The charge on one mole electron is:
A . \( 1.6 \times 10^{-19} \mathrm{C} \)
B. \( 96500 C \)
\( c \cdot 6.02 \times 10^{-23} C \)
\( C \)
D. \( 1.6 \times 10^{-23} C \)


STATEMENT - 1: The locus of the middle
points of equal chords of a circle with
centre at 0 is a circle with centre at 0
STATEMENT - 2 : The mid point of the equal chords are equidistant from the centre of the circle.
A. Statement - 1 is True, Statement - 2 is True, Statement 2 is a correct explanation for Statement - 1
B. Statement - 1 is True, Statement - 2 is True : Statement 2 is NOT a correct explanation for Statement- -
c. Statement - 1 is True, Statement - 2 is False
D. Statement-1 is False, Statement- - 2 is True


A reaction \( A+B \rightarrow C \) is second order
with respect to \( A \) and independent of \( B \) The rate expression for the reaction is:
A. \( r a t e=K[A][B] \)
B . rate \( =K[A]^{2}[B] \)
c. \( r a t e=K[A]^{2}[B]^{2} \)
D. rate \( =K[A]^{2} \)


At what height, the value of 'g' is half
that on the surface of the earth of
radius \( \boldsymbol{R} ? \)
A. \( R \)
в. \( 2 R \)
c. \( 0.414 R \)
D. \( 0.75 R \)


Find the mean and standard deviation
using short-cut method
60
\( \begin{array}{lll}61 & 62 & 63\end{array} \)
\( \boldsymbol{x}_{i} \)
\( f_{i} \)


A conductor AB lies along the axis of a
circular conducting loop \( \mathrm{C} \) of radius \( r . \) If
the current in the conductor AB varies
at the rate of \( x \mathrm{A} / \mathrm{s} \), then the induced
emf in the coil \( C \) is
A \( \cdot \frac{\mu_{0} r x}{2} \)
B \( \cdot \frac{1}{4} \pi r x \)
\( c \cdot \frac{\mu_{0} \pi x r}{2} \)
D. zero


Which of the following is a unit of distance?
A. second
B. Candela
c. мо।
D. Light year


Which postulate of Dalton's atomic theory can explain law of definite proportions?


Q Type your question
Youngs double slit apparatus. The
separation between maxima is
measured on a screen placed parallel to
the plane of the slits at a distance of
1.0 \( m \) from it as shown in figure. The
separation between the slits is \( 2 d= \)
1 \( m m \)
(a) If the incident beam falls normally on the double slit apparatus, find the \( y- \) coordinates of all the interface
minima of the screen
(b) If the incident beam makes an angle
of \( 30^{\circ} \) with the \( x- \) axis (as shown in fig)
find the \( y- \) coordinates of the first
minima on either side of the central
maximum.


An electron has \( u_{r m s} \) value at \( 27^{0} C \)
\( \left(\text { Given } \boldsymbol{m}_{e}=\mathbf{9 . 1 0 8} \times \mathbf{1 0}^{-\mathbf{3 1}} \mathbf{k g}\right) \)
This question has multiple correct options
A. \( 3.7 \times 10^{4} m / \) sec
B . \( 1.3 \times 10^{5} \mathrm{km} / \mathrm{hr} \)
c. \( 1.3 \times 10^{5} \mathrm{m} / \mathrm{sec} \)
D. \( 11.7 \times 10^{4} k m / h r \)


Which of the following is used as anesthetic?
в. \( C H C l_{3} \)
c. \( C H_{2} C l_{2} \)
D. \( D D T \)


Oxidative ozonolysis of 2-butene in the presence of zinc or dimethyl sulphide gives:
A. \( C H_{3} C H O \)
в. \( C H_{3} \) СООН
\( c \cdot C O_{2} \)
D. \( \left(C H_{3}\right)_{2} C O \)


In figure, \( P S \) is the bisector of \( \angle Q P R \) of
\( \triangle P Q R \) Prove that
\( \frac{Q S}{S R}=\frac{P Q}{P R} \)


\( A B C D E \) is a regular pentagon. A star
of five points \( A C E B D A \) is formed to
join their alternate vertices. The sum of
all five vertex angles of this star is
A. Two right angle
B. Three right angle
c. Four right angle
D. Five right angle


If \( \int \frac{2^{x}}{\sqrt{1-4^{x}}} d x=K \sin ^{-1}\left(2^{x}\right)+C \)
then \( K \) is equal to
A \( . e n 2 \)
в. \( \frac{1}{2} \ell n 2 \)
\( c \cdot \frac{1}{2} \)
D. \( \frac{1}{\ell n^{2}} \)


is the longest stage of meiotic division.
A. Prophase
B. Metaphase
c. Anaphase
D. Telophase


The temperature of transition from ferromagnetic property to paramagnetic property is called as:
A. Transition temperature
B. Critical temperature
c. Curie temperature
D. Triplet temperature


A pendulum having a bob of mass m is hanging in a ship sailing along the equator from east to west. When the
ship is stationary with respect to water,
the tension in the string is \( T_{0} . \) Find the difference between tension when the
ship is sailing with a velocity \( v \)
A . mv
B. 2 mv \( \omega \)
c. \( \frac{m v \omega}{2} \)
D. \( \sqrt{2} m v \omega \)


Find the order and degree of the
differential equation:
\( \left(\frac{d^{3} y}{d x^{3}}\right)^{2}+\left(\frac{d^{2} y}{d x^{2}}\right)^{3}+\left(\frac{d y}{d x}\right)^{4}+y^{5}=0 \)


The correct statement among the
following is:
A. smoke is carbon dispersed in air
B. butter is water dispersed in fat
C . greater is the valency of ion more will be its coagulating power
D. more is the gold number of a lyophobic sot, more is protecting power


f \( p, p+2, p+6 \) are in GP find \( p \)


The length, breadth and thickness of a block are measured with the help of a
meter scale. given \( \ell=(5.12+0.01) \mathrm{cm}, \mathrm{b} \)
\( =(10.15+0.01) \mathrm{cm}, \mathrm{t}=(5.28+0.01) \mathrm{cm} . \) The
percentage error in volume is:
A . 0.64\%
B. 0.28\%
c. 0.37\%
D. 0.48\%


If \( \boldsymbol{I}=\int_{2}^{3} \frac{2 \boldsymbol{x}^{5}+\boldsymbol{x}^{4}-\boldsymbol{2} \boldsymbol{x}^{3}+\boldsymbol{2} \boldsymbol{x}^{2}+\mathbf{1}}{\left(\boldsymbol{x}^{2}+\mathbf{1}\right)\left(\boldsymbol{x}^{4}-\mathbf{1}\right)} \boldsymbol{d} \boldsymbol{x} \)
then Iequals
A \( \cdot \frac{1}{2} \log 6+\frac{1}{10} \)
B \( \cdot \frac{1}{2} \log 6-\frac{1}{10} \)
c. \( \frac{1}{2} \log 3-\frac{1}{10} \)
D. \( \frac{1}{2} \log 2+\frac{1}{10} \)


Match the column
\( \begin{array}{lll}\text { A) Cryalite } & \text { P) } \mathrm{CazB}_{6} \mathrm{O}_{12} \mathrm{SH}_{2} \mathrm{O} \\ \text { B) Calemanite } & \mathrm{Q}) \mathrm{Al}_{2} \mathrm{O}_{3} 2 \mathrm{H}_{2} \mathrm{O} \\ \text { C) Bauxite } & \mathrm{R}) \mathrm{Na}_{3} \mathrm{AlF}_{6} \\ \text { D)Sidente } & \mathrm{S}) \mathrm{FeCO}_{3} \\ & \text { T) } \mathrm{Na}_{2} \mathrm{B}_{4} \mathrm{O}_{7} 1 \mathrm{OH}_{2} \mathrm{O}\end{array} \)


In an equilibrium, \( \boldsymbol{A}+\boldsymbol{B} \rightleftharpoons \boldsymbol{C}+\boldsymbol{D}, \boldsymbol{A} \)
and \( B \) are mixed in a vessel at
temperature \( \boldsymbol{T} \). The initial
concentration of \( A \) was twice the initial
concentration of \( B \). After the
equilibrium has reached, a
concentration of \( C \) was thrice the
equilibrium concentration of \( \boldsymbol{B} \)
Calculate \( \boldsymbol{K}_{\boldsymbol{c}} \)
(Nearest integer)


In a geometric sequence, the is the ratio of a term to the
previous term.
A. constant
B. common difference
c. common ratio
D. term


Sub atomic particles of atoms are:
A. protons
B. electrons
c. neutrons
D. all of these


Blackman's law of limiting factor is
applied to
A. Respiration
B. Transpiration
c. Photorespiration
D. Photosynthesis


The value of \( \sum_{i=1}^{10} r(i) \) is equal to
A \( \cdot \log \left[2-\frac{k}{H}\right] \)
в. \( 5 R\left[2+\frac{11 k}{H}\right] \)
c. \( _{5 R}\left[2-\frac{11 k}{H}\right] \)
D. \( 4 R\left[2-\frac{11 k}{H}\right. \)


Three dice are rolled. The probability that the same number will appear on
each of them is
A \( \cdot \frac{1}{36} \)
B. \( \frac{1}{12} \)
c. \( \frac{2}{49} \)
D. None


Write the number of vertical columns in
the modern periodic table. What are these columns called?


If the differential equation representing the family of all circles touching \( x- \) axis at the origin is \( \left(x^{2}-y^{2}\right) \frac{d y}{d x}= \)
\( \boldsymbol{g}(\boldsymbol{x}) \boldsymbol{y}, \) then \( \boldsymbol{g}(\boldsymbol{x}) \) equals:
A \( \cdot \frac{1}{2} x \)
в. \( 2 x^{2} \)
c. \( 2 x \)
D. \( \frac{1}{2} x^{2} \)


A person pulls a bucket of water from a well of depth \( h . \) If the mass of uniform
rope is \( m \) and that of the bucket full of
water is \( M, \) then work done by the
person is:
A \( \cdot\left(M+\frac{m}{2}\right) g h \)
B \( \cdot \frac{1}{2}(M+m) g h \)
c. \( (M+m) g h \)
D. \( \left(\frac{M}{2}+m\right) g h \)


The volume of air present in the lungs after forceful expiration is called as
A. Tidal volume
B. Residual air
c. complementary air
D. None of the above


Two batteries, one of emf 18 volts and
internal resistance \( 2 \Omega \) and the other of emf 12 volt and internal resistance 1\Omega,
are connected as shown.The voltmeter
will record a reading of:
A . 18 volt
B. 30 volt
c. 14 volt
D. 15 volt


Cake does not taste bitter due to
presence of
A. sodium carbonate
B. tartaric acid
c. citric acid
D. sodium bicarbonate


A man is walking on a road with a velocity \( 3 k m / h . \) Suddenly rain starts falling. Velocity of rain is \( 10 \mathrm{km} / \mathrm{h} \) in vertically downward direction. The relative velocity of the rain with respect to man is
A \( \cdot \sqrt{13} k m / h r \)
B. \( \sqrt{7} \mathrm{km} / \mathrm{hr} \)
c. \( \sqrt{109} \mathrm{km} / \mathrm{hr} \)
D. \( 13 \mathrm{km} / \mathrm{hr} \)


Which of the following option is
correctly matched?
\( \mathbf{A} \cdot S_{2} O_{9} ; \) contains no \( S-S \) linkage
B. \( S_{2} O_{6}^{2-} ; \) contains \( O-O \) linkage
\( \mathbf{C} \cdot\left(H P O_{3}\right)_{3} ; \) contains \( P-P \) linkage
D. \( S_{2} O_{6}^{2-} ; \) contains \( S-S \) linkage


Which of the following is a circular mouthed fish?
A. Myxine
B. Torpedo
c. Trygon
D. Scoliodon


\( \mathbf{4}_{\mathbf{1}} \boldsymbol{H}^{\mathbf{1}} \rightarrow_{\mathbf{2}} \boldsymbol{H} \boldsymbol{e}^{\mathbf{4}}+\mathbf{2} \boldsymbol{e}^{+}+\mathbf{2} \mathbf{6} \boldsymbol{M} \boldsymbol{e} \boldsymbol{V} \)
The above reaction represents
A. Fusion
B. Fission
c. \( \beta \) -decay
D. \( \gamma \) -decay


Find the volume of a tetrahedron whose
vertices are
\( \boldsymbol{A}(-1,2,3), B(3,-2,1), C(2,1,3) \) and
\( \boldsymbol{D}(-\mathbf{1},-\mathbf{2}, \mathbf{4}) \)


The two charges \( 7 \mu C \) and \( -2 \mu C \) are
separated by a distance of \( 18 \mathrm{cm} . \) The work required by you to separate the two charges infinitely away from each other is:
A . 0.7
B . -0.7 J
c. 1.4
D . -1. 4 J


The order and degree of the differential
equation of all parabola whose axis is \( x \) axis
\( A \cdot 2, \)
B. 2,
\( c \cdot 1,2 \)
D. 1,1


Which one of the following elements has the highest number of unpaired electrons?
\( \mathbf{A} \cdot_{25} M n \)
в. \( _{24} \mathrm{Cr} \)
\( \mathbf{c} \cdot_{96} C m \)
\( D \cdot 26 F e \)


In the isoelectronic series of metal
carbonyl, the \( C 0 \) bond strength is expected to increase in the order.
\( A \)
\( \left[M n(C O)_{6}\right]^{+}<\left[C r(C O)_{6}\right]<\left[V(C O)_{6}\right] \)
\( ^{\mathrm{B}}\left[V(C O)_{6}\right]^{-}<\left[C r(C O)_{6}\right]<\left[M n(C O)_{6}\right]^{+} \)
c. \( \left[V(C O)_{6}\right]^{-}<\left[M n(C O)_{6}\right]^{+}<\left[C r(C O)_{6}\right] \)
D. \( \left[C r(C O)_{6}\right]<\left[M n(C O)_{6}\right]^{+}<\left[V(C O)_{6}\right] \)


When \( H I \) is added in excess to
the unsymmetrical ether, it yields:
\( \mathbf{A} \cdot P h C H_{2} O H \)
в. \( P h I \)
c. \( H O C H_{2} C H_{2} P h-N O_{2} \)
D. \( I C H_{2} C H_{2} P h N O_{2} \)


How many one-fourths need to be 1 added to \( 2 \frac{1}{4} \) to make \( 4 ? \)
A . 3
B. 4
c. 5
D.


