Which compound in each of the
following pairs would have the higher boiling point ? Explain your answers.
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{O H} \boldsymbol{o r} \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{O C H}_{3} \)
\( \boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{O} \boldsymbol{H} \) or \( \boldsymbol{H} \boldsymbol{O C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{O} \boldsymbol{H} \)
(c)
(d)
\( (e) \)
\( (\mathrm{g}) \)
(h) Hexane \( \mathrm{CH}_{3}\left(\mathrm{CH}_{2}\right)_{4} \mathrm{CH}_{3} \) or nonane \( \mathrm{CH}_{3}\left(\mathrm{CH}_{2}\right)_{7} \mathrm{CH}_{3} \)
\( (\mathbf{i}) \)


It is essential for venous blood while
travelling from kidneys towards heart to pass through
A. Iliac vein
B. Inferior vena cava
c. Liver
D. Hepatic vein
E. Pulmonary vein


In the adjoining figure, \( A B C \) is
triangle in which \( A D \) is the bisector of
\( \angle A . \) If \( A D \perp B C, \) show that \( \Delta A B C \)
is isosceles.


Number of Partial Fractions of \( \frac{3 x^{2}+1}{\left(x^{2}+1\right)^{4}} \)
A .4
B. 3
\( c \cdot 2 \)
D.


How many of the given plants show phyllotaxy, where single leaf arises at each node?

Alstonia, Brassica, Calotropis, Chilli, Chinarose Guava, Datura, Sunflower
A. Three
B. Five
c. Four
D. Six


Blood glands of Pheretima occur in
segments
\( A \cdot 1,2 \) and 3
B. 3,4 and 5
\( c \cdot 4,5 \) and 6
D. 10, 11 and 12


Agarose is a polymer of:
A. glucose
B. agarobiose
c. polyacrylamide
D. bisacrylamide


In respiration, pyruvic acid is
A. Formed only when oxygen is available
B. One of the products of Krebs cycle
C. Broken down into two carbon fragments and \( \mathrm{CO}_{2} \)
D. A result of protein breakdown


State whether the following statement is true or false.
\( \frac{\cos A-\sin A+1}{\cos A+\sin A-1}=\operatorname{cosec} A+\cot A \)
(by using the identity \( \operatorname{cosec}^{2} \boldsymbol{A}=1+ \)
\( \left.\cot ^{2} A .\right) \)
A . True
B. False


What is meant by wattless component
of the current?


A uniform disc of mass \( m \) and radius \( R \)
is pivoted at the point \( P \) and is free to
rotate in a vertical plane. The center \( C \) of the disc is initially in a horizontal position with \( P \) as shown in the figure.
It is released from this position, then its
angular acceleration when the line \( \boldsymbol{P C} \)
is inclined to the horizontal at an angle
\( \theta \) is:
A \( \cdot \frac{2 g \cos \theta}{3 R} \)
B. \( \frac{g \sin \theta}{2 R} \)
c. \( \frac{2 g \sin \theta}{R} \)
D. \( \frac{2 g \sin \theta}{3 R} \)


\( A \) and \( B \) are two points with position vectors \( 2 \vec{a}-3 \vec{b} \) and \( 6 \vec{b}-\vec{a} \)
respectively. Write the position vector of a point P which divides the line
segment AB internally in the ratio 1: 2


Find the value of the unknown exterior
angle \( x \) in the following diagrams.


The B-H curve for a ferromagnet is
shown in the figure. The ferromagnet is placed inside a ling solenoid with 1000
turns/cm.. The current that should be passed in the solenoid to demagnetise
the ferromagnet completely is:
\( A \cdot 2 m A \)
В. \( 1 m A \)
\( c .3 m A \)
D. None of these


The boiling point of amines are higher than that of hydrocarbon because:
A. they form inter molecular H-bonds
B. they are polar
c. they form ionic bonds
D. both A and


If \( A \) and \( B \) are non-empty sets such that
\( A \supset B, \) then
\( \mathbf{A} \cdot B^{\prime}-A^{\prime}=A-B \)
B \( \cdot B^{\prime}-A^{\prime}=B-A \)
\( \mathbf{C} \cdot A^{\prime}-B^{\prime}=A-B \)
D \( \cdot A^{\prime} \cap B^{\prime}=B-A \)
E \( \cdot A^{\prime} \cup B^{\prime}=A^{\prime}-B^{\prime} \)


Which of the following electronic configuration represents a highly electropositive element?
A \( \cdot[H e] 2 s \)
B \( \cdot[X e] 6 s^{1} \)
\( \mathbf{C} \cdot[H e] 2 s^{2} \)
D \( \cdot[X e] 2 s^{2} \)


Which one of the following reactions is an example of oxidative decarboxylation?
A. Conversion of succinate to fumarate.
B. Conversion of fumarate to malate
C. Conversion of pyruvate to acetyl Co-A
D. Conversion of citrate to isocitrate


If \( \sqrt{x}+\sqrt{y}=4, \) then find \( \frac{d x}{d y} \) at \( y=1 \)
A . 3
B. 4
\( c \cdot-3 \)
D. -


When sound waves travel from one
medium to another, which of the
following physical quantities does NOT alter?
A. Amplitude
B. Velocity
c. Frequency
D. Intensity


Fill in the blanks:
The IUPAC name of the compound
\( \boldsymbol{H} \boldsymbol{C} \equiv \boldsymbol{C}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{3} \)
is


blo
Q Type your question
will be: [Stress is proportional to square
of the Strain for the elastic tissue of the
aorta].
\( A \)
в.
\( c \)
\( D \)


Identify Bronsted-Lowry acids in the reaction given below? \( \left[\begin{array}{c}\left.\boldsymbol{A l}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{6}\right]^{3+}+\boldsymbol{H} \boldsymbol{C O}_{3}^{-} \rightleftharpoons\end{array}\right. \)
\( \left[A l\left(H_{2} O\right)_{S}(O H)\right]^{2+}+H_{2} C O_{3} \)
The correct answer is:
\( A \cdot A, C \)
B. A, D
c. в, D
D. B, c


A point on the parabola \( y^{2}=18 x \) at
which the ordinate increase at twice the
rate of the abscissa is
\( \mathbf{A} \cdot(9 / 8,9 / 2) \)
в. (2,-4)
c. \( (-9 / 8,9 / 2) \)
D. (2,4)


Find the common ratio of GP whose first
term is \( 3, \) the last is 3072 and the sum
of the series is 4095
A .2
B. 3
\( c \cdot 4 \)
D. 6


The radius of germanium (Ge) nuclide
is measured to be twice the radius of Be
the number of nucleons in Ge are


Evaluate: \( \int_{0}^{\pi / 2} \sin ^{3} x \cdot \cos ^{3} x d x \)
A \( \cdot \frac{1}{12} \)
в. \( \frac{\pi}{24} \)
c. \( \frac{\pi}{12} \)
D. \( \frac{1}{24} \)


Assertion
(A): Rigidity modulus of a liquid is infinity. Reason (R): For a ductile material yield point and breaking point are separated by larger distance than for brittle materials on the stress-starin curve.
A. Both assertion and reason are true and the reason is correct explanation of the assertion
B. Both assertion and reason are true, but reason is not correct explanation of the assertion
c. Assertion is true, but the reason is false
D. Assertion is false, but the reason is true


Calculate the pH of a \( 0.033 M \)
ammonia solution, if \( 0.033 M N H_{4} C l \) is introduced in this solution at the
same temperature. \( \left(k_{b} \text { for } N H_{3}=\right. \) \( \left.1.77 \times 10^{-5}\right) \)


\( \boldsymbol{p}(\boldsymbol{x})=\mathbf{2} \boldsymbol{x}^{3}-\mathbf{3} \boldsymbol{x}^{2}-\mathbf{5} \) is a
polynomial
A . linear
B. cubic
c. quadratic
D. constant


A mass of \( 1 k g \) is thrown up with velocity of \( 1000 m / s . \) After 5 second, it explodes
into two parts. One part of mass 400 g
moves soen with a velocity \( 25 m / s \) calculate the velocity of other part just after the explosion \( \left(\boldsymbol{g}=\mathbf{1 0 m s}^{-\mathbf{2}}\right) \)


Mitosis
A. Leads to recombinant daughter cells
B. Is a reduction division
C. Leads to formation of parental type of daughter cells
D. Occurs in gametes


If the heart sound recording and ECG recordings are superimposed then the first heart sound would occur
A. At the P wave
B. Just after the P wave
c. Just before the QRS complex
D. Just after the QRS complex


What is \( \int_{0}^{1} \frac{\tan ^{-1} x}{1+x^{2}} d x \) equal to \( ? \)
A \( \cdot \frac{\pi}{4} \)
в.
c. \( \frac{\pi^{2}}{8} \)
D. \( \frac{\pi^{2}}{32} \)


A liquid of density \( 12 k g m^{-3} \) exerts a
pressure of \( 600 P a \) at a point inside a liquid. What is height of liquid column
above that point? \( \left(\boldsymbol{g}=\mathbf{1 0 m} \boldsymbol{s}^{-1}\right) \)


How does the electronic configuration of an atom relate to its position in the Modern Periodic Table?


Given a uniform electric field \( \overrightarrow{\boldsymbol{E}}=\mathbf{2} \times \)
\( 10^{3} \hat{i} \mathrm{N} / \mathrm{C} \). Find the flux of this field
through a square of side \( 20 \mathrm{cm}, \) whose plane is parallel to the \( y \) -z plane. What would be the flux through the same square, if the plane makes an angle of
\( 30^{\circ} \) with the \( x \) -axis?


If \( f(x)=\sin x-\cos x-a x+b \)
decreases for a where \( x \in R \) then?
This question has multiple correct options
\( \mathbf{A} \cdot a<1 \)
B. \( a>1 \)
c. \( a<\sqrt{2} \)
D. \( a>\sqrt{2} \)


\( \mathbf{A}=\left[\begin{array}{cc}\cos \alpha & \sin \alpha \\ -\sin \alpha & \cos \alpha\end{array}\right] \) then \( \mathbf{A} . \mathbf{A}^{\mathbf{T}} \)
A. Null matrix
в. А
\( c \cdot I \)
D. A


What are haustoria?


The flowing water of a river possesses
energy.
A. gravitational
B. potential
c. electrical
D. kinetic


Complete the paragraph given below by filling in the blanks.

Blood flows twice in heart. In pulmonary circulation, the oxygenated blood is
carried to from
of heart through The oxygenated blood from lings is carried back to
of the heart through This oxygenated blood
from heart is carried to all systems
through and the deoxygenated blood from the systems below and above the heart is supplied to of
heart through

Hence it is
called double circulation.


Give reasons Genetic code is universal.


If \( \vec{A} \) is perpendicular to \( \vec{B}, \) then
\( \mathbf{A} \cdot \vec{A} \times \vec{B}=0 \)
B . \( \vec{A} \cdot[\vec{A}+\vec{B}]=A^{2} \)
c. \( \vec{A} \cdot \vec{B}=A B \)
D. \( \vec{A} \cdot[\vec{A}+\vec{B}]=A^{2}+A B \)


Four 2 ohm resistors are connected
together along the edges of a square. A 10V battery of negligible internal resistance is connected across a pair of
the diagonally opposite corners of the square. The power dissipated in the
circuit is
A. \( 100 \mathrm{w} \)
B. 50w
\( c .25 w \)
D. 20w


Which of the following laws of motion is (are) involved in the motion of the
rocket?
A. Newton's first law of motion.
B. Newton's second law of motion
c. Newton's third law of motion
D. All the above


The molar heat capacity of a monoatomic gas is:
A. \( 4 / 2 R \)
в. \( 3 / 2 R \)
c. \( 5 / 2 R \)
D. zero


How did the name 'hydrogen' originate?


Solids get heated by
A. conduction
B. convection
c. radiation
D. all the above


The list price of a video is \( \operatorname{Rs} 10,500 . \) If the rate of sales tax is \( 10 \% \), then the total amount for purchasing the video is
A . Rs 12,500
B. Rs 11,550
c. Rs 11,000
D. Rs 12,000


During "inelastic collision "
a) There is a loss of kinetic energy.
b) Some of the kinetic energy is used to
deform the body.
c) Some of the kinetic energy is
liberated as heat.
d) There is a loss of mass energy.
A. Only a is true
B. Only b and c are true
\( c \cdot a, b \& c \) are true
D. b, c \& d are true


Listed below are four respiratory capacities (a -d) and four jumbled respiratory volumes of a normal human
adult
Respiratory capacities Respiratory volumes
(a) Residual volume 2500 mL
(b) Vital capacity \( 3500 \mathrm{mL} \)
(c) Inspiratory reserve volume 1200
\( \mathrm{mL} \)
(d) Inspiratory capacity 4500
\( \mathrm{mL} \)
Which one of the following is the correct matching of two capacities and volumes?
A \( . \) (a)4500 \( \mathrm{mL} \) (b)3500 \( \mathrm{mL} \)
B. (b)2500 \( \mathrm{mL} \) (с) 4500 \( \mathrm{mL} \)
c. \( (c) 1200 \mathrm{mL} \) (d)2500 \( \mathrm{mL} \)
D. (d) 3500mL (a)1200 \( m L \) L


Which of the following is/are true for reversible process? This question has multiple correct options
A . It is a quasi-static process.
B. Both the system and surrounding will return to their original state
c. only the system will return to their original state.
D. It is a very fast process.


