \left(\begin{array}{cc}8 & 2 \\ -1 & 7\end{array}\right) \)


Choose the correct answer from the
alternatives given
For measuring very high temperature,
we use
A. Mercury thermometer
B. Thermoelectric pyrometer
c. Platinum resistance thermometer
D. None of the above


A projectile of mass \( m \) is fired with
velocity \( v \) from a point as shown in
figure, neglecting air resistance, what
is the change in momentum when
leaving \( P \) and arriving at \( Q ? \)
\( A \cdot 0 \)
\( \mathbf{B} \cdot m v \)
\( \mathbf{c} \cdot 4 m v \)
D. \( \frac{2 m v}{\sqrt{3}} \)


Van't Hoff's factor for \( 0.01 M \) aqueous
solution of acetic acid is \( 1.04, \) then \( p H: \)
A . 3.4
B. 6.4
\( c .9 .6 \)
D. 10.6


Assertion
Motion of a ball bouncing elastically in
vertical direction on a smooth
horizontal floor is a periodic motion, but
not an SHM.
Reason
Motion is SHM when restoring force is proportional to displacement from
mean position.
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


\( = \)
\( \frac{1}{4} \)
\( = \)


Find the second order derivatives of
\( e^{x} \sin 5 x \)


The domain of \( \boldsymbol{f}(\boldsymbol{x})=\sqrt{\mathbf{2 5}-\boldsymbol{x}^{2}} \) is
\( \mathbf{A} \cdot(-\infty,-5) \)
B. \( (5, \infty) \)
c . [-5,5]
D. \( [-\infty, \infty] \)


Alnico is an alloy of
\( A \cdot \) Ai, \( \mathrm{Ni}, \mathrm{Cu}, \mathrm{P} \)
B. Al, Ni, Cu, Co
c. Al, Ni, As, O
D. Al, As, P, Pt


The frequency of a sound wave is 200 \( \mathrm{Hz} \) and its wavelength is \( 150 \mathrm{cm} . \) What is the distance travelled by a sound wave in the time of produce 150 waves?
A . \( 110.5 \mathrm{m} \)
B. 112.5 \( m \)
c. \( 115 \mathrm{m} \)
D. 120 \( m \)


that of copper. A \( 50 \mathrm{cm} \) length of copper
wire of diameter 2.0 mm is joined to a
\( 50 \mathrm{cm} \) length of steel wire of diameter
1.0 \( m m, \) making a combination wire of
length \( 1.0 \mathrm{m}, \) as shown. The
combination wire is stretched by a
weight added to its end. Both the copper
and the steel wires obey Hooke's
law. What is the ratio
\( A \cdot 4 \)
B. 2
\( c \cdot 1 \)
D. 0.5


A 6 -kg weight is fastened to the end of a steel wire of un-stretched length \( 60 \mathrm{cm} \)
It is whirled in a vertical circle and has
an angular velocity of 2 revolution per second at the bottom of the circle. The
area of cross-section of the wire is
\( 0.05 c m^{2} . \) Calculate the elongation of the
wire when the weight is at the lowest point of the path. Young's modulus of steel \( =2 \times 10^{11} \mathrm{Pa} \)


An electrophilic reagent must have?
A. A vacant orbital
B. An orbital containing one electron
C. An orbital containing two electron
D. All completely filled atomic orbitals


Which of the following is a soap?
A \( \cdot C_{17} H_{35} C_{6} H_{4} S O_{3} N a \)
в. \( C H_{3} \) СОО Na
c. \( C_{17} H_{35} \) COONa
D. \( C_{3} H_{8} O_{3} \)


At the bottom of a lake where the
temperature is \( \$ \$\{7\} \wedge\{0\} \backslash, \mathrm{C} \$ \$ \) the pressure is 2.8 atmosphere. An air bubble of radius \( 1 \mathrm{cm} \) at the bottom rises to
the surface. Where the temperature is \( \$ \$\{27\} \wedge\{0\} \backslash, \) C\$ \( \$ . \) The radius of the air
bubble at the surface is
A \( \cdot 3^{1 / 3} \)
B. \( 4^{1 / 3} \)
\( \mathbf{c} \cdot 5^{1 / 3} \)
D. \( 6^{1 / 3} \)


The spin-only magnetic moment of sodium nitroprusside ion is :
A . 3.9 BM
B. 5.9 Вм
c. О ВМ
D. 1.8 BM


The first law of refraction states that
the incident and refracted rays are in
the same
A . phase
B. plane
\( c \cdot \) both
D. none


Filament attached along the whole
length of anther is the condition called
A. Adnate
B. Dorsifixed
c. Basifixed
D. Versatile


The atomic weights of Be were
corrected by Mendeleev using the
formula:
\( \mathbf{A} \cdot \sqrt{v}=a(z-b) \)
B. \( m v r=\frac{n h}{2 \pi} \)
C. atomic weight = equivalent weight \( \times \) valency
D. equivalent weight = atomic weight \( \times \) valency


Assertion
White phosphorus can be cut with a
knife.
Reason
White phosphorus is soft.
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 incorrect but Reason is incorrect
D. Assertion is correct but Reason is incorrect


In the given figure, \( A B E D \) is a
parallelogram in which \( A B=D E= \)
\( 10 c m \) and the area of \( \triangle B E C \) is \( 72 c m^{2} \)
If \( C E=16 \mathrm{cm}, \) find the area of the
trapezium \( \boldsymbol{A B C D} \)


An easily disturbed ecosystem which
can recover after sometime after the
stoppage of damaging factor, is of
A. Low stability and high resilience
B. High stability and high resilience
c. Low stability and low resilience
D. High stability and low resilience


What happens during sublimation?
A. Kinetic energy decreases
B. Kinetic energy increases
c. No movement of particles
D. None of above


In a sample of H-atom, electrons make transition from 5th excited state to
ground state, producing all possible types of photons. Then, number of lines in infrared region are:
\( A \cdot 4 \)
B. 5
\( c \cdot 6 \)
D. 3


The cryoscopic constant for acetic acid is \( 3.6 K k g / \) mol. A solution of \( 1 g \) of a hydrocarbon in \( 100 g \) of acetic acid
freezes at \( 16.14^{\circ} \mathrm{C} \) instead of the usual
\( 16.60^{\circ} \mathrm{C} . \) The hydrocarbon contains \( 92.3 \% \) carbon. If the molecular formula
is \( C_{6} H_{6} . \) Find the value of \( x \) and \( y \)
A. \( x=2, y=4 \)
В. \( x=3, y=5 \)
c. \( x=4, y=4 \)
D. \( x=6, y=6 \)


Short Answer
How do Bacteria help plants use nitrogen?


Which of them is a property of lanthanides?

This question has multiple correct options
A. High ionization energies
B. Low ionization energies
c. colour
D. None of the above


n Fig., \( A B C \) and \( A M P \) are two right
triangles, right angled at \( B \) and \( M \)
respectively. Prove that:
\( \triangle A B C \sim \triangle A M P \)


Integrate: \( \left(\frac{a}{\sqrt{x}}+2 b \sqrt[3]{x^{2}}\right) \) w.r.t


Assertion
Heart can be assumed as electric
dipole.
Reason
Its ELOF are just same like a normal
dipole.
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


Centre of gravity of the circular ring will
be:
A. At the periphery
B. At the center
c. outside it
D. None


Reduce the equation \( 2 x+3 y=0 \) to
slope-intercept form and find its slope
and \( \boldsymbol{y}- \) intercept.


The life of the erythrocytes in mammalian blood is about
A. 120 days
B. 150 days
c. 190 days
D. 180 days


The site of action of insulin is:
A. mitochondria
B. nucleus
c. plasma membrane
D. DNA


Let, \( \vec{a} \) and \( \vec{c} \) are unit vectors and \( |\vec{b}|=4 . \) The angle between \( \vec{a} \) and \( \vec{c} \) is \( \cos ^{-1}\left(\frac{1}{4}\right) \cdot \operatorname{lf} \vec{b}-2 \vec{c}=\lambda \vec{a}, \) then \( \lambda \) is
equal to
A .3,4
в. -3,4
\( c \cdot 3,-4 \)
D. \( \frac{1}{4}, \frac{3}{4} \)


The colour of the solution/precipitate obtained in the elemental analysis of an organic compound and the molecule/ion responsible for the colour are given below. Choose the incorrectly matched pair.
A. Prussian blue - \( F e_{4}\left[F e(C N)_{6}\right]_{3} \) ] \( \cdot x H_{2} O \)
B. Black - PbS
C. Violet colour - \( \left[\mathrm{Fe}(\mathrm{CN})_{5} \mathrm{NOS}\right]^{4-} \)
D. Blood red colour - \( \left[\mathrm{Fe}(S C N)^{2}\right. \)
E. Yellow - \( \left(N H_{4}\right)_{2} M o O_{4} \)


\( \left[\begin{array}{lll}1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9\end{array}\right] \)
The new matrix obtained after adding
\( 2^{n d} \) row to 3 times \( 3^{r d} \) row is
A \( \cdot\left[\begin{array}{lll}1 & 2 & 3 \\ 4 & 5 & 6 \\ 25 & 29 & 33\end{array}\right] \)
В \( \cdot\left[\begin{array}{ccc}1 & 2 & 3 \\ 25 & -29 & -33 \\ 4 & 5 & 6\end{array}\right] \)
\( \mathbf{c} \cdot\left[\begin{array}{lll}1 & 2 & 3 \\ 7 & 8 & 9 \\ 4 & 5 & 6\end{array}\right] \)
D. \( \left[\begin{array}{ccc}1 & 2 & 3 \\ -25 & -29 & -33 \\ 4 & 5 & 6\end{array}\right] \)


A light ray emerging from the point source placed at \( \boldsymbol{P}(2,3) \) is reflected at
a point \( Q \) on the \( y \) -axis. It then passes through the point \( R(5,10) \). The
coordinates of \( Q \) are
A \( .(0,3) \)
B. (0,2)
c. (0,5)
(年. \( 0,5,5) \)
D. None of these


A piece of iron of mass 0.05 kg is
heated to a temperature of \( 200^{\circ} \mathrm{C} \) and
dropped into a beaker containing \( 0.4 \mathrm{kg} \)
of water at \( 20^{\circ} \mathrm{C} \). If the final
temperature of water and iron is \( 22.4^{\circ} \mathrm{C} \)
find the specific heat capacity of iron.
A . \( 354.04 J k g^{-1} K^{-1} \)
B. \( 454.04 J k g^{-1} K^{-1} \)
c. \( 554.04 J k g^{-1} K^{-1} \)
D. \( 654.04 J k g^{-1} K^{-1} \)


Assertion
Insulators do not allow flow of current
through them.
Reason
Insulators have no free charge carriers.
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


Solve \( 2 \cos ^{2} \theta-\sqrt{3} \sin \theta+1=0 \)


Assertion
Zeolites are good shape-selective
catalysts.
Reason
Zeolites have honeycomb like
structures.
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 angle between the line joining the centre and point of contact of a tangent and the tangent itself?
\( \mathbf{A} \cdot \mathbf{0} \)
B . 45
\( c .90 \)
D. \( 180^{\circ} \)


Grain alcohol, a product of yeast fermentaion of sugars in grains and fruits, is:
A. Ethanol
B. 1-Butanol
c. 2-Methyl-1-propanol
D. Methanol


\( \mathbf{A} \)
12 ohm resistor and a 0.21 henry
inductor are connected in series to an
AC source operating at \( 20 v \) olts, 50 cycle/second. The phase angle between the current and the source voltage is
A \( .30^{\circ} \)
В . \( 40^{\circ} \)
\( c \cdot 80^{\circ} \)
D. \( 90^{\circ} \)


Which postulate of Dalton's atomic theory is a result of the law of conservation of mass?


The freezing point of benzene decrease
by \( 0.45^{\circ} \mathrm{C} \) when \( 0.2 g \) of acetic acid is added to \( 20 g \) of benzene. If acetic acid associates to form a dimer in benzene, percentage association of acetic acid in
benzene will be: \( \left(K_{f} \text { for benzene }=\right. \)
\( \left.\mathbf{5 . 1 2} \boldsymbol{K} \boldsymbol{k g} \boldsymbol{m o l}^{-1}\right) \)
A. \( 64.6 \% \)
B. \( 80.4 \% \)
c. \( 74.6 \% \)
D. \( 94.6 \% \)


Animals with cleidoic eggs show
A. External fertilization, internal development
B. Internal fertilization, internal development
C. External fertilization, external development
D. Internal fertilization, external development


Identify the given diagrams and mark
the correct option.
\( A \cdot A, D \) are compound while \( B, C \) are simple leaves
B. \( A, D \) are simple while \( B, C \) are compound leaves
\( \mathrm{C} \cdot \mathrm{A}, \mathrm{B} \) are simple while \( \mathrm{C}, \mathrm{D} \) are compound leaves
D. \( A, B \) are compound while \( C, D \) are simple leaves


The maximum acceleration of a particle
in SHM is made two times keeping the
maximum speed to be constant. It is possible when
A. amplitude of oscillation is doubled while frequency remains constant
B. amplitude is doubled while frequency is halved
c. frequency is doubled while amplitude is halved
D. frequency is doubled while amplitude remains constant


Tranquilizers are also known as:
A. psychosomatic drugs
B. antipsychotic drugs
c. psychosystolic drugs
D. none of the above


Find the emf induced as a function of
time it is zero at \( t=0 \) and is increasing
in positive direction


\( P \) and \( Q \) are fixed points at the end of \( a \)
string. A transverse stationary wave of constant maximum amplitude is formed on the string.
\( P, R \) and \( Q \) are the only points on the
string where nodes are formed. S and T are two points on the string at a distance x from R.
What is the relationship between points s and T?
A. The same amplitude and in phase
B. Different amplitudes and in phase
C. The same amplitude and a phase difference of 180
D. Different amplitudes and a phase difference of 180


A plot of kinetic energy of the emitted electron against frequency of the incident radiation yields a straight line. The slope of the straight line is:
A. \( 0.66 \times 10^{-35} \)
В. \( 0.66 \times 10^{-33} \)
c. \( 0.33 \times 10^{-33} \)
D. \( 3.33 \times 10^{-35} \)


A millivoltmeter is connected in parallel to an axle of the train running with a speed of \( 180 \mathrm{km} / \) hour. If the vertical component of earth's magnetic field is \( 0.2 \times 10^{-4} W b / m^{2} \) and the distance
between the rails is \( 1 \mathrm{m} \), then the
reading of voltmeter will be :
A \( \cdot 10^{-2} \) volt
B. \( 10^{-4} \) volt
c. \( 10^{-3} \) volt
D. 1 volt


Assertion
If \( a^{2}+b^{2}=c^{2}, c \neq, a b \neq 0 \) then the non
zero solution of the equation \( \sin ^{-1} \frac{\boldsymbol{a} \boldsymbol{x}}{\boldsymbol{c}}+\sin ^{-1} \frac{\boldsymbol{b} \boldsymbol{x}}{\boldsymbol{c}}=\boldsymbol{\operatorname { s i n }}^{-1} \boldsymbol{x} \) is \( \pm \)
Reason
\( \sin ^{-1} x+\sin ^{-1} y=\sin ^{-1}(x+y) \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


What is Inorganic Chemistry?
A. Study of compounds which do not contain C-H bond.
B. Study of compounds containing C-H bond.
C. Study of acids.
D. Study of biological waste.