Arrange the following species according to their bond angle order:
(।) \( \boldsymbol{O}_{3} \)
(II) \( N O_{2}^{-} \)
(IIII) \( \boldsymbol{F} \boldsymbol{N} \boldsymbol{O} \)
A \( I>I I>I I I \)
\( I \)
В. \( I I>I>I I I \)
c. \( I I I>I I>I \)
D. \( I I>I I I>I \)


Which one of the following is correct?
A. Chlorides of both beryllium and aluminium have bridged chloride structures in solid phase
B. \( B_{2} H_{6} .2 N H_{3} \) is known as inorganic benzene
C. Boric acid is a protonic acid
D. Beryllium exhibits coordination number of six


In what ratio, the line joining (-1,1) and (5,7) is divided by the line \( x+y= \)
\( 4 ? \)


Which solution would have the most
altered boiling point?
A \( \cdot 1 M L i_{2} S O_{4} \)
в. \( 1 \mathrm{M} \mathrm{CuSO}_{4} \)
\( \mathrm{c} \cdot 1 \mathrm{M} C_{6} \mathrm{H}_{12} \mathrm{O}_{6} \)
D. 1 \( M \) NaCl


The value of \( \frac{1-\tan ^{2} 15}{1+\tan ^{2} 15} \) is
\( A \cdot 1 \)
B. \( \sqrt{3} \)
\( c \cdot \frac{\sqrt{3}}{2} \)
D.


is the anhydride of
\( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{3} \)
\( A \cdot S O_{2} \)
в. \( S O_{3} \)
c. \( H_{2} \) s
D. None of the above


During growth period, many adolescence get excessive growth,
resulting in to a symmetrically giant body. Why it happens so?


Aerobic cellular respiration has three
stages, and


The work done in the isothermal
reversible expansion of argon gas at
\( 27^{\circ} \mathrm{C} \) from \( 4.1 L \) to \( 16.1 L \) was equal to
4200 cal. What is the amount of argon
subjected to such an expansion?
\( \boldsymbol{A r}=\mathbf{4 0}, \ln \mathbf{4}=\mathbf{1 . 4}) \)
A \( .5 .0 g \)
в. \( 20.0 g \)
c. \( 200.0 g \)
D. \( 48.1 g \)


Find the least value of \( n \) for which
\( \left(\frac{1+i}{1-i}\right)^{n}=1 \)
This question has multiple correct options
A .4
B. 3
\( c .-4 \)
D.


To define probability disribution function we assign to each variable
A. the respective probabilities
B. the specific random values
c. some integers
D. none


Explain the reaction of the following
with ozone-
\( C_{2} H_{4} \)
\( K I \)
\( H g \)
\( P b S O_{4} \)


Two points \( A \) and \( B \) with coordinates (1,1) and (-2,3) respectively are given Find the locus of a point \( \boldsymbol{P} \) so that the
area of \( \triangle \boldsymbol{P A B} \) is \( \mathbf{9} \) sq.units.
A. \( 2 x-3 y-13=0 \)
B. \( 2 x+3 y-13=0 \)
c. \( 5 x-3 y-13=0 \)
D. \( 5 x+3 y-13=0 \)


The number of gram molecules of oxygen in \( 6.02 \times 10^{24} C O \) molecules is :
A. 10 gram molecules
B. 5 gram molecules
c. 1 gram molecules
D. 0.5 gram molecules


What weight of the non-volatile solute
urea \( \left(N H_{2}-C O-N H_{2}\right) \) needs to be
dissolved in 100 g of water by \( 25 \% \) ? (in \( g m) \)


The resultant of two forces \( 3 P \) and \( 2 P \) is
R. If the first force is doubled then the
resultant is also doubled. The angle
between the two forces is
A . \( 60^{\circ} \)
B. \( 120^{\circ} \)
\( c \cdot 30 \)
D. \( 135^{\circ} \)


In an isosceles trapezium, the length of the parallel sides, and the lengths of the non-parallel sides are all equal to \( 30 . \) In order to maximize the area of the
trapezium, the smallest angle should
be
\( A \cdot \frac{\pi}{6} \)
B.
\( c \cdot \frac{\pi}{3} \)
D.


Prove that one of every three
consecutive positive integer is divisible by 3


Two oxides of lead were separately reduced to metallic lead by heating in a current of, hydrogen and the following data obtained:
i) Mass of yellow oxide taken \( =3.45 g \)
Loss in mass during reduction \( =\mathbf{0 . 2 4 g} \)
ii) Mass of brown oxide taken \( =1.227 g \)
Loss in mass during reduction \( =\mathbf{0 . 1 6} \boldsymbol{g} \)
Show that the above data illustrate the
Law of Multiple Proportions.


What is the current through the resistor
\( 6 \Omega \) in the circuit shown in figure.
A . \( 10 / 3 \) A
B. \( 5 / 2 \) A
\( c \cdot 5 / 3 A \)
\( D \cdot 1 / 4 A \)


If \( a, b, c, d, e \) are five positive numbers
then
This question has multiple correct options
\( ^{\mathbf{A}} \cdot\left(\frac{a}{b}+\frac{b}{c}\right)\left(\frac{c}{d}+\frac{d}{e}\right) \geq 4 \cdot \sqrt{\frac{a}{e}} \)
B \( \cdot\left(\frac{a}{b}+\frac{c}{d}\right)\left(\frac{b}{c}+\frac{d}{e}\right) \geq 4 \cdot \sqrt{\frac{a}{e}} \)
c. \( \frac{a}{b}+\frac{b}{c}+\frac{c}{d}+\frac{d}{e}+\frac{e}{a} \geq 5 \)
D. \( \frac{b}{a}+\frac{c}{b}+\frac{d}{c}+\frac{e}{d}+\frac{a}{e} \geq \frac{1}{5} \)


Calculate the value of the following
determinant:
\( \left|\begin{array}{cccc}\mathbf{1}+\boldsymbol{a} & \mathbf{1} & \mathbf{1} & \mathbf{1} \\ \mathbf{1} & \mathbf{1}+\boldsymbol{b} & \mathbf{1} & \mathbf{1} \\ \mathbf{1} & \mathbf{1} & \mathbf{1}+\boldsymbol{c} & \mathbf{1} \\ \mathbf{1} & \mathbf{1} & \mathbf{1} & \mathbf{1}+\boldsymbol{d}\end{array}\right| \)


\( A B C \) is a triangle in which \( \angle B=2 \angle C . D \)
is a point on BC such that AD bisects \( \angle B A C \) and \( A B=C D . \) Find \( \angle B A C \)
A \( .72^{\circ} \)
\( ^{0} \)
B. \( 36^{\circ} \)
\( c \cdot 108^{\circ} \)
D. \( 90^{\circ} \)


The respiratory centre leading to faster breathing is on account of
A. Venous blood entering the respiratory centre
B. Arterial blood entering respiratory
c. Venous blood leaving the respiratory centre
D. Arterial blood leaving the respiratory centre


In case of a fire, before the fireman use
the water hoses, they shut off the main
electrical supply for the area. Explain why they do this.


A man is stranded in the middle of a
perfectly smooth island of ice, where there is no friction between the ground
and his feet. Under these
circumstances,
A. he can reach the desired corner by throwing any object in the same direction
B. he can reach the desired corner by throwing any object in the opposite direction
C. he has no chance of reaching any corner of the island
D. he can reach the desired corner by walking on the ground in that direction


A right circular cylinder just encloses a sphere of radius \( r \). Find ratio of the area
obtained in surface area of the sphere and curves surface area of the cylinder.


What will be the products in following
reactions?
\( (\mathbf{I}) \)
\( (\mathbf{I I}) \)
\( (\mathbf{I I I}) \)
\( A \)
B.
\( c \)
D. None


An object is allowed to roll down an inclined plane starting from rest (consider the object to be uniform and having same mass) then object having largest speed at the bottom of ground,
A. solid sphere
B. spherical sphere
c. solid disk
D. thin cylinder


An object is kept at \( 60 \mathrm{cm} \) in front of a plane mirror. If the mirror is now moved
\( 25 \mathrm{cm} \) away from the object, how is the image shifted from its previous position?
A . \( 25 \mathrm{cm} \) away
B. \( 25 \mathrm{cm} \) towards
c. \( 50 \mathrm{cm} \) away
D. \( 50 \mathrm{cm} \) towards


Assertion
A solution of sucrose in water is
dextrortatory while on hydrolysis in pressence of little hydrochloric acid, it becomes laveorotatory
Reason
Sucrose on hydrolysis gives unequal amounts of glucose and fructose as a result of which change in sign of
rotation is observed.
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 a heat engine?


Which of the following pair has the
same size?
\( \mathbf{A} \cdot \mathrm{Fe}^{2+}, \mathrm{Ni}^{2+} \)
B. \( z r^{4+}, \) Ti \( ^{4+} \)
\( \mathbf{c} \cdot z r^{4+}, H f^{4+} \)
\( \mathbf{D} \cdot \mathbf{z} \mathbf{n}^{2+}, \mathbf{H} \mathbf{f}^{4} \)


The decreasing order of boiling points of ethyldimethylamine, n- butylamine and diethylamine is \( n- \) Butylamine \( > \) Diethylamine > Ethyldimethylamine. This trend of the boiling point can be explained as:
A. boiling point increases with increase in molecular mass
B. tertiary amines have highest boiling point due to highest basicity
c. intermolecular hydrogen bonding is maximum in primary amines and absent in tertiary amines
D. intramolecular hydrogen bonding is present in tertiary amines


Assertion
If a charged particle is released from rest in a region of uniform electric and magnetic fields parallel to each other, it will move in straight line.
Reason
The electric field exerts no force on the
particle but the magnetic field does.
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 ring of hygroscopic teeth around the mouth of dehiscent capsule in mosses
is called as
A. Peristome
B. Annulus
c. Apophysis
D. Trabeculae


The purpose of stream of air in leaching
process of \( A g_{2} S \) is to?
A. Oxidises \( N a_{2} S \) formed into \( N a_{2} S_{2} O_{3} \)
B. Oxidises \( N a_{2} S \) formed into \( N a_{2} S_{2} O_{4} \)
c. oxidises \( N a_{2} S \) formed into \( N a_{2} O \)
D. Act as catalyst


State whether true or false:
The metal used in construction of a
bridge should have high Young's modulus.
A. True
B. False


A first order reaction takes 69.3
minutes for \( 50 \% \) completion. How much time will be needed for \( 80 \% \)
completion?


Consider two concentric spherical
metal shells of radii \( r_{1} \) and \( r_{2}\left(r_{2}>r_{1}\right) \)
If the outer shell has a charge q and the inner one is grounded, the charge on the
inner shell is :
A \( \cdot \frac{-r_{2}}{r_{1}} q \)
B. Zero
c. \( \frac{-r_{1}}{r_{2}} q \)
D. \( -q \)


The given rod is uniform and has a
mass m. Find the tension in the string.
A \( \cdot \frac{(m g \sin \theta)}{2} \)
B. \( \frac{m g \sin }{2} \)
c. \( \frac{(m g \cos \theta)}{2} \)
D. \( \frac{m g}{2} \)
E . \( m \)


a) Which types of an emulsion is 'vanishing cream'. Write its appropriate name
b) Draw neat and labelled diagram of above emulsion.


A salt derived from strong acid and
weak base will dissolve in water to give a solution which is:
A . acidic
B. basic
c. neutral
D. none of these


State whether true or false.
Rotation of moon around the earth is a
periodic motion.
A. True
B. False


A body throws a ball to his friend \( 20 m \)
away. The ball reaches to the friend in
4s. The friend then throws the ball back
to boy and it reaches the boy in \( 5 s \)
A . The average velocity is \( \frac{40}{9} \mathrm{ms}^{-1} \)
B. The average acceleration is zero
c. The average velocity is zero but average acceleration
is non zero
D. Average acceleration of the motion cannot be defined


Significant motion for the molecules of a monoatomic gas corresponds to :
A. translatory
B. vibratory
c. rotatory
D. none of these


Three forces are applied to a square
plate as shown in figure:

Find the point of application of the
resultant force, if this point is taken on
the side \( B C \)
A. The force is applied at the midpoint of the side \( B C \).
B. At point B
C. At point \( c \)
D. cannot be found


A player throws a ball which reaches the
other players in 4 sec.If the height of each player is \( 1.8 m . \) The maximum
height attained by the ball above the ground is \( -\ldots-\ldots \)
A . 19.4
B. 20.4
c. 21.4
D. 22.4


It is dangerous to cut a piece of yellow phosphorus in air. This is because:
A. it is poisonous
B. it gives off fumes
c. it may catch fire
D. it explodes in contact with air


In the adjacent rectangle
\( A B C D, \angle O C D=30^{\circ} . \) Calculate
\( \angle B O C . \) What type of triangle is \( B O C ? \)


Which of the following cannot be used as reagent (B) ?
A \( \cdot C H_{3} O \ominus \) at high temperature
B. \( C_{2} H_{5} O^{\ominus} \) at high temperature
\( c \)
at high temperature
D. \( C s O H+C_{2} H_{5} O H \)


n given Figure, \( D E \| B C . \) If \( A D= \)
\( \boldsymbol{x}, \boldsymbol{D} \boldsymbol{B}=\boldsymbol{x}-\boldsymbol{2}, \boldsymbol{A} \boldsymbol{E}=\boldsymbol{x}+\boldsymbol{2} \) and \( \boldsymbol{E} \boldsymbol{C}= \)
\( x-1, \) find the value of \( x \)


Assertion
The experimentally determined \( N-F \)
bond length in \( N F_{3} \) is greater than the
sum of the single bond covalent bond
radii of \( N \) and \( F \)
Reason
\( N \) and \( F \) both have high electron
density due to smaller atomic radii.
Thus, \( l p-b p \) repulsion increases bond-
length.
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.t


During the fusion of the male and female gametes, the male chromosome Y fused with the X chromosome of the
female. The offspring born will be
A. Boy
B. Girl
c. Twins
D. None of these


A boy playing on the roof of a \( 10 \mathrm{m} \) high building throws a ball with a speed of \( 10 m s^{-1} \) at an angle of \( 30^{\circ} \) with the horizontal. How far from the throwing point with the ball be at the height of 10 \( \mathrm{m} \) from the ground? \( (\boldsymbol{g}= \) \( 10 m s^{-2}, \sin 30^{\circ}=1 / 2, \cos 30^{\circ}= \)


For the half cell \( E^{o}=1.30 V . \) At \( p H=3 \)
electrode potential is:
A . \( 1.30 V \)
B. \( 1.20 V \)
c. \( 1.10 V \)
D . \( 1.48 V \)


If in an \( A . P . \) the sum of \( m \) terms is
equal to \( n \) and the sum of \( n \) terms is
equal to \( m, \) then prove that sum of
\( (m+n) \) terms is \( -(m+n) \)


Verify the \( \boldsymbol{A P}: \sqrt{\mathbf{3}}, \mathbf{2} \sqrt{\mathbf{3}}, \mathbf{3} \sqrt{\mathbf{3}}, \ldots \) and
find the product of the next two terms:


Which transition emits photon of
maximum frequency?
A. 2 nd spectral line of Balmer series
B. 2nd spectral line of Paschen series
C. 5 th spectral line of Humphery series
D. 1 st spectral line of Lyman series


Organic water pollutants is/are:
\( A \). ammonia
B. chloroform
c. fertilizers
D. all of above


If expressions for the magnetic field at a point due to a current element, in
C.G.S.system is given by \( \overrightarrow{d B}=\frac{\mu_{0}}{4 \pi} \frac{i(d \overrightarrow{d \times \vec{r}})}{a * r^{3}} \)
Find a.