The sum of the magnitude of two forces at a point is \( 16 \mathrm{N} \). If their resultant is
normal to the smaller force and has a
magnitude of 8 N. Then two forces are
A. 6 N, 10 N
B. 8 N, 8 N
c. 4 N, 12 \( N \)
D. 2 N, 14 N


If \( \boldsymbol{x}+\frac{\mathbf{1}}{\boldsymbol{x}}=\mathbf{7}, \) find \( \boldsymbol{x}^{\mathbf{3}}+\frac{\mathbf{1}}{\boldsymbol{x}^{\mathbf{3}}} \)


Calculate the maximum wavelength of Balmer series in the hydrogen spectrum. Calculate the corresponding wave number.
\( \boldsymbol{R}=\mathbf{1 . 0 9 7} \times \mathbf{1 0}^{\mathbf{7}} \boldsymbol{m}^{-\mathbf{1}} \)


Which of the following pair of
substances can react to produce \( \boldsymbol{H}_{2} \)
gas?
A. Hydrolith and water
B. Sodium and heavy water
c. \( \mathrm{Hg} \) and Boiling water
D. Iron and conc. sulphuric acid


Is it a closed curve?


\[
\begin{array}{l}
2 x-5 y=8 \\
4 x+k y=17
\end{array}
\]
For which of the following values of \( k \)
will the system of equations above have no solution?
A . -10
в. -5
c. 0
D. 5
E . 10


A buffer solution with \( p H=9 \) is to be
prepared by mixing \( N H_{4} C l \) and
\( N H_{4} O H . \) Calculate the number of
moles of \( N H_{4} C l \) that should be added
to 1 liter of
\( \mathbf{1} \boldsymbol{M} \boldsymbol{N} \boldsymbol{H}_{\mathbf{4}} \boldsymbol{O} \boldsymbol{H} \cdot \boldsymbol{K}_{\boldsymbol{b}}\left(\boldsymbol{N} \boldsymbol{H}_{4} \boldsymbol{O} \boldsymbol{H}\right)=\mathbf{1 . 8} \times \)
\( 10^{-5} \)


When formaldehyde is heated with phenol in the presence of an alkali, the product formed is:
A . rubber
B. bakelite
c. chloroprene
D. neoprene


A ray of light is incident on a plane
mirror and the angle of reflection is \( 50^{\circ} \)
Calculate the angle between the incident ray and the reflected ray.
A \( .50^{\circ} \)
B . \( 25^{\circ} \)
\( c \cdot 90^{\circ} \)
D. \( 100^{\circ} \)


When the same amount of zinc is
treated separately with excess of sulphuric acid and excess of sodium hydroxide, the ratio of volumes of hydrogen evolved is
A . 1: 1
B. 1: 2
c. 2: 1
D. 9: 4


The equivalent resistance across AB is:
A . \( 1 \Omega \)
3. 2 ?
\( c .3 \Omega \)
D. \( 4 \Omega \)


Give reasons as to why equal masses of different substances have different
volumes.
A. because they have different shapes
B. because they have different densities
c. because they have the same densities
D. none of these


The outer length, breadth and height of
a wooden box open at the top are \( 10 \mathrm{cm} \) \( 8 \mathrm{cm} \) and \( 5 \mathrm{cm} \) respectively. If the thickness of the wood is \( 1 \mathrm{cm} \), the total surface area of the box is
A \( \cdot 420 \mathrm{cm}^{2} \)
В. \( 452 \mathrm{cm}^{2} \)
\( \mathrm{c} \cdot 451 \mathrm{cm}^{2} \)
D. \( 483 \mathrm{cm}^{2} \)


Assertion
Kinematic equations are exact and are always correct.
Reason
The definitions of instantaneous
velocity and acceleration are true only for motion in which the magnitude and
direction of acceleration are constant
during the course of motion
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect.


If \( z=2-3 i, \) then show that \( z^{2}-4 z+ \)
\( 13=0 . \) Hence find the value of \( 4 z^{3}- \)
\( \mathbf{3} z^{2}+\mathbf{2} z+\mathbf{1 7 0} \)


\( C O_{2} \) is transported as
A. Dissolved in blood plasma
B. Carbonic acid
C. Carbaminohaemoglobin
D. Carbaminohaemoglobin, carbonic acid and dissolved in plasma


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


Catalytic activity of transition metals depends on:
A. their ability to exist in different oxidation states
B. the size of the metal atoms
c. the number of empty atomic orbitals available
D. none of these


The process described above in the
passage is regarding:
A. Ore dressing
B. Pyrometallurgical extraction
c. Hydrometallurgical extraction
D. Purification of metal.


\( (I E)_{1} \) of Be is greater than that of B but
\( (I E)_{2} \) of \( (B) \) is greater than that of Be.If
true enter 1 , else 0 .


The valves which allow blood to flow
from the ventricles into the arteries and
not in the opposite direction are
A. Bicuspid and tricuspid valves
B. AV valve (atrio ventricular valve) and semilunar valve
c. Aortic valve and mitral valve
D. Semilunar valve


The resistance of the network between
the terminals \( A \) and \( B \) is
\( A \cdot 30 \Omega \)
B. 20\Omega
\( c .50 \Omega \)
D. \( 60 \Omega \)


Stretching of a rubber band results in
A. No change in potential energy
B. Zero value of potential energy
C. Increase in potential energy
D. Decrease in potential energy


Which among the following is not a
property of mass?
A. It is the amount of matter contained in a body.
B. It is measured by a physical balance.
C. It varies as per the location.
D. Its S.I unit is kilogram.


Four identical rods each of mass \( M \) are
joined to form as square frame, the moment of inertia of the system about one of the diagonals is
A. \( \frac{13 M l^{2}}{3} \)
в. \( \frac{2 M l^{2}}{3} \)
c. \( \frac{M l^{2}}{6} \)
D. \( \frac{13 M l^{2}}{6} \)


In the laboratory prepration of hydrogen, pure zinc is not used because:
A. pure zinc becomes passive due to formation of oxide layer
B. pure zinc becomes passive due to the formation of sulphate layer over the metal
C. pure zinc reacts slowly with the acid
D. pure zinc reacts with acid vigorously and violently


Find the number, one third of which is 4
more than 5
A .27
B . 23
c. 25
D. 29


In which of the following cases, does the reaction go furthest to completion?
A \( \cdot K=10^{3} \)
B. \( K=10^{-2} \)
c. \( K=10^{5} \)
D. \( K=1 \)


A and B are two points on the axis and
the perpendicular bisector, respectively
of an electric dipole. A and B are far
away from the dipole and at equal
distances from it. The fields at \( A \) and \( B \)
\( \operatorname{are} \vec{E}_{A} \) and \( \vec{E}_{B} . \) Then:
\( \mathbf{A} \cdot \vec{E}_{A}=\vec{E}_{B} \)
B \( \cdot \vec{E}_{A}=2 \vec{E}_{B} \)
\( \mathbf{c} \cdot \vec{E}_{A}=-2 \vec{E}_{B} \)
D \( \cdot\left|\vec{E}_{B}\right|=\frac{1}{2}\left|\vec{E}_{A}\right| \), and \( \left|\vec{E}_{A}\right| \) is perpendicular to \( \vec{E}_{B} \)


If \( 8^{t h} \) term of an A.P is 15 , then the sum
of 15 terms is
A . 15
B. 0
c. 225
D. \( \frac{225}{2} \)


Two identical balls move towards each
other with velocities \( 3 u \) and \( 2 u \)
respectively. The velocity of centre of
mass is?
A . u
B. \( 2 u \)
c. \( \frac{u}{2} \)
D. \( \frac{3 u}{2} \)


Which of the following scales belong to
bony fish?
A. A tand C of bony fish
B. A, B and D of bony fish
C. \( B \) and D of bony fish
D. B and C of bony fish


Oxygen generally exhibits an oxidation
state of -2 only while the other
members of the group show oxidation states of +2,+4 and +6 also - explain.


\( 1.25 \mathrm{g} \) of a solid dibasic acid is completely neutralised by \( 25 \mathrm{mL} \) of 0.25 molar \( \boldsymbol{B a}(\boldsymbol{O H})_{2} \) solution. Molecular
mass of the acid is:
A. 100
B. 150
\( c \cdot 120 \)
D. 200


A ray of light from a liquid \( (\mu=\sqrt{3}) \) is
incident on a system of two right angled prism of refractive indices \( \sqrt{3} a n d \sqrt{2} \)
as shown in the figure. The light suffers zero net deviation when it emerges into
air from surface CD. If the angle of incidence (in degrees) is \( 5 n . \) Find \( n \) ?


Which of the reactants act as oxidant or
reductant if any:
\( 2 C u S O_{4}+S O_{2}+2 K B r+2 H_{2} O \rightarrow \)
\( 2 C u B r+2 H_{2} S O_{4}+K_{2} S O_{4} \)
A \( . C u S O_{4} \)
в. \( S O_{2} \)
c. Both of these
D. None of these


\( A B C D \) is a trapezium with \( A B \| C D \)
\( A D=B C=5 c m, A B=12 c m \) and
\( C D=7 c m, \) find the area of trapezium
ABCD.


In a cubic structure of diamond which
is made from \( X \) and \( Y \), where \( X \) atoms
are at the corners of the cube and \( Y \) at
the face centres of the cube. The
molecular formula of the compound is:
A. \( X_{2} Y \)
\( Y \)
в. \( X_{3} Y \)
c. \( X Y_{2} \)
D. \( X Y_{3} \)


Let \( A B C \) be an equilateral triangle
inscribed in circle \( 0 . \) M is a point on arc
BC. Lines AM, BM and CM are drawn.
Then \( \overline{\boldsymbol{A} \boldsymbol{M}} \) is:
A. equal to \( \overline{B M}+\overline{C M} \)
B. Less than \( \overline{B M}+\overline{C M} \)
c. greater than \( \overline{B M}+\overline{C M} \)
D. equal, less than, or greater than \( \overline{B M}+\overline{C M} \) depending upon the pos


Colchicine is an inhibitory chemical which
A. stops the functioning of centriole
B. prevents attaching of centromeres with rays
c. prevents the spindle formation in mitosis
D. prevent the formation of equatorial plane


Two identical thin rings each of radius \( r \) are coaxillary placed at a distance have equal charge q each. Work done in moving a charge \( q^{\prime} \) from the centre of one ring to that of the other is?
A . Infinity
В. \( \frac{q^{2}}{4 \pi \varepsilon_{0} r} \)
c. zero
D. \( \frac{q q^{\prime}}{4 \pi \varepsilon_{0} r} \)


Force acting between two small magnets, placed in end on position
\( 0.1 m \) apart from their centres is
(Given magnetic moment of each
magnet is \( \left.5 A m^{2}\right) \)
A . \( 0.6 N \)
B. \( 0.8 N \)
c. \( 0.15 N \)
D. \( 0.2 N \)


An electric dipole is kept in a uniform electric field, it experiences
A. a force and a torque
B. a force, but no torque
c. a torque, but no force
D. neither a force nor a torque


Cationic surfactant is:
A \( \cdot C_{17} H_{35} C O O N a \)
B.
\( \mathrm{c} \cdot C_{16} H_{33} N\left(C H_{3}\right)_{3} C l \)
D. None of the above


If \( n \) is an integer,what is the remainder when \( 5 x^{2 n+1}-10 x^{2 n}+3 x^{2 n-1}+5 \) is
divided by \( x+1 ? \)
A .
B. 2
\( c \cdot 4 \)
\( D \cdot-8 \)
\( E \cdot-13 \)


Which is correctly matched?
1. Arsenic poisoning- Black foot disease
2. Secondary Effluent treatment-
Biological process
3. Pyrolysis- Solid soil waste disposal
4. Tubifex- Water pollution indicator
5. Biomagnification - Degradable pollutants
A .1,2,3,5
в. 1,3,4,5
c. 2,3,4,5
D. 1,2,3,4
E .1,2,4,5


The five different colored graphs above represent different possible
relationship between voltage across a
resistor and current through the
resistor.
Which of the graphs shows the correct relationship for a resistor that obeys
Ohm's law?
A . Red
B. orange
c. Blue
D. Purple


Select the odd one out w.r.t.
basidiomycetes.
A. Sex organs are absent
B. Karyogamy and meiosis takes place in basidium
C. Fruiting body is called basidiocarp
D. Basidiospores are endogenously produced on basidium


How is ecliptic related to solar constellations?


Active transport across biomembrane
involves
A. Production of ATP
B. Requirement of energy
c. Production of toxin
D. Release of energy


Of the four structures displayed, which
does out fit the octet-rule description of the electron-dot model developed by G.N. Lewis?
\[
0=\mathbf{H}
\]
orbital
80
A . I
в. ॥
c.
D. (All four fit the Lewis model.)


Action of vaginal diaphragm is
A. Spermicidal
B. To prevent the sperm to come in contact with ova
C. To prevent the ova to come in the uterus.
D. Anti-implantational.


Most economical and effective method
to control pH of the soil is
\( A \cdot \operatorname{cac} O_{3} \)
\( \mathbf{B} \cdot \operatorname{Ca}(O H)_{2} \)
c. \( \operatorname{cacl}_{2} \)
D. \( \operatorname{ca}\left(N O_{3}\right)_{2} \)


Which of the following reaction is used to prepare colloidal sol by double decomposition?
A. \( A s_{2} O_{3}+3 H_{2} S \rightarrow A s_{2} S_{3}+3 H_{2} O \)
B . \( 2 A u C l_{3}+3 H C H O+3 H_{2} O \rightarrow 2 A u+3 H C O O H+ \)
\( 6 H C l \)
c. \( S O_{2}+2 H_{2} S \rightarrow 3 S+2 H_{2} O \)
D. \( F e C l_{3}+3 H_{2} O \rightarrow F e(O H)_{3}+3 H C l \)


lodised salt prevents
\( A \cdot \) TB
B. Anaemia
c. Goitre
D. Beri-beri


If \( \int_{0}^{y} \frac{1}{\sqrt{1+9 u^{2}}} d u=u, \) then \( \frac{d^{2} y}{d u^{2}} \) is
\( \mathbf{A} \cdot \sqrt{1+9 y^{2}} \)
В. \( \frac{1}{\sqrt{1+9 y^{2}}} \)
c. \( 9 y \)
D. \( 9 y^{2} \)


Give product of the following reaction.


A major constituent of vinegar is:
A. Methanoic acic
B. Benzoic acid
c. Ethanoic acid
D. Picric acid


In a circle of diameter \( 10 \mathrm{cm} \) the length of each of the 2 equal and parallel chords is \( 8 \mathrm{cm} \) Then the distance
between these two chords is
A. \( 6 \mathrm{cm} \)
B. 7 \( \mathrm{cm} \)
\( c \cdot 8 \mathrm{cm} \)
D. \( 9 \mathrm{cm} \)


A radioactive element \( X_{90}^{238} \) decays into
\( Y_{83}^{222} . \) The number of \( \beta \) -particles emitted
are
\( A \)
B. 2
\( c \cdot 4 \)
D. 6


The point \( P \) is on the \( y \) -axis. If \( P \) is equidistant from (1,2,3) and (2,3,4)
then \( \boldsymbol{P}_{\boldsymbol{y}}= \)
A \( \cdot \frac{15}{2} \)
B. 15
c. 30
D. \( \frac{3}{2} \)


If \( x \) is a binomial variable with \( P=\frac{1}{4} \) then the smallest value of \( n \) so that
\( P(x \geq 1)>0.70 \) is
A . 3
B. 4
\( c .5 \)
D. 6


What are braille characters?
A. Small triangular blocks that contains raised dots
B. Small rectangular blocks that contains raised dots
C. Small triangular blocks that contains suppressed dots
D. Small square blocks that contains raised dots


The nth term of the A.P. \( 3,7,11,15, \ldots . \) is given by -
A \( \cdot T_{n}=4 n-1 \)
в. \( T_{n}=3 n+4 \)
c. \( T_{n}=3 n-4 \)
D. \( T_{n}=2 n+1 \)


Hydroponics is a technique in which plants are grown in
A. Green house
B. Water saturated sand
c. Balanced nutrient solution
D. Purified distilled water


Which of the following statements is
incorrect?
A. Polypropylene is a thermoplastic polymer
B. Melamine-formaldehyde is a thermosetting polymer
C. Mixture of styrene and methyl methacrylate can form ionic addition polymer
D. Low density polythene is a poor conductor of electricity


short / Long answer type questions. How is it that in the gizzard its lining is not damaged while the soil containing sand particles is ground up?


