If \( A \) is a \( 3 * 3 \) singular matrix then
\( \boldsymbol{A}(\boldsymbol{A} \boldsymbol{d} \boldsymbol{j} \boldsymbol{A})= \)
\( A \cdot \) Det \( A \)
B.
\( c \cdot c \)
D. ±1


If one of the zeroes of the polynomial \( \boldsymbol{f}(\boldsymbol{z})=\boldsymbol{p}^{2} \boldsymbol{z}^{2}+\boldsymbol{8} \boldsymbol{z}+\boldsymbol{1} \boldsymbol{6} \) is reciprocal of
the other, then the value of \( p \) is:
\( A \ldots \pm 4 \)
B. - 5
\( c \cdot 6 \)
D. -


Using the principle mathematical induction, prove that \( \forall n \epsilon N \) \( \boldsymbol{I}_{n}=\int_{0}^{\pi / 2} \cos ^{n} \boldsymbol{x} \sin \boldsymbol{n} \boldsymbol{x} \boldsymbol{d} \boldsymbol{x} \)
\( =\frac{1}{2^{n+1}}\left[2+\frac{2^{2}}{2}+\frac{2^{3}}{3} \ldots+\frac{2^{n}}{n}\right] \)


If \( \boldsymbol{f}(\boldsymbol{x})=\cos \boldsymbol{\pi}(|\boldsymbol{x}|+[\boldsymbol{x}]), \) then \( \boldsymbol{f}(\boldsymbol{x}) \)
is/are (where [.] denotes greatest
integer function) This question has multiple correct options
A . continuous at \( x=\frac{1}{2} \)
B. continuous at \( x=0 \)
c. Differentiable in (2,4)
D. Differentiable in (0,1)


The process of reduction involves:
A. removal of hydrogen
B. gain of electrons
C. addition of oxygen
D. loss of electrons


What are the functions of the following in breathing? Diaphragm.


What would be the final temperature of
a mixture of \( 50 g \) of water at \( 20^{\circ} C \)
temperature and \( 50 g \) of water at \( 40^{\circ} C \)
temperature?


Assertion
Angina pectoris means "pain in the chest".
Reason
It results due to carrying of extra blood to the heart muscle.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A rigid body rotates about a fixed axis with variable angular velocity equal to \( (a b t) \) at \( t \) where a and \( b \) are
constants. The angle through which it rotates before it comes to rest is
A \( \cdot \frac{a^{2}}{b} \)
в. \( \frac{a^{2}}{2 b} \)
c. \( \frac{a^{2}}{4 b} \)
D. \( \frac{a^{2}}{2 b^{2}} \)


A copper ball of radius \( r \) is moving with
a uniform velocity \( v \) in the mustard oil
and the dragging force acting on the ball is \( F . \) The dragging force on the
copper ball of radius \( 2 r \) with uniform
velocity \( 2 v \) in the mustard oil is
A. \( F \)
в. \( 2 F \)
c. \( 4 F \)
D. \( 8 F \)


Define critical angle. Explain total internal reflection using a neat
diagram.


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


If the points \( a(1,2,-1), B(2,6,2) \) and \( c(\lambda,-2,-4) \) are collinear then \( \lambda \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B . 2
\( c .-2 \)
D.


The distance between earth and moon
is about \( 3.8 \times 10^{5} k m . \) At what point(s)
will the net gravitational force of earthmoon system be zero? [Given mass of
earth is 81 times the moon's mass)
\( \mathbf{A} \cdot 38 \times 10^{9} m \)
B . \( 38 \times 10^{7} m \)
c. \( 8 \times 10^{7} m \)
D. \( 3.8 \times 10^{7} m \)


A point \( P \) lies on the line whose end
points are \( \boldsymbol{A}(\mathbf{1}, \mathbf{2}, \mathbf{3}) \) and \( \boldsymbol{B}(\mathbf{2}, \mathbf{1 0}, \mathbf{1}) \)
If \( z \) -co-ordinate of \( P \) is \( 7, \) find sum of its
other co - ordinates.


Kamal and Monika appeared for an
interview for two vacancies. The
probability of Kamal's selection is \( \frac{1}{3} \) and that of Monika's selection is \( \frac{1}{5} . \) Find the probability that both of them will be
selected.


What is common between earthworm
and Periplaneta?
A. Both have red coloured blood
B. Both possess anal styles
c. Both have Malpighian tubules
D. Both have segmented body.


Following question is based on \( S c(Z= \)
21).
For any \( 1 s \) electron, \( Z^{*} \) (effective
nuclear charge) is :
A . 21.0
B. 20.65
c. 16.85
D. 9.75


topp
\( E \)
Q туре уочr question
\( n \)


The area bounded by \( y=3 x \) and \( y=x^{2} \) is (in square units)
A . 10
B. 5
c. 4.5
D.


Convert into improper fractions. \( 4 \frac{5}{6} \)


Integrate with respect to \( x \).
\( e^{x} \sin x \)


One among the lanthanoids, \( \boldsymbol{C} \boldsymbol{e}(\boldsymbol{I} \boldsymbol{I} \boldsymbol{I}) \)
can be easily oxidised to \( C e(I V) \) Explain


Ammonium sulfate is an example of:
A. an acid
B. a base
c. an acidic salt
D. a basic salt


The IUPAC name of the compound is:
\[
\mathrm{CH}_{3}-\mathrm{CH}-\mathrm{CH}-\mathrm{CH}_{2} \mathrm{NH}_{2}
\]
A. 2,3 -dimethylbutan-4-amine
B. 2, 4- dimethylbutan-1-amine
c. 2,4 - dimethylbutan-4-amine
D. 2,3 - dimethylbutan-1-amine


Electric field intensity at points in between and outside two thin separated parallel sheets of infinite dimension with like charges of same surface charge density \( (\sigma) \) are and
respectively
A \( \cdot \sigma / \epsilon_{0}, \sigma / \epsilon_{0} \)
в. \( 0, \sigma / \epsilon_{0} \)
\( c .0,0 \)
D. \( \sigma / \varepsilon_{0}, 0 \)


Crocodile lives for about
A . 10 years
B. 20 years
c. 40 years
D. 60 years


In bryophytes and pteridophytes, transport of male gametes requires
A. wind
B. Insects
c. Birds
D. water


Maximum hydrolysis occurs in the salt
of a weak acid and a weak base. If true
write \( 1, \) else write 0


(i) If specific heat of ice is 0.5 cal \( g^{-1} C^{-1}, \) then the amount of heat required to convert 10 g of ice from \( -5^{\circ} C \) to \( 0^{\circ} C \)
\( \mathbf{A} \cdot 15 \mathrm{cal} \)
B . \( 25 \mathrm{cal} \)
\( \mathbf{c} .50 \mathrm{cal} \)
D. 100 cal


The given figure shows a rectangle ABC inscribed in a circle as shown
alongside. \( f(A B=28 \mathrm{cm} \text { and } B C=21 \mathrm{cm}, \) Find the
area of the shaded portion of the given
figure
A . \( 374.5 \mathrm{cm}^{2} \)
В. 374.5 \( m^{2} \)
c. \( 3.745 \mathrm{cm}^{2} \)
D. \( 37.45 \mathrm{cm}^{2} \)


Give balanced equations for the following reactions:
(i) How will you convert ethyl amine to
methyl amine?
(ii) What is the effect of denaturation
on the structure of proteins?
(iii) Name the nitrogen base residues
present in DNA.


The zygospores of Rhizopus contain a high amount of fat globules. It is thick walled and the colour is
A . Green
B. White
c. Grey
D. Black


The lyophobic colloids are highly solvated.
A . True
B. False


n Fig., \( A B \) and \( C D \) are two diameters
of a circle with centre \( O, \) which are
perpendicular to each other. \( \boldsymbol{O B} \) is the
diameter of the smaller circle. If \( \boldsymbol{O A}= \)
\( \mathbf{7} \mathrm{cm}, \) find the area of the shaded region. \( \left[\boldsymbol{U s e} \boldsymbol{\pi}=\frac{\mathbf{2 2}}{\mathbf{7}}\right] \)
\( \mathbf{A} \cdot 60.5 \mathrm{cm}^{2} \)
B . \( 63.5 \mathrm{cm}^{2} \)
\( \mathbf{c} \cdot 66.5 \mathrm{cm}^{2} \)
D. \( 56.5 \mathrm{cm}^{2} \)


\( A=x / x \) is a two digit number, which
divisible by \( 2(\text { or }) 3 \) and \( x \leq 50, B= \)
\( x / x \) is a two digit number, which
divisible by 6 and \( x \leq 50 \).Find \( n(A \cup B)=? \)
\( n(A \cap B)=? \)


Solve:
\( \lim _{n \rightarrow 0} \frac{\sin a n}{\sin n} \)


Find the minimum load resistance
which can be used for the zener diode
as shown in figure. Given, \( \boldsymbol{V}_{\boldsymbol{Z}}= \)
\( \mathbf{1 0} \boldsymbol{V}, \boldsymbol{R}_{Z}=\mathbf{0} \mathbf{\Omega}, \boldsymbol{R}=\mathbf{4 5 0 \Omega}, \boldsymbol{I}_{Z}(\boldsymbol{m} \boldsymbol{i n})= \)
\( 2 m A \) and \( I_{Z}(\max )=60 m A \)
A . \( 0 \Omega \)
B. \( 333.3 \Omega \)
c. \( 31.95 \Omega \)
D. \( 319.5 \Omega \)


In sugarcane, the adventitious roots are called as
A. Prop roots
B. Prop and tuberous roots
c. Pneumatophores
D. None of the above


An inverted T-shaped object is placed on a smooth horizontal floor as shown in
figure
A force \( \boldsymbol{F} \) is applied on the system as
shown in figure. The value of \( x \) so that
the system performs pure transional motion is
A \( \cdot \frac{L}{4} \)
в. \( \frac{3 L}{4} \)
c. \( \frac{L}{2} \)
D. \( \frac{2 L}{2} \)


The magnetic moment of \( \boldsymbol{K}_{\mathbf{2}}\left[\boldsymbol{M} \boldsymbol{n} \boldsymbol{C l}_{4}\right] \)
corrected to the nearest integer is
\( \mathbf{A} \cdot 6 B M \)
в. \( 7 B M \)
\( \mathbf{c} \cdot 8 B M \)
D. \( 5 B M \)