The correct lists of the phylogenic
hierarchy is
A. Domain, kingdom, phylum, family, class, order, genus, species
B. Phylum, family, order, domain, class, kingdom, species, genus
C. Kingdom, domain, family, order, class, phylum, genus, species
D. Domain, kingdom, phylum, class, order, family, genus, species
E. Family, kingdom, order, domain, phylum, genus, class, species


A superconductor exhibits perfect:
A. ferrimagnetism
B. ferromagnetis
c. paramagnetism
D. diamagnetism


A square and a regular hexagon have the same perimeter. If the area of the
square is \( 2.25, \) calculate the area of the
hexagon.
A. 2.250
B. 2.598
c. 2.838
D. 3.464
E . 3.375


puric ouurce ungill I is placeu ac
distance \( L \) in front of the center of a
mirror of width \( d \) hung vertically on a
wall. A man walks in front of the mirror
along a line parallel to the mirror at a
distance \( 2 L \) from it as shown in Fig. the
greatest distance over which he can see
the image of the light source in the
mirror is
A \( \cdot \frac{d}{2} \)
B. \( d \)
c. \( 2 d \)
D. \( 3 d \)


Each year for 4 years, a farmer increased the number of trees in a certain orchard by \( \frac{1}{4} \) of the number of trees in the orchard the preceding year.
If all of the trees thrived and there were
6,250 trees in the orchard at the end of
the 4 -year period, how many trees were in the orchard at the beginning of the 4 year period?
A . 1250
B. 1563
\( \mathbf{c} .2250 \)
D. 2560
E . 2752


Which person had convinced people that matter could be divided forever?
A. Dalton
B. Democritus
c. Thomson
D. Aristotle
E. Rutherford


A filled shopping cart \( (30.0 k g) \) is being pushed rapidly toward the back of a store so that its velocity is \( -2.0 m / s \) What is the momentum of the cart, and
what is the kinetic energy of the cart??
A. Momentum \( 60.0(k g)(m) / s \), Kinetic energy \( 60.0 J \)
B. Momentum \( -60.0(k g)(m) / s \), Kinetic energy 60.05
c. Momentum \( 60.0(k g)(m) / s \), Kinetic energy -60.0 .
D. Momentum \( -60.0(k g)(m) / s \), Kinetic energy \( -60.0 J \)
E. Momentum \( 60.0(k g)(m) / s, \) Kinetic energy \( 120.0 J \)


Acidified water is electrolysed by using carbon electrodes. What is produced at positive carbon electrode?


Which of the following ratios does not change in DNA?
A. Cytosine:Adenine
B. Pyrimidine: Purine
c. Adenine : Guanine
D. Guanine: Deoxyribose
E. Thymine : Guanine


Assertion: For every chemical reaction
at equilibrium, the standard Gibbs energy of reaction is zero.
Reason: At constant temperature and pressure, chemical reactions are
spontaneous in the direction of decreasing Gibbs energy.
A. The Assertion is True, Reason is True; Reason is the correct explanation for Assertion
B. The Assertion is True, Reason is True; Reason is NOT a correct explanation for Assertion
c. The Assertion is True, Reason is False
D. The Assertion is False, Reason is True


Division of cells and tissues is an
important factor for establishing a multicellularity in an organism.
A. True
B. False


Fill in the blanks by choosing the appropriate word/words from those given in the brackets:
(square pyramidal, electrical, 74, 26, \( s p^{3} d^{2}, s p^{3} d, \) chemical, 68,32
tetrahedral, yellow, white, iodoform, Lucas).
A Galvanic cell converts
energy into


How many plant and animal types do exist on earth?


The given figure shows an actin (thin) filament. Identify the labelled parts \( A, B \) and \( C . \) and select the correct option.
A. A - Tropomyosin B - Troponin C - F-actin
B. A - Troponin B - Myosin C - Tropomyosin
c. A - Troponin B - Tropomyosin C - Myosin
D. A - Troponin B - Tropomyosin C - F-actin


Average torque on a projectile of mass
\( m, \) initial speed \( u \) and angle of
projection \( \theta \) between initial and final positions \( \mathrm{P} \) and \( \mathrm{Q} \) as shown in the figure about the point of projection is:
A \( \cdot \frac{m u^{2} \sin 2 \theta}{2} \)
в. \( m u^{2} \cos \theta \)
c. \( \mu^{2} \sin \theta \)
D. \( \frac{m u^{2} \cos \theta}{2} \)


If \( f(x) \) is a polynomial in \( x(>0) \)
satisfying the equation \( \boldsymbol{f}(\boldsymbol{x})+ \) \( f\left(\frac{1}{x}\right)=f(x) \cdot f\left(\frac{1}{x}\right) \) and \( f(2)=-7 \)
then \( f(3) \) is equal to
A . -26
в. -27
c. -28
D. -29


The white dwarf star mainly consists of
A. neutrons only
B. protons only
c. electrons only
D. protons and electrons


Which of the following options is correct
for the object having a straight line
motion represented by the graph shown
in figure?
A. The object moves with constantly increasing velocity from 0 to \( A \) and then it moves with constant velocity
B. Velocity of the object increases uniformly
c. Average velocity is zero.
D. The graph shown is impossible


If \( \boldsymbol{A}=\left[\begin{array}{cc}2 & 0 \\ 5 & -3\end{array}\right] \) and \( B=\left[\begin{array}{cc}-2 & 1 \\ 3 & -1\end{array}\right] \)
then find the trace of \( \left(A B^{T}\right)^{T} \)


The correct sequence in the evolution of
modern man is
A. Dryopithecus \( \rightarrow \) Australopithecus \( \rightarrow \) Homo habilis \( \rightarrow \) Homo erectus \( \rightarrow \) Homo sapiens
B. Australopithecus \( \rightarrow \) Dryopithecus \( \rightarrow \) Homo habilis \( \rightarrow \) Homo erectus \( \rightarrow \) Homo sapiens
C. Homo habilis \( \rightarrow \) Dryopithecus \( \rightarrow \) Australopithecus \( \rightarrow \) Homo erectus \( \rightarrow \) Homo sapiens
D. Austratopithecus \( \rightarrow \) Homoerectus \( \rightarrow \) Neanderthal man \( \rightarrow \) cro-magnon man \( \rightarrow \) modern man


A sphere of radius \( R \) is submerged in
water completely, what force should be
imparted to the sphere, so that every point in it experiences a constant volume stress
A. Force should be proportional to \( R \)
B. Force should be proportional to \( 1 / R \)
C. Force should be proportional to \( R^{2} \)
D. Force should be proportional to \( 1 / R^{2} \)


Given, \( \boldsymbol{A}=\{\text { Quadrilaterals }\}, \boldsymbol{B}=\{ \)
Rectangles \( \}, C=\{\text { Squares }\}, D=\{ \) Rhombuses \( \} . \) State whether the
following statement is correct or
incorrect. Give reasons.
\( \boldsymbol{D} \subset \boldsymbol{A} \)


Identify the substance oxidised, reduced, oxidising agent and reducing
agent for each of the following reactions
\( \boldsymbol{P b}_{(s)}+\boldsymbol{P b O}_{2(s)}+\mathbf{2 H}_{2} \boldsymbol{S O}_{4(a q)} \rightarrow \)
\( 2 P b S O_{4(s)}+2 H_{2} O_{(l)} \)


Excessive growth of planktonic algae in nutrient rich water is known as
A. Eutrophication
B. Stratification
c. Guttation
D. None of the above


If the masses of deuterium and that of
helium are 2.0140 amu and 4.0026
amu, respectively and that \( 22.4 \mathrm{MeV} \) energy is liberated in the reaction
\( _{6}^{3} L i+_{1}^{2} H \rightarrow_{2}^{4} H+_{2}^{4} H e, \) has the mass
of \( _{3}^{6} L i \) is
A . 6.015 amu
B. 6.068 amu
c. 5.980 amu
D. 6.00 amu


Consider the following statements and arrange in the order of true/false as given in the codes.
\( S_{1}: \) Sodium amalgam reacts with hot water and produces sodium hydroxide and hydrogen gas.
\( S_{2}: \) Sodium is more reactive than
potassium.
\( S_{3}: \) Alkaline earth metals dissolve in liquid ammonia to give deep blue-black solutions which are conducting.
\( S_{4}: \) Alkaline earth metal salts have
more number of water molecules as
compared to those of alkali metal salts.
A. TTFF
в. тFा
c. FTT
D. TFFT


If \( y=\frac{\sin x+\cos x}{\sin x-\cos x} \) find \( \frac{d y}{d x} \)


A uniform rod of mass \( 6 M \) and length
\( 6 l \) is bent to make an equilateral
hexagon. Its mutual inductance about an axis passing through the centre of mass and perpendicular to the plane of hexagon is
\( A \cdot 5 m l^{2} \)
В \( .6 m l^{2} \)
\( \mathrm{c} \cdot 4 m l^{2} \)
\( \mathbf{D} \cdot 12 m l^{2} \)


In the following circuit, the potential of
source is \( \boldsymbol{E}_{\mathbf{0}}=\mathbf{2 0 0} \) volts, \( \boldsymbol{R}=\mathbf{2 0 0 \Omega} \)
\( \boldsymbol{L}=\mathbf{0 . 1} \) henry, \( \boldsymbol{C}=\mathbf{1 0 . 6} \) farad and
frequency is variable, then the current
at \( f=0 \) and \( f=\infty \) is :
A. \( 0 A, 10 A \)
B. 10A, OA
C. \( 10 A, \) 10A
D. OA, OA


If \( A \) and \( B \) are invertible matrices, which
one of the following statement is/are
correct
This question has multiple correct options
A \( . A d j(A)=|A| A^{-1} \)
B. \( \operatorname{det}\left(A^{-1}\right)=|\operatorname{det}(A)|^{-1} \)
c. \( (A+B)^{-1}=B^{-1}+A^{-1} \)
D. \( (A B)^{-1}=B^{-1} A^{-1} \)


If \( e^{x}+e^{y}=e^{x+y}, \) find \( \frac{d y}{d x} \)


Let \( \boldsymbol{f}:(\boldsymbol{0}, \infty) \rightarrow \boldsymbol{R} \) and \( \boldsymbol{g}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) be
defined by \( f(x)=\sqrt{x} \) and \( g(x)=x \) Find \( \boldsymbol{f}+\boldsymbol{g}, \boldsymbol{f}-\boldsymbol{g}, \boldsymbol{f} \boldsymbol{g} \) and \( \frac{\boldsymbol{f}}{\boldsymbol{g}} \)


In which of the following organ of man, Entamoeba histolytica is found?
A. Rectum
B. Oral cavity
c. Stomach
D. Intestine


Which amongst the following has a polar covalent bond?
A. \( N a C l \)
в. \( N H_{3} \)
\( c \cdot O_{2} \)
D. \( C a O \)


The number of significant figures in
\( N_{0}=6.022 \times 10^{23} \) i.e., Avogadro's
number, is :
\( A \). three
B. four
c. twenty six
D. twenty seven


If the object placed at a principal focus
\( F_{1} \) of a convex lens, the ray diagram for the image formation.


The diameter of a wire as measured by
screw gauge was found to be
2.620,2.625,2.628 and \( 2.626 \mathrm{cm} \)
Calculate fractional error.


The height from earth's surface at
which acceleration due to gravity becomes \( \frac{g}{4} \) is (where \( g \) is acceleration due to gravity on the surface of earth and \( R \) is radius of earth)
A \( \cdot \sqrt{2} R \)
в. \( R \)
c. \( \frac{R}{\sqrt{2}} \)
D. 2R


Assertion
All pathogens are parasites but all parasites are not pathogens.
Reason
Majority of the parasites confer benefits
to the host.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion,
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


If \( 2^{x}-2^{y}=2^{x+y} \) then \( \frac{d y}{d x}= \)
\( \mathbf{A} \cdot 2^{y-x} \)
B . \( 2^{y / x} \)
\( \mathbf{c} \cdot-2^{y / x} \)
D. \( 2^{x / y} \)


Fill in the blanks with appropriate
words from the bracket: Covalent
compounds are formed by sharing electrons pairs between non-metallic atoms. Non-metallic atoms having valence electrons [4,5,6,7] share
one, two or three pairs of electrons
respectively.


Find the perpendicular distance from
\( \boldsymbol{A}(\mathbf{1}, \mathbf{0}, \mathbf{3}) \) to the line \( \overrightarrow{\boldsymbol{r}}=(\mathbf{4}, \mathbf{7}, \mathbf{1})+ \)
\( k(1,2,-2), k \in R . \) Also find the foot of
the perpendicular.


Masses of three wires of the same
metal are in the ratio 1: 2: 3 and their
lengths in the ratio \( 3: 2: 1 . \) Electrical
resistances of these wires will be in the
ratio
A. 1: 2: 3
B. 3: 2: 1
c. 1: 6: 27
D. 27: 6: 1


A function \( \boldsymbol{f}:(-\mathbf{3}, \mathbf{7}) \rightarrow \boldsymbol{R} \) is defined as
follows:
\( f(x)=\left\{\begin{array}{cc}4 x^{2}-1 ; & -3 \leq x<2 \\ 3 x-2 ; & 2 \leq x \leq 4 \\ 2 x-3 ; & 4<x \leq 6\end{array}\right. \)
Find:
\( \boldsymbol{f}(\mathbf{1})-\boldsymbol{f}(-\boldsymbol{3}) \)


Chemical equation of the industrial
preparation of \( \boldsymbol{S} \boldsymbol{O}_{3} \) is given?
\( 2 S O_{2}+O_{2} \rightleftharpoons 2 S O_{3}+ \) Heat
What is the influence of the following factors in this system at equilibrium?
(a) Increasing the amount of \( \boldsymbol{O}_{2} \)
(b) \( S O_{2} \) is removed from the system.
(c) Decreasing the temperature.


Consider the given compound and
arrange \( X, Y, Z \) in order of increasing
acid strengths?
\( A \cdot X>Z>Y \)
B. \( Z>X>Y \)
\( c \cdot x>Y>z \)
\( D \cdot Y>X>Z \)


The reaction \( \boldsymbol{C}_{12} \boldsymbol{H}_{26} \rightarrow \boldsymbol{C}_{6} \boldsymbol{H}_{12}+ \)
\( C_{6} H_{14} \) represents :
A. Substitution
B. synthesis
c. cracking
D. Addition.


