Assertion
In 5 th period, an element with \( Z=57 \) is
followed by element \( Z=72 \)
Reason
The intermediate elements are not
represented in the main body of the periodic table.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


An object is placed at a distance of \( \boldsymbol{f} / \mathbf{2} \)
from a convex lens. The image will be
A. At one of the focal, virtual and double its size
B. At \( 3 f / 2 \) real and inverted
c. At \( 2 f \) virtual anderect
D. None of these


Evaluate: \( \int \frac{2 x}{x^{2}} d x \)


In which of the following compounds is
hydroxylic proton the most acidic :
\( A \)
B
\( c \)
\( D \)


If \( a, b, c \) are three positive real number then show : \( \frac{a}{b+c}+\frac{b}{a+c}+ \)
\( \frac{c}{a+b} \geq \frac{3}{2} \)


Assertion
The density of nucleus is about \( 2.3 \times \) \( 10^{17} k g m^{-3} \) and all nucleus have
approximately same density.
Reason
The density of nucleus is independent of
mass present in it.
A. Assertion is correct but Reason is wrong
B. Assertion is wrong but Reason is correct
c. Both Assertion and Reason are correct and Reason is the correct explanation of Assertion
D. Both Assertion and Reason are correct but Reason is not the correct explanation of Assertion


Two trains \( A \) and \( B \) of length \( 400 m \)
each are moving on two parallel tracks
with a uniform speed of \( 72 \mathrm{km} \mathrm{h}^{-1} \) in
the same direction, with \( A \) ahead of \( B \)
The driver of \( B \) decides to overtake \( A \)
and accelerates by \( 1 \mathrm{m} \mathrm{s}^{-2} \). If after \( 50 \mathrm{s} \)
the guard of \( B \) just brushes past the
driver of \( A, \) what was the original
distance between them?


On a stationary sail boat, air is blown
from a fan attached to the boat. The
boat
A. moves in opposite direction in which the air is blown
B. does not move
c. moves in the same direction in which air blows
D. spins around


Rewrite the following table so as to
match the second and third columns
with the first column:
Column I \( \quad \) Column II \( \quad \) Column \( \begin{array}{l}\text { (1) Dispersion } \\ \qquad \begin{array}{l}\text { Long- } \\ \text { Sightedness }\end{array} & \begin{array}{l}\text { Twinkling } \\ \text { of stars }\end{array}\end{array} \) Splitting of
\( \begin{array}{ll}\text { (2) Refraction } & \text { White light into } \\ \text { component } \\ \text { colors. }\end{array} \)
\( \begin{array}{ll}\text { (3) } & \text { Change in the } \\ \text { Hypermetropia } & \text { direction of ray } \\ \text { of light due to } & \text { Spectrum } \\ \text { change in } & \text { of seven } \\ \text { medium. } & \text { colours }\end{array} \)


This salt of oxoacids of phosphorus is
used as washing detergent
A. wavellite
B. microcosmic salt
c. calgon
D. chlorapatite


Organisms called methanogens are most abundant in
A. Polluted stream
B. Cattle yard
c. sulphur rock
D. Hot spring


\( X e F_{n}(n=2,4,6) \) are oxidising agents
and thus estimation of Xe salts can be
determined by suitable methods.
\[
\boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{4}+\boldsymbol{4} \boldsymbol{K} \boldsymbol{I} \longrightarrow \boldsymbol{X} \boldsymbol{e}+\boldsymbol{2} \boldsymbol{I}_{2}+\boldsymbol{4} \boldsymbol{K} \boldsymbol{F}
\]
Write the increasing order of oxidising power of xenon compounds?
A. \( X e F_{2}<X e F_{4}<X e F_{6} \)
в. \( X e F_{2}<X e F_{6}<X e F_{4} \)
c. \( X e F_{6}<X e F_{4}<X e F_{2} \)
D. \( X e F_{6}=X e F_{4}=X e F_{2} \)


A ray of light from air is incident in water; then which property of light will not change in water?
A. Velocity
B. Frequency
c. Amplitude
D. colour


How many pairs of vertically opposite
angles are formed?


The mean of the numbers \( a, b, 8,5,10 \) is
6 and the variance is \( 6.80 . \) Then which
one of the following gives possible values of \( a \) and \( b ? \)
A \( . a=0, b=7 \)
В. \( a=5, b=2 \)
c. \( a=1, b=6 \)
D. \( a=3, b=4 \)


In the reaction sequence, \( C_{2} H_{5} C l+ \) \( K C N \stackrel{C_{2} H_{5} O H}{\longrightarrow} X \frac{H_{3} O \oplus}{\Delta} Y, \) what is the
molecular formula of Y?
\( \mathbf{A} \cdot C_{3} H_{6} O_{2} \)
в. \( C_{3} H_{5} N \)
c. \( C_{2} H_{4} O_{2} \)
D. \( C_{2} H_{6} O \)


toppr 5
Q Type your question
B.
\( c \)
\( D \)


Which of the following animals can regenerate arms and parts of the body?
(a) Star fish
(b) Brittle star
(c) Sea lily
(d) Aves
\( A \cdot a, b \) and \( c \)
B. a and b
\( c . \) b and d
D. a and c


A bullet weighing 10 g is fired with a velocity of \( 800 m s^{-1} . \) After passing
through a mud wall \( 1 \mathrm{m} \) thick, its
velocity decreases to \( 100 m s^{-1} \). Find the
average resistance offered by the mud wall.


Pick correct statements from among
the following:
a) Electric field and magnetic field are basically independent
b) Electric field and magnetic field are to aspects of the electromagnetic field
c) Electric field and magnetic field may be produced by charge at rest
d) A moving charge produces both electric and magnetic fields
A. a and b are correct
B. b and d are correct
\( c . \) b, cand d are correct
D. a, cand dare correct


Basic smallest unit of classification is
A. species
B. Family
c. class
D. Genus


Which can give both carbylamine test and carric ammonium nitrate test?
A. Asn-Gln
B. Lys-GIn
c. Asp-Lys
D. Lys-Ser


Find the centroid of Triangle whose
vertices are
\( \boldsymbol{A}(\mathbf{1}, \mathbf{2}, \mathbf{3}), \boldsymbol{B}(\mathbf{2},-\mathbf{1}, \mathbf{6}), \boldsymbol{C}(\mathbf{3}, \mathbf{2},-\mathbf{3}) \)
A \( .(2,1,2) \)
В. (2,-1,2)
c. (-2,-2,-2)
D. (1,2,1)


Choose the correct answers from the
alternatives given :
The pathway of aerobic respiration is completed in the
A. cytoplasm
B. mitochondrion
c. plasma membrane
D. nucleus


What is the emf \( \epsilon \) of the supply battery?
\( 4 \cdot 10 v \)
3. 15V
\( c \cdot 200 \)
D. 250


The oxidation states of central metal
ions of \( (A),(B) \) and \( (C) \) compounds are respectively:
A. \( +11,+ \) VI and \( + \) VII
B. \( +11,+ \) VI and \( +v \) I
c. \( +1 !,+ \) VII and \( + \) vII
D. \( +\mathrm{Vl} \), \( + \) VII and \( +\mathrm{V} \) I


A bob of mass \( m \), suspended by a string
of length \( l_{1} \) is given a minimum velocity required to complete a full circle in the vertical plane. At the highest point, it
collides elastically with another bob of mass \( m \) suspended by a string of length
\( l_{1}, \) which is initially at rest. Both the strings are mass-less and inextensible. If the second bob, after collision acquires the minimum speed required to complete a full circle in the vertical
plane, the ratio \( l_{1} / l_{2} \) is
\( \mathbf{A} \cdot \mathbf{1} \)
B. 3
\( c .5 \)
D. \( 1 / 5 \)


Q Type your question
weighs \( m^{\prime} . \) Ejection of fuel gas is at a
constant rate of \( m_{0} \) per second with a
constant velocity of \( u_{r e l} \) relative to the
rocket. Final speed of rocket after the
complete burn out of the fuel is given by
\( \boldsymbol{v}= \)
\( ^{\mathbf{A}} \cdot_{u_{r e l}} \log _{e} \frac{m}{m^{\prime}} \)
в. \( \quad u_{r e l} \log _{e} \frac{m_{0}}{m} \)
\( ^{\mathrm{c}} \cdot_{-u_{r e l}} \log _{e} \frac{m_{0}}{m^{\prime}} \)
D. \( -u_{r e l} \frac{d m}{m} \)


Blood contains:
A. positively charged particles
B. negatively charged particles
C . neutral particles
D. negatively as well as positively charged particles


Which of the following is a physical change?
A. Burning of coal
B. Photosynthesis
c. Dissolving sugar in water
D. Digestion of food


A convex lens is placed between object and a screen. The size of object is \( 3 c m \)
and an image of height \( 9 \mathrm{cm} \) is obtained on the screen. When the lens is
displaced to a new position, what will be the size of image on the screen?
\( A \cdot 2 c m \)
в. 6 ст
\( c .4 c m \)
D. \( 1 c m \)


Two identical particles each of mass
\( \mathrm{m} \) are projected from points \( \mathrm{A} \) and \( \mathrm{B} \) on
the ground with same initial speed \( u \)
making an angle \( \theta \) as shown in the
figure, such that their trajectories are
in the same vertical plane. The initial velocity of the centre of mass is
A . ucos \( \theta \)
B. 2u cos \( \theta \)
\( c \cdot u \sin \theta \)
D. 2u sin \( \theta \)


A pulley is hinged at the centre and a massless thread is wrapped around it. The thread is pulled with a constant
force \( F \) starting from rest. As the time increases:
A . its angular velocity increases, but force on hinge remains constan
B. its angular velocity remains same, but force on hinge increases
c. its angular velocity increases and force on hinge increases
D. its angular velocity remains same and force on hinge is constant


\( f \)
\( \vec{a}, b, \vec{c} \) be any three non-zero, non-
vecto topp
Happy Father's Day
\( c \)
D.
AS


Which of the following material is not used in making plate?
A. steel
B. Glass
c. Plastics
D. Leather


Assertion : \( \beta- \) particles are deflected
more than \( \alpha- \) particles in a given
electric field.

Reason: Charge on \( \alpha- \) particles is
larger than on \( \beta- \) particles.
A. If both (A) and (R) are correct, and (R) is the correct explanation of (A).
B. If both (A) and (R) are correct, but (R) is not the correct explanation of (A)
c. If (A) is correct, but (R) is incorrect.
D. If (A) is incorrect, but (R) is correct
E. If both (A) and (R) are incorrect


If \( I, m, n \) are the direction cosines of \( a \) line OP then the maximum value of
I.m.n is
A \( \cdot \frac{1}{\sqrt{3}} \)
в. \( \frac{1}{3 \sqrt{3}} \)
\( c \cdot \frac{1}{3} \)
D.


Why does the grinding wheels have length mass and moderate diameter?


Find the number of values of \( x \) of the
form \( 6 n, \) where \( n \) is an integer, in the
domain of the function \( \boldsymbol{f}(\boldsymbol{x})= \) \( \boldsymbol{x} \ln |\boldsymbol{x}-1|+\frac{\sqrt{\mathbf{6 4}-\boldsymbol{x}^{2}}}{\sin \boldsymbol{x}} \)


Utensils of a solar cooker are painted
with
A. White colour
B. Red colour
c. Green colour
D. Black colour


Read the above bar graph and answer
the following question:

Which state has the total production of
wheat and rice minimum?


The displacement in \( n^{t h} \) second of uniformly acelerated motion is given by \( \boldsymbol{S}_{\boldsymbol{n}^{t h}}=\boldsymbol{u}+\frac{\boldsymbol{a}}{2}(\boldsymbol{2} \boldsymbol{n}-1) . \) This equation is
dimensionally
A. correct
B. not correct
c. can be made correct by multiplying the right hand side of equation by n
D. can be made correct by dividing the left h and side of the equation by n


A cell can carry out its constant
and intensive metabolic activities with
relatively small amounts of such vital
components as ATP, \( N A D^{+}, \) coenzyme
A, etc. because it can
A. rapidly recycle these compounds
B. bypass reactions that require these compounds
c. incur an oxygen debt until these compounds become available
D. utilize substitute molecules in place of these compounds


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


Suppose that the lower half of the
concave mirror's reflecting in figure is covered with an opaque (non-reflective) material. What effect will this have on
the image of an object placed in front of the mirror?


Experiments were carried out to
investigate the effect of different \( \boldsymbol{p} \boldsymbol{H} \)
values on enzyme activities. (Time and temperature was kept constant)
(a) What interpretation can you draw from the graph?
(b) What happens to the pepsin reaction between \( p H 4 \) and \( 5 ? \) Why?
Observe the given graph and answer:


Which of the following is/are correct?
This question has multiple correct options
A. Random errors can not be estimated by repeating a measurement several (perhaps many) times.
B. Random errors can result due to unpredictable fluctuations in temperature or line voltage during experimental measurements.
C. Am impoperly "Zeroed" instrument (such as an ammeter) can result in systematic errors.
D. Large degree of precision implies accuracy.


If \( f(x) \) is a differentiable function in the
interval \( (0, \infty) \) such that \( f(1)=1 \) and \( \lim _{t \rightarrow x} \frac{t^{2} f(x)-x^{2} f(t)}{t-x}=1 \)
A \( \cdot \frac{25}{9} \)
в. \( \frac{23}{18} \)
c. \( \frac{13}{6} \)
D. \( \frac{31}{18} \)


Which process is responsible in
Hydrogen bomb?