Assertion
Newton's law of universal gravitation
states that a particle attracts every other particle in the universe using a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
Reason
Law of gravitation is analogous to magnetic force between the moving
charges.
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


An unbiassed die is toossed. Find the
probability that it is a multiple of 3


Draw the graph of the equation \( \frac{x}{4}+ \) \( \frac{y}{3}=1 . \) Also, find the area of the triangle
formed by the line and the coordinate
axes.


Which one of the following substance will be most suitable for cutting a very hard material?
A . Silicon carbide
B. Leadd
c. zinc metal
D. Sodium chloride crystal


If a simple pendulum of length \( L \) has maximum angular displacement \( \alpha \)
then the maximum kinetic energy of
bob of mass \( M \) is
\( \mathbf{A} \cdot \frac{1}{2} \frac{M L}{g} \)
в. \( \frac{M g}{2 L} \)
c. \( M g L(1-\cos \alpha) \)
D. \( \frac{M g L \sin \alpha}{2} \)


If \( f(x)=\frac{a^{x}}{a^{x}+\sqrt{a}}(a>0), \) evaluate
\( \sum_{r=1}^{2 n-1} 2 f\left(\frac{r}{2 n}\right) \cdot \) for \( n=8 \)


The S.D of a variable \( x \) is \( \sigma . \) The S.D of the variate \( \frac{\boldsymbol{a} \boldsymbol{x}+\boldsymbol{b}}{\boldsymbol{c}} \) where \( \boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c} \) are
constant, is
A \( \cdot\left(\frac{a}{c}\right) \sigma \)
В. \( \left|\frac{a}{c}\right| \sigma \)
\( ^{\mathrm{c}} \cdot\left(\frac{a^{2}}{c^{2}}\right) \sigma \)
D. none of these


Which of the following is not correctly matched for the organism and its cell
wall degrading enzyme?
A. Bacteria - Lysozyme
B. Plants cells - Cellulase
c. Alage - Methylase
D. Fungi - Chitinase


Identify the incorrect statements.
This question has multiple correct options
A. \( 1.6 \mathrm{g} \) of a hydrocarbon on combustion in excess of oxygen produces \( 1.2 \mathrm{g} \) of \( \mathrm{CO}_{2} \) and \( 0.4 \mathrm{g} \) of \( \mathrm{H}_{2} \mathrm{O} \). The data illustrates the law of conservation of mass.
B. The product of atomic mass and specific heat of any elements is a constant and is approximately 6.4 . This is known as Dulong Petit's law.
C. The atomic masses of the elements are usually fractional because they are mixtures of allotropes.
D. The best standard of atomic mass is hydrogen (1.008)


The ratio of \( j \) to \( k \) to \( l \) to \( m \) to \( p \) is 5 to 4 to 3 to 2 to \( 1 . \) If \( j=60, \) what is the
value of \( m ? \)
\( A \cdot 8 \)
B. 12
c. 24
D. 55


State two uses of regular reflection


Evaluate \( \int \frac{\boldsymbol{d} \boldsymbol{x}}{\sqrt{(\boldsymbol{x}-\boldsymbol{\alpha})(\boldsymbol{\beta}-\boldsymbol{x})}}, \boldsymbol{\beta}>\boldsymbol{\alpha} \)


An electric kettle consumes 1 kW of
electric power when operated at \( 220 \mathrm{V} . \) A fuse wire of what rating must be used for it??
A . 1A
B. 2A
\( c \cdot 4 A \)
D. 5A


The ionization potential of a hydrogen atom is \( 13.6 \mathrm{eV} \). The ionization potential
of \( B e^{3+} \) ion is:
A. \( 217.6 e V \)
в. \( 109.8 e V \)
c. \( 54.4 e V \)
D. \( 136.0 e V \)


The polarity of induced emf is given by
A. Ampere's circuital law
B. Biot-Savant's law
C. Lenz's law
D. Remlng's right hand rule
E. Flemhg's left hand rule


Show that the function \( x^{2}-x+1 \) is
neither increasing nor decreasing on (0,1)


n given figure the measure of \( \angle A+ \)
\( \angle B+\angle C+\angle D+\angle E+\angle F \) is ?
\( A \cdot 120 \)
3.720
\( c \cdot 360 \)
) .540


5 moles of oxygen are heated at constant
volume from \( 10^{0} C \) to \( 20^{0} C . \) The change in
internal energy of the gas is:
\( C_{p}=7.03 \mathrm{cal} \mathrm{mol}^{-1} \mathrm{K}^{-1} \) and \( R= \)
\( 8.31 J \mathrm{mol}^{-1} \mathrm{K}^{-1} \)
A . 125 call \( l \)
B. 252 call
c. 50 call
D. 500 call


Which of the following is not correct?
A. Acidic hydrolysis of ester is reversible
B. Hydrolysis of ester becomes faster after sometime due to the formation of \( C H_{3} C O O H \)
C \( . H^{+} \) formed during hydrolysis acts as autocatalyst
D. Alkaline hydrolysis of ester is reversible


A thermodynamic system is taken from an initial state i with internal energy
\( U_{i}=100 J \) to final state \( f \) along two
different paths iaf and ibf, as schematically shown in the figure. The work done by the system along the path
\( a f, i b \) and \( b f \) are \( W_{a f}=200 J, W_{i b}= \)
\( 50 J \) and \( W_{b f}=100 J \) respectively. The
heat supplied to the system along the
path iaf, ib and bf are \( Q_{i a f}, Q_{i b} \) and \( Q_{b f} \) respectively. If the internal energy of the
system in the state b is \( U_{b}=200 J \) and
\( Q_{i a f}=500 J, \) the ratio \( Q_{b f} / Q_{i b} \) is


\( \lim _{x \atop x \rightarrow \frac{\pi}{4}} \frac{1-\tan x}{1-\sqrt{2} \sin x} \)


Factorize \( 3 a^{5}-108 a^{3} \)
A \( \cdot 3 a^{3}(a-6)(2 a-6) \)
В \( \cdot 2 a^{3}(a+6)(7 a-6) \)
c. \( 2 a^{3}(a-6)(3 a+6) \)
D. \( 3 a^{3}(a+6)(a-6) \)


In L-C oscillation the maximum charge on the capacitor can be \( Q \). If at any instant, electric energy and magnetic energy associated with the current is
equal, then the charge on the capacitor at that instant is :
A \( \cdot \frac{Q}{\sqrt{2}} \)
в. \( \frac{Q}{2} \)
c. \( \frac{3 Q}{\sqrt{2}} \)
D. \( \frac{3 Q}{2} \)


The area between the curve \( y=2 x^{4}- \)
\( x^{2}, \) the \( x- \) axis and the ordinates of two
minima of the curve is:
A \( \cdot \frac{7}{120} \) sq.unit
B. \( \frac{9}{120} \) sq.unit
c. \( \frac{11}{120} \) sq.unit
D. \( \frac{13}{120} \) sq.unit


If a sphere and a cube have the same volume then the ratio of the surface of
the sphere to that of the cube is
A \( \cdot \sqrt{6}: \sqrt{\pi} \)
B. \( \sqrt[3]{3 \pi}: \sqrt[3]{3} \)
C \( \cdot \sqrt[3]{\pi}: \sqrt[3]{6} \)
D. none of these


Assertion
In physical adsorption, enthalpy of adsorption is very low.
Reason
In physical adsorption, attraction between gas molecules and solid surface is due to weak van der Waals
forces
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


An equiconvex lens is made from glass of refractive index \( 1.5 . \) If the radius of
each surface is changed from 5 \( \mathrm{cm} \) to
\( 6 c m, \) then the power:
A. Remains unchanged
B. Increases by 3.33 D
c. Decreases by 3.33 D
D. Decreases by \( 5.5 D \)


In order to save Taj, Supreme court has ordered the industries and vehicles to
switch to:
A . LPG
в. смG
c. unleaded petrol
D. All of the above


State whether the following statement
is true or False:

Human beings and most animals like birds, beer, bees, mosquitoes produce sound by the vibrations of their vocal chords.
A. True
B. False


Two electric field lines cannot cross
each other. Also, they cannot form closed loops. Give reasons.


Find the area of the region bounded by
the curve \( y^{2}=x \) and the lines \( x= \)
\( 4, x=9 \) and the \( x- \) axis in the first
quadrant.


A force \( (2 \hat{i}+\hat{j}-\hat{k}) N \) acts on a body
which is initially at rest. At the end of \( 20 s \) the velocity of the body is \( (4 \hat{i}+ \) \( \mathbf{2} \hat{\boldsymbol{j}}-\mathbf{2} \hat{\boldsymbol{k}}) \boldsymbol{m} \boldsymbol{s}^{-1}, \) then the mass of the
body is:
A. \( 8 \mathrm{kg} \)
B. \( 10 \mathrm{kg} \)
c. \( 5 k g \)
D. \( 4.5 \mathrm{kg} \)


The disintegration energy \( Q \) for the change \( _{Z}^{A} \mathbf{X} \stackrel{-\alpha}{\longrightarrow} \underset{Z-2}{A-4} \mathbf{D}+Q \) is given by
\( \boldsymbol{Q}=\left[\boldsymbol{M}\left(\begin{array}{l}A \mathbf{X} \\ Z\end{array}\right)-\boldsymbol{M}\left(\begin{array}{l}\boldsymbol{A}-\mathbf{4} \\ \boldsymbol{Z}-\mathbf{2}\end{array} \mathbf{D}\right)-\right. \)
\( \left.M\left(_{2}^{4} \mathbf{H e}\right)\right] C^{2}, \) where \( M \) represents the
mass of respective nuclei reported in
paranthesis and \( C \) is speed of light. For
\( \alpha \) -decay :
A. \( Q=+v e \)
В. \( Q=-v e \)
c. \( Q=0 \)
D. not related with \( Q \)


Which of the following paths is/are
feasible for the preparation of ether \( (A) ? \)
This question has multiple correct options
A. Path I
B. Path II
c. Path II
D. Path IV


At \( 298 K, \) given that:
\[
\begin{array}{c}
\boldsymbol{C u}(\boldsymbol{s})\left|\boldsymbol{C} \boldsymbol{u}^{2+}(\mathbf{1} . \boldsymbol{0} \boldsymbol{M}) \| \boldsymbol{A} \boldsymbol{g}^{+}(\mathbf{1} . \boldsymbol{0} \boldsymbol{M})\right| \boldsymbol{A} \boldsymbol{g}(\boldsymbol{s}) \\
\boldsymbol{E}_{c e l l}^{o}=\mathbf{0 . 4 6} \boldsymbol{V} \\
\boldsymbol{Z} \boldsymbol{n}(\boldsymbol{s})\left|\boldsymbol{Z} \boldsymbol{n}^{2+}(\mathbf{1} \cdot \mathbf{0} \boldsymbol{M}) \| \boldsymbol{C} \boldsymbol{u}^{2+}(\mathbf{1} . \boldsymbol{0} \boldsymbol{M})\right| \boldsymbol{C} \boldsymbol{u} \\
\boldsymbol{E}_{\text {cell }}^{o}=\mathbf{1 . 1 0} \boldsymbol{V}
\end{array}
\]
Then, the \( E_{\text {cell}} \) for the following reaction
at \( 298 K \) will be:
\[
\boldsymbol{Z} \boldsymbol{n}(\boldsymbol{s})\left|\boldsymbol{Z} \boldsymbol{n}^{2+}(\boldsymbol{0} \cdot \boldsymbol{1} \boldsymbol{M}) \| \boldsymbol{A} \boldsymbol{g}^{+}(\mathbf{1} \cdot \boldsymbol{0} \boldsymbol{M})\right| \boldsymbol{A} \boldsymbol{g}(s
\]
A . \( 1.56 V \)
в. \( 1.53 V \)
\( \mathbf{c} .2 .53 V \)
D. cannot be calculated due to insufficient data


A light rod of length \( 2 m \) is suspended
from the ceiling horizontally by means
of two vertical wires of equal length tied to its ends. One of the wires is made of
steel and is of cross section \( 0.1 \mathrm{cm}^{2} . \) A
weight is suspended from a certain
point of the rod such that equal stress are produced in both the wires.Which of the following are correct?
This question has multiple correct options
A. The ratio of tension in the steel and brass wires is 0.5
B. The load is suspended at a distance of \( 400 / 3 c m \) from the steel wire
c. Both (a) and
(b) are correct
D. Neither
(a) nor
(b) are correct


Sum of the series \( 4+6+9+13+ \)
\( 18+\ldots \) to \( n \) terms be \( = \)
\( \frac{\boldsymbol{n}}{\boldsymbol{k}}\left(\boldsymbol{n}^{2}+\boldsymbol{3} \boldsymbol{n}+\boldsymbol{m}\right) \cdot \) Find \( \boldsymbol{m}-\boldsymbol{k} ? \)


\( \boldsymbol{U}=\{\boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c}, \boldsymbol{d}, \boldsymbol{e}, \boldsymbol{f}, \boldsymbol{g}\},\left(\boldsymbol{A}^{\prime}\right)=\{\boldsymbol{b}, \boldsymbol{d}, \boldsymbol{f}\} \)
show that Venn diagram.


A motor car is traveling at \( 30 m s^{-1} \) on a circular road of radius \( 500 \mathrm{m} \). It is
increasing speed at the rate of \( 2 m s^{-2} \) The acceleration of car is :
A \( .2 m s^{-2} \)
В. 2.7 \( m s^{-2} \)
\( c \cdot 3 m s^{-2} \)
D. 3.7 \( m s^{-2} \)


toppr
Q Type your question
3. Flying foxes, member of Chiroptera
4. Proboscidea, the largest land animal
5. Primates with estrous or menstrual
cycle
6. Legormorphs with two pairs of
incisors with open root canals
7. Prototherians, sharing features with primitive vertebrates.
A. \( 1-A, 2-F, 3-C, 4-G, 5-D, 6-E, 7-B \)
B. 1- B, 2- G, 3- D, 4- A, 5- F, 6- E, 7- C
c. \( 1- \) В, \( 2-F, 3-C, 4-G, 5-D, 6-B, 7-E \)
D. \( 1- \) B, \( 2-F, 3-G, 4-A, 5-D, 6-E, 7-C \)


Why family is important?


In which direction does he move the
lens to focus the flame on the screen?


At what point on the curve \( y=x(x-4) \) on [0,4] is the tangent parallel to \( X \) -axis.


How many \( \sigma \) and bond present in
benzene \( \left(C_{6} H_{6}\right) \) molecule?


What happens when \( N a C N \) is added in
ore containing \( P b S \) and \( Z n S \) during
concentration by froth floatation method?