Let \( A \) and \( B \) be two events such that
\( \boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B})=\boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B}) . \) Then
Statement \( 1: P(A \cap \bar{B})=P(\bar{A} \cap B)= \)
0
Statement 2: If \( \boldsymbol{P}(\boldsymbol{A})+\boldsymbol{P}(\boldsymbol{B})=\mathbf{1} \)
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


Find the area bounded by the ellipse \( \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 \) and the ordinates \( x=0 \)
and \( x=a e, \) where \( b^{2}=a^{2}\left(1-e^{2}\right) \) and
\( e<1 \)


Differentiate between half life and
average life of a radioactive substance.


\( K_{C} \) for \( N_{2}+O_{2} \rightleftharpoons 2 N O \) at certain
temperature is \( 1.6 \times 10^{-3}, \) then \( K_{P} \) for
\( N O \rightleftharpoons 1 / 2 N_{2}+1 / 2 O_{2} \) at same
temperature will be:
A. \( 2 \times 10^{-2} \)
B . 25
\( c .5 \)
D. \( 1.6 \times 10^{-3} \)


A moving coil galvanometer has a coil with 175 turns and area \( 1 \mathrm{cm}^{2} \). It uses a
torsion band of torsion constant \( 10^{-6} \mathrm{N} \)
\( \mathrm{m} / \mathrm{rad} . \) The coil is placed in a magnetic field B parallel to its plane. The coil
deflects by \( 1^{\circ} \) for a current of \( 1 \mathrm{mA} \). The value of \( \mathrm{B}(\text { in } \text { Telsa }) \) is approximately.
A \( \cdot 10^{-3} \)
B . \( 10^{-1} \)
\( c \cdot 10^{-4} \)
D. \( 10^{-2} \)


Assertion
Reaction of liquor ammonia with nitric acid is a neutralization reaction.
Reason
Ammonia in the gaseous form or in
aqueous solution as ammonium
hydroxide neutralizes the nitric acid
forming the respective ammonium
salts.
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


Differentiate:
\( \sin ^{2} \boldsymbol{y}+\cos \boldsymbol{x} \boldsymbol{y}=\boldsymbol{K} \)


Find the area of the circle whose centre
is (-3,2) and (2,5) is a point on the circle.


The value of the function
\( \lim _{x \rightarrow 0} \frac{8}{x^{8}}\left(1-\cos \frac{x^{2}}{2}-\cos \frac{x^{2}}{4}+\cos \frac{x^{2}}{2}\right. \)
is
A \( \cdot \frac{1}{16} \)
B. \( \frac{1}{15} \)
c. \( \frac{1}{32} \)
\( D \)


If \( n \) identical water droplets falling under gravity with terminal velocity coalesce to form a single drop which has the terminal velocity \( 4 v \), find the
number n.


Force responsible for exudation of liquid
drops from the margin of the leaves is
A. Negative hydrostatic
B. Transpiration pull
c. Imbibition
D. Positive pressure


Differentiate between
external respiration and internal
respiration.


In figure, write another name for \( \angle 1 \)


A ball is dropped on to a horizontal plate from a height \( h=9 \mathrm{m} \) above it. If the
coefficient of restitution is \( e=1 / 2, \) the
total distance travelled before the ball
comes to rest is
A . \( 10 \mathrm{m} \)
B. 15 \( m \)
\( c \cdot 20 m \)
D. 25 m


Find the inverse of the following \( \operatorname{matrices} \boldsymbol{A}=\left(\begin{array}{ccc}\mathbf{2} & \mathbf{1} & \mathbf{3} \\ \mathbf{5} & \mathbf{3} & \mathbf{1} \\ \mathbf{3} & \mathbf{2} & \mathbf{3}\end{array}\right) \)


If \( A \) has 3 elements and \( B \) has 5
elements then \( A \times B \) has
elements.


Potassium on exposure to air gives:
This question has multiple correct options
A. Potassium peroxide
B. Potassium superoxide
c. Potassium dioxide
D. Potassium oxide


A convex lens of focal length \( \boldsymbol{f} \) is cut
into two halves as shown. Light rays
parallel to the principal axis
are incident on one half of the lens (say
\( \boldsymbol{L}_{1} \) ). This will form an image at :
\( A \cdot f \)
B. \( \frac{f}{2} \)
c. \( 2 f \)
D. \( \frac{f}{4} \)


f \( x+y=10 \), then the maximum value
of \( x y \) is
\( \mathbf{A} \cdot \mathbf{5} \)
B. 20
c. 25
D. None of these


if \( f(x)=\log _{x}(\ln x), \) then find \( f^{\prime}(x) \) at
\( x=e . \) Here in \( x \) means natural
logarithm of \( x, \) i.e. \( \log _{e} x \)
\( A \)
в. \( -e \)
\( c \cdot \frac{1}{e} \)
D. \( -\frac{1}{e} \)


In the Searle's method to determine the
Young's modulus of a wire, a steel wire of length \( 156 c m \) and diameter
\( 0.054 \mathrm{cm} \) is taken as experimental wire the average increase in length for 1.5 \( k g w t \) is found to be \( 0.050 c m \). then
the Ypung's modulus of the wire is
A \( .3 .002 \times 10^{11} N / m^{2} \)
В. \( 1.002 \times 10^{11} N / m^{2} \)
c. \( 2.002 \times 10^{11} N / m^{2} \)
D. \( 2.5 \times 10^{11} N / m^{2} \)


Draw the molecular orbital diagram of dioxygen and calculate bond order.


Draw the Lewis dot structure of the
following.
\( \boldsymbol{C O}_{3}^{2-}, \boldsymbol{H C l O}_{4}, \boldsymbol{H} \boldsymbol{N O}_{3} \)


\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{C H C l}_{2}+ \)
\( N a N H_{2} / N H_{3} \rightarrow \)
How many \( s p \) hybridized carbon atoms are present in the product.


5
5
5


If \( 60 \% \) of a first order reaction was
completed in 60 min then half life period is ?


The value of
\( \sin ^{-1}\left[\cot \left(\sin ^{-1} \sqrt{\left(\frac{2-\sqrt{3}}{4}\right)}\right)+\cos ^{-1}\right. \)
is
A . 0
в. \( \frac{\pi}{4} \)
\( c \cdot \frac{\pi}{6} \)
D. \( \frac{\pi}{2} \)


If \( \frac{3 \pi}{4}<\alpha<\pi, \) then \( \sqrt{2 \cot \alpha+\frac{1}{\sin ^{2} \alpha}} \)
is equal to
A. \( 1-\cot \alpha \)
B. \( 1+\cot \alpha \)
c. \( -1+\cot \alpha \)
D. \( -1-\cot \alpha \)


What type of conductor should we used to make water pipes in cold countries?
A. Good conductor
B. Poor conductor or bad conductor
C. Material does not help in such cases
D. None of the above


The relation "is congruent to" on the set of all triangles in a plane is
A. Reflexive only
B. Symmetric only
C. Transitive only
D. Equivalence only


In the given reaction, \( \boldsymbol{K}_{2} \boldsymbol{C r}_{2} \boldsymbol{O}_{7}+ \)
\( \boldsymbol{X} \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4}+\boldsymbol{Y} \boldsymbol{S} \boldsymbol{O}_{2} \rightarrow \boldsymbol{K}_{2} \boldsymbol{S} \boldsymbol{O}_{4}+ \)
\( \boldsymbol{C r}_{2}\left(\boldsymbol{S O}_{4}\right)_{3}+\boldsymbol{Z H}_{2} \boldsymbol{O} . \) Find \( \mathbf{X}, \mathbf{Y} \) and \( \mathbf{Z} \)


A certain sum is to be invested for a
certain time at simple interest at \( 6 \% \)
p.a., such that there is an increase of 24
\( \% \) in the sum. Find the time.
A . 2 years
B. 3 years
c. 4 years
D. 5 years


The numbers representing \( \boldsymbol{A} \cap \boldsymbol{B} \) are


If \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) is defined by \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{2} \boldsymbol{x} \)
\( \mathbf{3} \forall \boldsymbol{x} \boldsymbol{\epsilon} \boldsymbol{R}, \) which of the following is / are
correct?
\( \mathbf{A} \cdot f \) is a function
B. \( f \) is an injection
c. \( f \) is surjection
D. \( f \) is not onto


The distance between the points \( (\mathbf{0}, \mathbf{0}) \) and \( \left(5, \tan ^{-1} \frac{4}{3}\right) \) is
\( \mathbf{A} \cdot \mathbf{3} \)
B. 4
c. 5
D. 7


Prove that the line of centres of two
intersecting circles bisects their common chord.


Which of the following show stable or major form of tautomerism?
This question has multiple correct options
\( A \)
в.
\( c \)
D.


The density of water is maximum at:
A \( \cdot 40^{\circ} \mathrm{C} \)
B . \( 4^{\circ} \mathrm{C} \)
\( \mathrm{c} \cdot 14^{\circ} \mathrm{C} \)
D \( \cdot 24^{\circ} C \)


Ratio of maximum photocurrent which can be passed through the circuit :
\( A \cdot 5 / 4 \)
B. 9/5
\( c \cdot 9 / 4 \)
D. \( 9 / 2 \)


The image of the interval [-1,3] under
the mapping \( f(x)=4 x^{3}-12 x \) is
A. [-2,0]
B. [-8, 72]
c. [-8,0]
D. [-8,-2]


Telescope uses and
microscope uses
A. Two convex lenses, Two Concave lenses
B. One convex lens, One Concave lens
C. Two convex lens, one concave lens
D. Two convex lens, two convex lens


A stone is dropped from the top of a tower. If it hits the ground after 10 seconds, what is the height of the tower?
A. \( 400 \mathrm{m} \)
B. 450m
c. \( 500 \mathrm{m} \)
D. \( 490 \mathrm{m} \)


f \( x+y+z=\pi \) and
\( \Delta=\left|\begin{array}{ccc}\sin 3 x & \sin 3 y & \sin 3 z \\ \sin x & \sin y & \sin z \\ \cos x & \cos y & \cos z\end{array}\right| \)
then \( \Delta \) equals
\( A \)
в.
\( c . \)
\( D \)


Find the selling price when \( \mathrm{C.P}=\boldsymbol{R} \boldsymbol{s} . \boldsymbol{4 5 0}, \) profit \( =\mathbf{1 2 \%} \)


A mixture of three gases \( A, B \) and \( C \) is
passed first into acidified \( \boldsymbol{K}_{2} \boldsymbol{C r}_{2} \boldsymbol{O}_{7} \)
solution when \( A \) is absorbed turning
the solution green. The remainder of the gas is passed through excess of lime water which turns milky resulting in the absorption of \( B \). The residual gas \( C \) is absorbed by alkaline pyrogallol solution. However the original mixture does not turn lead acetate paper black. Identify \( \boldsymbol{A}, \boldsymbol{B} \& \boldsymbol{C} \)
A \( \cdot(A)-S O_{2} \)
\( (B)-C O \)
\( (C)-O_{2} \)
в. \( (A)-S O_{3} \)
\( (B)-C O \)
\( (C)-C O_{2} \)
c. \( (A)-S O_{2} \)
\( (B)-C O_{2} \)
\( (C)-O_{2} \)
D. \( (A)-S O_{2} \)
\( (B)-C O \)
\( (C)-C O_{2} \)


The mass of 3 copper gain is 1:3:5 and length 5: 3: 1 then the resistance?


Which one of the following reagent is useful for separating aniline from nitrobenzene?
A \( . a q . N a H C O_{3} \)
в. \( a q . N a H S O_{3} \)
с. \( a q . H C l \)
D. \( d i l . H_{2} S O_{4} \)


The microelement which is an integral part of electron carrier that transfers
electrons from cyt b-f complex to PS I is also a component of
A. Nitrate reductase
B. Cytochrome c-oxidase
c. IAA-oxidase
D. Dinitrogenase


What are real gases?


Calcium carbonate decomposes into calcium oxide and carbon
dioxide. The reactant is:
A. Carbon dioxide
B. Calcium oxide
c. calcium carbonate
D. None of the these


Identify the correct order of the size of the structures from the smallest to the
largest.
I= Bacterium
II = Enzyme
III= Nucleus
\( \mathrm{IV}= \) Chromosome
\( \mathrm{V}= \) Molecule of water
A. V- II-I-IV-III
c. \( v-1-11-111-1 v \)
E . II-V-IV-III


In structure ATP is similar to
A. DNA (deoxyribonucleotide)
B. RNA(ribonucleotide)
C. Ribonucleoside
D. Deoxyribonucleoside


Hydrogen bomb has been prepared by the fusion of:
This question has multiple correct options
A. Hydrogen
B. Deutrium (heavy hydrogen)
c. Tritium
D. Alpha particles


The concave mirrors are used in
A . reflecting telescope
B. magic-laterns
C. cinema projectors
D. all the above


Select the correct option:Who gave the
lamellar or sandwich model of cell
membrane?
A. singer and Nicolson
B. Danielli and Davson
c. J. Robertson
D. None of these


The number of solutions of the equation
\( \sin x=\cos 3 x \) in \( [0, \pi] \) is
A . 1
B . 2
\( c .3 \)
D.


