Which of the following alcohols cannot
be oxidized by \( K_{2} C r O_{7} ? \)
A. Ethanol
B. Tert butyl alcohol
c. Isopropyl alcohol
D. Allyl alcohol


Evaluate \( \lim _{x \rightarrow a} \frac{x^{7}-a^{7}}{x-a} \)


Match the following.
\( \mathbf{A} \cdot A-H, B-G, C-E, D-F \)
\( \mathbf{B} \cdot A-G, B-H, C-E, D-F \)
\( \mathbf{c} \cdot A-E, B-H, C-G, D-F \)
\( \mathbf{D} \cdot A-F, B-G, C-H, D-F \)


The displacement of a particle is given by \( \sqrt{x}=t+1 . \) Which of the following
statements about its velocity is true?
A. It is zero
B. It is constant but not zer
c. It increases with time
D. It decreases with time


Name the following The stage at which centresome attaching the two chromatids divide.


Pick up the correct statement(s):
This question has multiple correct options
A. All minerals are ores
B. All minerals cannot be ore
C. All ores are minerals
D. The mineral from which metals can be extracted
profitably are called ores


\( \int_{0}^{1} \frac{e^{x}}{1+e^{2 x}} d x \)


Mark the rule which is not correctly
stated about the determination of
significant figures.
A. Zeros preceding to first non-zero digit are not significant.
B. Zeros between two non-zero digits are not significant.
C. Zeros at the end or right of the number are significant if they are on the right side of the decimal point
D. All non-zero digits are significant


Let \( R \) be a relation from \( A= \)
\{1,2,3,4\} to \( B=\{1,3,5\} \) such that
\( \boldsymbol{R}=[(\boldsymbol{a}, \boldsymbol{b}): \boldsymbol{a}< \)
\( b, \text { where } a \epsilon A \text { and } b \epsilon B] . \) What is \( R \)
equal to?
A \( \cdot(1,3),(1,5),(2,3),(2,5),(3,5),(4,5) \)
B . (3,1),(5,1),(3,2),(5,2),(5,3),(5,4)
c. (3,3),(3,5),(5,3),(5,5)
D. (3,3),(3,4),(4,5)


Stress and pressure have the same
dimensions but pressure is not the same as stress.Why?


is a gas in an atmosphere that absorbs and emits radiation within the thermal infra-red
range.
A. Global gas
B. Greenhouse gas
c. Green gas
D. Noble gas


Quiescent centre is found in a plant at
A. Root tip
B. Shoot tip
c. Cambium
D. Leaf tip


Show that \( \cot 7 \frac{1^{\circ}}{2}=\sqrt{2}+\sqrt{3}+\sqrt{4}+ \)
\( \sqrt{6} \)


A heater of power \( \boldsymbol{P} \boldsymbol{W} \) raises the temperature of \( \mathrm{m} \) kg of a liquid by \( \Delta T K \) in time \( t s . \) Express the specific heat capacity of liquid in terms of above data
A \( \cdot c=\frac{P \Delta T}{m t} \)
в. \( c=\frac{P}{m \Delta T} \)
c. \( _{c}=\frac{P t}{m \Delta T} \)
D. \( c=\frac{P t}{\Delta T} \)


Which of the following statements are
true?
a. The spectrum of sunlight has 7 colors
b. Spectrum is seen due to bending of lights of different colors at different
angles with respect to the incident ray through a prism
c. Red light bends the least whereas violet light bends the maximum
d. Rainbow is an example of dispersion of light
A. a, band c
B. c and d
c. a, c and d
D. All of these


A hydrogen-like atom in ground state absorbs n photons having the same energy and its emits exactly n photons when electrons transition takes placed. Then, the energy of the absorbed photon
may be :
This question has multiple correct options
A. 91.8 eV
в. 40.8 eV
c. 48.4 eV
D. 54.4 eV


\( n \stackrel{L t}{\rightarrow} \infty \frac{1}{n}\left\{\sin ^{2} \frac{\pi}{2 n}+\sin ^{2} \frac{2 \pi}{2 n}+\ldots+\right. \)
\( \left.\sin ^{2} \frac{n \pi}{2 n}\right\}= \)
A.
в.
\( c \cdot 1 / 2 \)
D.


\( \boldsymbol{y}=\boldsymbol{x}^{4}, \) is moving with velocity \( \boldsymbol{V}=\boldsymbol{V}_{0} \boldsymbol{i} \)
in a non-uniform magnetic field \( \vec{B}= \)
\( \boldsymbol{B}_{0}\left(1+\left(\frac{\boldsymbol{y}}{\boldsymbol{L}}\right)^{\beta}\right) \hat{\boldsymbol{k}}, \) as shown in figure. If
\( V_{0}, B_{0}, L \) and \( \beta \) are positive constants
and \( \Delta \phi \) is the potential difference
developed between the ends of the wire,
then the correct statement(s) is/are?
This question has multiple correct options
A \( \cdot|\Delta \phi|=\frac{4}{3} B_{0} V_{0} L \) for \( \beta=2 \)
B. \( |\Delta \phi| \) remains same if the parabolic wire is replaced by a straight wire, \( y=x, \) initially, of length \( \sqrt{2} l \)
C \( \cdot|\Delta \phi|=\frac{1}{2} B_{0} V_{0} L \) for \( \beta=0 \)
D. \( |\Delta \phi| \) is proportional to the length of wire projected on y-axis


The length of time a satellite takes to orbit the earth depends on its:
A. launch speed
B. mass
c. distance from the earth
D. weight
E. orbital direction


Which of the following pairs is/are
correct?
(A) Main root - Storage
(B) Lateral root - Absorption
(C) Root hair - Conduction
A. All are correct
B. A and B
c. only
D. None of these


The figure shows a small circular coil of area A suspended from a point 0 by a string of length I in a uniform magnetic induction B in the horizontal direction. If
the coil is set into oscillations likes
simple pendulum by displacing it a
small angle \( \theta_{0} \) as shown, find emf induced in the coil as a function of time.
Assume the plane of the coil is always in the plane of string.


What is pseudo first order reaction?
Give one example of it.


\( \frac{8}{8} \)


As shown in the image, a series of enzymes catalyze the reaction that changes Molecule A into Molecule C. Molecule \( C, \) functions as a corepressor for the operon controlling production of Enzyme A when it binds with Molecule
D. If no Molecule D is present, which of the following is the most likely result of the presence of large amounts of Molecule C?
A. Concentration of Enzyme A will decrease.
B. Concentration of Enzyme A will increase
c. concentration of Molecule A will increase
D. Concentration of Enzyme B will decrease


The specific charge of a proton is \( 9.6 \times \) \( 10^{7} C / k g . \) The specific charge of an
alpha particle will be:
\( \mathbf{A} \cdot 9.6 \times 10^{7} C / k g \)
B . \( 19.2 \times 10^{7} C / k g \)
\( \mathbf{c} \cdot 4.8 \times 10^{7} C / k g \)
D. \( 2.4 \times 10^{7} C / k g \)


Two coils \( A \) and \( B \) have 200 and 400
turns respectively. A current of 1 A in coil
A causes a flux per turn of \( 10^{-3} \) Wh to
link with \( A \) and a flux per turn of \( 0.8 \times \) \( 10^{-3} \) Wh through B. The ratio of self-
inductance of \( A \) and the mutual
inductance of \( A \) and \( B \) is :
A. \( 5 / 4 \)
B. 1/1.6
c. 1.6
D.


In an interference pattern produced by
two identical slits, the intensity at the
site of the central maximum is I. The
intensity at the same spot when either
of the two slits is closed is \( I_{0} \). We must
have:
\( \mathbf{A} \cdot I=I_{0} \)
в. \( I=2 I_{0} \)
c. \( I=4 I_{0} \)
D. \( I \) and \( I_{\circ} \) are not related


toppr oGın
Q Type your question
position \( x=12 \mathrm{m} \) on the line.
A proton placed at any point on the line
between the two charges will
experience a net force due to the two
charges. The net force acting on the
proton is shown as a function of
position in the graph, where positive
values of force represent rightward
force.

What is the sign of each charge, and
which charge is stronger?
A. Charge 1 is positive, Charge 2 is positive, and the stronger charge is Charge 2 .
B. Charge 1 is negative, Charge 2 is positive, and the stronger charge is Charge 1
c. Charge 1 is positive, Charge 2 is negative, and the stronger charge is Charge 1.
D. Charge 1 is negative, Charge 2 is positive, and the stronger charge is Charge 2 .
E. Charge 1 is negative, Charge 2 is negative, and the stronger charge is Charge 1.


The emf of a voltaic cell can be given by :
A. SRP of cathode \( - \) SRP of anode
B. SRP of cathode \( + \) SRP of anode
C. SOP of cathode - SOP of anode
D. SOP of cathode \( + \) SOP of anode


Solve:
\( 4 x^{4}-5 x^{3}-7 x+1 \div 4 x-1 \)


Assertion: All molecules in a gas have
same speed. Reason: Gas contains molecules of
different size and shape.
Choose the appropriate option.
A. If both assertion and reason are true and the reason is a correct explanation of the assertion.
B. If both assertion and reason are true, but reason is not a correct explanation of the assertion.
c. If the assertion is true, but reason is false.
D. If both the assertion and reason are false


A block of mass \( m=0.1 \mathrm{kg} \) is released
from a height of \( 4 \mathrm{m} \) a curved smooth
surface. On the horizontal surface path
AB is smooth and path BC offers
coefficient of friction \( \mu=0.1 . \) If the
impact of block with vertical wall at \( C \) be perfectly elastic, find the total
distance covered by the block on the horizontal surface before coming to
rest. (Take \( \left.\mathfrak{g}=10 \frac{m}{s^{2}}\right) \)


Solve:
\( \left(y^{2}+10 y+24\right) \div(y+4) \)


Which of the following compounds will show stereoisomerism?
A. 1-phenylethanamine
B. phenylchloroethanoate
c. 3-chloro-3-ethynylpenta-1,4-diyne
D. 3-methylbutanoic acid


Assertion
2-butyne on controlled hydrogenation
with \( P d / C a C O_{3} \) in presence of \( P b O \)
gives cis- \( 2- \) butene
Reason
Hydrogenation occur at the surfaces of
metal containing adsorbed hydrogen.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Assertion
In case of bullet fired from gun, the ratio of kinetic energy of gun and bullet is equal to ratio of mass of bullet and gun.
Reason
In firing, momentum is conserved.
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 alternating emf of angular frequency \( \omega \) is applied across an inductance. The
instantaneous power developed in the
circuit has an angular frequency:
A \( \cdot \frac{\omega}{4} \)
B. \( \frac{\omega}{2} \)
\( c \cdot \omega \)
D. \( 2 \omega \)


ABCD is a square of side \( 100 \mathrm{m} . \) A cyclist
P starts from \( A \) and moves towards \( B \)
with a speed of \( 4 \mathrm{m} / \mathrm{s} \). At the same instant, a second cyclist Q starts from B
and moves towards C with speed of 3
\( \mathrm{m} / \mathrm{s} . \) If the angular velocity of \( \mathrm{Q} \) relative
to \( P \) after \( t \) seconds is \( \frac{4 \sin \theta+n \cos \theta}{\sqrt{(100-4 t)^{2}+n t^{2}}} \)
rad/s, find value of \( n \)


Hybridization and magnetic behaviour of complex \( \boldsymbol{K}_{\mathbf{4}}\left[\boldsymbol{M} \boldsymbol{n}(\boldsymbol{C} \boldsymbol{N})_{\boldsymbol{6}}\right] \) is:
A \( \cdot d^{2} s p^{3}, \) diamagnetic
B . \( d^{2} s p^{3} \), paramagnetic
\( \mathrm{c} \cdot s p^{3} d^{2}, \) diamagnetic
D. \( s p^{3} d^{2} \), paramagnetic


Show that the relation \( R \) in the \( \operatorname{set} A= \)
\{1,2,3,4,5\} given by \( R= \)
\( \{(a, b):|a-b| \text { is even }\}, \) is an
equivalence relation.


The boiling point of mercury is \( 367^{\circ} \mathrm{C} . \) A mercury thermometer can be used to
measure a temperature of \( 500^{\circ} \mathrm{C} \)
A. by filling the space above mercury with oxygen at highh pressure
B. by filling the space above mercury with nitrogen at low pressure
c. by filling the space above mercury with nitrogen at high pressure
D. by keeping the space above mercury as vacuum


Two electric resistors have equal values of resistance \( R \). Each can be operated
with a power of 320 watts\( (w) \) at 220 volts. If the two resistors are
connected in series to a 110 volts
electric supply, then the power generated in each resistor is
A . 90 watts
B. 80 watts
c. 60 watts
D. 20 watts


If a capacitance \( C \) is connected in series with an inductor of inductance \( L \)
then the angular frequency will be
A \( \cdot \sqrt{\frac{1}{L C}} \)
в. \( \sqrt{\frac{L}{C}} \)
c. LC
D. \( \sqrt{L C} \)


A boy playing on the roof top of a \( 10 \mathrm{m} \) high building throws a ball with a speed
of \( 10 \mathrm{m} / \mathrm{s} \) at an angle of \( 30_{0} \) with the
horizontal. How far from the throwing point will the ball be at the height of 10m from the ground.
\( \sin 30^{0}=\frac{1}{2} \)
\( \cos 30^{0}=\frac{\sqrt{3}}{2} \)
A. 8.66 \( \mathrm{m} \)
B. 5.20 \( \mathrm{m} \)
c. 4.33 m
D. 2.60 \( \mathrm{m} \)


Which of the following are close to ideal plastics?
This question has multiple correct options
A. Putty
B. Mudd
c. Rubber band
D. None of the above


Which solution is a conjugate acid/base pair with differing spectral absorbencies?
A. Chemical pH indicator
B. Acid/base buffer
c. Anhydrous solution
D. Hypotonic solution
E. supersaturated solution


Two identical spheres having charges \( 8 \mu C \) and \( -4 \mu C \) are kept at a certain
distance apart. Now they are brought into contact, after that again they are
kept at the same distance. Compare the forces in the two cases
A . 4: 1
B. 12: 1
c. 8: 1
D. 16: 1


A bullet of mass \( 10 g \) and speed
\( 500 m / s \) is fired into a door and gets embedded exactly at the center of the door. The door is \( 1.0 m \) wide and weighs \( 12 k g . \) It is hinged at one end and rotates about a vertical axis practically without friction. Find the angular speed of the door just after the bullet embeds
into it.