Solve the following system of equations \( \frac{\mathbf{6}}{\boldsymbol{x}+\boldsymbol{y}}=\frac{\mathbf{7}}{\boldsymbol{x}-\boldsymbol{y}}+\mathbf{3}, \frac{\mathbf{1}}{\mathbf{2}(\boldsymbol{x}+\boldsymbol{y})}= \)
\( \frac{1}{3(x-y)} \) where \( x+y \neq 0 \) and \( x \)
\( \boldsymbol{y} \neq \mathbf{0} \)


The area enclosed by \( \boldsymbol{x}^{2}+\boldsymbol{y}^{2}=\mathbf{4}, \boldsymbol{y}= \)
\( x^{2}+x+1, y=\left[\sin ^{2} \frac{x}{4}+\cos \frac{x}{4}\right] \) and \( x \)
-axis (where [.] denotes the greatest integer function) is:
A \( \cdot \frac{2 \pi}{3}+\sqrt{3}-\frac{1}{6} \)
В \( \cdot \frac{2 \pi}{3}+2 \sqrt{3}-\frac{1}{6} \)
c. \( 2 \sqrt{3}-\frac{1}{3} \)
D. \( \frac{\pi}{3}+\sqrt{3} \)


A fraction in reduced form is such that
when it is squared and then its numerator is increased by \( 25 \% \) and the
denominator is reduced to \( 80 \% \) it
results in \( 5 / 8 \) of the original fraction. The product of the numerator and denominator is.
A . 6
B. 12
c. 10
D. 7


State true or false:
Let \( \left|\left(\bar{z}_{1}-2 \bar{z}_{2}\right) /\left(2-z_{1} \bar{z}_{2}\right)\right|=1 \) and
\( \left|z_{2}\right| \neq 1, \) where \( z_{1} \) and \( z_{2} \) are complex
numbers, then \( \left|z_{1}\right|=2 \)


A log of wood of length \( l \) and mass \( M \) is floating on the surface of river perpendicular to the banks. One end of the log touches the banks. A man of
mass \( m \) standing at the other end
walks towards the bank. Calculate the
displacement of the log when he reaches the nearer end of the log.


An object A is moving with \( 5 \mathrm{m} / \mathrm{s} \) and \( \mathrm{B} \) is moving with \( 20 \mathrm{m} / \mathrm{s} \) in the same direction. (positive \( \mathbf{x} \) -axis). Find velocity of B with respect to A.
\( A \cdot 15 \mathrm{m} / \mathrm{s} \)
B. 20 \( \mathrm{m} / \mathrm{s} \)
\( c \cdot-15 m / s \)
D. -20 m/s


A can travelling at a speed of \( 20 \mathrm{m} / \mathrm{sec} \) to due north along the highway make it turns on to a side word that has due
east. If takes 50 sec for the ear to comp
lite the 50 sec for the end of 50 sec the
ear has a speed of \( 15 \mathrm{m} / \mathrm{sec} \) along the side road. Determine the magnitude of an acceleration over the 50 sec internal.


If vertices of a triangle are (0,4),(4,1) and \( (7,5), \) find its perimeter.


Assertion (A) : The net magnetic flux coming out of a closed surface is always zero. Reason
(R) : Unlike poles of equa strength exist together
A. Both A and R are true and R is the correct explanation of A
B. Both A and R are true and R is not correct explanation of
c. A is true, But R is false
D. A is false, But R is true


Rate of reaction (r) is plotted against
temperature (T) for an enzyme
catalysed reaction. Which of the
following is correct representation?
\( A \)
в.
c.
D.


A box of mass \( 50 k g \) is pulled along on
an inclined plane of \( 12 m \) length and \( 2 m \)
height by a constant force of \( 100 N \) from rest. It acquires a velocity of \( 2 m / s \) when
it reaches the top of the plane. The work done against friction in joules is
A . 50
B. 100
\( c \cdot 150 \)
D. 200


Rank the following solvents in decreasing order of ability to dissolve given compound.
\begin{tabular}{|l|}
\hline Solvent \\
\hline \( \mathrm{Et}_{2} \mathrm{O} \) \\
\( \mathrm{H}_{2} \mathrm{O} \) \\
\( \mathrm{EtOH} \) \\
\hline
\end{tabular}\( \rightarrow \underbrace{\bigcirc}_{\text {Solute }} \)
A. \( E t_{2} O>H_{2} O>E t O H \)
в. \( H_{2} O>E t O H>E t_{2} O \)
c. \( H_{2} O>E t_{2} O>E t O H \)
D. \( E t_{2} O>E t O H>H_{2} O \)


What is the fundamental component of universe known as?
A. Galaxy
B. Universe
c. Asteroids
D. meteors


State whether given statement is True or False

Apparent power is expressed in watts.
A. True
B. False


The \( 3 r d \) term of \( (2+\sqrt{3})^{3} \) is
A . 16
B. 17
c. 18
D. 19


\( \int_{0}^{\pi / 2} \frac{d_{X}}{4 \cos ^{2} x+9 \sin ^{2} x}= \)
A \( \cdot \frac{\pi}{12} \)
в.
c.
D.


The atomic weight of an atom is due to:
A. electrons and protons
B. electrons and neutrons
c. neutrons and protons
D. electrons, neutrons and protons


A sphere has a charge of \( +50 C . \) The absolute potential at a point at
distance of \( 10^{-12} \) m from the sphere is:
(Radius of the sphere is \( \left.<10^{-12} \text {m }\right) \)
A . \( 4500 \mathrm{V} \)
B . \( 45 \times 10^{23} \mathrm{V} \)
c. \( 4.5 \times 10^{23} V \)
D. \( 45 \times 10^{24} V \)


Impulse is equal to
A. momentum
B. change in momentum
C . rate of change of momentum
D. rate of change of force


The decreasing order of boiling points of the following is :
(।) \( R C O C l,(\|)(R C O)_{2} O,(\| I) \)
\( R C O N H_{2},(I V) R C O O H \)
A . ।> IV > || > II
B. |||>|| > IV > |
c. IV > III > I> II
D. II >|>||| > IV


Which of the following is not correct?
A. White and red phosphorus react with chlorine at room temperature
B. White phosphorus is metastable, while red phosphorus is stable
C. White phosphorus is lighter than red phosphorus
D. White phosphorus is highly poisionous, while red phosphorus is not


Diborane is a potential rocket fuel which undergoes combustion according to the reaction \( B_{2} H_{6(g)}+3 O_{2(g)} \rightarrow \)
\( B_{2} O_{3(s)}+3 H_{2} O(g) \) Form the following dada, calculation the enthalpy change for the combustion of diborane.
\( 2 B(s)+(3 / 2) O_{2(g)} \rightarrow B_{2} O_{3(s)} \)
\( \boldsymbol{\Delta} \boldsymbol{H}=-\mathbf{1 2 7 3} \boldsymbol{k J} \boldsymbol{m o l}^{-1} \boldsymbol{H}_{2(g)}+ \)
\( (1 / 2) O_{2(g)} \rightarrow H_{2} O(1) \quad \Delta H= \)
\( -286 k J m o l^{-1} H_{2} O_{(1)} \rightarrow H_{2} O_{(g)} \)
\( \Delta H=44 k J m o l^{-1} \)
\( 2 B(s)+3 H_{2(g)} \rightarrow B_{2} H_{6(g)} \)
\( \Delta \boldsymbol{H}=\mathbf{3 6 K J m o l}^{-1} \)


A charge \( Q \) is divided into two parts of \( q \)
and \( Q-q . \) If the Coulomb repulsion
between them when they are separated, is to be maximum, the ratio of \( \frac{Q}{q} \) should be:
A .2
в. \( 1 / 2 \)
\( c \cdot 4 \)
D. \( 1 / 4 \)


Rs. 1000 invested at \( 5 \% \) p.a simple interest, if the interest is added to the
principle after every 10 years, the
amount will become Rs. 2000 after
A. 15 years
B. \( \quad 16 \frac{2}{3} \) years
c. 18 years
D. 20 years


Write formula of following compound:
Mercury
(II) chloride


Why sulphur is added to the natural rubber?


In Ammonia-Boron trifluoride complex,
the donor molecule is Ammonia.
A. True
B. False


What is the difference between
unicellular and multi cellularlar
organisms in organisation of their cells?


When all the inputs of a NAND gate are connected together, the resulting circuit is:
A . a NOT gate
B. an AND gate
c. an OR gate
D. a NOR gate


In a hypothetical case, if the diameter of the earth becomes half of its present value and its mass becomes four times
of its present value, then how would the weight of any object on the surface of the earth be affected?
A. Weight is doubled
B. Weight is quadrapled
c. weight becomes 16 times
D. Weight remains same


The formation of diethyl ether from ethanol is catalysed by:
A. \( H_{2} S O_{4} \)
в. \( A l O_{3} \)
c. \( C u \)
D. \( N i \)


A metal disc of radius R rotates with an
angular velocity, \( \omega=1 r a d / s \) about an
axis perpendicular to its plane passing through its centre in a magnetic field of induction B acting perpendicular to the plane of the disc. The induced e.m.f. between the rim and axis of the disc is:
A \( . B R^{2} \)
B \( \cdot 2 B^{2} R^{2} \)
\( c \cdot B R^{3} \)
D. \( B R^{2} / 2 \)


Solve:
\( \lim _{x \rightarrow 3} \frac{x^{2}-9}{x-3} \)


Which of the following is not a mixture but a compound?
A. Soda water
B. Sea water
c. Soil
D. None of above


\( \frac{-1}{1} \)


In rising from the bottom of a lake to the top, the temperature of air bubble remains unchanged, but the diameter gets doubled. If \( h \) is the barometric
height (expressed in metres of mercury
of relative density \( \rho \) ) at surface of the lake, the depth of the lake (in metres) is
\( \mathbf{A} \cdot 8 \rho h \)
B. \( 4 \rho h \)
\( c \cdot 7 \rho h \)
D. \( 2 \rho h \)


Explain the acquired trait with examples.


