If \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}, \boldsymbol{g}(\boldsymbol{x})=\boldsymbol{2} \boldsymbol{x}^{2}+\mathbf{1} \) and \( \boldsymbol{h}(\boldsymbol{x})= \)
\( x+1 \) then \( (\text {hogof})(x) \) is equal to
A \( \cdot x^{2}+2 \)
B. \( 2 x^{2}+1 \)
c. \( x^{2}+1 \)
D. \( 2\left(x^{2}+1\right) \)


Molarity of a liquid \( H_{2} S O_{4} \) with density \( 1.2 g / c c \) is
A . 36.
B. 12.24
c. 1.224
D. 5.0


Natural history of man is
A. Anthropology
B. Anthology
c. Euthenics
D. Eugenics


Assertion
When an electric current is passed through an aqueous solution of sodium chloride, sodium ions move towards cathode and chloride ions move towards
anode.
Reason
Cathode is a negatively charged electrode and therefore attracts \( \mathrm{Na}^{+} \)
ions. Anode is a positively charged
electrode and therefore attracts \( \mathrm{Cl}^{-} \)
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. Assertion is incorrect but Reason is correct


A ball is thrown vertically upwards from the ground. It crosses a point at the height of \( 25 m \) twice at an interval of
4 secs. The ball was thrown with the
velocity of
A. \( 20 \mathrm{m} / \mathrm{sec} \)
B. \( 25 \mathrm{m} / \mathrm{sec} \)
c. \( 30 m / \)sec.
D. \( 35 \mathrm{m} / \mathrm{sec} \)


Let \( \boldsymbol{f}: \mathbb{R} \rightarrow \mathbb{R} \) be twice continuously
differentiable. Let \( \boldsymbol{f}(\mathbf{0})=\boldsymbol{f}(\mathbf{1})= \)
\( \boldsymbol{f}^{\prime}(\mathbf{0})=\mathbf{0} . \) Then
A \( . f^{\prime \prime}(x) \neq 0 \) for all \( x \)
B. \( f^{\prime \prime}(c)=0 \) for some \( c \epsilon \mathbb{R} \)
c. \( f^{\prime \prime}(x) \neq 0 \) if \( x \neq 0 \)
D. \( f^{\prime}(x)>0 \) for all \( x \)


A thin plano-convex lens of focal length
\( f \) is split into two halves. One of the
halves is shifted along the optical axis.
The separation between the object and
image planes is 1.8 m. The
magnification of the image formed by
one of the half lenses is 2

Find the focal length of the lens used.
\( \mathbf{A} \cdot 0.4 m \)
B. \( 0.8 m \)
\( \mathbf{c} .0 .6 m \)
D. \( 2 m \)


Graph the solution set
\( |x| \geq 3 \)
\( A \cdot(-3,3) \)
B \( \cdot(-\infty,-3] \cap[3, \infty) \)
\( \mathbf{c} \cdot(-\infty,-3) \cap(3, \infty) \)
D. [-3,3]
\( \langle 1,1,-7,6-5,-4 \)


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


Verify that \( y=a e^{-x} \) is a solution of \( \frac{d^{2} y}{d x^{2}}=\frac{1}{y}\left(\frac{d y}{d x}\right)^{2} \)


\( 0.57 g \) of an organic compound containing Phosphorus gave 2.47 g of ammonium phosphomolybdate by usual analysis. Calculate the percentage of Phosphorus in the given compound.
A . 78.5\%
B. 30\%
c. \( 5.41 \% \)
D. None of these


Evaluate: \( \int_{a}^{b} x d x \) using limit of sum.
A \( \cdot \frac{b^{2}-a^{2}}{3} \)
B. \( \frac{b^{2}+a^{2}}{2} \)
c. \( \frac{b^{2}-a^{2}}{2} \)
D. None of these


Q Type your question
of \( 0.7 m m \) diameter and suspended
vertically. The stone is now rotated in a horizontal plane at a rate such that wire
makes an angle of \( 85^{\circ} \) with the vertical
\( f Y=7 \times 10^{10} \mathrm{Nm}^{-2}, \sin 85^{\circ}=0.9962 \)
and \( \cos 85^{\circ}=0.0872, \) the increase in
length of wire is
\( A \cdot 1.67 \times 10^{-3} \mathrm{m} \)
B. \( 6.17 \times 10^{-3} \mathrm{m} \)
C \( \cdot 1.76 \times 10^{-3} \mathrm{m} \)
D. 7.16x10-3 \( m \)


Choose the correct answer.
\( \boldsymbol{H}_{3} \boldsymbol{O}^{+}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{O} \boldsymbol{H}^{-}(\boldsymbol{a} \boldsymbol{q}) \rightarrow \)
\( \mathbf{A} \cdot 2 H_{2} O(l) \)
в. \( 2 H_{2} O(s) \)
\( \mathrm{c} \cdot 2 \mathrm{H}_{2} \mathrm{O}(g) \)
D. \( H_{2} O(l) \)


A liquid will boil when:
A. enough salt has been added to it
B. the vapor pressure of the liquid is equal to the atmospheric or surrounding pressure
C. the vapor pressure of the liquid reaches \( 760 \mathrm{mmHg} \)
D. conditions favor the liquids molecules to be closer together
E. it has been brought up to a higher elevation


(i) Write the IUPAC name of the complex
\( \left[\boldsymbol{C r}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4} \boldsymbol{C l}_{2}\right] \boldsymbol{C l} \)
(ii) What type of isomerism is exhibited
by the complex \( \left[C o(e n)_{3}\right]^{3+} ? \) (en = ethane-1,2-diamine)
(iii) Why is \( \left[N i C l_{4}\right]^{2-} \) paramagnetic
but \( \left[N i(C O)_{4}\right] \) is diamagnetic?
(At. Nos. \( : \mathrm{Cr}=24, \mathrm{Co}=27, \mathrm{Ni}=28) \)


\( \sum_{i=1}^{2} \)


The heat capacity of a solid of mass 175
g is \( 315 J^{\circ} C^{-1} \). Calculate specific heat
capacity of solid.


In which of the following numbers, all the zeros are insignificant?
A . 0.0010
в. 0.00100
c. 0.001000
D. 0.001


Consider the following two statements A and B and identify the correct answer.
A) The work done in blowing a bubble of
volume \( V \) is \( W \), then the work done in
blowing a soap bubble of volume 2 V will be \( 2^{2 / 3} w \)
B) The excess pressure inside a soap bubble of diameter D and surface
tension \( \mathrm{S} \) is \( \frac{8 S}{D} \)
A. A\&B are false
B. A is false but B is true
C. A is true but B is false
D. A \& B are true


When the temperature of a metallic conductor is increased its resistance:
A. decreases
B. increases
c. may increase or decrease
D. remains the same


If a disc slides from top to bottom of an
inclined plane, it takes time \( t_{1} \). If it rolls, it takes time \( t_{2} . \) Now, \( \frac{t_{2}^{2}}{t_{1}^{2}} \) is
A \( \cdot \frac{1}{2} \)
B. \( \frac{2}{3} \)
\( c \cdot \frac{3}{2} \)
D. \( \frac{2}{5} \)


1 mol of ferric oxalate is oxidised
completely by \( x \) mol of \( M n O_{4}^{-} \) in acidic medium. Then, \( x \) is :
A . 1.2
в. 1.6
c. 1.8
D. 1.5


Light of frequency \( v \) is incident on a
metal of threshold frequency \( v_{0} . \) Then work function of metal will be:
A \( . h v \)
в. \( h v_{0} \)
\( \mathbf{c} \cdot h\left(v-v_{0}\right) \)
D. \( h\left(v+v_{0}\right) \)


Which one of the following heater element is used in electric press
A. Copper wire
B. Nichrome wire
c. Lead wire
D. Iron wire


The armature of a dc motor has \( 20 \Omega \)
resistance. It draws a current of \( 1.5 \mathrm{A} \)
when run by a \( 220 \mathrm{V} \) dc supply. The value of the back emf induced in it is
\( A \cdot 150 V \)
B. 170 V
c. \( 180 v \)
D. \( 190 \mathrm{v} \)


Which of the following countries of the world can be called socialist?
\( A \)
B. China
c. Nepal
D. U.S.A


Nuclei of isotopes differ in:
A. Number of protons
B. Number of neutrons
C. Number of neutrons and protons both
D. None of these


Let the interval \( I[-1,4] \) and \( f: I \rightarrow R \)
be a function such that \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{\boldsymbol{3}}- \)
\( 3 x \). Then the range of the function is
A . [2,52]
в. [-2,2]
\( \mathbf{c} \cdot[-2,52] \)
D. none of these


Two speakers A and B are placed 1 \( \mathrm{m} \)
apart, each produces sound waves of frequency \( 1800 \mathrm{Hz} \) in phase. \( \mathbf{A} \)
detector moving parallel to the line joining the speakers at a distance of 2.4
\( m \) away detects a maximum intensity
at 0 and then at \( P . \) Speed of the sound
wave is:
\( A \cdot 330 \mathrm{ms}^{-1} \)
B. 360 \( \mathrm{ms}^{-1} \)
c. \( 350 \mathrm{ms}^{-1} \)
D. \( 340 \mathrm{ms}^{-1} \)


Which of the following is correct?
\( A \cdot \sin 1^{\circ}>\sin 1 \)
B. \( \sin 1^{\circ}<\sin 1 \)
\( \mathbf{c} \cdot \sin 1^{\circ}=\sin 1 \)
D \( \cdot \sin 1^{\circ}=\frac{\pi}{180} \sin 1 \)


A \( 150 g \) cricket ball moving at a speed of \( 12 m / s \) is hit by a bat and turned back at a speed of \( 20 m / s . \) The duration of
impact is \( 0.1 s . \) What is the average
force exerted on the ball by the bat?


Assertion (A): Let \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) be a
function such that \( \boldsymbol{f}(\boldsymbol{X})=\boldsymbol{X}^{3}+\boldsymbol{X}^{2}+ \)
\( 3 X+\sin X, \) then \( f \) is one to one
Reason \( (R): f(x) \) is neither increasing nor decreasing function.
A. Both (A) and (R) are true and (R) is the correct explanation of (A)
B. Both (A) and (R) are true and (R) is not the correct explanation of (A).
c. (A) is true but (R) is false.
D. (A) is false but (R) is true


An oxide of lead changes to another insoluble oxide and soluble salt on
reaction with \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \)
(a) What is Oxide?
(b) What is insoluble oxide ?.
(c) What is soluble salt ?.
B \( \cdot(a) P b_{3} O_{3} ;(b) P b O_{2} ;(c) P b\left(N O_{3}\right)_{3} \)
C \( \cdot(a) P b_{3} O_{4} ;(b) P b O_{2} ;(c) P b\left(N O_{3}\right)_{2} \)
D. \( \left(\text { a) } P b_{3} O_{4} ;(b) P b O_{4} ;(c) P b\left(N O_{3}\right)_{3}\right. \)


\( A P \) and \( B P \) are the tangents drawn
from an external point \( \boldsymbol{P} \) to a circle with
center \( O \)
\( \angle A O B \) and \( \angle A P B \) are always
A. complementary
B. supplementary
c. obtuse angles
D. acute angles


Which of the following is considered to be the element between macro and
micro nutrients?
A. Iron
B. Nitrogen
c. Phosphorus
D. Manganese


Current flowing through the circuit


i. \( 0.1 M \) ethanol
ii. \( \mathbf{0 . 1} \boldsymbol{M} \boldsymbol{B} \boldsymbol{a}_{3}\left(\boldsymbol{P} \boldsymbol{O}_{4}\right)_{3} \)
¡¡ii.0.1 \( M N a_{2} S O_{4} \)
Increasing order of freezing point
A \( \cdot(i i)<(i i i)<(i) \)
B. \( (i i i)<(i i)<(i) \)
c. \( (i)<(i i)<(i i i) \)
D. \( (i i)<(i)<(i i i) \)


A ball of radius \( \boldsymbol{R}=\mathbf{1 0 . 0} \) cm rolls
without slipping on a horizontal plane
so that its centre moves with constant
acceleration \( a=2.50 \mathrm{cm} / s^{2} ; t=2.00 s \)
after the beginning of motion its
position corresponds to that shown in
Fig. Find:
(a) the velocities of the points \( A, B \) and
\( O \)
(b) the accelerations of these points.


Which of the following statements are correct about a planet rotating around the sun in an elliptical orbit? This question has multiple correct options
A . Its kinetic energy is constant
B. Its angular momentum is constant
c. Its real velocity is constant
D. Its time period is proportional to \( r^{3} \)


If \( y=A \sin (\omega t-k x), \) then the value of \( \frac{d y}{d x} \)
is
A. \( A \cos (\omega t-k x) \)
B. \( -A \omega \cos (\omega t-k x) \)
c. \( A k \cos (\omega t-k x) \)
D. \( -A k \cos (\omega t-k x) \)


Determine the nature of the roots of the
follwoing quadratic equation:
\( 2 x^{2}-6 x+3=0 \)


Generally transition elements for
coloured salts due to the presence of
unpaired electrons. Which of the following compound will be coloured in solid state?
A. \( A g_{2} S O_{4} \)
в. \( C u F_{2} \)
c. \( C u_{2} C l_{2} \)
D. \( Z n F_{2} \)


Write the units digit of the cube for 7171
\( A \cdot 1 \)
B. 2
\( c .5 \)
D. 3


A thief stole a box with valuable article
of weight \( W \) and jumped down a wall of
height \( h \). Before he reach the ground he
experienced a load of
A . zero
в. \( \frac{W}{2} \)
c. \( W \)
D. \( 2 W \)


A long block \( A \) is at rest on a smooth horizontal surface. A small block B
whose mass is half of mass of A is
placed on \( A \) at one end and is given an
initial velocity u as shown in Fig. 8.274 The coefficient of friction between the
blocks is \( \mu \)
This question has multiple correct options
A. Finally both move with a common velocity \( 2 u / 3 \)
B. Acceleration of B relative to A initially is \( 3 \mu g / 2 \) towards left.
c. Magnitude of total work done by friction is equal to the final kinetic energy of the system.
D. The ratio of initial to final momentum of the system is
1


Name any two copper-releasing Intra Uterine Devices(IUDs). List two reasons
that make them effective
contraceptives.


Assertion
\( H C l O_{4} \) is a stronger acid than \( H C l O_{3} \)
Reason

Oxidation state of chlorine in \( H C l O_{4} \) is
+7 and in \( H C l O_{3} \) is +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. Both Assertion and Reason are incorrect


A body absorbs 1000 calories of heat
when it is heated from \( 20^{0} C \) to \( 70^{0} C \)
The water equivalent of the body is
\( A \cdot 10 g \)
B. \( 15 \mathrm{g} \)
c. \( 20 g \)
D. 25


When water is boiled to \( 100^{\circ} \mathrm{C} \), it
converts into steam which on
condensation gives back water. Here, the heat given out is called
which
equal to the latent heat of
vapourization.