The ratio which divides the line joining
the points (2,3) and \( (4,2), \) also divides
the segment joining the point (1,2) and (4,3) is
A .1: 2
B. \( (3: 1) \)
c. \( (1: 4) \)
D. 1: 1


Write the formula of the following complexes. Pentamine carbonato chromium (III)
chloride


\( k=\lim _{x \rightarrow 2} \frac{x^{2}-x}{x} \) find \( k \)


A stone drop from height 'h' reaches to Earth surface in 1 sec. If the same stone
taken to Moon and drop freely then it will reaches from the surface of the
Moon in the time(The 'g' of Moon is \( 1 / 6 \) times of Earth)
A. \( \sqrt{6} \) second
B. 9 second
c. \( \sqrt{3} \) second
D. 6 second


What is the role of depressant in froth
floatation process?


The number of \( \alpha \) and \( \beta \) -particles
emitted in the conversion of \( g_{0} T h^{232} \) to
\( 82 P b^{208} \) are :
\( \mathbf{A} \cdot 6,4 \)
в. 4,6
\( c \cdot 8,6 \)
D. 6,8


If \( \boldsymbol{A}=\left[\begin{array}{cc}\mathbf{2} & \mathbf{1} \\ -\mathbf{1} & \mathbf{2}\end{array}\right], \boldsymbol{B}=\left[\begin{array}{cc}\mathbf{1} & -\mathbf{2} \\ \mathbf{2} & \mathbf{1}\end{array}\right], \boldsymbol{C}= \)
\( \left[\begin{array}{cc}1 & -3 \\ 2 & 1\end{array}\right], \) then which of the following is
true
A \( . A+B=B+A \) and \( A+(B+C)=(A+B)+C \)
B. \( A+B=B+A \) and \( A C=B C \)
c. \( A+B=B+A \) and \( A B=B C \)
D. \( A C=B C \) and \( A=B C \)


A copper wire of negligible mass, \( 1 m \)
length and cross-sectional area \( 10^{-6} m^{2} \)
is kept on a smooth horizontal table
with one end fixed. A ball of mass \( 1 k g \) is
attached to the other end. The wire and
the ball are rotating with an angular velocity of 20 rad/s. If the elongation in the wire is \( 10^{-3} m . \) Find the Young's
modulus of the wire (in terms of
\( \mathbf{1 0}^{11} \mathbf{N} / \boldsymbol{m}^{2} \mathbf{)} \)


A driver takes \( 0.20 s \) to apply the brakes after he sees a need for it. This is called
the reaction time of the driver. If he is
driving a car at a speed of \( 54 k m / h \) and the brakes causes a deceleration of
\( 6.0 m / s^{2}, \) find the distance traveled by
the car after he sees the need to put the
brakes on.
A . \( 18.63 m \)
в. \( 20 m \)
c. 26.85 m
D. 27.67m


The coordination number and oxidation
number of the central metal ion in the
complex \( \left[\boldsymbol{P t}(\boldsymbol{e n})_{2}\right]^{+2} \) is:
A. C.N. \( =2, \) O.N. \( =+2 \)
B. C.N. \( =6, \) O.N. \( =+4 \)
c. \( \mathrm{c.N.}=4, \mathrm{O} . \mathrm{N}_{.}=+4 \)
D. C.N.= \( 4,0 . \) N. \( =+2 \)


Find the equation of the tangent to the
curve \( y=x^{2}-7 \) at the point where it
cuts the \( y \) - axis.


Which among the following is a tranquilizer?
A. Aspirin
B. Valium
c. Penicillin
D. Sulphanilamide


A sphere and a cube have the same
surface area. Find out the ratio of the
volume of sphere to that to the cube.
A. \( 6: \pi \)
B . \( \sqrt{6}: \sqrt{\pi} \)
c. \( \sqrt{6}: \pi \)
D. \( 6: \sqrt{\pi} \)


The main features of Darwin's theory of evolution are
A. Struggle for existence
B. Natural selection
c. Survival of the fittest
D. All of the above


To construct a triangle similar to given \( \Delta A B C \) with sides equal to \( \frac{7}{5} \) of the
sides of \( \Delta A B C, \) a ray \( B X \) is drawn
such that \( \angle C B X \) is acute angle and
\( B_{1}, B_{2}, B_{3}, \dots \) are marked at equal
distances on \( B X \). The points to be
joined in the next step are:
в. \( B_{5}, C \)
\( \mathbf{c} \cdot B_{7}, C \)
D. \( B_{2}, C \)


The sum of mole fractions of solute and
solvent of a solution is equal to:
A. number of moles of solute
B. number of moles of solvent
c. number of moles of solution
D. unity


Which of the following is not possible?
\( \mathbf{A} \cdot S F_{4} \)
в. \( O F_{2} \)
\( \mathrm{c} \cdot O F_{4} \)
D. \( O_{2} F_{2} \)


A force time graph for the motion of a body is shown in figure. Change in
linear momentum between 0 and \( 8 s \) is :
\( A .0 \)
B. \( 4 N s \)
\( c .8 N s \)
D. none


toppr
Q Type your questióo
presence and absence of a catalyst are shown in dashed and solid lines,
respectively. Identify the correct plot for
the reaction
\( A \)
\( B \)
\( c \)
\( D \)


Isotopes are the atoms of the different element.
A . True
B. False


The polynomial \( p(x)=x^{4}-2 x^{3}+ \)
\( 3 x^{2}-a x+3 a-7 \) when divided by \( x+ \)
1 leaves the remainder 19
Find the value of \( a \). Also find the
remainder when \( p(x) \) is divided by \( x+ \)
2
A \( . a=5 ; 62 \)
В. \( a=4 ; 62 \)
c. \( a=5 ; 60 \)
D. \( a=4 ; 60 \)


Determine the osmotic pressure of a solution prepared by dissolving \( 2.5 \times \) \( 10^{-2} g \) of \( K_{2} S O_{4} \) in \( 2 L \) of water at 25
assuming that it is completely dissociated
\( \left(R=0.0821 L \operatorname{atm} K^{-1} m o l^{-1}, \) Molar \right.
\( \operatorname{mass} \) of \( K_{2} S O_{4}=174 \mathrm{g} m o l^{-1} \) ).


If one of the two slits of a Young's double slit experiment is painted over so that it transmits half the light intensity of the
other, then:
A. the fringe system would disappear
B. the bright fringes would be brighter \& dark fringes would be darker
c. the dark fringes would be brighter and bright fringes would be darker
D. bright as well as dark fringes would be darker


Which are prisms among the following?
(1)
(ii)
(iii)
(iv)


A \( 10 \mathrm{kg} \) object free-falling from a cliff.
Find out the velocity of the object after 1
sec and after 2 sec?
A. \( 9.8 \mathrm{m} / \mathrm{sec} \) after 1 sec and \( 19.6 \mathrm{m} / \mathrm{sec} \) after \( 2 \mathrm{sec} \)
B. \( 9.8 \mathrm{m} / \mathrm{sec} \) after 1 and \( 2 \mathrm{sec} \)
c. \( 9.8 \mathrm{m} / \mathrm{sec} \) after 1 sec and \( 29.4 \mathrm{m} / \mathrm{sec} \) after \( 2 \mathrm{sec} \)
D. \( 19.6 \mathrm{m} / \mathrm{sec} \) after \( 1 \mathrm{sec} \) and \( 29.4 \mathrm{m} / \mathrm{sec} \) after \( 2 \mathrm{sec} \)
E. Cannot determine with information provided


Who gave the principle of Electromagnetic induction?
A. Volta
B. Oerstead
c. Ampere
D. Faraday


Find the five rational numbers between
\( \frac{1}{6} \) and \( \frac{1}{3} \)


Find the value of \( \sin \left[\frac{1}{2} \cot ^{-1}\left(\frac{-3}{4}\right)\right] \)


If we know \( \Delta G^{\circ} \) of a reaction, which of
the following can be defined?
I. Cell potential, \( \boldsymbol{E}^{\circ} \)
II. Activation energy, \( \boldsymbol{E}_{\boldsymbol{a}} \)
III. Equilibrium constant, \( \boldsymbol{K}_{e q} \)
A. I and II only
B. I and III only
c. ॥ only
D. I, II, III
E. None of these


If \( c \) is the speed, \( \nu \) is frequency and \( \lambda \) is wavelength of EM waves, then
A \( . c=\nu \lambda \)
B. \( \frac{\lambda}{\nu}=c \)
c. \( \frac{\nu}{\lambda}=c \)
D. \( \frac{1}{\lambda}=\frac{c}{\nu} \)


P-P bond present in:
A. \( P_{4} O_{10} \)
в. \( P_{4} O_{6} \)
\( \mathbf{c} \cdot H_{4} P_{2} O_{6} \)
D. \( H_{4} P_{2} O_{7} \)


An ecosystem may be a small or a large sized based on kind of
A . Habit
B. Habitatat
c. components
D. Molecules


A battery of emf \( \epsilon_{0}=10 V \) is connected
across a \( 1 \mathrm{m} \) long uniform wire having
resistance \( 10 \Omega / m . \) Two cells of emf
\( \epsilon_{1}=2 V \) and \( \epsilon_{2}=4 V \) having internal
resistances \( 1 \Omega \) and \( 5 \Omega \) respectively are connected as shown in the figure. If
a galvanometer shows no deflection at
the point \( P, \) find the distance of point \( P \)
in cm from the point \( A \). (Round off the
answer to the nearest integer)


Three discs \( A, B \) and \( C \) having radii
\( 2 m, 4 m \) and \( 6 m \) respectively are coated with carbon black on their outer
surface. The wavelengths corresponding to the maximum intensity are
\( 300 m m, 500 m m \) and \( 800 m m \)
respectively. The power radiated by
them are \( Q_{A}, Q_{B} \) and \( Q_{C} \) respectively.
Then
A. \( Q_{A} \) is maximum
B. \( Q_{B} \) is maximum
c. \( Q_{c} \) is maximum


Identify the mode for the following data:
Number \( \mathbf{0} \) 12 \( \mathbf{6} \) \( \mathbf{9} \)
Frequency \( \quad 4 \quad 8 \)
A . 18
B. 12
c. Both A and B
D. 6


The term ecological succession was first given by
A. Odum
B. Clements
c. king
D. Hult


State whether the following sentences are always true, false or ambiguous. Justify your answer. The earth is the only planet where life exist.


If \( \sec \theta=2 x \) and \( y \tan \theta=2, \) then the
value of \( 2\left[x^{2}-\frac{1}{y^{2}}\right] \) is
\( \mathbf{A} \cdot \mathbf{1} \)
B. \( \frac{1}{2} \)
\( c \cdot \frac{1}{3} \)
D.


For \( \mathbf{0} \leq \boldsymbol{r} \leq \boldsymbol{n},^{\boldsymbol{n}} \boldsymbol{C}_{\boldsymbol{r}}= \)


If \( x^{3}+6 x^{2}+4 x+k \) is exactly divisible
by \( x+2, \) then \( k \) is equal to
A . - 6
B. - -
\( c \cdot-8 \)
D. -10


When \( C l_{2} \) is passed through cold dil
NaOH, the products are :
\( \begin{array}{llll}\text { A. } N a C l, & \text { NaOCl } & \text { and } & H_{2} O\end{array} \)
B. NaCl, \( \quad N a C l_{2} \) and \( H_{2} O \)
\( \begin{array}{lll}\text { C. } N a C l, & N a C l_{3} & \text { and } & H_{2} O\end{array} \)
D. \( N a C l, \quad N a C l_{4} \quad \) and \( \quad H_{2} O \)


Match the column I with column II.


Solve the differential equation: \( \frac{d y}{d x}- \) \( x \sin ^{2} x=\frac{1}{x \log x} \)


An electron is moving in a perpendicular magnetic field of strength \( 4 \times 10^{-3} T \) with a velocity of
\( 4 \times 10^{7} m / s . \) The radius of electron path
will be
\( \mathbf{A} \cdot 0.56 m \)
B. \( 0.056 m \)
\( c .56 m \)
D. \( 5.6 m \)


Find the distance between \( \mathrm{P}( \)
\( a \sin \alpha,-b \cos \alpha) \& Q(-a \cos \alpha, b \sin \alpha) \)


Water is flowing through a horizontal pipe in streamline flow. At the narrowest part of the pipe
A. velocity is maximum and pressure is minimum
B. pressure is maximum and velocity is minimumm
c. both the pressure and velocity are maximum
D. both the velocity and pressure are minimum


Two parallel conductors are placed at
right angles to metre scale, at the 2 cm
and \( 6 \mathrm{cm} \) marks, as shown. They carry
currents of \( 1 A \) and \( 3 A \) respectively as
shown in fig. They will produce zero magnetic field at the
A. Zero mark
B. \( 10 \mathrm{cm} \) mark
c. \( 3 c m \) mark
D. \( 6 \mathrm{cm} \) mark


Given \( 4 N H_{3}(g)+5 O_{2}(g) \rightarrow \)
\( \mathbf{4} \boldsymbol{N} \boldsymbol{O}(\boldsymbol{g})+\boldsymbol{6} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \)
The above reaction is an example of:
(i) displacement reaction
(ii) combination reaction
(iii) redox reaction
(iv) neutralisation reaction
A \( . \) (i) and (iv)
B. (ii) and (iii)
c. (i) and (iii)
D. (iii) and (iv)


If \( \overrightarrow{\boldsymbol{a}} \cdot \hat{\boldsymbol{i}}=\overrightarrow{\boldsymbol{a}} \cdot(\hat{\boldsymbol{i}}+\hat{\boldsymbol{j}})=\overrightarrow{\boldsymbol{a}} \cdot(\hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}})= \)
1 then \( \vec{a}= \)
A. \( \hat{i}+\hat{j} \)
в. \( \hat{i}-\hat{k} \)
\( c \)
D. \( \hat{i}+\hat{j}-\hat{k} \)


A uniform rod mass \( \mathrm{m} \) and length lis attached to smooth hinge at end \( A \) and to a string at end B as shown in figure. It
is at rest. The angular acceleration of
the rod just after the string is cut is:


Which of the following is most readily hydrolysed by aqueous NaOH solution.
\( A \)
в.
\( c \)
D.