A solid cylinder of mass \( 2 \mathrm{Kg} \) and radius
\( 0.2 \mathrm{m} \) is rotating about its own
axis without friction with angular
velocity 3 rad/s. A particle of mass 0.5
\( \mathrm{Kg} \) and moving with a velocity of \( 5 \mathrm{m} / \mathrm{s} \) strikes the cylinder and sticks to it as
shown in. The velocity of the system after the particle sticks it will be
A. 0.3 radians/sec
B. 5.3 radians/sec
c. 10.3 radians/sec
D. 8.3 Radians/sec


Assertion
A catalyst accelerates a chemical
reaction.
Reason
A catalyst decreases the activation
energy for a chemical reaction.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Find the equation of a circle if:
(i)center \( (a, b) \) and radius \( \sqrt{a^{2}+b^{2}} \)
(ii)center \( (a \sec \alpha, b \tan \alpha) \) and radius
\( \sqrt{a^{2} \sec ^{2} \alpha+b^{2} \sec ^{2} \alpha} \)


A plot of velocity versus time is shown
in figure. A single force acts on the body.
The correct statement is?
A. In moving from \( C \) to \( D \), work done by the force on the body is positive
B. In moving from \( B \) to \( C \), work done by the force on the
body is positive
C. In moving from \( A \) to \( B \), the body does work on the
system
D. In moving from \( O \) to \( A \), work is done by the body and is negative


Which of the following rules states that
with the increase of every \( 10^{\circ} \mathrm{C} \) temperature the rate of metabolic
activity gets doubled?
A. Van't Hoff's rule
B. Bergman's rule
c. Allen's rule
D. Jordon's rule


An upright object is placed at a
distance in front of a converging lens equal to twice the focal length \( 20 \mathrm{cm} \) of
the lens. On the other side there is a
concave mirror of focal length \( 15 \mathrm{cm} \)
separated from thelens by a distance of
70 cm. Then select the correct
statements from the following
his question has multiple correct options
A. Magnification for the system is \( 1 / 2 \)
B. Magnification for the system is
c. Final image by the system will real and at distance of \( 80 \mathrm{cm} \) from centre of curvature of spherical mirror
ification for the system is \( +1 / 2 \)


The the focal distance of an end of the
minor axis of any ellipse (reffered to its axes of \( x \) and \( y \) respectively) is \( k \) and
the distance between the foci is \( 2 h \)
then its equation is:
A \( \cdot \frac{x^{2}}{k^{2}}+\frac{y^{2}}{k^{2}+h^{2}}=1 \)
B. \( \frac{x^{2}}{k^{2}}+\frac{y^{2}}{h^{2}-k^{2}}=1 \)
\( ^{\mathrm{C}} \cdot \frac{x^{2}}{k^{2}}+\frac{y^{2}}{k^{2}-h^{2}}=1 \)
D. \( \frac{x^{2}}{k^{2}}+\frac{y^{2}}{h^{2}}=1 \)


Represent \( x \) on number line or find \( x \) \( \frac{3 x-2}{5}>\frac{4 x-3}{2} \)


The weight of a rider, driving scooter is assumed to be evenly distributed on both the tyres. The area of contact of
each tyre with the ground is \( 10 \mathrm{cm}^{2} \). If the pressure inside the tyres is 2 bar,
find the mass of the rider. \( (\boldsymbol{g}= \)
\( \left.10 m s^{-2}\right) \)
A. \( 40 \mathrm{kg} \)
B. 50 kg
\( c \cdot 60 \mathrm{kg} \)
D. 70 kg


If e.m.f of cell is \( \boldsymbol{E} \) with internal
resistance \( r \) and external resistance is
\( \boldsymbol{R}, \) then terminal voltage will be :
A \( \cdot \frac{E r}{R+r} \)
в. \( \frac{E R}{R+r} \)
c. \( E \)
D. \( \frac{E r R}{R+r} \)


Prove that \( \left[\begin{array}{ccc}1 & a & a^{2} \\ 1 & b & b^{2} \\ 1 & c & c^{2}\end{array}\right]= \)
\( (a-b)(b-c)(c-a) \)


Find the integral \( \int \frac{d x}{\sqrt{9 x-4 x^{2}}} \)


Two wires \( A \) and \( B \) of same length are made of same material. The figure represents the load F versus extension
\( \Delta x \) graph for the two wires. Then:
A. the cross sectional area of A is greater than that of B.
B. the elasticity of B is greater than that of A.
C. the cross-sectional area of B is greater than that of A.
D. the elasticity of A is greater than that of B.


During cytokinesis in plants, which of the following secretes the middle lamella?
A. Golgi body
B. SER
c. RER
D. Lysosomes


Reactions which involve
disproportionation of the oxides of nitrogen :
This question has multiple correct options
A \( \cdot 2 N O_{2}+H_{2} O \longrightarrow H N O_{3}+H N O_{2} \)
в. \( N_{2} O_{4} \rightarrow N O^{+}+N O_{3}^{\text {}} \)
c. \( 3 H N O_{2} \longrightarrow H N O_{3}+2 N O+H_{2} O \)
D. \( 3 N O \longrightarrow N_{2} O+N O_{2} \)


What are oxides? Write different types
of oxides with one example each.


Which of the following elements doesn't belong to group IIA or 2nd group?
A . Be
в. Мв
\( c \cdot L \)
D. ca


The shape of chlorate ion is:
A . angular
B. pyramidal
c. tetrahedral
D. trigonal planar


What is parental generation(p)?


Solid \rightleftharpoons liquid equilibrium can be achieved only at the melting point of the substance.
A. True
B. False


Which of the two meters, voltmeter or
potentiometer, is preferred to measure the emf of a battery? Why?


Solve: \( 3(2 x+y)=7 x y \) and
\( \mathbf{3}(\boldsymbol{x}+\mathbf{3} \boldsymbol{y})=\mathbf{1 1} \boldsymbol{x} \boldsymbol{y} \)
where, \( \boldsymbol{x} \neq \mathbf{0}, \boldsymbol{y} \neq \mathbf{0} \)
A \( \cdot x=3 ; y=\frac{1}{2} \)
в. \( x=1 ; y=\frac{3}{2} \)
c. \( x=4 ; y=2 \)
D. \( x=3 ; y=4 \)


\( \int e^{x} \frac{x-1}{(x+1)^{3}} d x \) is equal to
A \( \cdot \frac{e^{x}}{x+1}+C \)
в. \( \frac{e^{x}}{(x+1)^{2}}+C \)
c. \( -\frac{e^{x}}{x+1}+C \)
D. \( -\frac{e^{x}}{(x+1)^{2}}+C \)


Show that the relative \( R \) in the \( \operatorname{set} A= \)
\{1,2,3,4,5\} given by \( R= \)
\( \{(a, b):|a-b| \text { is even }\}, \) is an
equivalence relation. Show that all the
elements of \{1,3,5\} are related to each
other and all the elements of \{2,4\} are
related to each other. But no element of
\{1,3,5\} is related to any element of
\{2,4\}


Three charges \( -q, Q \) and \( -q \) are
placed at equal distances on a straight line. If the total potential energy of the system of three charges is zero, then the ratio \( Q: q \) is :
A . 1: 2
B . 2: 1
\( c \cdot 1: 1 \)
D. 1: 4


What is the equilibrium constant expression for the reaction,
\( \boldsymbol{P}_{4}(s)+\mathbf{5} O_{2}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{P}_{4} \boldsymbol{O}_{10}(s) \)
\( ^{\mathbf{A}} \cdot_{K_{c}}=\frac{\left[P_{4} O_{10}\right]}{\left[P_{4}\right]\left[O_{2}\right]^{5}} \)
в. \( _{K_{c}}=\frac{\left[P_{4} O_{10}\right]}{5\left[P_{4}\right]\left[O_{2}\right]} \)
\( \mathbf{c} \cdot_{K_{c}=\left[O_{2}\right]^{5}} \)
\( ^{\mathrm{D}} K_{c}=\frac{1}{\left[O_{2}\right]^{5}} \)


Describe Fisher-Tropsch process in the manufacture of propanone with equations two uses.


The given G.P \( 0.15,0.015,0.0015, \ldots 20 \) terms can be written as?


\( \boldsymbol{C H I}_{3} \) is commonly named as:
\( A \). iodoform.
B. iodo alkane
c. chloroform
D. iodine


toppr \( L \)
Q Type your question
bromobutane used as the reactant in
this reaction?
\( A \)
B.
\( c \)
\( D \)


State whether given statement is True or False.
The standard quantity used for comparison is called fundamental quantity.
A. True
B. False


The diameter of a copper wire is \( 2 \mathrm{mm} \) a steady current of 6.25 A is generated by \( 8.5 \times 10^{28} / m^{3} \) electrons flowing
through it. Calculate drift velocity of conduction electrons.


A battery having an emf of 12 Volt and an internal resistance of \( 2 \Omega \) is
connected to another battery having an
emf of 18 Volt and an internal
resistance of \( 2 \Omega \) in such a way that they
are opposing each other and the circuit is closed. Calculate the following.
1. Current flowing in the circuit.
2. Electrical power in the two batteries.
3.Terminal voltage of the two batteries.
4. Electric power consumed in the batteries.


Three similar oscillators, \( A, B, C \) have the same small damping constant \( r \)
but different natural frequencies \( \omega_{0}= \) \( (k / m)^{\frac{1}{2}}: 1200 H z, 1800 H z, 2400 H z .1 f \)
all three are driven by the same source at \( 1800 H z, \) which statement is correct
for the phases of the velocities of the
three?
A \( \cdot \phi_{A}=\phi_{B}=\phi_{c} \)
в. \( \phi_{A}<\phi_{B}=0<\phi_{c} \)
\( \mathbf{c} \cdot \phi_{A}>\phi_{B}=0>\phi_{c} \)
D \( \cdot \phi_{A}>\phi_{B}>0>\phi_{c} \)


In the given figure two lines \( A B \) and
\( C D \) intersect at \( O . O E \) is any ray such
that \( \angle B O E=80^{\circ} . \) If \( \angle B O D=30^{\circ} \)
then the find \( \angle E O C \)


A transverse wave of frequency \( 100 \mathrm{Hz} \) passes through water. The refractive index of water is \( 1.33, \) what will be the
frequency of the wave in water
A . 133 Н \( z \)
в. 100 Н \( z \)
\( c \cdot 75 \mathrm{Hz} \)
D. 165 нz


In the arrangement shown in figure, the
current through \( 5 \Omega \) resistor is
\( A \cdot 2 A \)
B. zero
c. \( \frac{12}{7} \)
D. \( 1 A \)


If \( f(x)=\int_{-1}^{1} \frac{\sin x}{1+t^{2}} d t \) then \( f^{\prime}\left(\frac{\pi}{3}\right) \) is
A. nonexistent
в. \( \pi / 4 \)
c. \( \pi \sqrt{3 / 4} \)
D. none of these


Assertion
Assertion: \( \mathrm{pH} \) of a buffer solution is not
affected by dilution.
Reason
Reason : \( p H=p K_{a}+ \)
\( \log \frac{\text {Conjugate acid, } \boldsymbol{B H}^{+}}{\text {Base}, \boldsymbol{B}} \)
A. If both the assertion and reason are true and reason is
the correct explanation of assertion.
B. If both the assertion and reason are true but reason is not the correct explanation of assertion.
C. If assertion is true but reason is false
D. If both assertion and reason are false.


Write one similarity and one difference
between the chemistry of lanthanoids and that of actinoids.


(i) What is meant by positive deviations from Raoult's Law ? Give an example.
(ii) What is the sign of \( \Delta_{m i x} H \) for positive derivation?


The bullet fired from a gun gets heated on striking a target because
A. it loses energy
B. mechanical energy is converted in to heat energy
c. of latent heat
D. specific heat


When a tall plant with round seeds (TTRR) crossed with a dwarf plant with
wrinkle seeds (ttrr), the \( F_{1} \) generation consists of tall plants with round seeds. What would be the proportion of dwarf
plant with wrinkle seeds in \( F_{1} \)
generation?
\( A \cdot 1 / 4 \)
B. 1/16
\( c \cdot 0 \)
D. \( 1 / 2 \)


A lens of glass is immersed in water.
What will be its effect on the power of
the lens?


The standard enthalpy of formation \( \left(\Delta_{f} H_{298}^{o}\right) \) for methane, \( C H_{4} \) is
\( -74.9 k J m o l^{-1} . \) In order to calculate
the average energy given out in the formation of a \( C-H \) bond from this, it
is necessary to know which one of the
following?
A. The dissociation energy of the hydrogen molecule, \( H_{2} \)
B. The first four ionisation energies of carbon.
C. The dissociation energy of \( H_{2} \) and enthalpy of sublimation of carbon (graphite).
D. The first four ionisation energies of carbon and electron affinity of hydrogen


When diazonium salt solution is
treated with \( K I, \) it forms:
A. bromobenzene
B. acid amide
c. phenol
D. iodobenzene


The purpose of a salt bridge in a
galvanic cell is to:
A. prevent accumulation of charges around the electrodes
B. facilitate continuity of the cell reaction
c. to produce current at a constant strength
D. all of the above


A source \( S_{1} \) is producing, \( 10^{15} \) photons
per second of wavelength \( 5000 A^{0} \)
Another source \( S_{2} \) is producing \( 1.02 \times \)
\( 10^{15} \) photon per second of wave length
\( 5100 A^{\circ}, \) then ratio of power of Source
\( \boldsymbol{S}_{2} \) and power of Source \( \boldsymbol{S}_{1} \)
A . 1.00
B. 1.02
\( c \cdot 1.04 \)
D. 2.00


A right triangle is drawn in a semicircle of radius \( \frac{1}{2} \) with one of its legs along the diameter. The maximum area of the triangle is
A \( \cdot \frac{1}{4} \)
B. \( \frac{3 \sqrt{3}}{32} \)
\( c \cdot \frac{3 \sqrt{3}}{16} \)
D.


How many sides does a pentagon have?
\( A \cdot 2 \)
B. 5
\( c \cdot 6 \)
D.


A redox reaction is one in which:
A. both the substance are reduced.
B. both the substance are oxidised.
C. one substance is reduced and other is oxidised.
D. all of the above.


The \( I U P A C \) name of \( K_{4}\left[F e(C N)_{6}\right] \) is:
A. potassium hexacyano ferrate \( (I I) \)
B. potassium hexacyanido ferrate \( (I I I) \)
c. tetrapotassium hexacyanido ferrate
D. all of the above


A fast blowing town has now 30,000 cattle, during the last few years, the number of cattle depreciates at the rate of \( 20 \% \).If depreciation continues at this rate what will be the cattle population
after 3 years?


The principal value of arg z where \( z= \) \( 1+\cos \frac{6 \pi}{5}+i \sin \frac{6 \pi}{5} \) is given by
A \( \cdot \frac{3 \pi}{5} \)
B. \( -\frac{\pi}{5} \)
\( c \cdot-\frac{3 \pi}{5} \)
D.


At what temperature will the mean molecular energy of a perfect gas be one-third of its value of \( 27^{\circ} \mathrm{C} ? \)
A \( \cdot 10^{\circ} \mathrm{C} \)
В . \( 10^{1} \mathrm{K} \)
\( c \cdot 10^{2} k \)
D. \( 10^{3} \) J


Discuss the trends in chemical
reactivity of group 15 elements.