The following question is relevant to the extraction of Aluminium:
Along with cryolite and alumina, another substance is added to the
electrolyte mixture. the substance is
A. Fluorspar
B. Mica
c. Nacı
D. None of these


\( \boldsymbol{P h C} \equiv \boldsymbol{C M e} \frac{\boldsymbol{H}_{3} \boldsymbol{O}^{+}, \boldsymbol{H} \boldsymbol{g}^{2+}}{\rightarrow} \)
Identify the product in the reaction.
\( \mathbf{A} \cdot P h C H_{2} C H_{2} C H O \)
в. \( \operatorname{Ph} \mathrm{hOCH}_{2} \mathrm{CH}_{3} \)
\( \mathbf{c} \cdot P h C H_{2} C O C H_{3} \)
D. Рh СОСОМ


Give the zeros of polynomial and list their multiplicities:
\( \boldsymbol{P}(\boldsymbol{x})=(\boldsymbol{x}+\mathbf{2})(\boldsymbol{x}-\mathbf{1}) \)


If Bohr radius is \( r_{0}, \) the corresponding de Broglie wavelength of the electron is
\( ^{\mathbf{A}} \cdot\left(\frac{2 \pi}{r_{o}}\right) \)
В \( \cdot\left(\frac{r_{o}}{2 \pi}\right) \)
c. \( \left(\frac{1}{2 \pi r_{o}}\right) \)
D. \( 2 \pi r_{o} \)


Roots are absent in
A. Wolffia
B. Utricularia
c. Nymphaea
D. Both A and B


Component of ETC of mitochondria is
A. Carotenoids
B. Plastocyanin
c. Phytochrome
D. Cytochrome oxidase


Name the hormones secreted by the following endocrine gland and specify one function.
Pancreas.


A piston exerting a pressure of 1.0 atmosphere rests on the surface of
water at \( 100^{\circ} \mathrm{C} \). The pressure is reduced to smaller extent and as a
result 10 g of water evaporates and absorbs \( 22.2 \mathrm{kJ} \) of heat. The change in internal energy is:
A . 18.24 k
B. 20.477 kJ
c. 22.05 kJ
D. 23.923 kJ


The following table gives the numbers of branches and number plants in a garden of a school
No. of
\[
\mathbf{2}
\]
branches \( \mathbf{3} \)
No. of plants
\( 14 \quad 21 \quad 28 \quad 20 \)
Calculate the mean, median and mode
of the above data.


A conducting loop rotates with constant
angular velocity about its fixed
diameter in a uniform magnetic field,
whose direction is perpendicular to that
fixed diameter
This question has multiple correct options
A. The emf will be maximum at the moment when flux is
zero
B. The emf will be 0 at the moment when flux is maximum
C. The emf will be maximum at the moment when plane of the loop is parallel to the magnetic field
D. The phase difference between the flux and the emf is \( \pi / 2 \)
E . answer required


The definition of resistance given by \( R=\frac{V}{I} \) holds good for:
A. conductors only
B. Metals only
c. Non-ohmic devices only
D. All conducting devices, whetheror not they obey onm's law


Mean deviation of the series \( a, a+ \)
\( \boldsymbol{d}, \boldsymbol{a}+\mathbf{2} \boldsymbol{d}, \ldots, \boldsymbol{a}+\boldsymbol{2 n} \boldsymbol{d} \) from its mean is
A \( \cdot \frac{(n+1) d}{(2 n+1)} \)
в. \( \frac{n d}{2 n+1} \)
c. \( \frac{(2 n+1) d}{n(n+1)} \)
D. \( \frac{n(n+1) d}{2 n+1} \)


The solution of \( x \cos ^{2} y(d x)+ \) \( \tan y(d y)=0 \) is:
\( \mathbf{A} \cdot x^{2}+\sec ^{2} y=c \)
B . \( x^{2}+c o t^{2} y=c \)
C \( \cdot x^{2}+\sin ^{2} y=c \)
D. \( x^{2}+\cos ^{2} y=c \)


Permanent hardness of water is due to
the presence of the bicarbonates of Ca, Mg and Fe. If this is true enter 1 , if false enter 0 .


Petroleum is:
A. lighter than water and soluble in it
B. heavier than water and insoluble in it
C. lighter than water and insoluble in it
D. heavier than water and soluble in it


Apart from \( N_{3} O, \) which other colourless gas supports combustion?
A \( . N O_{2} \)
в. \( O_{2} \)
c. \( N_{2} O_{4} \)
D. \( N O \)


A person is moving on a rough horizontal surface towards east. Then
the direction of friction force is towards:
A. west
B. East
C. Friction does not act
D. Information insufficient


S.I. Unit of universal gravitational
constant \( G \) is-
\( ^{\mathbf{A}} \cdot \frac{N m^{2}}{K g} \)
в. \( \frac{N m^{2}}{K g^{2}} \)
c. \( \frac{N m}{K g^{2}} \)
D. \( \frac{N m}{K g} \)


How many following oxyacids have peroxy linkage? \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{3}, \boldsymbol{H}_{2} \boldsymbol{S}_{2} \boldsymbol{O}_{8}, \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{2}, \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{5}, \boldsymbol{H} \boldsymbol{l} \boldsymbol{l} \)


A vector \( \bar{P}_{1} \) is along the positive \( x \) - axis.
If its cross product with another vector
\( \bar{P}_{2} \) is zero, then \( \bar{P}_{2} \) could be:
\( A \cdot 4 \hat{j} \)
в. \( -4 \hat{i} \)
c. \( (\hat{i}+\hat{k}) \)
D. \( -(\hat{i}+\hat{j}) \)


Assertion
Reed Swamp stage of hydrosere occurs in shallow water.
Reason
The stage is characterised by the presence of amphibious plants.
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 flask containing air (open to atmosphere) is heated from \( 300 K \) to
\( \mathbf{5 0 0 K} . \) The percentage of air escaped to the atmosphere is nearly?
A . 16.6
B. 40
c. 60
D. 20


Assertion
If the independent events \( \boldsymbol{A} \& \boldsymbol{B} \) are
such that \( \mathbf{0}<\boldsymbol{P}(\boldsymbol{A})<\mathbf{1}, \mathbf{0}<\boldsymbol{P}(\boldsymbol{B})< \)
1, then \( A \& B \) can not be mutually
exclusive.
Reason
Two events \( A \& B \) can not be mutually
exclusive, if \( \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B}) \neq \mathbf{0} \)
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


The molecules below are:
A. enantiomers
B. diastereomers
c. constitutional isomers
D. identical


Measure of \( \angle A \) in triangle \( \Delta A B C \) is
\( A \cdot 30^{\circ} \)
B. \( 15^{\circ} \)
\( c \cdot 20^{\circ} \)
D. \( 180^{\circ} \)


For what value of \( x, \) is the matrix \( A= \) \( \left[\begin{array}{ccc}\mathbf{0} & \mathbf{1} & \mathbf{- 1} \\ -\mathbf{1} & \mathbf{0} & \mathbf{3} \\ \boldsymbol{x} & \mathbf{- 3} & \mathbf{0}\end{array}\right] \) a skew symmetric
matrix?


A particle starts from a point \( A \) and
travels along the solid curve shown
in figure. Find approximately the position B of the particle such that the
average velocity between the position \( A \)
and \( \mathrm{B} \) has the same direction as
the instantaneous velocity at B.
A \( . x=5 m, y=3 m \)
B. \( x=3 m, y=2 m \)
c. \( x=6 m, y=2 m \)
D. \( x=5 m, y=2 m \)


\( 2- \) acetoxy benzoic acid is:
A. antiseptic
B. aspirin
c. antibiotic
D. mordant dye


An object is taken to height \( 2 \mathrm{R} \) above the surface of earth, the increase in potential energy is [R is radius of earth]
\( ^{\mathrm{A}} \cdot \frac{m g R}{2} \)
в. \( \frac{m g R}{3} \)
c. \( \frac{2 m g R}{3} \)
D. 2 mgR


The number of electrons, protons and
neutrons in an atom whose atomic
number is 11 and mass number 23 will
be:
A. 11,11,12
B. 11,12,11
c. 12,11,11
D. 23,11,23


The stabilizer used in the preparation of colloidal sol of mercury and sulphur is:
A. an ammonium salt
B. a citrate
c. \( K O H \)
D. both A and B


State and explain Ampere's circuital
law.


Which one of the following electrolytes used in Down's process of extracting sodium metal?
A. \( N a C l+K C l+K F \)
B. \( N a C l \)
c. \( N a O H+K C l+K F \)
D. \( N a C l+N a O H \)


An initially parallel cylindrical beam travels in a medium of refractive index
\( \boldsymbol{\mu}(\boldsymbol{I})=\boldsymbol{\mu}_{0}+\boldsymbol{\mu}_{2} \boldsymbol{I}, \) where \( \boldsymbol{\mu}_{0} \) and \( \boldsymbol{\mu}_{2} \)
are positive constants and lis the intensity of the light beam. The intensity of the beam is decreasing with increasing radius. The speed of light in the medium is
A. minimum on the axis of the beam
B. the same everywhere in the beam
c. directly proportional to the intensity
D. maximum on the axis of the beam


The electric potential at 0 is :
A \( \cdot \frac{\sqrt{2} q}{\pi \varepsilon_{0} a} \)
В. \( \frac{\sqrt{3} q}{\pi \varepsilon_{0} a} \)
c. \( \frac{q}{\pi \varepsilon_{0} a} \)
D. zero


If \( i=\sqrt{-1}, \) then select from the
following having the greatest value.
A \( \cdot i^{4}+i^{3}+i^{2}+i \)
B . \( i^{8}+i^{6}+i^{4}+i^{2} \)
\( \mathbf{c} \cdot i^{12}+i^{9}+i^{6}+i^{3} \)
D. \( i^{16}+i^{12}+i^{8}+i^{4} \)
E . \( i^{20}+i^{15}+i^{10}+i^{5} \)


\( H_{2} O, N O, C O \) are neutral oxides.
A. True
B. False


Magnification \( m= \)
This question has multiple correct options
\( \mathbf{A} \cdot \mathbf{v} / \mathbf{u} \)
B. u/v
\( \mathbf{c} \cdot h_{0} / h_{i} \)
\( \mathbf{D} \cdot h_{i} / h_{0} \)


The diagram shows four charges
\( \boldsymbol{q}_{1}, \boldsymbol{q}_{2}, \boldsymbol{q}_{3} \) and \( \boldsymbol{q}_{4} \) all lying in the plane of
the page. The diagram also shows the dotted circle that represents the cross-
section of a spherical Gaussian surface
Point \( P \) is a single point on that surface Which of the charges contributes to the net electric flux through the sphere?
A \( \cdot q_{1} \) and \( q_{3} \)
B. \( q_{2} \) and \( q_{4} \)
\( \mathbf{c} \cdot q_{1} \) and \( q_{2} \)
\( \mathbf{D} \cdot q_{3} \) and \( q_{4} \)
E \( . q_{1}, q_{2}, q_{3}, \) and \( q_{4} \)


The domain of \( \boldsymbol{f}(\boldsymbol{x})=\sqrt{\log \left(\frac{\mathbf{5} \boldsymbol{x}-\boldsymbol{x}^{2}}{\mathbf{6}}\right)} \)
is
A. \( 2 \leq x \leq 3 \)
в. \( 3 \leq x \leq 4 \)
c. \( -3 \leq x \leq-2 \)
D. \( 1 \leq x \leq 3 \)


An electric dipole coincides on the zaxis and its centre coincides with the
origin of the cartesian coordinate system. The electric field at an axial
point at a distance \( z \) from the origin is
\( E(z) \) and the electric field at an equatorial point at a distance \( y \) from
the origin is \( \boldsymbol{E}(\boldsymbol{y}) \)
Given that \( y=z>>a, \) which is true?
A. \( E(z) \) and \( E(y) \) are perpendicular
B. \( E(z) \) and \( E(y) \) are parallel
C. \( E(z) \) and \( E(y) \) are at \( 45^{\circ} \) to one another
D. None of these


A soap bubble of radius \( r_{1} \) is placed on
another soap bubble of radius \( r_{2}\left(r_{1}<\right. \)
\( r_{2} \) ). The radius \( R \) of the soapy film
separating the two bubbles is:
\( \mathbf{A} \cdot r_{1}+r_{2} \)
B . \( \sqrt{r_{1}^{2}+r_{1}^{2}} \)
c. \( \left(r_{1}^{2}+r_{1}^{2}\right) \)
D. \( \frac{r_{2} r_{1}}{r_{2}-r_{1}} \)


A solenoid of \( 0.4 m \) length with 500
turns carries a current of \( 3 A . \) A coil of
10 turns and of radius \( 0.01 m \) carries a
current of \( 0.4 A . \) The torque required to hold the coil with its axis at right angles to that of solenoid in the middle point of
it is:
A \( \cdot 6 \pi^{2} \times 10^{-7} N m \)
В. \( 3 \pi^{2} \times 10^{-7} N m \)
\( \mathbf{c} \cdot 9 \pi^{2} \times 10^{-7} N m \)
D. \( 12 \pi^{2} \times 10^{-7} N m \)


The structures of two compounds
and \( (I I) \) are given below. Which statement is correct?
\( \boldsymbol{F}_{2} \boldsymbol{C}=\boldsymbol{C}=\boldsymbol{C} \boldsymbol{F}_{2}(\boldsymbol{I}) \) and \( \boldsymbol{F}_{2} \boldsymbol{C}=\boldsymbol{C}= \)
\( \boldsymbol{C}=\boldsymbol{C} \boldsymbol{F}_{2}(\boldsymbol{I} \boldsymbol{I}) \)
A. Reductive ozonolysis of both gave the same product
B. Reductive ozonolysis of both gave different products
c. Reductive and oxidative ozonolysis of both gave different products.
D. Reductive and oxidative ozonolysis of (I) gave the same product but of \( (I I) \) gave different products.


Derive the equation of uniformly acceleration motion by graphical


The inductance of an inductor whose
reactance is \( 2.00 \Omega \) at \( 50.0 H z \) is \( \frac{x}{100} m H . \) Find \( x \)


The ends of the latus rectum of the
parabola \( \boldsymbol{x}^{2}+\mathbf{1 0 x}-\mathbf{1 6 y}+\mathbf{2 5}=\mathbf{0} \) are
A \( \cdot(3,4),(-13,4) \)
B. (5,-8),(-5,8)
c. (3,-4),(13,4)
D. (-3,4),(13,-4)


A planet of mass \( m \) is moving in an elliptical orbit round the sun of mass
\( M . \) If the maximum and minimum
distances of the planet from the sun be
\( l_{1} \) and \( l_{2}, \) the angular momentum of
the planet about the sun will be
A \( \cdot m \frac{G M m}{\sqrt{\left(l_{1}+l_{2}\right)}} \)
в. \( m \sqrt{\frac{l_{1}+l_{2}}{G M l_{1} l_{2}}} \)
c. \( m \sqrt{\frac{2 G M l_{1} l_{2}}{\left(l_{1}+l_{2}\right)}} \)
\( D \)


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


If the speed of light in a medium at a given temperature is \( 348 \mathrm{m} / \mathrm{s} \) at a
pressure of 2 atm. Now the pressure is increased to 5 atm, temperature remaining constant. Now the speed of sound in the same medium will be:
A. Less than \( 348 \mathrm{m} / \mathrm{s} \)
B. Greater than \( 348 \mathrm{m} / \mathrm{s} \)
c. Equal to \( 348 \mathrm{m} / \mathrm{s} \)
D. None of these


\( \int \frac{\boldsymbol{d x}}{\left(x^{2}+1\right)\left(x^{2}+4\right)}= \)
A \( \cdot \frac{1}{3} \tan ^{-1} x-\frac{1}{3} \tan ^{-1} \frac{x}{2}+c \)
B - \( \frac{1}{3} \tan ^{-1} x+\frac{1}{3} \tan ^{-1} \frac{x}{2}+c \)
c. \( \frac{1}{3} \tan ^{-1} x-\frac{1}{6} \tan ^{-1} \frac{x}{2}+c \)
\( \mathbf{D} \cdot \tan ^{-1} x-2 \tan ^{-1} \frac{x}{2}+c \)


Give the reasons of the following questions.
\( H_{2} O \) is liquid but \( H_{2} S \) is a gas at room temperature
\( N H_{3} \) has higher boiling point than \( P H_{3} \)


Clinging and epiphytic roots are found
in
A. Orchid
B. Tinospora
c. Rhizophora
D. Pothos


A manufacturer estimates that on
inspection \( 12 \% \) of the articles he has produced will be rejected. He accepts an
order to supply 4400 articles at Rs15 each. Calculate the least number of
articles he must manufacture) to
ensure the completion of the order
He estimates the profit on his outlay. including the manufacturing of rejected articles to be \( 20 \% \). Find the
\( \operatorname{cost} \) of manufacturing each article.