The \( S-S \) bond energy is:
\( \Delta \boldsymbol{H}_{f}^{o}(\boldsymbol{E} \boldsymbol{t}-\boldsymbol{S}-\boldsymbol{E} \boldsymbol{t})=-\mathbf{1 4 7 k J} / \boldsymbol{m o l} \)
\( \boldsymbol{\Delta} \boldsymbol{H}_{f}^{o}(\boldsymbol{E} \boldsymbol{t}-\boldsymbol{S}-\boldsymbol{S}-\boldsymbol{E} \boldsymbol{t})= \)
\( -202 k J / m o l \)
\( \Delta H_{f}^{o} S(g)=+223 k J / m o l \)
\( \mathbf{A} \cdot 168 k J \)
в. \( 126 k J \)
c. \( 278 k J \)
D. \( 575 k J \)


The cambium is an example of
A. Lateral meristem
B. Intercalary meristem
c. Apical meristem
D. Primary meristem


Find the limits of \( \frac{e^{m x}-e^{m a}}{x-a}, \) when \( x= \)
\( a \)


A point mass \( M \) moving with a certain velocity collides with a stationary point mass \( \frac{M}{2} . \) The collision is elastic and
one dimension. Let the ratio of the final velocities of \( M \) and \( \frac{M}{2} \) be \( x \). The value of \( x \) is :
\( A \cdot 2 \)
B. 3
\( c \cdot \frac{1}{2} \)
D.


A battery of e.m.f. E and internal
resistance \( r \) is connected to an external
resistance \( R \) the condition for
maximum power transfer is
A. \$\$ldisplaystyler
в. \( r>R \)
c. \( r=1 / R \)
\( \mathbf{D} \cdot r=R \)


The radius of a thin wire is \( 0.16 \mathrm{mm} \). The
area of cross-section taking significant figure into consideration in square
millimeters is?
A . 0.0804
B. 0.080
\( c \cdot 0.08 \)
D. 0.080384


A galvanometer of 50 gives full scale
deflection with 2 mA current as to
convert it into ammeter range of 10 A is connected with it then shunt resistance
will be
A . \( 0.1 \Omega \)
B. \( 0.2 \Omega \)
c. \( 0.01 \Omega \)
D. \( 0.001 \Omega \)


Choose the correct answer from the
alternatives given. Which of these is mismatched?
A. Post transcriptional control-nucleus
B. Translational control - cytoplasm
c. Transcriptional control - -nucleus
D. Postranslational control - nucleus


Derive an expression for the energy seated in a capacitor. In what form is
the energy stored in a charged capacitor?


Which of the following relations is
correct?
A \( \cdot v=w^{2} r \)
B . \( v=w r^{2} \)
c. \( v=w r \)
\( \mathbf{D} \cdot v=w^{2} r^{2} \)


What is meant by term bond order?
Write bond orders for \( N_{2}, O_{2} \)


When treated with conc.\( H C l, M n O_{2} \)
yields a gas \( (X) \) which further reacts
with \( C a(O H)_{2} \) to generate a white
solid \( (Y) . \) The solid \( Y \) reacts with
dil.HCl to produce the same gas \( X \) The solid \( Y \) is :
A. \( C a O \)
в. \( C a C l_{2} \)
c. \( C a(O C l) C l \)
\( \mathrm{D} \cdot \mathrm{CaCO}_{3} \)


Consider the following experiment and answer the question:
(A) When \( F e(C N)_{2} \) solution is treated with KCN solution, species formed does
not give tests of \( F e^{2+} \) and \( C N^{-} \)
(B) When \( K_{2} S O_{4} \) solution is treated
with \( A l_{2}\left(S O_{4}\right)_{3} \) solution, species formed gives tests of \( \boldsymbol{K}^{+}, \boldsymbol{A l}^{3+} \) and \( \boldsymbol{S} \boldsymbol{O}_{4}^{2-} \)
Species formed in experiment (B) is
A. complex
B. Double salt
c. Liquid crystal
D. None of these


Differentiate \( \frac{x^{2}+1}{x} \) w.r.t \( x \)


Brown, Red and Orange coloured bands
on a Carbon resistor are followed by silver band. The value of resistor is
\( \mathbf{A} \cdot 320 \Omega \pm 5 \% \)
B . \( 12 k \Omega \pm 5 \% \)
c. \( 320 \Omega \pm 10 \% \)
D. \( 12 k \Omega \pm 10 \% \)


The equation, \( \left[\begin{array}{ccc}\mathbf{1} & \boldsymbol{x} & \boldsymbol{y}\end{array}\right]\left[\begin{array}{ccc}\mathbf{1} & \boldsymbol{3} & \mathbf{1} \\ \mathbf{0} & \boldsymbol{2} & -\mathbf{1} \\ \mathbf{0} & \mathbf{0} & \mathbf{1}\end{array}\right]\left[\begin{array}{l}\mathbf{1} \\ \boldsymbol{x} \\ \boldsymbol{y}\end{array}\right]=[\mathbf{0}] \) has
for
(i) \( y=0 \)
(p) rational
roots
(ii) \( y=-1 \)
(q) irrational
roots
(r) integral roots
A \( . \) (i) \( (p) \) (ii) \( (r) \)
B. (i) (q) (ii) (p)
\( c \cdot(i)(p)(\text { ii) }(q) \)
D. (i) (r) (ii) (p)


Describe the mechanism of occurrence
of an earthquake with the help pf pictorial representation.


Let the starred carbon in the given amine has "R" configuration. What is the isomeric relationship between the
two form of this compound that are inter converted by amine inversion. Give your answer in integer form [Give : 1 for identical, 2 for enantiomer, 3 for diastereomer, 4 for functional isomer.


Find whether \( \alpha- \) decay or any of the
\( \beta- \) decay are allowed for \( _{89}^{226} A c \)


A mass of \( \mathrm{M} \) kg is suspended by a weightless string. The horizontal force required to displace it until the string
makes an angle of \( 45^{\circ} \) with the initial vertical is :
A. \( \mathrm{Mg}(\sqrt{2}-1) \)
B. \( \mathrm{Mg}(\sqrt{2}+1) \)
c. \( \mathrm{Mg} \sqrt{2} \)
D. \( \frac{\mathrm{Mg}}{\sqrt{2}} \)


The is the smallest unit of matter.
A. Element
B. Atom
c. Molecule
D. Electron


If \( a^{2} \sec ^{2} \theta-b^{2} \tan ^{2} \theta=c^{2} \) then prove
\( \operatorname{that} \sin ^{2} \theta=\frac{c^{2}-a^{2}}{c^{2}-b^{2}} \)


The area of cross-sections of three
metals roads of equal length and made
of same materials are \( A_{1}, A_{2} \) and \( A_{3} \)
respectively. when heated through the same change in temperature their
linear expansions are found to be \( \boldsymbol{I}_{1}, \boldsymbol{I}_{2} \)
and \( I_{3} \) respectively which among the following is the correct relation between
\( \boldsymbol{I}_{1}, \boldsymbol{I}_{2} \) and \( \boldsymbol{I}_{3} ? \)
\( \mathbf{A} \cdot I_{1}=I_{2}=I_{3} \)
\( \mathbf{B} \cdot I_{1}>I_{2}>I_{3} \)
\( \mathbf{c} \cdot I_{1}<I_{2}<I_{3} \)
\( \mathbf{D} \cdot I_{1}=I_{2}<I_{3} \)


A solution of glucose \( \left(C_{8} H_{12} O_{6}\right) \) is
isotonic with \( 5 g \) of urea
\( \left(N H_{2} C O N H_{2}\right) \) per litre of solution
The concentration of glucose is:
A. \( 48 / L \)
B. 8 g/L
c. 12 g/L
D. \( 15 \mathrm{g} / \mathrm{L} \)


Assertion
Cathode rays get deflected towards the positive plate of electric field.
Reason
Cathode rays consist of negatively charged particles known as electrons.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion,
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct.


The space above the mercury column in a barometer contains_ - \( -- \) (mercury,
water) vapour.


Match the following.
List

List I
1. Heavy water
A) Bicarbonates of \( M g \)
2. Temporary
B) No foreign ions in water hard water
3. Soft water
C) \( D_{2} O \)
4
Permanent
D) Sulphates and Chlorides of hard water \( M g \& C a \) in water
\( \mathbf{A} \cdot 1-C, 2-D, 3-B, 4-A \)
B . \( 1-B, 2-A, 3-C, 4-D \)
C \( .1-B, 2-D, 3-C, 4-A \)
D . \( 1-C, 2-A, 3-B, 4-D \)


A voltmeter and an ammeter are joined
in series to an ideal cell, giving readings \( \mathrm{V} \) and \( \mathrm{A} \) respectively. If \( \mathrm{a} \)
resistance equal to the resistance of the ammeter if now joined in parallel to
the ammeter
This question has multiple correct options
A. V will no change
B. V will increase slightly
c. A will become exactly half of its initial vale
D. A will become slightly more than half of its initial value


\( f_{a, b, c, d} \) are positive real numbers, then show that \( (a+b+c+ \)
\( d)\left(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}+\frac{1}{d}\right) \geq 16 . \) What happens
when the numbers are all equal?


Four resistors, \( 100 \Omega, 200 \Omega, 300 \Omega, \) and
\( 400 \Omega \) are connected to form four sides
of a square. The resistors can be connected in any order. What is the maximum possible equivalent resistance across the diagonal of the square?
A \( .210 \Omega \)
в. 240\Omega
\( \mathbf{c} .300 \Omega \)
D. 250\Omega


\( \cot ^{-1}(\sqrt{\cos \alpha})-\tan ^{-1}(\sqrt{\cos \alpha})=x \)
then \( \sin x \) is equal to
\( A \cdot \tan ^{2} \frac{\alpha}{2} \)
B \( \cdot \cot ^{2} \frac{\alpha}{2} \)
c. \( \tan \alpha \)
D. \( \cot \frac{\alpha}{2} \)


The moon is observed from two
diametrically opposite points on earth. The angle subtended at the moon by the
two directions of observations is \( 1^{\circ} 54^{\prime} \)
Given the diameter of the earth to be
about \( 2.276 \times 10^{7} m, \) compute the
distance of moon from the earth.
A \( \cdot 1 \times 10^{8} m \)
В. \( 6.84 \times 10^{8} \mathrm{m} \)
c. \( 6.84 \times 10^{10} m \)
D. \( 38.4 \times 10^{8} \mathrm{m} \)


is defined as the number of protons present in the nucleus of an atom.
A. Atomic number
B. Mass number
c. Both a and
D. None of these


The catalyst used in the Deacon's process for the manufacture of chlorine
is:
A \( . P t \)
в. \( C u C l_{2} \)
\( c \cdot V_{2} O_{5} \)
D. Fe


Solve each of the following pairs of equations by the elimination method. \( 2 x+3 y=8 \)
\( 4 x+6 y=7 \)


n Fig., if \( \boldsymbol{A B} \| \boldsymbol{C D} \) and \( \boldsymbol{C D} \| \boldsymbol{E} \boldsymbol{F} \), find
\( \angle A C E \)


Each pectoral girdle is made of
A. Two innominates
B. Two clavicles and two scapula
C. One clavicle and one scapula
D. Two clavicles and one scapula


If the median of the data
\( \boldsymbol{x}_{1}, \boldsymbol{x}_{2}, \boldsymbol{x}_{3}, \boldsymbol{x}_{4}, \boldsymbol{x}_{5}, \boldsymbol{x}_{6}, \boldsymbol{x}_{7}, \boldsymbol{x}_{8} \) is \( \boldsymbol{\alpha} \) and
\( \boldsymbol{x}_{1}<\boldsymbol{x}_{2}<\boldsymbol{x}_{3}<\boldsymbol{x}_{4}<\boldsymbol{x}_{5}<\boldsymbol{x}_{6}<\boldsymbol{x}_{7}< \)
\( x_{8}, \) then the median of \( x_{3}, x_{4}, x_{5}, x_{6} \) is
\( A \cdot \alpha \)
в. \( \frac{\alpha}{2} \)
c. \( \frac{\alpha}{3} \)
D. \( \frac{\alpha}{4} \)


. Ill.


Organisms which breakdown dead or waste matter in to simpler substances
is termed as
A. Producers
B. Consumers
c. Decomposers
D. Scavengers


Peat is formed form
A. Funaria
B. Sphagnum
c. Mosses
D. Liverworts


Given \( \boldsymbol{A}(\mathbf{0}, \mathbf{0}) \) and \( \boldsymbol{B}(\boldsymbol{x}, \boldsymbol{y}) \) with \( \boldsymbol{x} \in \)
(0,1) and \( y>0 . \) Let the slope of the line
\( A B \) equal to \( m_{1} . \) Point \( C \) lies on the line
\( x=1 \) such that the slope of \( B C \) equal
to \( m_{2} \) where \( 0<m_{2}<m_{1} . \) If the area of
the \( \triangle A B C \) can be expressed as \( \left(m_{1}-\right. \)
\( \left.m_{2}\right) f(x), \) then the largest possible
value of \( \boldsymbol{f}(\boldsymbol{x}) \) is
A.
в. \( \frac{1}{2} \)
c. \( \frac{1}{4} \)
D. \( \frac{1}{8} \)


Fill in the blank
A cylindrical resonance tube open at both ends fundamental frequency \( \boldsymbol{F} \) in
the air. Half-length of the tube is dipped vertically in the water. The fundamental frequency to the air column now is


Which of the following compound contain single covalent bond?
A. Oxygen
B. Nitrogen
c. Methane
D. carbon dioxide


Which one of the following is chloropicrin?
\( \mathbf{A} \cdot C C l_{3}-C\left(C H_{3}\right)_{2} \)
\( _{O H} \)
в. \( C C l_{3}-N O_{2} \)
c. \( C H C l_{2}-C H C l_{2} \)
D. \( C C l_{3} \) СНО


A free charged particle moves through a magnetic field. The particle may undergo a change in
A. Speed
B. Energy
c. Direction of motion
D. None of these


What is an electromagnet? How is it different from a permanent magnet? Describe one application of an electromagnet.


Distinguish between Asexual reproduction and Sexual reproduction.


The incorrect order of bond angles in the
above molecule is/are:
This question has multiple correct options
\( \mathbf{A} \cdot y=z>x \)
В \( . z>y>x \)
c. \( y>x>z \)
D. \( x>y>z \)


Whipped cream is an example of which of these?
[Note : Dispersed phase - dispersion medium phase].
A. Liquid - gas
B. Gas -liquid
c. Liquid-liquid
D. solid - liquid


Divide \( 4\left(2 x^{2}+5 x+3\right) \) by \( 2(2 x+3) \)


Proton, denteron and alpha particles of the same kinetic energy and moving in circular trajectories in a constant magnetic field. The radii of proton, denteron and alpha particles are
respectively \( r_{p}, r_{d} \) and \( r_{\alpha} . \) Which one of the following relations is correct?
A \( \cdot r_{\alpha}=r_{p}=r_{d} \)
B . \( r_{\alpha}=r_{p}<r_{d} \)
c. \( r_{\alpha}>r_{d}>r_{p} \)
D \( \cdot r_{\alpha}=r_{d}>r_{p} \)


Isopentane on monochlorination gives isomers and out of them
are optically active :
A . 3,1
B. 4,2
\( c .3,2 \)
D. 4,1


Rehman is making a wheel using spokes. He wants to fix equal spokes in such a way that the angles between any pair of consecutive spokes are equal. Help him by completing the following
table

Calculate the angle between a pair of consecutive spokes on a wheel with 15 spokes.