Analyse the first pair and complete the
second pair
\[
\text { Battery: } \overbrace{^{2}}{\mid \sqrt{\mathrm{TIME}} \longrightarrow} \quad \text { DC Generator: }
\]


Electrical potential at the centre of a charged conductor is:
A . zero
B. twice as that on the surface
c. half of that on the surface
D. same as that on the surface


The tangent to the curve \( y=x^{2}+6 \) at \( a \)
point (1,7) touches the circle \( x^{2}+ \) \( y^{2}+16 x+12 y+c=0 \) at a point \( Q \)
then the coordinate of \( Q \) then the
coordinate of \( Q \) are.
A. (-6,-11)
B. (-9,-13)
\begin{tabular}{l}
c. (-10,-15) \\
\hline
\end{tabular}
D. (-6,-7)


How does the electric field(E) between
the plates of a charged cylindrical capacitor vary with the distance r from the axis of the cylinder?
A \( \cdot E \propto \frac{1}{r^{2}} \)
в. \( \quad E \propto \frac{1}{r} \)
c. \( E \propto r^{2} \)
D. \( E \propto r \)


In the above diagram the number of
men who are married and in service is
\( 4 \cdot 2 \)
3
\( c \)
D. 17


The mode of the binomial distribution
for which mean and standard deviation
are 10 and \( \sqrt{5} \) respectively, is
A. 7
B. 8
\( c .9 \)
D. 10


The value of \( \int \sqrt{1+\sec x} d x \) is
\( A \cdot \sin ^{-1}(\sqrt{2} \sin x)+C \)
B \( \cdot 2 \sin ^{-1}\left(\sqrt{2} \sin \frac{x}{2}\right)+C \)
c. \( 2 \sin ^{-1}(\sqrt{2} \sin x)+C \)
D \( \cdot \sin ^{-1}\left(\sqrt{2} \sin \frac{x}{2}\right)+C \)


What is meant by refraction of light? State the laws of refraction.


If 2.2 kilowatt power is being transmitted at \( 44 \mathrm{KV} \) on a \( 20 \Omega \) line,
then power loss will be:
A. 0.1 watt
B. 1.4 watt
c. 100 watt
D. 0.05 watt


What are geostationary satellites?
Write any one use of them.


Places \( A \) and \( B \) are \( 80 k m \) apart from
each other on a highway. A car starts
from \( A \) and \( B \) other from \( B \) at the same
time. If they move in the some direction,
they meet in 8 hours and if they move in
opposite direction they meet in 1 hour
and 20 minutes Find the speeds of the
car


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


Explain the phenomenon of electromagnetic induction. Describe an
experiment to show that a current is set up in a closed loop when an external
magnetic field passing through the loop increases or decreases:


Corrosion of iron is :
\( A \cdot \) redox process
B. neutrilization process
C . precipitation process
D. none of the above


Which one of the following does not
follow octet rule?
A \( . P F_{3} \)
в. \( B F_{3} \)
\( c \cdot C O_{2} \)
D. \( C C l_{4} \)


\( \boldsymbol{n} \stackrel{L}{\rightarrow} \infty\left[\frac{1}{\boldsymbol{n}}+\frac{\boldsymbol{n}^{2}}{(\boldsymbol{n}+1)^{3}}+\frac{\boldsymbol{n}^{2}}{(\boldsymbol{n}+2)^{3}}+\right. \)
\( \left.\ldots+\frac{\mathbf{1}}{\mathbf{8 n}}\right]= \)
A. 2/5
B. 3/5
\( c \cdot 3 / 8 \)
D. \( 11 / 7 \)


A circular wire of diameter 30 mm is
placed \( 25 \mathrm{cm} \) away from a concave mirror of focal length \( 10 \mathrm{cm} . \) If area of
image is \( X \pi m m^{2}, \) what is the value of
x? The centre of the wire is on the axis of
the mirror, with its plane normal to the axis.


Evaluate \( \left|\begin{array}{lll}\boldsymbol{x} & \boldsymbol{x}^{2} & \boldsymbol{x}^{2} \\ \boldsymbol{y} & \boldsymbol{y}^{2} & \boldsymbol{y}^{2} \\ \boldsymbol{z} & \boldsymbol{z}^{2} & \boldsymbol{z}^{3}\end{array}\right| \)


Find the value of \( x \) and \( y \) using cross
multiplication method:
\( 5 x+y=15 \) and \( 2 x+6 y=34 \)
A. (-2,5)
в. (2,-5)
\( c \cdot(2,5) \)
D. (-2,-5)


In solid state \( P C l_{5} \) exist as an ionic
solid \( \left[\boldsymbol{P C l}_{4}\right]^{+}\left[\boldsymbol{P C l}_{6}\right]^{-} \) hybridisation
state of cation and anion respectively:
\( \mathbf{A} \cdot d s p^{2}, s p^{3} d^{2} \)
B \( \cdot s p^{3}, s p^{3} d^{2} \)
\( \mathbf{c} \cdot s p^{3} d^{2}, s p^{3} \)
D. \( s p^{3} d^{2}, d s p^{2} \)


The electric force on a unit positive charge at a given point in a system of charges is called
A . electric dipole moment
B. electric field intensity
c. electric potential
D. electric charge


Assertion
\( \pi_{b} \) and \( \pi^{*} \) orbitals obtained from \( 2 p \)
orbital are lying in the same plane.
Reason
Bonding M.O's are formed by constructive interference while
antibonding M.O's are formed by destructive interference.
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 resistance between \( A \& B \)


Find the vector joining the points \( P(2,3,0) \) and \( Q(-1,-2,-4) \) directed
from \( \boldsymbol{P} \) to \( \boldsymbol{Q} \)


An amphoteric substance is:
A. a substance that can act as both acids and base by being both proton acceptor and proton donor
B. a substance that acts as an acid by being both a proton acceptor and a proton donor
C. a substance that acts as a base by being both a proton acceptor and a proton donor
D. when a hydronium ion from a base reacts with a hydroxide ion from an acid to make water and a salt
E. a base that forms when an acid loses a proton


Integrate with respect to \( x \) \( \frac{1-\sin x}{x+\cos x} \)


The strength of 11.2 volume solution of
\( H_{2} O_{2} \) is: \( [ \) Given that molar mass of
\( \boldsymbol{H}=\mathbf{1} \boldsymbol{g} \boldsymbol{m o l}^{-1} \) and \( \boldsymbol{O}=\mathbf{1 6} \boldsymbol{g} \boldsymbol{m o l}^{-1} \mathbf{j} \)
A . \( 13.6 \% \)
в. \( 3.4 \% \)
\( c .34 \% \)
D. \( 1.7 \% \)


Which of the following statements are
correct?
This question has multiple correct options
A. One mole of \( P h N H N H_{2} \) reacts with 3 mol glucose to
form osazone
B. One mole of D-fructose reacts with 3 mol \( P h N H N H_{2} \)
to form osazone
C. One mole of D-2-deoxy glucose reacts with 1 mol \( P h N H N H_{2} \) to form phenylhyrazone
D. One mole of D-3-deoxy glucose reacts with 3 mol \( P h N H N H_{2} \) to form osazone


Electric charge is always conserved in physical process.
A. True
B. False


The value of \( \int_{0}^{\infty} \frac{x}{(1+x)\left(x^{2}+1\right)} d x \) is
A . \( 2 \pi \)
в.
c. \( \frac{\pi}{16} \)
D. \( \frac{\pi}{32} \)


How many spherical bullets can be made out of a cube of lead whose edge measures \( 22 \mathrm{cm}, \) each bullet being \( 2 \mathrm{cm} \) in diameter?
A . 1347
B. 2541
\( c .2662 \)
D. 5324


If \( 2 \sin 2 \theta=\sqrt{3}, \) then \( \tan \theta \) is
\( A \)
B. \( \frac{1}{\sqrt{3}} \)
\( c \cdot \sqrt{3} \)
D. \( \frac{1}{\sqrt{2}} \)


The IUPAC name of the compound is:
A. 1,2,3 -trihydroxypropane
B. 3-hydroxypentane-1,5-diol
c. 1,2,3 -hydroxypropane
D. propane-1,2,3-triol


Assertion
Statement-1 If \( a_{1}, a_{2}, a_{3}, \dots \dots \dots, a_{24} \) are
\( \ln \) A. P. such that \( a_{1}+a_{5}+a_{10}+a_{15}+ \)
\( \boldsymbol{a}_{20}+\boldsymbol{a}_{24}=\mathbf{2 2 5} \) then \( \boldsymbol{a}_{\mathbf{1}}+\boldsymbol{a}_{\mathbf{2}}+\boldsymbol{a}_{3}+ \)
\( \ldots .+a_{23}+a_{24}=900 \) because
Reason
Statement-2 In any A.P. sum of the terms equidistant from begining and end is constant and is equal to
the sum of the first and the last term,
A. Statement-1 is true, Statement-2 Is true and statement-2 is correct explanation for Statement-
B. Statement-1 is true, Statement-2 Is true and Statement-2 is NOT correct explanation for Statement
c. statement-1 is true, statement-2 is false
D. statement-1 is false, Statement-2 Is true


Which of the following combination of properties would be most desirable for a
cooking pot?
A. High specific heat and low conductivity
B. Low specific heat and high conductivity
c. High specific heat and high conductivity
D. Low specific heat and low conductivity


Consider the following statements:
\( A: p-p, p-n, n-n \) forces between
nucleons are not equal and charge
dependent
B: In nuclear reactor the fission reaction
will be in accelerating state if the value
of neutron reproduction factor \( k>1 \)
A. Both A and B are correct
B. Both A and B are wrongg
C. A is wrong and B is correct
D. A is correct and B is wrong


State whether given statement is True
or False

It is usually preferable to have a longer reverberation time in an auditorium for
music than one for speeches.
A. True
B. False


Find the real numbers \( x \) and \( y \) if \( (x- \)
\( i y)(3+5 i) \) is the conjugate of \( -6- \)
\( \mathbf{2 4 i . 1}+\boldsymbol{i} \mathbf{1}-\boldsymbol{i} \)


Find the ratio of the conduction
electrons to the total number of atoms
in the given conductor.
A. Almost 1: 4
B. Almost 1: 2
c. Almost 2: 1
D. Almost 1: 1


Among the following quantities:
(i) mass number
(ii) average mass of a Carbon atom in
amu
(iii) the charge of nucleus in amu and
(iv) mass of a Carbon -12 atom in grams
A. only (i) is whole number
B. only (i) and (iii) are whole number
c. only (i) and (iv) are whole numbers
D. only (iii) and (iv) are whole numbers


When any number is divided by 12,then
dividend comes \( \frac{1}{4} \) th of the other
number. By how much percent first number is greater than the second number.
A. 150
в. 200
c. 300
D. Data inadequate


Chemical equilibrium is dynamic
because:
A. the equilibrium attained quickly
B. the concentration of the reactants and products become same at equilibrium
c. the concentration of reactants and products are constant but different
D. both forward and backward reactions occur at all time with the same speedd


The perimeter of a semi-circular protector is \( 72 \mathrm{cm} \) then its radius is
\( \mathrm{cm} \)
A . 36
B. 28
\( c \cdot 14 \)
D. 7


A constant function is a periodic function.
A. True
B. False


If \( f(x)= \) \( \left\{\begin{array}{cc}(\mathbf{1}+|\sin \boldsymbol{x}|)^{\frac{a}{|\sin |}} & ;-\frac{\pi}{6}<\boldsymbol{x}<\mathbf{0} \\ \boldsymbol{b} & ; \boldsymbol{x}=\mathbf{0} \\ \boldsymbol{e}^{\left(\frac{\tan 2 x}{\tan 3 x}\right)} & ; \mathbf{0}<\boldsymbol{x}<\frac{\pi}{\mathbf{6}}\end{array}\right. \)
is a continuous function on \( \left(-\frac{\pi}{6}, \frac{\pi}{6}\right) \)
then
A \( \cdot a=\frac{2}{3}, b=e^{2} \)
в. \( a=\frac{1}{3}, b=e^{1 / 3} \)
c. \( _{a=\frac{2}{3}, b=e^{2 / 3}} \)
D. \( a=e^{2 / 3}, b=\frac{2}{3} \)


How does the Bohr theory of the
hydrogen atom differ from that of Schrodinger?