Which of the following pairs represents bactericidal antibiotic :
Erythromycin, ofloxacin, chloramphenicol, penicillin, and tetracycline
A . (i) (iii)
B. (ii) (iv)
c. (iii) (v)
D. (i) (iv)
E. (ii) (v)


\( 5 \mathrm{g} \) of a polymer of molar mass \( 50 k g m o l^{-1} \) is dissolved in \( 1 d m^{3} \)
solution. The height of solution \( (m m) \) that will represent its osmotic pressure if density of solution at
equilibrium is \( 0.96 \mathrm{kg} \mathrm{dm}^{-3} \) is (divide
answer by 5 and write nearest integer value).


A particle A with a mass \( m_{A} \) is moving
with a velocity v and hits a particle B of
mass \( m_{B} \) at rest. If motion is one
dimensional and take the collision is
elastic, then the change in the de Broglie wavelength of the particle A is
\( ^{\text {A }} \frac{h}{2 m_{A} v}\left[\frac{\left(m_{A}+m_{B}\right)}{\left(m_{A}-m_{B}\right)}-1\right] \)
в. \( \frac{h}{m_{A} v}\left[\frac{\left(m_{A}-m_{B}\right)}{\left(m_{A}+m_{B}\right)}-1\right] \)
c. \( \frac{h}{m_{A} v}\left[\frac{\left(m_{A}+m_{B}\right)}{\left(m_{A}-m_{B}\right)}-1\right] \)
D.
\[
\frac{2 h}{m_{A} v}\left[\frac{\left(m_{A}+m_{B}\right)}{\left(m_{A}-m_{B}\right)}+1\right]
\]


Write the Lewis structure of the nitrite
ion, \( N O_{2}^{-} \)


Which of the following arrangements represent increasing oxidation number of the central atom?
A \( \cdot C r O_{2}^{-}, C l O_{3}^{-}, C r O_{4}^{2-}, M n O_{4}^{-} \)
B . \( C l O_{3}^{-}, C r O_{4}^{2-}, M n O_{4}^{-}, C r O_{2}^{-} \)
c. \( C r O_{2}^{-}, C l O_{3}^{-}, M n O_{4}^{-}, C r O_{4}^{2-} \)
D. \( C r O_{4}^{2-}, M n O_{4}^{-}, C r O_{2}^{-}, C l O_{3}^{-} \)


Figure represents a negatively charged
gold leaf electroscope. Of the parts \( A, B \) C, D and E, state whether they are an
insulator or a conductor:
\( A \cdot A, B \) and \( E \) are conductors while \( D \) and \( C \) are insulators
B. B, D and E are conductors while A and C are insulators
\( c . A, D \) and \( E \) are insulators while \( B \) and \( C \) are conductors
D. A, Dand E are conductors while B and C are insulators


Which of the following is an antidiabetic drug:
A . Insulin
B. Penicillin
c. chloroquine
D. Aspirin


fthe matrix \( \left[\begin{array}{cc}\mathbf{2} & \mathbf{3} \\ \mathbf{5} & -\mathbf{1}\end{array}\right]=\boldsymbol{A}+\boldsymbol{B}, \) where
A is symmetric and B is skew symmetric, then \( B= \)
A. \( \left[\begin{array}{cc}2 & 4 \\ 4 & -1\end{array}\right] \)
B. \( \left[\begin{array}{cc}0 & -2 \\ 2 & 0\end{array}\right] \)
C \( \cdot\left[\begin{array}{cc}0 & 1 \\ -1 & 0\end{array}\right] \)
D. \( \left[\begin{array}{cc}0 & -1 \\ 1 & 0\end{array}\right] \)


Fill in the blanks:
\( (-100) \times(-6)=\dots \dots \dots \)


Relation \( \boldsymbol{R} \) in the set \( \boldsymbol{Z} \) of all integers
defined as \( \boldsymbol{R}= \)
\[
\{(x, y):(x-y) \text { is an integer }\}
\]
enter 1 -reflexive and transitive but not
symmetric 2-reflexive only 3-Transitive only 4-Equivalence
5-None


Among the following which one gives
output 1 in the AND gate.
A. \( A=0, B=0 \)
в. \( A=1, B=1 \)
c. \( A=1, B=0 \)
D. \( A=0, B=1 \)


A stone is thrown upwards and it rises
to a height of \( 200 m \). The relative velocity of the stone with respect to the earth will be maximum at :
A. Height of \( 100 m \)
B. Height of \( 150 m \)
c. Highest point
D. The ground


Match List-I with List-II.


The maximum value of \( 5 e|x \log x| \) for
\( \mathbf{0}<\boldsymbol{x} \leq \mathbf{1} \) is


Q Type your question.
different oxygen pressures.
The greatest difference in oxygen
saturation between hemoglobin and
myoglobin takes place at which of the
following pressure?
partial pressure
Myoglobin
\( A \cdot 1 k P a \)
в. \( 2 k P a \)
\( c .3 k P a \)
D. \( 4 k P a \)
\( E \)


\( \mathbf{A} \)
is the sum of some set of
terms of a sequence.
A. term
B. constant
c. series
D. sequence


Sodium chloride is used in soap
industry for soap's
A. decomposition
B. removal of hardness
c. precipitation
D. None of the above


Find the variance for the following data:
6,4,8,5,2,17


Convert the following improper fraction into mixed fraction.
\( \frac{11}{2} \)


Solve :
\( \int \frac{x^{2}+3 x-1}{(x+1)^{2}} d x \)


Which one of the following ion exhibits colour in aqueous solution?
\( A \cdot S c^{3} \)
B. Ni2
c. \( T_{i}^{4} \)
\( D \cdot z n^{+2} \)


1.0 \( \mathrm{kg} \) of water is contained in a \( 1.25 \mathrm{kW} \) kettle. Calculate the time taken for the
temperature of water to rise from \( 25^{\circ} C \)
to its boiling point \( 100^{\circ} \mathrm{C} \). Specific heat
capacity of water \( =4.2 J g^{-1} K^{-1} \)


If \( \boldsymbol{A}-\boldsymbol{A}^{\prime}=\mathbf{0}, \) then \( \boldsymbol{A}^{\prime} \) is
A. orthogonal matrix
B. symmetric matrix
c. skew-symmetric matrix
D. triangular matrix


If a line makes angles \( \alpha, \beta, \gamma \) and \( \delta \) with
the diagonals of a cube, Then, \( \cos ^{2} \alpha+ \) \( \cos ^{2} \beta+\cos ^{2} \gamma+\cos ^{2} \delta=\frac{a}{b}, \) where \( a \)
and \( b \) are in lowest form, find \( a+b \)
\( A \cdot 7 \)
B. 6
c. 8
D. None of these


A bar magnet \( 20 \mathrm{cm} \) in length is placed with its south pole towards geographic north. The neutral points are situated at a distance of \( 40 \mathrm{cm} \) from centre of the
magnet. If horizontal component of earth's field \( 3.2 \times 10^{-5} T, \) then pole
strength of magnet is :
\( A \cdot 5 \mathrm{Am} \)
B. 10 Am
c. \( 45 \mathrm{Am} \)
D. 20 Am


Assertion: If the activation energy of reaction is low, it proceeds at a faster rate.

Reason: Lowering activation energy increases the kinetic energy of molecules.
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
E. Both Assertion and Reason are false


Ampullary accessory hearts are present in
A. cockroach.
B. Frog.
c. Rabbit
D. Earthworm.


One serious drawback of semi-
conductor devices is
A. they do not last for long time.
B. they are costly.
c. they cannot be used with high voltage.
D. they pollute the environment


Paracetamol is:
A. methyl salicylate
B. phenyl salicylate
c. N-acetyl p-amino phenol
D. acetyl salicylic acid


\( 20 \% \) of \( N_{2} O_{4} \) molecule are dissociated
in a sample of \( \operatorname{gas} \) at 27 degree \( C \) and 760 torr mixture has the density at the equilibrium


Which is not true for a wave?
A. Wave velocity \( v=n \lambda \)
B. Energy is transferred during wave motion
C. All waves can pass through vacuum
D. Unit of wave velocity is \( m / s \)


The chalcocite is roasted and not
calcined during recovery of copper.If true enter 1 else 0
\( A \)


Draw and explain the process of
formation of image with a pinhole
camera?


A solid cylinder of mass \( 20 k g \) rotates about its axis with angular speed
100rads \( ^{-1} \). The radius of the cylinder is
\( 0.25 m . \) What is the kinetic energy associated with the rotation of cylinder? What is the magnitude of angular momentum of cylinder about its axis?
A. \( 62.5 T-s \)
B. \( 70.4 T-s \)
c. \( 79.6 T-s \)
D. \( 60.5 T-s \)


\( \mu^{2}+\frac{1}{\mu^{2}}=79 \)
find \( \mu+\frac{1}{\mu} \)


The weight of a body would not be zero:
A. at the centre of the earth
B. during a free fall
c. in interplanetary space
D. at the surface of the earth


If \( f(x)=\sin ^{-1}\left\{\frac{\sqrt{3}}{2} x-\frac{1}{2} \sqrt{1-x^{2}}\right\} \)
\( -\frac{1}{2} \leq x \leq 1, \) then \( f(x) \) is equal to :
\( ^{\mathbf{A}} \cdot \sin ^{-1}\left(\frac{1}{2}\right)-\sin ^{-1}(x) \)
B \( \cdot \sin ^{-1} x-\frac{\pi}{6} \)
\( c \cdot \sin ^{-1} x+\frac{\pi}{6} \)
D. none of these


Identify \( \boldsymbol{A}, \boldsymbol{B}, \boldsymbol{C}, \boldsymbol{D}, \boldsymbol{E}, \boldsymbol{F}, \boldsymbol{G} \)
\( \mathbf{K}_{2} \mathbf{C r}_{2} \mathbf{O}_{7} \stackrel{\mathbf{K O H}}{\longrightarrow}(\mathbf{A}) \frac{\mathbf{P} \mathbf{b}\left(\mathbf{C H}_{3} \mathbf{C O O}\right)_{2}}{\mathbf{C H}_{3} \mathbf{C O O H}}>(\mathbf{B}) \)
\( \mathbf{N H}_{4} \mathbf{C l} \)
\( (\mathrm{C}) \stackrel{\Delta}{\longrightarrow}(\mathrm{D})+(\mathrm{E}) \)
(gas) (green) \( \frac{|\mathbf{A}|, \Delta}{\mid} \)
(F) (metal) \( +(G) \) oxide


The correct form and the percentage of
\( C O_{2} \) carried by the blood in man is
A. Carboxyhaemoglobin- 70 \%
B. Bicarbonates - 30 \%
c. Dissolved gas in plasma- 3 \%
D. Bicarbonates - 70 \%


What are the two numbers whose sum
is 58 and difference is \( 28 ? \)


Predict the sign of \( \Delta S \) for each of the following processes, which occur at
constant temperature:
I. The volume of 2 mol of \( O_{2}(g) \)
increases from \( 44 L \) to \( 54 L \)
II. The pressure of 2 mil of \( O_{2}(g) \)
increases from 1 atm to 1.2 atm.
A \( \cdot(I) \rightarrow \Delta S=-v e ;(I I) \rightarrow \Delta S=-v e \)
в. \( (I) \rightarrow \Delta S=-v e ;(I I) \rightarrow \Delta S=+v e \)
c. \( (I) \rightarrow \Delta S=+v e ;(I I) \rightarrow \Delta S=-v e \)
D. \( (I) \rightarrow \Delta S=+v e ;(I I) \rightarrow \Delta S=+v e \)


A solenoid of \( 0.4 \mathrm{m} \) length with 500 turns carries a current of \( 3 \mathrm{A} \). A coil of 10
turns and of radius \( 0.01 \mathrm{m} \) carries a
current of 0.4 A. The torque required to hold the coil with its axis at right angle to that of the solenoid in the middle part
of it, is:
A \( \cdot 6 \pi^{2} \times 10^{-7} N m \)
В. \( 3 \pi^{2} \times 10^{-7} \mathrm{Nm} \)
c. \( 9 \pi^{2} \times 10^{-7} N m \)
D. \( 12 \pi^{2} \times 10^{-7} \mathrm{Nm} \)


The equations of \( L_{1} \) and \( L_{2} \) are \( y=m x \)
and \( \boldsymbol{y}=\boldsymbol{n} \boldsymbol{x}, \) respectively. Suppose \( \boldsymbol{L}_{\mathbf{1}} \)
makes twice as large of an angle with the horizontal(measured
counterclockwise from the positive \( x- \)
axis) as does \( L_{2} \) and that \( L_{1} \) has 4
times the slope of \( L_{2} . \) If \( L_{1} \) is not
horizontal, then the value of the
product(mn) equals.
\( A \cdot \frac{\sqrt{2}}{2} \)
B. \( -\frac{\sqrt{2}}{2} \)
c. 2
D. -2


Ali purchased a printer for \( R s .80,000 \)
After spending \( R s .5000 \) on repair and
Rs.1000 on a new part, he sold it at
\( 25 \% \) profit. At what price did he sell the printer?
A. \( R s .1,07,000 \)
в. \( R s .1,07,500 \)
c. \( R s .1,08,500 \)
D. Rs.2, 09,200


Fill in the blank:
1 light year \( =9.4607 \times-\dots \)
\( \mathbf{A} \cdot 10^{15} \)
B . \( 10^{-15} \)
\( c \cdot 10^{12} \)
D. \( 10^{2} \)


State S.I. unit of angular momentum
Obtain its dimensions.


A concave mirror forms the image of an
object on a screen. If the lower half of
the mirror is covered with an opaque
card, the effect would be to make the
A. image less bright.
B. lower half of the image disappear.
c. upper half of the image disappear.
D. image blurred.


Why fluorine shows anomalous
behaviour as compared to other halogens?