On photochemical decomposition of
\( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \) the products formed are :
A. \( N O \) and \( O_{2} \)
B. \( N O_{2} \) and \( O_{2} \)
c. \( N_{2} O_{4} \) and \( N O_{2} \)
D. \( N_{2} O_{5} \) and \( N O_{2} \)


A particle starts with initial speed \( u \) and retardation a to come to rest in
time \( T . \) The time taken to cover the first
half of the total path travelled is
A \( \cdot \frac{T}{\sqrt{2}} \)
в. \( T\left(1-\frac{1}{\sqrt{2}}\right) \)
c. \( \frac{T}{2} \)
D. \( \frac{3 T}{4} \)


constant \( \mathrm{k} \) are attached horizontally at the two ends of a uniform horizontally
rod \( A B \) of length \( \ell \) and mass \( m \). The rod
is pivoted at its centre 'O' and can rotate
freely in horizontal plane. The other ends
of the two spring are fixed to rigid supports as shown in figure. The rod is gently pushed through a small angle and released. The frequency of resulting
oscillation is:
\( \mathbf{A} \cdot \frac{1}{2 \pi} \sqrt{\frac{6 k}{m}} \)
B \( \cdot \frac{1}{2 \pi} \sqrt{\frac{2 k}{m}} \)
\( \mathbf{C} \cdot \frac{1}{2 \pi} \sqrt{\frac{k}{m}} \)
D. \( \frac{1}{2 \pi} \sqrt{\frac{3 k}{m}} \)


A parallel plate condenser with a dielectric of dielectric constant \( \boldsymbol{K} \)
between the plates has a capacity \( C \) and is charged to a potential \( V \) volt. The dielectric slab is slowly removed from between the plates and then reinserted. The net work done by the system in this process is :
A . zero
в. \( \frac{1}{2}\left[(K-1) C V^{2}\right. \)
c. \( \frac{C V^{2}(K-1)}{K} \)
D. \( (K-1) C V^{2} \)


Which hormones of the following endocrine glands lacks peptides,
amines and sulphur?
A. Hormone of anterior pituitary
B. Hormone of posterior pituitary and pancreas
c. Hormone of thyroid and adrenal gland
D. Hormone of testes and ovary


Asexual reproduction is seen in
A. Bacteria
B. Hydra
c. Strawberries
D. All of the above


Common salt is chemically sodium chloride \( (N a C l) \)
A. True
B. False


State the law of equipartition of energy


Why are multiple fuses used in
domestic electric circuit
A. It reduces the average cost
B. It increases efficiency of system
C. It guarantees system will always work perfectly
D. Failure of one of the fuses allow system to continue working in applications where fault has not ocured


A solid sphere of radius \( \boldsymbol{R}, \) made up of a
material of bulk modulus \( \boldsymbol{K} \) is
surrounded by a liquid in a cylindrical
container. A massless piston of area \( \boldsymbol{A} \)
floats on the surface of the liquid. When
a mass \( M \) is placed on the piston to
compress the liquid, the fractional
change in the radius of the sphere is
\( \mathbf{A} \cdot \frac{M g}{2 A K} \)
в. \( \frac{M g}{3 A K} \)
c. \( \frac{M g}{A K} \)
D. \( \frac{2 M g}{3 A K} \)


If \( A \) and \( B \) are mutually exclusive
events, then
A \( . P(A)=P(A-B) \)
B . \( P(B)=P(A-B) \)
c. \( P(A)=P(A \cap B) \)
D. \( P(B)=P(A \cap B) \)


Pick out the one which does not belong to the family.
A. Pepsin
B. Cellulose
c. Ptyalin
D. Lipase


The angular spread of central
maximum, in the diffraction pattern, does not depend on
A. the distance between the slit and sources
B. width of slitt
c. wavelength of light
D. frequency of light


The instantaneous potential difference between points \( A \) and \( B \) is (Phase angle
is \( \left.37^{0}\right) \)
A \( \cdot 8 \sin \left(50 \pi t+37 \frac{\pi}{180}\right) \)
B. \( 8 \sin \left(50 \pi t-37 \frac{\pi}{180}\right) \)
c. \( 10 \sin (50 \pi t) \)
D. \( 10 \cos (50 \pi t) \)


In which one of the following steps of citric acid cycle, FAD is reduced to \( \$ \$ \mathrm{FADH}_{-} 2 \$ \$ \)
A. Pyruvate Acetyl CoA
B. Succinic acid Malic acid
c. Malic acid Oxalosuccinic acid
D. Citric acid-Ketoglutaric acid
E. -Ketoglutasic Succinic acid


The solubility of gases in water
with rise in
temperature
A . increases
B. decreases
c. no change
D. None of the above


Which of the following contributes to
acid rain?
A. \( H_{2} \)
в. \( S O_{3} \)
c. \( C O \)
D. HCl
E. \( O_{3} \)


Resolve a weight of \( 10 \mathrm{N} \) in two directions which are parallel an perpendicular to a slope inclined at 30
to the horizontal,


Assertion
A body with constant acceleration
always moves along a straight line.
Reason
A body with constant acceleration may not speed up.
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. Reason is correct but assertion is incorrect


Which of the following statements about RNA is not correct?
A. It has a single strand
B. It does not undergo with the replication of bases
c. It does not contain any pyrimidine base
D. It controls the synthesis of proteins


Who supported the Four Element Concept of Empedocles?
A. Dalton
B. Avogadro
c. Einstein
D. Aristotle


\( \int \frac{e^{x}}{\left(e^{x}+2\right)\left(e^{x}-1\right)} d x= \)
A \( \cdot \frac{1}{3} \log \left|\frac{e^{x}-1}{e^{x}+2}\right|+c \)
в \( \cdot \frac{1}{3} \log \left|\frac{e^{x}+1}{e^{x}-1}\right|+c \)
c. \( \frac{1}{3} \log \left|\frac{e^{x}+1}{e^{x}+2}\right|+c \)
D. \( -\frac{1}{3} \log \left|\frac{e^{x}+1}{e^{x}+2}\right|+c \)


Human ancestors first to build hunts
and wear animal hides were
A. Peking Man
B. Java Man
c. cro-Magnon Man
D. Neanderthal Man


Evaluate:
\( \frac{5 \sin ^{2} 30^{0}+\cos ^{2} 45^{0}+4 \tan ^{2} 60^{0}}{2 \sin 30^{0} \cos 60^{0}+\tan 45^{0}}=\frac{55}{m} \)
Find \( m \)


Asexual reproduction produces offspring.
A. Genetically identical
B. Larger
c. Variable
D. None of the above


Find the locus of a variable point which is at a distance of 2 units from the \( y- \)
axis
A . \( x=\pm 2 \)
B . \( y=\pm 2 \)
c. \( x=\pm 4 \)
D. \( y=\pm 4 \)


State whether true or false.
If two bodies of different masses move
with the same momentum, then the heavier body will have the greater
velocity
A. True
B. False


If villis are absent in small intestine,
what will happen?


The temperature of a body in a room is
\( 100^{\circ} F . \) After five minutes, the
temperature of the body becomes \( 50^{\circ} F \)
After another 5 minutes, the
temperature becomes \( 40^{\circ} \mathrm{F} \). What is
the temperature of surroundings?


Which of the following contains the maxium number of atoms?
A \( \cdot 10 g \) of \( C a C O_{3} \)
B. \( 4 g \) of hydrogen
\( \mathbf{c} \cdot 9 g \) of \( N H_{4} N O_{3} \)
D. \( 1.8 g \) of \( C_{6} H_{12} O_{6} \)


The domain of \( \cos ^{-1} \frac{x-3}{2}-\log _{10}(4- \)
\( x) \) is
в. [1,4]
c. (1,4]
D. [1,4]


Area bounded by the curve \( y^{2}(2 a- \)
\( x)=x^{3} \) and the line \( x=2 a \) is:
\( A \cdot 3 \pi a^{2} \)
B. \( 2 \pi \)
c. \( 2 \pi a \)
D. \( 3 \pi \)


law gives the quantitative relationship between current and magnetic field due to the
current carrying conductor.


State the name of a regular polygon of 3 sides.
A. Equilateral triangle
B. Isoceles triangle
c. Scalene triangle
D. None of these


For which of the following is the modulus of rigidity highest?
A. glass
B. quartz
c. rubber
D. water


Consider a spherical Gaussian surface
of radius \( r>c, \) the net charge enclosed
by this surface is \( Y \times Q \). Find out the
value of \( \boldsymbol{Y} \) ?


\( \lim _{x \rightarrow 0}\left(x^{-3} \sin 3 x+a x^{-2}+b\right) \) exists and
is equal to \( 0, \) then
A \( \cdot a=-3 \) and \( b=\frac{9}{2} \)
B. \( a=3 \) and \( b=\frac{9}{2} \)
c. \( _{a=-3 \text { and } b=-\frac{9}{2}} \)
D. \( a=3 \) and \( b=-\frac{9}{2} \)


Determine the distance of 4 th dark
fringe from the left end of air cavity
A \( \cdot \frac{2 L}{6}+\lambda_{0} \)
B. \( _{L_{1}+} \frac{3 L}{4} \)
\( c \cdot \frac{4 L}{7} \)
D. \( \frac{5 L}{7} \)


Why tail of comets is formed,when it
comes closer to sun?
A. Ice presents in the comets gets vapourised
B. When is comes closer to sun, vapour converts in to ice
C. Dust particle in the comets gets heated
D. Water present in comets gets cooled


A vessel containing \( 50 k g \) of water of height \( 15 m \) is placed above the ground. Assuming the gravitational potential energy at ground to be zero. What will be the gravitational potential energy of water in the vessel ? \( \left(\boldsymbol{g}=\mathbf{1 0 m} \boldsymbol{s}^{-\mathbf{2}}\right) \)
A . \( 0 . J \)
в. \( 750 J \)
c. \( 3750 J \)
D. \( 7500 J \)


Nucleosomes are not present in
A . Plant
B. Animal
C. Bacteria
D. Both A and B


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


Solve \( e^{x} \tan y d x+\left(1-e^{x}\right) \sec ^{2} y d y= \)
0


\( I_{3}^{+} \) and \( I_{3}^{-} \) have same :
A. geometry
B. no .of lone pair(s)
c. bond angle
D. none of these


Water evaporates under atmospheric pressure. Without changing the temperature, the same water is placed in a partial vacuum. The rate of evaporation will
\( A \). increase
B. drop to zero
c. decrease
D. remain unaffected


Photochemical smog occurs in warm, dry and sunny climate. One of the following is not amongst the components of photochemical smog, identify it.
A \( \cdot N O_{2} \)
в. \( O_{3} \)
\( c \cdot s O_{2} \)
D. Unsaturated hydrocarbon


The principle pathways by which water is translocated in angiosperm is
A. Xylem and phloem together
B. Sieve tubes and membrane of phloem
c. sieve cells of phloem
D. Xylem vessel system


The sum of the coefficients of first three
terms in the expansion of \( \left(x-\frac{3}{x^{2}}\right)^{m}, x \neq 0, m \) being a natura
number, is \( 559 . \) Find the term of the
expansion containing \( \boldsymbol{x}^{\mathbf{3}} \)


If \( \boldsymbol{A}-\boldsymbol{B}=\boldsymbol{\phi}, \) then relation between \( \mathbf{A} \)
and B is
This question has multiple correct options
\( \mathbf{A} \cdot A \neq B \)
в. \( B \subset A \)
c. \( A \subset B \)
D. \( A=B \)


Vibrating bodies produce
A . light
B. sound
c. heat
D. all of the above


Given below are some elements of the
modern periodic table:
\( _{4} B e,_{26} F e,_{14} S i,_{19} K,_{20} C a \)
(i) Select the element that has one
electron in the outermost shell and
write its electronic configuration.
(ii) Select two elements that belong to the same group. Give reason for your
answer.
(iii) Select two elements that belong to the same period. Which one of the two
has bigger atomic size?


Study the following graph and mark the incorrect statement following it.
\( \mathbf{T}\left(^{\circ} \mathbf{C}\right) \)
A . At zero volume all lines meet at \( -273.15^{\circ} \mathrm{C} \). This
temperature is known as absolute zero
B. Each line of the volume vs temperature at constant pressure of graph is called isotherm
c. All gases obey charles' law at very low pressure and high temperature
D. Pressure remaining constant, volume of a gas is directly proportional to its absolute temperature


Find the equivalent capacitance across
\( A \) and \( B \)
\( ^{\mathrm{A}} \cdot \frac{35}{6} \mu F \)
в. \( \frac{25}{6} \mu F \)
c. \( 15 \mu F \)
D. none of these


A coil having 100 turns is kept in a uniform magnetic field of induction 0.5
T. If its area changes from \( 0.3 m^{2} \) to 0.1
\( m^{2} \) in 10 s, then the emf induced is
\( \mathbf{V} \)
\( A \cdot 2 \)
B. 1
\( c \cdot 4 \)
D.


\( \operatorname{Matrix} \boldsymbol{A}=\left[\begin{array}{ccc}\mathbf{1} & \mathbf{3} & \mathbf{3} \\ \mathbf{2} & \mathbf{4} & \mathbf{1 0} \\ \mathbf{3} & \mathbf{8} & \mathbf{4}\end{array}\right] \) is similar to
\( A \)
\[
\left[\begin{array}{lll}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1
\end{array}\right]
\]
в.
\[
\left[\begin{array}{ccc}
1 & 0 & 9 \\
0 & 1 & -2 \\
0 & 0 & -7
\end{array}\right]
\]
\( c \)
\[
\left[\begin{array}{lll}
1 & 0 & 5 \\
0 & 1 & 2 \\
0 & 4 & 1
\end{array}\right]
\]
D. Both A and B


The wavelength of the sound between
the source and the listener in metres is
\( 130 \times 10^{-x} \). Find the value of \( x \)


Treatment of \( 2- \) butene \( (\text { cis and trans }) \)
with N-bromosuccinimide in \( \boldsymbol{C C l}_{\mathbf{4}} \)
would yield mainly :
\( A \)
\( \mathrm{CH}_{3} \mathrm{CHBrCH}=\mathrm{CH}_{2} \) and \( \mathrm{CH}_{3} \mathrm{CH}=\mathrm{CHCH}_{2} \mathrm{Br} \)
B. \( \mathrm{CH}_{3} \mathrm{CH}=\mathrm{CBrCH}_{3} \) alone
\( c \)
\( \mathrm{CH}_{3} \mathrm{CH}=\mathrm{CHCH}_{2} \mathrm{Br} \) alone
D. \( \mathrm{CH}_{2} \mathrm{BrCH}_{2} \mathrm{CH}=\mathrm{CH}_{2} \) and \( \mathrm{CH}_{3} \mathrm{CH}=\mathrm{CHCH}_{2} \mathrm{Br} \)


SER and RER can be distinguished with
it's presence in
A. Protein synthesising cells
B. Protein and lipid synthesising cells
c. carbohydrates and fat synthesising cells
D. Fat and protein synthesising cells


If \( y=\cos ^{-1}\left(\frac{2 x}{1+x^{2}}\right), \) then \( \frac{d y}{d x} \) is equal
to
A \( \cdot-\frac{2}{1+x^{2}} \) of all \( |x|<1 \)
B. \( -\frac{2}{1+x^{2}} \) of all \( |x|>1 \)
c. \( \frac{2}{1+x^{2}} \) of all \( |x|<1 \)
D. None of the above


Lithium exists in nature in the form of
two isotopes, \( L i-6 \) and \( L i-7 \) with
atomic masses \( 6.0151 u \) and \( 7.0160 u \)
and the percentage 8.24 and 91.76 respectively. Calculate average atomic mass.