The products of a burning candle are:
A. ash and water vapour
B. \( C O_{2} \) and water vapour
c. wax and water vapour
D. only melted wax


The Sl unit of static coefficient of
friction is
A.
B. Nm
c. \( \frac{N}{m} \)
D. it is unit less


Ethyl acetoacetate when reacts with
one mole methyl magnesium iodide
then product of reaction will be:
\( A \)
в.
\( c \)
D.


Area of triangle formed by angle bisectors of coordinate axes and the
line \( y=6 \) in sq.units is
A . 36
B . 24
\( c \cdot 72 \)
D. 16


The function \( f(x)=\frac{x}{1+x \tan x} \) has
a point of minimum in the interval \( \left(0, \frac{\pi}{2}\right) \)
Bne point of maximum in the interval \( \left(0, \frac{\pi}{2}\right) \)
C. No point of maximum, no point of minimum in the interval \( \left(0, \frac{\pi}{2}\right) \)
Two points of maxima in the interval \( \left(0, \frac{\pi}{2}\right) \)


\( 25 m L \) of \( 0.107 M H_{3} P O_{4} \) was titrated
with \( 0.115 M \) solution of \( N a O H \) to the
end point identified by indicator bromocresol green. This required
\( 23.1 m L \) The titration was repeated using phenolphthalein as indicator. This time \( 25 m L \) of \( 0.107 M H_{3} P O_{4} \)
required \( 46.2 m L \) of the
\( \mathbf{0 . 1 1 5} M_{N a O H . \text { What is the }} \)
coefficient \( ^{\prime} \boldsymbol{n}^{\prime} \) in the following reaction?
\( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4}+\boldsymbol{n} \boldsymbol{O} \boldsymbol{H}^{-} \rightarrow\left[\boldsymbol{H}_{3-n} \boldsymbol{P} \boldsymbol{O}_{4}\right]^{n-}+ \)
\( \boldsymbol{n} \boldsymbol{H}_{2} \boldsymbol{O} \)


The dark muscular diaphragm in the human eye that controls the pupil is:
A. Iriss
B. Retina
c. cornea
D. Sclera


Assertion
For drying \( \boldsymbol{H}_{2} \mathrm{H} 2, \) Conc. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \)
H2SO4 cannot be used.
Reason
Conc. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) H2 on
absorbing H20H20 form moist \( \boldsymbol{H}_{2} \) H2 along with large amount of heat
which burn \( \boldsymbol{H}_{2} \) H2
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Assertion
On polishing the surface the friction
decreases upto certain limit but
increases beyond that
Reason
On polishing the surface, the irregularities are cut off but beyond a certain limit the surface molecules
exert strong attractive forces on each
other
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Which of the following statement is correct regarding properties of hydrogen?
A. Hydrogen can behave as a non-metal
B. Hydrogen can behave as a metal
c. Hydrogen can behave as a metalloid
D. None of the above


The molar solubility (in mol \( L^{-1} \) ) of a
sparingly soluble salt \( M X_{4} \) is 's'. The
corresponding solubility product is \( \boldsymbol{K}_{s p} \)
\( s \) can be given in terms of \( \boldsymbol{K}_{s p} \) by the relation:
A \( \cdot_{s}=\left[\frac{K_{p}}{256}\right]^{\frac{1}{5}} \)
B . \( s=\left[128 K_{s p}\right]^{\frac{1}{4}} \)
c. \( s=\left[26 K_{s p}\right]^{\frac{1}{3}} \)
D. \( _{s}=\left[\frac{K_{s p}}{128}\right]^{\frac{1}{4}} \)


The first term and the common
difference of the arithmetic progression
\( \mathbf{3}, \mathbf{1 0}, \mathbf{1 7}, \mathbf{2 4}, \dots \) is?
A. 7 and 3
B. 3 and 7
c. 3 and 10
D. Not defined


Only one element of form
hydride.
A. group
в. group 7
c. group 8
D. group


Two identical balls collide head on. The
initial velocity of one is \( 0.75 \mathrm{cm}^{-1} \). While
that of the other is \( -0.43 \mathrm{ms}^{-1} \). If the
collision is perfectly elastic. Their respective final velocities are
A \( .0 .75 \mathrm{ms}^{-1},-0.43 \mathrm{ms}^{-1} \)
B. \( -0.43 \mathrm{ms}^{-1}, 0.75 \mathrm{ms}^{-1} \)
c. \( -0.75 \mathrm{ms}^{-1}, 0.43 \mathrm{ms}^{-1} \)
D. \( 0.43 \mathrm{ms}^{-1}, 0.75 \mathrm{ms}^{-1} \)


The theory of atmospheric electricity explains which of the following
phenomena?
A. Free electricity causes thunderstorms
B. Current due to a charge
c. The high temperature causes people
D. None of the above


An n-type semiconductor is
A. Neutral
B. Positively charged
C . Negatively charged
D. Negatively or positively charged depending on the amount of impurity added


A point charge \( +Q \) having mass \( m \) is fixed on horizontal smooth surface.
Another point charge having magnitude \( +2 Q \& \) mass \( 2 m \) is projected horizontally towards the charge \( +\mathrm{Q} \) from the distance with velocity \( V_{0} \) Force applied by floor on the fixed charge in horizontal direction, when distance between charges becomes 'd'
A \( \cdot \frac{2 K Q^{2}}{d^{2}} \)
B. \( \frac{K Q^{2}}{d^{2}} \)
c. zero
D. none


Simplify and express with positive zponents \( \left[\left(\frac{\mathbf{9}}{\mathbf{1 1}}\right)^{-\mathbf{3}} \times\left(\frac{\mathbf{9}}{\mathbf{1 1}}\right)^{-\mathbf{7}}\right] \div \)
\( \left(\frac{9}{11}\right)^{-3} \)


Which one of these is an oxidative
process?
A. Addition of oxygen
B. Removal of electrons
C. Removal of \( H^{+} \) ions
D. All of the above


The elastic limit of an elevator cable is
\( 2 \times 10^{9} N / m^{2} . \) The maximum upward
acceleration that an elevator of mass
\( 2 \times 10^{3} k g \) can have when supported by
a cable whose cross-sectional area is
\( 10^{-4} m^{2}, \) provided the stress in cable would not exceed half of the elastic
limit would be
A \( \cdot 10 m s^{-2} \)
B. \( 50 m s^{-2} \)
\( \mathrm{c} \cdot 40 \mathrm{ms}^{-2} \)
D. Not possible to move up


The velocity of a particle is zero at time
\( t=2, \) then
A. displacement must be zero in the interval \( t=0 \) to \( t= \) 2
B. acceleration may be zero at \( t=2 \)
c. velocity must be zero for \( t>2 \)
D. acceleration must be zero at \( t=2 \)


Chlamydomonas nivalis colours the snow
A . Red
B. Yellow
c. Green
D. Purple brown


Which of the following is NOT changed of Xe in given reaction?
\( 2 X e O F_{4}+S i O_{2} \rightarrow 2 X e O_{2} F_{2}+S i F_{4} \)
A. Hybridisation of \( x \) e
B. Number of d-orbital(s) is hybridisation
c. Number of \( O-X e-F \) bond angle
D. Covalency of \( x \) e


When \( _{90} T^{228} \) transforms to \( _{83} B i^{212}, \) then the number to the emitted \( \alpha \) and \( \beta \) particles is, respectively:
\( \mathbf{A} \cdot 8 \alpha, 7 \beta \)
в. \( 4 \alpha, 7 \beta \)
c. \( 4 \alpha, 4 \beta \)
D. \( 4 \alpha, 1 \beta \)


If each capacitors has capacitance \( c \) in
the given figure, then find \( C_{A B} \)
\( A \)
в. \( C / 2 \)
\( 3 C / 2 \)
2. none of the abov


\( \frac{\boldsymbol{x}^{\boldsymbol{4}}+\boldsymbol{2} \boldsymbol{4} \boldsymbol{x}^{2}+\boldsymbol{2} \boldsymbol{8}}{\left(\boldsymbol{x}^{2}+\mathbf{1}\right)^{3}}= \)
A. \( \frac{1}{x^{2}+1}+\frac{22}{\left(x^{2}+1\right)^{2}}+\frac{5}{\left(x^{2}+1\right)^{3}} \)
B. \( \frac{1}{x^{2}+1}-\frac{22}{\left(x^{2}+1\right)^{2}}+\frac{5}{\left(x^{2}+1\right)^{3}} \)
C \( \frac{1}{x^{2}+1}+\frac{22}{\left(x^{2}+1\right)^{2}}+\frac{28}{\left(x^{2}+1\right)^{3}} \)
D. \( \frac{1}{x^{2}+1}+\frac{23}{\left(x^{2}+1\right)^{2}}+\frac{4}{\left(x^{2}+1\right)^{3}} \)


\( \frac{-}{0} \)
\( \frac{0}{0} \)
\( \frac{\alpha}{\alpha} \)
\( \alpha \)


The average length of time required to
complete a jury questionnaire is 40 minutes, with a standard deviation of 5 minutes. What is the probability that it will take a prospective juror between 30
and 50 minutes to complete the questionnaire?
A. About \( 85 \% \)
B. About \( 90 \% \)
c. About \( 95 \% \)
D. none


Find the solution of \( (2 x+y+1) d x+ \)
\( (4 x+2 y-1) d y=0 \)
A \( \cdot 2 y-x+\log (2 x+y-1)=k \)
B . \( y+x+\log (2 x+y-1)=k \)
c. \( y-x+\log (2 x+y-1)=k \)
D. \( 2 y+x+\log (2 x+y-1)=k \)


f \( 3 x-2 y=5 \) and \( 3 y-2 x=3 \) then
find the value of \( (\boldsymbol{x}+\boldsymbol{y}) \)


If the equation \( 136\left(x^{2}+y^{2}\right)=(5 x+ \)
\( 3 y+7)^{2} \) represents a conic, then its
length of latus rectum is
A \( \cdot \frac{7}{2 \sqrt{34}} \)
B. \( \frac{7}{\sqrt{34}} \)
c. \( \frac{14}{\sqrt{34}} \)
D. \( \frac{9}{\sqrt{34}} \)


State whether the statement is true or
false:

The relation between the measurable
properties of gases can be obtained by gas laws.