When ethyl alcohol is heated with a
paste of bleaching powder, we get an intermediate compound. The formula of
that compound is:
\( \mathbf{A} \cdot C_{2} H_{5} C l \)
в. \( C C l_{3} C H O \)
\( \mathbf{c} \cdot C H_{3} I \)
D. \( C C l_{3} \) СОСН \( _{3} \)


In each of the following figure \( A B \| C D \)
Find the value of \( x \) in each case.


If \( A \) and \( B \) are square matrices of same order and \( \mathrm{B} \) is a skew-symmetric
matrix, show that \( A^{\prime} B A \) is a skew
symmetric matrix.


A body of mass \( 10 k g \) is moving with a
velocity \( 20 m s^{-1} . \) If the mass of the body is doubled and its velocity is halved, find the ratio of the initia
kinetic energy to the final kinetic
energy.


A ladder of mass \( M \) and length \( L \) is
supported in equilibrium against a smooth vertical wall and a rough horizontal surface, as shown in figure. If \( \theta \) be the angle of inclination of the rod
with the horizontal, then calculate
(a) normal reaction of the wall on the
ladder
(b) normal reaction of the ground on the
ladder
(c) net force applied by the ground on
the ladder


The half-life of radio isotope is 4 hr. If initial mass of the isotope was 200 g, then mass remaining after 24 hr will be
A \( .1 .042 \mathrm{g} \)
B. 2.084 g
c. 3.125 g
D. 4.167 g


Find the following product.
\( \operatorname{str} \times 7 r^{2} s^{2} \)


One of the following is wrong about
male reproductive organs of earthworm
A. Two fluid-filled testis sacs with pair of spermiducal funnel attached to vasa differentia
B. Two pairs of seminal vesicles
C. Four pairs of spermathecae
D. One pair of prostate gland
E. All of the above


Two spheres of the same material, but of radii \( R \) and \( 3 R \) are allowed to fall
vertically downwards through a liquid of
density \( \rho . \) The ratio of their terminal velocities is:
A .1: 3
B. 1: 6
c. 1: 9
D. 1: 1


Assertion
A Diamond sparkles more than a glass imitation cut to the same shape.
Reason
The refractive index of diamond is less
than that of glass.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


What is meant by the term inertia?
A. There is natural tendency for objects to resist changes in their state of motion.
B. A measure of an object's resistance to changes in a rotation direction.
C. A force is a push or a pull that acts upon an object as a results of its interaction with another object.
D. A measurement of the amount of matter something contains.


Considering the formation, breaking and strength of hydrogen bond, predict which of the following mixtures will show a positive deviation from
Raout's law?
A. Methanol and acetone
B. Chloroform and acetone
c. Nitric acid and water
D. Phenol and aniline


The fusion of an organic compound with solid sodium hydroxide is undertaken for testing nitrogen,sulphur and halogens. This test is called:
A. Dumas method
B. Carius method
c. Kjeldahl's method
D. Lassaigne's test


A solution of copper oxide was prepared by heating, igniting and precipitation. Which of the following method will give higher ratio of copper oxide?
A. Heating
B. Precipitation
c. Ignition
D. All of the above will give the same ratio


Find the sum of first 25 terms of an AP
whose nth term is \( 1-4 n \)


Draw a neat labelled diagram of human heart showing external features.


Solve \( \tan x<2 \)


The length of common chords of circles \( x^{2}+y^{2}+p x=0 \) and \( x^{2}+y^{2}+g y=0 \) is
\( A \cdot \frac{2 p q}{\sqrt{p^{2}+q^{2}}} \)
c. \( \frac{p q}{\sqrt{p^{2}+q^{2}}} \)
D. \( \frac{2 p q}{p^{2}+q^{2}} \)


The quantity of water that should be added to reduce \( 9 \mathrm{ml} \) lotion containing \( 50 \% \) alcohol to a lotion containing \( 30 \% \)
alcohol is :
A. \( 3 \mathrm{m} \)
B. \( 4 \mathrm{m} \)
\( c \cdot 5 m \)
D. \( 6 \mathrm{m} \)


A bi-convex lens is formed with two
plano-convex lenses as shown in the figure. Refractive index n of the first
lens is 1.5 and that of the second lens is
1.2. Both curved surfaces are of the
same radius of curvature \( \mathrm{R}=14 \mathrm{cm} . \) For
this bi-convex lens, for an object
distance of \( 40 \mathrm{cm}, \) the image distance will be
A. \( -280.0 \mathrm{cm} \)
B. \( 440.0 \mathrm{cm} \)
\( c .21 .5 \mathrm{cm} \)
D. \( 13.3 \mathrm{cm} \)


A car is being driven at a constant speed of \( 5 m / s \) by a force of \( 3 \times 10^{8} N \)
It takes 2 minutes to reach its
destination. What is the work done?
A \( .15 \times 10^{8} J \)
B . \( 18 \times 10^{10} J \)
c. \( 6 \times 10^{10} J \)
D . \( 10 \times 10^{8} J \)


Find the eccentricity and length of latus rectum of hyperbola \( \frac{x^{2}}{25}-\frac{y^{2}}{9}=1 \)


In EMP pathway,ATP is directly formed in the conversion of
I)Fructose 1,6 -bisphosphate to glyceraldehyde -3-phosphate II)Phosphoenolpyruvate to pyruvate acid
III)1 \( , 3 \) -bisphosphoglyceric acid to 3 phosphoglyceric acid IV)3-phosphoglyceric acid to 2phosphoglyceric acid The correct combination is
A . IV,
B. ॥ , Iv
c. ॥ा,॥
D. ।."|


True or False.
Aeroplanes are made from alloys of Iron.


Action of alcoholic \( A g N O_{3} \) on
chlorobenzene is similar to the action
on:
A. allyl chloride
B. vinyl chloride
c. isopropyl chloride
D. benzyl chloride


Thickening of trunk in woody plants is
due to
A. Cambium
B. Apical meristem
c. intercalary meristem
D. epidermis


The amount of work has to be done in
assembling three charged particles at
the vertices of an equilateral triangle
A .434
в. 334
c. 234 」
D. 134 J


Which one of the following electronic configuration corresponds to the element with maximum electopositive
character?
A \( \cdot[K r] 5 s^{1} \)
в. \( [N e] 3 s^{1} \)
c. \( [A r] 4 s^{1} \)
D. \( [X e] 6 s^{1} \)


kilometer is decimeter.
A \( \cdot 10^{4} \)
B . \( 10^{5} \)
\( c \cdot 10^{3} \)
D. \( 10^{6} \)


Find the missing frequencies if the
mean of the given data is 53
\( \begin{array}{lllll}\text { Age in } & 0- & 20- & 40- & 60- \\ \text { years } & 20 & 40 & 60 & 80\end{array} \)
Number of
15
\( F_{1} \)
People


If \( \cos x+\cos ^{2} x=1, \) prove that \( \sin ^{2} x+ \)
\( \sin ^{4} x=1 \)


The length of the day from today when the sun is directly overhead till tomorrow again when the sun is directly overhead can be determined by the
A. rotation of earth about its own axis
B. revolution of earth around sun
c. inclination of axis of rotation of earth from the plane of revolution.
D. rotation of earth about its own axis as well as its revolution around sun


Find the amount obtained by investing \( , 20,000 \) at \( 10 \% \) p.a.compound interest for two years, compounded annually.
A . 22000
B. 24000
c. 26000
D. 24200


Let \( x_{1}, x_{2}, \dots . . x_{n} \) be values taken by a
variable \( \boldsymbol{X} \) and \( \boldsymbol{y}_{1}, \boldsymbol{y}_{2}, \dots \dots \boldsymbol{y}_{n} \) be the
values taken by variable \( Y \) such that
\( \boldsymbol{y}_{i}=\boldsymbol{a} \boldsymbol{x}_{i}+\boldsymbol{b} ; \quad \boldsymbol{i}=\mathbf{1}, \boldsymbol{2}, \ldots \boldsymbol{n} . \) Then
A \( . \operatorname{Var}(Y)=a^{2} \operatorname{Var}(X) \)
B. \( \operatorname{Var}(X)=a^{2} \operatorname{Var}(Y) \)
c. \( \operatorname{Var}(X)=\operatorname{Var}(X)+b \)
D. none of these


Lateral line system occurs in
A. Star fish
B. Jelly fish
c. Dog fish
D. All of the above


Find the additive inverse of: \( \sqrt{5} \)


State whether the given statement is
true or false:
Neutralisation is a double
displacement reaction
A. True
B. False


Which one of the following species loses one or more electrons in the chemical
reaction shown?
\( M g+C u^{2+} \rightarrow M g^{2+}+C u \)
A. \( M g^{2+} \)
в. \( C u \)
c. \( C u^{2+} \)
D. \( M g \)


Name the logic gate which generates
high output when at least one input is
high.


How is the distance related with time
for the motion under uniform
acceleration such as the motion of a
freely falling body starting from rest?
\( \mathbf{A} \cdot S \propto t^{2} \)
в. \( S \propto t \)
c. \( s \propto \frac{1}{t^{2}} \)
D. \( s \propto \frac{1}{t} \)


Which will have highest refractive
index?
A. Bucket having full of water
B. Bucket having half filled water
c. Both A and B will have equal Refractive index
D. None


Give preparation of Calcium oxide.


A coin is tossed 40 times and it showed
tail 24 times.The probability of getting a head was:
A \( \cdot \frac{2}{5} \)
B. \( \frac{3}{5} \)
\( c \cdot \frac{1}{2} \)
D. \( \frac{17}{40} \)


\( L_{1} \) and \( L_{2} \) are 2 tangent \( y^{2}=16 x \) which
markes angle \( \tan ^{-1} \frac{1}{3} \) with the tangent
\( T^{\prime} \) to the same parabola at the end point of latus rectum which the ordinate then find the area of \( \triangle \) formed
\( \boldsymbol{L}_{1}, \boldsymbol{L}_{2} ? \)


Find the mean deviation about the
mean of the following data:
\( \mathbf{1 5}, \mathbf{1 7}, \mathbf{1 0}, \mathbf{1 3}, \mathbf{7}, \mathbf{1 8}, \mathbf{9}, \mathbf{6}, \mathbf{1 4}, \mathbf{1 1} \)
A . \( 3 . \)
B. 3.
\( c .3 .3 \)
D. 3.


In which of the following reactions, the equilibrium remains unaffected on addition of small amount of argon at
constant volume?
\( \mathbf{A} \cdot H_{2(g)}+I_{2(g)} \rightleftharpoons 2 H I_{(g)} \)
B. \( P C l_{5(g)} \rightleftharpoons P C l_{3(g)}+C l_{2(g)} \)
C. \( N_{2(g)}+3 H_{2(g)} \rightleftharpoons 2 N H_{3(g)} \)
D. The equilibrium will remain unaffected in all the three cases


\( \ln a R, L, C \) circuit, three elements is
connected in series by an a.c. source. If frequency is less than resonating frequency then net impedance of the circuit will be
A. capacitive
B. inductive
c. capacitive or inductive
D. pure resistive


In the above network, current flows from
\( T \) to \( M, \) when
A. p closed, q closed and ropened
B. p closed, q opened and r closed
c. p opened; q closed and r closed
D. All the above


\( i= \)
\( k \)
\( L \)


The animals which are adapted to the
cold have
A. Heavy fur on their skin
B. Small body size
c. No layer of fat under the skin
D. Both A and B


A cooperative society of farmers has 50 hectares of land to grow two crops \( A \) and
B. The profits from crops A and B per hectare are estimated as Rs 10,500 and Rs 9,000 respectively. To control weeds, a liquid herbicide has to be used
for crops \( A \) and \( B \) at the rate of 20 litres
and 10 litres per hectare, respectively.
Further not more than 800 litres of
herbicide should be used in order to
protect fish and wildlife using a pond which collects drainage from this
land. Keeping in mind that the
protection of fish and other wildlife is more important than earning profit, how much land should be allocated to each
crop so as to maximize the total profit? Form an LPP from the above and solve it graphically. Do you agree with the message that the protection of wildlife is utmost necessary to preserve the balance in environment?


A free nucleus of mass 24 amu, intially at rest emits a gamma photon. The
energy of the photon is \( 7 M e V \). The
kinetic energy of recoiling nucleus is
approximately equal to [Take; 1 am \( u= \) \( \mathbf{9 . 3 1} \boldsymbol{M e V} \)
A . \( 3.3 k e V \)
B. 4.4keV
c. \( 1.1 k e V \)
D. 2.5keV


Sodium hydroxide is found in:
A . lime water
B. milk of magnesia
C. window cleaner
D. soap


toppr
Q Type your question
acids pictured, which of the following
would be the LEAST soluble in water?
A. Histidine
B. Lysine
C. Alanine
D. Cysteine


Find the value of \( p \) such that quadratic
equation \( (\boldsymbol{p}-\mathbf{1 2}) \boldsymbol{x}^{2}-\boldsymbol{2}(\boldsymbol{p}-\mathbf{1 2}) \boldsymbol{x}+ \)
\( 2=0 \) has equal


State whether the given statement is true or false:
Highest fluorides of oxygen is \( \boldsymbol{O} \boldsymbol{F}_{2} \)
whereas sulphur forms \( S F_{6} \)
A. True
B. False


Find the \( X \) product:
\( \mathbf{A} . \) НСООН
B.
\( c \)
D.