Statement \( 1: \ln \) an electrolytic cell, the anode becomes positive and the cathode becomes negative.
Statement 2: Anions migrate to the anode and cations migrate to the
cathode.
A. Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation of Statement 1
B. Both the Statement 1 and Statement 2 are correct, but Statement 2 is NOT the correct explanation of Statement 1.
c. Statement 1 is correct, but Statement 2 is not correct
D. Statement 1 is not correct, but Statement 2 is correct


Which of the following statements are
correct for \( \boldsymbol{H} \boldsymbol{C} \boldsymbol{N} \) molecule?
This question has multiple correct options
A. Two \( N \) -bonds are perpendicular to each other
B. Lone pair lying in the orbital which is perpendicular to both \( N \) -bonds
C. The dipole moment value is non zero
D. The direction of dipole moment is from \( N \) to \( H \) -atom


A thin horizontal uniform rod \( A B \) of
mass \( m \) and length \( l \) can rotate freely about a vertical axis passing through its end \( A . \) At a certain moment, the end
\( B \) starts experiencing a constant force
\( F \) which is always perpendicular to the original position of the stationary rod
and directed in a horizontal plane. Find the angular velocity of the rod as a function of its rotation angle \( \theta \) measured relative to the initial position


Matrices obtained by changing rows and columns is called
A. rectangular matrix
B. transpose
c. symetric
D. None of the Above


What is the normal hemoglobin content of an adult man?
A. \( 85 g / L \) of blood
B. \( 105 g / L \) of blood
c. \( 145 g / L \) of blood
D. \( 185 g / L \) of blood


Consider the two idealised systems
(i) a parallel plate capacitor with large plates and small separation and
(ii) a long solenoid of length \( L>>R \)
radius of cross - section.
In
(i) \( \bar{E} \) is ideally treated as a constant between plates and zero outside. In (ii) magnetic field is constant inside the solenoid and zero outside. These
idealised assumptions, however, contradict fundamental laws as below.
A. case (i) contradicts Gauss's law for electrostatic fields
B. case
(ii) contradicts Gauss's law for electrostatic field
\( c \cdot \) case
(i) agrees with \( \oint \bar{E} . \overline{d l}=0 \)
D. case
(ii) contradicts \( \oint \bar{H} . \overline{d l}=I_{e m} \)


Soft drink and baby feeding bottles are generally made up of:
A. Polyester
B. Polyurethane
c. Polyurea
D. Polystyrene


Assertion
Nitric acid cannot be concentrated
beyond \( 68 \% \) by boiling.
Reason
Nitric acid usually consist of maximum boiling azetrope of nitric acid and water
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


\( \boldsymbol{A}+\mathbf{2} \boldsymbol{B} \rightleftharpoons \mathbf{2} \boldsymbol{C}+\boldsymbol{D} \) initial
concentration of \( B \) was 1.5 times that
of \( A, \) but the equilibrium concentration of \( A \) and \( B \) are found to be equal. The equilibrium constant for the reaction is:
A . 4
B. 8
c. 12
D. 16


Is it possible to define the matrix AB and BA when :
A has 4 rows and \( \mathrm{B} \) has 4 columns


The vascular cambium normally gives
rise to
A. Periderm
B. Phelloderm
c. Primary phloem
D. Secondary xylem


If the perimeter of an isosceles triangle
is \( 11 \mathrm{cm} \) and its base is \( 5 \mathrm{cm}, \) its area is \( \frac{5}{4} \sqrt{11} \mathrm{cm}^{2} . \) State true of false and give reason


Symbols \( _{35}^{79} B r \) and \( ^{79} B r \) can be written, whereas symbols \( _{79}^{35} B r \) and \( ^{35} B r \) are not acceptable. Answer briefly:


Give its two shortcoming over reflecting
type telescope.


By selling 144 hens Mahesh suffer a loss equal to the selling price of 6 hens. Find his loss percent??


A car driver knows four different
routes from Delhi to Amritsar. From
Amritsar to Pathankot, he knows three
different routes and from Pathankot to
Jammu he knows two different routes.
How many routes does he know from Delhi to Jammu?
A .4
B. 8
\( c \cdot 12 \)
\( D \cdot 24 \)
E. 36


Find whether \( \alpha \) - decay or any of the \( \beta- \) decay are allowed for \( _{89}^{226} A c \) Given
masses are:
\( M\left(_{89}^{226} A c\right)=226.028356 a m u \)
\( M\left(_{87}^{222} F r\right)=222.017415 a m u \)
\( M\left(_{90}^{226} T h\right)=226.017388 a m u \)
\( M\left(_{88}^{226} R a\right)=226.025406 a m u \)
\( M\left(_{2}^{4} H e\right)=4.002603 a m u \)


The reaction is balanced if \( 5 H_{2} O_{2}+ \)
\( \boldsymbol{x} \boldsymbol{C l} \boldsymbol{O}_{2}+\mathbf{2} \boldsymbol{O} \boldsymbol{H}^{-} \rightarrow \boldsymbol{x} \boldsymbol{C l}^{-}+\boldsymbol{y} \boldsymbol{O}_{2}+ \)
\( 6 H_{2} O \)
The value of \( y \) is :


Forbidden gap in a pure conductor is
A. 0 eV
B. 0.7 eV
c. \( 1.1 \mathrm{eV} \)
D. 6 eV


A solution is prepared by adding 2 g of substance \( A \) to 18 g of water. The mass percent of the solute is:
A . 10
B. 20
c. 40
D. 25


Which one of the following undergoes reaction with \( 50 \% \) sodium hydroxide solution to give the corresponding alcohol and acid?
A. Phenol
B. Benzaldehyde
c. Butanal
D. Benzoic acid


What would be the electron dot
structure of a molecule of sulphur
which is made up of eight atoms of sulphur?


Which plant did mendel select for his experiments ? Why? Explain any three charateristics the same.


A body is lying on the surface of earth.Suppose that the earth suddenly loses its power of attraction, then
A. the weight of body will become zero
B. the weight of body will become infinite
c. the mass of the body will become zero
D. the body will vanish in air


One method of producing \( N H_{3} \) is by
heating ammonium chloride, \( N H_{4} C l \)
with \( C a O \)
\( \mathbf{2} N \boldsymbol{H}_{4} \boldsymbol{C l}+\boldsymbol{C a O} \rightarrow \mathbf{2} \boldsymbol{N} \boldsymbol{H}_{3}+\boldsymbol{C a} \boldsymbol{C l}_{2}+ \)
\( \boldsymbol{H}_{2} \boldsymbol{O} \)
Explain why the reaction of \( N H_{4} C l \)
with \( C a O \) produces ammonia.


Which one of the following relations on \( R( \) set of real numbers) is an
equivalence relation
\( \mathbf{A} \cdot a R_{1} b \Leftrightarrow|a|=|b| \)
в. \( a R_{2} b \Leftrightarrow a \geq b \)
\( \mathbf{c} \cdot a R_{3} b \Leftrightarrow a \) divides \( b \)
D \( \cdot a R_{4} b \Leftrightarrow a<b \)


In a meeting, \( 70 \% \) of the members favour and \( 30 \% \) oppose a certain proposal. A member is selected at
random and we take \( \boldsymbol{X}=\mathbf{0} \) if he
opposed, and \( X=1 \) if he is in favour.
Find \( \boldsymbol{E}(\boldsymbol{X}) \) and \( \boldsymbol{V} \boldsymbol{a} \boldsymbol{r}(\boldsymbol{X}) \)


toppr
Q Type your question
4
B
\( c \)
D. None of these


A loop of capillary running parallel to the Henle's loop.


The exponential form of 512 is \( 2^{k} \) then
value of \( k \) is


The nucleotide sequence on antisense strand of DNA which is transcribed as
codon that specifies the amino acid serine is
A. TCA
B. AGUU
c. TAC
D. ccc


The acceleration of the system will be
A \( \frac{g}{2} \)
в. \( \frac{g}{4} \)
c. \( \frac{7 g}{24} \)
\( D \cdot g \)
8


If an electron is travelling at \( 200 \mathrm{m} / \mathrm{s} \) with \( 1 ~ m / s \) uncertainty, theoretical
uncertainty in its \( \mu m \) will be?
A . 14
B. 58
c. 70
D. 97


A convex lens has focal length \( 30 \mathrm{cm} \). If an object is placed at a distance of 15 \( \mathrm{cm} \) from it then the magnification produced by the lens is?
A . 6.66
B. 0.5
c. 1
\( D \)


Calculate the pH of \( 0.1 \mathrm{M} \) solution of \( (\mathrm{i}) \)
\( N a H C O_{3}, \) (ii) \( N a_{2} H P O_{4} \) and (iii)
\( N a H_{2} P O_{4} \)
Given that:
\( \boldsymbol{C O}_{2}+\boldsymbol{H}_{2} \boldsymbol{O} \rightleftharpoons \boldsymbol{H}^{+}+\boldsymbol{C} \boldsymbol{O}_{3}^{2-} ; \boldsymbol{K}_{1}= \)
\( 4.2 \times 10^{-7} \mathrm{M} \)
\( \boldsymbol{H} \boldsymbol{C O}_{3}^{-} \rightleftharpoons \boldsymbol{H}^{+}+\boldsymbol{C} \boldsymbol{O}_{3}^{2-} ; \boldsymbol{K}_{2}=\boldsymbol{4} . \boldsymbol{8} \times \)
\( 10^{-11} \mathrm{M} \)
\( \boldsymbol{H}_{2} \boldsymbol{P} \boldsymbol{O}_{4} \rightleftharpoons \boldsymbol{H}^{+}+\boldsymbol{H}_{2} \boldsymbol{P} \boldsymbol{O}_{4}^{-} ; \boldsymbol{K}_{1}=\mathbf{7 . 5} \times \)
\( 10^{-3} \mathrm{M} \)
\( \boldsymbol{H}_{2} \boldsymbol{P} \boldsymbol{O}_{4}^{-} \rightleftharpoons \boldsymbol{H}^{+}+\boldsymbol{H} \boldsymbol{P} \boldsymbol{O}_{4}^{2-} ; \boldsymbol{K}_{2}= \)
\( \mathbf{6} \cdot \mathbf{2} \times \mathbf{1} \mathbf{0}^{-\mathbf{8}} \mathbf{M} \)
\( \boldsymbol{H} \boldsymbol{P} \boldsymbol{O}_{4}^{2-} \rightleftharpoons \boldsymbol{H}^{+}+\boldsymbol{P} \boldsymbol{O}_{4}^{3-} ; \boldsymbol{K}_{3}=\mathbf{1 . 0} \times \)
\( 10^{-12} \mathrm{M} \)


A 5000 kg rocket is set for vertical
firing. The exhaust speed is \( 800 \mathrm{ms}^{-1} \)
To give an upward acceleration of \( 20 \mathrm{ms} \)
\( -2, \) the amount of gas ejected per second to supply the needed thrust is \( \left(g=10 m s^{-2}\right) \)
A . \( 127.5 \mathrm{kg} \mathrm{s}^{-1} \)
B . \( 137.5 \mathrm{kg} \mathrm{s}^{-1} \)
c. \( 187.5 \mathrm{kg} \mathrm{s}^{-1} \)
D. \( 185.5 \mathrm{kg} \mathrm{s}^{-1} \)


Beauty of Bougainvillea flower is due to
A. corolla
B. Calyx
c. Bracts
D. Androecium


The glomerular membrane has a permeability about
A. 100 to 500 times as great as usual capillary
B. 20 times greater than capillary
c. 10 times greater than capillary
D. Same as capillary


The displacement of the medium in a
sound wave is given by the equation;
\( \boldsymbol{y}_{1}=\boldsymbol{A} \cos (\boldsymbol{a} \boldsymbol{x}+\boldsymbol{b} \boldsymbol{t}) \) where \( A, \) a \( \& \boldsymbol{b} \) are
positive constants. The wave is
reflected by an obstacle situated at \( x= \)
0, The intensity of the reflected wave is 0.64 times that of the incident wave.
The wavelength of the incident wave is
Find the value of \( x: \) \( \boldsymbol{a} \)


\( (i) N_{2}(g)+O_{2}(g) \rightleftharpoons 2 N O(g) K_{1} \)
\( (i i)\left(\frac{1}{2}\right) N_{2}(g)+\left(\frac{1}{2}\right) O_{2}(g) \rightleftharpoons N O(g) K_{2} \)
\( (i i i) 2 N O(g) \rightleftharpoons N_{2}(g)+O_{2}(g) K_{3} \)
\( (i v) N O(g) \rightleftharpoons\left(\frac{1}{2}\right) N_{2}(g)+\left(\frac{1}{2}\right) O_{2}(g) K_{4} \)
What is the correct relation between
\( \boldsymbol{K}_{1}, \boldsymbol{K}_{2}, \boldsymbol{K}_{3} \) and \( \boldsymbol{K}_{4} ? \)
This question has multiple correct options
A. \( K_{1} \times K_{3}=1 \)
B . \( \sqrt{K_{1}} \times K_{4}=1 \)
\( \mathbf{c} \cdot \sqrt{K_{3}} \times K_{2}=1 \)
D. None of the above