What is the function of germ pore?
A. Absorption of water for seed germination
B. Initiation of pollen tube
C. Release of male gametes
D. Release of female gametes


Merlin's grass is
A. Equisetum
B. Isoetes
C . Ophioglossum
D. Selaginella


Draw a scientifically correct labelled diagram of a human eye and answer the questions based on it:

State the nature of the image formed of the object on the screen inside the eye.


In a Wheatstone bridge if the battery and galvanometer are interchanged then the deflection in galvanometer will:
A. Change in previous direction
B. Not change
c. change in opposite direction
D. None of these


Ankit was given an increment of \( 10 \% \) on his salary is \( \boldsymbol{R} \boldsymbol{s} . \boldsymbol{3} \boldsymbol{5} \boldsymbol{7} \boldsymbol{5}, \) what was his
salary before increment?


Geometric shapes of the complexes \( (p) \)
(q) and (r) formed by the following
reactions respectively are:
\( \boldsymbol{C u}^{2+}(\boldsymbol{a q})+\boldsymbol{K} \boldsymbol{C} \boldsymbol{N}(\boldsymbol{a} \boldsymbol{q})(\boldsymbol{e} \boldsymbol{x} \boldsymbol{c} \boldsymbol{e} \boldsymbol{s} \boldsymbol{s}) \rightarrow \)
\( \operatorname{complex}(p) \)
\( \boldsymbol{C o}^{2+}(\boldsymbol{a q})+\boldsymbol{K} \boldsymbol{N} \boldsymbol{O}_{2}(\boldsymbol{s})+\boldsymbol{H}^{+}(\boldsymbol{a} \boldsymbol{q}) \rightarrow \)
\( \operatorname{complex}(\boldsymbol{q}) \)
\( Z n^{2+}(a q)+N a O H(a q)(e x c e s s) \rightarrow \)
\( \operatorname{complex}(r) \)
A. Tetrahedral, octahedral and square planar
B. Tetrahedral, octahedral and tetrahedral
C. Square planar, octahedral and tetrahedral
D. Octahedral, octahedral and tetrahedral


A fair die is rolled once.
STATEMENT - 1: The probability of getting a composite number is \( 1 / 3 \)
STATEMENT - 2: There are three
possibilities for the obtained number
\( (i) \)
the number is a prime number (ii) the number is a composite number (iii) the
number is \( 1, \) and hence probability of
getting a prime number \( =1 / 3 \)
A. Statement - 1 is True, Statement - 2 is True, Statement 2 is a correct explanation for Statement - 1
B. Statement - 1 is True, Statement - 2 is True : Statement 2 is NOT a correct explanation for Statement -
c. Statement - 1 is True, Statement - 2 is False
D. Statement - 1 is False, Statement - 2 is True


In spectrochemical series, chlorine is
above water i.e., \( \boldsymbol{C l}>\boldsymbol{H}_{2} \boldsymbol{O} . \) This is due
to:
A. Good \( \pi- \) acceptor properties of \( C l \)
B. Strong \( \sigma- \) and good \( \pi- \) acceptor properties of \( C l \)
c. Good \( \pi \) - donor properties of \( C l \)
D. Larger size of \( C l \) than \( H_{2} O \)
E. None of the option


Resistance of a resistor at temperature
\( t^{0} \boldsymbol{C} \) is \( \boldsymbol{R}_{t}=\boldsymbol{R}_{0}\left(\mathbf{1}+\boldsymbol{\alpha} \boldsymbol{t}+\boldsymbol{\beta} \boldsymbol{t}^{2}\right) . \) Here \( \boldsymbol{R}_{0} \)
is the resistance at \( 0^{0} C . \) The
temperature coefficient of resistance at
temperature \( t^{0} C \) is
A \( \cdot \frac{\left(1+\alpha t+\beta t^{2}\right)}{\alpha+2 \beta t} \)
в. \( \alpha+2 \beta t \)
c. \( \frac{\alpha+2 \beta t}{\left(1+\alpha t+\beta t^{2}\right)} \)
D. \( \frac{\alpha+2 \beta t}{2\left(1+\alpha t+\beta t^{2}\right)} \)


pH of \( 1 \mathrm{M} \) HA (weak acid) is 2 . Hence,
vant Hoff factor is
A . 1.2
B. 1.02
c. \( 1 . \)
D. 1.01


An aeroplane cruising in the air is an example of
A. uniform motion
B. non uniform motion
c. either uniform or non uniform motion
D. neither uniform nor non uniform motion


Which of the following is considered as the first impact of a pill taken for medical abortion?
A. It blocks the release of hormone progesterone
B. It delays the menstrual cycle
c. It delays release of estrogen
D. None of the above


Gypsum is added to cement in order to:
A. prolong hydration
B. increase strength after hydration
c. decrease heat of hydration
D. reduce curing time


Although \( C N^{-} \) ion and \( N_{2} \) molecule
are isoelectronic, yet \( N_{2} \) molecule is chemically inert because of:
A. presence of more number of electrons in bonding orbitals
B. a bond energy
c. absence of bond polarity
D. uneven electron distribution


If \( \theta \) is the polarizing angle for a medium
in which the speed of light is \( v \), then according to Brewster's Law:
\( \mathbf{A} \cdot \theta=\sin ^{-1}(c / v) \)
B \( \cdot \theta=\tan ^{-1}(c / v) \)
\( \mathbf{c} \cdot \theta=\cos ^{-1}(c / v) \)
D. \( \theta=\sin ^{-1}(v / c) \)


IUPAC name for the this compound is:
A. 2,5,5-trimethyl-3-hexanol
B. 1,1,4,4-pentamethylbutanol
c. 2,3,5-trimethyl-3-hexanol
D. 1,1,4 -pentamethylbutanol


A coin is tossed 3 times, the total number of possible outcomes is:
A . 3
B. 4
\( c .6 \)
\( D \)


Secondary growth does not occur in monocots as their vascular bundles are
A . Radial
B. Scattered
c. Enclosed by sclerenchyma
D. closed


\( H_{2} \) does not show litmus test. From
this, we can say, that the oxide of
hydrogen is in nature.


The specific latent heat of ice is 383 \( J g^{-1} \)
A. True
B. False


Archaebacteria common in marshes
and rice fields are
A. Methanogens
B. Halophiles
c. Thermoacidophiles
D. All of the above


Compressibility factor for \( \boldsymbol{H}_{2} \) behaving
as real gas is :
\( A \)
В \( \cdot\left(1-\frac{a}{R T V}\right) \)
c. \( \left(1+\frac{P b}{R T}\right) \)
D. \( \frac{R T V}{(1-a)} \)


If \( \boldsymbol{A}=\left[\begin{array}{rr}4 & \boldsymbol{x}+\mathbf{2} \\ \mathbf{2} \boldsymbol{x}-\mathbf{3} & \boldsymbol{x}+\mathbf{1}\end{array}\right] \) is symmetric
then \( x= \)
\( A \cdot 3 \)
B. 5
\( c \cdot 2 \)
D. 4


Two planets of radii \( r_{1} \) and \( r_{2} \) are made from the same material. The ratio of the
acceleration due to gravity \( g_{1} / g_{2} \) at the
surfaces of the two planets is:
A \( \cdot r_{1} / r_{2} \)
в. \( r_{2} / r_{1} \)
C \( \cdot\left(r_{1} / r_{2}\right)^{2} \)
D. \( \left(r_{2} / r_{1}\right)^{2} \)


Afferent nerve fiber conducts impulse
from
A. C.N.S to effector
B. Receptor to C.N.S
c. Receptor to effector
D. Effector to receptor


Points \( (a, 0),(0, b) \) and (1,1) are
collinear, if:
A \( \cdot \frac{1}{a}+\frac{1}{b}=1 \)
B. \( \frac{1}{a}-\frac{1}{b}=1 \)
c. \( a+b=1 \)
\( \mathbf{D} \cdot a-b=a b \)


A body dropped from a height \( h \) with initial velocity zero, strikes the ground with a velocity \( 3 m / s \). Another body of same mass dropped from the same height \( h \) with an initial velocity of \( 4 m / s \) The final velocity of second mass, with which it strikes the ground is
A. \( 5 m / s \)
в. \( 12 \mathrm{m} / \mathrm{s} \)
\( \mathrm{c} \cdot 3 \mathrm{m} / \mathrm{s} \)
D. \( 4 m / s \)


Find the equations of the straight line
which passes through the point (-3,8) and cut positive intercepts on the coordinates axes whose sum is 7 .


From the following figure, can we say
that \( \boldsymbol{A B}>\boldsymbol{C D} \)
If true then enter 1 else enter 0 .


\( \Delta \mathrm{ABC} \sim \Delta \mathrm{LBN}, \ln \Delta \mathrm{ABC}, \mathrm{AB}=6.1 \mathrm{cm} \angle \mathrm{B} \)
\( =45^{\circ}, \mathrm{BC}=5.4 \mathrm{cm} ; \frac{A C}{L N}=\frac{4}{7} . \) Construct
\( \Delta A B C \) and \( \Delta L B N \)


The negative of the distance rate of change of potential energy is equal to:
A. force acting on the particle in the direction of displacement
B. acceleration of the particle, perpendicular to displacement
c. power
D. impulse


In how many of the given years was the production of fertilizers more than the
average production of the given years?
ion of Fertilizers by a com
\( A \)
B. 2
\( c \cdot 3 \)
\( D \cdot 4 \)


Pick out the suitable appliances to conserve the electric energy
(Florescent bulbs, copper choke, solar
water heater, electric water heater,
tungsten bulbs, electric choke)


Which one of the following reactions of
Xenon compounds is not feasible?
\( \mathbf{A} \cdot \mathrm{X} \mathrm{e} \mathrm{O}_{3}+6 \mathrm{HF} \rightarrow \mathrm{XeF}_{6}+3 \mathrm{H}_{2} \mathrm{O} \)
B. \( 3 \mathrm{XeF}_{4}+6 \mathrm{H}_{2} \mathrm{O} \rightarrow 2 \mathrm{Xe}+\mathrm{Xe} \mathrm{O}_{3}+12 \mathrm{HF}+1.5 \mathrm{O}_{2} \)
\( \mathbf{C} \cdot 2 \mathrm{X} \mathrm{e} \mathrm{F}_{2}+2 \mathrm{H}_{2} \mathrm{O} \rightarrow 2 \mathrm{Xe}+4 \mathrm{HF}+\mathrm{O}_{2} \)
D. \( \mathrm{XeF}_{6}+\mathrm{RbF} \rightarrow \operatorname{Rb}\left[\mathrm{XeF}_{7}\right] \)


The covalent compound which does not give a positive test in Lassaigne's test is:
A . 1,3-dinitrobenzene
B. glycine
c. urea
D. hydrazine


The equation of an equipotential line in an electric field is \( y=2 x, \) then the
electric field strenght vector at (1,2) may be:
A \( .4 \hat{i}+3 \hat{j} \)
B. \( 4 \hat{i}+8 \hat{j} \)
c. \( 8 \hat{i}+4 \hat{j} \)
D. \( -8 \hat{i}+4 \hat{j} \)


What is de Broglie wavelength
associated with an \( e^{-} \) accelerated
through potential difference \( =100 \mathrm{kV} ? \)
\( A \cdot 3.88 \mathrm{pm} \)
B. 4.23 pm
c. \( 4.78 \mathrm{pm} \)
D. \( 5.03 \mathrm{pm} \)


What is \( \boldsymbol{A} \) ?
A \( \cdot T s O-C H_{2}-C \equiv C H \)
в. \( T s O_{2}-C H_{2}-C \equiv C H \)
\( c \cdot T s O-C H_{2}-C-C H \)
D. none of the above


The alkali metals follow the noble gases
in their atomic structure. What
properties of these metals can be predicted from this information?


Choose the correct answer from the
alternatives given :
If the sequence of nitrogen bases of the coding strand of DNA in a transcription unit is: \( 5-A \) T \( G A A T G-3 \) the sequence of bases in its RNA
transcript would be
A. 5-AUGAAUG-3
B. 5-UACUUAC-3
c. 5 сАUUсАU 3
D. 5-GUAAGUA-3.


A drunkard walking in a narrow lane takes 5 steps forward and 3 steps backward,followed again by 5 steps
forward and 3 steps backward, and so on. Each step is \( 1 \mathrm{m} \) long and requires 1
s. Plot the \( x \) -t graph of his motion. Determine graphically and otherwise how long the drunkard takes to fall in a
pit \( 13 \mathrm{m} \) away from the start.


A graph plotted between \( \log \left(\frac{x}{m}\right) \) vs \( \log P(P \) is pressure of gas in atm) shows a straight line with slope equal
to 1 and intercept equal to \( 0.4771 . \) The extent of adsorption \( \left(\frac{x}{m}\right) \) of gas at the
pressure 2 atm is :


If \( A, B, C \) are angles of a triangle, then the minimum value of \( \tan ^{2} \frac{A}{2}+ \) \( \tan ^{2} \frac{B}{2}+\tan ^{2} \frac{C}{2} \) is


Calculate net heat supplied to the gas during complete process.