Nutrition in Amoeba is
A. Holophytic
B. Holozoic
c. Saprophytic
D. Parasitic


A road roller of length \( 3 l \) metres and radius \( \frac{l}{3} \) metres can cover a field in 100 revolutions, moving once over. The area of the field in terms of I is
\( (\pi) l^{2} m^{3} \)


The rate of evaporation of a given liquid depends only on the surface area of the liquid exposed to air.
A. True
B. False


Which of the following phosphate are
cyclic among these?
A. \( H_{5} P_{3} O_{10} \)
В. \( H_{6} P_{4} O_{13} \)
\( \mathbf{c} \cdot H_{5} P_{5} O_{15} \)
D. \( H_{7} P_{5} O_{16} \)


Escape velocity for a projectile at
earth's surface is \( v_{e} . \) A body is projected form earth's surface with velocity \( 2_{v_{e}} \)
The velocity of the body when it is at infinite distance from the centre of
the earth is
A \( \cdot v_{e} \)
B. \( 2 v_{e} \)
\( c \cdot \sqrt{2 v} \)
D. \( \sqrt{3} v_{e} \)


Velocity of a body moving along a straight line with uniform acceleration
(a) reduces by \( \frac{3}{4} \) of its initial velocity in
time \( t_{0} . \) The total time of motion of the
body till its velocity becomes zero is
A \( \cdot \frac{4}{3} t_{0} \)
в. \( \frac{3}{2} t_{0} \)
c. \( \frac{5}{3} t_{0} \)
D. \( \frac{8}{3} t_{0} \)


Give one word or a phrase for the
following statement:
The process by which sulphide ore is concentrated:


A radio can tune to any station in
\( 7.5 M H z \) to \( 12 M H z \) band. The
corresponding wavelength band is
A. \( 40 \mathrm{m} \) to \( 25 \mathrm{m} \)
B. \( 30 \mathrm{m} \) to \( 25 \mathrm{m} \)
\( \mathrm{c} .25 \mathrm{m} \) to \( 10 \mathrm{m} \)
D. \( 10 \mathrm{m} \) to \( 5 \mathrm{m} \)


The area of rectangle is \( 540 \mathrm{cm} \) and its
length is \( 36 \mathrm{cm} \). Find its width and perimeter.


A line formly changed eonducting sphere of \( 24 m \) diameter has a surface
change density of \( 80.0 \mu c / m^{2} \)
(i) Find the charge on the sphere
(ii) What is the total electric flux learning the surface of the sphere?
A \( \cdot 1.447 \times 10^{-3} c, 1.63 \times 10^{8} \frac{N m^{2}}{C} \)
В. \( _{2.447} \times 10^{-3} c, 1.63 \times 10^{8} \frac{N m^{2}}{C} \)
c. \( _{1.447} \times 10^{-3} c, 2.63 \times 10^{8} \frac{N m^{2}}{C} \)
D. \( 41.447 \times 10^{-3} c, 1.63 \times 10^{8} \frac{N m^{2}}{C} \)


Among the following the irreversible
process is
A. free expansion of gas
B. extension or compression of spring
C. motion of an object on a perfectly frictionless surface
D. all of them


If \( x=A \cos 4 t+B \sin 4 t, \) then \( \frac{d^{2} x}{d t^{2}}= \)
\( A \)
B . \( -16 x \)
\( c .15 x \)
D. \( 16 x \)
E . \( -15 x \)


Factorize:
\( 3+2 a-a^{2} \)


If \( \boldsymbol{z}=\mathbf{1}+\boldsymbol{i}, \) then the multiplicative
inverse of \( \left.z^{2} \text { is (where } i=\sqrt{-1}\right) \)
\( \mathbf{A} \cdot 2 i \)
в. \( 1-i \)
c. \( -\frac{i}{2} \)
D.


For three numbers \( a, b, c \) product of the
average of the numbers, \( a^{2}, b^{2}, c^{2} \) and \( \frac{1}{a^{2}}, \frac{1}{b^{2}}, \frac{1}{c^{2}} \) cannot be less than
A . 1
B. 3
\( c .9 \)
D. none of these


In which of the following cases work is said to be done?
A. A man pushing a roller and displacing it
B. A boy sleeping
c. Girl writing in Examm
D. All of these


If the simple interest on a certain sum of money for 15 months at \( 7 \frac{1}{2} \% \) p.a. exceeds the simple interest on the same sum for 8 months at \( 12 \frac{1}{2} \% \) p.a. by
Rs. \( 32.50, \) the sum is
A. Rs. 3750
B. Rs. 3520
c. Rs. 3120
D. Rs. 3010


Shooting stars are actually not meteors.
A. True
B. False


Non-metals do not have lustre which
means:
A. they do not have a shining surface
B. they can't produce sound
C. they can't conduct heat
D. none of the above


Write one main difference between
asexual and sexual mode of reproduction. Which species is likely to have comparatively better chances of survival- the one reproducing asexually or the one reproducing sexually? Give the reason to justify your answer


How many generation and genotypic cells are present in angiosperm seeds.
A. Three and two respectively
B. One and two respectively
c. Two and three respectively
D. One and three respectively


Define calorimetry.


Nature of climax community depends
upon
A. water
B. Temperature
c. Soil fertility
D. Climate


State whether the given statement is True or False.

Statement : Sodium nitrate on heating
\( \operatorname{gives} N O_{2} \)
A. True
B. False


What is the greatest value of \( \theta \) lying between \( 0^{0} \) and \( 720^{0} \) whose tangent is \( -\frac{1}{\sqrt{3}} ? \)
A \( \cdot 690^{\circ} \)
\( ^{0} \)
в. \( 510^{\circ} \)
c. \( 330^{\circ} \)
D. \( 150^{\circ} \)


Differentiate between.
Atrial systole and ventricular systole


Find a quadratic polynomial each with the give numbers as the sum and product of its zeros respectively. \( \sqrt{\mathbf{2}}, \frac{\mathbf{1}}{\mathbf{3}} \)


Write Sl unit of magnetic dipole
moment.


Match the following:
List - 1 List - 2
a) Burning candle
e) line spectrum
f) continuous
b) Sodium vapour \( \quad \) spectrum
c) Bunsen flame
g) bond spectrum
g) Dark lines in solar
h) Absorption spectrum \( \quad \) spectrum
\( A \cdot a-g, b-e, c-f, d-h \)
B. \( a-g, b-f, c-e, d-h \)
C. \( a-f, b-g, c-e, d-h \)
D. \( a-f, b-e, c-g, d-h \)


The set representing the correct order of
the first ionization potential is:
A. \( K>N a>L i \)
в. \( B e>M g>C a \)
c. \( B>C>N \)
D. \( G e>S i>C \)


\( \mathbf{3} \boldsymbol{H} \boldsymbol{C} \equiv \boldsymbol{C} \boldsymbol{H} \frac{r e d h o t}{\boldsymbol{F} e}(\boldsymbol{A}) \frac{C \boldsymbol{H}_{3} C \boldsymbol{O} C l}{A l C l_{3}} \)
\( (B) \frac{N i / H_{2}}{25^{o} C} C+D \)
Relation betwen \( C \) and \( D \)
A . Identical
B. Enantiomer
c. Diastereomer
D. Position


The species, having bond angles of \( 120^{\circ} \) is:
A. \( B C l_{3} \) вслз
в. \( P H_{3} \)
c. \( C l F_{3} \)
D. \( N C l_{3} \)


Find the angle of incidence for which
angle of deviation from a liquid drop is minimum in a primary rainbow.
A . \( 30^{\circ} \)
B . \( 40^{\circ} \)
\( c \cdot 50^{\circ} \)
D. \( 60^{\circ} \)


A box is put on a scale which is
adjusted to read zero,when the box is
empty. A stream of pebbles is then
poured into the box from a height \( h \)
above its bottom at a rate of n pebbles
collide with the box such that they
immediately come to rest after collision, the scale reading at time \( t \) after the pebbles begin to fill the box is:
\( \mathbf{A} \cdot m n\{\sqrt{(2 g h)}+g t\} \)
B. \( \{\sqrt{(2 g h)+g t}\} \)
c. \( \{\sqrt{(2 g h)-g t}\} \)
D \( \cdot \operatorname{mn}\{(2 g h)-g t\} \)


What is the use of coordination
compounds for purification of water Medical and catalyst


The structure of 6-hydroxyheptanal is:
\( \mathbf{A} \cdot C H_{3}-C H_{2}-C H(O H)-C H_{2}-C H_{2}-C H_{2}- \)
\( C H O \)
B. \( C H_{3}-C H_{2}-C H_{2}-C H(O H)-C H_{2}-C H O \)
\( \mathbf{c} \cdot C H_{3}-C H(O H)-C H_{2}-C H_{2}-C H_{2}-C H O \)
D. \( C H_{3}-C H(O H)-C H_{2}-C H_{2}-C H_{2}-C H_{2}- \)
\( C H O \)


An ice-cream cone consisting of the
cone is surmounted by a hemisphere.The common radius of a
hemisphere \( \& \) cone is \( 3.5 \mathrm{cm} \) \& the
total height of ice cream is \( 12.5 \mathrm{cm} \)
Calculate the volume of ice-cream in
the solid shape.