STATEMENT-1: If \( a b^{2} c^{3}, a^{2} b^{3} c^{4}, a^{3} b^{4} c^{5} \)
are in A.P.
\( (a, b, c>0), \) then the minimum value of
\( a+b+c \) is 3
STATEMENT-2: Arithmetic mean of any
two numbers is greater than geometric
mean of the numbers.
A. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is the correct explanation for STATEMENT-1
B. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1
C . STATEMENT-1 is True, STATEMENT-2 is False
D. STATEMENT-1 is False, STATEMENT-2 is True


The shape of the interference fringes, on
the screen is
A . circle
B. ellipse
c. parabola
D. straight line


A charged cloud system produces an
electric field in the air near the earths
surface.A particle of charge \( -2 \times 10^{-9} \mathrm{C} \) is
acted on by a downward electrostatic
force \( 3 \times 10^{-6} N \) of when placed in the
field,The gravitational and electrostatic
force,Respectively,exerted on a proton
placed in this field are
A \( .1 .64 \times 10^{-26} \mathrm{N}, 2.4 \times 10^{-16} \mathrm{N} \)
B . \( 1.64 \times 10^{-26} \mathrm{N}, 1.5 \times 10^{3} \mathrm{N} \)
C \( .1 .56 \times 10^{-18} \mathrm{N}, 2.4 \times 10^{-16} \mathrm{N} \)
D. \( 1.5 \times 10^{3} \mathrm{N}, 2.5 \times 10^{-16} \mathrm{N} \)


"Chlorine type" laundry bleaches are in reality aqueous solution of :
A . НОС l
в. \( H C l O_{3} \)
c. \( N a C l O_{3} \)
D. \( N a O C l \)


toppr
Q Type your que
Autotrophic Yes
res
Presence o vascu ss
Flow
roduce
Shirin had been on a holiday to Ooty. In
her school, she has studied about the
interesting world of plants. On the day of her return she collected four groups of
plants I, II, III and IV. She carefully noted some of their details and arranged the information in the form of a table as
given below. Her teacher agreed to tell her descriptions about all plants if she could by looking at the information in the table say which of the groups of plants she collected represented pteridophytes. Take a look at the data and suggest which of the groups could be of pteridophytes.
A. Plantgroup!
B. Plant group I I
c. Plantgroup III
D. Plant group IV


The resistance of wire is 20 ohm. The
wire is stretched to three times of its length. Then the resistance will be :-
\( \mathbf{A} \cdot 6.67 \Omega \)
B. \( 60 \Omega \)
c. \( 120 \Omega \)
D. \( 180 \Omega \)


The mean of \( x_{1} \) and \( x_{2} \) is \( M_{1} \) and that of
\( \boldsymbol{x}_{1}, \boldsymbol{x}_{2}, \boldsymbol{x}_{3} \ldots . . \boldsymbol{x}_{4} \) is \( \boldsymbol{M}_{2} \)
then the mean of \( a x_{1}, a x_{2}, \frac{x_{3}}{a}, \frac{x_{4}}{a} \) is?
A. \( \frac{a M_{1}+M_{2}}{2} \)
\( ^{\mathbf{B} \cdot} \frac{a M_{1}+\left(\frac{M_{2}}{a}\right)}{2} \)
c. \( \frac{1}{2 a}\left[\left(a^{2}-1\right) M_{1}+M_{2}\right] \)
D \( \cdot \frac{1}{2 a}\left[\left(a^{2}-1\right) M_{1}+2 M_{2}\right] \)


If \( f(x) \) and \( g(x) \) are functions such that \( \boldsymbol{f}(\boldsymbol{x}+)=\boldsymbol{f}(\boldsymbol{x}) \boldsymbol{g}(\boldsymbol{y})+\boldsymbol{g}(\boldsymbol{x}) \boldsymbol{f}(\boldsymbol{y}), \) then the
value of \( \left|\begin{array}{lll}\boldsymbol{f}(\boldsymbol{\alpha}) & \boldsymbol{g}(\boldsymbol{\alpha}) & \boldsymbol{f}(\boldsymbol{\alpha}+\boldsymbol{\theta}) \\ \boldsymbol{f}(\boldsymbol{\beta}) & \boldsymbol{g}(\boldsymbol{\beta}) & \boldsymbol{f}(\boldsymbol{\beta}+\boldsymbol{\theta}) \\ \boldsymbol{f}(\boldsymbol{\gamma}) & \boldsymbol{g}(\boldsymbol{\gamma}) & \boldsymbol{f}(\boldsymbol{\gamma}+\boldsymbol{\theta})\end{array}\right| \)
A \( \cdot f(\alpha) \cdot f(\beta) \cdot f(\gamma) \)
B.
\( \mathbf{c} \cdot g(\alpha) \cdot g(\beta) \cdot g(\gamma) \)
D. None of these


Quicklime is made by heating
limestone. Which equation represents this reaction?
A \( \cdot C a C O_{3} \rightarrow C a+O_{2}+C O \)
в. \( C a C O_{3} \rightarrow C a O+C O_{2} \)
\( \mathrm{c} \cdot \mathrm{CaCO}_{3}+\mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{CaO}+\mathrm{H}_{2} \mathrm{CO}_{3} \)
D. \( C a C O_{3}+H_{2} O \rightarrow C a(O H)_{2}+C O_{2} \)


The image of the origin in the line joining the points (-9,4,5) and (11,0,-1) is
A. (2,4,4)
в. (1,2,2)
c. (1,2,3)
D. (2,2,1)


In the electrolytic reduction of alumina, the electrolyte is covered with coke powder because, if :
A. prevents oxidation of aluminium formed
B. reacts with aluminium forming aluminium carbide
c. prevents heat loss from electrolyte
D. None of the above


A regular hexagon of maximum possible area is cut off from an equilateral triangle. The ratio of the area of the triangle to the area of hexagon will be-
A \( \cdot \sqrt{\frac{3}{2}} \)
B. \( \frac{\sqrt{6}}{2} \)
c. \( \frac{3}{\sqrt{2}} \)
D. \( \frac{3}{2} \)


If \( \cos ^{-1} x-\sin ^{-1} x=0, \) then \( x \) is
equal to
A \( \cdot \pm \frac{1}{\sqrt{2}} \)
B.
c. \( \sqrt{2} \)
D. \( \frac{1}{\sqrt{2}} \)


It is required to hold equal charges, \( \boldsymbol{q} \) in
equilibrium at the corners of a square. What charge when placed at the centre
of the square will do this?


Two sets of candidates are competing for the positions on the board of directors of a company. The probabilities that first and second sets will win are 0.6 and 0.4 respectively. If the first set wins the probability of introducing a new product is 0.8 and the corresonding probability if the second set wins is 0.3. The probability that the new product will be introduced
is \( 0.1 k . \) Find the value of \( k \)


n given figure, ABCD is a rectangle, having \( A B=20 \mathrm{cm} \) and \( B C=14 \mathrm{cm} \)
Two sectors of \( 180^{\circ} \) have been cut-off.
Calculate the area of the shaded region.


Lateral meristem is also called
A. Xylem
B. Phloem
c. vascular bundle
D. Cambium


SONAR emits which of the following
waves?
A. Radio waves
B. Micro waves
c. Ultrasonic waves
D. Gamma rays


What will be the wavelength of an
electron moving with \( \frac{1}{10} t h \) of velocity of light?
A \( \cdot 2.43 \times 10^{-11} \mathrm{m} \)
В . \( 243 \times 10^{-11} \) и
\( c .0 .243 m \)
D. 2.43 \( \times 10^{-4} \mathrm{m} \)


A heater of power \( \boldsymbol{P} \boldsymbol{W} \) raises the
temperature of \( m k g \) of a liquid by
\( \Delta T K \) in time \( t s . \) Express the specific heat capacity of liquid in terms of above
data
A \( \cdot \frac{P t}{\Delta T} \)
B. \( \frac{P t(\Delta T+273)}{m(\Delta T)^{2}} \)
c. \( \frac{P}{m \Delta T} \)
D. \( \frac{P t}{m \Delta T} \)


Let \( C \) and \( A \) be the circumference and
the area of a circle respectively. If \( x C \) is
the circumference of another circle
whose area is \( 2 A \), then \( x \) equals
\begin{tabular}{l}
A \( \cdot 2 \sqrt{2} \) \\
\hline
\end{tabular}
B. 2
\( c \cdot \sqrt{2} \)
D. \( \frac{1}{2} \)


The construction of \( \Delta P Q R \) given that
\( Q R=5.2 \mathrm{cm} \) angle \( Q=50 . \) Is it
possible when the difference of \( P Q \) and
PR is \( 3.5 \mathrm{cm} \) ? justify.


Two particles start simultaneously from the same point and move along two straight lines, one with uniform velocity
\( \boldsymbol{v} \) and other with a uniform acceleration
\( a . \) If \( \alpha \) is the angle between the lines of
motion of two particles then the least value of relative velocity will be at time
given by
B. \( (v / a) \cos \alpha \)
\( \mathbf{D} \cdot(v / a) \cot \alpha \)


Prove that \( \int_{0}^{\pi / 2} \ln (\sin x) d x= \)
\( \int_{0}^{\pi / 2} \ln (\cos x) d x= \)
\( \int_{0}^{\pi / 2} \ln (\sin 2 x) d x=-\frac{\pi}{2} . \ln 2 \)


In which of the following products are
obtained from fossil fuels?
This question has multiple correct options
A . coal
B. Coke
c. coal tar
D. coal gas


Blood circulation that starts as
capillaries and terminate as capillaries is called
A. Hepatic circulation
B. Portal circulation
c. Renal circulation
D. Lymphatic circulation


Discuss the consequences of
lanthanide contraction.


To \( 1.0 L \) solution containing 0.1 mol
each of \( N H_{3} \) and \( N H_{4} C l, 0.05 \) mol
NaOH is added. The change in pH will be \( \left(p K_{a} \text { for } C H_{3} C O O H=4.74\right) \)
A . 0.30
B . -0.30
c. 0.48
D . -0.48


The equation of the normal to the curve \( x=a \cos ^{3} \theta, y=a \sin ^{3} \theta \) at the point
\( \boldsymbol{\theta}=\frac{\boldsymbol{\pi}}{\boldsymbol{4}} \) is
\( \mathbf{A} \cdot x=0 \)
В. \( y=0 \)
c. \( x=y \)
D. \( x+y=a \)


The disease caused by asbestos is
A. Emphysema
B. Paralysis
c. Diarrhoea
D. Dysentery


How many moles of \( N H_{3} \) are there in
\( 250 \mathrm{cm}^{3} \) of a \( 30 \% \) solution, the specific
gravity of which is \( 0.90 ? \)
A . 3.97 moles
B. 6.37 moles
c. 3.70 moles
D. 3.50 moles


Solve the following differential equation \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\boldsymbol{x}-\mathbf{1} \)
A \( \cdot y=x^{2}+x \)
B . \( y=x^{2} \)
c. \( y=x^{2}-x \)
D. None of the above


Histogen found at the tip of root apical meristem is
A. Plerome
B. Periblem
c. Calyptrogen
D. Dermatogen


A charge is moving across a junction,
then.
A. Momentum will be conserved
B. Momentum will not be conserved
C. At some places momentum will be conserved and at some other places momentum will not be conserved
D. None of these


What are weak electrolytes?
A. Compounds which in fused or in the aqueous solution state are partially dissociated
B. Compounds which are poor conductors of electricity
C. Both A and B
D. None of the above


In a CE amplifier, the input ac signal to be amplified is applied across.
A. Forward biased emitter-base junction
B. Reverse biased collector-base junction
c. Reverse biased emitter-base junction
D. Forward biased collector-base junction


\( N_{2} O_{5} \) decomposes according to equation:
\[
\mathbf{2} N_{2} \boldsymbol{O}_{\mathbf{5}} \rightarrow \mathbf{4} \boldsymbol{N} \boldsymbol{O}_{\mathbf{2}}+\boldsymbol{O}_{\mathbf{2}}
\]
What does \( -\frac{\boldsymbol{d}\left[\boldsymbol{N}_{2} \boldsymbol{O}_{5}\right]}{\boldsymbol{d} t} \) denote?


Sterile part of Cycas microsporophyll is
A. Apophysis
B. Sporophore
C. Middle partt
D. Lower partt


In which type of aestivation the petal arrangement is 2 external, 2 internal
and 1 partly external and partly internal?
A. Twisted
B. Imbricate
c. Quincuncial
D. valvate


What should be the magnitude and
direction of electric field?
A \( \cdot 7 N c^{-1}, \) Vertically up \( \perp \) to velocity
B. \( 7 N c^{-1} \), horizontally and \( \perp \) to velocity
C . \( 14 N c^{-1} \), horizontally parallel to velocity
D. none of these


Nylon is an example of thermoplastic.
A. True
B. False


Time required for coffee to have \( 105^{\circ} \mathrm{F} \)
temperature is
\( A \cdot 6 \min \)
B. 6.43 min
c. \( 7.23 \min \)
D. 7.63 min


Solve :
\( \int \frac{\cos x-\sin x)}{(1+\sin 2 x)} d x \)


The chemical substances released by
activated spermatozoa, that acts on the ground substances of the follicle cells
is
A. Progesterone
B. Hyaluronidase
c. Relaxin
D. Gonadotropin
E. Teratogen


What will be the self inductane of a coil
of 100 turns if a current of \( 5 A \) produces
a magnetic flux \( 5 \times 10^{-5} \) Wb?
\( \mathbf{A} \cdot 1 m H \)
в. \( 10 \mathrm{mH} \)
\( c \cdot 1 \mu H \)
D. \( 10 \mu H \)


Two bodies of masses \( 0.1 k g \) and \( 0.4 k g \) move towards each other with velocities
\( 1 m / s \) and \( 0.1 m / s \) respectively. After
collision they stick together. In \( 10 s \) the combined mass travels a distance of :
A. zero
B. \( 12 m \)
c. \( 0.12 m \)
D. \( 1.2 m \)


toppr \( = \)
Q Type your question
\( A \)
\( B \)
\( c \)
\( D \)


A man swims across a river with speed
of \( 5 k m h^{-1} \) (in still water), while a boat
goes upstream with speed \( 12 k m h^{-1} \) (in still water). How fast and in which
direction does the man appear to go to
the boatman? Given that the speed of flowing water is \( 2 k m h^{-1} \)


How much amount of volume of air is in
lungs as FRC?
A. \( 1500 \mathrm{ml} \) to \( 1600 \mathrm{ml} \)
B. 2100 m| to 2500 m1
c. 2500 \( \mathrm{ml} \) । to \( 3000 \mathrm{ml} \)
D. 1600 \( \mathrm{ml} \) to \( 2100 \mathrm{ml} \)


A steel girder of length \( l \) rests freely on two supports (figure shown above). The moment of inertia of its cross-section is
equal to \( I . \) Neglecting the mass of the
girder and assuming the sagging to be slight, if the deflection \( \lambda \) due to the
force \( \boldsymbol{F} \) applied to the middle of the \( \operatorname{girderis} \lambda=\frac{1}{(40+x)} \frac{F l^{3}}{E I}, \) find the
value of \( \boldsymbol{x} \)


If \( 6.12 \% \) of \( \frac{7}{13} \) is 43 percent of \( x, \) what is
the value of \( x ? \)
A . .077
в. .77
\( c .7 .66 \)
D. 8.13
E. 11.49


Metallurgical process of zinc involves
roasting of zinc sulphide followed by reduction. Metallic zinc distills over as
it is volatile and impurities like \( \mathrm{Cu}, \mathrm{Pd} \) and Fe gets condensed. The crude metal obtained is called spelter, which may be purified by:
This question has multiple correct options
A . electrolysis process
B. fractional distillation
c. polling
D. heating with iodine


The function \( f(x)=x^{3}-7 x^{2}+25 x+ \)
8 has exactly roots.
\( A \cdot 2 \)
B.
\( c .3 \)
D.