Which of the following is true in the case of a reversible process:
A. There will be energy loss due to friction
B. System and surroundings will not be in thermodynamic equilibrium
c. Both system and surroundings retain their initial states
D. Both A and C


Thermal power plants make use of:
A. fast flowing water
B. uranium and thorium
C. coal, petroleum and natural gas
D. none of these


If \( f(x)=\sin x \) and \( g(x)=\cos x \) then
\( D *(f \circ g) \) is equal to
\( \mathbf{A} \cdot-\sin 2(\cos x) \sin x \)
B. - sin (cos \( x \) ) \( \sin x \)
c. \( -\sin ^{2}(\cos x) \sin x \)
D. \( -\sin (\cos x) \sin ^{2} x \)


Which of the following petroleum product is used for dry cleaning?
A . Grease
B. Kerosene
c. Diesel
D. Petrol


The number of continuous functions on
R which satisfy \( (f(x))^{2}=x^{2} \) for all \( x \in \)
\( \boldsymbol{R} \) is
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c \cdot 4 \)
D. 8


In the velocity-time graph, the distance travelled by the particle between 1.0 sec
and 4.0 sec, is approximately
\( A \cdot 50 m \)
B. \( 40 \mathrm{m} \)
\( c \cdot 30 m \)
D. 20 \( m \)


Six boys and girls sit in a row randomly Find the probability that the six girls sit together.
A \( \cdot p=\frac{1}{95040} \)
B. \( _{p}=\frac{1}{132} \)
c. \( _{p}=\frac{1}{924} \)
D. \( p=\frac{1}{66} \)


Who discovered Braille system?
A. Franklin Braille
B. Stephen Braille
C. Louis Braille
D. Peter Braille


In the adjoining figure, \( \angle A P O=42^{\circ} \)
and \( \angle C Q O=38^{\circ} . \) Find the value of \( \angle \)
POQ.
\( \mathbf{A} \cdot 68^{\circ} \)
B. \( 72^{\circ} \)
\( c \cdot 80^{\circ} \)
D. \( 126^{\circ} \)


The number of \( \pi \) -bonds and \( \sigma \) -bonds in
the Lewis structure of \( S O_{3} \) is :
A \( .3 \sigma, 1 \pi \)
в. \( 3 \sigma, 2 \pi \)
c. \( 3 \sigma, 3 \pi \)
D. None of these


A person is suffering from long standing constipation. It is likely that
A. His intestinal bacteria will get killed by poisonous gases produced by accumulated faeces.
B. He will suffer from piles.
C. He will feel severe pain in the stomach due to accumulated faeces.
D. He will suffer from vitamin B deficiency as its absorption is inhibited.


Which one of the following hormone never reaches to cytoplasm?
A. Estrogen
B. FSH
c. Progesterone
D. Testosterone


\( \int_{0}^{\pi} \boldsymbol{f}(\boldsymbol{x}) \boldsymbol{d} \boldsymbol{x}= \)
A \( \cdot \frac{4}{\pi} \)
в. \( \frac{8}{\pi} \)
\( c \cdot \frac{8}{\pi^{2}} \)
D.


A long circular tube of length \( 10 m \) and
radius \( 0.3 \mathrm{m} \) carries a current I along its curved surface as shown. A wire-loop of resistance 0.0005 ohm and of radius 0.1
\( \mathrm{m} \) is placed inside the tube with its axis coinciding with the axis of the tube. The
current varies as \( \boldsymbol{I}=\boldsymbol{I}_{0} \cos (\boldsymbol{3} \boldsymbol{0} \boldsymbol{0} \boldsymbol{t}) \)
where \( I_{0} \) is constant. If the magnetic
moment of the loop is \( N \mu_{0} I_{0} \sin (300 t) \)
then 'N' is


Oxygen is not evolved when :
This question has multiple correct options
A. potassium chlorate is heated.
B. sodium peroxide reacts with water.
c. ammonium nitrate is heated.
D. zinc oxide is treated with NaOH.


The distance between the origin and the centroid of the tetrahedron whose vertices are \( (\mathbf{0}, \mathbf{0}, \mathbf{0}) \)
\( (a, 0,0),(0, b, 0),(0,0, c) \) is?
A \( \cdot \sqrt{a^{2}+b^{2}+c^{2}} \)
B. \( \frac{\sqrt{a^{2}+b^{2}+c^{2}}}{2} \)
c. \( \frac{\sqrt{a^{2}+b^{2}+c^{2}}}{4} \)
D. \( 4 \sqrt{a^{2}+b^{2}+c^{2}} \)


Let \( \boldsymbol{A}=\boldsymbol{R}-\{\mathbf{3}\} \) and \( \boldsymbol{B}=\boldsymbol{R}-\{\mathbf{1}\} \)
Then, \( \boldsymbol{f}: \boldsymbol{A} \rightarrow \boldsymbol{B}: \boldsymbol{f}(\boldsymbol{x})=\frac{(\boldsymbol{x}-\boldsymbol{2})}{(\boldsymbol{x}-\boldsymbol{3})} \) is?
A. One-one and into
B. One-one and onto
c. Many-one and into
D. Many-one and onto


A container is filled with water \( (\mu= \)
1.33) upto a height of \( 33.25 \mathrm{cm} . \) A
concave mirror is placed \( 15 \mathrm{cm} \) above
the water level and the image of an object placed at the bottom is formed \( 25 \mathrm{cm} \) below the water level. The focal
length of the mirror is
\( \mathbf{A} \cdot 10 \)
B. 15
\( c .20 \)
D. 25


Do plants breathe?


Find each of the following products:
(a) \( -10 \times 9 \)
(b) \( (-20) \times(-10) \)
(c) \( (-4) \times(-6) \)


\( \lim _{n \rightarrow \infty}\left[\frac{1}{n^{2}} \sec ^{2} \frac{1}{n^{2}}+\frac{2}{n^{2}} \sec ^{2} \frac{4}{n^{2}}+\ldots+\frac{1}{r}\right. \)
A \( \cdot \frac{1}{2} \sec 1 \)
B \( \cdot \frac{1}{2} \csc 1 \)
\( c . \tan 1 \)
D. \( \frac{1}{2} \tan \)


Two force point charges \( +q \) and \( +4 q \)
are a distance \( \ell \) apart. A third charge \( q_{1} \)
is so placed that the entire system is in equilibrium. Find the location,
magnitude and sign of the third charge.
This question has multiple correct options
A \( \cdot q_{1}=\frac{4}{9} q \)
B. \( q_{1}=\frac{-4}{9} q \)
\( \mathbf{C} \cdot q_{1} \) is to be placed at a distance \( \ell / 3 \) from \( q \)
D. \( q_{1} \) is to be placed at a distance \( \frac{2 \ell}{3} \) from \( 4 q \)


Brownish branches coming down from
crown of Banyan tree and reaching the soil are
A. Prop roots
B. Stilt roots
c. Additional trunks
D. Pillar branches


The equation \( x^{2}-2=[\sin x], \) where \( [.] \)
denotes the greatest integer function, has
This question has multiple correct options
A. infinity many roots
B. exactly one integer root
c. exactly one irrational root
D. exactly two roots


Dalton said that
cannot be divided.


Q Type your question.
smooth pulley as shown in figure. If the system is released from rest, find the
work done by tension on both \( 1 \mathrm{kg} \) and 2 kg blocks in 1 s. (Take \( g=10 m / s^{2} \) )
A \( \cdot \frac{200}{9} J,-\frac{200}{9} J \)
В. \( -\frac{200}{9} J,+\frac{200}{9} J \)
c. \( +\frac{200}{9} J,+\frac{200}{9} J \)


The hybridization of carbon atoms in
\( \boldsymbol{C}-\boldsymbol{C} \) single bond of \( \boldsymbol{C H} \equiv \boldsymbol{C}- \)
\( \boldsymbol{C H}=\boldsymbol{C H}_{2} \) is :
A \( s p^{3}-s p^{3} \)
is \( s s p^{3}-s p^{3} \)
B \( \cdot s p^{2}-s p^{3} \)
\( \mathbf{c} \cdot s p-s p^{2} \)
D. \( s p^{3}-s p \)


The following data are obtained when dinitrogen and dioxygen react together to form different compounds:
Mass of dinitrogen \( \quad \) Mass of dioxygen
\( 14 \mathrm{g} \) \( 16 g \)
\( 14 \mathrm{g} \) 328
\( 28 \mathrm{g} \) 32 \( g \)
\( 28 g \) \( 80 g \)
Which law of chemical combination is
obeyed by the above experimental data?
A. Law of conservation of mass
B. Law of definite proportions
c. Law of multiple proportions
D. Avogadro's Law


If the extension of the string when it
makes a constant angle relative to vertical is \( \frac{2 m \sqrt{g^{2}+a^{2}}}{x \pi r^{2} Y} l . \) Find \( x \)


The steps for the manufacture of nitric
acid by Ostwald process are given. Arrange them in sequence.
(a) Recirculation of nitric oxide
(b) Addition of \( H_{2} O \) to nitrogen dioxide
(c) Oxidation of nitric oxide
(d) Catalytic oxidation of ammonia
\( A \cdot d c b a \)
B. \( d \) c a \( b \)
\( c \cdot c d b a \)
D. \( \operatorname{cd} a b \)


Range of the function \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \sin ^{2}\left(x^{4}\right)+\cos ^{2}\left(x^{4}\right) \) is
\( A \cdot(-\infty, \infty) \)
B . \{1\}
c. (-1,1)
D. (0,1)


The correct relation between the size of
the obstacle and wavelength of light in order to observe the diffraction effect is
A \( \cdot a_{/ \lambda}=0 \)
B \( \cdot a_{/ \lambda}=0 \)
\( c \cdot a_{/ \lambda}=\infty \)
\( \mathbf{D} \cdot a_{/ \lambda}=150 \)


Evaluate the following integral
\( \int \frac{1}{\sqrt{a^{2}+b^{2} x^{2}}} d x \)


Let \( \mathbf{y}(\mathbf{x}) \) be the solution of the
differential equation \( (\mathbf{x} \log \mathbf{x}) \frac{\mathbf{d y}}{\mathbf{d x}}+\mathbf{y}=2 \mathbf{x} \log \mathbf{x},(\mathbf{x} \geqslant 1) \)
Then \( \mathbf{y}(\mathbf{e}) \) is equal to :
A.
B. 2
\( c \cdot z \)
D.


According to M.O. theory for the atomic
species " \( C_{2} \) " which is not correct? This question has multiple correct options
A. Bond order is zero and it is paramagnetic
B. Bond order is zero and it is diamagnetic.
C. Bond order is two and it is paramagnetic
D. Bond order is two and it is diamagnetic.


Let \( f(x) \) be a function satisfying \( f(x+ \) \( \boldsymbol{y})=\mathbf{f}(\mathbf{x}) \mathbf{f}(\mathbf{y}) \) for all \( \boldsymbol{x}, \boldsymbol{y} \in \mathbf{R} \) and
\( \mathbf{f}(\mathbf{x})=\mathbf{1}+\mathbf{x} \mathbf{g}(\mathbf{x}), \) where \( \lim _{x \rightarrow 0} \mathbf{g}(\mathbf{x})=\mathbf{1} \)
then \( f^{\prime}(x) \) is equal to
A. \( x g(x) \)
в. \( \mathrm{g}^{\prime}(\mathrm{x}) \)
c. \( f(x) \)
D.


What are represented by the equation \( \boldsymbol{x}^{3}+\boldsymbol{y}^{3}+(\boldsymbol{x}+\boldsymbol{y})(\boldsymbol{x} \boldsymbol{y}-\boldsymbol{a} \boldsymbol{x}-\boldsymbol{a} \boldsymbol{y})=\mathbf{0} \)


The electric potential energy between a proton and an electron is given by \( U= \) \( U_{0} l n \frac{r}{r_{0}}, \) where \( r_{0} \) is a constant.
Assuming Bohr's model to be
applicable, write the variation of \( ^{\prime} \boldsymbol{r}^{\prime} \)
with \( n, n \) being the principal quantum number.
\( \mathbf{A} \cdot r_{n} \propto n \)
\( \mathbf{B} \cdot r_{n} \propto 1 / n \)
c. \( r_{n} \propto n^{2} \)
D. \( r_{n} \propto 1 / n^{2} \)


A ball of mass \( 200 g \) falls from a height
of \( 5 m . \) What is its K.E. when it just
reaches the ground?
A . \( 9.8 J \)
в. \( 98 J \)
\( \mathrm{c} .980 \mathrm{J} \)
D. None of these


Which of the following configurations has the highest ionization energy?
A \( \cdot 1 s^{2} 2 s^{2} 2 p^{1} \)
B \( \cdot 1 s^{2} 2 s^{2} 2 p^{3} \)
C \( \cdot 1 s^{2} 2 s^{2} 2 p^{2} \)
D. \( 1 s^{2} 2 s^{2} 2 p^{4} \)


Dryopithecus is more similar to-
A . Ape
B. Gorilla
c. Chimpanzee
D. Man


The number of neutrons accompanying the formation of \( _{54}^{139} X e \) and \( _{38}^{94} S r \) from the absorption of a slow neutron by \( _{92}^{235} U \) followed by nuclear fission is:
\( \mathbf{A} \cdot \mathbf{0} \)
B . 2
c. 1
D. 3


How is the transference of heat energy
by radiation prevented in a calorimeter?


In the given reaction:
\( 4 H_{3} P O_{3} \longrightarrow 3 H_{3} P O_{4}+P H_{3} \)
Equivalent weight of \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{3} \) is :
A. 41.00
B. 54.67
c. 72.89
D. 82.00


Explain human digestive system so as to explain the phenomenon of absorption, Assimilation and Egestion.


To eliminate \( x \) from equations \( x+y+ \)
\( 3 x=12 \rightarrow \ldots . . \) (1) \( \& 8 x+3 y=17 \rightarrow \ldots \)
(2), equation (2) is to be multiplied by
\( A \cdot 8 \)
в. \( -\frac{1}{2} \)
\( c \cdot \frac{1}{2} \)
D. 3


An electric dipole is held in a uniform
electric field.
(i) Show that the net force acting on it is
zero
(ii) The dipole is aligned parallel to the field. Find the work in rotating it through the angle of \( 180^{\circ} \)


\( \frac{x-2}{1}=\frac{y-3}{1}=\frac{z-4}{-1} \& \frac{x-1}{k}= \)
\( \frac{\boldsymbol{y}-\boldsymbol{4}}{\boldsymbol{2}}=\frac{\boldsymbol{z}-\boldsymbol{5}}{\boldsymbol{2}} \) are coplanar then \( \mathbf{k}=? \)
A. any value
B. exactly one value
c. exactly 2 values
D. exactly 3 values


Find \( a, b, c \) if \( a(1,3,2)+b(1,-5,6)+ \)
\( c(2,1,-2)=(4,10,-8) \)


A person holds a bucket of weight \( 60 N \)
He walks \( 7 m \) along the horizontal path
and then climbs up a vertical distance
of 5 m. The work done by the man is:
A . \( 300 J \)
в. \( 420 J \)
c. \( 720 J \)
D. none of these


(a) Differentiate between three
segments of a transistor on the bias of
their size and level of doping.
(b) How is a transistor biased to be in
active state?
(c) With the help of necessary circuit diagram, describe briefly how n-p-n transistor in CE configuration amplifies a small sinusoidal input voltage. Write
the expression for the ac current gain.