A thin circular ring of mass \( \mathrm{M} \) and radius R is rotating about its axis with a constant angular velocity \( \omega . \) Two objects, each of mass \( \mathrm{m}, \) are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with an angular velocity:
A. \( \frac{M \omega}{(M+m)} \)
в. \( \frac{\omega(M-2 m)}{(M+2 m)} \)
c. \( \frac{M \omega}{M+2 m} \)
D. \( \frac{\omega(M+2 m)}{M} \)


i) Solve for \( x: \tan ^{-1}(x-1)+ \)
\( \tan ^{-1} x+\tan ^{-1}(x+1)=\tan ^{-1} 3 x \)
ii) Prove that \( \tan ^{-1}\left(\frac{6 x-8 x^{3}}{1-12 x^{2}}\right)- \)
\( \tan ^{-1}\left(\frac{4 x}{1-4 x^{2}}\right)=\tan ^{-1} 2 x ;|2 x|< \)
\( \frac{1}{\sqrt{3}} \)


Name the tissue represented by the jute fibres used for making the ropes


Transportation in the living organisms
is necessary, because of the following
reasons
A. Food, oxygen, water and other essential substances are distributed through this system
B. It displaces the excretory wastes from the cells of the body to the excretory organs from where they are expelled out
c. Temperature and pressure throughout the body are kept uniform
D. All of the above


The insulator of electricity is :
A. copper
B. silk
c. human body
D. acidulated water


2kg of lce block should be dropped from "x km' height to melt completely. The 8 kg of ice block should be dropped from height
\( A \cdot 4 x k m \)
B. \( \times \mathrm{km} \)
c. \( 2 \times \mathrm{km} \)
D. 3x


The IUPAC name of the compound is:
A. 3- Methyl- 5 - heptanone
B. 5-Methylheptan-3-one
c. 5 - Ethyl - 5 - hexanone
D. 2 - Ethyl - 4 - hexanone


Rod-like elongated sclereids in the
seed-coats of pulses are called as
A. Astrosclereids
B. Macrosclereids
c. Trichosclereids
D. Brachysclereids


A radioactive isotope decays as \( z A^{n} \rightarrow z-2 B^{m-4} \rightarrow z-1 C^{m-4} . \) The half
lives of \( A \) and \( B \) are 6 months and 10
months respectively. Assuming that
initially only \( A \) was present, will it be possible to achieve radioactive
equilibrium for \( B \). If \( s o, \) what would be
the ratio of nuclei of \( A \) and \( B \) at
equilibrium. What would happen if the half lives of \( A \) and \( B \) were 10 month and
6 month.


Anaerobic process that takes place after glycolysis is called as
A . TCA
B. Calvin cycle
c. Krebs cycle
D. Fermentation


Assertion: Ozone is an allotrope of
oxygen Reason: Oxygen is bluish-colored liquid
and in singlet state it is para-magnetic.
A. If both assertion and reason are true and the reason is a correct explanation of the assertion
B. If both assertion and reason are true but reason is not a correct explanation of the assertion
c. If the assertion is true but reason is false
D. If both the assertion and reason are false
E. If the assertion is false but the reason is true


A current of \( 965 A \) is passed for 100 sec
between inert electrodes in \( 500 m L \)
solution of \( 2 M C u S O_{4} . \) The molarity of solution after electrolysis would be:
(Assume no change in volume)
A \( .2 M \)
в. \( 1 M \)
c. \( 4 M \)
D. \( 0.5 M \)


A simple harmonic motion is represented by \( \boldsymbol{x}(\boldsymbol{t})=\sin ^{2} \boldsymbol{\omega} \boldsymbol{t}- \)
\( 2 \cos ^{2} \omega t . \) The angular frequency of
oscillation is given by?
\( A \cdot \omega \)
B. 2
c. \( 4 \omega \)
D. \( \frac{\omega}{2} \)
E.


Of the 200 students at College \( T \) majoring in one or more of the sciences, 130 are majoring in chemistry and 150 are majoring in biology. If at least 30 of the students are not majoring in either chemistry or biology, then the number of students majoring in both chemistry and biology could be any number from
A. 2020 to 50
B. 40 to 70
c. 50 to 130
D. 110 to 130
E. 110 to 150


Which features adapt penguins to live
in extremely cold conditions?
A. A white colour thick skin and less fat
B. Thin skin, large eyes, white fur
c. White colour, thick skin and lot of fat
D. White body, paws for swimming, gills for respiration


A bullet of mass \( 8 g \) strikes a vertical
wooden plank \( 5 c m \) thick with a velocity of \( 200 m / s \) in a horizontal direction and emerges out of at \( 150 \mathrm{m} / \mathrm{s} \) in same direction find retarding force bullet experience in wood for what additional thickness bullet will just emerge on
other side


A standing wave is represented by \( \boldsymbol{Y}= \) \( 5 \cos (200 t-0.05 x) \) where \( Y \) and \( A \) are
in metres, t is in seconds and \( x \) is in
metre. Velocity of wave is
A \( .10 \mathrm{m} / \mathrm{s} \)
B. \( 4 \times 10^{3} \mathrm{m} / \mathrm{s} \)
c. \( 0.00025 \mathrm{m} / \mathrm{s} \)
D. \( 4000 \mathrm{m} / \mathrm{s} \)


The acceleration due to gravity \( g \) and density of the earth \( p \) are related by which of the following relations? (Here \( G \) is the gravitational constant and \( R \) is the radius of the earth)
A \( \cdot p=\frac{4 \pi}{3 G R d} \)
в. \( _{p}=\frac{3 g}{4 \pi G R} \)
c. \( _{p}=\frac{3 G}{4 \pi G R} \)
D. \( p=\frac{4 \pi G R}{3 G} \)


What is the number of electrons that
would weigh \( 1 k g \) ? Mass of an electron
is \( 9.11 \times 10^{-31} k g \)


Chemical formula of baking soda is:
A. \( M g S O_{4} \)
в. \( N a_{2} C O_{3} \)
c. \( N a H C O_{3} \)
D. \( M g C O_{3} \)


Show that the points \( \boldsymbol{O}(\mathbf{0}, \mathbf{0}), \boldsymbol{A}(\mathbf{2},-\mathbf{3}, \mathbf{3}), \boldsymbol{B}(-\mathbf{2}, \mathbf{3},-\mathbf{3}) \) are
collinear. Find the ratio in which each point divides the segment joining the other two.


Which statement is/are true?
This question has multiple correct options
A. Two non-zero non-collinear vectors are linearly dependent
B. Any two collinear vectors are linearly independent.
C. Two non-zero non-collinear vectors are always linearly independent
D. \( A \) and \( B \) both are true.


Solve: \( -\frac{5 x-4}{8}-\frac{x-3}{5}=\frac{x-6}{4} \)


Enzymes of oxidative phosphorylation
occur in
A. Endoplasmic reticulum
B. Chloroplasts
c. Mitochondria
D. Golgi apparatus


If a person tests plant hormones for increasing the crop yield, he sprays a large plot with a selected hormone to
determine its effect in hybrid vigor. Which of the following he should avoid?
A \( .2,4- \) D
B. IAA
c. Gibberellin
D. Cytokinin
E. Abscisic acid


The relation between velocity of sound in gas \( (v) \) and \( r . m . s \) velocity of
molecules of gas \( v_{r . m . s} \) is
A \( \cdot v=v_{r, m \cdot s}(\gamma / 3)^{1 / 2} \)
B . \( v_{r . m . s}=v(2 / 3)^{1 / 2} \)
\( \mathbf{c} \cdot v=v_{r . m . s} \)
D . \( v=v_{r . m . s}(3 / \gamma)^{1 / 2} \)


Indicate the types of isomerism exhibited by the following complex and
draw the structure of this isomer.
\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{5}\left(\boldsymbol{N} \boldsymbol{O}_{2}\right)\right]\left(\boldsymbol{N} \boldsymbol{O}_{3}\right)_{2} \)


In a simple harmonic motion \( (\mathrm{SHM}) \)
which of the following does not hold?
A. The force on the particle is maximum at the ends
B. The acceleration is minimum at the mean postion
C. The potential energy is maximum at the mean position
D. The kinetic energy is maximum at the mean position


The volume of a vessel is V. The volume of
the barrel of pump is \( \mathrm{v} \). After \( n \) strokes of
the exhaust pump, what the pressure of
air inside the vessel if the original
pressure inside the vessel is \( \mathrm{P}_{0} \) ?
A \( \cdot P_{0}\left(\frac{V}{V+v}\right)^{n} \)
B \( \cdot P_{0}\left(\frac{V+v}{V}\right)^{n} \)
\( \mathbf{c} \cdot \frac{P_{0} V}{V+v} \)
D. \( \frac{P_{0}(V+v)}{v} \)


Two waves of same frequency but amplitudes equal to \( a \) and \( 2 a \) travelling in the same direction superimpose out of phase. The resultant amplitude will be
A. \( \sqrt{a^{2}+2 a^{2}} \)
B. \( 3 a \)
\( c \cdot 2 a \)
\( D \)


Which of the following configuration
represents a noble gas?
\( \mathbf{A} \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 3 d^{10} 4 s^{2} 4 p^{6} 4 d^{10} 5 s^{2} \)
B \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 3 d^{10} 4 s^{2} 4 f^{14} 5 s^{2} \)
\( \mathbf{c} \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 3 d^{10} 4 s^{2} 4 p^{6} 4 d^{10} 5 s^{2} 5 p^{6} \)
D \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 3 d^{10} 4 s^{2} 4 p^{6} 4 d^{10} 5 s^{2} 5 p^{3} \)


within what respective limits must
\( A / 2 \) lie when \( 2 \sin A / 2= \)
\( +\sqrt{1+\sin A}-\sqrt{1-\sin A} \)


Prove that the points \( \boldsymbol{A}= \) \( (1,2,3), B(3,4,7), C(-3,-2,-5) \) are
collinear \( \& \) find the ratio in which \( B \)
divides \( \boldsymbol{A C} \)
A .2: 5
B . 2: 3
c. 2: 8
D. 2: 7


Among the following, the strongest acid
is :
A. \( C_{6} H_{5} C H_{2} N H_{2} \)
в. \( C_{6} H_{5} \) СООН
c. \( m-C H_{3} O C_{6} H_{4} C O O H \)
D . \( p-C H_{3} O C_{6} H_{4} \) COOH


Which of the following is not a function
of Iymph node?
A. Antibody formation
B. WBC production
c. store RBC
D. To destroy bacteric


If \( \boldsymbol{a} * \boldsymbol{b}=|\boldsymbol{a}-\boldsymbol{b}| \) then \( \boldsymbol{6} * \boldsymbol{8} \) will be
A . -2
B. 14
\( c \cdot 2 \)
D. cannot be determined


Which one is correct relation?
This question has multiple correct options
\( \mathbf{A} \cdot \Delta G=\Delta G^{o}+R T \ln Q \)
\( \mathbf{B} \cdot-\Delta G^{o}=R T \ln K \)
\( \boldsymbol{\alpha} \boldsymbol{H}=n F\left[T\left(\frac{\partial E}{\partial T}\right)_{P}-E\right] \)
D \( \quad E^{o}=\frac{R T}{n F} \ln K \)


The ATP forms a complex with:
A. \( M g^{2+} \)
в. \( C a^{2} \)
\( \mathbf{c} \cdot B e^{2+} \)
D. \( B a^{2} \)


The maximum number of possible interference maxima, for slit-separation
equal to twice the wavelength,in Young's double-slit experiment, is
A . Infinite
B. Five
c. Three
D. zero


Find the difference between total
surface area \( \& \) curved surface area of a hemisphere of radius \( 21 \mathrm{cm} \)
\( \mathbf{A} \cdot 1376 \mathrm{cm}^{2} \)
B . \( 1386 \mathrm{cm}^{2} \)
\( \mathbf{c} \cdot 1396 \mathrm{cm}^{2} \)
D. \( 1404 \mathrm{cm}^{2} \)


What is the \( \left[O H^{-}\right] \) in a \( 0.01 M \) solution
of aniline hydrochloride? \( K_{b} \) for aniline
is \( 4.0 \times 10^{-10} ? \)


In the Boolean algebra: \( \boldsymbol{A}+\boldsymbol{B} \) is equal
to:
\( A \cdot A+B \)
B. \( \bar{A}+\bar{B} \)
c. \( \overline{A . B} \)
D. \( \bar{A} . \bar{B} \)


The angles of dip at the poles and the equator respectively are :
A \( \cdot 30^{0}, 60^{\circ} \)
\( ^{0}, 66^{0} \)
В. \( 90^{0}, 0^{0} \)
c. \( 30^{0}, 90^{\circ} \)
D. \( 0^{0}, 0^{0} \)


The fourth term of a G.P. is 27 and the
7th term is \( 729, \) find the G.P.


Mario's Pizza has 2 choices of crust:
deep dish and thin-and-crispy. The restaurant also has a choice of 5
toppings: tomatoes, sausage, peppers, onions, and pepperoni. Finally, Mario's offers every pizza in extra cheese as well as regular. If Linda's volleyball team decides to order a pizza with 4 toppings. how many different choices do the teammates have at Mario's Pizza?
A \( \cdot 24 \)
в. 32
\( c \cdot 28 \)
D. 20


If \( f: R \rightarrow R \) be defined by \( f(x)=e^{x} \)
and \( g: R \rightarrow R \) be defined by \( g(x)= \)
\( \boldsymbol{x}^{2} . \) The mapping \( \boldsymbol{g} \circ \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) be
defined by \( (\boldsymbol{g} \circ \boldsymbol{f}(\boldsymbol{x}))=\boldsymbol{g}(\boldsymbol{f}(\boldsymbol{x})) \forall \boldsymbol{x} \in \boldsymbol{R} \)
Then
A. \( g \circ f \) is injective but \( f \) is not injective
B. \( g \circ f \) is injective and \( g \) is injective
c. \( g \circ f \) is injective but \( g \) is not injective
D. \( g \circ f \) is surjective and \( g \) is surjective


The phase of the cell cycle in which DNA
synthesis takes place is
A \( \cdot G_{1} \) phase
B. S phase
c. \( G_{2} \) phase
D. \( G_{0} \) phase


In thiosulphuric acid:
A. each sulphur atom is in identical oxidation state.
B. there is a \( S=S \) linkage present.
C. one \( S \) atom is in +2 and other sulphur atom is in +4 oxidation state.
D. there is only one replaceable hydrogen atom.