During what kind of process is there no change in internal energy?
A. adiabatic
B. isothermal
c. isobaric
D. cyclic (one cycle)
E. Two of the answers are correct


The ratio of the ratii of two circular
cones of hte same height is 1: 2 and height of each come is \( \sqrt{3} \) times the smaller radius then curved surface areas of two cones will be the ratio of
A . 2: 5
В. \( 10: 2 \sqrt{3} \)
c. \( 1: \sqrt{7} \)
D. 3:2


The \( K_{s p} \) of \( C a(O H)_{2} \) is \( 4.42 \times 10^{-5} \) at
\( 25^{\circ} \mathrm{C} . \mathrm{A} 500 \mathrm{m} L \) of saturated solution of
\( \boldsymbol{C} \boldsymbol{a}(\boldsymbol{O} \boldsymbol{H})_{2} \) is mixed with equal volume
of \( 0.4 M \) NaOH. How much \( C a(O H)_{2} \)
in \( m g \) is precipitated?
A. \( 659.2 \mathrm{mg} \)
в. \( 759.2 \mathrm{mg} \)
c. \( 578.2 \mathrm{mg} \)
D. \( 785.2 \mathrm{mg} \)


between conductors carrying currents
\( I_{1} \) and \( I_{2} \) is varied. Which of the
following graphs correctly represents
the variation of force \( (\boldsymbol{F}) \) between the
conductors and distance \( (\boldsymbol{d}) \) ?
\( A \)
в.
\( c \)
D. none of these


The number of radioactive nuclei that
were present after \( 7 h \) is
\( A \cdot 2 \times 10^{4} \)
B . \( 1.25 \times 10^{8} \)
c. \( 1.875 \times 10^{6} \)
D. \( 1.25 \times 10^{4} \)


The tympanum of the ear receive the sound in the form of
A. compressions
B. rarefaction
c. both
D. none


A gas behaves more closely as an ideal
gas at:
A. low pressure and low temperature
B. low pressure and high temperature
c. high pressure and low temperature
D. high pressure and high temperature


A beam of light consisting of two wavelengths, 800 nm and 600 nm is used to obtain the interference fringes
in a Young's double slit experiment on a
screen place \( 1.4 \mathrm{m} \) away. If the two slits are separated by \( 0.28 \mathrm{mm} \), Calculate the least distance from the central bright maximum where the bright fringes of the two wavelengths coincidence.


The shape of \( \left(C H_{3}\right)_{3} N \) is pyramidal
because:
A. nitrogen forms three \( s p^{3} \) hybridised \( \sigma \) bonds with carbon atoms of methyl groups and there is one nonbonding electron pair
B. nitrogen forms three \( s p^{2} \) hybridised \( \sigma \) bonds with carbon atoms of methyl groups and fourth orbital forms \( \pi \) bond
C. nitrogen has five valencies which are arranged in pyramidal shape
D. the unpaired electron present on nitrogen is delocalised


Find the \( 31^{s t} \) term of an AP whose \( 11^{t h} \)
term is 38 and the \( 16^{t h} \) term is 73


Of the following statements about
enzymes, which ones are true?
(i) enzymes lack in nucleophilic groups
(ii) enzymes are highly specific both in binding chiral substrates and in
catalyzing their reactions
(iii) enzymes catalyze chemical reactions by lowering the activation energy
(iv) pepsin in proteolytic enzyme
\( A \cdot(i) \)
B. (i) and (iv)
c. (i) and (iii)
D. (ii), (iii) and (iv)


The diagram shows the stress v/s strain
curve for the materials \( A \) and \( B \). From
the curve:
A. \( A \) is brittle but \( B \) is ductile
B. \( A \) is ductile and \( B \) is brittle
c. Both \( A \) and \( B \) axe ductile
D. Both \( A \) and \( B \) axe brittle strain


When \( 4 A \) of current is passed through a \( \mathbf{1} . \mathbf{0} \boldsymbol{L}, \mathbf{0 . 1 0} \boldsymbol{M} \boldsymbol{F} \mathbf{e}^{\mathbf{3}+}(\mathbf{a q}) \) solution for \( \mathbf{1} \boldsymbol{h} \)
it is partly reduced to \( F e(s) \) and partly
of \( F e^{2+}(a q) \)
Identify the correct statement(s).
This question has multiple correct options
A. 0.10 mole of electrons are required to convert all \( F e^{3+} \) to \( F e^{2} \)
B. 0.025 mol of \( F e(s) \) will be deposited.
c. 0.075 mol of iron remains as \( F e^{2} \)
D. 0.050 mol of iron remains as \( F e^{2} \)


State whether given statement is True or False.

Lightning rods are placed on houses to reduce risk of lightning damage to low.
A. True
B. False


The plane \( \frac{x}{2}+\frac{y}{3}+\frac{z}{1}=1 \) meets the co
ordinate axes in the points \( \boldsymbol{A}, \boldsymbol{B}, \boldsymbol{C} \)
respectively. The area of triangle \( \boldsymbol{A B C} \)
in square units is :
A \( \cdot \frac{5}{2} \)
B. \( \frac{7}{2} \)
\( c \cdot \frac{9}{2} \)
D. None of these


An ideal voltmeter is connected in Fig.
The current in circuit is
\( A, 2 A \)
B. 2.5
c. infinity
D. zero


Find the middle term in the expansion
of :
\( \left(\frac{x}{a}-\frac{a}{x}\right)^{10} \)


Explain the formation of stationary waves by analytical method. Show the
formation of the stationary wave diagramatically.


and
D in the given figure and match the
correct names from the list (i - viii)
given below.
(i) Reissner's membrane
(ii) Basilar membrane
(iii) Tectorial membrane
(iv) Organ of Corti
(v) Hair cells
(vi) Ototlith organ
(vii) Scala media
(viii) Scala vestibuli
A. \( A-(\text { ii) }, B-(v), C- \) (iii), D - (i)
B. A - (vii), B - (iv), C - (ii), D - (iii)
C. \( A-(v \text { ii }), B-(i v), C-(i), D-(i i) \)
D. \( A-(v \text { ii }), B-(v i), C-(i), D- \) (iii)


The annual salaries of employees in a large company are approximately normally distributed with a mean of \( \mathbf{5 0}, \mathbf{0 0 0} \) and a standard deviation of \( 20,000 . \) What percent of people earn
between 45,000 and \( 65,000 ? \)
A . \( 56.23 \% \) \%
B . \( 47.4 \% \)
c. \( 37.2 \% \)
D. 38.56\%


Nitrate ion on reacting with conc.
\( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) gives:
A. nitrogen dioxide
B. nitrogen pentaoxide
\( c . \) nitrous oxide
D. None of the above


Which of the following is/are true?
A. The wind blows because of differences in air pressure from one location to another
B. Wind blows from areas of high pressure toward areas of low pressure
C. If the high pressure area is very close to the low pressure area, or if the pressure difference is very great, the wind can blow very fast
D. All of the above


Given \( \boldsymbol{A}=\sin ^{2} \boldsymbol{\theta}+\cos ^{4} \boldsymbol{\theta}, \) then for all
real \( \theta, \) which of the following is true?
A. \( 1 \leq A \leq 2 \)
в. \( \frac{3}{4} \leq A \leq 1 \)
c. \( \frac{13}{16} \leq A \leq 1 \)
D. \( \frac{3}{4} \leq A \leq \frac{13}{16} \)


\( \sqrt{2} \sec x+\tan x=1 \)


Using elementary row transformations,
find the inverse of the matrix
\( \left[\begin{array}{ccc}1 & 2 & 3 \\ 2 & 5 & 7 \\ -2 & -4 & 5\end{array}\right] \)


Protists which are diploid, reproduce sexually by the process of
A. Zygotic meiosis
B. Cyst formation
c. Binary fission
D. Gametic meiosis


What happens when an acid or base is
mixed with water?


The nerve cord of cockroach is
A. Double, ventral and solid
B. Double dorsal and hollow
C. single, dorsal and solid
D. single, ventral and hollow


The plane \( X O Z \) divides the join of
(1,-1,5) and (2,3,4) in the ratio \( \lambda: 1 \)
then \( \lambda \) is
A . -3
в. \( \frac{1}{4} \)
\( c \cdot 3 \)
D. \( \frac{1}{3} \)


Water in adjacent xylem moves into the phloem by process of :
A. Simple diffusion
B. Active transport
c. osmosis
D. Facilitated diffusion


Find the smallest number by which the following number must be multiplied to obtain a perfect cube 243
\( A \cdot 3 \)
B.
\( c \cdot 0 \)
D.


The follwoing combined logic gate diagram is eqivalent to
A. NOR gate
B. oR gate
c. AND gate
D. NAND gate


What are galvanic cells? Explain the construction and working of galvanic cell with an example?


Order from least to greatest:
\( \frac{8}{18} \)
ii) 0.8
iii) \( 40 \% \) of 1


What are gene? Where are they located?


Potassium hexachloroplatinate
\( \boldsymbol{K}_{2}\left[\boldsymbol{P}_{2} \boldsymbol{i} \boldsymbol{C l}_{3}\right] \) adopts anti-fluorite crystal
structure. Which of the following ions adopts \( f c c \) arrangement?
A \( \cdot C l^{-} \) ions
B. \( K^{+} \) ions
\( \mathbf{c} \cdot P t^{4+} \) ions
D. \( \left[P t C l_{6}\right]^{2-} \) ions


Write the three steps involved in the
mechanism of acid catalysed
dehydration of ethanol to ethene.


If the sum of a certain number of terms
of the \( A P 25,22,19, \ldots . \) is \( 116 . \) Find the
last term.


A closely wound solenoid \( 80 \mathrm{cm} \) long has 5 layers of windings of 400 turns each. The diameter of the solenoid is 1.8
\( \mathrm{cm} . \) If the current carried is \( 8.0 \mathrm{A} \)
estimate the magnitude of B inside the solenoid near its centre.


The physical quantity corresponding to the rate of change of displacement is
A. speed
B. velocity
c. acceleration
D. retardation


The central mineral element seen in
chlorophyll molecule is
A. Iron
B. Magnesium
c. Manganese
D. Sulphur


Find the percentage ionization of \( 0.2 \mathrm{M} \) acetic acid solution, whose disassociation constant is \( 1.8 \times 10^{-5} \)


State true or false:
In a square \( A B C D \), diagonals meet at
O. \( P \) is a point on \( B C \) such that \( O B= \)
\( B P, \) then
\( \angle P O C=\left(22 \frac{1}{2}\right)^{0} \)
A. True
B. False


To design the body of an aircraft,
aluminium alloys are used. Give
reasons.


Find the cost of operating an electric toaster for \( 2 h r s, \) if it draws a current of
\( 8 A \) on a \( 110 V \) circuit. The cost of
electric energy is \( \boldsymbol{R} \boldsymbol{s} \boldsymbol{2} . \boldsymbol{5} / \boldsymbol{k} \boldsymbol{W} \boldsymbol{h} \)
A. Rs 4.40
в. Rs 6
c. \( R s 8.20 \)
D. Rs 2.20


Outline the principles behind the refining of metals by the following methods:
(i) Zone refining method
(ii) Chromatographic method


In the metallurgy of zinc, the reducing agent employed in reducing the zinc oxide to crude zinc metal in the last
stage is:
A . \( A l \)
B. \( L i \)
c. coke
D. Water gas
E . \( H_{2} \) gas


In 2001 , the world's population was
\( 250000 . \) With a growth rate of approximately \( 14 \% \), what was the population in \( 2011 ? \)


Assertion
Balmer series lies in the visible region of electromagnetic spectrum.
Reason \( \frac{1}{\lambda}=R\left[\frac{1}{2^{2}}-\frac{1}{n^{2}}\right], \) where \( n=3,4,5 \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


Acid when reacts with metal release
hydrogen gas but there is one acid which when reacts with metal does not
release hydrogen except for two metals. Prove this statement.


The displacement of centre of mass of
\( A_{B} \) system till the string becomes
vertical is:
A. zero
B. \( L(1-\cos \theta) \)
c. \( \frac{L}{2}(1-\cos \theta) \)
D. None of these


Find the emf induced in the coil shown
in figure.The magnetic fields is perpendicular to the plane of the coil and is constant.
A. zero
B. Infinity
c. can't say
D. None of these


Type of Hybridisation of \( N \) and \( C- \)
\( N-C \) bond angle in \( \left(C H_{3}\right)_{3} N \) are
and \( _{-}--_{-}- \) respectively
\( \mathbf{A} \cdot s p^{3}, 108^{\circ} \)
B. \( s p^{2}, 120^{\circ} \)
c. \( s p^{3}, 109^{\circ} 28^{\prime} \)
D. \( s p^{2}, 117.5^{\circ} \)


If \( A \) is a square matrix so that
\( A a d j A=\operatorname{diag}(k, k, k) \) then \( |a d j A|= \)
\( A \cdot k \)
B . \( k^{2} \)
c. \( k^{3} \)
\( \mathbf{D} \cdot k^{4} \)


One mole of a complex compound
\( \boldsymbol{C} \boldsymbol{o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{5} \boldsymbol{C l}_{3} \) gives three moles of
ions on dissolution in water. One mole
of the same complex reacts with two
moles of \( A g N O_{3} \) and yields two moles
of \( A g C l(s) . \) The complex is:
A \( \cdot\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}\right] \mathrm{Cl} . \mathrm{NH}_{3} \)
B . \( \left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}\right] \mathrm{Cl}_{2} . \mathrm{NH}_{3} \)
\( \mathbf{c} \cdot\left[\operatorname{Co}\left(N H_{3}\right)_{5} C l\right] C l_{2} \)
D \( \cdot\left[\operatorname{Co}\left(N H_{3}\right)_{3} C l\right] C l_{3} .2 N H_{3} \)


A mixture of ethyl iodide and n-propyl iodide is subjected to wurtz reaction.
The hydrocarbon which will be majorly formed is:
A. butane
B. propane
c. pentane
D. hexane


In Paramecium, beating of cilia is controlled by
A. Neuromotor system
B. Kinety
c. Kinetosome
D. Pellicle


The solar constant for the earth is \( S \). The
surface temperature of the sun is \( \boldsymbol{T} \boldsymbol{K} \)
The sun subtends an angle \( \theta \) at the
earth.
This question has multiple correct options
\( A \cdot S \propto T^{4} \)
в. \( S \propto T^{2} \)
c. \( S \propto \theta^{2} \)
\( \mathbf{D} \cdot S \propto \theta \)


The velocity-time graph for an object is shown

How can the total displacement of the
object be determined?
A . area1 - area2
B. \( \frac{(a r e a 1-a r e a 2)}{2} \)
c. area1 \( + \) area2
D. area2 - area1


A point P lies on the x-axis and has
abscissa 5 and a point \( Q \) lies on \( y \) -axis
and has ordinate \( -12 . \) Find the distance
\( \mathrm{PQ} \)
A. 13 units
B. 8 units
c. 15 units
D. 11 units


Assertion
Clothes washed with soap using hard
water do not absorb dyes evenly.
Reason

Hard water contains calcium and
magnesium 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 candle is placed at a distance of 20 \( \mathrm{cm} \) from a converging lens of focal length \( 15 \mathrm{cm} . \) The image obtained on the
screen is :
A. upright and magnified
B. inverted and magnified
c. inverted and diminished
D. upright and diminished


List the factor determine the type of
bond that will be formed between two
atom?