A coin is dipped in the molten wax in a glass tube. When we heat the upper part of the glass tube, the wax around the coil will not melt because:
A. Wax has a very high melting point
B. Wax is a good conductor of heat
c. Glass is a good conductor of heat
D. Wax or glass are bad conductors


Car A and car B start moving simultaneously in the same direction along the line joining them car A with a constant acceleration \( \boldsymbol{a}=\mathbf{4} \boldsymbol{m} / \boldsymbol{s}^{2} \) while
car \( \mathrm{B} \) moves with a constant velocity \( \mathrm{V}= \) \( 1 \mathrm{m} / \mathrm{s} . \) At \( \mathrm{t}=0 \) car \( \mathrm{A} \) is \( 10 \mathrm{m} \) behind car \( \mathrm{B} \)
Find the time when car A over takes car
B.
A . 2 s
в. 2.5
\( c \cdot 1 s \)
D. 1.5 \( s \)


Which of the following molecule having least bond angle?
\( \mathbf{A} \cdot H_{2} S e \)
в. \( H_{2} \).
c. \( N F_{3} \)
D. \( P F_{3} \)
E. \( P H_{3} \)


Assertion
Most nuclear power stations in India have been constructed near sources of
water
Reason
Nuclear power stations require a great quantity of water cooling purposes.
A. Both A and R are true and R explains A.
B. Both A and R are true but R does not explain A
c. A is true and R is false.
D. A is false and R is true


At constant pressure and at \( 290 K, \) the heatnof combustion of glucose (s) was found to be \( -2723.78 k J . \) Calculate the
heat of combustion of glucose at
constant volume. (Assume water to be
in gaseous state)


A circular coil of wire carries a current.
\( P Q \) is a part of a very long wire carrying
a current and passing close to the circular coil. If the direction of currents
are those as shown in the Figure, what
is the direction of force acting on \( P Q ? \)
A. Parallel to \( P Q \), towards \( P \)
B. Parallel to \( P Q \), towards \( Q \)
C. At right angles to \( P Q \), towards right
D. At right angles to \( P Q \), towards left


Looking into a mirror one finds his image long and thin; the mirror is:
A. Concave
B. convex
c. cylindrical
D. Parabolic


Three equal resistors connected in
series across a source of e.m.f.
dissipate 10 watts of power. What will be the power dissipated in watts if the same resistors are connected in paralle
across the same source of e.m.f.?
A. \( 10 W \)
в. \( 30 W \)
c. \( 90 W \)
D. \( \frac{10}{3} W \)


\( f(x)=\frac{x^{2}-16}{x-4}+a \) for \( x<4 \)
\[
=\mathbf{3} x^{2}+4 x+b, \quad \text { for } \quad x>4
\]
continuous at \( x=4, \) find \( a \) and \( b \)


Consider the electric dipole moment \( (p=2 q a) \) shown in the figure. The
electric field at a point \( \boldsymbol{P}(\boldsymbol{x}, \boldsymbol{y}, \boldsymbol{0}) \) in the
polar coordinate system is :
A \( \cdot \frac{k_{e} p}{r^{3}}[(2 \cos \theta) \hat{r}-(\sin \theta) \hat{\theta}] \)
B. \( \frac{k_{e} p}{r^{3}}[(2 \cos \theta) \hat{r}+(\sin \theta) \hat{\theta} \)
c. \( \frac{k_{e} p}{r^{3}}[-(2 \cos \theta) \hat{r}+(\sin \theta) \hat{\theta} \)
D. \( \frac{k_{e} p}{r^{3}}[-(2 \cos \theta) \hat{r}-(\sin \theta) \hat{\theta} \)


If the mass of the Sun were ten times
smaller and the universal gravitational constant were ten times larger in magnitude, which of the following is not
correct?
A. Time period of a simple pendulum on the Earth would decrease
B. Raindrops will fall faster
c. 'g'on the Earth will not change
D. Walking on the ground would become more difficult


When a p-n diode is reverse biased, then
A. no current flows
B. the depletion region is increased
C. the depletion region is reduced
D. the height of the potential barrier is reduced


Electromagnetic radiation with maximum wavelength is:
A . ultraviolet
B. radiowave
c. x-ray
D. infrared


A magnetic dipole is placed in a uniform magnetic fields, B, the potential energy is minimum when dipole is
A. Parallel to B
B. Perpendicular to B
c. Inclined at an angle of 450 to \( B \)
D. Anti-parallel to B


Find the cube root of 39304 by estimation method.
A . 24
B. 44
\( c .34 \)
D. 54


If the true value for a result is \( 4.00 \mathrm{cm} \)
and a student takes two measurements
and reports the result as \( 3.94 \mathrm{cm} \) and
\( 3.95 \mathrm{cm}, \) then these values are:
A. Precise and accurate
B. Precise but are not accurate
c. Accurate but not precise
D. Neither accurate nor precise


A rod is hinged at centre and rotated by applying the torque starting from rest , the power developed by the torque with respect to time is of
A. cubic nature
B. quadratic nature
c. linear nature
D. sinusoidal nature


If \( y=\tan ^{-1}\left(\frac{4 x}{1+5 x^{2}}\right)+ \)
\( \tan ^{-1}\left(\frac{2+3 x}{2-3 x}\right), \) then \( \frac{d y}{d x} \) is
\( \frac{1}{1+4 x^{2}} \)
- s. \( \frac{3}{1+4 x^{2}} \)
\( \frac{5}{1+25 x^{2}} \)
\( \frac{5}{\left(1+25 x^{2}\right)}-\frac{1}{\left(1+x^{2}\right)}-\frac{1.5}{\left(1+2.25 x^{2}\right)} \)


Primary and secondary valency of \( P t \) in
\( \left[\boldsymbol{P t}(\boldsymbol{e n})_{2} \boldsymbol{C l}_{2}\right] \boldsymbol{C l}_{2} \) are:
\( A \cdot 2,4 \)
в. 2,
\( c \cdot 6,6 \)
D. 4,2


In non-cyclic photophosphorylation there is photolysis of 12 water
molecules. How many \( \boldsymbol{H}^{+} \) are formed?
A \( .24 H^{+} \)
B . 36 \( H^{+} \)
c. \( 12 H^{+} \)
D . 32 \( H^{+} \)


If \( \bar{a}=\hat{i}-\hat{j}+\hat{k} \) and \( \bar{b}=2 \hat{i}+\hat{j}+3 \hat{k} \)
then the vector along \( \bar{a}+\bar{b} \) is
A \( \cdot \frac{3 \hat{i}+4 \hat{k}}{5} \)
B. \( \frac{-3 \hat{i}+4 \hat{k}}{5} \)
c. \( \frac{-3 \hat{i}-4 \hat{k}}{5} \)
D. none


If \( (\sqrt{3}-i)^{n}=2^{n}, n \in Z, \) then \( n \) is
multiple
\( A \cdot 6 \)
B. 10
\( c .9 \)
D. 12


Calculate the rate constant of a
reaction at \( 293 K \) when the energy of
activation is \( 103 k J \) mol\( ^{-1} \) and the rate
constant at \( 273 K \) is \( 7.87 \times 10^{-7} s^{-1} \)
\( \left(\boldsymbol{R}=\mathbf{8 . 3 1 4} \times \mathbf{1 0}^{-\mathbf{3}} \mathbf{k J} \mathbf{m o l}^{-\mathbf{1}} \mathbf{K}^{-1}\right) \)


If a circular coil of 100 turns and radius
10cm carries a current of \( 1 \mathrm{A} \), find the
magnetic dipole moment of the coil.


An open vessel containing the liquid upto a height of \( 15 \mathrm{m} \). A small hole is
made at height of \( 10 \mathrm{m} \) from the base of the vessel, then the initial velocity of
efflux is \( \left(\boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{2}\right) \)
\( A \cdot 1 \mathrm{m} / \mathrm{s} \)
B . \( 10 \sqrt{2} \mathrm{m} / \mathrm{s} \)
\( c \cdot 5 m / s \)
D. \( 10 \mathrm{m} / \mathrm{s} \)


Find the length of a chord that is at a distance of \( 5 \mathrm{cm} \) form the centre of a
circle of radius \( 13 \mathrm{cm} \)
\( A \cdot 20 \mathrm{cm} \)
B . \( 24 \mathrm{cm} \)
c. \( 15 \mathrm{cm} \)
D. \( 12 \mathrm{cm} \)


Electric field as a function of distance
from the centre of a uniformly charged solid sphere is mathematically:
A . a discontinuos function
B. inversely related to distance from the centre
c. proportional to distance from the centre
D. none of the above


Light rays (gold) are shown passing across the boundaries of different
colored transparent materials in three different cases below. The black dashed
line segments represent normal to the surfaces. Four different materials are
shown

Based on the way that the light moves through the materials, what is the ranking of the materials according to the values of their indices of refraction,
greatest first?
A. red, green. blue, purple.
B. purple, green, red, blue
c. blue, green, purple, red
D . . red, green, purple
E . green, purple, red, blue


The rate constant for the forward and
backward reactions of hydrolysis of
ester are \( 1.1 \times 10^{-2} \) and \( 1.5 \times 10^{-3} \)
respectively. The equilibrium constant of the following reaction is:
\( \boldsymbol{C H}_{3} \boldsymbol{C O O C}_{2} \boldsymbol{H}_{5}+\boldsymbol{H}^{+} \rightleftharpoons \)
\( \boldsymbol{C H}_{3} \boldsymbol{C O O H}+\boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{O H} \)
A . 6.33
в. 7.75
\( c .7 .33 \)
D. 8.33


Transition metals are good electrical
conductor because
A. they are metals
B. they are solids
C. they have free electrons in outer energy levels
D. they are hard


The short wavelength limit for the
Lyman series of the hydrogen spectrum is 913.4 A.Calculate the short
wavelength limit from Balmer series of
the hydrogen spectrum.


An electromagnetic wave is propagating along \( x \) -axis. At \( x=1 \mathrm{m} \) and
\( t=10 s, \) its electric vector \( |\bar{E}|=6 V / m \) then the magnitude of its magnetic
vector is:
A \( \cdot 2 \times 10^{-8} T \)
В. \( 3 \times 10^{-7} T \)
c. \( 6 \times 10^{-8} T \)
D. \( 5 \times 10^{-7} T \)


(a) Write an equation of reaction of
chlorine with hot and concentrated
NaOH solution.
(b) Why are all the five bonds of \( \boldsymbol{P C l}_{5} \) not equivalent? Explain.


8
8
8


What is the major product in the given
reaction?
product
\( A \)
B.
\( c \)


If \( \frac{1-3 p}{2}, \frac{(1+4 p)}{3}, \frac{1+p}{6} \) are the
probabilities of three mutually exclusive and exhaustive events,then
the set of all values of p is
B. \( \left[-\frac{1}{4}, \frac{1}{3}\right] \)
c. \( \left[0, \frac{1}{3}\right] \)
\( D \cdot(0, \infty) \)


The top of the atmosphere is about 400
kV with respect to the surface of the earth, corresponding to an electric field
that decreases with altitude. Near the
surface of the earth, the field is about
\( 100 V m^{-1} \)
Still, we do not get an electric shock as we step out of our house into the open house, because (assume the house to
be a steel cage so that there is no field inside)
A. There is a potential difference between our body and the ground
B . \( 100 \mathrm{Vm}^{-1} \) is not a high electric field so that we do not feel the shock
c. our body and the ground forms an equipotential surface
D. The dry atmosphere is not a conductor


Assertion
\( \int_{0}^{\pi / 2} x \cot x d x=\frac{\pi}{2} \log 2 \)
Reason
\( \int_{0}^{\pi / 2} \log \sin x d x=-\frac{\pi}{2} \log 2 \)
A. Both Assertion \& Reason are individually true \& Reason is correct explanation of Assertion
B. Both Assertion \& Reason are individually true but Reason is not the , correct (proper) explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true


During refraction of light, which of the following quantities change? This question has multiple correct options
A. Frequency
B. Phase
c. speed
D. wavelength


Two metal plates having a potential difference of \( 800 \mathrm{V} \) are \( 2 \mathrm{cm} \) apart. It is
found that a particle of mass \( 1.96 \times \) \( 10^{-15} K g \) remain suspended in the
region between the plates. The charge on the particle must be:
\( A \cdot 3 e \)
B. \( 4 e \)
\( c \cdot 6 e \)
D. \( 8 e \)


Nickel and cadmium are used in
combination.
A. As a catalyst
B. In alloys that can resisthigh pressure
c. In electric batteries having a very long life
D. In cooking utensils


Spindle fibres attach on to
A. Telomere of the chromosome
B. Kinetochore of the chromosome
c. Centromere of the chromosome
D. Kinetosome of the chromosome


If \( A \& B \) are two events such that
\( P(B) \neq 1, B^{C} \) denotes the event
complementary to B, then This question has multiple correct options
\( ^{\mathbf{A}} \cdot P\left(A / B^{C}\right)=\frac{P(A)-P(A \cap B)}{1-P(B)} \)
B . \( P(A \cap B) \geq P(A)+P(B)-1 \)
C . \( P(A)><P(A / B) \) according as \( P\left(A / B^{C}\right)><P(A) \)
D \cdot \( P\left(A / B^{C}\right)+P\left(A^{C} / B^{C}\right)=1 \)


Guttation occurs through
A. Hydathodes
B. Lenticels
c. cuticle
D. None of these


\( \boldsymbol{\Delta} \boldsymbol{H}^{0} \) for the raection \( \boldsymbol{X}_{(\boldsymbol{g})}+\boldsymbol{Y}_{(\boldsymbol{g})} \rightleftharpoons \)
\( Z_{(g)} \) is \( -4.6 \mathrm{Kcal} \), the value of \( \Delta U^{0} \) of the
reaction at \( 227^{\circ} \mathrm{C} \) is \( R= \)
\( 2 c a l m o l^{-1} K^{-1} \)
A. - -3.6kcal
B . - -5.6kcal
c. -4.6kcal
D. - -2.6kcal


In the adjacent figure, the bisector of
\( \angle A \) and \( \angle B \) meet in a point \( P . \) If \( \angle C= \)
\( 100^{\circ} \) and \( \angle D=60^{\circ}, \) find the measure
of \( \angle A P B \).


Pressure is dimensionally:
This question has multiple correct options
A. Force per unit area
B. Energy per unit volume
C. Momentum per unit area per second
D. Momentum per unit volume


Solve the differential equation \( \left(1-x^{2}\right) \frac{d y}{d x}+x y=a \)
A \( .-y=-a x+c \sqrt{\left(1-x^{2}\right)} \)
В . \( y=-a x+c \sqrt{\left(1-x^{2}\right)} \)
C. \( -y=a x+c \sqrt{\left(1-x^{2}\right)} \)
D. None of these


What happens when there is no interaction between the objects?
A. Force comes in action
B. Force does not come in action
c. Force may or may not come in action
D. None of the above is correct


Show that the points \( \boldsymbol{A}(\mathbf{1}, \mathbf{2}, \mathbf{3}) \)
\( \boldsymbol{B}(-1,-2,-3), C(2,3,2) \) and \( D(4,7,3) \)
are the vertices of a parallelogram.