Consider the function \( f(x)=0.75 x^{4}- \)
\( x^{3}-9 x^{2}+7 \)
Consider the following statements:
1. The function attains local minima at
\( x=-2 \) and \( x=3 \)
2. The function increases in the interval
(-2,0)
Which of the above statements is/are
correct?
A. 1 only
B. 2 only
c. Both 1 and 2
D. Neither 1 nor


the price, a customer will pay for the bicycle if the Sales Tax is increased
by \( 6 \% \)


If \( x=\sin ^{-1} t \) and \( y=\log \left(1-t^{2}\right), \) then
\( \frac{d^{2} y}{d x^{2}} \) at \( t=1 / 2 \) is
A \( \cdot \frac{-8}{3} \)
в. \( \frac{8}{3} \)
\( c \cdot \frac{3}{4} \)
D. \( \frac{-3}{4} \)


\( \int \tan ^{2} x d x \)
A \( \cdot \tan x-x+c \)
B. \( \tan x+c \)
c. \( \tan x-x \)
D. None of the above


At the height \( 80 m, \) an aeroplane is moving with \( 150 m / s . \) A bomb is dropped from it so as to hit a target. At what distance from the target should the bomb be dropped? \( (\text { Given } g= \)
\( \left.10 m / s^{2}\right) \)
A. \( 605.3 \mathrm{m} \)
B. \( 600 m \)
\( c .80 m \)
D. 230 \( m \)


The total number of lone pairs of
electrons in \( N_{2} O_{3} \)


In rabbit, oxygenated blood flows from
A. Left auricle to left ventricle during auricular systole
B. Right auricle to right ventricle during ventricular systole
C. Right ventricle to aorta during ventricular systole
D. Pulmonary vein to left auricle during auricular systole


Name the device that uses an
electromagnet
A. Electric bell
B. Barometer
c. Lactometer
D. All the above


Assertion
Following reaction is a
disproportionation reaction:
\( \boldsymbol{B} \boldsymbol{r}_{2}+\boldsymbol{2} \boldsymbol{O} \boldsymbol{H}^{-} \rightarrow \boldsymbol{B} \boldsymbol{r} \boldsymbol{O}^{-}+\boldsymbol{B} \boldsymbol{r}^{-}+ \)
\( 2 H_{2} O \)
Reason
\( B r_{2} \) is oxidized to \( B r O^{-} \) as well as
reduced to \( B r^{-} \)
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


In a process a neutron which is initially at rest, decays into a proton, an electron and an antineutrino. The ejected
electron has a momentum of \( \boldsymbol{p}_{1}= \)
\( 2.4 \times 10^{-26} k g m / s \) and the antineutrino
has \( p_{2}=7.0 \times 10^{-27} k g m / s . \) Find the
recoil speed of the proton if the electron and the antineutrino are ejected (a) along the same direction (b) in mutually perpendicular directions
(Mass of the proton \( \boldsymbol{m}_{\boldsymbol{p}}=\mathbf{1 . 6 7} \times \mathbf{1 0}^{-\mathbf{2 7}} \)


Circles are described on the major axis and the line joining the foci of the ellipse \( 3 x^{2}+2 y^{2}=6 \) as diameters.
Then the radii of the circles are in the
ratio:
A \( \cdot \sqrt{2}: 1 \)
B. \( \sqrt{3}: 1 \)
\( c .3: 2 \)
D. 5: 4


Correct choice for bryophytes covering
is
A. Capsule
B. Pellicle
c. calcareous shell
D. Suberin cell wall


Charges of \( \frac{10}{3} m C \) are placed at the four vertices of a square of side \( 8 \mathrm{cm} \). The
electric potential at the centre is :
в. \( 900 \sqrt{2} M V \)
c. \( 1500 \sqrt{2} M V \)
D. \( 9000 \sqrt{2} M V \)


n a circuit given below calculate the
potential difference between points \( B \)
and \( D \). Also find the potential
difference across the terminals of \( G \)
and \( \boldsymbol{H} \)


n the fig, if the lines \( P Q \) and \( R S \)
intersect at point \( T \) such that \( \angle P R T= \)
\( 40^{\circ}, \angle R P T=92^{\circ} \) and \( \angle T S Q=70^{\circ} \)
find \( \angle S Q T \) (in degrees)


Assertion : The heavier p-block
elements do not form strong \( \pi \) bonds.
Reason: The heavier elements of \( \mathrm{p} \)
block form \( d \pi-d \pi \) bonds.
A. Both A and R are true and R is the correct explanation of \( A \)
B. Both A and R are true but R is not the correct explanation of A
c. A is true but R is false.
D. A is false but R is true.


Use of thermometer is based on which
law of thermodynamics?
A. zeroth
B. First
c. second
D. Third


If \( \left|z_{1}\right|=\left|z_{2}\right|=\left|z_{3}\right|=\left|z_{4}\right|=1 \) and \( z_{1}+ \)
\( z_{2}+z_{3}+z_{4}=0, \) then least value of the
expression
\[
\begin{array}{c}
\boldsymbol{E}=\left|\boldsymbol{z}_{1}-\boldsymbol{z}_{2}\right|^{2}+\left|\boldsymbol{z}_{2}-\boldsymbol{z}_{3}\right|^{2}+\mid \boldsymbol{z}_{3}- \\
\left.\boldsymbol{z}_{4}\right|^{2}+\left|\boldsymbol{z}_{4}-\boldsymbol{z}_{1}\right|^{2} \text { is }
\end{array}
\]
\( A \cdot 6 \)
B. 8
c. 10
D. 12


The number of hydrogen bonds present in the sequence of a stretch of a double helical DNA \( 5^{1} \) ATGCCTAA \( 3^{1}, \) is:
A . 16
B. 19
\( c \cdot 24 \)
D. 20


Which of the following is a fossil pteridophyte?
A. Lycopodium
B. Lygodium
c. Psilotum
D. Rhynia


The wavelength of a spectral line
coming from a star is changed by the motion of the star from 6000 A to 6001
A. What is the velocity of the star with respect to earth? (The velocity of light is \( 3 \times 10^{8} \mathrm{m} / \mathrm{sec} \)
A \( \cdot 5 \times 10^{4} \mathrm{m} / \mathrm{sec} \) receding
B. \( 5 \times 10^{4} \mathrm{m} / \mathrm{sec} \) approaching
c. \( 3 \times 10^{4} \mathrm{m} / \) sec receding
D. 3 \( \times 10^{4} \mathrm{m} / \) sec approaching


An oxy acid contains three hydrogen
atoms, one phosphorus atom and four oxygen atoms. Write the formula of the
compound formed by the negative radical of the given acid with ammonium ion
\( \mathbf{A} \cdot\left(N H_{4}\right)_{2} P O_{4} \)
В. \( N H_{4} P O_{3} \)
c. \( M H_{4} P O_{3} \)
D. \( \left(N H_{4}\right)_{3} P O_{4} \)


\( \operatorname{Given} \boldsymbol{E}_{\boldsymbol{C r}^{3+} / \boldsymbol{C r}}^{\circ}=-\mathbf{0 . 7 2}, \boldsymbol{E}_{\boldsymbol{F e}^{2+} / \boldsymbol{F} e}^{\circ}= \)
\( -\mathbf{0 . 4 2} \boldsymbol{V} \)
The potential for the cell, \( \boldsymbol{C r}\left|\boldsymbol{C r}^{3+}(\mathbf{0 . 1} \boldsymbol{M}) \| \boldsymbol{F} \boldsymbol{e}^{2+}(\mathbf{0 . 0 1 M})\right| \boldsymbol{F e} \) is:
A \( .-0.26 V \)
B . \( 0.26 V \)
\( \mathrm{c} .0 .339 \mathrm{V} \)
D. \( -0.339 V \)


Evaluate \( \int \frac{\boldsymbol{x}^{2}}{\mathbf{9}+\mathbf{1 6 x}^{\mathbf{6}}} \boldsymbol{d} \boldsymbol{x} \)
A \( \frac{1}{16} \tan ^{-1}\left(\frac{4 x^{3}}{3}\right)+c \)
в. \( \frac{1}{36} \tan ^{-1}\left(\frac{3 x^{3}}{4}\right)+c \)
c. \( \frac{1}{16} \tan ^{-1}\left(\frac{3 x^{3}}{4}\right)+c \)
D. \( \frac{1}{36} \tan ^{-1}\left(\frac{4 x^{3}}{3}\right)+c \)


A man is climbing a staircase.
The energy he uses depends on:
This question has multiple correct options
A. The height of the staircase.
B. The weight of his body
c. The time taken to roach the top
D. The mass of his body.


In the two dimensional motions:
A. \( x-t \) graph gives actual path of the particle
B. \( y-t \) graph gives actual path of the particle
c. \( \sqrt{x^{2}+y^{2}} \) versus t graph gives the actual path of the particle
D. \( y-x \) graph gives actual path of particle


Which of the followings is most primitive division?
A. Lycopsida
B. Pteropsida
c. Psilopsida
D. sphenopsida


Solve the equation \( \tan ^{-1}\left(\frac{1-x}{1+x}\right)= \)
\( \frac{1}{2} \tan ^{-1} x, x>0 \)


Use Venn diagrams to verify De'Morgan's law of complementation
\( (\boldsymbol{A} \cup \boldsymbol{B})^{\prime}=\boldsymbol{A}^{\prime} \cup \boldsymbol{B}^{\prime} \)


The straight line \( 3 x+4 y-12=0 \)
meets the coordinate axes at \( A \) and \( B \).
An equilateral triangle \( A B C \) is
constructed. The possible coordinates
of vertex \( C \) are
This question has multiple correct options
\( ^{\mathbf{A}} \cdot\left(2\left(1-\frac{3 \sqrt{3}}{4}\right), \frac{3}{2}\left(1-\frac{4}{\sqrt{3}}\right)\right) \)
B \( \cdot\left(-2(1+\sqrt{3}), \frac{3}{2}(1-\sqrt{3})\right) \)
\( \left(2(1+\sqrt{3}), \frac{3}{2}(1+\sqrt{3})\right) \)
\( \left(2\left(1+\frac{3 \sqrt{3}}{4}\right), \frac{3}{2}\left(1+\frac{4}{\sqrt{3}}\right)\right) \)


Which part of the ear vibrates when sound waves enter our ear?
A. Ear canal
B. Eardrum
c. Pinna
D. cochlea


Find the derivatives of the following
functions.
(a) \( \cot ^{3} x \)
(b) \( \sin \sqrt{x} \)


Sum of all the three interior angles of a
triangle is equal to
A \( .360^{\circ} \)
B . \( 120^{\circ} \)
c. \( 180^{\circ} \)
D. \( 90^{\circ} \)


The value \( (s) \) of \( k \) for which the
quadratic equation \( k x^{2}-k x+1=0 \)
has equal roots is
\( \mathbf{A} \cdot k=0 \)
B. \( k=4 \)
c. \( k=0,4 \)
D. \( k=-4 \)


\( K 0_{2}( \) potassium super oxide ) is used in
oxygen cylinder in space and
submarines. This is because it
A. absords \( C O_{2} \) and increase \( O_{2} \) content
B. eliminates moisture
c. absords \( C O_{2} \)
D. produces ozone


A proton moves a speed of \( 7.45 \times \) \( 10^{5} m / s \) directly towards a free proton
initially at rest. Find the distance of the
closet approach for the two protons.


What is the required condition, if the light incident on one face of a prism, does not emerge from the other face?
A \( \cdot_{n}<\operatorname{cosec}\left(\frac{A}{2}\right) \)
в. \( n<\sec \left(\frac{A}{2}\right) \)
\( \mathbf{c} \cdot n>\sec A \)
D. \( n>\operatorname{cosec}\left(\frac{A}{2}\right) \)


By fractional distillation, only \( 68 \% \)
\( H N O_{3} \) can be formed. Further
increasing concentration is not
possible. Give reason.


General electronic configuration of
lanthanides is:
\( \mathbf{A} \cdot(n-2) f^{1-14}(n-1) d^{0-1} n s^{2} \)
B . \( (n-2) f^{10-14}(n-1) d^{10-1} n s^{2} \)
C \( \cdot(n-2) f^{0-14}(n-1) d^{10} n s^{2} \)
D. \( (n-2) d^{0-1}(n-1) f^{1-14} n s^{2} \)


While charging the lead storage battery
A. \( P b S O_{4} \) anode is reduced to \( P b \)
B. \( P b S O_{4} \) cathode is reduced to Pb
\( \mathrm{c} \cdot P b S O_{4} \) cathode is oxidised to \( \mathrm{Pb} \)
D. \( P b S O_{4} \) anode is oxidised to \( P b O_{2} \)


If you look at this object from the top,
what will you see?


By looking at the Lewis structure of an ammonia \( \left(\mathrm{NH}_{3}\right) \) molecule, shape of an ammonia molecule is described by
which one of the following?
A. Trigonal pyramidal
B. T-shaped
c. Square planar
D. Trigonal planar
E. Tetrahedral


State whether true or false:
Speed of sound can never exceed the
average molecular speed in a fluid.
A. True
B. False


Three coins are tossed. Describe two
events \( A \) and \( B \) which are mutually
exclusive.