Among the following compounds, identify total number of compounds
that liberate \( C O_{2} \) gas on reaction with
\( N a H C O_{3} \)


Which of the following species has four lone pairs of electrons in its outer shell
?
A . \( I \)
в. \( O \)
\( c \cdot C l \)
D. \( H e \)


Pancreatic juice is
A. Alkaline in nature
B. Acidic in nature
C. Contains variety of enzymes
D. Both A and C


Given the following bond dissociation enthalpies (kJ mol-1) :
\begin{tabular}{c|c}
\( \boldsymbol{P} \equiv \boldsymbol{P} \) & \( \mathbf{4 9 0} \) \\
\( \boldsymbol{P}-\boldsymbol{P} \) & \( \mathbf{2 0 9} \) \\
\( \boldsymbol{N} \equiv \boldsymbol{N} \) & \( \mathbf{9 4 6} \) \\
\( \boldsymbol{N}-\boldsymbol{N} \) & \( \mathbf{1 6 0} \)
\end{tabular}
Compare the enthalpy changes for the process and comment if the reactions are possible
(i) \( 2 P_{2}(g) \longrightarrow P_{4}(g) \)
(ii) \( 2 N_{2}(g) \longrightarrow N_{4}(g) \)
A . (i) possible (II) not possible
B. (i) possible (II) possible
\( c \cdot \) (i) not possible (II) possible
D. (i) not possible (II)not possible


The use of plastic material polyesters is
in:
A. toys
B. combs
c. recording tapes
D. All of the above


Due to refraction, sunrise appears
sun comes to horizon and
sunset appears sun leaves
horizon respectively.
A. before, after
B. after, before
c. before, before
D. after, after


A viral preparation was inactivated in a chemical bath. The inactivation process was found to be first order in virus
concentrations. At the beginning of the experiment, \( 2.0 \% \) of the virus was found
to be inactivated per minute. The k for
inactivation process is:
A \( \cdot 3 \times 10^{-4} s^{-1} \)
В. \( 4 \times 10^{-4} s^{-1} \)
c. \( 5 \times 10^{-4} s^{-1} \)
D. \( 6 \times 10^{-4} s^{-1} \)


Two coins are tossed, \( A \) is the event of
getting at most one head, \( B \) is the event
getting both heads, \( C \) is the event of getting same face on both the coins. The events \( A \) and \( B \) are:
A. Mutually exhaustive
B. Mutually exclusive
c. same
D. None of these


A transparent solid cylindrical rod has a refractive index of \( \frac{2}{\sqrt{3}} . \) It is surrounded by air. A light ray is incident at the mid-
point of one end of the rod as shown in
the figure. The incident angle \( \theta \) for
which the light ray grazes along the wall
of the rod is -
\( \mathbf{A} \cdot \sin ^{-1}\left(\frac{1}{2}\right) \)
B. \( \sin ^{-1}\left(\frac{\sqrt{3}}{2}\right) \)
\( c \cdot \sin ^{-1}\left(\frac{2}{\sqrt{3}}\right) \)
D \( \cdot \sin ^{-1}\left(\frac{1}{\sqrt{3}}\right) \)


One mole of an ideal monoatomic gas is heated a constant pressure of one
atmosphere from \( 0^{\circ} C \) to \( 100^{\circ} \mathrm{C} \). Then
the work done by gas is
\( \mathbf{A} \cdot 6.56 J \)
В. \( 8.32 \times 10^{2} J \)
c. \( 12.48 \times 10^{2} J \)
D. \( 20.8 \times 10^{2} J \)


How many terms are there in the
sequence \( 4,11, \ldots \ldots ., 298 ? \)


Two bodies, each of mass \( \mathrm{M} \), are kept
fixed with a separation 2 L. A particle of mass \( m \) is projected from the midpoint of the line joining their centres, perpendicular to the line. The gravitational constant is G. The correct statement(s) is (are).
A. The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is \( 4 \sqrt{\frac{G M}{L}} \)
B. The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is \( 2 \sqrt{\frac{G M}{L}} \)
C. The minimum initial velocity of the mass \( m \) to escape the gravitational field of the two bodies is \( \sqrt{\frac{2 G M}{L}} \)
D. The energy of the mass m remains constant


Give reason for the higher boiling point
of ethanol in comparison
to methoxymethane.


An electric dipole ( dipole moment p) is
placed at a radial distance \( r>>a \) ( Where a
is dipole length) from an infinite line of
charge having linear charge density \( +\lambda \)
dipole moment vector is aligned along the radial vector \( \vec{r} \) force experienced by
the dipole is:-
A \( \cdot \frac{\lambda p}{2 \pi \varepsilon_{o} r^{2}}, \) attractive
B. \( \frac{\lambda p}{2 \pi \varepsilon_{o} r^{3}}, \) attractive
C \( \cdot \frac{\lambda p}{2 \pi \varepsilon_{o} r^{2}}, \) repulsive
D. \( \frac{\lambda p}{2 \pi \varepsilon_{o} r^{3}}, \) repulsive


The angle between the normal and the reflected ray is \( 40^{0} . \) Find the angle of incidence.
A \( \cdot 50^{\circ} \)
\( ^{0} \)
B. 20
\( c \cdot 40^{\circ} \)
D. Can't be predicted


A silicon optical fibre with a core
diameter large enough has a core refractive index of 1.50 and a cladding
refractive index 1.47. Determine
(i) the critical angle at the core cladding interface,
(ii) the numerical aperture for the fibre
(iii) the acceptance angle in air for the fibre.


\( A(3,-4), B(5,-2), C(-1,8) \) are the
vertices of \( \triangle A B C . D, E, F \) are the midpoints of sides \( \overline{B C}, \overline{C A} \) and \( \overline{A B} \) respectively. Find area of \( \triangle A B C . \) Using
coordinates of \( D, E, F, \) find area of
\( \triangle D E F . \) Hence show that the \( A B C= \)
\( \mathbf{4}(D E F) \)


Assertion
A potentiometer having 10 wires is more accurate than the potentiometer
having 1 wire
Reason
Potential gradient of 10 -wire
potentiometer is much less
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


\( \int \frac{x^{5}}{x^{2}+9} d x \)


In which case geometry of the molecule is pyramidal?
\( \mathbf{A} \cdot N\left(C H_{3}\right)_{3} \)
в. \( N\left(S i H_{3}\right)_{3} \)
c. Both (a) and (b)
D. None of these


Write the difference between unisexual
and bisexual animal. Give one example
of each.


\( \ln \) an \( A C \) circuit, the potential across an inductance and resistance joined in series are respectively \( 16 V \) and \( 20 V \)
The total potential difference across the circuit is
\( \mathbf{A} \cdot 20.0 V \)
B . \( 25.6 V \)
c. \( 31.9 V \)
D. 33.6 \( V \)


When a glass rod is rubbed with silk,
the charge acquired by the silk is :
A. negative
B. positive
c. partly positive and partly negative
D. none of these


Which of the following dissociate to
give \( \boldsymbol{H}^{+} \) easily?
A \( \cdot H_{2} O \)
в. \( H_{2} S \)
\( \mathbf{c} \cdot H_{2} T e \)
D. \( H_{2} S e \)


The area bounded by curve \( y= \)
\( \sin 2 x(x=0 \quad \text { to } \quad x=\pi) \) and \( X \) -axis is
A .4
B. 2
c.
D.


\( \$ 760 \) is invested for 3 years at a rate of \( 4.5 \% \) per year simple interest. Work out the total interest at the end of
the 3 years


What statement is correct for Keto -
enol tautomerism?
This question has multiple correct options
A. Tautomersim is catalysed by acid and base.
B. Tautomers are present in a dynamic equilibrium state.
C. Generally keto form is more stable than enol form in mono ketones.
D. Atomic arrangements are same in tautomerism.


Spiracles of cockroach which are larger and always kept open are
A. First and second pairs
B. First and third pairss
c. First and tenth pairs
D. Second and third pairs


The perimeter of a square field is \( 40 \mathrm{m} \) more than another square field. Three
times the area of the smaller field is 50
\( m^{2} \) more than the area of the larger field. Find the sides of both the fields.


Find the oxidation number of Calcium
in \( C a O \)
\( A \cdot+1 \)
B. - -
\( c \cdot+2 \)
\( D \cdot-2 \)


A step down transformer is connected
to 2400 volts line and 80 amperes of current is found to flow in output load.
The ratio of the turns in primary and secondary coil is \( 20: 1 . \) If the
transformer efficiency is \( 100 \% \), then the current flowing in the primary coil will be
\( \mathbf{A} \cdot 1600 \mathrm{amp} \)
B. 20 amp
c. 4 amp
D. 1.5 amp


Which of the following will produce hydrogen on decomposition by metals like \( N a, K, C a ? \)
A. Boiling water
B. Steam
c. cold water
D. All of the above


Electromagnetic theory suggests that
the light consists of:
A. Magnetic vector only
B. Electric vector only
C. Electric and magnetic vectors perpendicular to each other
D. Parallel electric and magnetic vector


The de Broglie wavelength of an electron
in a metal at \( 27^{\circ} \mathrm{C} \) is \( \left(\text {Given } \boldsymbol{m}_{e}=\right. \)
\( \mathbf{9 . 1} \times \mathbf{1 0}^{-\mathbf{3 1}} \mathbf{k g}, \boldsymbol{k}_{\boldsymbol{B}}=\mathbf{1 . 3 8} \times \)
\( \left.10^{-23} J K^{-1}\right) \)
A \( \cdot 6.2 \times 10^{-9} \mathrm{m} \)
В. \( 6.2 \times 10^{-10} \mathrm{m} \)
\( \mathbf{c} \cdot 6.2 \times 10^{-8} m \)
D. \( 6.2 \times 10^{-7} m \)


Which one of the following is an extensive property?
A. Enthalpy
B. Concentration
c. Density
D. Viscosity


A body drinks \( 500 \mathrm{mL} \) of \( 9 \% \) glucose solution. The number of glucose molecules he has consumed is :
[Molecular weight of glucose \( =180] \)
A \( \cdot 0.5 \times 10^{23} \)
B . \( 1.0 \times 10^{23} \)
c. \( 1.5 \times 10^{23} \)
D. \( 2.0 \times 10^{23} \)


What is electrostatic precipitation?


Assertion: The rate at which sugar
dissolves in water increases with
stirring
Reason: Stirring exposes the surface of a solute crystal to a less concentrated
layer of solution.
A. Both Assertion and Reason are correct and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are correct but Reason is the correct explanation of Assertion
c. Assertion is correct but Reason is not correct
D. Assertion is not correct but Reason is correct
E. Both Assertion and Reason are not correct


A man produce sound with trumpet. A wave has a wavelength of \( 8.75 \mathrm{mm} \) and frequency of \( 40 \mathrm{kHz} \). If the man receives an echo after reflecting from the wall 0.4 s later. Calculate the distance between
man and the wall.
\( A \cdot 35 \mathrm{m} \)
B. 70
c. \( 105 \mathrm{m} \)
D. \( 140 \mathrm{m} \)
E. \( 175 \mathrm{m} \)


Assertion
A cyclotron cannot accelerate neutrons.
Reason
Neutrons are neutral.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


Butylated hydroxy toluene as a food
additive acts as :
A. flavouring agent
B. emulsifier
c. antioxidant
D. colouring agent


Choose the correct options:
This question has multiple correct options
\( \mathbf{A} \cdot \mathrm{PCl}_{5}(\text { solid }) \) dissociates into \( \mathrm{PCl}_{4}^{+} \) and \( \mathrm{PCl}_{6}^{-} \)
B. LiH reacts with AlH forming LiAlH \( _{4} \).
C \( . N H_{3} \) is protonated.
D. \( H_{3} P O_{2} \) on heated forms \( P H_{3} \) and \( H_{3} P O_{3} \)


The equation of motion of a body falling under gravity is given by \( \frac{d v}{d t}=g- \) \( \frac{g}{\lambda^{2}} v^{2} . \) The Velocity as a function of time
is? given that \( \boldsymbol{v}=\mathbf{0} \boldsymbol{t}=\mathbf{0} \)
A \( \cdot v=\lambda^{2} \tan h^{-1} \frac{g t}{\lambda} \)
B. \( v=\lambda \cot h^{-1} \frac{g t}{\lambda} \)
c. \( v=\lambda \tan h^{-1} \frac{g t}{\lambda} \)
D. \( v=\lambda \cot ^{2} h^{-1} \frac{g t}{\lambda} \)


Determine the osmotic pressure of a solution prepared by dissolving 25 mg
of \( K_{2} S O_{4} \) in 2 litre of water at \( 25^{\circ} C \)
assuming that it is completely dissociated.