A car starts from rest, moves with an
acceleration \( a \) and then decelerates at \( b \)
for some time to come to rest. If the
total time taken is \( t, \) the maximum
velocity is
A \( \cdot \frac{a b t}{a+b} \)
B. \( \frac{a^{2}}{a+b} \)
c. \( \frac{a t}{a+b} \)
D. \( \frac{b^{2}}{a+b} \)


The gas which is used for cooking at our home is
A. oxygen
B. Nitrogen
c. L.P.G (liquefied petroleum gas)
D. C.N.G (compressed natural gas)


A car tyre has air at 1.5 atm at 300 K.If \( P \)
increases to 1.75 atm with volume same
the temperature will be
\( A \cdot 350^{0} C \)
в. з5ок
c. \( 300^{\circ} \mathrm{C} \)
D. 300k


An object performing S.H.M. with mass of \( 0.5 k g, \) force constant \( 10 N / m \) and amplitude \( 3 c m . \) What is the speed at \( x=2 ? \)


A body in a laboratory takes 4 minutes
to cool from \( 61^{\circ} \mathrm{C} \) and \( 59^{\circ} \mathrm{C} \). If the
laboratory temperature is \( 30^{\circ} C \) then
the time taken by it to cool from \( 51^{\circ} \mathrm{C} \) to
\( 49^{\circ} C \) will be:
\( A \cdot 8 \min \)
B. 6 min
\( c .5 \mathrm{min} \)
D. 4 min


Prove that: \( \tan \left(11 \frac{1^{\circ}}{4}\right)= \)
\( \sqrt{4+2 \sqrt{2}}-(\sqrt{2}+1) \)


Two dice are thrown. The events \( A, B \)
and \( C \) are as follows:
A : getting an even number on the first die
B : getting an odd number on the first die
C : getting the sum of the numbers on the dice \( \leq 5 \)

State true or false : (give reason for your answer)
(i) \( A \) and \( B \) are mutually exclusive
(ii) \( A \) and \( B \) are mutually exclusive and exhaustive
(iii) \( \boldsymbol{A}=\boldsymbol{B}^{\prime} \)
(iv) \( A \) and \( C \) are mutually exclusive
(v) \( A \) and \( B^{\prime} \) are mutually exclusive
(vi) \( A^{\prime}, B^{\prime}, C \) are mutually exclusive and exhaustive


A body of mass \( 1 k g \) is moving with
velocity \( 30 m s^{-1} \) due north. It is acted on by a force of \( 10 \mathrm{N} \) due west for 4
seconds. Find the velocity of the body after the forces cases to act.
A \( \cdot 50 \mathrm{m} / \mathrm{s} ; \tan ^{-1}\left(\frac{3}{4}\right) \)
в. \( _{100} m / s ; \tan ^{-1}\left(\frac{4}{3}\right) \)
c. \( 50 \mathrm{m} / \mathrm{s} ; \tan ^{-1}\left(\frac{3}{5}\right) \)
D. \( 100 \mathrm{m} / \mathrm{s} ; \tan ^{-1}\left(\frac{4}{5}\right) \)


Considering \( \triangle G=\triangle H-T \triangle S, \) a
spontaneous reaction will occur when :
A. \( \triangle G \) is positive and \( \triangle S \) is positive
B. \( \triangle G \) is positive and \( \triangle S \) is negative
c. \( \triangle H \) is negative and \( \triangle S \) is positive
D. \( \triangle H \) is negative and \( \triangle S \) is negative
E. \( \triangle H \) is positive and \( \triangle T \) is negative


\( H_{2} O_{2} \) is a stronger reducing agent and
a weaker oxidizing agent. If this is true enter 1 , if false enter 0 .


What is the Cartesian sign convention used for spherical mirrors?


A convex lens of focal length \( f_{1} \) is kept
in contact with a concave lens of focal
length \( f_{2} \). Find the focal length of the combination.


Read the bar graph shown in Fig. 23.10
and answer the following question:
State whether true or false:

The number of commercial banks in
1983 is less than double the number of
commercial banks in 1969
A. True
B. False


State Faraday's first law of electrolysis.


Five long wires \( A, B, C, D \) and \( E \) each
carrying I are arranged to form edges of
a pentagonal prism as shown in figure.
Each wire carries current out of the
plane of paper, the magnetic induction at a point on the axis 0 is (axis 0 is at a
distance \( R \text { from each wire }) \) is then
A . equal to zero
B. less than zero
c. more than zero
D. infinite


Assertion
Plastic grocery bags do not block drains during rains.
Reason
Plastics are lighter than water and
hence float over water
Read the above assertion and reason
and choose the correct option regarding
¡t.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Solve the system of inequalities graphically:
\( x-2 y \leq 3,3 x+4 y \geq 12, x \geq 0, y \geq 1 \)


\( \frac{ }{2} \)
8
\( \frac{d}{d} \)
\( d \)


\( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\frac{\boldsymbol{x}+\boldsymbol{y}+\mathbf{1}}{\mathbf{2} \boldsymbol{x}+\mathbf{2} \boldsymbol{y}+\mathbf{3}}, \) its solution is \( \boldsymbol{x}+ \)
\( y+\frac{k}{3}=c e^{3(x-2 y)}, \) what is \( k \)
\( A \)
B. 2
\( c \cdot 5 \)
D. 4


Find the equivalent fraction of \( \frac{36}{48} \) of denominator 4
A \( \cdot \frac{6}{4} \)
B. \( \frac{3}{4} \)
\( c \cdot \frac{4}{3} \)
D. \( \frac{4}{5} \)


Scorpio is an example of:
A. Comet
B. constellation
c. Asteroid
D. Meteorite


If \( \mathbf{a}+\mathbf{b}+\mathbf{c}=\mathbf{0}, \) then the equation
\( 3 a x^{2}+2 b x+c=0 \) has at least one
root in
This question has multiple correct options
A \( .(1,2) \)
в. (0,1)
c. (-1,1)
D. (2,3)


The relation between time and distance
of a moving body is \( t=5 x^{2}+7 x+8 \)
The acceleration of the body will be :
\( \mathbf{A} \cdot-10 v^{3} \)
B. \( -10 v^{2} \)
\( c \cdot 10 v^{3} \)
D. \( 10 v^{2} \)


Given
\( \boldsymbol{V}=\boldsymbol{t}^{2}+\boldsymbol{2} \boldsymbol{t}+\boldsymbol{3} \)
Find average speed between time
interval \( t_{1} \& t_{2} ? \)


The atomicity of a noble gas is:
\( A \cdot 2 \)
B.
\( c \cdot 0 \)
D.


Anionic surfactants are
This question has multiple correct options
A. \( C_{15} H_{31} \) COONa
в.
c. \( C_{18} \mathrm{H}_{37} \mathrm{NH}_{3} \mathrm{Cl} \)
D. all of the above


Find the unit vector in the direction of
vector \( \overrightarrow{P Q}, \) where \( P \) and \( Q \) are the
points (1,2,3) and \( (4,5,6), \) respectively
Answer required


A vector \( \vec{a} \) has components 2 p and 1 with respect to a rectangular cartesian system. This system is rotated through a certain angle about the origin in the counter clockwise sense. If, with respect
to the new system, \( \vec{a} \) components \( \boldsymbol{p}+\mathbf{1} \) and \( 1, \) then?
A. \( p=0 \)
B. \( p=1 \) or \( p=-\frac{1}{3} \)
c. \( _{p}=-1 \) or \( p=\frac{1}{3} \)
D. \( p=1 \) or \( p=-1 \)


In a survey of 364 children aged \( 19-36 \)
months, it was found that 91 liked to
eat potato chips. If a child is selected at random, the probability that he/she does not like to eat potato chips is :
A . 0.25
B. 0.50
c. 0.75
D. 0.80


If the mass of a microscopic particle a well as its speed are halved, the debroglie wavelength associated with the particle will
A. increased by a factor more than 2
B. increases by a factor of 2
c. decreases by a factor of 2
D. decrease by a factor more than 2


Two magnets of equal mass are joined at right angles to each other as shown Magnet 1 has a magnetic moment 3
times that of magnet 2. This arrangement is pivoted so that it is free to rotate in the horizontal plane. In
equilibrium what angle will the magnet
1 subtend with the magnetic meridian
A \( \cdot \tan ^{-1}\left(\frac{1}{2}\right) \)
B. \( \tan ^{-1}\left(\frac{1}{3}\right) \)
\( c \cdot \tan ^{-1}(1) \)
D. \( 0^{\circ} \)


Find the co-ordinates of a point lying on the line \( \frac{\boldsymbol{x}-\mathbf{2}}{\mathbf{3}}=\frac{\boldsymbol{y}+\mathbf{3}}{\mathbf{4}}=\frac{\boldsymbol{z}-\mathbf{1}}{\mathbf{7}} \) which
is at a distance 10 units from (2,-3,1)
\begin{tabular}{l}
A. (32,37,71) \\
\hline
\end{tabular}
в. (-28,-43,-69)
c. (-32,-37,-71)
D. None of these


Which of the two have almost similar
size?
В. \( _{41} N b \) and \( _{73} T a \)
\( \mathbf{c} \cdot_{39} Y \) and \( _{57} L a \)
D. \( _{20} C a \) and \( _{31} I r \)


A set of ordered pairs.


Flash and thunder are produced simultaneously. But thunder is heard a
few seconds after the flash is seen.
Why?


Number of Chiral C-atoms in glucose
and fructose are
A. 4 in each
B. 3 in each
c. 4 in glucose and 3 in fructose
D. 3 in glucose and 4 in fructose


Find the product of \( (a-3)(a-5)(a-7) \)


How do you define specific heat ? What is specific heat of water?


In how many ways we can select 3
letters of the word PROPORTION?


Two smooth cylindrical bars weighing Weach lie next to each other in contact.
A similar third bar is over the two bars
as shown in figure. Neglecting friction, the minimum horizontal force on each
lower bar necessary to keep them together is
A \( \cdot \frac{W}{2} \)
в.
c. \( \frac{W}{\sqrt{3}} \)
D. \( \frac{W}{2 \sqrt{3}} \)


Heptane and octane form an ideal
solution. At \( 373 K \), the vapour
pressures of the two liquid components are \( 105.2 k P a \) and \( 46.8 k P a \)
respectively. What will be the vapour pressure of a mixture of \( 26.0 \mathrm{g} \) of
heptane and \( 35 g \) of octane?


The isoelectronic pair is:
A. \( C l_{2} O, I C l_{2} \)
в. \( C l_{2}, C l O_{3}^{-} \)
\( \mathbf{c} \cdot I F_{2}^{+}, I_{3}^{-} \)
D. \( C l O_{2}^{-}, C l F_{2} \)


A CD(Compact disc ) is read from the bottom by a semiconductor laser with wavelength \( 700 n m \) passes through a
plastic substrate of refractive index 1.8
When the beam encounters 0 pit, part of the beam is reflected from the pit and part from the flat region. These two beams interfere with each other. What
must be the minimum depth of the pit, So that part of the beam reflected from the pit and part reflected from the flat surface cancel out? (This cancellation
allows the player to recognize beginning and end of a pit)
A. \( 0.197 \mu m \)
B. \( 0.395 \mu m \)
\( c .0 .22 \mu m \)
D. \( 0.11 \mu \) m


A balloon of mass \( \mathrm{m} \) is rising with an acceleration a. A fraction of its mass is
detached from the balloon.lts
acceleration will


The correct statement regarding \( S O_{2} \)
molecule is:
A. two \( p \pi-d \pi \) bonds
B. molecule has 2 lone pair, 2 \( \sigma \) bonds and \( 2 \pi \) bonds
c. two \( p \pi-p \pi \) bonds
D. one \( p \pi-p \pi \) bond and one \( p \pi-d \pi \) bond


The codon for anticodon 3'-UUUA-5' is
A. \( 3^{\text {'-AAU-S }} \)
B. 5'-UAAA-3'
c. 5'-AAAU-3
D. 3'-UAAU-5'


In DNA hydrogen bond occurs between
A. Phosphate and nitrogenous base
B. Sugar and phosphate group
c. Nitrogenous bases
D. sugar and nitrogenous base


Protists are
A. Unicellular and prokaryote
B. Unicellular and eukaryote
C. Multicellular and eukaryote
D. Autotroph and heterotroph
\( A \cdot A, B \) and \( C \)
B. B, C and D
\( c \cdot c \) and \( D \)
D. B and D


Two \( n \times n \) square matrices \( A \) and \( B \) are
said to be similar if there exists a non-
singular matrix \( \boldsymbol{P} \) such that
\( \boldsymbol{P}^{-1} \boldsymbol{A} \boldsymbol{P}=\boldsymbol{B} \)
If \( A \) and \( B \) are similar matrices such
that \( \operatorname{det}(A)=1, \) then
A. \( \operatorname{det}(B)=1 \)
B. \( \operatorname{det}(A)+\operatorname{det}(B)=0 \)
c. \( \operatorname{det}(B)=-1 \)
D. none of these


A train is moving at \( 30 m s^{-1} \) in still air. The frequency of the locomotive whistle
is \( 500 \mathrm{Hz} \) and the speed of sound is 345
\( m s^{-1} . \) The apparent wavelengths of sound in-front of and behind the
locomotive are respectively.
A. \( 0.65 \mathrm{m}, 0.73 \mathrm{m} \)
B. \( 0.63 \mathrm{m}, 0.75 \mathrm{m} \)
c. \( 0.60 \mathrm{m}, 0.85 \mathrm{m} \)
D. \( 0.60 \mathrm{m}, 0.75 \mathrm{m} \)


The amount of work done in joules, when one unit electric charge moves from one point to another point in an electric circuit is called:
A . electric current
B. electric resistance
c. electric conductance
D. potential difference


Let \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x} \sqrt{\mathbf{4} \boldsymbol{a} \boldsymbol{x}-\boldsymbol{x}^{2}},(\boldsymbol{a}>\mathbf{0}) . . \) Then
\( f(x) \) is decreasing in:
This question has multiple correct options
A. \( (5 a, \infty) \)
)
в. \( (-\infty, 0) U(4 a, \infty) \)
c. Always increasing
D. None of the above


Find the area of the isosceles triangle
with base \( 16 \mathrm{cm} \) and vertical angle
\( \mathbf{6 0}^{\circ} \mathbf{4 0}^{\prime} \)


Prove that \( \tan ^{-1} \frac{\sqrt{1+x^{2}}-1}{x}= \)
\( \frac{1}{2} \tan ^{-1} x, x \neq 0 \)


Assertion
The decrease in speed of sound at high altitudes is due of fall in pressure at
this altitude.
Reason
The speed of sound is the same at all pressures and varies with temperature only.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is incorrect but Reason is correct
D. Both Assertion and Reason are incorrect


Choose the correct option for the following. \( \boldsymbol{n} !=\boldsymbol{n}(\boldsymbol{n}-1)(\boldsymbol{n}-\boldsymbol{2}) \dots . . .3 .2 .1 \)
A. True
B. False
c. Ambiguous
D. Data insufficient


Fill in the blanks.
The most dangerous radiation released by radioactive materials is


The area of a triangle, whose vertices \( \operatorname{are}(3,2),(5,2) \) and the point of intersection of the lines \( \boldsymbol{x}=\boldsymbol{a} \) and \( \boldsymbol{y}= \)
\( 5, \) is 3 square units. What is the value of
\( \boldsymbol{a} ? \)
A . 2
B. 3
\( c \cdot 4 \)
D. 5


Which of the following is an analgesic?
A. Ofloxacin
B. Penicillin
c. Aminoglycosides
D. Paracetamol


Nodulated roots bearing family is
A. Mimosoideae
B. Cesalpinoideae
C. Papilionaceae
D. Solanaceae


\( \int \frac{x-\sin x}{1-\cos x} d x= \)
A \( \cdot \log |1-\cos x|+c \)
B . \( \log |x-\sin x|+c \)
c. \( _{x \tan } \frac{x}{2}+c \)
D. \( -x \cot \frac{x}{2}+c \)


The electron microscope is based on the principle of
A. photoelectric effect
B. particle nature of electrons
c. particle nature of electron
D. dual nature of matter


Choose the correct answer from the
alternatives given Drowsiness, felt after a heavy lunch, is
due to:
A. increased blood pressure
B. decreased blood pressure
c. decreased pulse rate
D. increased pulse rate


Wavelength of first line of Balmer series
of hydrogen atom is \( 6560 A \). Find wavelength of third line of this series.