The direction ratios of the line \( \boldsymbol{x}-\boldsymbol{y}+ \)
\( z-5=0=x-3 y-6 \) are
A. 3,1,-2
в. 2,-4,1
c. \( \frac{3}{\sqrt{14}}, \frac{1}{\sqrt{14}}, \frac{-2}{\sqrt{14}} \)
D. \( \frac{2}{\sqrt{14}}, \frac{-4}{\sqrt{14}}, \frac{1}{\sqrt{14}} \)


When \( 1 \% \) of \( C_{2} H_{5} O H \) is added to
\( C H C l_{3}, \) the phosgene present in
chloroform is converted to:
A. \( C H_{3} C O O C_{2} H_{5} \)
в. \( C H_{3} \) СОСН\( _{3} \)
c. \( \left(C H_{3} C H_{2} O\right)_{2} C O \)
D. \( C H_{3} \) СООН


For \( 0<x<1 \) the value of \( \cos ^{-1} x+ \)
\( \cos ^{-1}(-x)=? \)
\( \mathbf{A} \cdot \mathbf{0} \)
в. \( \pi \)
\( c .-\pi \)
D. none of these


\( \left|\begin{array}{ccc}1 & \cos \alpha & \cos \beta \\ \cos \alpha & 1 & \cos \gamma \\ \cos \beta & \cos \gamma & 1\end{array}\right|= \)
\( \left|\begin{array}{ccc}\mathbf{0} & \cos \boldsymbol{\alpha} & \cos \boldsymbol{\beta} \\ \cos \boldsymbol{c} & \boldsymbol{0} & \cos \gamma \\ \cos \boldsymbol{\beta} & \cos \gamma & \boldsymbol{0}\end{array}\right| \) then
A \( \cdot \cos \alpha+\cos \beta+\cos \gamma=0 \)
B. \( \cos \alpha \cdot \cos \beta \cdot \cos \gamma=0 \)
C \( \cdot \cos ^{2} \alpha+\cos ^{2} \beta+\cos ^{2} \gamma=1 \)
D. \( \sum \cos \alpha \cos \beta=0 \)


Lenses of power \( 3 D \) and \( -5 D \) are
combined to from a compound lens.An object is placed at a distance of \( 50 \mathrm{cm} \) from this lens. The position of its image will be; -
\( A \cdot-10 \mathrm{cm} \)
\( B .+10 \mathrm{cm} \)
\( c .-25 \mathrm{cm} \)
\( D \cdot+25 \mathrm{cm} \)


A salesman has a \( 70 \% \) chance to sell a
product to any customer. The behaviour of successive customers is independent. If two customers \( A \) and \( B \) enter, what is the probability that the salesman will sell the product to
customer A or B?
A . 0.98
B. 0.91
c. 0.70
D. 0.49


If a rubber ball is taken at the depth of \( 200 m \) in a pool, its voulme decreases by
\( 0.1 \% \). If the density of the water is \( 1 \times \) \( 10^{3} k g / m^{3} \) and \( g=10 m / s^{2}, \) then the
volume elasticity in \( N / m^{2} \) will be
A \( \cdot 10^{8} \)
B . \( 2 \times 10^{8} \)
\( c \cdot 10^{9} \)
D. \( 2 \times 10^{9} \)


When the planet Jupiter is at a distance
of 824.7 million kilometers from the
Earth,its angular diameter is measured to be 35.72 of arc. Calculate the
diameter of Jupiter.


A molecule of gas in a container hits one wall (1) normally and rebounds back. It suffers no collision and hits the
opposite wall (2) which is at an angle of
\( 30^{\circ} \) with wall 1

Assuming the collisions to be elastic
and the small collision time to be the
same for both the walls, the magnitude
of average force by wall 2. \( \left(F_{2}\right) \) provided to the molecule during collision satisfy :
A \( \cdot F_{1}>F_{2} \)
в. \( F_{1}<F_{2} \)
c. \( F_{1}=F_{2} \), bothnon-zero
D. \( F_{1}=F_{2}=0 \)


Can a physical quantity have units but still be dimensionless?


If the area of two similar triangles are equal, prove that they are congruent.


Which of the following represents a
synthetic detergent?
A. \( C_{15} H_{31} \) COOK
в. \( C H_{3}\left(C H_{2}\right)_{6} C O O N a \)
\( c \)
D. None of the above


What is photo diode? Mention its one
use.


What is the reactance in ohms of a
\( 2.00 H \) inductor at a frequency of
\( \mathbf{5 0 . 0 H z} ? \)


Which of the following shows particle nature of light ?
A. Refraction
B. Interference
c. Polarization
D. Photoelectric effect


Suppose that two objects \( A \) and \( B \) are
moving with velocities \( \vec{v}_{A} \) and \( \vec{v}_{B} \) (each with respect to some common frame of
reference). Let \( \vec{v}_{A B} \) represent the velocity of \( A \) with respect to \( B \). Then
A \( \cdot \vec{v}_{A B}+\vec{v}_{B A}=0 \)
в. \( \vec{v}_{A B}+\vec{v}_{A B}=0 \)
c. \( \vec{v}_{A B}=\vec{v}_{A}+\vec{v}_{B} \)
D. \( \vec{v}_{A B} \neq \vec{v}_{A B} \)


For the equation given below, find the slope and the y-intercept:
\( \boldsymbol{x}+\mathbf{3} \boldsymbol{y}+\mathbf{5}=\mathbf{0} \)
A \( \cdot \frac{1}{3} \) and \( \frac{5}{3} \)
в. \( -\frac{1}{3} \) and \( -\frac{5}{3} \)
\( \mathrm{c} \cdot_{-3} \) and \( \frac{3}{5} \)
D. 3 and \( -\frac{5}{3} \)


Find the electric field at \( z>0.5 d \)
\( \mathbf{A} \cdot E=0 \)
B \( \cdot E=-\frac{\sigma}{\epsilon_{0}} \hat{k} \)
\( \mathbf{c} \cdot E=\frac{\sigma}{\epsilon_{0}} \hat{k} \)
D・ \( E=-\frac{\sigma}{2 \epsilon_{n}} \hat{k} \)


Amoeba sticks to substratum by means
of
A. Rough surface
B. Plasmalemma
c. Protein
D. None of the above


When \( 10.0 \mathrm{ml} \) of arsenious sulphide sol
and \( 1.0 \times 10^{-4} M B a C l_{2} \) are mixed
turbidity due to precipitation appears after just 2 hours. The effective ion and its coagulating value are, respectively?
A \( \cdot C l^{-}, 10 \mathrm{mmol} / \mathrm{L} \)
B . \( C l^{-}, 20 \mathrm{mmol} / \mathrm{L} \)
C. \( B a^{2+}, 10 \mathrm{mmol} / \mathrm{L} \)
D. \( B a^{2+}, 20 \mathrm{mmol} / \mathrm{L} \)


When \( C l_{2} \) gas is dissolved in water,
there is disproportion to \( H C l O \) and
\( \boldsymbol{H} \boldsymbol{C l} \)
A. True
B. False


The number of silicon atomes per \( m^{3} \) is
\( 5 \times 10^{28} . \) This is doped simultaneously
with \( 5 \times 10^{28} \) atoms per \( m^{3} \) of Arsenic
and \( 5 \times 10^{20} \) per \( m^{3} \) atoms of Indium.
Calculate the number of electrons and
holes. Given that \( n_{1}=1.5 \times 10^{16} m^{-3} \)
Is the material \( n \) -type or \( p- \) type?


7
Q Type your question
form a hydrogen molecule?
\( \mathbf{A} \)
\( B \)
\( \mathbf{C} \)
\( D \)


At \( p H=4, C r_{2} O_{4}^{2-} \) exists as:
A \( \cdot C r O_{4}^{2-} \)
в. \( C r O_{3} \)
\( \mathrm{c} \cdot \mathrm{Cr} \mathrm{O}_{2}^{2+} \)
D. \( C r_{2} O_{7}^{2} \)


The foci of an ellipse are \( S(-2,-3), S^{\prime}(0,1) \) and its \( e=\frac{1}{\sqrt{2}} \)
then the directrix corresponding to the
focus \( S^{\prime} \) is:
A. \( x+2 y-5=0 \)
B . \( x+2 y-9=0 \)
c. \( x+2 y-11=0 \)
D. none of these


Assertion: Nitrogen is inactive in normal chemical reactions.
Reason: The bond dissociation energy
is directly proportional to reactivity
A. Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion
B. Both Assertion and Reason are correct but the Reason is not the correct explanation of the Assertion
c. Assertion is correct but the Reason is incorrect
D. Assertion is incorrect but the Reason is correct


The soap molecule has a:
A. hydrophilic head and a hydrophobic tail
B. hydrophobic head and a hydrophilic tail
C. hydrophobic head and a hydrophobic tail
D. hydrophilic head and a hydrophilic tail


Rutherford could not explain:
This question has multiple correct options
A. stability of an atom
B. spectrum of hydrogen atom
C. Circular motion of electrons
D. The spiral path of electrons


In the detection test of carbon and
hydrogen with cupric oxide, hydrogen is oxidized to
A. water
B. methane
c. hydride
D. lime water


The number of moles of acetic
anhydride \( \left(A c_{2} O\right) \) needed to react
completely with sucrose, is:


Assertion
Inert electrolytes like KCI \( , K N O_{3} \) are
used in salt bridge.
Reason
Salt bridge provides an electric contact between the two solutions without
allowing them to mix with each other
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Find the number of sides of a regular
polygon if each interior angle is \( 135^{\circ} \)


Explain chromyl chloride test with equation.


If \( \frac{\mathbf{3} \boldsymbol{x}+\mathbf{2}}{(\boldsymbol{x}+\mathbf{1})\left(\mathbf{2} \boldsymbol{x}^{2}+\mathbf{3}\right)}=\frac{\boldsymbol{A}}{(\boldsymbol{x}+\mathbf{1})}+ \)
\( \frac{B x+C}{\left(2 x^{2}+3\right)} \) then \( A+C-B= \)
A.
B. 2
\( c \cdot 3 \)
\( D \)


What are the coefficients of all in lowest
term after balancing the reaction?
\( \ldots \boldsymbol{C}_{4} \boldsymbol{H}_{10}+\ldots . \boldsymbol{O}_{2} \rightarrow \ldots \boldsymbol{C} \boldsymbol{O}_{2}+\ldots . \boldsymbol{H}_{2} \boldsymbol{O} \)
B. 2,13,8,10
c. 1,6,1,5
D. 3,10,16,20
E .4,26,16,20


Give the principle of moving coil galvanometer? What is the advantage of radial magnetic field in the galvanometer?


\( \boldsymbol{A}+\boldsymbol{B} \rightleftharpoons \boldsymbol{C}+\boldsymbol{D}, \boldsymbol{K}_{c} \) for this reaction is
10. If 1,2,3,4 mole/litre of \( A, B, C \) and
\( D \) respectively are present in a
container at \( 25^{\circ} C, \) the direction of
reaction will be
A. From left to right
B. From right to left
c. Reaction is at equilibriumm
D. Unpredictable


The median of the following distribution
is
\( 35 . \) Find the value of \( a \) and \( b \)
\( \begin{array}{ll}\text { Class - Interval } & \text { Number of Workers } \\ \text { 0-10 } & 10 \\ \text { 10-20 } & \text { 20 } \\ \text { 20-30 } & \text { a } \\ \text { 30-40 } & \text { 40 } \\ \text { 40-50 } & \text { b } \\ \text { 50-60 } & \text { 25 } \\ \text { 60-70 } & \text { 15 } \\ \text { Total } & \text { 170 }\end{array} \)


\( 10 m L \) of a solution of \( N a O H \) is found
to be completely neutralised by \( 8 m L \) of
a given solution of \( \boldsymbol{H} \boldsymbol{C l} \). If we take \( 20 m L \) of the same solution of \( N a O H \)
the amount \( H C l \) solution (the same
solution as before) required to neutralise it will be:
\( \mathbf{A} \cdot 4 m L \)
B. \( 8 m L \)
c. \( 12 m L \)
D. \( 16 m L \)


The specific heat of an ideal gas varies
as
\( \mathbf{A} \cdot T^{3} \)
в. \( T^{2} \)
c. \( T^{\text {। }} \)
D. \( T^{\circ} \)


The value of the integral \( \int_{-2}^{2}(1+ \) \( 2 \sin x) e^{|x|} d x \) is equal to
A .
B. \( e^{2}-1 \)
c. \( 2\left(e^{2}-1\right) \)
D.


State the converse, inverse and
contrapositive of the conditional
statement : 'If a sequence is bounded,
then it is convergent.


Find whether the lines representing the following pair of linear equation
intersect at a point, are parallel or coincident \( \cdot \frac{3 x}{2}-\frac{5 y}{3}=-2 ; \frac{x}{3}+\frac{y}{2}= \)
\( \mathbf{1 3} \)
\( \mathbf{6} \)


A vessel of 250 litre was filled with 0.01
mole of \( S b_{2} S_{3} \) and 0.01 mole of \( H_{2} \) to
attain the equilibrium at \( 440^{\circ} \mathrm{C} \) as :
\[
\begin{array}{r}
\boldsymbol{S b}_{2} \boldsymbol{S}_{3}(\boldsymbol{s})+\mathbf{3} \boldsymbol{H}_{2}(\boldsymbol{g}) \rightleftharpoons \mathbf{2} \boldsymbol{S} \boldsymbol{b}(\boldsymbol{s})+ \\
\mathbf{3} \boldsymbol{H}_{2} \boldsymbol{S}(\boldsymbol{g})
\end{array}
\]
After equilibrium, the \( H_{2} S \) formed was analysed by dissolved it in water and treating with excess of \( P b^{2+} \) to give
1.19g of \( P b S \) as precipitate. What is the
value of \( \boldsymbol{K}_{c} \) at \( \mathbf{4 4 0}^{\circ} \boldsymbol{C} \)
A .
B. 2
\( c \cdot 4 \)
D.


The person who has been awarded the
title of the Father of Physics of \( 20^{t h} \) century is
A. Madame Curie
B. C V Raman
c. Neils Bohr
D. Albert Einstein


Which of the following exhibits only +3 oxidation state?
A. \( T h \)
в. \( A c \)
\( c . P a \)
D. \( U \)


Self-ordered proto-protein contacted with water and by self-assembly gave rise to
A. Protocell
B. Protobiont
c. Eobiont
D. All of the above


The drug used as post operative analgesic in medicine is:
A. L-Dopa
B. Amoxycilin
c. sulphapyridine
D. Morphine


The common ratio of the geometric
sequence \( a_{n}=3^{n-1} \) is
\( A \)
B. 2
\( c \cdot 3 \)
D. 4


If the product of two positive numbers
is 256 then the least value of their sum
is
A . 32
B . 16
c. 48
D. 40


Plant hormones are
A. Growth regulators
B. Growth promoters
c. Growth inhibitors
D. None of the above


A false balance has equal arms. An
object weights \( \boldsymbol{w}_{1} \) when placed in one
pan and \( w_{2} \) when placedin the other pan. Then weight w of the object is
в. \( \frac{w_{1}+w_{2}}{2} \)
\( ^{\mathbf{c}} \cdot\left(\frac{w_{1}^{2}+w_{2}^{2}}{2}\right)-1 \)
\( \mathbf{D} \cdot \sqrt{w_{1}^{2}+w_{2}^{2}} \)


The core of electromagnet is made of soft iron, because
a) susceptibility of soft iron is very high
b) coercivity of soft iron is very low
A. only a is correct
B. only b is correct
c. both a and b are correct
D. both a and b are wrong


Work is always done on a body when:
\( A \). a force acts on it
B. it moves through a certain distance
C. it experiences an increase in energy through a mechanical influence
D. none of these


Some oils and fats give a bad smell and taste because of
A. rancidity
B. decomposition reaction
c. hydrogenation reaction
D. double displacement reaction


Region/regions of the atmosphere where temperature decreases with
altitude is/are:
A. thermosphere
B. stratosphere
c. troposphere
D. ozonosphere


Which soil horizon contains humus?
A. A-Horizon
B. B-Horizon
c. C-horizon
D. Bedrock