Those substance which can be
separated by steam distillation are:
A. steam volatile and insoluble in water
B. steam volatile and soluble in water
c. steam volatile and sparingly soluble in water
D. in liquid form in steam and solid form in wate


Find the greatest value of \( \boldsymbol{f}(\boldsymbol{x})= \)
\( x^{2} \log x \) on \( [1, e] \)
\( \mathbf{A} \cdot \mathbf{0} \)
B \( \cdot e^{2} \)
c. \( e / 2 \)
D.


A man eats \( 200 g \) of rice a day and he has enough rice to last him for 35 days. How long would the stock of rice last him if he were to eat \( 250 g \) rice a day.
A . 42
в. 21
c. 28
D. 49


The presence of \( C O_{2} \) in the atmosphere results in:
A . rusting
B. dusting.
c. electroplating.
D. freezing.


If the value of \( g \) at a place is decreased by
\( 2 \% . \) The barometric height of the mercury
A. Increases by \( 2 \% \)
B. Decreases by \( 2 \% \)
C . Remains unchanged
D. Sometime increases and sometime decreases


Both gymnosperms and angiosperms bear seeds, then why are they classified separately?


A mixture in which the mole ratio of \( \boldsymbol{H}_{2} \)
and \( O_{2} \) is 2: 1 is used to prepare water
by the reaction:
\( \mathbf{2} \boldsymbol{H}_{\mathbf{2}}(\boldsymbol{g})+\boldsymbol{O}_{\mathbf{2}}(\boldsymbol{g}) \rightarrow \mathbf{2} \boldsymbol{H}_{\mathbf{2}}(\boldsymbol{g}) \boldsymbol{O} \)
The total pressure in the container is
\( 0.8 \operatorname{atm} \) at \( 20^{\circ} \mathrm{C} \) before the reaction. The
final pressure (in atm) at \( 120^{\circ} \mathrm{C} \) after
the reaction, assuming \( 80 \% \) yield of water is (as nearest integer):


\( \frac{1^{3}}{1}+\frac{1^{3}+2^{3}}{1+3}+\frac{1^{3}+2^{3}+3^{3}}{1+3+5}+\dots n \)
terms \( = \)
A. \( \frac{n\left(2 n^{2}+9 n+13\right)}{24} \)
B. \( \frac{n\left(2 n^{3}+9 n+13\right)}{8} \)
c. \( \frac{n\left(n^{2}+9 n+13\right)}{24} \)
D. \( \frac{n\left(n^{2}+9 n+13\right)}{8} \)


Copy the diagram and complete it by drawing two rays to show the formation
of an image of the object \( A B . \) State the size, position and nature of the image formed.


Why do lories carry heavy load have
more tyres with spread tyres?


Some organic compounds are given in
List I and their uses in List II. Choose the
correct matching.
List 1
\( (A) \) Triodomethane
\( (i) \) Solvent for alkaloids
\( (B) p, p^{\prime} \) -dichlorodipheny \( 1-\quad \) Propellent in trichloroethane aerosols
(C) Trichloromethane
(iii) Antiseptic
\( (D) \) Dichloromethane
\( (i v) \) Insecticide
A \( \cdot(A)-(i i),(B)-(i v),(C)-(i),(D)-(i i i) \)
B. \( (A)-(i i i),(B)-(i v),(C)-(i),(D)-(i i) \)
c. \( (A)-(i i),(B)-(i),(C)-(i v),(D)-(i i i) \)
D. \( (A)-(i i i),(B)-(i),(C)-(i v),(D)-(i i) \)
E \( .(A)-(i),(B)-(i i i),(C)-(i i),(D)-(i v) \)


Which of the following statement(s) is
(are) not correct with reference to
ferrous and ferric ions?
A \( \cdot F e^{3+} \) gives brown colour with potassium ferricyanide
B. \( F e^{2+} \) gives blue ppt with potassium ferricyanide
C \( \cdot F e^{3+} \) gives red colour with potassium sulphocyanide
D. \( F e^{2+} \) gives brown colour with potassium sulphocyanide


A man throws a ball vertically upward
and it rises through \( 20 \mathrm{cm} \) and returns to his hands. What was the initial
velocity \( (u) \) of the ball and for how much
time \( (T) \) it remained in the air? \( (g= \) \( \left.10 m / s^{2}\right) \)
A. \( u=10 \mathrm{m} / \mathrm{s}, T=2 s \)
B. \( u=10 \mathrm{m} / \mathrm{s}, T=4 s \)
c. \( u=20 \mathrm{m} / \mathrm{s}, T=2 s \)
D. \( u=20 \mathrm{m} / \mathrm{s}, T=4 s \)


3 cards are given, one of them is red on both sides, one is blue on both sides \( \& \)
one is blue on one side red on the other
side. One of them is chosen randomly \( \& \) put on the table. It shows red colour on
the upper side. The chance of the other
side of the card being red is:


Solve:
\( \frac{7 x-3}{2 x+3}=\frac{5}{4} \)


The surface area of the wooden door is
\( 416 m^{2} . \) The length and width of the
door is \( 12 \mathrm{m} \) and \( 10 \mathrm{m} \) respectively. Find its height.
A \( .2 m \)
в. \( 4 m \)
\( c .6 m \)
D. \( 8 m \)


Passage of a current for 548 seconds
through a silver coulometer results in the deposition of \( 0.746 \mathrm{g} \) of silver. What is the current (in A)?
A . 1.22
в. 1.16
c. 1.07
D. 1.00


The value of \( \int_{\pi^{3} / 27}^{\pi^{3} / 8} \sin x d t, \) where \( t=x^{3} \)
is
A \( \cdot \frac{\pi^{2}}{6}+(3-\sqrt{3}) \pi-3 \)
B. \( \cos \frac{\pi^{3}}{27}-\cos \frac{\pi^{3}}{8} \)
c. \( \frac{\pi^{2}}{6} \)
D. none of these


Critical angle for certain medium is
\( \sin ^{-1}(0.6) . \) The polarizing angle of that
medium is :
A \( \cdot \tan ^{-1}(1.5) \)
В \( \cdot \tan ^{-1}(0.8) \)
c. \( \tan ^{-1}(1.6667) \)
D. \( \tan ^{-1}(0.667) \)


Write the units digit of the cube for 109
\( A \cdot 1 \)
B. 7
\( c .9 \)
D. 3


The number of Points of Inflexion in \( \boldsymbol{y}= \)
\( x^{3}-3 x^{2}+3 x \) are:
\( A \cdot 0 \)
B.
\( c \cdot 2 \)
D. 3


As the temperature of liquid is increased, mass \& volume will
A. both change
B. mass change \& volume is fixed
c. Mass remains same \( \& \) volume increases
D. both remain same


Write the differences between mitosis
and meiosis.


toppr LoGin
Q Type your question
\( r \)
larger without changing anything else.
If the plate area is made larger after the
capacitor has been disconnected, what
will happen to the charge on the plates,
the voltage across the plates, and the
value of capacitance for this capacitor?
Value after Plate Area is
A . capacitor Property increased Charge on Plates smaller Voltage Across smaller Plates
Capacitance smaller
B. Value after Plate Area is Capacitor Property increased
Charge on Plates larger Voltage Across smaller Plates Capacitance \( \quad \) large
\( c \)
Value after Plates Area is Capacitor Property increased
Change on Plates same Voltage Across larger Plates Capacitance smaller
Value after Plates Area is
D. capacitor Property increased
Change on Plates Same Voltage Across same Plates Capacitance larger
Value after Plates Area is
E. capacitor Property increased Change on Plates same Voltage Across smaller Plates

Capacitance larger


Assertion
Magnetic force is always perpendicular to the magnetic field.
Reason
Electric force is along the direction of electric field.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion,
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


In a group of 1000 people, there are 750 who can speak Hindi and 400 who can
speak Bengali. How many can speak Bengali ?


VA group elements are known as:
A. halogens
B. normal elements
c. chalcogens
D. pnicogens


A student requires hard water for an experiment in his laboratory which is not available in the neighbouring area. In the laboratory there are hard water. Select from the following groups of salts, a group, each salt of which when
dissolved in distilled water will make it
hard.
A. Sodium chloride, Potassium chloride
B. Sodium sulphate, Potassium sulphate
c. sodium sulphate, Calcium sulphate
D. Calcium sulphate, Calcium chloride


If \( \mathrm{M} \) and \( \mathrm{N} \) are any two events, the
probability that not exactly one of them occurs is for an event set \( A \), the
complement is \( \boldsymbol{A}^{o} \)
A. \( P(M)+P(N)-2 P(M \cap N) \)
В. \( P(M)+P(N)-P(M \cap N) \)
C \( \cdot P\left(M^{o}\right)+P\left(N^{o}\right)-2 P\left(M^{o} \cup N^{o}\right) \)
D. \( P\left(M \cap N^{o}\right)+P\left(M^{o} \cup N\right) \)


\( \frac{\sin i}{\sin r}= \) constant, the value of constant depends upon
a) Pair of media
b) Color of incident light
c) Wave length
d) Refracting nature of material
A. Only on a
B. Only on b
c. only on a, d
D. All a, b, c, d


When a coil is connected to a \( 100 \mathrm{V} \) DC
supply, the current is 2 A. When the
same coil is connected to AC source
\( E=100 \sqrt{2} \sin \omega t, \) the current is \( 1 A \)
Find the inductive reactance used in
the circuit.


Assertion: The resistance of a
milliammeter is greater than that of
ammeter

Reason: Shunt resistance in case of
a milliammeter is more than that of
ammeter
A. Both (A) and (R) are true and
(R) is the correct explanation of A
B. Both (A) and (R) are true but (R) is not the correct explanation of A
c. (A) is true but (R) is false
D. (A) is false but (R) is true


Compounds derived from the alkanes from the replacement of one or more than one hydrogen atoms from halogen atoms are called as:
A. alkyl halide
B. haloalkanes
c. halo arenes
D. both \( A \) and \( B \)


Carbon dioxide is necessary for plants. Why do we consider it as a pollutant?


Find the unit vectors along \( \vec{A} \) and \( \vec{B} \) where \( \vec{A}=3 \hat{i}-2 \hat{j}+4 \hat{k} \) and \( \vec{B}=4 \hat{i}- \)


The speed of the striking mass after collision is
A. \( u / 2 \) backwards
B.
c. \( u / 3 \) in same direction
D. \( u / 7 \) backwards


In a double-slit experiment, the distance between the two slits is 1 m \( m \)
and the screen is placed \( 1 m \) away. What
should be the width of each slit to
obtain 20 maxima of double slit pattern
within the central maximum of the
single slit pattern?
A . \( 0.05 \mathrm{cm} \)
B. \( 0.02 \mathrm{cm} \)
c. \( 0.01 \mathrm{cm} \)
D. \( 0.08 \mathrm{cm} \)


Triangle is formed by the lines \( \boldsymbol{x}+\boldsymbol{y}= \)
\( \mathbf{0}, \boldsymbol{x}-\boldsymbol{y}=\mathbf{0} \) and \( \ell \boldsymbol{x}+\boldsymbol{m} \boldsymbol{y}=\mathbf{1 .} \) If
\( \ell \) and \( m \) follow the condition \( \ell^{2}+ \)
\( m^{2}=1 ; \) then the locus of its
circumcentre is
A \( \cdot\left(x^{2}-y^{2}\right)^{2}=x^{2}+y^{2} \)
B . \( \left(x^{2}+y^{2}\right)^{2}=\left(x^{2}-y^{2}\right) \)
C \( \cdot\left(x^{2}+y^{2}\right)=4 x^{2} y^{2} \)
D. \( \left(x^{2}-y^{2}\right)^{2}\left(x^{2}+y^{2}\right)=1 \)


Match column I and column II


Find the focal length of a convex mirror
whose radius of curvature is \( 32 \mathrm{cm} \)


A \( 0.2 \Omega \) resistor and \( 15 \mu \) rapacitor are connected in series to a \( 220 \mathrm{V}, 50 \mathrm{Hz} \) ac source. The impedance of the circuit is
A . \( 250 \Omega \)
в. \( 268 \Omega \)
c. \( 29.15 \Omega \)
D. \( 291.5 \Omega \)


A current of \( 0.6 A \) produces a deflection of 30 in the tangent galvanometer. Calculate the value of current will
produce a deflection of 60
A. \( 1.2 \mathrm{A} \)
в. 1.8 А
c. 2.4 А
D. 3.0 A


A ray \( O P \) monochromatic light is
incident on the face \( A B \) of prism
\( A B C D \) near vertex \( B \) at an incident
angle of \( 60^{\circ} \) (see figure). If the refractive index of the material of the prism is \( \sqrt{3} \) which of the following is (are) correct?
rhis question has multiple correct options
A. The ray gets totally internally reflected at face \( c D \)
B. The ray comes out through face AD
c. The angle between the incident ray and the emergent ray is \( 90^{\circ} \)
D. The angle between the incident ray and the emergent
ray is \( 120^{\circ} \)


Two identical sinusoidal waves each of
amplitude \( 5 m m \) with a phase difference of \( \frac{\pi}{2} \) are travelling in the same direction in a string. The amplitude of the resultant wave (in \( m m \) ) is:
A. zero
B. \( 5 \sqrt{2} \)
c. \( \frac{5}{\sqrt{2}} \)
D. 2.5


The domain of the function \( \boldsymbol{f}(\boldsymbol{x})= \) \( \log _{4}\left(\log _{5}\left(\log _{3}\left(18 x-x^{2}-77\right)\right) \) is \right.
A. \( x \in(4,5) \)
в. \( x \in(0,10) \)
c. \( x \in(8,10) \)
D. None of these


One year ago a man was eight times old as his son. Now his age is equal to the square of his son's age. Represent this situation in form of a quadratic equation


Enzyme, vitamins and hormones can be classified into a single category of biological chemicals, because all of
these
A. Decrease metabolism.
B. Are conjugated proteins.
C. Are exclusively synthesized in the body of a living organism as at presentt
D. Help in regulating metabolism


Define watson-crick model of DNA


Snapshot for a rope shown, at an instant is carrying a travelling wave towards
right, created by source vibrating with the frequency "n". Then,
This question has multiple correct options
A. the speed of the wave is \( (4 \mathrm{n}) \) (distance ab)
B. the particle at point a will be in the present phase of after \( \frac{4}{3 n} \) sec.
C . the phase difference between b and e is \( \frac{3 \pi}{2} \)
D. the wave is harmonic