Identify the conductors from the
following:
Eraser, paper, matchstick, copper wire, polythene
A . eraser
B. copper wire
c. paper
D. polythene


The number of solutions for the system of equations \( 2 x+y=4,3 x+2 y=2 \)
and \( \boldsymbol{x}+\boldsymbol{y}=-\boldsymbol{2} \) is
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c \cdot 3 \)
D. infinitely many
E .


Assertion: When diamagnetic material is placed in a non-uniform magnetic field, it tends to move from stronger to
the weaker part of the magnetic field. Reason : Diamagnetic materials possess strong magnetism.
A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true and 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


In the figure above, lines \( l \) and \( k \)
intersect at point \( Q . \) If \( m=40^{\circ} \) and
\( p=25^{\circ}, \) what is the value of \( x ? \)
A \( \cdot 15^{\circ} \)
B. \( 20^{\circ} \)
\( c \cdot 25 \)
D. \( 40^{\circ} \)
\( E \cdot 65^{\circ} \)


Find the value of \( x, \) if \( \tan ^{-1}\left(\frac{2 x}{1-x^{2}}\right)+\cot ^{-1}\left(\frac{1-x^{2}}{2 x}\right)= \)
\( \frac{2 \pi}{3}, x>0 \)


The wavelength of the first member of
the Balmer series of hydrogen is \( 6563 \times 10^{-10} m . \) Calculate the
wavelength of its second member.


What is the product in the following
reaction?
A. Benzoquionone
B. Cyclohexane-1-one
c. Benzoic sulphate
D. Benzoic acid


A zinc electrode is placed in a \( 0.1 \mathrm{M} \)
solution at \( 25^{0} C . \) assuming that the salt is \( 20 \% \) dissociated at this dilutions
calculate the electrode reduction
potential. \( \boldsymbol{E}^{0}\left(\boldsymbol{Z} \boldsymbol{n}^{2+} \mid \boldsymbol{Z} \boldsymbol{n}\right)=-\mathbf{0 . 7 6} \boldsymbol{V} \)


A ball is thrown vertically upwards with speed \( 10 \mathrm{m} / \mathrm{s} \) and it comes back at
initial point with same speed. At what point during flight is the ball's acceleration greatest?
A. The answer cannot be determined from this information
B. The acceleration remains constant throughout the flight
c. Just after lunch
D. Just5 before landing
E. At the highest point of the flight


Find the degree of the following polynomial \( 2 x+4+6 x^{2} \)


Name the structure shown in the figure
Also label 1 and 2


A sample of an ideal gas is contained in
a cylinder. The volume of the gas is suddenly decreased. A student makes the following statements to explain the change in pressure of the gas.
I. The average kinetic energy of the gas atoms increases.
II. The atoms of the gas hit the walls of the cylinder more frequently.
III. Temperature of the gas remains unchanged. Which of these statements is true?
A. I and II only
B. I and III only
c. ॥ and III only
D. I, II and III


If the difference between the
circumference and the radius of a circle
is \( 37 c m, \) then using \( \pi=\frac{22}{7}, \) the
circumference (in cm) of the circle is:
A . 154
B. 44
c. 14
D.


\( A=(2,3,0) \) and \( B=(2,1,2) \) are two
points. If the points \( P, Q \) are on the line
\( A B \) such that \( A P=P Q=Q B, \) then
\( \boldsymbol{P Q}= \)
\( A \cdot 2 \sqrt{2} \)
B. \( 6 \sqrt{2} \)
\( c \cdot \sqrt{\frac{8}{9}} \)
D. \( \sqrt{2} \)


Write the expression for electric intensity at a point due to point charge and explain the terms.


Assertion: Both reactions are Lewis
acid-base reactions?
¡. \( \boldsymbol{N} \boldsymbol{H}_{3}+\boldsymbol{B} \boldsymbol{F}_{3} \longrightarrow \boldsymbol{H}_{3} \boldsymbol{N}-\boldsymbol{B} \boldsymbol{F}_{3} \)
ii. \( \boldsymbol{M} \boldsymbol{g}+\boldsymbol{S} \longrightarrow \boldsymbol{M} \boldsymbol{g}^{2+}+\boldsymbol{S}^{2-} \)
Reason: Lewis acid-base reaction
involve the donation of lone pair electrons from base to acid. This
donation results in a coordinate bond.
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
E. Both Assertion and Reason are incorrect


A sample of a liquid has an initial volume of \( 1.5 L . \) The volume is reduced
by \( 0.2 m L, \) when the pressure increases
by \( 140 k P a . \) What is the bulk modulus
of the liquid.
A . \( 1.05 \times 10^{9} \) Pa
B . \( 1.05 \times 10^{5} \) Pa
\( \mathbf{c} \cdot 3.05 \times 10^{9} \mathrm{Pa} \)
D. \( 3.05 \times 10^{5} \) Pa


Auxanometer is meant for measuring
A. Respiratory activity
B. Photosynthesis activity
c. Growth activity
D. osmotic pressure


An object thrown vertically up from the ground passes the height \( 5 m \) twice in an interval of \( 10 s . \) What is its time of
flight?
A \( \cdot \sqrt{28} s \)
в. \( \sqrt{86} s \)
c. \( \sqrt{104} s \)
D. \( \sqrt{72} s \)


is the most dangerous soil
contaminant.
A. Organic waste
B. Radioactive waste
c. chemical fertilizer
D. Both A and B


Silver ore dissolves in dilute solution of
NaCN in the presence of air to form:
A \( . A g C N \)
В \( \cdot\left[A g(C N)_{2}\right]^{-} \)
c. \( A g S C N \)
\( \mathbf{D} \cdot\left[A g(C N)_{4}\right] \)


Assertion
A \( 30 \% \) solution of \( H_{2} O_{2} \) is marketed as
100 volume' hydrogen peroxide.
Reason
1 L of \( 30 \% \) H \( _{2} \) O \( _{2} \) will give 100 mL of
oxygen at STP.
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 dispersed phase in a colloidal
solution is


A plane polarized light is incident normally on the tourmaline plate. Its \( \overrightarrow{\boldsymbol{E}} \)
vectors, make an angle of \( 60^{\circ} \) with the
optic axis of the plate. Find the \( \% \) difference between initial and final maximum values of \( \overrightarrow{\boldsymbol{E}} \) vectors.


The heating element in an electric iron is made up of :
A. nichrome
B. iron
c. constantan
D. tungsten


While studying saponification reaction,
a student measures the temperature of the reaction mixture and also finds its
nature using blue/red litmus paper. On
the basis of his observations the correct
conclusion would be:
A. the reaction is exothermic and the reaction mixture is acidic
B. the reaction is endothermic and the reaction mixture is acidic
C. the reaction is exothermic and the reaction mixture is neutral
D. the reaction is exothermic and the reaction mixture is basic
E. the reaction is endothermic and the reaction mixture is basic.


Which of the following relationship are correctly match?
This question has multiple correct options
\( A \)
B.
\( c \)
Positional isome
\( D \)
and


In \( \triangle \boldsymbol{A B C} \) and \( \triangle \boldsymbol{D E F}, \angle \boldsymbol{B}=\angle \boldsymbol{E}= \)
\( 90^{\circ} ; A C=D F a n d B C=E F \)
Then
triangles are congruent.
A. True
B. False


An object is placed at a distance of 10 \( \mathrm{cm} \) (in a medium of ) from the pole of a spherical refracting surface bounding a
medium of 1.5 if the image formed is virtual and at a distance of \( 40 \mathrm{cm} \) then the spherical surface iscalculate the Radius of curvature:


What happens when concentrated
\( H_{2} S O_{4} \) is added to calcium flouride?


A chord PQ of a length 12 cm subtends
an angle of \( 120^{\circ} \) at the center of a circle
Find the area of the minor segment cut
off by chord PQ.


How many structural isomers are possible for a compound with molecular
formula \( C_{3} H_{7} C l \) ?
\( A \cdot 2 \)
B. 7
\( c .5 \)
D.


If the elevation in boiling point of a solution of non-volatile, non-electrolytic and non-associating solute in a solvent \( \left(K_{b}=x K k g m o l^{-1}\right) \) is \( y K, \) then the depression in freezing point of solution of same concentration would be:
\( \left[\boldsymbol{K}_{f} \text { of the solvent }=\boldsymbol{z} \boldsymbol{K} \boldsymbol{k} \boldsymbol{g} \boldsymbol{m o l}^{-1}\right] \)
A \( \cdot \frac{2 x z}{y} \)
в. \( \frac{y z}{x} \)
c. \( \frac{x z}{y} \)
D. \( \frac{y z}{2 x} \)
E \( \cdot \frac{x z}{2 y} \)


Define common ion effect.


Solve for \( x, \sin ^{2} 2 x=(\sin 2 x) \)


Fill in the blanks with approprite words.
The cell wall of Gram -ve bacteria is
comparatively less \( \ldots \ldots . . . . \) than Gram +ve bacteria


Assertion
Nuclear forces are independent of
charges.
Reason
Nuclear force is not a short range force.
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 magnetic flux linked with a coil
varies as \( \phi=3 t^{2}+4 t+9 . \) what is the
magnitude of the emf at \( t=2 s ? \phi \) is in
Wh.