Find the equation of the line perpendicular to the line \( \boldsymbol{x}-\mathbf{7} \boldsymbol{y}+\mathbf{5}= \)
0 and having \( x \) -intercept 3


Which of the following are advantages
of AC over DC ?
A. Easily stepped up and down for long transmission with fairly low loss
B. Easy to generate with AC Generator/motor from rotary sources (e.g. turbines)
c. Easy to make powerful, reliable motors (induction type
D. all of the above


Preparation of soyabean milk and its comparison with the natural milk.


Groundwater accumulates between the
layer of hard rocks. It is known as:
A. pond
B. water table
c. surface water
D. aquifer


Male and female birds have the
following set of chromosomes.
A. zz and zw
B. \( x x \) and \( x 0 \)
c. zz and zo
D. \( x \) y and \( x x \)


In Fig. sides \( P Q \) and \( R Q \) of \( \Delta P Q R \) are
produced to points \( S \) and \( T \)
respectively. If \( \angle S P R=135^{\circ} a \) and
\( \angle P Q T=110^{\circ} . \) Find \( \angle P R Q \)


Which of the following is true for the resultant polymer product formed, when molecules of pthalic acid react with molecules of glycerol?
A. cross-link polymer
B. linear polymer
c. branch polymer
D. none of mentioned


toppr
Q Type your question_
the force acting on particle \( A ? \)
\( \mathbf{A} \)
\( B \)
\( \mathbf{C} \)
D.
\( E \)


Which group in p-block elements shows highest positive oxidation state?
A . 16
B. 17
c. 18
D. 15


A tightly-wound long solenoid has n turns per unit length,radius r and
carries a current \( i . \) A particle having
charge \( q \) and mass \( m \) is projected from a point on the axis in the direction
perpendicular to the axis.The maximum speed for which particle does not strike
the solenoid will be
A \( \cdot \frac{\mu_{o} q r n i}{2 m} \)
B. \( \frac{\mu_{o} q r n i}{m} \)
c. \( \frac{2 \mu_{o} q r n i}{3 m} \)
D. None of these


The absorption of minerals due to difference in the electropotential gradient without use of energy is?
A. Active absorption
B. Passive absorption
c. osmotic absorption
D. None of the above


If \( P, Q, R \) are collinear points such that \( \boldsymbol{P}(\boldsymbol{3}, \boldsymbol{4}), \boldsymbol{Q}(\boldsymbol{7}, \boldsymbol{7}) \) and \( \boldsymbol{P} \boldsymbol{R}=\mathbf{1 0}, \) find \( \boldsymbol{R} \)


Which of the following complex has five unpaired electrons?
\( \mathbf{A} \cdot\left[M n\left(H_{2} O\right)_{6}\right]^{2+} \)
B . \( \left[M n(C N)_{6}\right]^{3} \)
\( \mathbf{c} \cdot\left[C r C l_{3}\left(H_{2} O_{3}\right]\right. \)
D. \( \left[A g\left(N H_{3}\right)_{2}\right] \)


How many coordination isomer are
possible for the following compound? (excluding the given structure of molecule)
\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{6}\right]^{3+}\left[\boldsymbol{C r}\left(\boldsymbol{N O}_{2}\right)_{6}\right]^{3+} \)


Fuming sulphuric acid is commercially known as:
A. Caro's acid
B. Marshall'sacid
c. oleum
D. Sulphurous acid


In anaphase I, each chromosome is
composed of
A. One chromatid
B. Two chromatid
c. Four chromatid
D. Many chromatid


The angular velocity of the bob
performing SHIM
\( A \cdot \) is a constant
B. is high when it is at mean position
C. is less when it is at extreme position
D. cannot be determined


The cells in the retina that are able to
distinguish between different colours
are :
A. Rod shaped
B. Cone-shapedd
c. Cuboid shaped
D. Long and flat


A large number of particles are moving towards each other with velocity \( V \)
having directions of motion randomly distributed. What is the average relative velocity between any two particles averaged over all the pairs?
A. \( 4 V / \pi \)
в. \( 4 \pi V \)
\( c \cdot V \)
D. \( \pi V / 4 \)


An example for cationic detergent is?
A. NaLs
B. СТАВ
c. Trimethyl phosphate
D. All


\( P\left(\frac{B}{A}\right) \) is defined only when:
A . \( A \) is a sure event
B. \( B \) is a sure event
c. \( A \) is not an impossible event
D. \( B \) is an impossible event


8 different things are arranged around a
circle. In how many ways can 3 objects be selected when no two of the selected
objects are consecutive.


Atomic number is given by the number of \( \quad \) of an atom.
A. neutrons
B. electrons
c. protons
D. All of the above


A particle oscillates simple harmonically with a period of 16 s. Two second after crossing the equilibrium position its velocity becomes \( 1 \mathrm{m} / \mathrm{s} \). The amplitude is
A \( \cdot \frac{\pi}{4} \mathrm{m} \)
B. \( \frac{8 \sqrt{2}}{\pi} \mathrm{m} \)
c. \( \frac{8}{\pi} \mathrm{m} \)
D. \( \frac{4 \sqrt{2}}{\pi} \mathrm{m} \)


To construct a parallelogram, the minimum number of measurements
required is
A. 5
B. 4
\( c \cdot 3 \)
D.


A very slight decrease in atomic radius
occurs in a transition series when
compared with that in a representative series. This is due to:
A. shielding effect
B. penetrating effect
c. inert pair effect
D. bonding nature


Multiplication distributes over
substraction of rational numbers.
If true then enter 1 and if false then
enter 0


Two rigid boxes containing different ideal gases are placed on a table. Box \( A \)
contains one mole of \( N_{2} \) at temperature
\( T_{0}, \) while box \( \mathrm{B} \) contains one mole of \( \boldsymbol{H}_{2} \)
at temperature \( 7 / 3 T_{0} . \) The boxes
are then put into thermal contact with
each other and heat flows between them
until the gases reach a common final temperature [lgnore the heat capacity of boxes]. Then the final
temperature of the gases \( T_{f} \) in terms of
\( \boldsymbol{T}_{0} \) is
A \( \cdot T_{f}=\frac{5}{2} \) To
B \( T_{f}=\frac{3}{7} T o \)
c. \( T_{f}=\frac{5}{3} \) To
D. \( T_{f}=\frac{3}{2} \) To


State any three demerits of Mendeleev's
periodic table.


If \( \boldsymbol{\alpha}, \boldsymbol{\beta}, \boldsymbol{\gamma}, \boldsymbol{\delta} \) are the smallest \( + \) ive angles
in ascending order of magnitude which have their sines equal to a +ive quantity \( \lambda \) then the value of \( 4 \sin \frac{\alpha}{2}+ \) \( 3 \sin \frac{\beta}{2}+2 \sin \frac{\gamma}{2}+\sin \frac{\delta}{2}= \)
A \( \cdot 2 \sqrt{1-\lambda} \)
B. \( 2 \sqrt{1+\lambda} \)
c. \( 2 \sqrt{\lambda} \)
D. \( 2 \sqrt{\lambda+2} \)


In redox reactions, oxidation state of oxidising agent and reducing agent respectively
A. Increases and decreases
B. Decreases and increases
c. Increases and remains same
D. Decreases and remains same


Which gases were unknown at the time of Mendeleev?
A. Oxygen
B. Noble gases
\( c \cdot C O_{2} \)
D. None of the above


What is the maximum numbers of
sterioisomers that could exist for the
compound below?
\( A \)
B
\( c \cdot 10 \)
\( D \)


The coordinates of the vertices of a
triangle are \( \left(x_{2}, y_{2}\right) \) and \( \left(x_{3}, y_{3}\right) . \) The line joining the first two is divided in the ratio I : \( k \), and the line joining this point of division to the opposite angular point is then divided in the ratio \( \mathrm{m}: \mathrm{k}+ \)
I. Find the coordinates of the latter point of section.


To know the opinion of the students about Mathematics, a survey of 200 students was conducted. The data is
recorded in the following table:
Opinion:

Dislike
Number of students: \( \quad 135 \quad \) 65

Find the probability that a student chosen at random likes Mathematics


Find out the major product in given reaction.
\( \boldsymbol{H}_{5} \boldsymbol{C}_{6} \boldsymbol{C H O}+ \)
\( \boldsymbol{H}_{3} \boldsymbol{C C H}_{2} \boldsymbol{C H O} \stackrel{\text {dil.NaOH}}{\longrightarrow} ? \)


Change of state is also called as
A. phase change
B. mass change
c. volume change
D. particle change


Assertion:At constant pressure when a
gas is heated from 40 to \( 41^{0} \mathrm{C} \), the increase in volume is \( \frac{1}{273} \) of its initial volume at \( 273 \mathrm{K} \)
Reason:Volume coefficient of gas is \( \frac{1}{273}^{0} C \)
A. Both assertion (A) and reason
(R) are correct and gives the correct explanation
B. Both assertion (A) and reason
(R) are correct but R doesnt give the correct explanation
C. A is true but R is false
D. A is false but R is true


At a certain place, the angle of dip \( 30^{\circ} \) and the horizontal component of earth's
magnetic field is 0.50 oerested.The earth's total magnetic field (in oerested) is
A. \( \sqrt{3} \)
B.
c. \( \frac{1}{\sqrt{3}} \)
D. \( \frac{1}{2} \)


Find the degree of homogeneity of function \( \boldsymbol{f}(\boldsymbol{x}, \boldsymbol{y})=\boldsymbol{a} \boldsymbol{x}^{2 / 3}+\boldsymbol{h} \boldsymbol{x}^{1 / 3} \boldsymbol{y}^{1 / 3}+ \)
\( b y^{2 / 3} \)
\( A \cdot 2 / 3 \)
B. 2
\( c \cdot 3 \)
D. 3/2


What is the angle between \( \vec{A} \) and the resultant of \( (\overrightarrow{\boldsymbol{A}}+\overrightarrow{\boldsymbol{B}}) \) and \( (\overrightarrow{\boldsymbol{A}}-\overrightarrow{\boldsymbol{B}}) \)
\( \mathbf{A} \cdot 0^{\circ} \)
B \( \cdot \tan ^{-1}\left(\frac{A}{B}\right) \)
\( ^{\mathbf{c}} \cdot \tan ^{-1}\left(\frac{B}{A}\right) \)
D. \( \tan ^{-1}\left(\frac{A-B}{A+B}\right) \)


It takes you 9.5 minutes to walk with an average velocity of \( 1.2 m / s \) to the north
from the bus stop to museum entrance. What is your displacement? (in m)
A. 684
в. 540
c. 525
D. 565


Name the first artificial satellite sent by Russia in space.


Which of the following factors do not influence the capacity of a capacitor?
A. distance between the plates
B. material of the plates
c. area of the plates
D. curvature of the plates


Energy of electron is an orbit of H-atom is
A. Positive
B. Zero
c. Negative
D. Unity


IUPAC name of this compound \( \boldsymbol{H}_{3} \boldsymbol{C} \quad \boldsymbol{C}_{2} \boldsymbol{H} \)
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2}-\underset{\boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{C H}_{2} \boldsymbol{C H}_{3}}{\boldsymbol{C}} \boldsymbol{H}-\boldsymbol{C}_{2} \boldsymbol{H}_{5} \)


(a) Derive a relation for electric field
due to an electric dipole at a point on the equatorial plane of the electric dipole. Draw necessary diagram.
(b) An electric dipole of charge \( \pm 1 \mu C \) exists inside a spherical Gaussian
surface of radius \( 1 c m \). Write the value
of outgoing flux from the Gaussian
surface.
(c) Potential on the surface of a
charged spherical shell of radius \( 10 \mathrm{cm} \)
is \( 10 V . \) Write the value of potential at \( 5 c m \) from its centre.


if \( \sin \theta=\frac{4}{5}, \) Find the value of \( \frac{4 \tan \theta-5 \cos \theta}{\sec \theta+4 \cot \theta} \)


Consider the following elementary reaction,
\[
\mathbf{2 A}+\boldsymbol{B}+\boldsymbol{C} \rightarrow \boldsymbol{\text {Products.}}
\]
All reactant are present in the gaseous
state and reactant \( C \) is taken in excess.
What is the rate expression of the
reaction?
\( \mathbf{A} \cdot \) Rate\( =k[A]^{2}[B][C] \)
B . Rate\( =k[A]^{2}[B] \)
\( c \)
\[
\text {Rate}=k \frac{[A]^{2}[B]}{[C]}
\]
D. Rate\( =k[C]^{0} \)


Draw a labelled diagram of a moving coil galvanometer and explain its
working. What is the function of radial magnetic field inside the coil?


In humans, the \( _{--}-_{-}-_{-} \) fluid present in pericardium protects the heart from injuries.
A. Pleural
B. Mucosal
c. Pericardial
D. None of the above


Show that the position vector of the point \( P, \) which divides the line joining the points \( A \) and \( B \) having position vector \( \vec{a} \) and \( \vec{b} \) internally in the ratio \( m: n \) is \( \frac{m \vec{b}+n \vec{a}}{m+n} \)


The ionisation constant of acetic acid is
\( 2 \times 10^{-5} . \) The \( p H \) of buffer containing
acetic acid and sodium acetate is 4.7
The acid and salt ratio in the buffer is :
\( A \). one : one
B. ten: one
c. one : ten
D. two : one


Find the continued products:
\( (\mathbf{i})(\boldsymbol{x}+\mathbf{2})(\boldsymbol{x}-\mathbf{2})\left(\boldsymbol{x}^{\mathbf{2}}-\mathbf{4}\right) \)
(ii) \( (a x+b)(a x-b)\left(a^{2} x^{2}+b^{2}\right) \)


Soil that is rich in soluble salts is
A. Laterite
B. Halomorphic
c. calcimorphic
D. None of these


The area (in sq. units) of the region
bounded by the curves \( y=2^{x} \) and \( y= \)
\( |x+1|, \) in the first quadrant is:
\( ^{\mathbf{A}} \cdot \frac{3}{2}-\frac{1}{\log _{e} 2} \)
в. \( \frac{1}{2} \)
\( ^{\mathrm{C}} \cdot \log _{e} 2+\frac{3}{2} \)
D.