Find \( \lim _{x \rightarrow(2 n+1) \pi^{+}} \sin \left([\sin x] \frac{\pi}{6}\right), \) where []
is a greatest integer function and \( n \epsilon I \)
A. 0
B. \( \frac{1}{2} \)
\( c \cdot-\frac{1}{2} \)
D. none of these


Co-ordinate of point P on a number line is
7. Find the coordinate of point on the
Number line which is at a distance of 8
units right to point \( P \)


Which of the following are not
characteristic features of fabaceae?
A. The root system, compound leaves and raceme inflorescence
B. Flowers actinomorphic, twisted aestivation and gamopetalous
c. Stamens 10 , introrse, basifixed, dithecous
D. Monocarpellary, ovary superior and bent stigma
E. Fruit is legume


Ritu was given four test tubes
containing different solutions as shown
in figure. Choose the incorrect option.
\( A \cdot 1 \) and 2 turn blue litmus to red.
B. 1 and 4 turn China rose indicator to green
C. Phenolphthalein remains colourless with 2 and 3
D. 4 turns turmeric solution to red


The transport system in plants is made
up of
A. Xylem
B. Vascular tissues
c. Phloem
D. None of the above


A polynomial \( p(x) \) when divided by \( x^{2}- \)
\( 3 x+2 \) leaves remainder \( 2 x-3 . \) Then
A. \( p(x) \) must have a root between 1 and 2
B. \( p(x) \) cannot have a root between 0 and 3
c. \( p(x) \) must have a real root but mayor may not be between o and 3
D. \( p(x) \) need not have a real root


If \( p \) and \( q \) are the lengths of
perpendiculars from the origin to the \( \operatorname{lines} x \cos \theta-y \sin \theta=k \cos 2 \theta \) and
\( x \sec \theta+y \csc \theta=k, \) respectively prove
that \( p^{2}+4 q^{2}=k^{2} \)


The argument of the complex number \( z=\sin \alpha+i(1-\cos \alpha) \) is
A \( \cdot 2 \sin \frac{\alpha}{2} \)
B. \( \frac{\alpha}{2} \)
\( c \cdot a \)
D. none of these


Four charges are arranged at the
corners of a square ABCD as shown in
figure. The force on a positive charge
kept at the centre of the square is:
A. zero
c. along diagonal BD
D. perpendicular to the side AB


Which of the following pairs do not
match?
A. Rotational power - Joule
B. Torque - Newton meter
C. Angular displacement - Radian
D. Angular acceleration - Radian/sec \( ^{2} \)


Find the value of \( \theta \) for attaining a max
value of \( \sin ^{p} \theta \cos ^{q} \theta \) is
A \( \cdot \tan ^{-1} \frac{p}{q} \)
B. \( \tan ^{-1} \frac{\sqrt{p}}{\sqrt{q}} \)
c. \( \tan ^{-1}(p+q) \)
\( \mathbf{D} \cdot \tan ^{-1} q \)


\( y=-1 \)
\( \left.\langle\bigcirc\rangle-\mathrm{cH}_{2} \mathrm{Br}+\mathrm{Ho}-\bigcirc\right\rangle-\mathrm{Br} \)
\( \langle\bigcirc\rangle-_{\mathrm{o}_{\mathrm{H}}}^{\mathrm{cH}_{2}+\mathrm{B}_{\mathrm{r}}}\langle\bigcirc\rangle-\mathrm{B}_{\mathrm{r}} \)
\( \left.\langle\bigcirc\rangle-\mathrm{cH}_{2} \prec \bigcirc\right\rangle- \) ов
но \( \left.\langle\bigcirc\rangle-\text { сн }_{2} \prec \bigcirc\right\rangle \) в


When sulphur is reacted with ozone in
water,the product formed is:
A \( . H_{2} \)
в. \( H_{2} S O_{3} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{SO}_{4} \)
D. \( H_{2} S_{2} O_{8} \)


fa maxima is formed at a detector
then the magnitude of wavelength \( \lambda \) of the wave produced is given by
A . \( \pi R \)
в. \( \frac{\pi R}{2} \)
с. \( \frac{\pi R}{4} \)
D. all of these


Find \( 7^{t h} \) term of \( \left(\frac{4 x}{5}-\frac{5}{2 x}\right)^{9} \)
A. \( \frac{10050}{x^{3}} \)
в. \( \frac{10500}{x^{3}} \)
c. \( \frac{1050}{x^{3}} \)
D. \( \frac{1000}{x^{3}} \)


What is the general solution of the
differential equation \( e^{x} \tan y d x+ \)
\( \left(1-e^{x}\right) \sec ^{2} y d y=0 ? \)
A・sin \( y=c\left(1-e^{x}\right) \) where \( c \) is the constant of integration
B \cdot \( \cos y=c\left(1-e^{x}\right) \) where \( c \) is the constant of integration
C \( \cdot \cot y=c\left(1-e^{x}\right) \) where \( c \) is the constant of integration
D. None of the above


Assertion
\( P H_{3} \) exists but \( P H_{5} \) does not exist
while both \( P C l_{3} \) and \( P C l_{5} \) exist.
Reason
\( P H_{3} \) has \( s p^{3} \) -hybridization.
A. The Assertion is true, Reason is true and Reason is the
correct explanation for Assertion
B. The Assertion is true, Reason is true and Reason is NOT the correct explanation for Assertion
C. The Assertion is true, Reason is false.
D. The Assertion is false, Reason is true.


Which of the following are isomers?
A . 3 PGA and 2 PGA
B. PGAL and DHAP
c. Glucose and Fructose
D. All of these


If a stone is thrown vertically up and it
is caught after time \( t \) seconds, then the maximum height reached by it is


Vessels occur in
A. All angiosperms, all gymnosperms and some pteridophytes
B. All angiosperms and some gymnosperms
C. Most angiosperms, a few gymnosperms and pteridophytes
D. All pteridophytes


The correct way to represent \( 10^{9} W \) is
\( \mathbf{A} \cdot 1 G W \)
в. \( 1 M W \)
\( \mathbf{c} \cdot 1 T W \)
D. none of these


Which of the following information is
incorrect regarding the above graph
A. The body travels \( 15 \mathrm{m} \) in the first 3 seconds.
B. The speed of the body after 5 seconds is zero
C. The initial speed of the body is \( 10 \mathrm{m} / \mathrm{s} \).
D. The body travels \( 25 \mathrm{m} \) in the first 6 seconds.


The cuticle present above the epidermis is helpful in reducing
A. Transpiration
B. Respiration
c. Photosynthesis
D. None of the above


The volume of an auditorium is \( 100 \mathrm{m} \times \)
\( 50 m \times 15 m . \) The reverberation time in
that auditorium is 2 s when the person
who is giving a speech is at a distance of \( 5 \mathrm{m} \) from a wall. The reverberation
time if the same person gives speech at a distance 10m from the wall is
A . \( 1 \mathrm{s} \)
B. 2
\( c \cdot 0.5 s \)
D. 4 s


Find the angle subtended at the centre
of the circle by an are whose length is \( 15 \mathrm{cm} \) if the radius of the circle is
\( \mathbf{2 5} \mathrm{cm} \)


The value of the expression \( \mathbf{2}^{k}\left(\begin{array}{l}n \\ \mathbf{0}\end{array}\right)\left(\begin{array}{l}\boldsymbol{n} \\ \boldsymbol{k}\end{array}\right)-\mathbf{2}^{k-1}\left(\begin{array}{l}\boldsymbol{n} \\ \mathbf{1}\end{array}\right)\left(\begin{array}{l}\boldsymbol{n}-\mathbf{1} \\ \boldsymbol{k}-\mathbf{1}\end{array}\right)+ \)
\( 2^{k-2}\left(\begin{array}{l}n \\ 2\end{array}\right)\left(\begin{array}{l}n-2 \\ k-2\end{array}\right) \dots+ \)
\( (-1)^{k}\left(\begin{array}{c}n \\ k\end{array}\right)\left(\begin{array}{c}n-k \\ 0\end{array}\right) \) is
\( A \cdot\left(\begin{array}{l}n \\ k\end{array}\right. \)
\( ^{\mathbf{B}} \cdot\left(\begin{array}{c}n+1 \\ k\end{array}\right) \)
c. \( \left(\begin{array}{c}n+1 \\ k+1\end{array}\right) \)
D. \( \left(\begin{array}{l}n-1 \\ k-1\end{array}\right) \)


Which of the following processes is used in extractive metallurgy of magnesium?
A. Fused salt electrolysis
B. Self reduction
c. Aqueous solution electrolysis
D. Thermite reduction


A mass \( m \) rests at height \( 2 h \) above the floor, while a mass \( 2 m \) rests at a height of \( 3 h . \) How much more gravitational
potential energy does \( 2 m \) have
compared to \( m \) if the gravitational field is uniform?
\( \mathbf{A} \cdot \mathbf{0} \)
в. \( m g h \)
c. \( 2 m g h \)
D. \( 3 m g h \)
E . \( 4 m g h \)


State any one phenomenon in which moving particles exhibit wave nature.


A 0.001 molal solution of a complex
represented as \( P t\left(N H_{3}\right)_{4} C l_{4} \) in water had freezing point depression of
\( \mathbf{0 . 0 0 5 3 ^ { \circ }} \mathbf{C .} \) Given, \( \boldsymbol{K}_{f} \) for \( \boldsymbol{H}_{2} \boldsymbol{O}= \)
1.86 Kmolality \( ^{-1} \). Assuming 100\%
ionisation of the complex, write the ionisation nature and formula of
complex
A \( \cdot P t\left[\left(N H_{3}\right)_{4} C l_{2}\right] C l_{2} \rightarrow P t\left[\left(N H_{3}\right)_{4} C l_{2}\right]^{2+} 2 C l \)
B . \( P t\left[\left(N H_{3}\right)_{4} C l_{2}\right] C l_{2} \rightarrow P t\left[\left(N H_{3}\right)_{4} C l_{2}\right]^{+} C l \)
c. \( P t\left[\left(N H_{3}\right)_{4} C l_{2}\right] C l_{2} \rightarrow 2 P t\left[\left(N H_{3}\right)_{4} C l_{2}\right]^{+} C l \)
D. \( P t\left[\left(N H_{3}\right)_{4} C l_{2}\right] C l_{2} \rightarrow P t\left[\left(N H_{3}\right)_{4} C l_{2}\right]^{3+} 3 C l \)


Which layer of the atmosphere contains
the ozone layer?
A. Stratosphere
B. Troposphere
c. Exosphere
D. Mesosphere


The below frequency distribution table
represents the blood groups of 30
students of a class. Use this table to
determine the probability that a student of this class, selected at
random, has blood group \( A B \)
Blood group Number of students
\( A \) 9
\( B \) 6
th 3
12
Total 30


Let \( \boldsymbol{A}=\mathbf{1}, \mathbf{2}, \mathbf{3} . \) Then number of
equivalence relations containing \( (\mathbf{1}, \mathbf{2}) \) is
A .
B . 2
\( c .3 \)
D.


Find the slope of the line perpendicular to \( A B \) if \( A=(0,-5) \) and \( B=(-2,4) \)


Formation of lonic \( M g C l_{2} \) is
accelerated by:
A. stable octet configuration of \( M g^{+2} \)
B. stable octet configuration of \( C l \)
c. high lattice enthalpy
D. all of these


What are the oxidation number of the
underlined elements in \( \underline{C} \boldsymbol{H}_{3} \underline{\boldsymbol{C}} \boldsymbol{O} \boldsymbol{O} \boldsymbol{H} \)


A small satellite revolves around a
planet in an orbit just above planet's surface. Taking the mean density of the planet \( 8000 \mathrm{kg} m^{-3} \) and \( G=6.67 \times \)
\( 10^{-11} \mathrm{N} m^{-2} / k g^{-2}, \) find the time period
of the satellite.


The maximum value of static friction is
called limiting friction.
A. True
B. False


Determine the contrapositive of the following statement:
It never rains when it is cold.


Find the square of 43 without multiplication.
A . 2401
в. 4801
\( c .1842 \)
D. 1849


Verify Lagrange's mean value theorem for the following function on the indicated interval. In each case find a
point \( ^{\prime} c^{\prime} \) in the indicated interval as
stated by the Lagrange's mean value theorem:
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{3}-\boldsymbol{2} \boldsymbol{x}^{2}-\boldsymbol{x}+\boldsymbol{3} \) on \( [\mathbf{0}, \mathbf{1}] \)


Which of the following relations is correct for electromagnetic waves:
A \( \cdot \frac{\partial^{2} E}{\partial x^{2}}=\frac{1}{c^{2}} \frac{\partial^{2} E}{\partial t^{2}} \)
\( ^{\mathrm{B}} \frac{\partial^{2} E}{\partial x^{2}}=\left(\frac{\partial E}{\partial t}\right)^{2} \)
c. \( \frac{\partial^{2} E}{\partial x^{2}}=\frac{c^{2} \partial^{2} E}{\partial t^{2}} \)
D. \( \frac{\partial^{2} E}{\partial x^{2}}=c \frac{\partial^{2} E}{\partial t^{2}} \)


How would you name the given
compounds? \( \boldsymbol{H}-\stackrel{\boldsymbol{C}}{\boldsymbol{C}}-\stackrel{\boldsymbol{C}}{\boldsymbol{C}}-\stackrel{\boldsymbol{C}}{\boldsymbol{C}}-\stackrel{\boldsymbol{C}}{\mid}_{\boldsymbol{I}} \boldsymbol{H}=\boldsymbol{C} \equiv \boldsymbol{C}-\boldsymbol{H} \)
A. Hexyne
B. Hex-5-yne
c. Hexane
D. Hexene


The reaction of Sodium methoxide with
\( \boldsymbol{R}_{2} \boldsymbol{C H} \boldsymbol{X} \) is:
A \( \cdot S N^{1} \)
в. \( S N^{2} \)
c. Elimination
D. Substitution


Pis a point on an equipotential surface
S. The field at Pis E.
This question has multiple correct options
A. E must be perpendicular to s in all cases
B. E will be perpendicular to S only if S is a plane surface.
C. E cannot have a component along a tangent to S.
D. E may have a nonzero component along a tangent to if \( \mathrm{S} \) is a curved surface.