What is lens \( B \) called?
Parallel
point of distant


In a heat engine, heat energy is converted into mechanical energy.
A. True
B. False


Polyribosomes are aggregation of
\( A \cdot \) ribosomes and rRNA
B. peroxisomes
C. several ribosomes held together by a string of mRNA
D. rRNA


What is the relationship between thermal energy and intermolecular interaction energy of a substance in
three states in terms of \( X \) and \( Y ? \)
Gas\( \rightarrow \)Liquid\( \rightarrow \)Solid
Predominance of \( \boldsymbol{X} \)
Predominance of \( \boldsymbol{Y} \)
A. \( x \) -Thermal energy, Y- Intermolecular interactions
B. X-Thermal energy, Y-Thermal energy
c. \( x \) -Intermolecular interactions, Y-Thermal energy
D. x-ıntermolecular interactions, Y-Intermolecular interactions


Assertion
There is a physical significance of
matter waves.
Reason
Both interference and diffraction occurs
in it.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion.
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion.
C. Assertion is correct but Reason is incorrect.
D. Both Assertion and Reason are incorrect.


Which monomer is responsible for the flexibility property in \( \boldsymbol{P H B V} \) ?
A \( \cdot H O-_{C H_{3}}^{C H}-C H_{3}-C O O H \)
в. \( H O-\quad \begin{array}{c}C H \quad-C H_{2}-C O O H \\ \quad_{c h_{2}-c H_{3}}\end{array} \)
c. \( H O-_{c H_{3}}^{C H}-C H_{2}-C H_{2}-C O O H \)
D. \( H O-\underset{c h_{2}-c H_{3}}{C H}-C H_{2}-C H O \)


If \( \eta \) represents the coefficient of
viscosity and \( T \) the surface tension, then the dimension of \( \frac{T}{\eta} \) is same as that of :
This question has multiple correct options
A. length
B. mass
c. velocity
D. speedd


In which of the following substances the resistance decreases with the increase
in temperature?
A. carbon
B. constantan
c. copper
D. Silver


Express the following in the simplest
form \( \tan ^{-1}\left(\frac{\cos x}{1+\sin x}\right), \frac{-\pi}{2}<x<\frac{\pi}{2} \)


Which of the following statement is true about PVC (polyvinyl chloride) and polythene?
A. They are thermoplastics
B. They are thermosetting plastics
c. They are examples of natural substances
D. They are natural fibres


A capacitor contains two square plates
with side lengths \( 5.0 \mathrm{cm} . \) The plates are separated by \( 2.0 \mathrm{mm} . \) Dry air fills the space between the plates. Dry air has a dielectric constant of 1.00 and
experiences dielectric breakdown when the electric field exceeds \( 3.010^{4} V / c m \) What is the magnitude of charge that
can be stored on each plate before the capacitor exceeds its breakdown limit and sends a spark between the plates?
\( \mathbf{A} \cdot 6.6 \times 10^{-8} C \)
В. \( 6.6 \times 10^{-5} C \)
c. \( 3.3 \times 10^{-7} C \)
D . 3.3 \( \times 10^{-8} \mathrm{C} \)
E . \( 8.1 \times 10^{-2} C \)


Barbiturates acts as:
A. hypnotic i.e., sleep producing
B. non-narcotic analgesics
C. activator of neurotransmitters
D. anti allergic drugs


Find the derivative of \( \csc ^{2} x, \) by using
first principle of derivatives.


Assertion
The value of acceleration due to gravity
does not depend upon mass of the body
Reason
Acceleration due to gravity is a constant quantity
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


For dissociation of limestone in the slag
zone of the blast furnace. The reaction
is:
A. exothermic accompanied by increase in entropy
B. endothermic accompanied by decrease in entropy
C. endothermic accompanied by increase in entropy
D. exothermic with no change in entropy


Young's double slit experiment is performed at 589 nm light with a distance of \( 2.00 \mathrm{m} \) between the slits
and the screen. The tenth
interference minimum is observed 7.26
\( \mathrm{mm} \) from the central maximum. The
spacing of the slits is
A. \( 15.4 m m \)
B. \( 154 m m \)
c. \( 1.54 m m \)
D. \( 0.154 \mathrm{mm} \)


What is tailing of Mercury?


The electrophile which is considered to be an active agent in the nitration of
benzene is:
A \( . N O_{2} \)
в. \( N O^{+} \)
\( \mathbf{c} \cdot N O_{2}^{+} \)
D. \( H N O_{2}^{+} \)


(a) Explain the experiment performed by Griffith on Streptococcus pneumoniae. What did he conclude from this
experiment?
(b) Name the three scientists who
followed up Griffiths experiments.
(c) What did they conclude and how?


Assertion
Glycolysis is the first step of respiration in which glucose completely breaks into \( C O_{2} \) and \( H_{2} O \)
Reason
In this process, there is net gain of twenty four molecules of ATP.
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


2 moles carbon reacts with 2 moles
oxygen to produce moles of
\( \boldsymbol{C O}_{2} \)
\( A \cdot 1 \)
B. 2
\( c \cdot 3 \)
D. 4


What is the common name of
propanone?
A. Oxobutane
B. Acetone
c. Ethyl acetone
D. Ethyl methyl ketone


Prove that Pancreas is an endocrine as
well as exocrine gland.


The sequence \( 6,12,24,48 \dots \) is a
A . geometric series
B. arithmetic sequence
c. geometric progression
D. harmonic sequence


Consider the following process \( \Delta \)
\( \boldsymbol{H}(\boldsymbol{k} \boldsymbol{J} / \boldsymbol{m} \boldsymbol{o l}) \)
\( \frac{1}{2} \boldsymbol{A} \rightarrow \boldsymbol{B} \)
\( \mathbf{3} \boldsymbol{B} \longrightarrow \mathbf{2} \boldsymbol{C}+\boldsymbol{D} \)
\( \boldsymbol{E}+\boldsymbol{A} \longrightarrow \mathbf{2} \boldsymbol{D} \)
For; \( \boldsymbol{B}+\boldsymbol{D} \longrightarrow \boldsymbol{E}+\mathbf{2} \boldsymbol{C}, \boldsymbol{\Delta} \boldsymbol{H} \) will be :


A water barrel stands ona table of
heighth. If a small hole is punched in the side of the barrel at its base, it is
found that the resultant stream of water
strikes the ground at a horizontal distance \( R \) from the barrel.What is the
depth of water in the barrel?


The area enclosed between the curve
\( \boldsymbol{y}^{2}=\boldsymbol{x} \) and \( \boldsymbol{x}^{2}=\boldsymbol{y} \) is equal to


For the reaction \( 2 H g O(s) \rightarrow 2 H g(l)+ \)
\( \boldsymbol{O}_{2}(\boldsymbol{g}) \)
\( \mathbf{A} \cdot \Delta H>0 \) and \( \Delta S<0 \)
B. \( \Delta H>0 \) and \( \Delta S>0 \)
c. \( \Delta H<0 \) and \( \Delta S<0 \)
D. \( \Delta H<0 \) and \( \Delta S>0 \)


An electron gun with its collector at a
potential of \( 100 V \) fires out electrons in
a spherical bulb containing hydrogen gas at low pressure \( \left(\sim 10^{-2} m m \text { of } \mathrm{Hg}\right) \)
A magnetic field of \( 2.83 \times 10^{4} T \) curves
the path of the electrons in a circular
orbit of radius \( 12.0 \mathrm{cm} \). (The path can be viewed because the gas ions in the path
focus the beam by attracting electrons, and emitting light by electron capture, this method is known as the fine beam
tube method. Determine \( e / m \) from the
data.


A streamlined and almost symmetrical
car of mass \( M \) has centre of gravity at a
distance \( p \) from the rear wheel, \( q \) from
the front wheel and \( h \) from the road. If
the car has required power and friction,
the maximum acceleration developed without tipping over towards back is:
A \( \cdot \frac{p g}{h} \)
в. hg\( q \)
c. \( \frac{h M g}{q} \)
D. \( \frac{p h}{g} \)


Which of the following alkanes has neither secondary nor tertiary hydrogens?
A. Isobutane
B. Isopentane
c. Pentane
D. Neopentane


The colour of blood is red due to the
presence of
A. Magnesium
B. Cytoglobin
c. Haemoglobin
D. All of the above


How does the magnitude of the electric
field at \( \mathrm{B} \) compare for these three cases
в. ।>॥>॥||
D. II>1>11
\( E \cdot 1=11=11 \)


If angular speed of the rod just after the impact is \( \frac{1}{2} \sqrt{\frac{x g}{2 l}}, \) find the value of \( x \)


In a cyclic process, a gas is taken from state \( A \) to \( B \) via path \( -I \) as shown in
the indicator diagram and taken back
to state \( A \) from state \( B \) via path \( -I I . \) In
the complete cycle:
A. Work is done by the gas
B. Heat is ejected by the gas
c. No work is done by the gas
D. Nothing can be said about work as data is insufficient


The range of \( \mathbf{f}(\mathbf{x})=\frac{\sin \boldsymbol{\pi}\left[\mathbf{x}^{2}-\mathbf{1}\right]}{\mathbf{x}^{4}+\mathbf{1}} \) is
A. \( R \)
в. [-1,1]
c. \{0,1\}
D. \{0


The edible green alga rich in protein is
A. Porphyra
B. Chlorella
c. Laminaria
D. chondrus crispus


In balancing the half reaction:
\( S_{2} O_{3}^{2-} \rightarrow S(s), \) the number of electrons
that must be added is :
A. 2 on the right
B. 2 on the left
c. 3 on the right
D. 4 on the left


The equivalent conductance at infinite
dilution of \( B a C l_{2}, H_{2} S O_{4} \) and \( H C l \)
aqueous solutions are \( x_{1}, x_{2} \) and \( x_{3} \)
respectively. The equivalent
conductance of \( B a S O_{4} \) solution is:
A. \( x_{1}+x_{2}-x_{3} \)
В. \( x_{1}-x_{2}-x_{3} \)
c. \( x_{1}+x_{2}-2 x_{3} \)
D. \( x_{1}-2 x_{2}-x_{3} \)


If the magnetic moment of a dioxygen species is \( 1.73 \mathrm{BM} \), it may be:
\( A \cdot O_{2} \) or \( O_{2}^{-} \)
B. \( O_{2}^{-} \) or \( O_{2}^{+} \)
\( c \cdot O_{2} \) or \( O_{2}^{+} \)
D. \( O_{2}, O_{2}^{-} \) or \( O_{2}^{+} \)


What is the formula mass unit of \( \boldsymbol{H} \boldsymbol{C l} \) ?
A . 36.5
B. 35.5
c. 32.5
D. 34.5


Which instrument is used to see around
corners?
A. Kaleidoscope
B. Telescope
c. Periscope
D. compound microscope


Pelvis is a part of
A. Skeletal system
B. Kidneys
C. Brain
D. Both A and B


Among the following interactions, the one of least significance in nuclear physics is
A. nuclear interaction
B. gravitational interaction
c. electrostatic interaction
D. electromagnetic interaction


If \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\boldsymbol{x}^{-3} \) then \( \boldsymbol{y} \)
A. \( -\frac{1}{2 x^{2}}+c \)
в. \( \frac{1}{2 x^{2}}+c \)
c. \( -\frac{1}{3 x^{3}}+c \)
D. \( -\frac{1}{4 x^{4}}+c \)


The state of matter with the least
intermolecular forces of attraction is :
A . solid state
B. liquid state
c. gaseous state
D. plasma state


Sound waves from a tuning fork \( \boldsymbol{F} \) reach
a point \( \boldsymbol{P} \) by two separate routes \( \boldsymbol{F} \boldsymbol{A} \boldsymbol{P} \)
and \( F B P . F B P \) is \( 12 \mathrm{cm} \) larger than
FAP.There is silence at \( P \). If the
separation becomes \( 2 \mathrm{cm} \), the sound
becomes maximum at \( P \) and at \( 36 c m \)
there is again silence and so on. The least frequency of tuning fork is
A . 1357 Hz
в. 1735 нz
c. \( 1375 \mathrm{Hz} \)
D. 1400 нz


Solve \( : \sin ^{2}(0)+\cos ^{2}(0) \)


Molar heat capacity is given by:
A \( \cdot \frac{d Q}{d T} \)
в. \( d Q \times d T \)
c. \( \Sigma Q \frac{1}{d T} \)
D. none of these


When one litre of a saturated solution of
\( \boldsymbol{P b C l}_{2} \) (molecular weight \( =\mathbf{2 7 8} \) g/mol)
is evaporated, the residue is found to
weigh 2.78 g. If \( K_{s p} \) of \( P b C l_{2} \) is
represented as \( y \times 10^{-6}, \) then find the
value of \( \boldsymbol{y} \)
\( A \cdot 4 \)
B. 5
\( c \cdot 6 \)
D.


\( \cos ^{2} \alpha-\sin ^{2} \alpha=\tan ^{2} \beta . \) then show
that \( \tan ^{2} \alpha=\cos ^{2} \beta-\sin ^{2} \beta \)


Burning of coal and wood causes
A. pollution of air
B. decrease of non-renewable source of energy
C. both (a) and (b)
D. neither (a) or (b).


Sea lettuce is the common name for
A. Laminaria
B. Fucus
c. Sargassum
D. Ulva


Electromotive force of a cell is basically
\( \mathbf{a} \)
\( A \cdot \) force
B. power
c. work
D. current capacity


Linear magnification is
A. Positive for an inverted image
B. Negative for an erect image
C. Zero for an inverted image
D. Negative for an inverted image


Which species is polar?
A. Trans-hex-3-ene
B. Trans-but-2-ene
c. \( P C l_{5} \)
D. \( X e F_{6} \)


Which of the following metal is leached by cyanide process?
\( A \cdot A B \)
B. Na
\( c \cdot A \)
D. cu


Calculate the following limits. \( \lim _{n \rightarrow \infty} \frac{\frac{1}{2}+1+\frac{3}{2}+\ldots \frac{n}{2}}{0.25 n^{2}+n+3}, n \epsilon N \)


Select the correct statements about the
electrolysis
This question has multiple correct options
A. Electric current is used to drive a non spontaneous reaction
B. \( \Delta G \) is positive for chemical process during electrolysis
C. Cations and anions move towards the anode in the anode and cathode respectively
D. Over voltage is generally associated with anode in the electrolysis of \( N a C l(a q) \)


Write the free radical mechanism for
the polymerisation of ethene.


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


In the triangle, find the measures of the
angles.
A \( \cdot 40^{\circ}, 60^{\circ}, 80^{\circ} \)
B \( \cdot 45^{\circ}, 60^{\circ}, 75^{\circ} \)
c. \( 45^{\circ}, 45^{\circ}, 90^{\circ} \)
D. \( 50^{\circ}, 60^{\circ}, 70^{\circ} \)


To find out the concentration of \( S O_{2} \) in
the air (in parts per million, i.e., \( p p m \) ),
the data was collected for 30 localities
in certain city and is presented below:
Concentration of \( S O_{2} \) \( f(\operatorname{in} p p m) \) Frequency \( 2^{2} \) reeter
\( 0.00-0.04 \)
\( 0.04-0.08 \)
\( 0.08-0.12 \) 9
\( 0.12-0.16 \) 2
\( 0.16-0.20 \) 4
\( 0.20-0.24 \) 2
Find the mean concentration of \( S O_{2} \) in
the air.