The maximum kinetic energy of the
photoelectrons emitted is doubled when the wavelength of light incident on the
photosensitive surface changes from \( \lambda_{1} \)
to \( \lambda_{2} \). Deduce expressions for the threshold wavelength and work function
for the metal surface in terms of \( \lambda_{1} \) and
\( \lambda_{2} \)


\( \sum_{i}^{\infty} \)


Which of the following are the advantages of having low centre of gravity? This question has multiple correct options
A. It can corner at high speed,
B. Much less risk of toppling over
c. It requires enough turning force to tip you over
D. None of the above


Air contains \( 79 \% N_{2} \) and \( 21 \% O_{2} \) by
volume. If the barometric pressure is \( 750 m m H g \) the partial pressure of
oxygen is:
\( \left(d N_{2}=1.25, d O_{2}=1.42 g / m\right) \)
A. \( 157.5 \mathrm{mm} \) of \( \mathrm{Hg} \)
в. \( 175.5 \mathrm{mm} \) of \( \mathrm{Hg} \)
c. \( 315.0 \mathrm{mm} \) of \( \mathrm{Hg} \)
D. None


The simultaneous equations, \( \boldsymbol{y}=\boldsymbol{x}+ \)
\( \mathbf{2}|\boldsymbol{x}| \) \& \( \boldsymbol{y}=\mathbf{4}+\boldsymbol{x}-|\boldsymbol{x}| \) have the solution
set
\( ^{\mathrm{A}} \cdot\left(\frac{4}{3}, \frac{4}{3}\right) \)
в. \( \left(4, \frac{4}{3}\right) \)
\( ^{c} \cdot\left(-\frac{4}{3}, \frac{4}{3}\right) \)
D. None of these


Let \( z \) and \( w \) be two non-zero
complex numbers such that \( |z|=|\boldsymbol{w}| \)
and \( \arg (z)+\arg (w)=\pi, \) then \( z \)
equals
A. \( -w \)
в. \( w \)
\( c \cdot \bar{w} \)
D. \( -\bar{w} \)


In the quadrilateral \( \boldsymbol{A B C D}, \boldsymbol{A D}= \)
\( C D \) and \( \angle A=90^{\circ}=\angle C . \) Prove that
\( \boldsymbol{A B}=\boldsymbol{B C} \)


The total work done on a particle is
equal to the change in its kinetic
energy.
This statement is true for which of the
condition?
A. always
B. only if the forces acting on the body are conservative
C. only if the forces acting on the body are gravitational
D. only if the forces acting on the body are elastic.


A reaction that occurs only when heat
is added is best described as:
A. Exothermic
B. Endothermic
c. An equilibrium process
D. spontaneous
E. Non-spontaneous


When the observer and reflector are at
rest, the echo and the original sound differ in
A. Frequency
B. Wavelength
c. velocity
D. Intensity of sound


Two brass solid spheres have radiii in the ratio \( 1: 2 . \) About the axis passing through their centres, the ratio of thier moments of inertia of is:
A .1: 4
B. 1: 8
c. 1: 16
D. 1: 32


Number of moles of solute in solution is
represented by :
A. \( M \times V(L) \)
в. \( M \times V(m l) \)
c. \( m \times V(L) \)
D. \( N \times V(m l) \)


A condition is which the body's internal
environment remains relatively constant within limits is
A. Hematoma
B. Homeostasis
c. Haemopoiesis
D. Hemostasis


The MacArthur-Forrest process is used for the extraction of:
A. \( C u \)
в. \( A g \)
c. \( F e \)
D. \( Z n \)


Choose the correct statement about the
properties of magnetic lines of forces.
A. Lines of force are not imaginary lines
B. Lines of force cannot be mapped on paper
c. Lines of force do not intersect each other
D. Lines of force always intersect each other


Which one of the following does not
contains electrons in \( 4 s \) subshells?
Given that : Atomic numbers: \( \boldsymbol{T} \boldsymbol{i}= \)
\( \mathbf{2 2}, \boldsymbol{V}=\mathbf{2 3}, \boldsymbol{C r}=\mathbf{2 4}, \boldsymbol{M} \boldsymbol{n}=\mathbf{2 5} \)
A \( \cdot T i \)
B. \( V^{\text {t }} \)
\( c \cdot C r^{+} \)
D. \( M n^{+} \)


Instantaneous displacement current
\( 1 A \) in the space between the parallel
plates of \( 1 \mu F \) capacitor can be
established by changing the potential difference at the rate of:
A \( .0 .1 V / s \)
B. \( 1 V / s \)
c. \( 10^{6} V / s \)
D. \( 10^{-6} V / s \)


A reaction takes place in three steps with an individual rate constant and
activation energy, as given below.
Rate constant Activation
energy
Step 1 \( \quad \boldsymbol{k}_{\mathbf{1}} \quad \boldsymbol{E}_{\boldsymbol{a}_{1}}= \)
\( 180 k J / m o l \)
Step 2 \( \quad \boldsymbol{k}_{2} \quad \boldsymbol{E}_{\boldsymbol{a}_{2}}= \)
\( \mathbf{8 0 k J} / \) mol
Step 3 \( \quad k_{3} \quad \quad E_{a_{3}}= \)
\( \mathbf{5 0 k J / m o l} \)
And overall rate constant, \( k= \) \( \left(\frac{k_{1} k_{2}}{k_{3}}\right)^{2 / 3} \)
The overall activation energy of the reaction will be:
A. \( 140 k J / \) mol
в. \( 150 k J / m o l \)
c. \( 130 k J / m o l \)
D. \( 120 k J / m o l \)


We are able to see objects around us
because
A. The objects absorb all the light
B. The light reflected from the object enters our eyes
C. Light can be reflected
D. Light travels in straight lines


A heavy nucleus at rest breaks into two fragments which fly off with velocities
in the ratio \( 8: 1 . \) the ratio of de-broglie
wavelengths of fragments are
A . 1: 2
B. 1: 8
c. 4: 1
D. None of these


Which of the following carbohydrate is essential constituent of plant cell wall?
A. Starch
B. Sucrose
c. Cellulose
D. Maltose


In a one-dimensional elastic collision,
the relative velocity of approach before collision is equal to:
A. sum of the velocities of the bodies
B. \( e \) times the relative velocity of separation after collision
c. \( 1 / e \) times the relative velocity of separation after collision
D. relative velocity of separation after collision


Which of the following exhibits different colors in acidic and basic solutions?
A. Buffer
B. Indicator
C. Arrhenius acid
D. Arrhenius base
E. Neutral condition


Electron affinity of chlorine is \( -3.61 \mathrm{eV} \) \( I P \) value of the same element is 12.967
eV. \( 3 \times 10^{23} \) atoms of chlorine are
converted to \( C l^{-} \) ions and the energy
liberated is used to ionize chlorine
atoms to \( C l^{+} \) ions. How many chlorine atoms could be ionized in the above
process?
A \( .5 .45 \times 10^{21} \)
В. \( 6.11 \times 10^{18} \)
c. \( 8.35 \times 10^{22} \)
D. \( 7.11 \times 10^{28} \)


\( \frac{2}{3}(x-5)-\frac{1}{4}(x-2)=\frac{9}{2} \)


The differential equation for which \( \sin ^{-1} x+\sin ^{-1} y=c \) is given by:
A \( \cdot \sqrt{1-x^{2}} d y+\sqrt{1-y^{2}} d x=0 \)
B \( \cdot \sqrt{1-x^{2}} d x+\sqrt{1-y^{2}} d y=0 \)
C \( . \sqrt{1-x^{2}} d x-\sqrt{1-y^{2}} d y=0 \)
D. \( \sqrt{1-x^{2}} d y-\sqrt{1-y^{2}} d x=0 \)


Which law of Newton is called the law of
equilibrium?
A. Newtons first law of motion
B. Newtons second law of motion
c. Newtons third law of motion
D. Newtons law of gravitation


\( \ln H \) -atm spectrum \( V \) is the wave
number
\( \boldsymbol{V}_{1}=\boldsymbol{V}_{\min }+\boldsymbol{V}_{\max } \) for Lyman series
\( \boldsymbol{V}_{1}=\boldsymbol{V}_{\min }+\boldsymbol{V}_{\max } \) for Balmer series
then \( V_{1}: V_{2} \)
A . 9: 2
B. 3: 2
\( c .5: 2 \)
D. 7: 2


Evaluate:
\( (-10)+(+19) \)


The number of straight lines that are equally inclined to the threedimensional coordinate axes, is
A .2
B. 4
\( c .6 \)
D. 8


The inferior part of the nasal septum is formed by the
A. Incus
B. Vomer
c. stapes
D. All of the above


In a third order determinant, each
element of the first column consists of
sum of two terms, each element of the second column consists of sum of three
terms and each element of the
third column consists of sum of four
terms. Then it can be decomposed into n determinants, where n has the value
\( \mathbf{A} \cdot \mathbf{1} \)
B. 9
c. 16
D. 24


If a function is everywhere continuous
and differentiable such that \( f^{\prime}(x) \geq 6 \)
for all \( \boldsymbol{x} \epsilon[\mathbf{2}, \mathbf{4}] \) and \( \boldsymbol{f}(\mathbf{2})=-\mathbf{4}, \) then
\( \mathbf{A} \cdot f(4)<8 \)
в. \( f(4) \geq 8 \)
c. \( f(4) \geq 2 \)
D. none of these


Consider the following statements:
(a) Real image is always inverted
(b) Virtual image is always erect
(c) Image formed by a concave lens is always real and inverted Which of the above statement(s) is/are
correct?
A. Only (a)
B. Only (b)
c. (a) and (b)
D. All of the above


Solution of \( |4 x+3|+|3 x-4|=12 \) are
A \( \cdot x=-\frac{7}{3}, \frac{3}{7} \)
в. \( x=-\frac{5}{2}, \frac{2}{5} \)
c. \( _{x=-\frac{11}{7}}, \frac{13}{7} \)
D. \( x=-\frac{13}{7}, \frac{11}{7} \)


Assertion
A small power circuit that is isolated from ground typically is less dangerous.
Reason
Its contacting just one power wire will
not form a complete circuit path, and it
is too small to collect large dangerous
atmospheric charge potentials.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The power output of an automobile engine is advertised to be 200 hp at 600 rpm. Find the corresponding torque.
\( A \cdot 137 N m \)
в. 237Nm
c. 337Nm
D. 287Nm


Write all the four quantum no.for \( \boldsymbol{p}- \)
electrons of \( _{7} \mathbf{N}^{14} \)
A \( \cdot n=3, l=2, m=-1,0,+1 ; s=+\frac{1}{2} \) and \( -\frac{1}{2} \)
B. \( n=2, l=1, m=-1,0,+1 ; s=+\frac{1}{2} \) or \( -\frac{1}{2} \)
c. \( _{n=2, l=1, m=-1,0,+1 ; s=+\frac{1}{2}} \)
D. \( n=2, l=0, m=0 ; s=+\frac{1}{2} \) and \( -\frac{1}{2} \)


The acceleration \( \alpha \) of a particle moving with an velocity \( u \) varies with distance
\( x \) as \( a=k \sqrt{x} \) where \( k \) is a constant. Th
distance covered by the particle when its velocity become \( 3 u \) is given by
\( ^{\mathrm{A}} \cdot\left(\frac{3 u^{2}}{k}\right)^{2 / 3} \)
B. \( \left(3 k u^{2}\right)^{4 / 3} \)
\( ^{\mathrm{C}} \cdot\left(\frac{6 u^{2}}{k}\right)^{2 / 3} \)
D. \( \left(\frac{u^{2}}{3 k}\right)^{2 / 3} \)


If \( \boldsymbol{I}=\int_{0}^{1 / \sqrt{3}} \frac{\boldsymbol{d} \boldsymbol{x}}{\left(1+\boldsymbol{x}^{2}\right) \sqrt{1-\boldsymbol{x}^{2}}} \) then \( \boldsymbol{I} \) is
equal to
\( \mathbf{A} \cdot \pi / 2 \)
B. \( \pi / 2 \sqrt{2} \)
c. \( \pi / 4 \sqrt{2} \)
D . \( \pi / 4 \)


A and B are:
\( \mathrm{B} \prec \mathrm{NaBH}_{4}\langle\quad \mathrm{CH}=\mathrm{CH}-\mathrm{CHO} \stackrel{\mathrm{H}_{2} / \mathrm{Pt}}{\longrightarrow} \mathrm{A} \)
\( A \)
\( \left\langle-\mathrm{cH}_{2} \mathrm{CH}_{2} \mathrm{cHo},\langle\quad\rangle_{\mathrm{CH}}=\mathrm{cH}-\mathrm{cH}_{2} \mathrm{OH}\right. \)
\( c \)
\( \left\langle\mathrm{CH}=\mathrm{CH}-\mathrm{CH}_{2} \mathrm{OH} \) in both cas \right.
\( D \)
\( \left\langle\mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{OH} \) in both cases \right.


The molecule which does not exhibit
strong hydrogen bonding is:
A. Methyl amine
B. Diethyl ether
c. Acetic acid
D. Glucose


Who was the discoverer of neutrons???
A. Ernest Rutherford
B. J. J. Thomson
c. James Chadwick
D. None of the above


In which of the following species,
the inter-atomic bond angle is \( 109^{\circ} 28^{\prime} ? \)
A \( . N H_{4}^{+},\left(B F_{4}\right) \)
B . \( \left(N H_{4}\right)^{+}, B F_{3} \)
c. \( N H_{3}, B F_{4} \)
D. \( \left(N H_{2}\right)^{-}, B F_{3} \)


\( C N^{\ominus} \) ion is oxidised by a powerful
oxidising agent to \( N O_{3}^{\ominus} \) and \( C O_{2} \) or
\( C O_{3}^{2-} \) depending on the acidity of the
reaction mixture.
\( \boldsymbol{C N}^{\ominus} \longrightarrow \boldsymbol{C O}_{2}+\boldsymbol{N O}_{3}^{\ominus}+\boldsymbol{H}^{\oplus}+\boldsymbol{n} e^{-} \)
What is the number \( (n) \) of electrons
involved in the process?