When 1 -pentyne \( (A) \) is treated with \( 4 N \)
alcoholic \( K O H \) at \( 175, \) it is converted
slowly into an equilibrium mixture of
1.3\% 1-pentyne (A) 95.2\% 2-pentyne (B)
and \( 3.5 \% \) of 1,2 -pentadiene \( (C) . \) The
equilibrium was maintained at 175 Calculate \( \Delta G \) for the following
equilibria.
\[
\begin{array}{l}
\qquad \boldsymbol{\Delta G}_{1}=? \\
\qquad \boldsymbol{B} \boldsymbol{G}_{2}=?
\end{array}
\]
From the calculate value of \( \Delta G_{1} \) and
\( \Delta G_{2} \) indicate the order of stability of \( A, B \) and \( C . \) Write a reasonable reaction mechanism showing all international leading to \( A, B \) and \( C \)


Which of the following is/are the main agents of soil erosion?
A) Wind and water
B) Rocks
c) sand
\( A \cdot A \)
B. A \& B
\( c \cdot B \& C \)
D. A, B, C


\( \boldsymbol{P} \frac{\boldsymbol{K} \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{4} / \boldsymbol{K} \boldsymbol{O} \boldsymbol{H}}{\longrightarrow} \boldsymbol{Q} \frac{\text {Sodalime}}{\Delta} \boldsymbol{R} \frac{\boldsymbol{C H}_{3} \boldsymbol{C l}}{\boldsymbol{a n h y} \cdot \boldsymbol{A l} \boldsymbol{C l}_{3}} \boldsymbol{S} \)
If \( P \) and \( S \) are toluene, \( Q \) and \( R \)
and \( ----- \) respectively.
A. Benzaldehyde, Benzoic acid
B. Benzaldehyde, Sodium benzoate
C. Benzoic acid, Benzene
D. Benzene, Benzoic acid


To produce a minimum reflection of wavelengths near the middle of visible spectrum (550nm), how thick should a
coating of \( M g F_{2}(\mu=1.38) \) be
vacuum-coated on a glass surface?
A \( \cdot 10^{-7} \)
B \( \cdot 10^{-10} \)
\( \mathbf{c} \cdot 10^{-9} m \)
D. \( 10^{-8} m \)


Molten NaCl conducts electricity due to the presence of :
\( \mathbf{A} \cdot \) free molecules
B. free ions
c. free electrons
D. free atoms


Let \( \boldsymbol{f}(\boldsymbol{x})=\mathbf{2} \boldsymbol{x}^{\mathbf{3}}+\mathbf{3} \boldsymbol{x} \forall \boldsymbol{x} \in \boldsymbol{R}, \) then
equation of tangent for \( y=f^{-1}(x) \) at
\( \boldsymbol{x}=\mathbf{5} \) will be
A \( \cdot 9 y-x=4 \)
В. \( 9 y-4 x=-19 \)
c. \( 49 y-9 x=4 \)
D. \( 9 y-2 x=-1 \)


Electrolyte for silver plating is:
A. potassium nitrate solution
B. dilute sulphuric acid
C. double cyanide of silver and potassium solution
D. any of the above


When there occurs a transition from
\( \boldsymbol{n}=\mathbf{3} \) to \( \boldsymbol{n}=\mathbf{2} \) state in the hydrogen
the atom recoils. If \( \boldsymbol{E}_{1}-\boldsymbol{E}_{2}=\mathbf{1} . \mathbf{9} e \boldsymbol{V} \)
then the ratio of \( K E \) of recoil and the
photon energy is of the order of
A . 10
B . \( 10^{-9} \)
\( \mathrm{c} \cdot 10^{-6} \)
D. \( 10^{-11} \)


Assertion
Sulphuric acid is more viscous than
water.
Reason
Concentrated sulphuric acid has a
great affinity for water.
A. If both assertion and reason are correct and the reason
is the correct explanation of the assertion.
B. If both assertion and reason are correct, but the reason is not the correct explanation of the assertion.
C. If assertion is correct, but reason is incorrect
D. If assertion is incorrect, but reason is correct.


The gas \( A_{2} \) in the left flask allowed to
react with gas \( B_{2} \) present in right flask
\( \operatorname{at} \boldsymbol{A}_{2}(\boldsymbol{g})+\boldsymbol{B}_{2}(\boldsymbol{g}) \rightleftharpoons \mathbf{2} \boldsymbol{A} \boldsymbol{B}(\boldsymbol{g}), \boldsymbol{K}_{C}=\boldsymbol{4} \)
at \( 27^{\circ} C . \) What is the concentration of
\( A B \) when equilibrium is established?
A . 1.33 М
В. 0.66 М
c. 0.33 М
D. 2.66 М


List a few flight adaptations in birds.


'POISE' is the:
A. C.G.S. unit of surface tension
B. C.G.S. unit of viscosity
C. M.K.S. unit of viscosity
D. M.K.S. unit of surface energy


If \( \tan 9^{\circ}=\frac{P}{q}, \) then the value of
\( \frac{\sec ^{2} 81^{\circ}}{1+\cot ^{2} 81^{\circ}} ? \)


The hysterisis curve is studied
generally for
A. ferromagnetic materials
B. paramagnetic materials
c. diamagnetic materials
D. All of the above


The density of a gas is found to be \( 1.56 g / L \) at \( 745 \mathrm{mm} \) pressure and \( 65^{\circ} \mathrm{C} \)
What is the molecular mass of the
gas?
\( \mathbf{A} \cdot 44.2 u \)
в. \( 4.42 u \)
c \( .2 .24 u \)
D. 22.4u


f \( \tan ^{-1}\left(\frac{x-1}{x-2}\right)+\tan ^{-1}\left(\frac{x+1}{x+2}\right)= \)
4
then \( x \) is


It is a chemical reaction where two
reactants, each containing the same element but with a different oxidation
number, will form a product in which the elements involved reach the same
oxidation number. This reaction is
called:
A. Comproportionation reaction
B. Disproportionation reaction
c. Reduction
D. Double displacement reaction


Evaluate \( \int_{0}^{2}\left(x^{2}-x\right) d x \)


The area enclosed by the polynomial function of least degree satisfying \( \lim _{x \rightarrow 0}\left[1+\frac{f(x)}{x^{3}}\right]^{\frac{1}{x}}=e \) and the circle
\( x^{2}+y^{2}=2 \) above the \( X \) -axis is
in square units.
\( A \)
\[
\frac{3}{5}+\frac{\pi}{2}
\]
B.
\[
\frac{2}{5}-\frac{\pi}{2}
\]
c. \( \frac{2}{5}+\frac{\pi}{2} \)
D.
\[
\frac{1}{5}+\frac{\pi}{2}
\]


A stone thrown into still water, creates a
circular wave pattern moving radially outwards. If \( r \) is the distance measured
from the centre of the pattern. the amplitude of the wave aries as
A \( \cdot r^{-1 / 2} \)
B . \( r^{-1} \)
\( c \cdot r^{-2} \)
D. \( r^{-3 / 2} \)


\( \lim _{x \rightarrow 0} \frac{\sqrt{1-\cos 2 x}}{\sqrt{2} x} \) is equal


Let \( R \) be a relation from \( A=\{1,2,3,4\} \) to \( \mathrm{B}=\{1,3,5\} \) such that
\( R=[(a, b): a<b, \text { where } a \varepsilon A \text { and } b \varepsilon B] \)
What is RoR \( ^{-1} \) equal to?
A \( \cdot(1,3),(1,5),(2,3),(2,5),(3,5),(4,5) \)
B. (3,1),(5,1),(3,2),(5,2),(5,3),(5,4)
c. (3,3),(3,5),(5,3),(5,5)
D. (3,3),(3,4),(4,5)


Assertion
\( \sum_{r=0}^{100}\left(^{500-r} C_{3}\right)+^{400} C_{4}=^{501} C_{4} \)
Reason
\( \boldsymbol{n} \boldsymbol{C}_{\boldsymbol{r}}+^{\boldsymbol{n}} \boldsymbol{C}_{\boldsymbol{r}-\boldsymbol{1}}=\boldsymbol{n}+\boldsymbol{1} \boldsymbol{C}_{\boldsymbol{r}} \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is
not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


The total number of elements in the
group \( I B \) is:
A . 4
B. 5
\( c .7 \)
D. 9


The distance of the point (1,-2,3) from the plane \( \boldsymbol{x}-\boldsymbol{y}+\boldsymbol{z}=\mathbf{5} \) measured
parallel to the line. \( \frac{x}{2}=\frac{y}{3}=\frac{z}{-6}, \quad \) is :
\( A \)
B. 6/7
\( c \cdot 7 / 6 \)
D. \( 1 / 6 \)


Two billiard balls undergo a head-on collision. Ball 1 is twice as heavy as ball
2. Initially, ball 1 moves with a speed \( v \)
toward ball 2 which is at rest.
Immediately after collision, ball 1 travels at a speed of \( v / 3 \) in the same
direction. What type of collision has occured?
A. inelastic
B. elastic
c. completely inelastic
D. cannot be determined from the information giver


The value of \( \int \frac{d^{2}}{d x^{2}}\left(\tan ^{-1} x\right) d x \) is equal
to
A \( \cdot \frac{1}{1+x^{2}}+c \)
B. \( \tan ^{-1} x+c \)
c. \( x \tan -\frac{1}{2} \log \left(1+x^{2}\right)+C \)
D. \( \frac{1+x^{2}}{2}+c \)


Given that \( 1 \mathrm{cu} . \mathrm{cm} \) of marble weights 25
gms, the weight of a marble block 28
\( \mathrm{cm} \) in width and \( 5 \mathrm{cm} \) thick is \( 112 \mathrm{kg} \) The length of the block is:
A. \( 26.5 \mathrm{cm} \)
в. 32 \( \mathrm{cm} \)
c. \( 36 \mathrm{cm} \)
D. 37.5 cm


The number of hours for which students
of a particular class watched television
during holidays is shown through the
given graph.
Answer the following.
(i) For how many hours did the
maximum number of students watch
TV?
(ii) How many students watched TV for
less than 4 hours?
(iii) How many students spent more
than 5 hours in watching TV?


If an oscillation copper disc is placed in a
magnetic field, then
A. The frequency of oscillations is decreasing continuously.
B. The frequency of oscillations is increasing continuously.
C. The frequency of oscillations is constant
D. None of these.


Solve: \( \sqrt{\mathbf{2}} \boldsymbol{x}+\sqrt{\mathbf{3}} \boldsymbol{y}=\mathbf{0} \)
\( \sqrt{\mathbf{3}} \boldsymbol{x}-\sqrt{\mathbf{8}} \boldsymbol{y}=\mathbf{0} \)


One of the fundamental particles is missing in one of the isotopes. Then particle and isotope are respectively:
A. neutron, protium
B. neutron, tritium
c. proton, protium
D. electron, tritium


Let \( A=\{1,2\} \) and \( B=\{3,4\} . \) Find the
number of relations from \( \boldsymbol{A} \) to \( \boldsymbol{B} \)


The current inside a copper voltameter:
A. is half the outside value
B. is the same as the outside value
C. is twice the outside value
D. depends on the concentration of \( C u S O_{4} \)


Paired fins of fishes are
A. Caudal and ventral
B. Dorsal and ventral
C . Pectoral and pelvic
D. Caudal and pectoral


A battery of e.m.f. \( \boldsymbol{E} \) has an internal resistance 'r'. A variable resistance \( \boldsymbol{R} \) is
connected to the terminals of the
battery. A current \( I \) is drawn from the
battery. \( V \) is the terminal P.D. If \( R \) alone
is gradually reduced to zero, which of
the following best describes \( I \) and \( V ? \)
A. I approaches \( E / r, V \) approaches \( E \)
B. I approaches infinity, \( V \) approaches \( E \)
c. \( I \) approaches zero, Vapproaches \( E \)
D. I approaches \( E / r, V \) approaches zero


Before: \( C u O+ \) porcelain boat \( =62.869 g \)
\( C a C l_{2}+U-t u b e=80.483 g \)
After:Porcelain boat+contents =
\( 54.869 g \)
CaCl \( _{2}+ \) U-tube \( =89.483 \mathrm{g} \)
Reactions: \( Z n(s)+2 H C l(a q) \rightarrow \)
\( Z n C l_{2}(a q)+H_{2}(g) \) then \( H_{2}(g)+ \)
\( \boldsymbol{C u} \boldsymbol{O}(\boldsymbol{s}) \rightarrow \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g})+\boldsymbol{C u}(\boldsymbol{s}) \)
What type of reaction occurred in the
porcelain boat?
A . Electrolysis
B. Double displacement
c. Reduction and oxidation
D. Decomposition or analysis
E. Combination or synthesis


If \( R \) is the maximum horizontal range of a particle, then the greatest height attained by it is:
A. \( R \)
в. \( 2 R \)
c. \( \frac{R}{2} \)
D. \( \frac{R}{4} \)


Give two definitions of mutual
inductance and write its unit.


Which of the following is used for preserving biological specimens?
A. Formaldehyde
B. Ether
c. Ethyl alcohol
D. None of these


Vegetable oils like wheat germ oil, sunflower oil, etc. are the good source of
?
\( A \). vitamin \( K \)
B. vitamin E
c. vitamin D
D. vitamin A


Increase 80 by \( 40 \% \)


The energy change in an electron jump is given by:
A. \( \Delta E=h c / \lambda \)
B. \( \Delta E=h \lambda / c \)
c. change in kinetic energy
D. azimuthal quantum number


The potential energy of the electron
present in the ground state of \( L i^{+2} \) ion is represented by:
A \( \cdot \frac{+3 e^{2}}{4 \pi \varepsilon_{0} r} \)
в. \( \frac{-3 e}{4 \pi \varepsilon_{0} r} \)
c. \( \frac{-3 e^{2}}{4 \pi \varepsilon_{0} r} \)
D. \( \frac{-9 e^{2}}{4 \pi \varepsilon_{0} r} \)


If the input frequency of a full wave
rectifier is \( 50 H z \) ac. Its output frequency is
A. \( 50 H z \) pulsating dc
B. \( 100 H z \) pulsating do
c. \( 200 H z \) pulsating dc
D. \( 500 H z \) pulsating dc


What is the half-life of a radioactive
substance if \( 87.5 \% \) of any given amount of the substance disintegrate in 40 minutes?
A. 160 min
B. 10 min
\( c \cdot 20 \min \)
D. 13 min


On treating roll sulphur with an aqueous solution of calcium hydroxide:
A. plastic sulphur is prepared
B. milk of sulphur is prepared
c. rhombic sulphur is prepared
D. roll sulphur


f \( \triangle \boldsymbol{P} \boldsymbol{Q} \boldsymbol{R} \cong \triangle \boldsymbol{C} \boldsymbol{A} \boldsymbol{B}, \boldsymbol{P} \boldsymbol{Q}=\boldsymbol{C} \boldsymbol{A} . \) If true
enter 1 else 0


If a ball is thrown up with a certain velocity. It attains a height of \( 40 \mathrm{m} \) and comes back to the thrower, then
A. Total distance covered by it is \( 40 \mathrm{m} \)
B. Total displacement covered by it is \( 80 \mathrm{m} \)
c. Total displacement is zero
D. Total distance covered by it is zero


The English physician, William Harvey discovered the circulation of blood.
A. A.D. 1578 -1656
B. A.D. 1578 -1658
c. A.D. 1578 -1657
D. A.D. 1578 -1660


Vessel shown in the figure has two
sections of areas of cross section \( \boldsymbol{A}_{\mathbf{1}} \)
and \( A_{2} . \) A liquid of density \( \rho \) fills both
sections up to a height \( h \) in each. Neglect atmospheirc pressure
A. The pressure at the base of the vessel is \( 2 h \rho g \)
B. The force exerted by the liquid on the base is \( 2 h \rho A_{2} g \)
C. The weight of the liquid is less thatn \( 2 h g \rho A_{2} \)
D. Walls of the vessel at the level \( x \) exert a downward
force \( h g \rho\left(A_{2}-A_{1}\right) \) on the liquid.