The gas other than oxygen used as an anaesthetic.
в. \( P_{2} O_{5} \)
\( c \cdot C O_{2} \)
D. \( S O_{2} \)


Two cars are moving on perpendicular
roads. When ear- 1 sounds a horn of
frequency \( n, \) then the apparent
frequency of sound heard by car-2 is is velocity of sound)
A \( \cdot n\left[\frac{V_{1}+V_{2}}{V_{1}-V_{2}}\right. \)
B. \( n\left[\frac{V_{1}+V_{2} \cos \theta_{2}}{V_{1}-V_{2} \cos \theta_{1}}\right. \)
C \( \cdot n\left[\frac{V \cos \theta_{2}}{V_{1} \cos \theta_{1}}\right] \)
D. \( n\left[\frac{V+2 v_{0} \cos \theta_{1}}{V-2 V_{1} \cos \theta_{2}}\right. \)


Amphitrichous flagellation has
A. Flagella absent
B. Flagella at one end
c. Flagella at both the ends
D. Flagella all around


The volume strength of \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) solution
is \( 10 . \) It means:
A \( \cdot \) at \( \operatorname{s.} \). \( . P . \) 10 \( g \) solution of \( H_{2} O_{2} \) gives 10 mL of \( O_{2} \)
B. at S.T.P. 1 g equivalent of \( H_{2} O_{2} \) gives \( 10 \mathrm{mL} \) of \( O_{2} \)
c. at st.P. 10 litre solution of \( H_{2} O_{2} \) gives \( 10 \mathrm{mL} \) of \( O_{2} \)
D. at S.T.P. 1 mL solution of \( H_{2} O_{2} \) gives \( 10 \mathrm{mL} \) of \( O_{2} \)


Solve the system of in equations \( \frac{x}{2 x+1} \geq \frac{1}{4} ; \frac{6 x}{4 x-1}<\frac{1}{2} \)


The distance between the plates of a
parallel plate capacitor is \( d \). A metal
plate of thickness \( d / 2 \) is placed between the plates. The capacitance would be then be
A. Unchanged
B. Initial
c. zero
D. Doubled


Which of the following compounds does not have a trigonal planar geometry?
A \( . B H_{3} \)
B. \( C O_{3}^{2} \)
\( \mathrm{c} \cdot \mathrm{SO}_{3}^{2-} \)
D. \( N O_{3} \)


Find the modulus and argument of the complex numbers. \( \frac{5-i}{2-3 i} \)


What is the torque on the bar?


When an electric current is passed through an electric bulb, it becomes
warm when touched. Give reasons.


For which one of the following system
\( \Delta \boldsymbol{E}<\Delta \boldsymbol{H} ? \)
A \( \cdot 2 S O_{2(g)}+O_{2(g)} \rightarrow 2 S O_{3(g)} \)
B. \( N_{2(g)}+O_{2(g)} \rightarrow 2 N O_{(g)} \)
C. \( 2 N H_{3(g)} \rightarrow N_{2(g)}+3 H_{2(g)} \)
D. \( H_{2(g)}+I_{2(g)} \rightarrow 2 H I_{(g)} \)


A freely falling body covers half of its journey from the top of a tower in \( 0.5 s \)
What is the height of the tower?
A \( .4 .9 m \)
B. \( 2.45 m \)
\( \mathrm{c} .9 .8 \mathrm{m} \)
D. \( 9 m \)


A man is walking from east to west on a level rough surface. The force on the
man is directed:
A. From west to east
B. From east to west
c. From north to south
D. From south to north


Discuss how the classification system has undergone several changes over a period of time?


\( Z n C O_{3} \) is thermally more stable than
\( M g C O_{3} \) because:
A. \( M g(O H)_{2} \) exhibits only basic properties while \( Z n(O H)_{2} \) is amphoteric
B. polarising action of \( Z n^{2+} \) with 18 -electron configuration on the anion is larger than that of \( M g^{2+} \) with a noble-gas electron configuration and of same size and charge
\( c . \) both
(a) and (b) are correct
D. none of the above is correct


Two partners invest Rs 120000 and Rs
84000 in a business and agree that \( 70 \% \) of the profit should be divided
equally between them and the remaining profit is to be treated as interest on capital. If one person gets Rs 900 more than the other then find the
total profit made in the business.


Find the output \( F \) of the logic circuit
given below


Kirchhoff's first law ie, \( \Sigma i=0 \) at a
junction is based on the law of conservation of
A. Charge
B. Energy
c. Momentum
D. Angular momentum


A coil of self-inductance \( L \) is connected
in series with a bulb B and an AC
source. Brightness of the bulb decreases when :
A. frequency of the AC source is decreased
B. number of turns in the coil is reduced
C . a capacitance of reactance \( X_{C}=X_{L} \) is included in the same circuit
D. an iron rod is inserted in the coil


Two particles having the same momentum enter at right angles into same magnetic field and travel in circular paths of radius \( r_{1} \) and \( r_{2} \). The
ratio of their charges is:
A \( \cdot \frac{r_{1}}{r_{2}} \)
B. \( \left(\frac{r_{1}}{r_{2}}\right)^{1 / 2} \)
\( ^{c} \cdot\left(\frac{r_{1}}{r_{2}}\right)^{2} \)
D. \( \left(\frac{r_{1}}{r_{2}}\right)^{-1} \)


For the wave shown in figure, find its amplitude, frequency and wavelength if its speed is \( 300 \mathrm{m} / \mathrm{s} \). Write the equation
for this wave as it travels out along the
\( +x \) -axis if its position at \( t=0 \) is as
shown.


Saprolegnia is a best example for demonstrating
A. Heterospory
B. Dichogamy
c. Herkogamy
D. Diplanetism


Which of the following has highest melting point?
A. Magnesium
B. Barium
c. Calcium
D. Beryllium


The moments of inertia of a thin square
plate \( A B C D \) of uniform thickness
about an axis passing through the
centre \( \boldsymbol{O} \) and perpendicular to the plate
are
This question has multiple correct options
\( \mathbf{A} \cdot I_{1}+I_{2} \)
B. \( I_{3}+I_{4} \)
c. \( I_{1}+I_{3} \)
D. \( I_{2}+I_{3} \)


Calculate the force of gravitation between two objects of masses \( 80 \mathrm{kg} \) and \( 1200 \mathrm{kg} \) kept at a distance of \( 10 \mathrm{m} \) from each other.Given \( (G=\mathbf{6 . 6 7} \times \)
\( \left.10^{-11} N m^{2} / k g^{2}\right) \)


Aluminium oxide may be electrolysed
at \( 1000^{\circ} \mathrm{C} \) to furnish aluminium metal.
The cathode reaction is \( A l^{3+}+3 e^{-} \rightarrow \)
Al. To prepare \( 5.12 \mathrm{kg} \) of aluminium
metal by this method would require:
A \( \cdot 5.49 \times 10^{1} C \) of electricity
B . \( 5.49 \times 10^{4} C \) of electricity
c. \( 1.83 \times 10^{7} C \) of electricity
D. \( 5.49 \times 10^{7} C \) of electricity


\( S \) is one focus of an ellipse and \( P \) is any point on the ellipse. If the maximum and minimum values of \( S P \) are \( m \) and
\( \boldsymbol{n} \) respectively, then the length of semi
major axis is
A . AM of \( m, n \)
в. G.M. of \( m, n \)
с. нм от \( m, n \)
D. AGP of \( m, n \)


Two cohorent monochromatic light beams of intensities \( 4 \mid \) and 9 I interfere
in a Young's double slit experimental setup to produce a fringe pattern on the screen. The phase difference between
the beams at two points \( P \) and \( Q \) on the
screen are \( \pi / 2 \) and \( \pi / 3 \) respectively.
Then the ratio of the two intensities
\( \boldsymbol{I}_{\boldsymbol{P}} / \boldsymbol{I}_{Q} \) is
A. 0
в. \( \frac{6}{19} \)
c. \( \frac{13}{19} \)
D. \( \frac{6}{13} \)


Convert to percent
\( \frac{33 \frac{1}{3}}{100} \)


The transition from the state \( n=4 \) to
\( \boldsymbol{n}=\mathbf{3} \) in a hydrogen like atom results in
ultraviolet radiation. Infrared radiation
will be obtained in the transition from
\( \mathbf{A} \cdot 2 \rightarrow 1 \)
B . \( 3 \rightarrow 2 \)
c. \( 4 \rightarrow 2 \)
D. \( 5 \rightarrow 4 \)


The steps for decreasing friction
includes:

This question has multiple correct options
A. ball bearing used in moving parts of a machine
B. the streamlined shape of an aircraft
C. the layer of air between the hull of a hovecraft
D. none of these


The activity of certain preparation decreases by \( 75 \% \) after 7.0 days. Tha half life of the sample is [Take \( \ln (0.4)= \) -0.916]
A . 2.9 days
B. 5.3 days
c. 3.5 days
D. 6 days


\( \boldsymbol{a}=\mathbf{1}, \boldsymbol{d}=\mathbf{2}, \) find \( \boldsymbol{S}_{\mathbf{1 0}} \)


If \( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{1} & \mathbf{2}\end{array}\right], \boldsymbol{B}=\left[\begin{array}{ll}\mathbf{3} & \mathbf{4}\end{array}\right] \) then \( \boldsymbol{A}- \)
\( \boldsymbol{B}= \)
\( \mathbf{A} \cdot\left[\begin{array}{ll}-2 & -2\end{array}\right] \)
B. \( \left[\begin{array}{ll}2 & 2\end{array}\right] \)
\( \mathbf{c} \cdot\left[\begin{array}{ll}-3 & -1\end{array}\right] \)
D. None of these


State true or false:
If \( 4^{2 x}=\frac{1}{32}, \) then the value of \( x \) is \( -\frac{5}{4} \)
A. True
B. False


Arrange \( C e^{3+}, L a^{3+}, P m^{3+}, \) and \( Y b^{3+} \)
in increasing order of their ionic radius:
A \( \cdot Y b^{3+}<P m^{3+}<C e^{3+}<L a^{3} \)
в. \( C e^{3+}>Y b^{3+}<P m^{3+}<L a^{3+} \)
c. \( Y b^{3+}>P m^{3+}<L a^{3+}<C e^{3+} \)
D. none of these


Typical embryosac of Angiosperms is
A. Tetranucleated
B. Eight nucleated and seven celled
C. Tetranucleated and seven celled
D. Tetranucleated and tetra celled


\( \boldsymbol{C a} \boldsymbol{C O}_{\boldsymbol{3}(\boldsymbol{s})} \rightarrow \boldsymbol{C a O}_{(s)}+\boldsymbol{C O}_{\boldsymbol{2}(\boldsymbol{g})} \boldsymbol{\Delta} \boldsymbol{H}= \)
\( +180 K J \)
If entropies of limestone, lime and carbon dioxide are 93,39 and
\( \mathbf{2 1 3} \boldsymbol{J} / \boldsymbol{m o l} / \boldsymbol{K} . \) Then \( \boldsymbol{\Delta} \boldsymbol{S}_{\boldsymbol{t o t a l}} \) in \( \boldsymbol{J} \boldsymbol{K}^{-1} \) at
\( \mathbf{3 0 0 K} \) is:
A. 159
в. -44
\( c .700 \)
D. - 650


The states of hybridisation of boron and
oxygen atoms in boric acid \( \left(\mathbf{H}_{3} \mathbf{B O}_{3}\right) \) are respectively:
A. sp and sp \( ^{2} \)
B. \( s p^{2} \) and \( s p^{3} \)
c. sp 3 and \( s p^{2} \)
D. sp3 and sp3


The depletion of ozone involves the following steps:
Step \( 1: O_{3} \frac{K_{1}}{k_{2}} O_{2}+O(\text { fast }) \)
\( \operatorname{step} 2: 0_{3}+O \longrightarrow 2 O_{2}(\text { slow }) \)
The predicted order of the reaction will be:


Write the supplement of each of the
following angles: \( 138^{\circ} \)


Which of the following is/are aerosols? This question has multiple correct options
A. Smoke
в. мilk
c. Butter
D. Fog


Solve: \( |\cos x|=\cos x-2 \sin x \)
A \( \cdot x=(2 n+1) \pi+\frac{\pi}{4} \)
B \( \cdot x=(2 n+1) \pi+\frac{\pi}{2} \)
C \( \cdot x=2 n \pi+\frac{\pi}{4} \)
D \( \cdot x=2 n \pi+\frac{\pi}{2} \)


The probability that at least one of the
events \( A \) and \( B \) occurs is \( 0.6, \) If \( A \) and \( B \)
occur simultaneously with probability
0.2, then \( \boldsymbol{P}(\overline{\boldsymbol{A}})+\boldsymbol{P}(\overline{\boldsymbol{B}}) \) is
A. 0.4
B. 0.8
\( c \cdot 1.2 \)
D. 1.4


Assertion
The zygote developed from sexual reproduction is diploid.
Reason
In sexual reproduction, haploid
gametes fuse and form zygote.
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


\( \int_{0}^{\pi / 2} \sin x \cos x d x \) is equal to:


What is the largest side of the triangle?
A. \( \overline{A B} \)
в. \( \overline{B C} \)
\( c \cdot \overline{C A} \)
D. \( \overline{A C} \)


Which of the following scientist has made a significant contribution in the field of classification?
A. Pasteur
B. Oparin
c. Darwin
D. Linnaeus


Solve: \( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}(\operatorname{cosec} \boldsymbol{x})=? \)


Choose the correct answer from the
alternatives given. In an experiment, oat (Avena sativa) seedlings were grown under the same conditions of temperature, moisture and light. Their tips were removed and divided into four groups. Each group was given different treatments and the growth was measured carefully after keeping them in dark for 16 Firs. Which of the following groups had the most growth?
A. In Group I, the tip was put back on each seedling
B. In Group II, a block of agar gel containing juice of 10 tips was placed on top of each seedling
c. In Group III, nothing was placed on top of each seedling
D. In Group IV, a drop of water was placed on top of each seedling


Evaluate:
\( \int \sec x \tan x d x \)


Why \( C l F_{3} \) exists but \( F C l_{3} \) does not?