How many double covalent bonds can a single carbon atom form at a time?
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot 3 \)
\( D \)


Which of the following is not found in renal cortex;
1. Henle's loop
2. Vasa recta
3. Glomerulus
4. Bowman capsule
\( A \cdot 1,2 \) and 3
B. 1 and 2
\( c \cdot 2 \) and 4
D. 1 and 3


Choose the correct statements among
the following:
This question has multiple correct options
A. Water has highest specific heat compared to all solids are liquids.
B. Water is used in car radiators due to its high specific heat.
C. When heat is supplied to a body is greater the specific heat of a substance lesser will be the change in temperature
D. Specific heat of a substance does not depend on the nature of material.


The oxidation state of oxygen of \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) in the final products when it reacts with
\( \boldsymbol{A} \boldsymbol{s}_{2} \boldsymbol{O}_{3} \) is :
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot-1 \)
D. - -


Bile juice contains no digestive enzymes, yet it is important for digestion. Why?


Zeisse's salt is:
\( \mathbf{A} \cdot\left[P t\left(N H_{3}\right)_{2} C_{12}\right] \)
B \( \cdot K\left[P t C l_{3}\left(C_{2} H_{4}\right)\right] \)
\( \mathbf{C} \cdot F e\left(C_{5} H_{5}\right)_{2} \)
D. None of these


Find the inverse of the following matrix, using elementary transformations:
\( \boldsymbol{A}=\left[\begin{array}{lll}\mathbf{2} & \mathbf{3} & \mathbf{1} \\ \mathbf{2} & \mathbf{4} & \mathbf{1} \\ \mathbf{3} & \mathbf{7} & \mathbf{2}\end{array}\right] \)


Which of these particles having the same kinetic energy has the largest de Broglie wavelength?
A. Electron
B. Alpha particle
c. Proton
D. Neutron


A picture frame has dimensions
\( 24 \mathrm{cm} \times 28 \mathrm{cm} . \) Find the area of the
picture


Chlorine gas is added to drinking water
and swimming pools to destroy bacterias and microorganisms.
A. True
B. False


Assertion (A): According to the principle of conservation of energy all heat can be converted
into mechanical work
Reason (R): Due to various losses, it is impossible to convert all heat into
mechanical work
A. Both Assertion and Reason are true and reason is correct explanation of Assertion
B. Both Assertion and Reason are true but reason is not correct explanation of Assertion
c. Assertion is true but reason is false
D. Both assertion and reason are false


Evaluate: \( \int(\boldsymbol{P}+\boldsymbol{Q}) \boldsymbol{d} \boldsymbol{x} \)
\( \mathbf{A} \cdot \int P d x+\int Q d x \)
в. \( \int P d x+Q+C \)
c. \( \int P d x-\int Q d x \)
D. None of the above


How many structural isomers with the
molecular formula \( C_{4} H_{10} O \) give infra red absorptions both at approximately \( 1200 \mathrm{cm}^{-1} \) and at approximately 3400 \( c m^{-1} ? \)
A . 2
B. 4
\( c \cdot 6 \)
D.


The sum of the \( n \) terms of the series
\( 1.2 .5+2.3 .6+3.4 .7+\ldots . n \) terms is


Now protozoans are not included in kingdom Animalia, because these are
A. Unicellular prokaryotes
B. Multicellular prokaryotes
c. Unicellular eukaryotes
D. Mostly asymmetrical


Which of the following metal exists in
free state?
A. Gold
B. Platinum
C. Mercury
D. All of above


Which of the following is a steroid?
A. Insulin
B. Vitamins
c. cytokinins
D. Estrogen


Hess law is applicable for determination of enthalpy of
A . Reaction
B. Formation
c. Transition
D. All of above


Area enclosed by the curves \( y= \)
\( \ln x ; y=\ln |x| ; y=|\ln x| \) and \( y= \)
\( |\ln | x|| \) is equal to
\( A \cdot 2 \)
B. 4
\( c \cdot 8 \)
D. cannot be determined


Bullets of mass \( 40 g \) each are fired from a machine gun with a velocity of \( 10^{3} m / s . \) If the person firing the bullets experience an average force of \( 200 N \) then the number of bullets fired per
minute will be:
A. 300
в. 600
c. 150
D. 75


In a potentiometer experiment, the balancing length of potentiometer of a cell of e.m.f \( 1.5 \mathrm{V} \) in the secondary is 440 cm. A resistance \( 5 \Omega \) is connected
between the terminals of cell, the balancing length is \( 400 \mathrm{cm} . \) Then
a) internal resistance of the cell is \( 0.5 \Omega \)
b) terminal voltage of the cell is \( 15 / 11 v \)
c) Potential gradient of the potentiometer wire is \( \frac{1.5}{40} V / c m \)
d) potential difference across the potoentiometer wire of length \( 10 \mathrm{m} \) is nearly \( 3.4 \mathrm{V} \)
A. a,b are correct
B. a,b and c are correct
\( c . \) a, b and d are correct
D. a,b,c and d are correct


Which of the following allows solids to conduct electricity?
A. Non-polar covalent bonding
B. Ionic bonding
c. Polar covalent bonding
D. Hydrogen bonding
E. Metallic bonding


Identify the incorrect match related to structure of given interhalogen compounds.
A . IF \( _{7} \) -Pentagonal bipyramidal
B. ClFs-Trigonal bipyaramid
c. \( B r F_{3} \) -Bent T-shped
D. ClF-Linear


The protein in blood which gives resistance to diseases is
A. Thrombin
B. Albumin
c. Immunoglobulin
D. Fibrinogen


During reflex the sensory neurons do not pass directly to the brain.
A. True
B. False


Select in each pair, and one having lower ionization energy and explain the
reason
(a) \( I \) and \( I^{-} \)
(b) \( B r \) and \( K \)
(c) \( L i \) and
\( \boldsymbol{L} \boldsymbol{i}^{+} \)
(d) \( B a \) and \( S r \)
(e) \( O \) and \( S \)
(f) \( B e \)
and \( B \)
(g) \( N \) and \( O \)


A wire is stretched to double its length.
The strain is :
A. infinity
B.
c. zero
D. 0.5


Which one of the following is not the characteristic property of carbon?
A . It exhibits catenation
B. It forms compounds with multiple bonds.
c. Its melting point and boiling point are exceptionally high
D. It show semi-metallic character.


Write two difference between saturated
hydrocarbons and unsaturated hydrocarbons.


How much work is done in moving a
charge of \( 2 C \) across two points having
a potential difference of \( 12 V ? \)


Calculate the difference in the number
of carbon atoms in 1.0 g of \( C-14 \) isotope and \( 1.0 \mathrm{g} \) of \( C-12 \) isotope.
A \( .7 .2 \times 10^{21} \)
B. \( 6.2 \times 10^{20} \)
C \( \cdot 6.2 \times 10^{22} \)
D. \( 7.2 \times 10^{20} \)


Express \( \int_{0}^{4} x^{3} d x \) as limit of sum and thus evaluate it.


The line drawn through the centre of a circle to bisect a chord is perpendicular to the chord?


A synthetic indicator phenolphthalein
gives colour in acidic solution.
A . red
B. blue
\( c . \) pink
D. colourless


A boy can throw a stone up to maximum
height of 10cm. The maximum
horizontal distance that the boy can
throw the same stone up to will be?


The relation \( R \) defined on the \( \operatorname{set} A= \)
\{1,2,3,4,5\} by \( R= \)
\( \left\{(a, b):\left|a^{2}-b^{2}\right|<16\right\}, \) is not given by
A \( \cdot\{(1,1),(2,1),(3,1),(4,1),(2,3)\} \)
B・ \{(2,2),(3,2),(4,2),(2,4)\}
c. \{(3,3),(4,3),(5,4),(3,4)\}
D. none of these


The order, degree of the differential
equation satisfying the relation \( \sqrt{1+x^{2}}+\sqrt{1+y^{2}}=\lambda(x \sqrt{1+y^{2}}) \)
\( \left.y \sqrt{1}+x^{2}\right) \) is
A . 1,1
в. 2,
c. 3,2
D. 0,1


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


\( x \)
\( y_{x}^{i} \)
\( y_{x}^{y} \)
\( x \)


Chloroquin is a drug which is used to control:
A. Pneumonia
B. Malaria
c. Pain
D. ordinary fever


Which of the following statement is correct regarding the mechanism of action of ANF?
A. It causes vasodilation
B. It is secreted in response to high blood pressure
c. It is secreted in response to high blood volume.
D. All of the above


Two coils \( A \) and \( B \) are placed parallel to
each other at a very small distance apart. The coil \( A \) is connected to an A.C.
supply. \( G \) is a very sensitive
galvanometer.When the key \( K \) is closed.
A. A constant deflection will be observed in the galvanometer for a \( 50 \mathrm{Hz} \) supply
B. Small variations will be observed in the galvanometer due to applied voltage of \( 50 \mathrm{Hz} \)
c. oscillations in the galvanometer may be observed when the input a.c. voltage has a frequency of 1 to \( 2 H z \)
D. No variations will be observed in the galvanometer even when the input a.c. voltage has a frequency of 1 to \( 2 \mathrm{H} \)


\( Z n O(S)+A \rightarrow Z n(s)+B: \)
A \( \cdot a=H_{2}, b=O_{2} \)
В \( . a=C, b=C O \)
\( \mathbf{c} \cdot a=S, b=S O_{2} \)
D. \( a=N, b=N O \)


\( N H_{3} \) in Amoeba is excreted by
A. Food vacuole
B. contractile vacuole
c. Plasma membrane
D. Both B and C


In one year lightning produces how much amount of usable nitrogen fertilizer?
A . 250000 tons
B. 25000 tons
c. 250 tons
D. 25 tons


Two trains \( A \) and \( B \) which are \( 100 \mathrm{km} \)
apart are travelling towards each other on different tracks with the initial speed
of \( 50 \mathrm{km} / \mathrm{h} \) for both. The train \( \mathrm{A} \)
accelerates at \( 20 \mathrm{kmh}^{-2} \) and the train \( \mathrm{B} \)
retards at the rate \( 20 k m h^{-2} \) The
distance covered by the train A when they cross each other is approximately:
A. \( 45 \mathrm{km} \)
B. 55 km
\( c . \) 150 \( \mathrm{km} \)
D. \( 162 \mathrm{km} \)


State whether the given statement is
True or False \( \int_{0}^{2} e^{x^{2}} d x \) can be represented as
\( 2 \lim _{n \rightarrow \infty} \frac{1}{n}\left[e^{0}+e^{\frac{4}{n^{2}}}+e^{\frac{16}{n^{2}}}+\ldots \ldots+e^{\frac{2(n-1)^{2}}{n^{2}}}\right] \)
A. True
B. False


The second pregnancy of a woman terminates due to anaemia of the
foetus. She has never had a blood
transfusion. On the basis of this, which
of the following is correct?
A. Child from the first pregnancy is Rh' ve
B. The husband of the woman is \( R h^{+} \) ve
c. The woman is Rh- ve
D. All the above


The succession of both hydrarch and xerarch leads to
A. Highly dry conditions
B. Excessive wet conditions
c. Medium water conditions
D. Xeric conditions


The D.E. whose solution is \( \boldsymbol{y}=\boldsymbol{c}_{1}+\boldsymbol{c}_{2} \boldsymbol{e}^{\boldsymbol{x}} \)
is:
\( \mathbf{A} \cdot y^{\prime \prime}=y \)
B . \( y^{\prime \prime}=y^{\prime} \)
c. \( y^{\prime \prime}+y=0 \)
D \cdot \( y^{\prime \prime}+y^{\prime}=0 \)


Relation between the power (P) consumed by a device, its resistance
(R) and voltage (V) across it.
\( A \cdot P=V R \)
B. \( \quad P=\frac{V^{2}}{R} \)
\( c \cdot p=\frac{V}{t} \)
D. None


If the \( 6^{t h} \) term and \( 12^{t h} \) term of an A.P.
are 30 and 75 respectively, find the sum
of its 20 terms.
A. 1275
в. 1150
\( c .1140 \)
D. 1130


How many Br groups present in compound \( \mathrm{H} \)


Exudation of xylem sap on cutting of a shoot is due to
A. Gutttation
B. Root pressure
c. Transpiration
D. None of the above


The standard molar heats of formation
of ethane, \( C O_{2} \) and \( H_{2} O(l) \) are
respectively -21.1,-94,1 and \( -68.3 k c a l . \) The standard molar heat of
combustion of ethane will be:
A. \( -372 k c a l \)
В. \( -240 k c a l \)
c. \( 162 k c a l \)
D. \( 183.5 k c a l \)


In slime moulds, the somatic phase is
A. Naked
B. Covered by cell wall
c. Diploid
D. Haploid


The term "bark" means
A. Phellem, phelloderm and vascular cambium
B. Phellem, phellogen, phelloderm and secondary phloem
C. Periderm and secondary xylem
D. Cork cambium and cork


In the adjacent figure value of \( x \)
\( \mathbf{A} \cdot 67^{\circ} \)
В. 157
\( \mathrm{c} \cdot 179^{\circ} \)
\( \mathbf{D} \cdot 360^{\circ} \)


Ammonium carbamate when heated to
\( 200^{0} C \) gives a mixture of \( N H_{3} \) and
\( C O_{2} \) with a vapour density of \( 13 . \) What is the degree of dissociation of
ammonium carbamate?
A \( \cdot \frac{3}{2} \)
B \( \cdot \frac{1}{2} \)
\( c \cdot 2 \)
D. 1


What is back emf in a DC motor?


The source of male sex hormones is
A. Interstitial cells of the testis
B. Cells lining the seminal vesicles
C . Cells lining vas deferens
D. The acrosomal vesicles


Match the compounds in Column I with their characteristics/tests/reactions
\( (s) \)
reagent(s)/stereochemistry/isomer(s) given in Column II. Matching can be one
or more than one.
Column I Column I
Reaction \( \quad \) Product and name of the reaction


Consider the reaction:
\( \mathbf{C l}_{2}(\mathbf{a q})+\mathbf{H}_{2} \mathbf{S}(\mathbf{a q}) \rightarrow \mathbf{S}(\mathbf{s})+ \)
\( \mathbf{2 H}^{+}(\mathbf{a q})+\mathbf{2} \mathbf{C l}^{-}(\mathbf{a q}) \)
The rate equation for this reaction is \( = \)
\( \mathbf{k}\left[\mathbf{C l}_{2}\right]\left[\mathbf{H}_{2} \mathbf{S}\right] \)
Which of these mechanisms is/are consistent with this rate equation?
\( (\mathrm{A}) \mathrm{Cl}_{2}+\mathrm{H}_{2} S \rightarrow \mathrm{H}^{+}+\mathrm{Cl}^{-}+\mathrm{Cl}^{+}+ \)
\( \mathbf{H S}^{-}(\text {slow }) \)
\( \mathbf{C l}^{+}+\mathbf{H S}^{-} \rightarrow \mathbf{H}^{+}+\mathbf{C l}^{-}+\mathbf{S}(\text { fast }) \)
(B) \( \mathbf{H}_{2} \mathbf{S} \Leftrightarrow \mathbf{H}^{+}+\mathbf{H S}^{-} \) (fast
equilibrium) \( \mathbf{C l}_{2}+\mathbf{H S}^{-} \rightarrow \mathbf{2 C l}^{-}+\mathbf{H}^{+}+\mathbf{S}(\text { slow }) \)
A. B only
B. Both A and B
c. Neither A nor B
D. A only


a) How many different words can be
formed using the letters of the
word HARYANA?
b) How many of these begin with H and
end with N?
c) In how many of these \( \mathrm{H} \) and \( \mathrm{N} \) are
together?