The radius of a hemispherical balloon increases from \( 7 \mathrm{cm} \) to \( 14 \mathrm{cm} \) as air is
being pumped into it. Find the ratios of the surface areas of the balloon in the
two cases.


A ball drops from a ceiling of a room, and after rebounding twice from the floor reaches a height equal to half that
of the ceiling. Show that coefficient of restitution is \( \sqrt[4]{\frac{1}{2}} \)


Radial vascular bundles occur in
A. Stem
B. Monocot stem
c. Dicot stem
D. Root


Which of the following will form lactone
on treatment with NaOH?
A. \( \alpha- \) Bromo acid
B. \( \beta- \) Bromo acid
c. \( \beta \) - Hydroxy acid
D. \( \delta- \) Bromo acid


The cost of \( 30 \mathrm{m} \) cloth is Rs. 450
Find the cost of \( 26 \mathrm{m} \) cloth.


What is the scientific name of Asian
tiger mosquito?
A. Aedes aegypti
B. Aedes albopictus
c. Aedes taeniorhynchus
D. Aedes albolineatus


If \( \phi(x)=f(x)+x f^{1}(x) \) then \( \int \phi(x) d x \)
is equal to
A. \( (x+1) f(x)+k \)
В. \( (x-1) f(x)+k \)
c. \( x f(x)+k \)
D. None of these


At two different places, the angles of dip
are respectively \( 30^{\circ} \) and \( 45^{\circ} . \) At these
two places the ratio of horizontal component of earth's magnetic field is:
A. \( \sqrt{3}: \sqrt{2} \)
B. \( 1: \sqrt{2} \)
c. 1: 2
D. \( 1: \sqrt{3} \)


One of the method for purification of water is sedimentation.
A. True
B. False


Which of the following is correct?
A. Formic acid is used in medicine for the treatment of
gout
B. Propanoic acid is used as an antiseptic in the preservation of fruit juice
C. Ethanoic acid is a coagulating agent in rubber industry
D. None of these


Find the inverse of the matrix
\( \mathbf{A}=\left[\begin{array}{ccc}\mathbf{0} & \mathbf{1} & \mathbf{2} \\ {[\mathbf{0 . 3 e m}] \mathbf{1}} & \mathbf{2} & \mathbf{3} \\ {[\mathbf{0 . 3 e m}] \mathbf{3}} & \mathbf{1} & \mathbf{1}\end{array}\right] \)


The combustions of benzene (I) gives
\( \boldsymbol{C O}_{2}(\boldsymbol{g}) \) and \( \boldsymbol{H}_{2} \boldsymbol{O}(l) . \) Given that heat of
combustion of benzene at constant
volume is \( -3263.9 k J \) mol\( ^{-1} \) at \( 25^{\circ} C \)
heat of combustion \( \left(\text { in } k J m o l^{-1}\right) \) of
benzene at constant pressure will be:
\( \left(\boldsymbol{R}=\mathbf{8 . 3 1 4} \boldsymbol{J} \boldsymbol{K}^{-1} \boldsymbol{m o l}^{-1}\right) \)
A \( .+3260 \)
B . -3267.6
\( \mathbf{c} .+4152.6 \)
D. -452.46


Radiations of intensity \( 0.5 \mathrm{W} / \mathrm{m} 2 \) are striking a metal plate. The pressure on the plate is
A \( \cdot 0.166 \times 10^{-8} N / m 2 \)
В. \( 0.332 \times 10-8 N / m^{2} \)
c. \( 0.111 \times 10-8 N / m^{2} \)
D. \( 0.083 \times 10-8 N / m^{2} \)


A particle is thrown vertically upwards. Its velocity at half of the height is \( \mathbf{1 0} \boldsymbol{m} / \boldsymbol{s}, \) then the maximum height
attained by it will be: \( \left(g=10 m / s^{2}\right) \)
A . \( 10 m \)
в. \( 20 m \)
\( c .15 m \)
D. \( 25 m \)


The growth of pollen tubes towards ovules is due to
A. Hydrotropism
B. Chemotropism
c. Geotropism
D. Phototropism


Chlorobenzene on fusing with solid
NaOH (at \( 623 \mathrm{K} \) and 320 atm
pressure) gives:
A. benzene
B. benzoic acid
c. phenol
D. benzene chloride


Starting from rest, when a body moves with uniform acceleration, then distances covered after 1 st, 2 nd, \( 3 r d, \)
seconds are in the ratio
A . 1: 2: 3: 4
B. 1:4:9:16...
c. 1: 3: 5: 7
D. 2:3:5:7...


Prepare the truth table for the following
statement pattern
\( (\boldsymbol{p} \vee \sim \boldsymbol{q}) \rightarrow(\boldsymbol{r} \wedge \boldsymbol{p}) \)


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


Find the sum of the series \( 1.3^{2}+ \)
\( 2.5^{2}+3.7^{2}+ \) to \( n \) terms.


The line passes through \( \left(-1, \frac{\pi}{2}\right) \) and perpendicular to the line \( \sqrt{3} \sin \theta+ \) \( 2 \cos \theta=\frac{4}{r} \) is:
A \( .2=\sqrt{3} r \cos \theta-2 r \sin \theta \)
в. \( 5=2 \sqrt{3} r \sin \theta+4 r \cos \theta \)
c. \( 2=\sqrt{3} r \cos \theta+2 r \sin \theta \)
D. \( 8=2 \sqrt{3} r \sin \theta-4 r \cos \theta \)


A rain drop of radius 0.3 mm has a
terminal velocity in air= \( 1 \mathrm{m} / \mathrm{s} \). The
viscocity of air is \( 8 \times 10^{-5} \) poise. The
viscous force on it is:
A \( .45 .2 \times 10^{-4} \) dyne
B . \( 101.73 \times 10^{-5} \) dyne
C. \( 16.95 \times 10^{-4} \) dyne
D. \( 16.95 \times 10^{-5} \) dyne


The magnetic moment of a bar magnet is
0.256 amp.m \( ^{2} \). Its pole strength is 400
milli amp. m. It is cut into two equal
pieces and these two pieces are arranged
at right angles to each other with their unlike poles in contact (or like poles in contact). The resultant magnetic
moment of the system is
A \( \cdot \sqrt{2} \times 256 \times 10^{-3} A m^{2} \)
B . \( 250 \times 10^{-3} \mathrm{Am}^{2} \)
c. \( \frac{256}{\sqrt{2}} \times 10^{-3} \mathrm{Am}^{2} \)
D \( \cdot \frac{128}{\sqrt{2}} \times 10^{-3} \mathrm{Am}^{2} \)


Write a polynomial of degree 5 using variable \( x \)


An \( L C R \) circuit has \( L=10 m H, R= \)
\( 150 \Omega \) and \( C=1 \mu F \) connected in
series to a source of \( 150 \sqrt{2} \) cos \( \omega t \) volt.
At a frequency that is \( 50 \% \) of the resonant frequency, calculate the average power (in \( \boldsymbol{w} \boldsymbol{a} \boldsymbol{t} \boldsymbol{t} \) ) dissipated per
cycle.


Calculate the distance travelled by a
man walking at a speed of \( 5 \mathrm{km} / \mathrm{hr} \) in 36 minutes.
\( A \cdot 3 \mathrm{km} \)
B. \( 4 \mathrm{km} \)
\( c \cdot 5 k m \)
\( D \cdot 6 \mathrm{km} \)


Ten different letters of an alphabet are given. Words with 5 letters are formed from these given letters. Then the number of words which have at least
one letter repeated is
A . 69760
B. 30240
c. 99748
D. None of these


A \( 1200 \mathrm{kg} \) car is braked to a stop from \( 100 \mathrm{km} / \mathrm{h} . \) If \( 60 \% \) of this energy appears in the steel brake drums, whose total mass is \( 10 \mathrm{kg} \) its temperature will rise
by \( \left(s_{\text {steel }}=450 \mathrm{J} / \mathrm{kg} \mathrm{K}\right) \)
A . \( 31.2^{\circ} \mathrm{C} \)
B. \( 61.7^{\circ} \mathrm{C} \)
c. \( 92.1^{\circ} \mathrm{C} \)
D. \( 42.1^{\circ} \mathrm{C} \)


Which of the following gases is adsorbed most by activated charcoal?
A. \( C O_{2} \)
в. \( N_{2} \)
\( \mathrm{c} \cdot \mathrm{CH}_{4} \)
D. \( H_{2} \)


If the standard deviation of 5,7,9 and
11 is \( 2, \) then the coefficient of variation
is?
A . 15
B . 25
c. 17
D. 19


The number of integral values of k for which the equation \( \sin ^{-1} x+ \)
\( \tan ^{-1} x=2 k+1 \) has a solutions is:
A . 1
B. 2
\( c .3 \)
D. 4


The electronegative elements between which the H-bond is formed principally in aqueous ammonia are:
A. \( O, O \)
B. \( N, N \)
\( c . O, N \)
D. Both \( O, O \) \& \( N, N \)


Amount of water a soil can hold against the pull of gravity is known as
A. Hygroscopic water
B. Storage capacity
c. Gravitational water
D. Field capacity


toppr
Q Type your question
electrons via the nitrogen-nitrogen
double bonds.

The azo dye obtained on reacting 4
aminophenol with nitrous acid (in
dilute hydrochloric acid) below \( 10^{\circ} \mathrm{C} \)
and coupling the resulting diazonium
salt with phenol is:
\( \mathbf{A} \)
B.
\( \mathbf{c} \)
\( D \)


Calculate the de Broglie wavelength associated with a helium atom in a
helium gas sample at \( 27^{\circ} \mathrm{C} \) and 1 at \( \mathrm{m} \)
pressure.
\( \mathbf{A} \cdot 7.3 \times 10^{-11} \) metre.
B . \( 3.6 \times 10^{-10} \) metre.
c. \( 7.3 \times 10^{-10} \) metre.
D. \( 3.6 \times 10^{-11} \) metre.


The value of \( \cos \left(\tan ^{-1}\left(\frac{3}{4}\right)\right) \) is
\( A \cdot \frac{4}{5} \)
B.
\( c \cdot \frac{3}{4} \)
D.


For the configuration of media of
permitivities \( \varepsilon_{o}, \varepsilon \) and \( \varepsilon_{o} \) between
parallel plates each of area \( A \), as show
in figure, the equivalent capacitance is
\( \mathbf{A} \cdot \varepsilon_{0} A / d \)
В \( \cdot \varepsilon_{0} \varepsilon A / d \)
C. \( \frac{\varepsilon_{0} \varepsilon A}{d\left(\varepsilon+\varepsilon_{0}\right)} \)
D. \( \frac{\varepsilon_{0} \varepsilon A}{\left(2 \varepsilon+\varepsilon_{0}\right)} \)


Which of the following statements are
correct?
This question has multiple correct options
A. \( \Delta H \) is -ve for exothermic reaction
B. \( \Delta H \) is +ve for exothermic reactions
C. The heat of neutralization of strong acids and strong bases is constant
D. The enthalpy of fusion is positive


Which of the following statements is
true about \( \boldsymbol{C a}(\boldsymbol{O H})_{2} ? \)
A. It is used in the preparation of bleaching powder
B. It is light blue solid
c. It does not process disinfectant property
D. It is used in the manufacture of cement


Define the term placentation.


Fuse blows because
A. There is a high voltage connected across the circuit
B. There is a high current flowing through the circuit
C. There is a high charge that has passed through the circuit
D. The effective resistance of the circuit is too high


Which of the following metal can be cut
with the knife?
A. Gold
B. Potassium
\( c . \) Iron
D. None of the above


The equivalent capacitance between points \( A \) and \( B \) for the given figure is
\( A \cdot 1 F \)
В. \( 2 F \)
\( c .3 F \)
2.4


In which case, a spontaneous reaction is possible at any temperature?
A. \( \Delta H-v e, \Delta S+v e \)
в. \( \Delta H-v e, \Delta S-v e \)
c. \( \Delta H+v e, \Delta S+v e \)
D. none of these


f a particle is executing SHM, with an amplitude \( A, \) the distance moved and the displacement of the body in a time equal to its period are
\( A \cdot 2 A, A \)
B. \( 4 A, \),
\( c \cdot A, A \)
D. \( 0,2 A \)


Balance the following equation:
\( \boldsymbol{C u}(\boldsymbol{s})+\boldsymbol{A} \boldsymbol{u}^{\oplus} \longrightarrow \boldsymbol{A u}(\boldsymbol{s})+\boldsymbol{C u}^{2+} \)
\( \mathbf{A} \cdot C u(s)+2 A u^{\oplus} \longrightarrow A u(s)+C u^{2+} \)
B \( \cdot C u(s)+2 A u^{\oplus} \longrightarrow 2 A u(s)+C u^{2+} \)
\( \mathbf{c} \cdot 2 C u(s)+A u^{\oplus} \longrightarrow 2 A u(s)+2 C u^{2+} \)
D \( \cdot 2 C u(s)+A u^{\oplus} \longrightarrow 2 A u(s)+C u^{2+} \)


The orbital angular momentum and
angular momentum (classical
analogue) for the electron of \( 4 s \) -orbita
are respectively, equal to:
A \( \cdot \sqrt{12} \frac{h}{2 \pi} \) and \( \frac{h}{2 \pi} \)
B. zero and \( \frac{2 h}{\pi} \)
c. \( \sqrt{6} h \) and \( \frac{2 h}{\pi} \)
D. \( \sqrt{2} \frac{h}{2 \pi} \) and \( \frac{3 h}{2 \pi} \)


What are the suggested reasons for
population explosion?