Lowest value of variance can be:
\( A \cdot 1 \)
B. -
c. 0
D. None of these


If the angle of dip at a certain place is
\( 45^{\circ} \) then the horizontal component \( \boldsymbol{H} \)
vertical component \( V \) and total
intensity \( I \) of earth's magnetic field have the correct relationship given by :
A. \( H=\sqrt{2} V \)
В. \( I=\sqrt{2} V \)
\( \mathbf{c} \cdot H=2 V \)
D. \( H=\sqrt{2} H \)


Formulate a cell from the following electrode reactions:
(a) \( C I_{2(g)}+2 e^{-} \longrightarrow 2 C I_{(a q)}^{-} \)
\( (b) 2 I_{(a q)} \longrightarrow I_{2(s)}+2 e^{-} \)


\( H C N \) undergoes nucleophilic addition reaction to give product of :
A. hydrogen cyanide
B. hydroxynitrile.
c. hydroxyl amine
D. all of the above


Find \( \frac{d y}{d x} \) of \( \sin ^{2} y+\cos x y=k \)


A progressive wave of frequency
\( \mathbf{5 0 0} \boldsymbol{H z} \) is travelling with a velocity of
\( 360 m s^{-1} . \) The distance between two
point \( 60^{\circ} \) out of phase is
A \( .2 .1 m \)
B. \( 0.12 m \)
c. \( 0.21 m \)
D. \( 1.2 m \)


The wattage of an electric heater which
draws 5 A current when connected to a
\( 220 \mathrm{V} \) supply is


Which of the following lights has maximum wavelength?
A \( \cdot \gamma \) - rays
B. X - rays
c. UV - rays
D. Visible rays


An \( \alpha \) - particle travels in a circular path
of radius \( 0.45 \mathrm{m} \) in a magnitude field \( \mathrm{B} \) \( =1.2 \mathrm{Wb} / \mathrm{m}^{2} \) with a speed of \( 2.6 \times 10^{7} \)
\( \mathrm{m} / \mathrm{s} . \) The period of revolution of the \( \alpha \)
particle is:
B . (b) 1.1 \( \times 10^{-6} \) s
c. \( \left(\text { с ) } 1.1 \times 10^{-7} \) s \right.
D. (d) 1.1 \( \times 10^{8} \) s


A solenoid is connected to a source of
constant e.m.f. for a long time. A soft iron piece is inserted into it. Then, which of the following is/are correct? This question has multiple correct options
A. Self-inductance of the solenoid gets increased
B. Flux linked with the solenoid increases; hence, steady state current gets decreased
C. Energy stored in the solenoid gets increased
D. Magnetic moment of the solenoid gets increased


Find the value of \( \lim _{x \rightarrow 0} \frac{2 x^{2}+3 x+4}{2} \)
A .2
B.
c. \( 3 \sqrt{5} \)
D. \( 2 \sqrt{5} \)


Choose the correct answer from the
alternatives given
Plant growth depends on:
A . cell division
B. hormones
c. cell enlargement
D. all of these


incident on a coated glass plate. If \( 25 \% \) of the incident light is reflected from
the upper surface and \( 50 \% \) of light is
reflected from the lower surface of the
glass plate, the ratio of maximum to
minimum intensity in the interference
region of the reflected light is
\( A \)
B.
\( c \cdot \frac{5}{8} \)
\( D \cdot 8 \)
\( \overline{5} \)


The amount of heat necessary to raise
the temperature of 0.2 mol of \( N_{2} \) at
constant pressure from \( 37^{\circ} C \) to \( 337^{\circ} C \) will be
\( \mathbf{A} \cdot 746 J \)
в. 1746 Л
c. 2746 cal
D. \( 3746 J \)


Arithmetic mean for ungrouped data can be calculated by
A. assumed mean method
B. direct method
c. step deviation method
D. all of the above


In the estimation of sulphur by Carius Method, \( 0.468 g \) of an organic compound afforded \( 0.668 g \) of barium sulphate. Find the percentage of sulphar in that compound.
A . \( 12.85 \% \)
B . \( 15.66 \% \)
c. \( 19.60 \% \)
D. \( 25.35 \% \)


The conductivity of saturated solution of \( B a S O_{4} \) is \( 3.06 \times 10^{-6} \) mho \( c m^{-1} \)
and its equivalent conductance 1.53 \( \operatorname{mhocm}^{2} e q^{-1} . \) The \( K_{s p} \) for \( B a S O_{4} \) will
be:
A \( \cdot 10^{3} M \)
В. \( 4 \times 10^{6} M \)
c. \( 10^{-3} M \)
D. \( 4 \times 10^{-6} M \)


According to the Census Report 2011 India's population grew between 2001 \( 2011, \) at annual average rate of
A . \( 1.64 \% \)
B . 2.14\%
c. 2.25\%
D . 1.34\%


The relation between \( u, v \) and \( r \) is:
A \( \cdot r=\frac{2 u v}{u+v} \)
B. \( r=\frac{2}{u+v} \)
c. \( r=\frac{2(u+v)}{(u v)} \)
D. None of these


A hollow chaeged mental sphere has radius \( r . \) if the potential difference between its surface and a point at a distance \( 3 r \) from the center is 'v' then
electric field intensity at a distance 3 r
is
A \( \cdot \frac{v}{2 r} \)
B. \( \frac{v}{3 r} \)
c. \( \frac{v}{6 r} \)
D. \( \frac{v}{4 r} \)


A solenoid of length \( 1.0 m, \) radius \( 1 \mathrm{cm} \)
and total turns 1000 wound on it,
carries a current of 5 A. Calculate the
magnitude of the axial magnetic field inside the solenoid. If an element was to
move with a speed of \( 104 m / s \) along the
axis of this current carrying solenoid, what would be the force experienced by this electron?


If point \( p \) lies in first octant, then the \( \operatorname{sign} \) of \( x- \) coordinate will always be
\( A \cdot+ \)
в.
c. \( x \) coordinate is always 0
D. \( x \) coordinate can be \( + \) or \( - \)


\( E \) and \( F \) are points on the sides \( P Q \) and
\( P R \) respectively of a \( \Delta P Q R \) For each of
the following cases state whether \( \boldsymbol{E F} \| \boldsymbol{Q} \boldsymbol{R} \)
(1) \( P E=3.9 c m, E Q=3 \mathrm{cm}, P F= \)
\( \mathbf{3 . 6} \) cm and \( \boldsymbol{F R}=\mathbf{2 . 4} \)
(2) \( P E=4 c m, Q E=4.5 \mathrm{cm}, P F= \)
\( 8 \mathrm{cm} \) and \( R F=9 \mathrm{cm} \)
(3) \( P Q=1.28 \mathrm{cm} \mathrm{PR}= \)
\( \mathbf{2 . 5 6} \mathbf{c m}, \boldsymbol{P} \boldsymbol{E}=\mathbf{0 . 1 8} \mathbf{c m} \) and \( \boldsymbol{P} \boldsymbol{F}= \)
\( \mathbf{0 . 3 6} c \boldsymbol{m} \)


Which of the following, when dissolved in distilled water, makes it a
good conductor?
A. Potassium iodide
B. common salt
c. Potassium dichromate
D. All of the above


The number of combination of 16
things, 8 of which are alike and the rest
different, taken 8 at a time is
\( ? \)


In the given reaction:
\( \boldsymbol{C H}_{3}-\underset{C D_{3}}{C_{\mid} H-C H}^{O H} \)
\( \boldsymbol{C H}_{3} \frac{\operatorname{conc.H}_{2} \mathrm{SO}_{4} / \Delta}{\text { Alkenes }} \)
Total number of alkenes (Including stereo isomers) formed will be


One end of a slack wire (Youngs
modulus \( Y, \) length \( L \) and cross
sectional area \( A \) ) is clamped to a rigid wall and the other end to a block (mass
m) which rests on a smooth horizontal
plane. The block is set in motion with a speed v. What is the maximum
distance the block will travel after the
wire becomes taut?
A \( \cdot v \sqrt{\frac{m L}{A Y}} \)
B. \( v \sqrt{\frac{2 m L}{A Y}} \)
c. \( v \sqrt{\frac{m L}{2 A Y}} \)
D \( \cdot L \sqrt{\frac{m v}{A Y}} \)


A flexible wire loop in the shape of a circle has a radius that grows linearly with time. There is a magnetic field perpendicular to the plane of the loop that has a magnitude inversely proportional to the distance from the
center of the loop, \( B(r) \propto \frac{1}{r} . \) How does
the emf vary with time?
A. \( E \propto r^{2} \)
в. \( E \propto t \)
\( c \cdot E \propto \sqrt{t} \)
D. \( E \) is constant


In a trapezium, the vector \( \overline{B C}=\lambda \overline{A D} \)
and \( \bar{P}=\overline{A C}+\overline{B D}=\mu \overline{A D}, \) then
A. \( \mu=\lambda+1 \)
в. \( \lambda=\mu+1 \)
c. \( \lambda+\mu=1 \)
D. \( \mu=2+\lambda \)


The redistribution of intensity on account of the superposition of two waves is called as:
A. Refraction
B. Polarisation
c. Interference
D. Non of these


If \( A_{3} x_{3} \) and \( d e t A=2 \) then \( d e t A^{-1}= \)
A \( \cdot \frac{1}{2} \)
B. -
\( c \cdot \frac{1}{4} \)
D. -


R with centre at the origin, carrying
uniform positive surface charge
density. The variation of the magnitude of the electric field \( |\vec{E}(r)| \) and the
electric potential \( V(r) \) with the distance
from the centre, is best represented by
which graph?
\( A \)
B.
\( c \)
D.


The output power in a step-up
transformer is
A. Greater than the input power
B. Equal to the input power
C. Maintained even during the power cut
D. Less than the input power


Methyl amine reacts with acetyl chloride to form:
A. \( C H_{3} N H_{2} \)
B. \( C H_{3} N H N a \)
c. \( C H_{3} N H C O C H_{3} \)
D. \( \left(C H_{3}\right)_{2} N C O C H_{3} \)


Write chemical name of bleaching powder. Which gas is released when it is exposed to air? Write chemical
reaction involved in preparation of bleaching powder.


Hydrogen atoms, in a \( \boldsymbol{H}_{2} \) molecule
their electrons.
A. share
B. donate
\( c . \) accept
D. none of the above


If \( \int \frac{\log (t+\sqrt{1+t^{2}})}{\sqrt{1+t^{2}}} d t=\frac{1}{2}(g(t))^{2}+C \)
where \( C \) is a constant, then \( g(2) \) is
equal to
A \( \cdot \frac{1}{\sqrt{5}} \log (2+\sqrt{5}) \)
B . \( 2 \log (2+\sqrt{5}) \)
c. \( \log (2+\sqrt{5}) \)
D \( \cdot \frac{1}{2} \log (2+\sqrt{5} \)


A satellite in earth orbit experiences a
small drag force as it enters the earth's atmosphere. Two students were asked consequence of this Student-A : The satellite would slow
down as, it spirals towards earth due to work of frictional force.

Student-B : The satellite speed up due
to earths gravitational pull as it spirals
towards earth.
A. A is correct, B is wrong
B. B is correct, A is wrong
c. both are correct
D. both are wrong


Bleaching powder contains a salt of an
oxoacid as one of its components. The anhydride of that oxoacid is
A. \( C l_{2} O \)
в. \( C l_{2} O_{7} \)
c. \( C l O_{2} \)
D. \( C l_{2} O_{6} \)


In a experiment to measure the height of a bridge by dropping a stone into water underneath,if the error in the
measurement of times is \( 0.1 s \) at the
end of \( 2 s \),then the error in the
estimation of the height of the bridge
will be
\( \mathbf{A} \cdot 0.49 m \)
B. \( 0.98 m \)
c. \( 1.96 m \)
D. \( 2.12 m \)


Which structure is known as lower lip of cockroach?
A. Labrum
B. Labium
c. Mantum
D. Submentum


\( \lim _{x \rightarrow 1} \frac{(2 x-3)(\sqrt{x}-1)}{2 x^{2}+x-3} \cdot \) is \( \frac{-1}{b} \) Find


The layer of atmosphere between \( 10 \mathrm{km} \)
to \( 50 k m \) above the sea level is called
as:
A. troposphere
B. mesosphere
c. stratosphere
D. thermosphere


Let y be an implicit function of \( \mathbf{x} \) defined by \( \mathbf{x}^{2 \mathbf{x}}-\mathbf{2} \mathbf{x}^{\mathbf{x}} \cot \boldsymbol{y}-\mathbf{1}=\mathbf{0} \)
Then \( y^{\prime}(1) \) equals
A . -1
B.
\( c \cdot \log 2 \)
D. \( -\log 2 \)


\( \boldsymbol{f}:(\boldsymbol{0}, \infty) \rightarrow(\boldsymbol{0}, \infty) \) defined by
\( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{ll}2^{x} & \boldsymbol{x} \in(\mathbf{0}, \mathbf{1}) \\ \mathbf{5}^{\boldsymbol{x}} & \boldsymbol{x} \in[\mathbf{1}, \infty)\end{array}\right. \)
A. one-one but not onto
B. onto but not one-one
c. neither one - one nor onto
D. bijective


The tangents are drawn from origin and the point \( (\boldsymbol{g}, \boldsymbol{f}) \) to the circle \( \boldsymbol{x}^{2}+\boldsymbol{y}^{2}+ \)
\( 2 g x+2 f y+c=0 . \) Find the distance
between chords of contact.
A \( \cdot \frac{2\left(g^{2}+f^{2}-c\right)}{\sqrt{g^{2}+f^{2}}} \)
B. \( \frac{g^{2}+f^{2}-c}{\sqrt{g^{2}+f^{2}}} \)
c. \( \frac{g^{2}+f^{2}-c}{2 \sqrt{g^{2}+f^{2}}} \)
D. none of these


A constant force \( \boldsymbol{F} \) is applied in
horizontal direction as shown. Contact
force between \( M \) and \( m \) is \( N \) and
between \( m \) and \( M^{\prime} \) is \( N^{\prime} \) then:
A \( . N=N^{\prime} \)
B. \( N>N^{\prime} \)
C \( . N^{\prime}>N \)
D. Cannot be determined


What is sublimation


If a man of mass Mjumps to the ground from a height \( h \) and his centre of mass
moves a distance \( x \) in the time taken
by him to 'hit' the ground, and the average force acting on him (assuming his retardation to be constant during his impact with the ground) is
A. \( M g h / x \)
в. \( M g x / h \)
c. \( M g(h / x)^{2} \)
D. \( M g(x / h)^{2} \)


The most stable anion of the oxoacid of
chlorine is :
A \( \cdot C l O^{-} \)
B. \( C l O_{2}^{-} \)
\( \mathrm{c} \cdot \mathrm{ClO}_{3}^{-} \)
D. \( C l O_{4}^{-} \)


Let \( S=\{1,2,3, \dots .40\} \) and let \( A \) be a
subset of \( S \) such that no two elements
in \( A \) have their sum divisible by 5 What
is the maximum number of elements
possible in \( \boldsymbol{A} \) ?
A . 10
B . 13
c. 17
D. 20


A uniform steel rod of \( 5 m m^{2} \) cross
section is heated from \( 0^{\circ} C \) to \( 25^{\circ} C . \)
Calculate the force which must be
exerted to prevent it from expanding.
Also calculate strain.
(a for steel \( =12 \times 10^{-6} /^{\circ} \mathrm{C} \) and \( \gamma \) for
steel \( \left.=20 \times 10^{10} N / m^{2}\right) \)


A cylindrical capacitor has two co-axial cylinders of length \( 15 \mathrm{cm} \) and radii 1.5 \( \mathrm{cm} \) and \( 1.4 \mathrm{cm} . \) The outer cylinder is earthed and the inner cylinder is given a charge of \( 3.5 \mu C . \) Determine the
capacitance of the system and the potential of the inner cylinder. Neglect end effects (i.e., bending of field lines at the ends)


\( \ln \) an \( A C \) circuit voltage \( V=V_{0} \sin w t \)
and inductor L is connected across the
circuit. Then the instentaneous power
will be
A \( \cdot \frac{V_{0}^{2}}{2 w l} \sin w t \)
B. \( \frac{-V_{0}^{2}}{2 w l} \sin w t \)
c. \( \frac{V_{0}^{2}}{2 w l} \sin 2 w t \)
D. \( \frac{V_{0}^{2}}{w l} \sin w t \)


An object is placed beyond twice the focal length of a convex lens. Find the
position nature and size of the image with the help of a ray diagram.