If \( z=\sqrt{\frac{1-i}{1+i}}, \) then arg \( z= \)
A. \( \frac{\pi}{4}, \frac{\pi}{2} \)
B. \( -\frac{\pi}{4}, \frac{\pi}{2} \)
c. \( \frac{3 \pi}{4}, \pi \)
D. \( -\frac{\pi}{4}, \frac{3 \pi}{4} \)


In Bohr series of lines of hydrogen
spectrum, the third line from the red
end corresponds to which one of the following inter - orbit jumps of the electron for Bohr orbits in an atom of
hydrogen ?
\( \mathbf{A} \cdot 3 \rightarrow 1 \)
B . \( 5 \rightarrow 2 \)
c. \( 2 \rightarrow 5 \)
D. \( 3 \rightarrow 2 \)


In prokaryotes, there are no membranebound organelles.
A. True
B. False


After doing experiment, it is found that
a saturated solution of \( B a S O_{4} \) at \( 25^{\circ} \mathrm{C} \)
contains \( 3.9 \times 10^{-5} \) mole / liter of \( B a^{2+} \)
ion. What is the value of \( K_{s p} \) of the
\( \boldsymbol{B} \boldsymbol{a} \boldsymbol{S} \boldsymbol{O}_{4} ? \)
A \( .1 .5 \times 10^{-4} \)
В. \( 1.5 \times 10^{-9} \)
c. \( 1.5 \times 10^{-10} \)
D. \( 3.9 \times 10^{-10} \)
E \( .39 \times 10^{-9} \)


A ball weighing 15 g is tied to a string 10 cm long. Initially the ball is held in the position such that the string is
horizontal. The ball is now released. A
nail N is situated vertically below the support at a distance

The minimum value of L such that the
string will be wound round the nail is
A \( .2 \mathrm{cm} \)
в. 4 ст
\( c .6 \mathrm{cm} \)
D. \( 8 \mathrm{cm} \)


At a place on the surface of earth vertical component of earths field is two times that of horizontal component.
Then the latitude angle at the place is
\( \mathbf{A} \cdot \tan ^{-1}(2) \)
B \cdot \( \tan ^{-1}(1 / 2) \)
\( c \cdot 45^{\circ} \)
D. \( 0^{\circ} \)


In a batch of 10 articles, 4 articles are
defective. 6 articles are taken from the
batch for inspection If more than 2 articles in this batch are defective, the whole batch is rejected Find the
probability that the batch will be rejected.


Write an equivalent exponential form for radical expression. \( \sqrt[3]{13} \)


A spherical body of diameter D is falling in viscous medium. Its terminal velocity is proportional to:
\( \mathbf{A} \cdot V_{1} \propto D^{1 / 2} \)
B. \( V_{1} \propto D^{3 / 2} \)
\( \mathbf{c} \cdot V_{1} \propto D^{2} \)
D. \( V_{1} \propto D^{5 / 2} \)


\( \mathbf{1 0} \quad \boldsymbol{d} \boldsymbol{m}^{3} \) of \( \boldsymbol{N}_{2} \) gas and \( \mathbf{1 0} \quad \boldsymbol{d} \boldsymbol{m}^{3} \) of gas
\( x \) at the same temperature contain the same number of molecules. The gas \( X \) is
A \( . C O \)
в. \( C O_{2} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \)
D. \( N O \)


Lenz's law of electromagnetic induction corresponds to the:
A. law of conservation of charge
B. law of conservation of energy
c. law of conservation of momentumm
D. law of conservation of angular momentum


Two co-axial lenses of power \( +4 D \) and \( -2 D \) are placed in contact. The focal length of combination is
\( \mathbf{A} \cdot 0.5 m \)
B. \( 0.25 \mathrm{m} \)
c. \( 0.16 m \)
D. \( -0.5 m \)


When a neutron collides with a quasi
free proton, it loses half of its energy on the average in the every collission. How many collisions, on the average, are required to reduce a 2 MeV neutron to a thermal energy df \( 0.04 \mathrm{eV} \)
A . 30
B. 22
\( c .35 \)
D. 26


Evaluate:
\( \lim _{x \rightarrow 0} \frac{\sqrt{1+2 x^{2}}-\sqrt{1-2 x^{2}}}{x^{2}} \)


A stone falls freely under gravity. It
covers distances \( h_{1}, h_{2} \) and \( h_{3} \) in the
first 5 seconds, the next 5 seconds and
the next 5 seconds respectively. The relation between \( h_{1}, h_{2} \) and \( h_{3} \) is
A \( \cdot h_{1}=2 h_{2}=3 h_{3} \)
B. \( h_{1}=\frac{h_{2}}{3}=\frac{h_{3}}{5} \)
c. \( h_{2}=3 h_{1} \) and \( h_{3}=3 h_{2} \)
D. \( h_{1}=h_{2}=h_{3} \)


Out of the following statements, the one which correctly describes a satellite
orbiting about the earth is
A. There is no force acting on the satellite
B. The acceleration and velocity of the satellite are roughly in the same direction
c. The satellite is always accelerating about the earth
D. The satellite must fall, back to earth when its fuel is exhausted


\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}} \sqrt{\cos \boldsymbol{x}}= \)


What is the maximum concentration of
equimolar solutions of ferrous sulphate and sodium sulphide so that when mixed in equal volumes, there is no precipitation of iron sulphide?(For iron sulphide, \( \boldsymbol{K}_{s p}=\mathbf{6 . 3} \times \mathbf{1 0}^{-\mathbf{1 8}} \) ).


Assertion
During \( \beta \) -decay, a new element with atomic number greater than one is
obtained.
Reason Protons and neutrons keep on changing
into one another through meson
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Which letter above represents a \( 3 \lambda \)
difference in path length?
A. Position A
B. Position B
c. Position \( c \)
D. Position D
E. Position E


ff \( z \neq 0 \) is a complex number,then prove
that \( \operatorname{Re}(z)=\mathbf{0} \Longrightarrow \operatorname{Im}\left(z^{2}\right)=\mathbf{0} \)


If \( y=A e^{m x}+B e^{n x}, \) show that \( \frac{d^{2} y}{d x^{2}}- \)
\( (\boldsymbol{m}+\boldsymbol{n}) \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}+\boldsymbol{m} \boldsymbol{n} \boldsymbol{y}=\mathbf{0} \)


\( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\boldsymbol{B r}+ \)
\( \boldsymbol{C H}_{3} \boldsymbol{O}^{-} \frac{\boldsymbol{C H}_{3} \boldsymbol{O H}}{\boldsymbol{6 0 ^ { o } \boldsymbol { C }}} \boldsymbol{P r o d u c t}(\boldsymbol{I}) \)
\( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\boldsymbol{B r}+ \)
\( \left(\boldsymbol{C H}_{3}\right)_{3} \boldsymbol{C O}^{-} \frac{\left(\boldsymbol{C H}_{3}\right)_{3} \boldsymbol{C}-\boldsymbol{O H}}{60^{\circ} \boldsymbol{C}} \boldsymbol{P r o d u c t}(\boldsymbol{I I}) \)
Select the correct options among the following. This question has multiple correct options
A. \( C H_{3} O^{-} \) is a good nucleophile as well as a strong base and the primary bromide is converted into ether in the reaction (I)
B. \( C H_{3} O^{-} \) is a good nucleophile as well as a strong base forming the corresponding alkene in the reaction (I)
c. primary bromide is attacked by the bulky strong base forming the corresponding alkene in the reaction (II)
D. primary bromide is attacked by the bulky good nucleophile forming the corresponding ether


Assertion
A disc rotates along the clockwise
direction and direction of angular velocity is upwards
Reason
The linear velocity of points on the disc
are directed towards the centre
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


f \( a, b, c \) are non-zero and different from
1, then the value of
\( \left|\begin{array}{ccc}\log _{a} 1 & \log _{a} b & \log _{a} c \\ \log _{a}\left(\frac{1}{b}\right) & \log _{b} 1 & \log _{a}\left(\frac{1}{c}\right) \\ \log _{a}\left(\frac{1}{c}\right) & \log _{a} c & \log _{c} 1\end{array}\right| \)
A . 0
B. \( 1+\log _{a}(a+b+c) \)
\( \mathbf{c} \cdot \log _{a}(a b+b c+c a) \)
D. 1
\( E \cdot \log _{a}(a+b+c) \)


Balance the chemical reaction of
laboratory preparation method of dihydrogen:
A. \( Z n+2 H^{+} \rightarrow Z n^{2+}+H_{2} \)
B. \( Z n^{2+}+2 H^{-} \rightarrow Z n+H_{2} \)
c. \( Z n^{2+}+2 H^{+} \rightarrow Z n^{2+}+H_{2} \)
D. None of the above


The mean of five observations is 4 and
their variance is \( 5.2 . \) If three of these
observations are 2,4 and \( 6, \) then the other two observations are
A. 3 and 5
B. 2 and 6
c. 4 and 4
D. 8 and 10
E. 1 and 7


Find the ratio in which the point
\( P(5,4,-6) \) divides the line segment
joining the points \( A(3,2,-4) \) and \( B(9,8,-10) . \) Also, find the harmonic conjugate of \( \boldsymbol{P} \)


The magnitude of non-contact force depends upon:
A. distance between two bodies
B. area of contact
c. both of them
D. none of the above


A large force is acting on a body for a short time. The impulse imparted is
equal to the change in :
A. Acceleration
B. Momentum
c. Energy
D. Velocity


In ozonolysis of benzene, how many molecules of ozone are added?


The activation energy of a catalysed reaction is more than the activation
energy of the uncatalysed reaction.
A. True
B. False


Solve
\( \sin ^{-1}(\cos x) \)


Simple barometer was first discovered
in
A. 1886
B. 1991
\( c .1643 \)
D. 1362


Find the domain of \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \log _{10} \log _{2} \log _{\pi / 2}\left(\tan ^{-1} x\right)^{-1} \)


The vertices of \( \Delta A B C \) are (-2,1),(5,4)
and (2,-3) respectively Find the area of triangle


The general formula for saturated
hydrocarbons is :
A. \( C_{n} H_{2 n+2} \)
B. \( C_{n} H_{2 n} \)
c. \( C_{n} H_{2 n-2} \)
D. \( C_{n} H_{2 n-n} \)


Which of the following statement is
wrong about chloroform?
A. Chloroform is used as an anesthetic.
B. Chloroform has distorted tetrahedral shape.
c. Chloroform is used as a solvent.
D. Chloroform has \( s p^{2} \) hybridized carbon atom.


The space above the mercury column in a barometer is torricellian vacuum.
A. True
B. False


Construct a \( \triangle \boldsymbol{X} \boldsymbol{Y} \boldsymbol{Z} \) in which \( \boldsymbol{X} \boldsymbol{Y}=\boldsymbol{4} . \mathbf{5} \)
\( \mathrm{cm}, Y Z=5 \mathrm{cm} \) and \( Z X=6 \mathrm{cm} \)


By simply looking at the pair of angles
given in figure. State which of the angle
in the pairs is greater.


\( \int \frac{1}{x\left(x^{n}+1\right)} d x \)


In the figure shown, the plastic region
occurs
A. Before point \( A \)
B. Beyond point A
c. Between points A and
D. Between points D and E


What would happen if in a gene encoding a polypeptide of 50 amino acids, \( 25^{t h} \) codon (UAU) is mutated to
UAA?
A. A polypeptide of 24 amino acids will be formed.
B. Two polypeptides of 24 and 25 amino acids will be formed
c. A polypeptide of 49 amino acids will be formed
D. A polypeptide of 25 amino acids will be formed


If A lies in the second quadrant and \( \mathbf{3} \tan \boldsymbol{A}+\mathbf{4}=\mathbf{0}, \) the value of \( \mathbf{2} \cot \boldsymbol{A}- \)
\( 5 \cos A+\sin A \) is equal to
A \( \cdot-\frac{53}{10} \)
в. \( \frac{23}{10} \)
\( c \cdot-\frac{37}{10} \)
D. \( \frac{7}{10} \)


In the given quadrilateral \( A B C D, B C=38 \) \( \mathrm{cm}, \mathrm{QB}=27 \mathrm{cm}, \mathrm{DC}=25 \mathrm{cm} \) and \( \mathrm{AD} \perp \)
DC find the radius of the circle.


toppr \( t \)
Q Type your question
\( A \)
\( B \)
\( c \)
\( D \)


An automobile dealer provides motor
cycles and scooters in three body
patterns and 4 different colours each The number of choices open to
a customer is
\( A \cdot^{5} C_{3} \)
в. \( ^{4} C_{3} \)
c. \( 4 \times 3 \)
D. \( 4 \times 3 \times 2 \)


If three times the larger of two numbers is divided by the smaller, we get 4 as the quotient and 8 as the remainder. If
five times the smaller is divided by the larger, we get 3 as the quotient and 5 as the remainder. Find the numbers.


Convert each part of the ratio to percentage:
2: 3: 5


Find out \( F \) in the given flowchart.
\( \mathbf{A} \). cathode
B. anode
c. electrolyte
D. none of these


Azeotropic mixtures?
A. Boil at different temperatures
B. Are mixtures of solids
C . Are constant boiling mixtures
D. None of the above


What is the ratio of heat generation in \( \mathrm{R} \)
and \( 2 R \) in same time in.


At \( 25^{\circ} C \lambda_{\infty}\left(H^{+}\right)=3.4982 \times \)
\( 10^{-2} S m^{2-1} \lambda_{\infty}\left(O H^{-}\right)=1.98 \times \)
\( 10^{-2} \mathrm{Sm}^{2-1} \)
Given: Sp. conductance \( =\mathbf{5 . 1} \times \)
\( 10^{-6} S m^{-1} \) for \( H_{2} O, \) determine \( p H \) and
\( \boldsymbol{K}_{\boldsymbol{w}} \)


Sea lion belongs to
A. class Reptilia
B. Subclass Prototheria
c. superclass Pisces
D. Order Carnivora