State the following statement is True or False
Mean Deviation is used where the
number of values are large
A. True
B. False


A vector \( a=(x, y, z) \) of length \( 2 \sqrt{3} \)
which makes equal angles with the vectors \( b=(y,-2 z, 3 x) \) and \( c= \)
\( (2 z, 3 x,-y) \) and is perpendicular to
\( \boldsymbol{d}=(1,-1,2) \) and makes an obtuse angle with y-axis is
B. \( (1,1, \sqrt{10}) \)
D. none of these


In a certain process 500 cal of heat is
given to a system and the system does \( 100 J \) of work. The increase in internal
energy of the system is
A . 40 cal
в. 82 cal
c. 1993 J
D. 2193 J


\( 6 H_{2} O+6 C O_{2} \frac{\text {sunlight}}{\text {Chlorophyll}} ? \)
A. \( C_{6} H_{12} O_{6}+6 O_{2} \)
в. \( C_{6} H_{6} O_{6}+8 O_{2} \)
c. \( C_{5} H_{12} O_{17}+C O_{2} \)
D. \( C_{6} H_{11} O_{17}+H_{2} O \)


After switch is closed, current drawn
from the battery is
\( A \cdot 6 A \)
3.1 .54
\( c .3 A \)
0.44


The catalyst used in laboratory
preparation of oxygen is:
A. \( M g O \)
в. \( M n O_{2} \)
\( c \cdot P t \)
D. \( F e \)


In a triangle \( A B C, \) bisector of angle \( C \)
meets the side \( A B \) at \( D \) and
circumcentre at E. The maximum value
of CD.DE is equal to
A \( \cdot a^{2} / 4 \)
B . \( b^{2} / 4 \)
c. \( c^{2} / 4 \)
D. \( (a+b)^{2} / 4 \)


A simple harmonic oscillator has an
acceleration of \( 1.25 \mathrm{m} / \mathrm{s}^{2} \) at \( 5 \mathrm{cm} \) from
the equilibrium. Its period of oscillation is:
A \( \frac{4 \pi}{5} \) s
в. \( \frac{5 \pi}{2} \) s
c. \( \frac{2 \pi}{5} \) s
D. \( \frac{2 \pi}{25} \) s


\( \ln \operatorname{an} A . P, \) if \( m^{t h} \) term is \( n \) and \( n^{t h} \) term
is \( \mathrm{m} . \) Then find \( p^{t h} \) term \( (\boldsymbol{m} \neq \boldsymbol{n}) \)


Evaluate \( \lim _{x \rightarrow 0} \frac{x \tan x}{(1-\cos x)} \)


Give the products formed on reductive
ozonolysis with LAH and oxidative
ozonolysis with \( \boldsymbol{H}_{2} \boldsymbol{O}_{2}, \) from the
compounds.
A. Propan-1,3-diol and propan-1,3-dioic acid
B. Propan-1,2-diol and propan-1,3-dioic acid
C. Propan-1,3-diol and propan-1,2-dioic acid
D. Propan-1,2-diol and propan-1,2-dioic acid


\( \tan ^{-1}(2)+\tan ^{-1}(3)= \)


How will you test in the laboratory, whether the given sample of water is hard or soft?


In a factory there are three types of
Machines \( M_{1}, M_{2} \) and \( M_{3} \) which produces \( 25 \%, 35 \% \) and \( 40 \% \) of the
total products respectively. \( M_{1}, M_{2} \) and
\( M_{3} \) produces \( 2 \%, 4 \% \) and \( 5 \% \) defective
products, respectively. What is the percentage of non-defective products?
A . \( 89 \% \)
B. \( 97.1 \% \)
c. \( 96.1 \% \)
D. \( 86.1 \% \)


A body of mass \( 1 k g \) is thrown with a
velocity of \( 10 m s^{-1} \) at an angle of \( 60^{\circ} \)
with the horizontal. Its momentum at
the highest point is:
\( \mathbf{A} \cdot 2 \mathrm{kg} \mathrm{ms}^{-1} \)
B. 3 \( k g m s^{-1} \)
\( \mathbf{c} \cdot 4 k g m s^{-1} \)
D. 5 kg \( m s^{-1} \)


When total internal reflection occurs
from a prism, of incident
light is reflected back to denser
medium. Fill on the blank.
A . 50\%
B. \( 100 \% \)
c. 20\%
D. 70\%


What is the oxidation state of
Phosphorus in \( \boldsymbol{P C l}_{3} \) ?
A \( .+5 \)
B. +3
\( c \cdot+1 \)
D. -


Stomatal frequency means
A. Number of stomata per unit area of leaf surface
B. Number of epidermal cells per unit area of leaf surface
C. Number of mesophyll cells per unit area of leaf surface
D. None of the above


State the principle on which a hydraulic
press works.
A. Archimedes principle
B. Bernoulli's principle
c. Pascals Law
D. None of these


A compound possess \( 8 \% \) sulphur by mass. The least molecular mass is:
A . 200
B. 400
\( c \cdot \) 155
D. 355


The length of two sides of triangle are 6
\( \mathrm{cm} \) and \( 10 \mathrm{cm} . \) Between what two wholes
numbers should lie the measure of the
third sides?


Non-myelinated nerve fibres occur in
A. Cranial nerves
B. Autonomic nerves
c. optic nerves
D. Spinal nerves


If one mole of an ideal gas goes through the process \( A \rightarrow B \) and \( B \rightarrow C . \) Given
that \( T_{A}=400 K, \) and \( T_{c}=400 K . \) If
\( \frac{P_{A}}{P_{B}}=\frac{1}{5}, \) then find the heat supplied to the gas.
A . 2059.2 J
в. 3659.23
c. 2225.2 J
D. 2659.23


In the given replacement reaction, the reaction will be most favourable if \( \boldsymbol{M} \)
happens to be:
\( \mathbf{A} \cdot K \)
в. \( R b \)
c. \( L i \)
D. Na


Balance the following redox reactions in acidic medium :
\[
Z n+N O_{3}^{-} \longrightarrow Z n^{2+}+N_{2}
\]
A \( \cdot 5 Z n+2 N O_{3}^{-}+12 H^{+} \rightarrow 5 Z n^{2+}+N_{2}+3 H_{2} O \)
B . \( 5 Z n+2 N O_{3}^{-}+12 H^{+} \rightarrow 5 Z n^{2+}+N_{2}+6 H_{2} O \)
\( \mathrm{c} \cdot 5 Z n+2 N O_{3}^{-}+6 H^{+} \rightarrow 3 Z n^{2+}+N_{2}+6 H_{2} O \)
D. None of these


A part of an electric circuit is shown in
the figure below :
Using Kirchhoff's 2nd law, find the
current \( I \) flowing through the \( 4 \Omega \) resistor


Fill in the blanks
The longest chord of a circle is a
of the circle.


\( \int \frac{x^{2}-8 x+7}{\left(x^{2}-3 x-10\right)^{2}} d x= \)
\( \boldsymbol{P} \log |\boldsymbol{x}-\mathbf{5}|+\boldsymbol{Q} \frac{\mathbf{1}}{\boldsymbol{x}-\mathbf{5}}- \)
\( \boldsymbol{R} \cdot \log |\boldsymbol{x}+\mathbf{2}|-\boldsymbol{S} \cdot \frac{\mathbf{1}}{\boldsymbol{x}+\mathbf{2}}+\boldsymbol{c} . \) Then
A \( \cdot P=-\frac{45}{98} \)
в. \( Q=\frac{8}{49} \)
\( c \cdot R=\frac{15}{49} \)
D. All of these


With respect to graphite and diamond, which of the statement(s) given below is (are) correct:
A. Graphite is harder than diamond
B. Graphite has higher electrical conductivity then diamond
c. Graphite has higher thermal conductivty then diamond
D. Graphite has highter \( C-C \) bond order then diamond.


What is the surface charge density on
the
(i) inner surface
(ii) outer surface of the shell


If \( S_{n}=\sum_{r=0}^{n} \frac{1}{n} \) and \( t_{n}=\sum_{r=0}^{n} \frac{r}{n}, \) then
\( \frac{\boldsymbol{t}_{\boldsymbol{n}}}{\boldsymbol{s}_{\boldsymbol{n}}}= \)
A \( \cdot \frac{1}{2} n \)
в. \( \frac{1}{2} n-1 \)
c. \( n-1 \)
D. \( \frac{2 n-1}{2} \)


The molarity of \( 98 \% \)
\( \mathbf{H}_{2} \mathbf{S O}_{4}(\boldsymbol{d}=\mathbf{1} . \mathbf{8} \boldsymbol{g} / \boldsymbol{m} \boldsymbol{L}) \) by weight is:
A. 6 .
B. 18M
c. 10 м
D. 4 M


Assertion
Benzonitrile is prepared by the reaction of chlorobenzene with potassium cyanide.
Reason
Cyanide \( (\stackrel{\ominus}{C} N) \) is a strong nuclophile
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


\( 150 \mathrm{g} \) of ice is mixed with \( 100 \mathrm{g} \) of water at temperature \( 80^{\circ} \mathrm{C} \). The latent heat of ice is 80 ca/g and the specific heat of water is \( 1 \mathrm{cal} / \mathrm{g}-^{\circ} \mathrm{C} \). Assuming no
heat loss to the environment, the amount of ice which does not melt is
A. \( 100 \mathrm{g} \)
B. 08
c. \( 150 \mathrm{g} \)
D. 50g


What are these structures from A to D?
Select labels from the following.
A. A- Blaststyles, B- hydranth, C- planula larva, D- sexual zooids
B. A- Blaststyles, B- hydranth, C- sexual zooids, Dplanula larva
C. A- Hydranth, B- blaststyles, C- sexual zooids, Dplanula larva
D. A- Hydrant, B- blaststyles, C- planula larva, D- sexual zooids


The number average molecular mass and mass average molecular mass of a polymer are 30,000 and 40,000 respectively. The PDI of the polymer is
\( \mathbf{A} \cdot<1 \)
B \( .>1 \)
\( c \cdot 1 \)
D.


Spheres \( P \) and \( Q \) are uniformly
constructed from the same material
which is a good conductor of heat and the
radius of \( Q \) is thrice the radius of \( P \). The
rate of fall of temperature of \( P \) is \( x \) times
that of \( Q . \) When both are at the same surface temperature, the value of \( x \) is :
A \( \cdot \frac{1}{4} \)
B. \( \frac{1}{3} \)
\( c .3 \)
D.


What are seismic waves caused by?
A. Volcanoes
B. Traffic
c. Earthquakes
D. Heavy rain


A particle moves along the \( x \) -axis with a
position given by the equation \( \boldsymbol{x}=\mathbf{5}+ \)
\( 3 t, \) where \( x \) is in meters, and \( t \) is in
seconds. The positive direction is east Which of the following statements about the particle is false?
A. The particle is east of the origin at \( t=0 \)
B. The particle is at rest at \( t=0 \)
c. The particle's velocity is constant
D. The particle's acceleration is constant


The number of significant figures in 0.002930 is
A. 6
B. 5
\( c \cdot 4 \)
D.


In the formation of compound (E) from
(A), the name of the reaction is:
A. Elbs persulphate oxidation
B. Mannich reaction
c. Dakin's reaction
D. Oppenauer oxidation


The equilibrium \( \boldsymbol{A}_{4}(\boldsymbol{g})+\boldsymbol{6} \boldsymbol{B}_{2}(\boldsymbol{g}) \rightleftharpoons \)
\( 4 A B_{3}(g) \) is established in a closed
container by taking equal moles of
\( A_{4}(g) \) and \( B_{2}(g) . \) Which of the following options must be correct at equilibrium?
\( \mathbf{A} \cdot\left[A_{4}\right]<[B]_{2} \)
B . \( \left[B_{2}\right]>\left[A B_{3}\right] \)
c. \( \left[A_{4}\right]<\left[A B_{3}\right] \)
D. None of the above


Which one of the following name is correctly matched with its particular name taxonomic category?
A. Angiospermae- family
B. Homo- species
c. Bryophyta- order
D. Equus- genus


Draw the intensity pattern for single slit diffraction and double slit interference.
Hence, state two differences between
interference and diffraction patterns.


(a) Write Gauss' law for magnetism in the form of Maxwell's equation.
(b) Write the value of \( \frac{1}{\sqrt{\mu_{0} \varepsilon_{0}}} \)


In Freundlich adsorption equation \( \frac{\boldsymbol{x}}{\boldsymbol{m}}= \) \( k p^{1 / n} \) the value of \( n \) is :
A. always greater than one
B. always smaller
c. always equal to one
D. greater than one at low temperature and smaller than one at high temperature


Find the median of the following
numbers
\( \mathbf{1 1}, \mathbf{1 3}, \mathbf{8}, \mathbf{1 0}, \mathbf{1 5}, \mathbf{1 8}, \mathbf{1 2}, \mathbf{7}, \mathbf{9}, \mathbf{1 6} \)
A . 12
B. 11
c. 11.5
D. 12.5


The amino acid \( _{-1-}- \) is obtained by
microbial process by lactobacillus delbrueckii
A. itaconic acid
B. lactic acid
c. gluconic acid
D. citric acid


The resistance of all the wire between
any two adjacent dots is \( R \). The
equivalent resistance between \( A \) and \( B \)
as shown is
A . \( 7 R / 13 \)
B. \( 7 R / 6 \)
c. \( 14 R / 8 \)
D. \( 15 R / 7 \)


For which of the following ores forth floatation method is used for
concentration?
A . Haematite
B. zinc blende
c. Magnetite
D. carnallite


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


Which of the following is the most reactive non-metal?
A. Chlorine
B. Hydrogen
c. Fluorine
D. Selenium


According to molecular orbital theory, the total number of bonding electron
pairs in \( \boldsymbol{O}_{2} \) is:
A .2
B. 3
\( c .5 \)
D. 4


Fibre (longest plant cell), belongs to which tissue?
A. Parenchyma
B. Collenchyma
c. sclerenchyma
D. Aerenchyma


A stone of attached to a rope of length
\( =80 \mathrm{cm} \) is roated with a speed of 240 rpm. If the rope breaks, find the height to which the stone rises
A . \( 10.3 \mathrm{m} \)
B. 41.2 \( m \)
c. \( 20.6 \mathrm{m} \)
D. 24.9


Imagine an atom made up of proton and a a hypothetical particle of double the mass of the electron but having the same charge as the electron. Apply the Bohr atom model and consider all
possible transitions of this hypothetical
particle to the first excited level. The longest wavelength photon that will be
emitted has wavelength \( \lambda \) (give in term
of the Rydberg constant R for the hydrogen atom) equal to
\( A \cdot 9 / 5 R \)
B. 36/5 R
c. \( 18 / 5 \) R
D. 4/ R


The amplitude of the wave shown above
is:
\( A \cdot 8.0 \mathrm{m} \)
B. 2.0 \( m \)
\( c \cdot 4.0 \mathrm{m} \)
D. 1.0
E . \( 0.5 \mathrm{m} \)


If the graphs of \( y=f(x) \) and \( y=g(x) \)
intersect in coincident points the \( \lambda \) can take values:
This question has multiple correct options
A . 3
B. 1
\( c \cdot-1 \)
D.