The conducting rod \( a b \), as shown in figure makes contact with metal rails
\( c a \) and \( d b . \) The apparatus is in a uniform
magnetic field of \( 0.800 T, \) perpendicular to the plane of the figure. In what
direction does the current flow in the
rod?
\( A \cdot b \) to \( a \)
B. a to
\( c . \) a to b and then b to a
D. a to


The reagents / conditions K, L and M are
respectively:
\( \mathbf{A} \cdot B a(O H)_{2}, K C N \) and \( C H C l_{3} / N a O H \) heat, \( H_{3} O^{+} \)
B. \( H_{2} O \) boil, \( C O_{2} / K O H \) and \( A c_{2} O-A c O N a \), heat
c. steam \( ; C H C l_{3} / N a O H, \) heat, \( H_{3} O^{+} \) and \( A c_{2} O- \) \( A c O N a, \) heat
D. \( C u_{2} C l_{2} / H C l, N a O H / h i g h \quad P \) and \( C O_{2} \mid N a O H, \) heat
E. Blank


Using mathematical induction prove
that:
\[
\frac{\frac{1}{1.2 .3}+\frac{1}{2.3 .4}+\frac{1}{3.4 .5}+\ldots . .+}{n(n+1)(n+2)}=\frac{n(n+3)}{4(n+1)(n+2)}
\]


A train moves in north direction with a
speed of \( 54 \mathrm{km} / \mathrm{h} \) A monkey is running on the roof of the train, against its motion with a velocity of \( 18 \mathrm{km} / \mathrm{h} \). with respect to train. The velocity of monkey as observed by a man standing on the
ground is :
A. \( 5 \mathrm{m} / \mathrm{s} \) due south
B. \( 25 \mathrm{m} / \mathrm{s} \) due south
c. \( 10 m / s \) due south
D. \( 10 \mathrm{m} / \mathrm{s} \) due north


The correct order for the increasing
extent of hydrolysis is:
\( \mathbf{A} \cdot P O_{4}^{3-}<H P O_{4}^{2-}<H_{2} P O_{4}^{-} \)
B. \( H_{2} P O_{4}^{-}<H P O_{4}^{2-}<P O_{4}^{3-} \)
\( \mathbf{c} \cdot H P O_{4}^{2-}<P O_{4}^{3-}<H_{2} P O_{4}^{-} \)
D \( \cdot P O_{4}^{3-}<H_{3} P O_{4}^{-}<H P O_{4}^{2-} \)


A charge \( Q \) is kept at the corner of a cube. Electric flux passing through one of those faces not touches that charge
is:-
\( ^{A} \cdot \frac{Q}{24 \epsilon_{0}} \)
в. \( \frac{Q}{3 \epsilon_{0}} \)
c. \( \frac{Q}{8 \epsilon_{0}} \)
D. \( \frac{Q}{6 \epsilon_{0}} \)


The nth term of a sequence is \( 3 n-2 . \) Is
the sequence an A.P.? If so, find its 10 th
term


Divide 28 into four parts in A.P. so that
ratio of the product of first and third with the product of second and fourth is 8:15.Now find the largest term in those
four terms ?


For perfectly rigid bodies, the elastic constants \( Y, B \) and \( n \) are
A. \( Y=B=n=0 \)
B. \( Y=B=n \) -infinity
c. \( Y=2 B=3 n \)
D. \( Y=B=n=0.5 \)


The resistance of a wire at room
temperature \( 30^{\circ} \mathrm{C} \) is found to be \( 10 \Omega \)
Now to increase the resistance by \( 10 \% \) the temperature of the wire must be:
[The temperature coefficient of resistance of the material of the wire is
\( \left.0.002 \text { per }^{\circ} C\right] \)
A \( \cdot 36^{\circ} \mathrm{C} \)
в. \( 83^{\circ} \) С
\( \mathbf{c} \cdot 63^{\circ} C \)
D. \( 33^{\circ} \mathrm{C} \)


If \( 4 \bar{i}+7 \bar{j}+8 \bar{k}, 2 \bar{i}+3 \bar{j}+4 \bar{k} \) and \( 2 \bar{i}+ \)
\( 5 \bar{j}+7 \bar{k} \) are the position vectors of the
vertices \( A, B \) an \( C \) of triangle \( A B C, \) the position vector of the point where the bisector of \( \angle \mathrm{A} \) meets BC is?
A \( \cdot \frac{2}{3}(-6 \bar{i}-8 \bar{j}-6 \bar{k}) \)
B \( \cdot \frac{2}{3}(6 \bar{i}+8 \bar{j}+6 \bar{k}) \)
c. \( \frac{1}{3}(6 \bar{i}+13 \bar{j}+18 \bar{k}) \)
D. \( 2(\bar{i}+\bar{j}+\bar{k}) \)


Find the multiplicative inverse of the
complex number \( 4-3 i \)


Which of the following are crystalline
allotropic forms of sulphur?
A. Sulphur is used in preparation of conducting wires
B. A mixture of zinc and sulphur on heating with sulphur produces a greyish residue of zinc sulphide
C. Sulphur is an element belonging to VI A group
D. Sulphur is a nonmetallic element


The remainder in the division of \( 14 x^{2}- \)
\( 53 x+45 \) by \( 7 x-9 \) is
A . -3
B. \( 7 x \)
c. 90
D.


Points in which abscissa and ordinate
have different signs will lie in
A. Ist and IIIrd quadrants
B. Illrd and IVth quadrants
c. Ilnd and Illrd quadrants
D. IInd and IVth quadrants


At \( 25^{0} C \) a solution containing 0.2 g of polyisobutene in \( 100 \mathrm{mL} \) of benzene
developed a rise of \( 2.4 \mathrm{mm} \) at osmotic equilibrium. Calculate the molecular weight of polyisobutene if the density of solution is \( 0.88 \mathrm{g} / \mathrm{mL} \)


The magnetic fields through two identical rings made of copper and wood are changing at the same rate. The induced electric field in copper ring will be :
A. more than that in the wooden ring
B. less than that in the wooden ring
c. finite and that in the wooden ring will be zero
D. same as that in the wooden ring


The work done by a body on application of a constant force is directly
proportional to the distance traveled by the body. Express this in the form of an equation in two variables and draw the graph of the same by taking the
constant force as 5 units. Read from the
graph, the work done when the distance traveled by the body is 0 units.
A. 0 units
B. 2 units
c. 1 units
D. 3 units


Which of the following statements is correct according to the basic concept of thermodynamics which govern the
feasibility of a metallurgical process?
A. When the value of \( \triangle G \) is positive for the equation \( \Delta G= \) \( \triangle \mathrm{H}-\mathrm{T} \Delta \mathrm{S} \), the reaction will proceed
B. If reactants and products of two reactions are put together and net \( \triangle G \) is -ve, the overall reaction will occur
c. on increasing the temperature, the value of \( \triangle G \) becomes +ve
D. Feasibility of thermal oxidation of an ore can be established by Ellingham diagram in which a straight line shows the reduction reaction will proceed.


True or False
According to JJ. Thomson mode
electrons revolve around the nucleus.


In series L-C-R resonant circuit, to
increase the resonant frequency:
A. \( L \) will have to be increased
B. C will have to be increased
c. LC will have to be decreased
D. LC will have to be increased


\( \operatorname{Given} f(x)=\left\{\begin{array}{l}x, 0 \leq x<\frac{1}{2} \\ \frac{1}{2}, x=\frac{1}{2} \\ 1-x, \frac{1}{2}<x \leq 1\end{array} \) and \right.
\( g(x)=\left(x-\frac{1}{2}\right)^{2}, x \epsilon R, \) Then the area
(in sq.units) of the region bounded by the curves \( y=f(x) \) and \( y=g(x) \) between the lines \( 2 x=1 \) and \( 2 x=\sqrt{3} \)
is
\( ^{A} \cdot \frac{1}{3}+\frac{\sqrt{3}}{4} \)
B. \( \frac{1}{2}-\frac{\sqrt{3}}{4} \)
c. \( \frac{1}{2}+\frac{\sqrt{3}}{4} \)
D. \( \frac{\sqrt{3}}{4}-\frac{1}{3} \)


Which of the following quantities will be zero for alpha particles at the point of closest approach to the gold atom in Rutherford's scattering of alpha particles?
A. Acceleration
B. Kinetic energy
c. Potential energy
D. Electrical energy


In a molecule of phosphorus (V) oxide,
there are:
A. \( 4 P-P, 10 P-O \) and \( 4 P=O \) bonds
B. \( 12 P-O \) and \( 4 P=O \) bonds
c. \( 2 P-O \) and \( 4 P=P \) bonds
D. \( 6 P-P, 12 P-O \) and \( 4 P=P \) bonds


As per modern classification of solar
system, number of planets excluding Earth is:
\( A \cdot 7 \)
B. 8
\( c .9 \)
D. 10


Which metal foil is used for packing of some of the medicine tablets?


t is known that an urn containing altogether 10 balls was filled in the following manner: A coin was tossed 10 times, and according as it showed heads or tails, one white or on black ball was put into the urn. Balls are drawn
from this urn one at a time, 10 times in
succession (with replacements) and every one turns out to be white. The
chance that the urn contains nothing but white balls is \( \frac{1}{2^{k}} . \) Find the value of \( k \)


Given the structural formula for the
following:
\( 2- \) methyl propane


What is \( \int_{1}^{e} x \ln x d x \) equal to?
\( ^{\mathrm{A}} \cdot \frac{e+1}{4} \)
B. \( \frac{e^{2}+1}{4} \)
c. \( \frac{e-1}{4} \)
D. \( \frac{e^{2}-1}{4} \)


Find the sum: \( \sqrt{2}+\sqrt{8}+\sqrt{18}+ \)
\( \sqrt{32} \ldots . . \) up to \( n \) terms


Which one of the following statements is not correct of for a junction transistor?
A. The base region is very thin.
B. Emitter is more heavily doped as compared to collector.
c. Emitter and collector can be interchanged
D. The surface area of collector is quite large as compared to emitter.


When two liquid of same volume but
different densities \( \rho_{1} \) and \( \rho_{2} \) are mixed
together, then the density of the mixture is
A \( \cdot \frac{p_{1}+p_{2}}{2} \)
B . \( p_{1}+p_{2} \)
c. \( \frac{2 p_{1} p_{2}}{p_{1}+p_{2}} \)
D. \( 2 p_{1}+2 p_{2} \)


The maximum amount of \( C a C O_{3} \) that
can be obtained from 4 g of calcium as per the sequence of reaction is:
\( \boldsymbol{C a} \rightarrow \boldsymbol{C a O} \rightarrow \boldsymbol{C a} \boldsymbol{C O}_{3} \)
A . \( 20 g \)
B. 40
\( c \cdot 10 g \)
D. 80


Ultra pure silicon is prepared by
reduction of \( S i O_{2} \) with carbon.
A. True
B. False


The value of \( \int_{-\pi}^{\pi}\left(1-x^{2}\right) \sin x \cos ^{2} x d x \)
is
A. 0
в. \( _{\pi}-\frac{\pi^{3}}{3} \)
c. \( 2 \pi-\pi^{3} \)
D. \( \frac{7}{2}-2 \pi^{3} \)


Which one of the following is a renewable resource?
A. Natural gas
B. Petroleum
c. wind
D. coal


Adenine is \( 30 \%, \) what would be the
percentage of guanine?
A . 10\%
B. 20\%
c. 30\%
D. 40\%


Give the balance equation for the following laboratory preparation:
Ethane from sodium propionate
A \( \cdot C H_{3} C H_{2} C O O N a+N a O H \rightarrow C_{2} H_{6}+N a_{2} C O_{3} \)
в. \( C H_{3} C H_{2} C O O N a+2 N a O H \rightarrow C_{2} H_{4}+N a_{2} C O_{3} \)
c. \( C H_{3} C H_{2} \) COONa \( + \) NaOH \( \rightarrow C_{2} H_{4}+N a_{2} C O_{3} \)
D. \( C H_{3} C H_{2} C O O N a+2 N a O H \rightarrow 2 C H_{4}+N a_{2} C O_{3} \)


The number of significant figures in \( 6.02 \times 10^{23} \) is :
A . 23
B. 3
\( c \cdot 4 \)
D. 26


Which of the following is not the characteristic feature of flowering plants?
A. They include non-woody trees and shrubs.
B. They have stems, leaves and roots
c. They produce seeds
D. They have finely divided leaves called fronds.


Identify the compound (C).
\( \mathbf{A} \)
\( B \)
\( c \)
D. None


Three capacitances, each of \( 3 \mu F, \) are provided. These cannot be combined to
provide the resultant capacitance of :
A \( .1 \mu F \)
в. \( 2 \mu F \)
c. \( 4.5 \mu F \)
D. \( 6 \mu F \)


The solubility of gas in liquid is directly proportional to the pressure over the solutions at a given temperature.
A. True
B. False


In the figure, from the handkerchief
from four corners, sectors \( P, Q, R \) and \( S \)
each of \( 2 \mathrm{cm} \) are cut, whose sum is \( \boldsymbol{P}+ \)
\( Q+R+S=A_{1} \) and a circle of
diameter \( 4 \mathrm{cm} \) from the centre is cut
whose area is \( A_{2}, \) then is
possible.
A. \( A_{1} \neq A_{2} \)
B. \( A_{1}<A_{2} \)
c. \( A_{1}>A_{2} \)
D. \( A_{1}=A_{2} \)


What will happen if the secretion of parietal cells of gastric glands is
blocked with an inhibitor?
A. In the absence of HCI secretion, inactive pepsinogen is not converted into the active enzyme pepsin.
B. Enterokinase will not be released from the duodena mucosa and so trypsinogen is not converted to trypsin.
c. Gastric juice will be deficient in chymosin
D. Gastric juice will be deficient In pepsinogen