Branch of biology dealing with heredity and variations is
A. Ecology
B. Evolution
c. Palaeontology
D. Genetics


In hypermetropia, the image of near object is formed:
A. Before the retina
B. On retina
c. Behind the retina
D. Above the retina


\( C H_{3} C H_{2} C O C l \) What is the name of
this compound?
A. Butanoyl chloride
B. Propanoyl chloride
c. 1 chloro propanone
D. None of these


The conductivity of intrinsic semiconductor decreases with increase
in temperature
A. True
B. False


In a packet there are m different books, n different pens and p different pencils. The number of selections of at least one
article of each type from the packet is
A \( \cdot 2^{m+n+p}-1 \)
B . \( (m+1)(n+1)(p+1)-1 \)
\( \mathbf{c} \cdot 2^{m+n+p} \)
D - \( \left(2^{m}-1\right)\left(2^{n}-1\right)\left(2^{p}-1\right) \)


Resonance in a molecule results in:
A. Destabilisation
B. Stabilisation
c. Increase in bond length
D. None of the above


How many alkyne/ alkynes gives following ketone as the only product on hydrolysis by sulphuric acid, water and
\( \boldsymbol{H} \boldsymbol{g} \boldsymbol{S} \boldsymbol{O}_{4} ? \)
4
B. 2
\( c \)
\( D \)


The compound \( l-(N-\text {ethyl}-N- \)
methyl \( )- \) propanamine forms non-
superimposable mirror images. But this compound does not show optical activity because of the:
A. Absence of a chiral N atom
B. Presence of chiral N atom
c. Presence of lone pair on \( \mathrm{N} \) atom
D. Rapid flipping of one form into the other


Describe an experiment to show that a black (or dull) surface is a better
absorber of heat radiations than a
polished one.


How many of the following plants given below possess open (X) and closed vascular bundles (Y) respectively? Brassica, Tulipa, Capsicum, Gloriosa, Nicotiana, Aloe, Cicer, Asparagus, Petunia, Colchicum, Sesbania, Zea.
\( A \cdot X=6, Y=6 \)
B. \( x=4, Y=8 \)
c. \( x=5, Y=7 \)
D. \( x=9, Y=3 \)


Arrange the following limits in the ascending order:
(1) \( \lim _{x \rightarrow \infty}\left(\frac{1+x}{2+x}\right)^{x+2} \)
(2) \( \lim _{x \rightarrow 0}(1+2 x)^{3 / x} \)
(3) \( \lim _{\boldsymbol{\theta} \rightarrow \mathbf{0}} \frac{\sin \boldsymbol{\theta}}{\mathbf{2} \boldsymbol{\theta}} \)
(4) \( \lim _{x \rightarrow 0} \frac{\log _{e}(1+x)}{x} \)
A. 1,2,3,4
B. 1,3,4,2
c. 1,4,3,2
D. 3,4,1,2


Current is induced in a coil by
electromagnetic induction when
A. Only the coil moves in a magnetic field
B. Only the magnet moves towards the coil
C. Coil and the magnet move with respect to each other
D. None of the above


A body is projected horizontally from the top of a tower with initial velocity
\( 18 m s^{-1} . \) It hits the ground at angle \( 45^{\circ} \)
What is the vertical component of velocity when strikes the ground?
B. \( 18 m s^{-1} \)
\( \mathrm{D} \cdot 9 \mathrm{ms}^{-1} \)


Ordered pair that satisfy the equation
\( \boldsymbol{x}+\boldsymbol{y}+\mathbf{1}<\mathbf{0} \) is:
в. (-2,0)
c. (2,-4)
D. Both (B) and (C)


In the formation of sulphur trioxide by
the contact process \( 2 S O_{2}(g)+ \)
\( O_{2}(g) \rightarrow 2 S O_{3}(g) \)
The rate of reaction is expressed as \( -\frac{d\left(O_{2}\right)}{d t}= \)
\( 2.5 \times 10^{-4} \) mol
\( L^{-1} \sec ^{-1} \) The rate of disappearance of
\( \left(\boldsymbol{S O}_{2}\right) \) will be:
A. \( 5 \times 10^{-4} \) molL \( ^{-1} S^{-1} \)
В. \( -1.25 \times 10^{-4} \) тод \( L^{-1} S^{-1} \)
c. \( 3.75 \times 10^{-4} \) molL \( ^{-1} S^{-1} \)
D. \( 50.0 \times 10^{-4} \) molL \( ^{-1} S^{-1} \)


During summer, if you go near the lake, you feel relief from heat. Why?


Phenol is heated with a solution of a
mixture of \( K B r \) and \( K B r O_{3} . \) The major
product obtained in the above reaction
is:
A. 2 -bromophenol
B. 3-bromophenol
c. 4 -bromophenol
D. 2,4,6 -tribromophenol


Which of the following is/are autoredox
reactions?
This question has multiple correct options
A \( \cdot P_{4}+O H \longrightarrow H_{2} P O_{2}^{\ominus}+P H_{3} \)
B . \( S_{2} O_{3}^{2-} \rightarrow S O_{4}^{2-}+S \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{O}_{2} \longrightarrow \mathrm{H}_{2} \mathrm{O}+\mathrm{O}_{2} \)
D. \( _{A g C l}+N H_{3} \rightarrow\left[A g\left(N H_{3}\right)_{2}\right] C l \)


One litre of a sample of hard water
contain \( 4.44 m g C a C l_{2} \) and \( 1.9 m g \) of
\( M g C l_{2}, \) what is the total hardness in
terms of ppm of \( \boldsymbol{C} \boldsymbol{a} \boldsymbol{C O}_{3} \)
\( A \cdot 2 \) ppm
B. 3 ppm
c. 4 ppm
D. 6 ppm


A square of side \( 3 \mathrm{cm} \) is located at a
distance \( 25 \mathrm{cm} \) from a concave mirror
of focal length \( 10 \mathrm{cm} \). The center of square is at the axis of the mirror and the plane is normal to axis of mirror. The
area enclosed by the image of the square is :
A \( \cdot 4 c m^{2} \)
в. \( 6 \mathrm{cm}^{2} \)
c. \( 16 \mathrm{cm}^{2} \)
D. \( 36 c m^{2} \)


Identify the products \( A \) and \( B \)


\( \left(\frac{2 a x}{a^{2}+x^{2}}\right)+\frac{1}{3}\left(\frac{2 a x}{a^{2}+x^{2}}\right)^{3}+ \)
\( \frac{1}{5}\left(\frac{2 a x}{a^{2}+x^{2}}\right)^{5}+\dots= \)
\( A \cdot \log (a+x) \)
B. \( \log (a-x) \)
\( ^{\mathbf{C}} \cdot \log \left(\frac{a+x}{a-x}\right) \)
\( D \)


The oxoacid of sulphur which contains
two sulphur atoms in different
oxidation states is:
A. pyrosulphurous acid
B. hyposulphurous acid
c. pyrosulphuric acid
D. persulphuric acid


The colour of iodine is:
A . violet
B. green
c. white
D. brown


\( (1+i)^{n} \) find min \( + \) ve integer n such
that it represents (i) an integer
(ii) a +ve integer


On heating with conc. \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3}, \) proteins give yellow color. This test is called:
A . oxidising test
B. xanthoproteic test
c. Hoppe's test
D. acid-base test


Find domain and range of
\( \boldsymbol{R}=\{(\boldsymbol{a}, \boldsymbol{b}) / \boldsymbol{a} \in \boldsymbol{N}, \boldsymbol{a}<\mathbf{5} \text { and } \boldsymbol{b}=\mathbf{2}\} \)


Amongst the following the total number
of elements, which produce \( \boldsymbol{H}_{2} \) gas with sodium hydroxide is:
\( \mathrm{Zn}, \mathrm{Al}, \mathrm{Sn}, \mathrm{Pb}, \mathrm{P}, \mathrm{Si} \)
A. 3
B. 4
\( c \cdot 5 \)
\( D \cdot 6 \)


Two charges when kept at a distance of \( 1 m \) apart in vacuum have some force of
repulsion. If the force of repulsion between these two charges be same, when placed in an oil of dielectric
constant \( 4, \) the distance of separation is :
\( \mathbf{A} \cdot 0.25 m \)
в. \( 0.4 m \)
\( c .0 .5 m \)
D. \( 0.6 m \)


Two spherical bodies having masses \( M \) and \( 3 M \) and radii \( r \) and \( 4 r \) respectively are released in free space rest such that the initial separation between their
centres is \( 13 r \). If only force is gravitational attraction distance covered by the smaller bodyjust before collision is.
A \( \cdot 6 r \)
B . \( 2 r \)
c. \( \frac{9}{4 r} \)
D. \( \frac{39 r}{4} \)


\( \boldsymbol{f}(\boldsymbol{x})=\sec \boldsymbol{x}-\cos \boldsymbol{x}, \boldsymbol{x} \boldsymbol{\epsilon}(\mathbf{0}, \boldsymbol{\pi} / \mathbf{2}) \)
find \( \mathrm{f}^{\prime}(\mathbf{x}) \)


Why a saturated hydrocarbon does not undergo addition reactions?
A. They have low stability
c. They have low boiling points
D. All of above


If the relation between acceleration and
time for an object is given by \( a=2 t+ \)
\( 4 t^{2} \)
Calculate the position of object from the origin at \( t=4 s(\text { At } t=0, v=0, x=0) \)


Potential difference is measured in
joules.
A . True
B. False


The presistence of the eye is only for:
A. \( 1 / 100 \) th of a second
B. 1/120th of a second
c. \( 1 / 16 \) th of a second
D. \( 1 / 20 \) oth of a second


The no. of \( \boldsymbol{P}-\boldsymbol{O}-\boldsymbol{P} \) bond(s) in cyclic
metaphosphoric acid is(are):
\( \mathbf{A} \cdot \mathbf{0} \)
B . 2
\( c .3 \)
D.


Logically equivalent statement to \( \boldsymbol{p} \leftrightarrow \boldsymbol{q} \)
is
\( \mathbf{A} \cdot(p \rightarrow q) \wedge(q \rightarrow p) \)
\( \mathbf{B} \cdot(p \wedge q) \vee(q \rightarrow p) \)
\( \mathbf{c} \cdot(p \wedge q) \rightarrow(q \vee p) \)
D. none of these


An optical device used by watch repairers is


Draw the magnetic field lines of the field produced by a current carrying circular loop. Explain with reason whether the field will be stronger at a
point at the center of loop or near the circumference of loop.


Predict major product \( Y \) in the following reaction:
\( A \)
B.
\( c \)
D. Both b and c


Identify the wrong statement.
\( A . \) In an electric field two equipotential surfaces can never intersect
B. A charged particle free to move in an electric field shall always move in the direction of \( E \)
C. Electric field on the surface of a charged conductor is always normal to the surface
D. The electric potential decrease along a line of force in an electric an electric field


What is the least number which must
be subtracted from 369 to make it a
perfect cube?
\( \mathbf{A} \cdot \mathbf{8} \)
B . 26
\( c \cdot 2 \)
D. 25


\( \left(C H_{3}\right)_{3} C M g B r \) on reaction with \( D_{2} O \)
produces:
A \( \cdot\left(C H_{3}\right)_{3} C D \)
в. \( \left(C H_{3}\right)_{3} C O D \)
\( \mathbf{c} \cdot\left(C D_{3}\right)_{3} C D \)
D \( \cdot\left(C D_{3}\right)_{3} O D \)


The fraction of a radioactive material
which remains active after time \( t \) is
\( \mathbf{9} / \mathbf{1 6} . \) The fraction which remains active after time \( t / 2 \) will be
A \( \cdot \frac{4}{5} \)
B. \( \frac{7}{8} \)
\( c \cdot \frac{3}{5} \)
D. \( \frac{3}{4} \)


What type of a relation is "Less than" in the set of real numbers?
A. only symmertric
B. only transitive
c. only reflexive
D. equivalence relation


A ball of mass \( m \) moving with a speed
\( 2 v_{0} \) collides head-on with an identical
ball at rest. If \( e \) is the coefficient of
restitution, then what will be the ratio of velocity of two balls after collision?
A \( \cdot \frac{1-e}{1+e} \)
в. \( \frac{1+e}{1-e} \)
c. \( \frac{e-1}{e+1} \)
D. \( \frac{e+1}{e-1} \)


Simplify: \( \left(-\frac{4}{5}\right)^{4} \)


The ammonia evolved from the
treatment of \( 0.30 g \) of an organic compound for the estimation of nitrogen was passed in \( 100 m L \) of 0.1 \( M \) sulphuric acid. The excess of acid required \( 20 m L \) of \( 0.5 M \) sodium hydroxide solution for complete neutralization. The organic compound is:
A. acetamide
B. benzamide
c. urea
D. thiourea


If \( y=\tan ^{-1}\left(\frac{2^{x}}{1+2^{2 x+1}}\right), \) then \( \frac{d y}{d x} \) at
\( \boldsymbol{x}=\mathbf{0} \) is \( ? \)
\( A \cdot-\frac{1}{5} \)
B. 2
\( c \cdot \epsilon 2 \)
D. none of these


What is the range of wavelength of the spectrum of white light in \( n m ? \)
A. \( 400 n m \) to \( 500 n m \)
B. \( 500 n m \) to \( 600 n m \)
c. \( 600 n m \) to 800 nm
D. All the above


The value of \( 500.0 m+600 m m \) with
due regards to significant figures is:
\( \mathbf{A} .501 m \)
в. 500.6 т
c. \( 500.600 m \)
D. none of these


If \( z_{1} \) and \( z_{2} \) are two non-zero complex number such that \( \left|\frac{z_{1}}{z_{2}}\right|=2 \) and
\( \arg \left(z_{1} z_{2}\right)=\frac{3 \pi}{2}, \) then \( \frac{\overline{z_{1}}}{z_{2}} \) is equal to
A. 2
B . - -
\( c \cdot-2 \)
D.


If two events \( A \) and \( B \) are such that
\( \boldsymbol{P}\left(\boldsymbol{A}^{\prime}\right)=\mathbf{0 . 3}, \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 4} \) and
\( \boldsymbol{P}\left(\boldsymbol{A} \cap \boldsymbol{B}^{\prime}\right)=\mathbf{0 . 5}, \operatorname{then} \boldsymbol{P}\left(\frac{\boldsymbol{B}}{\boldsymbol{A} \cup \boldsymbol{B}^{\prime}}\right) \)
equala
A \( \cdot \frac{3}{4} \)
B.
\( c \cdot \frac{1}{4} \)
D.