Write any four applications of \( ^{\prime} f^{\prime}- \) block
elements.


Assertion
All the ores are mineral
Reason
Ores contain metals in combined state
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 and Reason is correct


The evidence to show that there must
be force acting on Earth and directed
towards the Sun is.
A. phenomenon of day and night
B. apparent motion of the Sun around the Earth
c. revolution of Earth around the sun
D. deviation of the falling bodies towards east


Two waves \( A \) and \( B \) have wavelength
\( 0.01 A^{\circ} \) and \( 9000 A^{\circ} \) respectively. Compare the speeds of these waves
when they travel in vacuum.
A . 1: 9
B. 9: 1
c. 1: 1
D. None of the above


Select the incorrect geometry for
hybridization:
A. \( s p= \) linear
В \( \cdot s p^{3} d= \) Т.В.Р.
\( \mathbf{c} \cdot s p^{3} d^{2}=P . B . P \)
D. All are correct


The sum of the first \( n \) terms of a
sequence is \( \frac{7^{n}-6^{n}}{6^{n}}, \) Find its \( n^{t h} \) term Determine whether the sequence is A.P.
or G.P


Two concentric spheres of radii R and 2R are charged. The inner sphere has a
charge of \( 1 \mu \mathrm{C} \) and the outer sphere has a charge of \( 2 \mu \mathrm{C} \) of the same sign: The potential is \( 9000 \mathrm{V} \) at a distance \( 3 \mathrm{R} \)
from the common centre. The value of \( \mathrm{R} \)
is :
\( A \cdot 1 m \)
B. 2 \( m \)
\( c \cdot 3 m \)
D. \( 4 \mathrm{m} \)


The value of \( 5 \sqrt{-8} \) is
A. \( 10 i \sqrt{4} \)
В. \( 20 i \sqrt{2} \)
c. \( 10 i \sqrt{2} \)
D. None of these


With a highly advanced precision instrument:
A. percentage error can be reduced
B. totally accurate value can be measured
c. true value can be found out
D. all the above


Barbiturates are potent
A. Hypnotics
B. Antimicrobials
c. Antacids
D. Antiseptics
E. Antiallergics


There is symbiotic algae in the secretory cells of Hydra. It is
A. Nostoc
B. Anabaena
c. zoochlorellae
D. All of the above


Inertia is that property of a body by
virtue of which the body is
A. Unable to change by itself the state of uniform motion
B. Unable to change by itself the state of rest and or uniform linear motion
C. Unable to change by itself the state of rest
D. Unable to change by itself the direction if motion


A body travels uniformly a distance of \( (13.8 \pm 0.2) m \) in a time \( (4.0 \pm 0.3) s \)
Calculate its velocity with error limits.
What is the percentage error in
velocity?


When \( K C N \) is added to \( C u S O_{4} \)
solution, there is formation of the stable
water soluble complex. This complexis:
A \( \cdot K_{4}\left[C u(C N)_{6}\right. \)
В \( \cdot K_{3}\left[C u(C N)_{4}\right] \)
\( \mathbf{c} \cdot_{K_{2}}\left[C u(C N)_{4}\right] \)
D \( \cdot K\left[C u(C N)_{3}\right] \)


The center of a circle represented by the
equation \( (x-2)^{2}+(y+3)^{2}=100 \) is
located in Quadrant
\( A \)
B. I
\( c \)
\( D \cdot|v| \)


Phenolpthalein is type of indicator.
A. Natural indicator
B. Universal indicator
c. synthetic indicator
D. None of the above


The volume of ethyl alcohol (density \( 1.15 g / c c) \) that has to be added to
prepare \( 100 \mathrm{cc} \) of \( 0.5 \mathrm{M} \) ethyl alcohol
solution in water is :
A . \( 1.15 c c \)
B. \( 2 c c \)
c. \( 2.15 c c \)
D. 2.30 \( c c \)


Which orbital has two angular nodal
planes ?
\( A \cdot s \)
B. \( p \)
\( c \cdot d \)
D. \( f \)


Instruments used to draw circle
A. scale and setsquare
B. scale and protractor
C. scale and compass
D. scale


If the gravitational potential on the surface of earth is \( V_{0} \) then potential at a
point at height half of the radius of earth is
A \( \cdot \frac{V_{0}}{2} \)
в. \( \frac{2}{3} V_{0} \)
c. \( \frac{V_{0}}{3} \)
D. \( \frac{3 V_{0}}{2} \)


Evaluate:
\( \int x \log (x+1) d x \)


A vector of magnitude \( |\Psi| \) is turned
through angle \( \frac{\phi}{2} . \) The magnitude of
change in the vector is given by
A \( \cdot 2 \mid \Psi \| \cos \phi / 4 \)
B . \( |\Psi| \mid \sin \phi / 4 \)
\( \mathbf{C} \cdot|\Psi|^{2}|\sin \phi / 4|^{2} \)
D. \( 2|\Psi \| \sin \phi / 4| \)


State whether the given statement is
true or false:
Caro's acid is an oxidising agent.
A. True
B. False


Uniform soil erosion by running water is
A . Gully erosion
B. Rill erosion
c. Riparian erosion
D. sheet erosion


Locomotive structures found in some
protists include
A. Muscles
B. Flagella
c. Tentacles
D. contractile vacuoles


Needles \( N_{1}, N_{2}, N_{3} \) are made of a
ferromagnetic, a paramagnetic and a diamagnetic substance respectively. A
magnet when brought close to them will:
A. attract \( N_{1} \) and \( N_{2} \) strongly but repel \( N_{3} \)
B. attract \( N_{1} \) strongly, \( N_{2} \) weakly and repel \( N_{3} \) weakly
C. attract \( N_{1} \) strongly, but repel \( N_{2} \) and \( N_{3} \) weakly
D. attract all three of them


The potential energy of an object of a mass m moving in xy plane in a conservative field is given by U=ax+by, where \( x \) and \( y \) are position coordinates of the object. Find magnitude of acceleration :-
A \( \cdot \frac{\sqrt{a^{2}+b^{2}}}{2 m} \)
\( ^{\text {В } \cdot \frac{a^{2}+b^{2}}{m}} \)
c. \( \sqrt{a^{2}+b^{2}} \)
D. None


A uniform, horizontal beam of light is incident upon a prism as shown in the fig. The prism is in the shape of a
quarter cylinder of radius \( R=5 c m, \) and has a refractive index \( \frac{2}{\sqrt{3}} . \) A patch on the table for a distance \( x \) from the
cylinder is unilluminated. The value of \( x \)
is
A . \( 2.5 \mathrm{cm} \)
в. 5 ст
\( c \cdot 5 \sqrt{3} \mathrm{cm} \)
D. \( 10 \mathrm{cm} \)


In the circuit shown below, the key Kis
closed at \( t=0 . \) The current through the battery is:
A. \( \frac{\mathrm{VR}_{1} \mathrm{R}_{2}}{\sqrt{\mathrm{R}_{1}^{2}+\mathrm{R}_{2}^{2}}} \) at \( \mathrm{t}=0 \) and \( \frac{\mathrm{V}}{\mathrm{R}_{2}} \) at \( \mathrm{t}=\infty \)
\( \frac{V}{R_{2}} a t t=0 \) and \( \frac{V\left(R_{1}+R_{2}\right)}{R_{1} R_{2}} \) at \( t=\alpha \)
C \( \cdot \frac{\mathrm{V}}{\mathrm{R}_{2}} \mathrm{att}=0 \) and \( \frac{\mathrm{VR}_{1} \mathrm{R}_{2}}{\sqrt{\mathrm{R}_{1}^{2}+\mathrm{R}_{2}^{2}}} \) at \( \mathrm{t}=\infty \)
\( \frac{V\left(R_{1}+R_{2}\right)}{R_{1} R_{2}} a t t=0 \) and \( \frac{V}{R_{2}} \) at \( t=\infty \)


An alternating voltage (in volts) given by \( V=200 \sqrt{2} \sin (100) t \) is connected
to \( 1 \mu F \) capacitor through an ideal ac ammeter in series. The reading of the
ammeter and the average power consumed in the circuit shall be
A \( .20 m A, 4 W \)
в. \( 20 m A, 0 \)
c. \( 20 \sqrt{2} m A, 8 W \)
D. \( 20 \sqrt{2} \mathrm{mA}, 4 \sqrt{2} \mathrm{W} \)


Calculate the area of a trapezoid with bases of 22 and \( 10 \mathrm{m}, \) and a height of 15
\( \mathrm{m} \)
A \( .240 m^{2} \)
В. \( 230 m^{2} \)
c. \( 220 m^{2} \)
D. \( 210 m^{2} \)


Which of the process is the reversible
process?
A. The free expansion of gas
B. Stirring the liquid in thermal contact with the reservoir will convert the work done into heat
C. The quasi-static isothermal expansion of ideal gas in cylinder fitted with frictionless piston
D. Diffusion of gas from cylinder


Glycosidic linkage is an:
A. amide linkage
B. ester linkage
c. ether linkage
D. acetyl linkage


Form the differential equation from the following primitives, where constant is arbitrary. \( \boldsymbol{y}=\boldsymbol{c} \boldsymbol{x}+\boldsymbol{2} \boldsymbol{c}^{2}+\boldsymbol{c}^{\boldsymbol{3}} \)


Ruchi was given four unknown metals
\( P, Q, R \) and \( S, \) the performed the
following experiments to check the reactivity of the unknown metals. If reaction occurred in only beaker 3
then which of the following metals is least reactive?
\( A \cdot P \)
B. \( Q \)
\( c \cdot R \)
\( D \)


If \( k(x)=4 x^{3} a \) and \( k(3)=27, \) what is
\( k(2) ? \)
\( A \cdot 9 \)
B. 8
c. 17
D. 12


Your school has been selected by the department of education to organise and host an interschool seminar on
'Reproductive Health-Problems and
Practices'. However, many parents are reluctant to permit their wards to attend it. Their argument is that the topic is "too embarrassing'. Put forth four arguments with appropriate reasons and explanation to justify the topic to be very essential and timely.


Ammonia is dried over:
A. Quick lime
B. Slaked lime
c. Phosphorus pentoxide
D. con. H \( _{2} \mathrm{SO}_{4} \)


If the binding energy per nuclear in \( L i^{7} \) and \( H e^{4} \) nuclei are respectively
\( \mathbf{5 . 6 0} M e V \) and \( 7.06 M e V, \) then energy of reactor \( L i^{7}+P \rightarrow 2_{2} H e^{4} \) is:
A. \( 19.6 \mathrm{MeV} \)
B. \( 2.4 \mathrm{MeV} \)
c. \( 8.4 \mathrm{MeV} \)
D. \( 17.6 \mathrm{MeV} \)


What are the characteristics of the
following colloids? Give one example of
each
(i) Multimolecular colloids (ii)
Lyophobic sols (iii) Emulsions


Match the class of compounds given in
column-I with their functions given in
column-II


A student was asked to prove a statement by induction. He proved
(i) \( P(5) \) is true and
(ii) Trutyh of \( P(n) \Rightarrow \) truth of \( p(n+1), n \in \)
\( \mathbf{N} \)
On the basis of this, he could conclude that \( P(n) \) is true for
A. no \( n \in N \)
B. all n \in N
c. all \( n \geq 5 \)
D. None of these


Number of possible isomers for the
complex \( \left[\text { Co }\left(e n_{2}\right) C l_{2}\right] C l \) will be (en:
ethylenediamine) is:
\( A \cdot 3 \)
B. 4
\( c \cdot 2 \)
D.


A boat with a sail, has an electric fan
inside. When the fan starts, the boat
A. cannot move
B. can move
c. moves depending on wind directions
D. moves depending on the speed of the fan


Which of these is a part of your digestive system?
A. Stomach
B. Pancreas
c. Rectum
D. All of the above.


Why does sulphur on reacting with concentrated nitric acid gives sulphuric acid instead of sulphur dioxide?
A. It has greater reactivity with acid.
B. End valency for oxidation 6.
c. End valency for oxidation 4
D. All of the above


The reaction \( \boldsymbol{C} \boldsymbol{H}_{2}=\boldsymbol{C} \boldsymbol{H}_{2}+ \)
\( C H_{3} C O C l \stackrel{A l C l_{3}}{\longrightarrow} \) gives the product


\( \boldsymbol{f}: \boldsymbol{A} \rightarrow \boldsymbol{B} \) defined by \( f(x)=2 x+3 \) and if
\( A=\{-2,-1,0,1,2\} B=\{-1,1,3,5,7\} \) then which
type of function is \( f ? \)
A. One-one
B. onto
c. Bijection
D. constant


Write the structure of prop\( -2-e n- \)
\( 1- \) amine


The sum of the first \( n \) terms of the
series \( 1^{2}+2 \cdot 2^{2}+3^{3}+2 \cdot 4^{2}+5^{2}+ \)
\( 2 \cdot 6^{2}+\cdots \) is \( \frac{n(n+1)^{2}}{2} \) when \( n \) is even
when \( n \) is odd the sum is
A \( \cdot \frac{3 n(n+1)}{2} \)
B. \( \frac{n^{2}(n+1)}{2} \)
c. \( \frac{n(n+1)^{2}}{4} \)
D. \( \left[\frac{n(n+1)}{2}\right]^{2} \)


a body moving with a uniform accleration crosses a distance \( 15 m \) in
the second and 23 m second. The
displacement in 10 s will be.


State True or False.
Thomson discovered isotopes.
A. True
B. False


In a single throw of two dice, find the probability that neither a doublet nor a total of 8 will appear.
A \( \cdot \frac{11}{36} \)
в. \( \frac{5}{18} \)
c. \( \frac{13}{18} \)
D. \( \frac{3}{16} \)


To keep machines running smoothly and to avoid wear and tear of machines,
the best and the most commonly used lubricant is:
A. Powder
B. Sand
\( c \cdot \) oil
D. water


If the selling price of 5 articles is equal
to the cost price of 6 articles, find the
profit or loss per cent.