Monochromatic green light of wavelength 550 nm illuminates two parallel narrow slits \( 7.7 \mu \mathrm{m} \) apart. The
angular deviation \( \theta \) of third order (for \( m \)
\( =3 \) ) bright fringe in radian and in degrees respectively are:
A \( .21 .6,12.4^{\circ} \)
в. \( 0.216,1.24^{\circ} \)
c. \( 0.216,12.4^{\circ} \)
D. \( 216,1.24^{\circ} \)


In which of the following do two lighter atoms combine to form one heavier
atom?
A. Radioactive tracer
B. Radioactive carbon dating
c. Radiation therapy
D. Nuclear fission
E. Nuclear fusion


Name the following metals:
A metal present in period \( 3, \) group 1 of the periodic table


\( \mathbf{f}\left|\begin{array}{lll}\boldsymbol{x}^{\boldsymbol{k}} & \boldsymbol{x}^{\boldsymbol{k}+\boldsymbol{2}} & \boldsymbol{x}^{\boldsymbol{k}+\boldsymbol{3}} \\ \boldsymbol{y}^{\boldsymbol{k}} & \boldsymbol{y}^{\boldsymbol{k}+\boldsymbol{2}} & \boldsymbol{y}^{\boldsymbol{k}+\boldsymbol{3}} \\ \boldsymbol{z}^{\boldsymbol{k}} & \boldsymbol{z}^{\boldsymbol{k}+\boldsymbol{2}} & \boldsymbol{z}^{\boldsymbol{k}+\boldsymbol{3}}\end{array}\right| \)
三室 \( (x-y)(y-z)(z-x)\left(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}\right) \)
then
A. \( k=-3 \)
B. \( k=-1 \)
\( \mathbf{c} \cdot k=1 \)
D. \( k=3 \)


On burning fuel produces amount of heat.
A. large
B. less
c. very less
D. no heat


\( \underbrace{E}_{E} \)


An electron accelerated by \( 200 \mathrm{V} \) enters a magnetic field .If its velocity is \( 100 \mathrm{m} / \mathrm{sec} \). then \( (\mathrm{e} / \mathrm{m}) \) for it will be:
\( (\mathrm{C} / \mathrm{Kg}) \)
A. \( 1.75 \times 10^{10} \)
B. \( 1.75 \times 10^{11} \)
c. \( 1.75 \times 10^{9} \)
D. \( 1.75 \times 10^{6} \)


No rusting takes place in absence of moisture.
A . True
B. False


The thigh bones(femurs),each of cross-
sectional area \( 10 \mathrm{cm}^{2} \) support the
upper part of the human body of mass 40 kg.Average pressure sustained by the femurs is:
\( \mathbf{A} \cdot 10^{3} N / m^{2} \)
B . \( 2 \times 10^{5} \mathrm{Nm}^{-2} \)
c. \( 6 \times 10^{-5} \mathrm{Nm}^{-2} \)
D. \( 10^{-3} \mathrm{Nm}^{-2} \)


The energy releasing metabolic process in which substrate is oxidised without
an external electron acceptor is
A. Fermentation
B. Aerobic respiration
c. Photorespiration
D. Glycolysis


Which of the following oxidation state is common for all lanthanoids?
\( A \cdot+2 \)
\( B \cdot+3 \)
\( c \cdot+4 \)
\( D \cdot+5 \)


Electromagnetic waves are transverse in nature is evident by
A. polarization
B. interference
c. reflection
D. diffraction


If \( \boldsymbol{A}=\left[\begin{array}{ll}\boldsymbol{a} & \boldsymbol{x} \\ \boldsymbol{y} & \boldsymbol{a}\end{array}\right] \) and if \( \boldsymbol{x} \boldsymbol{y}=\mathbf{1}, \) then
\( \operatorname{det}\left(A A^{T}\right) \) is equal to:
\( \mathbf{A} \cdot a^{2}-1 \)
B \( \cdot\left(a^{2}+1\right)^{2} \)
c. \( 1-a^{2} \)
D. \( \left(a^{2}-1\right)^{2} \)
E \( \cdot(a-1)^{2} \)


Given the true statement: If a
quadrilateral is a square, then it is a rectangle. It follows that, of the converse
and the inverse of this true statement.
A. Only the converse is true
B. only the inverse is true
c. Both are true
D. Neither is true
E. The inverse is true, but the converse is sometimes true


Iqbal treated a lustrous, divalent element M with sodium hydroxide. He observed the formation of bubbles in
reaction mixture. He made the same
observations when this element
was treated with hydrochloric acid. He find that the produced gas is:
A \( . H_{2} \)
в. \( C l_{2} \)
\( c \cdot O_{2} \)
D. None of the above


The heat of formation of ethane is
\( -19.46 K c a l . \) Bond energies of \( H- \) \( -H, C--H, \) and \( C--C \) bonds are
104.18,99.0 and \( 80.0 K c a l \)
respectively. If the heat of atomisation of graphite is \( x \) then find out the value
of \( x \)
A . \( x=171 \) K cal \( l \)
В. \( x=-171 \) К cal
c. \( x=0 \) Kcal
D. None of these


An aqueous solution of NaCl on
electrolysis gives \( \boldsymbol{H}_{2(g)^{\prime}}, \boldsymbol{C l}_{2(g)} \) and
NaOH according to the reaction
\( \mathbf{2} C l_{(a q)}^{-}+\mathbf{2} \boldsymbol{H}_{2} \boldsymbol{O} \rightleftharpoons \mathbf{2} \boldsymbol{O} \boldsymbol{H}_{(a q)}^{-}+\boldsymbol{H}_{2(g)}+ \)
\( C l_{2(g)} \)
A direct current of 25 amperes with a current efficiency of \( 62 \% \) is passed through 20 liters of NaCl solution (20\% by weight). Write down the reactions taking place at the anode and the cathode. How long will it take to produce \( 1 \mathrm{kg} \) of \( C l_{2} ? \) in hrs. (write the value to the nearest integer).


The bond order of \( H_{2}^{-} \) ion is \( \frac{1}{2} . \) If it has 2 bonding electrons, calculate the number of antibonding electrons
A . 4
B. 3
\( c \cdot 2 \)
D.


The name of the element having atomic number \( 100, \) was adopted in the honour of :
A. Alfred Nobel
B. Enrico Fermi
c. Dmitri Mendeleev
D. Albert Einstein


Ammonia gas cannot be dried by passing through:
This question has multiple correct options
A \( \cdot \) conc. \( H_{2} S O_{4} \)
B. anhydrous \( C a O \)
\( \mathbf{c} \cdot P_{2} O_{5} \)
D. \( \mathrm{CuSO}_{4} \)


The number of integral terms in \( (\sqrt{3}+\sqrt[8]{2})^{64} \) is
\( \mathbf{A} \cdot \mathbf{8} \)
B. 7
\( c .9 \)
D. 6


The term 'keel' is used for special type
of
A. Sepals
B. Petals
c. stamens
D. carpels


In YDSE, the source is placed symmetrical to the slits. If a transparent slab is placed in front of the upper slit, then(slab can absorb a
fraction of light)

This question has multiple correct options
A. intensity of central maxima will not change
B. intensity of central maxima may change
c. central maxima will be shifted up
D. intensity of dark fringes will be always zero


What is optoelectronic junction
devices? Write any two names of optoelectronic junction devices.


The refractive index \( (\mu) \) of glass is found to have the values
1.49,1.50,1.52,1.54 and 1.48
Calculate the mean value of refractive
index.


The sources of energy obtained in a nuclear reaction are :
A. Mass defect
B. Binding energy
c. Fission
D. Fusion
E. All of these


The equilibrium constant \( \boldsymbol{K}_{\boldsymbol{p}} \) for the
reaction \( \boldsymbol{P} \boldsymbol{C l}_{5(g)} \leftrightharpoons \boldsymbol{P} C l_{3(g)}+\boldsymbol{C l}_{2(g)} \) is
16. If the volume of the container is
reduced to half of its original volume,
the value of \( K_{p} \) for the reaction at the
same temperature will be :
A . 32
B. 64
\( c \cdot 16 \)
D. 4


A particle is executing S.H.M. with amplitude A and Time period T. Time
taken by the particle to reach from
extreme position to \( \frac{A}{2} \)
\( A \cdot \frac{T}{6} \)
B・亞
\( c \cdot \frac{T}{3} \)
\( D \cdot \frac{T}{4} \)


The area (in square units) of a regular hexagon of side of which is 2 units
each, is
A. 8.2
B. 10.4
c. 12.5
D. 18.7


Three blocks \( A, B \) and \( C \) are connected
together with the help of strings as shown in figure. The masses are respectively \( 10 \mathrm{kg}, 30 \mathrm{kg} \) and \( 50 \mathrm{kg} \)
They are pulled by a force of 18 N on a frictionless horizontal surface
Calculate the following:
(i) Tension \( T_{1} \) in the first string
(ii) Tension \( T_{2} \) in the second string and
(iii) Acceleration of the blocks.


Compound \( A \) undergoes formation of cyanohydrins which on hydrolysis gives
lactic acid \( \left(\boldsymbol{C H}_{3} \boldsymbol{C H O H} \boldsymbol{C O O H}\right) \)
Therefore, compound \( \boldsymbol{A} \) is:
A. formaldehyde
B. acetaldehyde
c. acetone
D. benzaldehyde


Solve
\( \mathbf{7}>\mathbf{3} \boldsymbol{x}-\mathbf{8} ; \boldsymbol{x} \in \boldsymbol{N} \)
В. \{1,2,3,4\}
c. (1,15)
D. None of these


If a block moving up at \( \boldsymbol{\theta}=\mathbf{3 0}^{\mathbf{0}} \) with a
velocity \( 5 \mathrm{m} / \mathrm{s}, \) stops after \( 0.5 \mathrm{sec}, \) then
\( \mu \) is:
A. 0.48
B. 1.25
\( c \cdot 0.58 \)
D. none of the above


n quadrilateral ABCD \( \angle \mathrm{B}=90^{\circ}, \angle \mathrm{C}-\angle \)
\( \mathrm{D}=\mathbf{6 0}^{\circ} \) and \( \angle \mathbf{A}-\angle \mathbf{C}-\angle \mathbf{D}=\mathbf{1 0}^{\circ} . \) Find
\( A, \angle C \) and \( \angle D \)


Find the sum of the following.
i) -5,-4,-6 and -17


f \( \boldsymbol{R}=\{(\boldsymbol{x}, \boldsymbol{y}): \boldsymbol{x}+\mathbf{2} \boldsymbol{y}=\mathbf{8}\} \) is a
relation on \( N, \) write the range of \( R \)


If in the fermentation of sugar in an
enzymatic solution that is \( 0.2 M \), the
concentration of the sugar is reduced to \( 0.06 M \) in \( 10 h \) to \( 0.03 M \) in \( 20 h, \) what
is the order of the reacation:
A . 1
B. 2
\( c .3 \)
D.