Three coins are tossed. Describe
two events \( A \) and \( B \) which are mutually
exclusive but not exhaustive.


If the diagonals of a parallelogram are
equal, it is a
A. rectangle
B. square
c. trapezium
D. none of these


Two identical rods each of mass \( \mathrm{m} \) and
length L,are rigidly joined and
suspended in a vertical plane so as to oscillate freely about an axis normal to
the plane of paper passing through 'S'
(point of suspension).Find the time
period of such small oscillations.


The unit of reduction factor of tangent galvanometer is
A. Ampere
B. Gauss
c. Radian
D. No units


In the given circuit, battery is ideal current through the battery is \( \frac{x V}{2 R} . \) Find
the value of \( x \)


A cubical room is formed with 6 plane
mirror. An insect moves along diagonal of the floor with uniform speed. The velocity of its image in two adjacent walls are \( 20 \sqrt{2} \mathrm{cm} / \mathrm{s} \). Then the velocity of image formed by the roof is
\( \mathbf{A} \cdot 20 \mathrm{cm} / \mathrm{sec} \)
B. \( 40 \mathrm{cm} / \mathrm{sec} \)
\( \mathrm{c} \cdot 9 \mathrm{cm} / \mathrm{sec} \)
D. \( 45 \mathrm{cm} / \mathrm{sec} \)


Indicate the types of isomerism exhibited by the following complexes and draw the structures for these
isomers:
\( \mathbf{A} \cdot K\left[\operatorname{Cr}\left(H_{2} O\right)_{2}\left(C_{2} O_{4}\right)_{2}\right] \)
в. \( \left[\operatorname{Co}(e n)_{3}\right] C l_{3} \)
\( ^{\mathbf{c}} \cdot\left[\operatorname{Co}\left(N H_{3}\right)_{5}\left(N O_{2}\right)\right]\left(N O_{3}\right)_{2} \)
D \( \cdot\left[\operatorname{Pt}\left(N H_{3}\right)\left(H_{2} O\right) C l_{2}\right] \)


A mass of material exists in its solid
form at its melting temperature \( 10^{\circ} \mathrm{C} \) The following processes then occur to
the material:

Process 1: An amount of thermal energy
\( Q \) is added to the material and \( \frac{3}{4} \) of the material melts.
Process 2: An identical additional
amount of thermal energy \( Q \) is added to
the material and the material is now a
liquid at \( 50^{\circ} \mathrm{C} \)

What is the ratio of the latent heat of
fusion to the specific heat of the liquid
for this material?
A . 80
B. 60
c. 40
D. 20


The values of \( k, \) so that the equations
\( 2 x^{2}+k x-5=0 \) and \( x^{2}-3 x-4=0 \)
have one root in common, are
A \( \cdot_{3, \frac{27}{2}} \)
в. \( 9, \frac{27}{4} \)
c. \( _{-3, \frac{-27}{4}} \)
D. \( -3, \frac{4}{27} \)


The van der Waal's constants for a gas
\( \operatorname{are} a=3.6 a t m \quad L^{2} m o l^{2}, b= \)
\( \mathbf{0 . 6 L} \quad \boldsymbol{m o l}^{-1} . \) If \( \boldsymbol{R}= \)
\( \begin{array}{lll}\mathbf{0 . 0 8} \mathbf{L} & \mathbf{a t m} & \mathbf{K}^{-\mathbf{1}} \mathbf{m o l}^{-\mathbf{1}} \text { and the }\end{array} \)
Boyle's temperature \( (K) \) is \( T_{0} \) of this
gas, then what is the value of \( \frac{T_{B}}{15} ? \)


A beam of length \( l \) lies on the \( +x \) axis
with its left end on the origin. A cable pulls the beam in negative y-direction with a force \( \boldsymbol{F}=\boldsymbol{F}_{0}\left(1-\frac{\boldsymbol{x}}{\boldsymbol{l}}\right) . \) If the axis
is fixed at \( x=0 \) then find the torque.
\( \mathbf{A} \cdot-F_{0} l \)
B. \( \frac{F_{0} l}{2} \)
\( c \cdot-\frac{F_{0} l}{2} \)
D. none of these


Why is diffusion insufficient to meet
the oxygen requirements of multicellular organisms like humans?


Assertion
The terms action and reaction in the
third law of motion stand for
simultaneous mutual forces between a
pair of bodies.
Reason
In this contex action always precede or
cause reaction.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The pair in which phosphorous atoms
have a formal oxidation state of +3 is:
A. pyrophosphorous and hypophosphoric acids
B. orthophosphorous and hypophosphoric acids
C. pyrophosphorous and pyrophosphoric acids
D. orthophosphorous and pyrophosphorous acids


All linear pairs are
A. Supplementary
B. vertically opposite
C . right angles
D. none


invented a pump to extract air out of the vessel.
A. otto von Guericke
B. Newton
c. Albert Einstein
D. Gallileo


Find out shape and hybridisation of the
following molecules \( \left(\boldsymbol{P} C l_{5}, \boldsymbol{N} \boldsymbol{H}_{3}, \boldsymbol{H}_{2} \boldsymbol{O}\right. \)
\( \boldsymbol{S F}_{6} \)


A metal cylinder of length \( L \) is
subjected to a uniform compressive
force \( F \) as shown in the figure. The
material of the cylinder has Young's modulus \( Y \) and Poisson's ratio \( \sigma \). The
change in volume of the cylinder is:
\( ^{\mathrm{A}} \cdot \frac{\sigma F L}{Y} \)
B. \( \frac{(1-\sigma) F L}{Y} \)
\( c \)
\( D \)


Loop of Henle occurs in
A. cortex
B. Medulla
c. Pelvis
D. Ureter


Suppose \( n \) is a natural number such that \( \left|i+2 i^{2}+3 i^{3}+\ldots+n i^{n}\right|=18 \sqrt{2} \)
where \( i \) is the square root of \( -1 . \) Then \( n \)
is.
\( \mathbf{A} \cdot \mathbf{9} \)
B. 18
\( c \cdot 36 \)
D. 72


For which one of the following input combinations, the given logic circuit
gives the output \( Y=1 ? \)
\( \mathbf{A} \cdot A=0, B=0, C=0 \)
В. \( A=0, B=1, C=0 \)
C \( . A=0, B=1, C=1 \)
D. \( A=1, B=1, C=1 \)
E \( . A=1, B=0, C=1 \)


Find the equation of the parabola that satisfies the following conditions: Focus (0,-3)\( ; \) directrix \( y=3 \)


Evolution of different species in a given
area starting from a point and spreading to other geographical area is
known as
A. Adaptive radiation
B. Natural selection
c. Migration
D. Divergent evolution


Which of the following statements is
wrong about isotopes?
A. Isotopes have same number of electrons
B. Isotopes have same chemical properties
C. Isotopes have same number of neutrons
D. Isotopes have same number of protons


An ideal gas is mixture of \( C_{2} H_{6} \) and
\( C_{2} H_{4} \) occupies 281 at 1 atm 8273 k. The
mixture reacts completely with 128 g of \( O_{2} \) to produce \( C O_{2} \) pf water vapour
Mole fraction of \( C_{2} H_{6} \) in the mixture
will be:
A. 0.4
B. 0.6
\( c \cdot 0.2 \)
D. 0.8


The incorrect statement regarding
biogas is
A. It predominantly contains methane
B. Production involves anaerobic digestion of organic wastes
C. Dung can be used for generation of biogas
D. It does not contain hydrogen sulphide


Name the planet which is least dense among all the planets.
A. Mercury
B. Mars
c. Saturn
D. Jupiter


A soft drink can has a circular base
with diameter \( 7 \mathrm{cm} \) and height \( 12 \mathrm{cm} . \) A powder tin has a square base with side
\( 7 c m \) and height \( 12 c m . \) What is the difference in their capacities?
A \( \cdot 126 c m^{3} \)
В. \( 132 c m^{3} \)
\( \mathrm{c} \cdot 146 \mathrm{cm}^{3} \)
D. \( 150 \mathrm{cm}^{3} \)


The reverberation times in a cinema
theatre are \( 3 s, 2 s \) when it is empty,
filled with audience respectively. The
reverberation time when the theatre is
half filled with audience is
A . 2.3 s
B. 2.4
\( c .2 .5 \mathrm{s} \)
D. 2.6 s


The distance of a particle as a function of time is shown below. The graph
indicates that
A. The particle starts with certain velocity but the motion is retarded and finally the particle stops
B. The velocity of the particle is constant throughout
C. The acceleration of the particle is constant throughout.
D. The particle starts with another constant velocity then the motion is in acceleration for some time then finally the particle moves with another constant velocity.


The side of a square sheet is increasing at the rate of \( 4 \mathrm{cm} \) per minute. The rate by which the area increasing when the side is \( 8 \mathrm{cm} \) long is.
\( \mathbf{A} \cdot 60 \mathrm{cm}^{2} / \mathrm{minute} \)
B. \( 66 \mathrm{cm}^{2} / \) minute
c. \( 62 \mathrm{cm}^{2} / \mathrm{minute} \)
D. \( 64 \mathrm{cm}^{2} / \mathrm{minute} \)


Which are correct regarding stability of
solution?
This question has multiple correct options
A. Lyophilic solutions are stabilised due to a layer of solvent round solution particles.
B. Lyophobic solutions are stabilised due to presence of charge.
C. Addition of Iyophilic brings in more stability to Iyophobic.
D. Addition of Iyophobic brings in more stability to Iyophillic.


Assertion
Potentiometer is used only to compare
potential differences.
Reason
The potentiometer draws current from the voltage source being measured.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The value of acceleration due to gravity,
at earth surface is \( g \). Its value at the
centre of the earth, which we assume as
a.sphere of radius \( R \) and of uniform mass density, will be:
\( \mathbf{A} \cdot 10 R m / s^{2} \)
B. zero
c. \( 5 R m / s \)
D. \( 20 R m / s^{2} \)


Boiling point of heavy water is:
A \( .3 .82^{\circ} \mathrm{C} \)
B . \( 42^{\circ} \mathrm{C} \)
c. \( 100^{\circ} \mathrm{C} \)
D. \( 101.42^{0} C \)


If the susceptibility of dia, para and ferro magnetic materials are Xd. \( X p . X f \) respectively, then
A. \( X d<X p<X f \)
в. \( X f<X p<X d \)
c. \( X f<X d<X p \)
D. \( X d<X f<X p \)


What is the composition of last droplet of liquid remaining in equilibrium with
vapour?
A \( . x_{A}=0.6 ; x_{B}=0.4 \)
B . \( x_{A}=0.5 ; x_{B}=0.5 \)
c. \( x_{A}=0.7 ; x_{B}=0.3 \)
D. \( x_{A}=0.3 ; x_{B}=0.7 \)


PQR is a right-angled triangle with \( \mathrm{QS} \) as the perpendicular to the hypotenuse. The ratio PS : SR is equal to
A. \( \mathrm{QP}: \mathrm{QR} \)
B \( \cdot Q P^{2}: Q R^{2} \)
\( c \cdot 2: 3 \)
D. None of the above


Out of the following whose elasticity is independent of temperature
A. stee
B. copper
c. Invar steel
D. glass


Glycolysis is conversion of
A. Glucose to glycogen
B. Glycogen to glucose
c. Glucose to pyruvic acid
D. Glucose to citric acid


State True or False.
The radial wave function for the ground state of \( H \) -atom decreases
exponentially towards zero as \( r \)
increases.
A. True
B. False


The vapour density of oxygen is than air.
A. more
B. less
c. depends on temperature
D. none of the above


Mendeleev's classified elements in:
A. Increasing order of atomic number
B. Increasing order of atomic masses
C. Decreasing order of atomic masses
D. Decreasing order of atomic number


Construct a \( \triangle A B C \) in which the base
\( B C=5 \mathrm{cm}, \angle B A C=40^{\circ} \) and the
median from \( \boldsymbol{A} \) to \( \boldsymbol{B} \boldsymbol{C} \) is \( \boldsymbol{6} \mathrm{cm} . \) Also
measure the length of the altitude from
\( A \)


Assertion
Heavy water is used as amoderator in
nuclear reactors.
Reason
Heavy water is made of an isotope of
helium.
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


Presence of moisture in contact
process:
A. activates the catalyst
B. deactivates the catalyst
c. increases the product
D. makes the catalyst porous


The deeper we go inside a flowing river, fluid friction:
A. decreases
B. increases
c. remains same
D. becomes zero


The correct statement about \( I C l_{5} \) and
\( \boldsymbol{I} \boldsymbol{C l}_{4}^{-} \) is:
A \( \cdot I C l_{5} \) is trigonal bipyramidal and \( I C l_{4}^{-} \) is tetrahedral
B. \( I C l_{5} \) is square pyramidal and \( I C l_{4} \) is tetrahedral
C . \( I C l_{5} \) is square pyramidal and \( I C l_{4}^{-} \) is square planar
D. both are isostructural


If \( A \) is \( P h C^{+} H_{2} \) and \( B \) is \( C H_{2}=C H- \) \( C^{+} H_{2}, \) the greater number of resonating structure is of
\( A \cdot A \)
B. B
c. both A and B
D. None of these


Nature of equipotential surface for a
point charge is:
A. Ellipsoid with charge at foci
B. Sphere with charge at the center of the sphere
C. Sphere with charge on the surface of the sphere
D. Plane with charge on the surface


Match the List I with the List II.
A. \( A-i v, B-i, C- \) ii, D - iii
B. A - v, B - i, C - ii, D - iii
C. \( A-i v, B-i, C- \) iii, \( D-i i \)
D. \( A-i, B-i v, C- \) ii, \( D \) -iii