If \( \sin ^{-1}\left(x-\frac{x^{2}}{2}+\frac{x^{3}}{4}-\dots \infty\right)+ \)
\( \cos ^{-1}\left(x^{2}-\frac{x^{4}}{2}+\frac{x^{6}}{4}-\dots \infty\right)=\frac{\pi}{2} \)
and \( 0<x<\sqrt{2} \) then \( x= \)
\( A \cdot \frac{1}{2} \)
B.
\( c \cdot \frac{-1}{2} \)
D. -


What happens when some charge is placed on a soap bubble?
A. Its radius decreases
B. Its radius increases
c. The bubble collapses
D. None of the above


The tangent EF and EG are drawn from E
to the circle with centre 0. The diameter
Fl and the tangent EG, when produced,
intersect at H. If \( \angle \mathrm{IFG}=28^{\circ}, \) calculate
(a) \( \angle \mathrm{EFG} \)
(b) \( \angle \mathrm{FEG} \)
(c) \( \angle \mathrm{HGl} \)


Which part of human eye controls the amount of light entering the eye?
A. Cornea
B. Retina
c. Pupil
D. Iriss


Two convex lenses have focal lengths 10
\( \mathrm{cm} \) and \( 40 \mathrm{cm} . \) If a telescope has to be
made by using these two lenses
1. The distance between the lenses
should be \( 50 \mathrm{cm} \)
2. The distance between the lenses
should be \( 30 \mathrm{cm} \)
3. The magnifying power of this
telescope will be 5
4. An inverted image will be produced in this telescope Which two of the give are correct?
A. 1 and 4
B. 2 and 4
c. 1 and 3
D. 3 and 4


Kirchhoff's law of junction, \( \sum I=0 \), is based on
A. Conservation of energy
B. conservation of charge
c. conservation of energy as well as charge
D. conservation of momentum


The measurement of each angle of a
polygon is \( 160^{\circ} . \) The number of its sides
is?
A . 15
B. 18
c. 20
D. 30


Which of the following reagents can form a phenylhydrazone with dimethyl ketone?
\( \mathbf{A} \cdot\left[N H_{3} O H\right]^{\oplus} C l^{\ominus} \)
в. \( P h N H N H_{2} \)
c. \( N H_{2} N H C O N H_{2} \)
D. \( H C N \)


The distance travelled by a body during last second of its upward journey is \( \boldsymbol{d} \) when the body is projected with certain velocity vertically up. If the velocity of projection is doubled, the distance travelled by the body during the last second of its upward journey is
A \( .2 d \)
B. \( 4 d \)
c. \( \frac{d}{2} \)
D. \( d \)


Let the observations \( x_{i}(1 \leq i \leq 10) \) satisfy the equations, \( \sum_{i=1}^{10}\left(x_{i}-5\right)=10 \) and \( \sum_{i=1}^{10}\left(x_{i}-5\right)^{2}=40 . \) If \( \mu \) and \( \lambda \) are the mean and the variance of the
observations, \( x_{1}-3, x_{2}-3, \dots ., x_{10} \)
3, then the ordered pair \( (\mu, \lambda) \) is equal
to?
A . (6,6)
в. (3,6)
\( c .(3,3) \)
D. (6,3)


A vertical stick \( 12 \mathrm{m} \) long casts a
shadow \( 8 \mathrm{m} \) long on the ground. At the
same time a tower casts the shadow of
length \( 40 \mathrm{m} \) on the ground. Determine the height of the tower


A particle is moving around a circular
path with uniform angular speed ( \( \omega \) ) The radius of the circular path is \( (r) \)
The acceleration of the particle is:
A \( \cdot \frac{\omega^{2}}{r} \)
в. \( \frac{\omega}{r} \)
c. \( v \)
D. \( v r \)


The line \( x=y \) touches a circle at the
point \( (1,1) . \) If the circle also passes through the point (1,-3) then its radius is:
\begin{tabular}{l}
A \( .3 \sqrt{2} \) \\
\hline
\end{tabular}
B. 3
c. \( 2 \sqrt{2} \)
D. 2


Which of the following statement is
true?
A. Benzaldehyde is used in perfumery industry
B. Formaldehyde is used for silvering mirrors
C. Acetone is used as a commercial solvent
D. All of the above


Figure shows two processes \( A \) and \( B \) on
a system. Let \( \Delta Q_{1} \) and \( \Delta Q_{2} \) be the heat
given to the system in processes \( A \) and
B respectively. Then
A \( \cdot \Delta Q_{1}>\Delta Q_{2} \)
B . \( \Delta Q_{1}=\Delta Q_{2} \)
c. \( \Delta Q_{2}<\Delta Q_{2} \)
\( \mathbf{D} \cdot \Delta Q_{1}<=\Delta Q_{2} \)


Concentration of \( \boldsymbol{N} \boldsymbol{H}_{4} \boldsymbol{C l} \) and \( \boldsymbol{N} \boldsymbol{H}_{4} \boldsymbol{O} \boldsymbol{H} \)
in a buffer solution are in the ratio of
\( 1: 10, \mathrm{Kb} \) for \( N H_{4} O H \) is \( 10^{-10} . \) The pH of
the buffer is:
(BHU, 1994)
A .4
B. 5
\( c \cdot 9 \)
D. 1


If
\( (1-p)\left(1+3 x+9 x^{2}+27 x^{3}+81 x^{4}+\right. \)
\( 1-p^{6}, p \neq 1 \) then the value of \( \frac{p}{x} \) is
A \( \cdot \frac{1}{3} \)
B. 3
\( c \cdot \frac{1}{2} \)
D. 2


An electrical appliance has a rating 100 W, 120 V. The resistance of element of
appliance when in use is :
\( \mathbf{A} \cdot 1 \cdot 2 \Omega \)
B. \( 144 \Omega \)
c. \( 120 \Omega \)
D. \( 100 \Omega \)


Commercial silk is obtained from
A. cocoon
B. Caterpillar
c. Adult moth
D. Both egg and adult moth


If a shunt of \( \frac{1}{10} t h \) of the coil resistance is applied to a moving coil galvanometer, its sensitivity becomes
A. 10 fold
в. \( \frac{1}{10} \) fold
c. 11 fold
D. \( \frac{1}{11} \) fold


Which of the following expressions is known as Clausius inequality?
A \( \cdot \oint \frac{d q}{T} \leq 0 \)
В \( \cdot \oint \frac{d q}{T}=0 \)
c. \( \oint \frac{T}{d q} \leq 0 \)
\( \mathbf{D} \cdot \oint \frac{d q}{T} \geq \leq 0 \)


Mud houses are cooler in summer and
warmer in winter because
A. mud is a good conductor of heat
B. mud is a superconductor of heat
c. mud is a bad conductor of heat
D. none of these


\( \boldsymbol{C a O}(\boldsymbol{s})+\boldsymbol{H}_{3} \boldsymbol{O}^{+}+\boldsymbol{C l}^{-} \longrightarrow \)
Addition of solid calcium oxide to a
solution of hydrochloric acid as given, results in the formation of:
(1) \( C a^{2+} \)
(2) \( H_{2} O \)
(3) \( \boldsymbol{H}_{\mathbf{2}} \)
A. If 1,2 and 3 are correct
B. If only 1 and 2 are correct
c. If only 2 and 3 are correct
D. If only 1 is correct
E. If only 3 is correct


A tank of size \( 10 m \times 10 m \times 10 m \) is ful
of water and built on the ground. If \( g= \)
\( 10 m s^{-2}, \) the potential energy of the
water in the tank is
A \( .5 \times 10^{7} J \)
В. \( 1 \times 10^{8} J \)
c. \( 5 \times 10^{4} J \)
D. \( 5 \times 10^{5} J \)


The value of the sum \( \sum_{n=1}^{13}\left(i^{n}+i^{n+1}\right) \) where \( i=\sqrt{-1}, \) equals
\( \mathbf{A} \cdot i \)
B . \( i-1 \)
\( c \cdot-i \)
D.


Urease is :
\( A \cdot \) a vitamin
B. an enzyme
c. a protein
D. an amino acid


Which one of the following is the correct pathway for propagation of cardiac impulse?
A. SA node \( \rightarrow \) Bundle of his \( \rightarrow \) Purkinje fibres
B. AV node \( \rightarrow \) Bundle of his \( \rightarrow \) SA node \( \rightarrow \) Purkinje fibres
c. SA node \( \rightarrow \) Purkinje fibres \( \rightarrow \) AV node \( \rightarrow \) Bundle of his
D. Purkinje fibres \( \rightarrow \) AV node \( \rightarrow \) SA node \( \rightarrow \) Bundle of his


Which of the following do not produce flame on burning?
A . Petrol
B. coal
c. L.P.
D. Kerosene


A square of side L meters lies in the \( x-y \)
plane in a region where the magnetic field is given by \( \overline{\boldsymbol{B}}=\boldsymbol{B}_{0}(\mathbf{2} \hat{\boldsymbol{i}}+\boldsymbol{3} \hat{\boldsymbol{j}}+ \)
\( 4 \hat{k}) T, \) where \( B_{0} \) is constant. The magnitude of flux passing through the
square is:
\( \mathbf{A} \cdot 8 B_{0} L^{2} W b \)
B. \( 12 B_{0} L^{2} W b \)
c. \( 4 B_{0} L^{2} W b \)
D. \( \sqrt{4 \times 29} B_{0} W b \)


Reaction of acetic acid, \( C H_{3} C O_{2} H \)


A water tank is filled with water upto
height H. A hole is made in a tank wall at a depth D from the surface of water The distance \( X \) from the lower end of
wall where the water stream from tank
strikes the ground is:
B \( .2 \sqrt{D(H+D)} \)
c. \( 2 \sqrt{D(H-D)} \)
\( D \cdot \sqrt{D} \)


\( \int \frac{1}{x+x \log x} d x \)


A naturally occuring sample of copper consists of \( 69.2 \% \) of \( ^{63} \mathrm{Cu} \) and \( 30.8 \% \) of
\( ^{65} \mathrm{Cu} . \) The relative mass of \( ^{63} \mathrm{Cu} \) is 62.93
and that of \( ^{65} \mathrm{Cu} \) is \( 64.93 . \) Find the
atomic mass of a naturally occuring sample of copper.
A. 64.348
B. 63.546
c. 64.12
D. none of these


In a slow reaction, rate of reaction
generally with time.
A. decreases
B. increases
c. sometimes increases and sometimes decrease
D. remain constant


Which species does not exist?
A \( \cdot\left(\operatorname{Sn} C l_{6}\right)^{2-} \)
B. \( \left(G e C l_{6}\right)^{2-} \)
c. \( \left(C C l_{6}\right)^{2-} \)
D. \( \left(S i C l_{6}\right)^{2-} \)


How many carbon atoms are there in
the simplest alkane capable of exhibiting chain isomerism?
A. three
B. five
c. four
D. six


If the sum of the measures of two
angles is \( 540^{0} \) and their difference is
\( 60^{0}, \) find their measures in radians.


Solve \( \int \frac{1}{x^{2} \cos ^{2}(1 / x)} d x \)
A . \( \tan x \)
B. - tan \( x \)
\( c \cdot \cot x \)
D. - co


\( \int \frac{1}{1+\sin x} d x= \)
A \( \cdot \tan x+\sec x+c \)
B. \( \tan x-\sec x+c \)
c. \( \cot x-\operatorname{cosec} x+c \)
D. - \( \cot x+\sec x+c \)


Gases have the
density and rigidity
A. least
B. maximum
c. intermediate
D. none


If same quantity of electricity is passed
through \( C u C l \) and \( C u S O_{4}, \) the ratio of
the weights of \( C u \) deposited from
\( C u S O_{4} \) and \( C u C l \) is :
A .2: 1
B. 1: 2
c. 1: 1
D. 4: 1


The figure indicates the potential
energy curve of a diatomic molecule
What will be the value of binding
energy?


If a cricket ball hits you, it will hurt much more than a tennis ball would when moving with the same velocity because:
A. a cricket ball is bigger
B. a cricket ball has more mass
c. a cricket ball has less density
D. none of the above


A cubical block of mass \( m \) and side \( L \)
rests on a rough horizontal surface with
coefficient of friction \( \mu . \) A horizontal
force \( \boldsymbol{F} \) is applied on the block as shown in the figure. If the coefficient of friction is sufficiently high so that the block does not slide before toppling, the minimum force required to topple the block is:
\( A \cdot \frac{m g}{4} \)
B. \( \frac{m g}{8} \)
\( c \cdot \frac{m g}{2} \)
D. \( m g(1-\mu) \)


Nuclei of a radio-active element \( A \) are
being product at a constant rate \( \alpha \). The
element has a decay constant \( \lambda \). At time
\( t=0 \) there are \( N_{0} \) nuclei of the element
present
(a) Calculate the number of nuclei \( A \) as
a function of time \( t \)
(b) If \( \alpha=2 N_{0} \lambda \), calculate the number
of nuclei of \( A \) after one half-life of \( A \)
and also the limiting value of \( N \) as \( t \rightarrow \)
\( \infty \)


Oils on treating with hydrogen in the presence of palladium or nickel catalyst form fats, this is an example of:
A. addition reaction
B. substitution reaction
c. displacement reaction
D. oxidation reaction


Select the correct matches:
(a) Sedimentary nutrient cycle Nitrogen cycle (b) Pioneer species Lichens
(c) Secondary succession Burnt forest (d) Pyramid of biomass in sea - upright
A. a, b, and donly
B. b, and conly
c. a, and conly
D. b, and donly


Which of the following is a correct nomenclature?

This question has multiple correct options
A. Felis domesticus
B. Felis domestica
c. Magnifera indicus
D. tamarindus indica


What is the nature of bond in \( C a H_{2} ? \)


What do you mean by electromagnetic
waves? Write the names of all
electromagnetic waves from gamma rays to radio waves in order of their increasing wavelengths.


A compound which gives oxygen on moderate heating is?
A. \( Z n O \)
в. \( A l_{2} O_{3} \)
\( \mathrm{c} \cdot F e_{2} O_{3} \)
D. Hgo


Two boats \( A \) and \( B \) having same speed relative to river are moving ina river Boat A moves normal to the river
current as observed by an observer moving with velocity of river current.Boat B moves normal to the river
as observed by the observer on the ground.
A. To a ground observer boat B moves faster than A
B. To a ground observer boat A moves faster than B
c. To the given moving observer boat B moves faster than A
D. To the given moving observer boat A moves faster than B


Exonephric secretion in earthworm is
by
A. Septal nephridia
B. Pharyngeal nephridia
c. Integumentary nephridia
D. Both B and C


In a solution \( 0.04 M F e C l_{2}, 0.02 M \)
\( F e C l_{3} \) and \( 0.01 M H C l, \) how large may
be its \( p H \) (nearest integer) without
there being precipitation of either
\( \boldsymbol{F} \boldsymbol{e}(\boldsymbol{O} \boldsymbol{H})_{2} \) or \( \boldsymbol{F} \boldsymbol{e}(\boldsymbol{O} \boldsymbol{H})_{3} ? \boldsymbol{K}_{s p} \) of
\( F e(O H)_{2} \) and \( F e(O H)_{3} \) are \( 8 \times 10^{-16} \)
and \( 4 \times 10^{-38} \) respectively.


Arrange the following in increasing order of their acidic character:
Benzoic acid, Phenol, Cresol


While measuring the acceleration due to gravity by a simple pendulum, a
student makes a positive error of \( 1 \% \) in the length of the pendulum and a negative error of \( 3 \% \) in the value of time
period. His percentage error in the
measurement of \( g \) by the relation \( g= \)
\( 4 \pi^{2}\left(l / T^{2}\right) \) will be
A . \( 2 \% \)
в. \( 4 \% \)
c. \( 7 \% \)
D. \( 10 \% \)


The focal length of a concave mirror is
10 \( c m . \) Find its radius of curvature.
\( \mathbf{A} \cdot 25 \mathrm{cm} \)
в. 5 ст
c. \( 10 \mathrm{cm} \)
D. \( 20 \mathrm{cm} \)


Blood plasma contains
A. 60\% water
B. 80\% water
c. \( 90 \% \) water
D. 98\% water


Which one is found in males only?
A. X-chromosome
B. Y-chromosome
c. \( 2 x \) -chromosomes
D. \( x+x \) -chromosomes