Which of the following activities is easier to perform?
A. dragging a box
B. lifting a box
c. rolling a drum of same weight as box
D. all of the above need same effort


A point on the parabola \( y^{2}=18 x \) at
which the ordinate increases at twice
the rate of the abscissa is
A. (2,6)
(年) (2,6)
в. (2,-6)
\( ^{\mathrm{c}} \cdot\left(\frac{9}{8},-\frac{9}{2}\right) \)
D \( \cdot\left(\frac{9}{8}, \frac{9}{2}\right) \)


What is the mass defect and the
binding energy of \( _{27} C o^{59} \) which has a
nucleus of mass of \( 58.933 u ? \)
\( \left(\boldsymbol{m}_{\boldsymbol{p}}=\mathbf{1 . 0 0 7 8 u}, \boldsymbol{m}_{\boldsymbol{n}}=\mathbf{1 . 0 0 8 7 u}\right) \)
B. 617.914 MeV
c. 17.914 Mev
D. 717.914 Mev


Find the equation of the line that
passes through the points (-1,0) and
(-2,4)


\( \lim _{x \rightarrow \infty}(\sqrt{x+\sqrt{x}}-\sqrt{x}) \) is equal to
\( \mathbf{A} \cdot \mathbf{1} \)
B.
\( c \cdot \frac{1}{2} \)
D. none of these


The process of lead action in a simple
voltaic cell
A. Catalyses the process of electrolysis
B. Increases the efficiency of the cell
c. Decreases the efficiency of the cell
D. Increases the charge carriers


A parallel plate capacitor is connected to a battery. The quantities charge, voltage, electric field and energy associated with this capacitor are given
by \( Q_{0}, V_{0}, E_{0}, \) and \( U_{0} \) respectively. \( A \) dielectric slab is now introduced to fill
the space between the plates with the battery still in connection. The corresponding quantities now given by \( Q, V, E \) and \( U \) are related to the
previous ones are :
A \( \cdot Q>Q_{0} \)
в. \( V>V_{0} \)
c. \( E>E_{0} \)
D. \( U<U_{0} \)


For a black body at a temperature of
\( 727^{\circ} \mathrm{C}, \) Its radiated power is 60 watt
and temperature of the surrounding is
\( 227^{\circ} \mathrm{C} \) If the temperature of the black
body is changed to \( 1227^{\circ} \mathrm{C} \), Then its radiating power will be
\( \mathbf{A} \cdot 304 W \)
B. 320 W
c. \( 240 W \)
D. \( 120 W \)


Find the area of the figure bounded by
the following curves \( y=(x-1)^{2},+y=0, x=2, x=3 \)


In the figure shown below reactant \( \boldsymbol{A} \)
represented by square) is in equilibrium with product \( \boldsymbol{B} \) represented by circle). The equilibrium
constant is:
\( A \)
в.
\( c \cdot 4 \)
\( D \)


Which one of \( \boldsymbol{P C l}_{4}^{+} \) and \( \boldsymbol{P C l}_{4}^{-} \) is not likely to exist and why?


A pulley fixed to the ceiling carries a
thread with bodies of masses \( m_{1} \) and
\( m_{2} \) attached to its ends. The masses of
the pulley and the thread are negligible, friction is absent. Find the acceleration
\( \boldsymbol{w}_{C} \) of the centre of mass of this system
A \( \cdot \frac{\left(m_{1} m_{2}\right)^{2} \vec{g}}{\left(m_{1}-m_{2}\right)^{2}} \)
B. \( \frac{\left(m_{1}+m_{2}\right)^{2} \vec{g}}{\left(m_{1}-m_{2}\right)^{2}} \)
c. \( \frac{\left(m_{1} m_{2}\right)^{2} \vec{g}}{\left(m_{1}+m_{2}\right)^{2}} \)
D. \( \frac{\left(m_{1}-m_{2}\right)^{2} \vec{g}}{\left(m_{1}+m_{2}\right)^{2}} \)


A binary compound between an
unknown element \( E \) and hydrogen contains \( 91.27 \% E \) and \( 8.73 \% H \) by mass. If the formula of the compound is
\( \boldsymbol{E}_{3} \boldsymbol{H}_{8} . \) Calculate the atomic mass of \( \boldsymbol{E} \)


Main source of most of the organic compounds is :
A. coal tar
B. petroleum
\( c \cdot \) both \( A \& B \)
D. ammonia


Roll a die ten times and record the
outcomes in the form of table.


\( \boldsymbol{C}_{2} \boldsymbol{H}_{6} \stackrel{\mathbf{9 0 0}^{\circ} \boldsymbol{C}}{\longrightarrow} \boldsymbol{C}_{2} \boldsymbol{H}_{4}+\boldsymbol{H}_{2} \)
Above reaction is called as
A. combustion
B. rearrangement
c. pyrolysis
D. cleavage


The sum of probabilities of all possible
events is always


What will be happened an electric current is passed through a conducting solution?
A. heating solution
B. some chemical reactions
c. cooling
D. increase resistance


The ions \( M g^{+2} \) and \( P O_{4}^{-3} \) combine to
form compounds:
\( \mathbf{A} \cdot M g_{3}\left(P O_{4}\right)_{2} \)
в. \( M g_{2}\left(P O_{4}\right)_{2} \)
c. \( M g_{2}\left(P O_{4}\right)_{3} \)
D. \( M g_{3}\left(P O_{4}\right)_{3} \)


The minimum of \( f(x)=\frac{1+x+x^{2}}{1-x+x^{2}} \)
occurs at \( x= \)
\( A \cdot-1 \)
B.
\( c \cdot 2 \)
\( D \ldots-2 \)


Which of the followoing molecules have
S-configuration for the chiral centre?
\( A \)
B.
c. Both (A) and (B)
D. None of these


Solve each pair of equation by using the substitution method.
\( \boldsymbol{x}+\frac{\mathbf{6}}{\boldsymbol{y}}=\mathbf{6} \)
\( \mathbf{3} \boldsymbol{x}-\frac{\mathbf{8}}{\boldsymbol{y}}=\mathbf{5} \)
A \( . x=3 \) and \( y=-2 \)
в. \( x=30 \) and \( y=2 \)
c. \( x=3 \) and \( y=2 \)
D. None of these


Find the product of \( (7 x+3 y)(7 x-y) \)


If an atom contains one electron and
one proton, what charge will it carry?
A. Positive
B. Neutral
c. Negative
D. All of the above


Which of the following quantities does not depends upon the orbital radius of the satellite?
A \( \cdot \frac{T}{R} \)
в. \( \frac{T^{2}}{R} \)
c. \( \frac{T^{2}}{R^{2}} \)
D. \( \frac{T^{2}}{R^{3}} \)


A piece of zinc may be distinguished from a piece of magnesium by:
(1) determining which conducts electricity
(2) determining which releases \( H_{2} \) gas from a 1-molar hydrochloric acid solution
(3) measuring the density of each
A. If 1,2 and 3 are correct
B. If only 1 and 2 are correct
c. If only 2 and 3 are correct
D. If only 1 is correct
E. If only 3 is correct


Let \( x \) be a real number \( [x] \) denotes the
greatest integer function, and \( \{x\} \)
denotes the fractional part and \( (x) \) denotes the least integer function,then solve the following.
\( [2 x]-2 x=[x+1] \)
\( ^{A} \cdot\left\{-1,-\frac{1}{2}\right\} \)
в. \( \left\{-1, \frac{1}{2}\right\} \)
c. \( \left\{1,-\frac{1}{2}\right\} \)
D \( \cdot\left\{1, \frac{1}{2}\right\} \)


When ethyl hydrogen sulphate is heated with excess of alcohol at \( 410 K \) the
product obtained is:
A. ethane
B. ethylene
c. diethyl ether
D. diethyl sulphate


Explain sex determination in humans with a neat labelled diagram.


\( \mathbf{A} \)
is a mixture of two or more
substances in a single phase.
A. Element
B. Compound
c. Solution
D. None of above


Two non-metal atoms are likely to form covalent bonds on combination.
A. True
B. False


Range of \( \sin ^{-1} x-\cos ^{-1} x \) is
\( ^{\mathbf{A}} \cdot\left[\frac{-3 \pi}{2}, \frac{\pi}{2}\right] \)
В \( \cdot\left[\frac{-5 \pi}{3}, \frac{\pi}{3}\right. \)
\( ^{\mathbf{c}} \cdot\left[\frac{-3 \pi}{2}, \pi\right] \)
D. \( [0, \pi] \)


If the angle of incidence is \( 50^{\circ}, \) then
calculate the angle between the incidence ray and the reflected ray.
A \( .50^{\circ} \)
B . \( 100^{\circ} \)
\( \mathrm{c} \cdot 130^{\circ} \)
D. \( 80^{\circ} \)


A 0.2 molar solution of formic acid is
\( 3.2 \% \) ionized, its ionization constant is:
A \( \cdot 9.6 \times 10^{-3} \)
B . \( 2.1 \times 10^{-4} \)
c. \( 1.25 \times 10^{-6} \)
D. \( 2.1 \times 10^{-8} \)


\( 5 g m \) of steam at \( 100^{\circ} C \) is passed into calorimeter containing liquid, Temperature of liquid rises from \( 32^{\circ} C \)
to \( 40^{\circ} \mathrm{C} . \) Then water equivalent of calorimeter and content is
A. 40 gram
B. 375 gram
c. 300 gram
D. 160 gram


State, whether the following statement
is True or False:

Homologous series can be represented by a general formula


Assertion
Two coherent point sources of light having non-zero phase difference are separated by a small distance. Then, on the perpendicular bisector of line segment joining both the point sources,
constructive interference cannot be
obtained.
Reason
For two waves from coherent point sources to interfere constructively at a
point, the magnitude of their phase
difference at that point must be \( 2 m \pi \)
(where \( m \) is a non-negative integer)
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


Define Poisson's ratio.


What is the IUPAC name of succinic
acid?


\( \ln \mathrm{BP} 120 / 80, \) the numerator 120
indicates


The correct statement(s) for orthoboric
acid is/are:
This question has multiple correct options
A. It behaves as a weak acid in water due to self
ionization.
B. Acidity of its aqueous solution increases upon addition of ethylene glycol
C. It has a three dimensional structure due to hydrogen bonding.
D. It is a weak electrolyte in water.


Find \( x \) in the following figures:


"Golden algae" is the common name of algae belonging to
A. Chrysophyta
B. Pyrrophyta
c. Euglenophyta
D. cyanophyta


Calculate the kinetic energy of 5 mole of
a gas at \( 27^{\circ} \mathrm{C} \) in erg and calorie.


Explain why :
(a) A body with large reflectivity is a poor emitter
(b) A brass tumbler feels much colder
than a wooden tray on a chilly day
(c) An optical pyrometer (for measuring high temperatures ) calibrated for an ideal black body radiation gives too low a value for the temperature of a red hot iron piece in the open but gives a correct value for the temperature when the same piece is in the furnace
(d) The earth without its atmosphere would be inhospitably cold
(e) Heating systems based on circulation of steam are more efficient
in warming a building than those based on circulation of hot water


How much silver will be obtained by that quantity of current which displaces
5.6 litre of \( \boldsymbol{H}_{2} \) ?
A . \( 54 g \)
в. \( 13.5 g \)
c. \( 20 g \)
D. \( 108 g \)


Oxysomes were discovered by
A. Palade
B. Benda
c. Fernandes-Moran
D. Luch and Rich


Roots of plants grow away from light due to
A. Gravitropism
B. Chemotropism
c. Heliotropism
D. Phototropism


Which of the following force doesn't change with distance?
A. Electrostatic force
B. Gravitational force
c. Frictional force
D. Magnetic force


If the coordinates of the one end of a
diameter of a circle are (2,3) and the coordinates of its centre are (-2,5)
then the coordinates of the other end of
the diameter are:
A. (-6,7)
в. (6,-7)
c. (6,7)
(は)
D. (-6,-7)


\( 25.6 \mathrm{g} \) of sulphur in 100 g benzene shows depression in freezing point of
\( 5.12^{\circ} \mathrm{C} . K_{f} \) for benzene is
\( 5.12^{\circ} \mathrm{Ckg} \) mol\( ^{-1} . \) The molecular
formula of sulphur in benzene is:
\( A \cdot S_{2} \)
в. \( S_{6} \)
\( \mathrm{c} \cdot S_{8} \)
D. \( S_{12} \)


A rectangular coil 100 turns and size \( 0.1 m \times 0.05 m \) is placed perpendicular
to a magnetic field of \( 0.1 \mathrm{T} \). If the field drops to \( 0.05 \mathrm{T} \) in 0.05 second, the magnitude of the e.m.f. induced in the coil is
\( A \cdot 2 \)
B. 3
c. 0.5
D.


If \( a-b=0.9 \) and \( a b=0.36 ; \) find \( a^{2}- \)
\( \boldsymbol{b}^{2} \)
\( \mathbf{A} \cdot \pm 7.65 \)
B . ±1.35
\( \mathrm{c} .\pm 1.5 \)
D. ±4.5


Which of the following does not belong to the kingdom Protista?
A. Chrysophytes
B. Euglenoids
c. Ascomycetes
D. Dinoflagellates


Lightning is:
A. caused by accumulation of charges in cloud
B. caused by dispersion of charges in cloud
C . caused by rotation of charges in cloud
D. none of the above


If the mean of a binomial distribution is
\( 25, \) then its standard deviation lies in
the interval
A \( \cdot[0,5] \)
в. [0,6]
c. [0,25]
]
D. [0,28


Find the derivative of \( 99 x \) at \( x=100 \)


The ice floats on water because:
A. solids have lesser density than liquids
B. it has open-cage like structure in which lesser molecules are packed per mL than water
C . ice is lighter than water
D. when ice is formed water molecules come closer and start floating.


Find the locus of the point, the sum of the squares of whose distances from
the planes \( \boldsymbol{x}+\boldsymbol{y}+\boldsymbol{z}=\mathbf{0}, \boldsymbol{x}-\boldsymbol{y}=\mathbf{0} \)
\( x+y-2 z=0 \) is 7


Tricology is the study of
A. Tetrapods
B. Hair
C. Developmental abnormalities
D. Ageing


\( \mathbf{A}=\cos 20^{0} \cos 40^{0} \cos 60^{0} \cos 80^{0} \)
\( \mathbf{B}=\cos 6^{0} \cos 42^{0} \cos 66^{0} \cos 78^{0} \)
\( \mathbf{C}=\cos \mathbf{3} \mathbf{6}^{\mathbf{0}} \cos \mathbf{7} \mathbf{2}^{\mathbf{0}} \cos \mathbf{1 0} \mathbf{8}^{\mathbf{0}} \cos \mathbf{1} \mathbf{4} \mathbf{4}^{\mathbf{0}} \)
A. \( A>B>C \)
в. \( B>C>A \)
c. \( C>A>B \)
D. \( A=B=C \)