\( A B C \) is a right-angled triangle, where \( A B \) and \( B C \) are \( 25 \mathrm{cm} \) and \( 60 \mathrm{cm} \)
respectively. A metal sphere of \( 2 \mathrm{cm} \)
radius charged to a potential of \( 9 \times 10^{5} \)
Vis placed at \( B \) as shown in Fig. Find the amount of work done in carrying a
positive charge of 1 coulomb from \( C \) to
\( \boldsymbol{A}: \)
\( A \cdot 21 k J \)
В. \( 42 k J \)
\( c \cdot 14 k J \)
D. \( 52 k J \)


The total number of matrices
\( \boldsymbol{A}= \)
\( \left(\begin{array}{ccc}0 & 2 x & 2 x \\ 2 y & y & -y \\ 1 & -1 & 1\end{array}\right),(x, y \in R, x \neq y) \) for
which \( \boldsymbol{A}^{\boldsymbol{T}} \boldsymbol{A}=\mathbf{3} \boldsymbol{I}_{3} \) is:
\( A \)
B. 2
\( c .3 \)
\( D \)


\( \underbrace{k}_{k} \)


The highly water soluble alkaline earth
metal fluoride is:
A. \( C a F_{2} \)
в. \( B a F_{2} \)
c. \( M g F_{2} \)
D. \( B e F_{2} \)


\( \mathbf{2} \boldsymbol{A}+\boldsymbol{B} \rightarrow \boldsymbol{C}+\boldsymbol{D} \)
In this reaction, if we double the
concentration of \( A, \) reaction rate
become two times. And in another
experiment, we double the
concentration of \( A \) and \( B \), reaction rate
again become two times. What is the
order of this reaction?
A
B. 3
\( c \cdot 2 \)
D. 1.5


For the reaction \( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{B} \boldsymbol{r}_{2}(\boldsymbol{g}) \rightarrow \)
\( 2 H B r(g), \) the experiment data
suggested that \( r=k\left[H_{2}\right]\left[B r_{2}\right]^{1 / 2} . \) The
molecularity and order of the reaction are respectively:
A. 2, 3/2
B. 3/2,3/2
c. Not defined, 3/2
D. \( 1,1 / 2 \)


Right aortic arch is present in?
A. Mammals only
B. Birds only
C. Both reptiles and birds
D. Both birds and mammals


An example of natural fibre is :
A . Nylon
B. Rayon
c. Jute
D. Terylene


An electric dipole coincides on the zaxis and its centre coincides with the origin of the cartesian coordinate system. The electric field at an axial
point at a distance \( z \) from the origin is
\( E(z) \) and the electric field at an
equatorial point at a distance \( y \) from
the origin is \( E(y) \)

Given that \( y=z>>a \), the value of
\( \frac{E(z)}{E(y)} \) is
A . 1
B. 2
\( c .4 \)
D. 3


A man is know to speak the truth 3 out if 4 times. He throws a die and reports
that it is a six. The probability that it is actually a six is:
A \( \cdot \frac{3}{8} \)
B. \( \frac{1}{5} \)
\( c \cdot \frac{3}{4} \)
D. None of these


Equipment needed to determine the
heat of reaction
A. Buret
B. Calorimeter
c. Manometer
D. Geiger counter
E. Voltmeter


A varying current in a coil change from
\( 10 A \) to 0 in 0.5 sec. If the average emf
induced in the coil is \( 220 V \), the self
inductance of the coil is :
A . \( 5 H \)
в. \( 6 H \)
\( c .11 H \)
D. \( 12 H \)


Which of the following statement is
correct?
\( \mathbf{A} \cdot S-S \) bond is present in \( H_{2} S_{2} O_{6} \)
B. In peroxosulphuric acid \( \left(H_{2} S O_{5}\right) \) sulphur is in +8 oxidation state
C. Copper powder along with \( A l_{2} O_{3} \) and \( K_{2} O \) is used as a
catalyst in the preparation of \( N H_{3} \) by Haber's process
D. Change in enthalpy is positive for the preparation of \( S O_{3} \) by catalytic oxidation of \( S O_{2} \)


A magnetic needle free to rotate in a vertical plane parallel to the magnetic meridian has its north tip pointing
down at \( 22^{0} \) with the horizontal. The
horizontal component of the earth's magnetic field at the place is known to be \( 0.35 G . \) Determine the magnitude of
the earth's magnetic field at the place.
A . 0.12
B. 1.23
\( c \cdot 4.56 \)
D. 0.38


Some of alkali metal salts are coloured
\( N a_{2} C r O_{4}- \) yellow, \( K M n O_{4}- \) pink
\( K_{2} M n O_{4} \) -green. It is due to:
A. cations are coloured ions
B. anions are coloured ions
c. both \( A \) and \( B \)
D. none of the above


The amount of heat required to change 1 kg of ice to water without a change in temperature is known as:
A. Specific latent heat of vaporisation
B. Specific latent heat of fusion
c. latent heat of vaporisation
D. latent heat of fusion


If \( I=\int \frac{1}{e^{x}} \tan ^{-1}\left(e^{x}\right) d x, \) then I equals
A \( \cdot-e^{-x} \tan ^{-1}\left(e^{x}\right)+\log \left(1+e^{2 x}\right)+C \)
B. \( x-e^{-x} \tan ^{-1} e^{x}-\frac{1}{2} \log \left(1+e^{x}\right)+C \)
c. \( x-e^{-x} \tan ^{-1}\left(e^{x}\right)-\frac{1}{2} \log \left(1+e^{2 x}\right)+C \)
D. none of these


Which of the following is compound \( X \) of
the synthesis?
\( A \)
в.
\( \mathrm{c} \cdot \begin{array}{c}^{o H} \\ \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}-\mathrm{CH}_{2} \mathrm{Br}\end{array} \)
D.
\[
C H_{3} C H_{2} C H-C H_{2}
\]
\( O B r \)
\( _{O H} \)


Assertion
Algal blooms occur in nutrient poor
water.
Reason
Algal blooms make water unfit for
human consumption but cause enormous growth of fish.
A. Both A and R are true and R is the correct explanation of
B. Both A and R are true and R is not the correct explanation of
c. A is true but R is false
D. Both A and R are false


A short length of DNA molecule has 80 thymine and 80 guanine bases. The total number of nucleotids in the DNA
fragment is
A \( \cdot 160 \)
B. 40
\( c \cdot 80 \)
D. 320
E. 640


If \( \cos \theta=\frac{8}{10} \) and \( \theta \) is acute, what is the
value of \( \operatorname{cosec} \theta ? \)
A \( \cdot \frac{10}{6} \)
в. \( \frac{8}{10} \)
\( c \cdot \frac{1}{8} \)
D. \( \frac{10}{7} \)


In the uranium radioactive series, the initial nucleus is \( _{92} U^{238} \) and that the final nucleus is \( _{82} P b^{206} . \) When uranium nucleus decays to lead the number of \( \alpha \)
particles and \( \beta- \) particles emitted are:
A. \( 8 \alpha, 6 \beta \)
в. \( 6 \alpha, 7 \beta \)
c. \( 6 \alpha, 8 \beta \)
D. \( 4 \alpha, 3 \beta \)


The area of the parallelogram whose adjacent sides are \( \overline{\boldsymbol{P}}=\mathbf{3} \overline{\boldsymbol{i}}+\mathbf{4} \overline{\boldsymbol{j}}, \overline{\boldsymbol{Q}}= \)
\( -5 \bar{i}+7 \bar{j} \) is (in sq. units)
A . 20.
B. 82
\( c \cdot 4 \)
D. 46


Consider a circle with unit radius. There
are seven adjacent sectors, \( S_{1}, S_{2}, S_{3} \ldots S_{7}, \) in the circle such that
their total area is \( \frac{1}{8} \) of the area of the circle. Further, the area of the jth sector
is twice that of the \( (j-1)^{t h} \) sector, for
\( j=2, \dots .7 \)
Find the area of the sector \( \boldsymbol{S}_{1} \)
\( \mathbf{A} \cdot \frac{3 \pi}{1016} \)
В. \( \frac{\pi}{508} \)
c. \( \frac{\pi}{1016} \)
D. \( \frac{\pi}{336} \)


Which of the following is not a condensation polymer?
A. Nylon - 6,6
в. РТFE
c. Dacron
D. Glyptal


\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}\left\{\cot ^{-1} \frac{\sqrt{1+\boldsymbol{x}}-\sqrt{1-\boldsymbol{x}}}{\sqrt{1+\boldsymbol{x}}+\sqrt{1-\boldsymbol{x}}}\right\}= \)
\( A \cdot \frac{1}{\sqrt{1-x^{2}}} \)
B \( \cdot \frac{-1}{2 \sqrt{1-x^{2}}} \)
\( \mathbf{C} \cdot \frac{1}{1+x^{2}} \)
D. \( \frac{-1}{2\left(1+x^{2}\right)} \)


State whether true or false.
A couple can never be replaced by a single force.
A. True
B. False


TLC of human blood is about?
\( \mathbf{A} \cdot 5000-6000 \) per \( \mathrm{ml} \) of blood
B. \( 5000-11000 \) per ml of blood
C \( .5000-11000 \) per cubic mm of blood
D. \( 2000-6000 \) per cubic mm of blood


The distance of Neptune and Saturn
from the sun are nearly \( 10^{13} \mathrm{m} \) and \( 10^{12} \) \( \mathrm{m} \) respectively. Assuming that they move in circular orbits, their periodic times would be in the ratio of
A . 10
в. 100
c. \( 10 \sqrt{10} \)
D. 1000


State True or False.
\( N F_{3} \) is stable but \( N C l_{3} \) and \( N I_{3} \) are
explosive in nature.
A. True
B. False


Match List-I with List-II
\( \begin{array}{ll}\text { List-I } & \text { List-II } \\ \text { A. Molarity } & \text { i) no units } \\ \text { B. Molality } & \text { ii) gm.equivalents/lit } \\ \text { C. Normality } & \text { iii) mol/lit } \\ \text { D. Mole fraction } & \text { iv) moles/kg. solvent }\end{array} \)
\( \mathbf{A} \)
B. A-iv, B-v, C-ii, D-i
C . A-iii, B-iv, C-i, D-i
D-i
D. A-iii, B-iv, C-ii,


\( \int \frac{d x}{\left(1+x^{2}\right)^{2}} \)


Explain briefly the following terms with suitable examples:
(i) Protonema
(ii) Antheridium
(iii) Archegonium
(iv) Diplontic
(v) Sporophyll
(vi) Isogamy


What is the mass of a mole of water
containing \( 50 \% \) of heavy water \( \left(D_{2} O\right) ? \)
\( A \cdot 18 g \)
B. 198
\( c \cdot 20 g \)
D. 21


A solid sphere, a thin hoop, and a solid cylinder all roll down an incline plane
from rest. All three have a mass, \( m \) and
a radius, \( r \) and all start at the same
position on the ramp. Which of the following correctly describes the order in which they would reach the bottom of the ramp?
A. First the hoop, then cylinder, then sphere
B. First the cylinder, then hoop, then sphere
c. First the sphere, then hoop, then cylinder
D. First the sphere, then cylinder, then hoop
E. First the cylinder, then the sphere, then the hoop


R.Q. İs measured by
A. Mercury manometer
B. Respirometer.
c. Auxanometer.
D. Calorimeter.


\( \mathbf{1} c c \) of \( \mathbf{0 . 1} \boldsymbol{N} \boldsymbol{H} \boldsymbol{C l} \) is added to \( \mathbf{1} \) litre
solution of sodium chloride. The \( \boldsymbol{p} \boldsymbol{H} \) of
the resulting solution will be:
A. 7
B.
\( c \cdot 10 \)
D. 4


Which of the following will have the highest first ionization energy?
A. Halogens
B. Alkali metals
c. Alkaline earth metals
D. Noble gases
E. Lanthanides


Which of the following statement is
correct?
A. Oxidation involves gain of electron
B. Substance which is reduced is reducing agent
C. Exothermic process involves absorption of heat
D. Oxidation involves loss of electrons


Find the area of the region bounded by the curve \( y^{2}=x \) and the lines \( x= \)
\( 1, x=4 \) and the \( x \) -axis.


Sodium bicarbonate is less soluble in
water than potassium bicarbonate, it is
due to:
A. low molecular weight of \( N a H C O_{3} \) as compared to \( K H C O_{3} \)
B. hydrogen bonding, sodium bicarbonate contains a dimeric anionic structure in potassium bicarbonate, anions forman infinite chain
C. hydrogen bonding, potassium bicarbonate contains a dimeric anionic structure while in sodium bicarbonate, anions form an infinite chain
D. \( K H C O_{3} \) is thermally less stable than \( N a H C O_{3} \)


A mass 'm' is fixed at \( x=a \) on a
parabolic wire with its axis vertical and
vertex at the origin as shown in the
figure. The equation of parabola is \( x^{2}= \)
4ay. The wire frame is rotating with
constant angular velocity \( \omega \) about \( Y \)
axis. The acceleration of the bead is
\( A \cdot \frac{a}{4} \omega^{2} \)
B. \( a \omega^{2} \)
c. zero
\( D \)


\( \times \frac{1}{10}=\frac{1}{30} \times \frac{1}{40} ; \) the value of \( x \) is
A \( \cdot \frac{1}{120} \)
B. 400
c. 120
D. \( \frac{1}{400} \)


In which of the following year, the depletion of the ozone layer have been
noticed?
A . 1979
в. 1980
\( c . \) 1981
D. 1982


Which planets are called inner planets?


Ohm is the SI unit of:
A . resistance
B. capacitance
c. voltage
D. current


Show that the function \( f(x)=2 x+ \) \( \cot ^{-1} x-\log \{x+\sqrt{\left(1+x^{2}\right)}\} \)
increasing \( \forall \mathrm{R} \)


If \( y=\frac{x \sin ^{-1} x}{\sqrt{1-x^{2}}}, \) prove that \( (1- \)
\( \left.x^{2}\right) \frac{d y}{d x}=x+\frac{y}{x} \)


The distance of the point (1,-2,3) from the plane \( \boldsymbol{x}-\boldsymbol{y}+\boldsymbol{z}=\mathbf{5} \) measured
parallel to the line \( \frac{x}{2}=\frac{y}{3}=\frac{z-1}{-6} \) is
A .
B . 2
\( c \cdot 4 \)
D. None of these