During extraction of metals, electrolytic refining is used to obtain pure metals. What is the
electrolyte used?
A. Silver salt
B. Copper(II) sulphate
c. sodium chloride
D. Both A and B


Fill in the blank:
Hunter constellation can be used to
locate
A. Pole star
B. Apollo
c. sirius
D. Rigel


Humification results in the formation of
substance.
A. Colloidal and Basic
B. Acidic and Dark colored
c. Amorphous and Light colored
D. Light coloured colloidal


Two snails in the same class can also
belong to which group?
A. Order
B. species
c. Genus
D. Family
E. Phylum


A point mass starts moving in a straight line with constant acceleration
"a". At a time \( t \) after the beginning of
motion, the acceleration changes sign,
without change in magnitude.
Determine the time \( t_{0} \) from the
beginning of the motion in which the
point mass returns to the initial
position.
\( \mathbf{A} \cdot(2+\sqrt{3}) t \)
B \( \cdot(2+\sqrt{2}) t \)
\( \mathbf{c} \cdot(3+\sqrt{2}) t \)
D. \( (12+\sqrt{2}) t \)


The ends of a quadrant of a circle have the coordinates (1,3) and \( (3,1) . \) Then the
centre of such a circle is
A. (2, 2)
B. (1,1)
\( c \cdot(4,4) \)
\( D \cdot(2,6) \)


If in a system of forces acting on a rigid
body \( \mathrm{R} . \mathrm{G} \neq 0, \) then the given system of forces is equivalent to
A. degenerate wrench
B. non-degenerate wrench
c. a couple
D. a single force


If the sum of two unit vector is a unit
vector, then the magnitude of their difference is:
A. \( \sqrt{3} \)
B. \( \sqrt{2} \)
c. \( \sqrt{5} \)
D. \( \frac{1}{\sqrt{2}} \)


The most acidic compound among the following is
A. phenol
B. ethanol
c. 3,5 -dinitrophenol
D. 4,4 -methoxyphenol


A land surveyor records the various
treatments of a field in his
measurement book as given below. The
area of the field surveyed is (all reading
are in meters):
\( A \cdot 6000 \) sq. \( m \)
B. 7000 sq. \( m \)
c. 7500 sq. \( m \)
D. 8250 sq.


Curie temperature is the temperature
above which:
A. paramagnetic material becomes ferromagnetic material
B. ferromagnetic material becomes diamagnetic material
C. ferromagnetic material becomes paramagnetic material
D. paramagnetic material becomes diamagnetic material


A candle placed \( 25 \mathrm{cm} \) form a lens
forms an image on a screen placed \( 75 \mathrm{cm} \) on the other side of the lens. The
focal length and type of the lens should
be
A. \( +18.75 \mathrm{cm} \) and convex lens
B. \( -18.75 \mathrm{cm} \) and concave lens
c. \( +20.25 \mathrm{cm} \) and convex lens
D. \( -20.25 \mathrm{cm} \) and concave lens


Bohr's model can
explain
This question has multiple correct options
A. The spectrum of hydrogen atom only.
B. Spectrum of an atom or ion containing single electron only.
C. The stability of atom.
D. The solar spectrum.


The property of a medium necessary for wave propagation is its
A. elasticity
B. low resistance
c. inertia
D. all of the above


Find the value of following on the basis of significant figure rule:
The height of a man is \( 5.87532 \mathrm{ft} \). But measurement is correct upto three significant figures. The correct height is?
A \( .5 .86 \mathrm{ft} \)
B. \( 5.87 \mathrm{ft} \)
c. \( 5.88 \mathrm{ft} \)
D. \( 5.80 \mathrm{ft} \)


If a line makes angles \( \alpha, \beta, \gamma \) with axes
of co-ordinates, then \( \cos 2 \alpha+\cos 2 \beta+ \)
\( \cos 2 \gamma \) is equla to
A . -2
B. -
c. 1
D. 2


Which of the following is not the function of large intestine?
A. Absorption of water
B. Nutrient absorption
c. secretion of mucus to lubricate faeces
D. Temporary storage faeces in rectum


The - ...... coordinates the movement of the
voluntary muscles.


The rate of reaction is doubled for every
\( 10^{\circ} \mathrm{C} \) rise in temperature. The increase
in rate as result of increase in
temperature from \( 10^{\circ} \mathrm{C} \) to \( 100^{\circ} \mathrm{C} \) is:
A . 112
B. 512
\( c \cdot 400 \)
D. 256


The \( 4^{t h} \) term of an AP is 14 and its \( 12^{t h} \)
term is \( 70 . \) What is its first term?
A . -10
B. -7
\( c \cdot 7 \)
D. 10


Atomic number of an atom is equal to
the
A. number of protons
B. number of electrons
\( c . \) both a and \( b \)
D. sum of proton and electron


Construct a cyclic quadrilateral ABCD when \( A B=6 c m, B C=5.5 c m, \angle A B C= \)
\( \mathbf{8 0}^{\circ} \) and \( \mathbf{A D}=\mathbf{4 . 5 c m} \)


Which of the following statement is/are
correct?
(A) All green plants can prepare their own food.
(B) Most animals are autotrophs.
(C) \( C O_{2} \) is not required for
photosynthesis.
(D) Oxygen is liberated during photosynthesis.
Choose the correct answer from the
options given below.
\( A \cdot(A) \) and \( (D) \)
B. (B) only
c. (B) and (C)
D. (A) and (B)


The molar conductivity of a solution of a weak acid \( \boldsymbol{H} \boldsymbol{X}(\mathbf{0 . 0 1} \boldsymbol{M}) \) is \( \mathbf{1 0} \) times
smaller than the molar conductivity of a
solution of a weak acid \( \boldsymbol{H} \boldsymbol{Y}(\mathbf{0 . 1} \boldsymbol{M}) . \) If
\( \boldsymbol{\lambda}_{\boldsymbol{X}^{-}}^{\circ} \approx \boldsymbol{\lambda}_{\boldsymbol{Y}^{-}}^{\circ}, \) the difference in their \( \boldsymbol{p} \boldsymbol{K}_{\boldsymbol{a}} \)
values, \( \boldsymbol{p} \boldsymbol{K}_{\boldsymbol{a}}(\boldsymbol{H} \boldsymbol{X})-\boldsymbol{p} \boldsymbol{K}_{\boldsymbol{a}}(\boldsymbol{H} \boldsymbol{Y}), \) is
(consider degree of ionization of both
acids to be \( <<1 \) )


Assertion
Non-sense codon are responsible for termination of peptide chain.
Reason
Non-sense codons are not recognised by
tRNA.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A cylinder vessal open at the top has
diameter \( 20 \mathrm{cm} \) and height \( 14 \mathrm{cm} . \) Find
the cost of tin-plating it on the inside at the rate of 50 paisa per hundred square
centimeter.


Which one is closest to modern man?
A. Cro-Magnon Man
B. Neanderthal Man
c. Homo erectus
D. Homo habilis


If \( A \) and \( B \) have \( n \) elements in
common,then the number of elements
common to \( \boldsymbol{A} \times \boldsymbol{B} \) and \( \boldsymbol{B} \times \boldsymbol{A} \) is:


What should be the length of the metal rod used as lightning conductor?
A. shorter than the walls of the building
B. Same length or equals.
c. Taller than the walls of the building
D. Nothing specific, can be of any length.


The major role of fluorspar which is added in small amount in the
electrolytic reduction of \( A l_{2} O_{3} \)
dissolved in fused cryolite is :
This question has multiple correct options
A. as a catalyst
B. to make the fused mixture very conducting
c. to lower the temperature of melting
D. to decreases the rate of oxidation of carbon at the anode


Number of possible mono-chloro benzene is:
\( \mathbf{A} \cdot \mathbf{1} \)
B. 3
\( c \cdot 5 \)
\( D \)


ABCD is a parallelogram. The sides AB
and \( A D \) are produced to \( E \) and \( F \) respectively, such that \( A B=B E \) and \( A D= \)
DF.
Hence \( \Delta B E C \cong \Delta D C F \)
State whether the above statement is
true or false.
A. True
B. False


T M V has a size of
\( \mathbf{A} \cdot 50 n m \times 10 n m \)
В. \( 100 n m \times 20 n m \)
c. \( 300 \times 18 n m \)
D. \( 500 n m \times 24 n m \)


The theory states that living organisms originate from pre-existing organisms
A. Theory of Catastrophism
B. Theory of Panspermia
c. Biogenesis theory
D. Theory of Spontaneous generation


Why is \( -273^{\circ} \mathrm{C} \) called absolute zero?


Write the number of surfaces of a right circular cylinder.


Find the eccentricity of that ellipse,
whose latus rectum is half of the minor
axis.


The energy of activation for the reaction
is:
A. \( E_{a}=2.9311 \times 10^{5} \)
В. \( E_{a}=2.3933 \times 10^{5} \)
C . \( E_{a}=2.1398 \times 10^{5} \)
D. None of these


A mapping is defined as \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \)
\( R, f(x)=\cos x . \) Show that it is neither
one-one nor surjective.


Let \( R \) be the relation on \( Z \) defined by
\( \boldsymbol{R}=\{(\boldsymbol{a}, \boldsymbol{b}): \boldsymbol{a}, \boldsymbol{b} \in \boldsymbol{Z}, \boldsymbol{a}-\boldsymbol{b} \) is an
integer \( \} . \) Find the domain and range of
\( \mathrm{R} \)


Divide \( \left(\frac{\boldsymbol{y}}{\boldsymbol{6}}+\frac{\boldsymbol{2} \boldsymbol{y}}{\boldsymbol{3}}\right) \div\left(\boldsymbol{y}+\frac{\boldsymbol{2} \boldsymbol{y}-\mathbf{1}}{\boldsymbol{3}}\right) \)


Which of the following has the largest size?
\( \mathbf{A} \cdot R b^{-} \)
В. \( M g^{+2} \)
\( \mathbf{c} \cdot L i^{+} \)
D. \( B a^{+2} \)


Which of the following alcohols gives the best yield of dialkyl ether on being heated with a trace of sulphuric acid?
A. 2 - Pentanol
B. 2 -Methyl - 2 - butanol
c. 1- Pentanol
D. 2- Propanol


Which of the following quantities connected with SHM do not vary
periodically?
A. Total energy
B. Velocity
c. Displacement
D. Acceleration


The correct relation between frequency and time period is
\( ^{\mathbf{A}} \cdot T=\frac{1}{f} \)
B \( \cdot T=\sqrt{\frac{1}{f}} \)
c. \( T=\frac{1}{2 f} \)
D. \( T=\frac{2}{f} \)


If the volume of spherical ball is increasing at the rate of \( 4 \pi c c / \) sec then
the rate of change of its surface area
when the volume is \( 288 \pi c c \) is
A \( \cdot \frac{4}{3} \pi c m^{2} / \) sec
в. \( \frac{2}{3} \pi c m^{2} / \) sec
\( \mathrm{c} \cdot 4 \pi \mathrm{cm}^{2} / \mathrm{sec} \)
D. \( 2 \pi c m^{2} / \) sec


A strong magnetic field is applied on a stationary electron. Then the electron:
A. moves in the direction of the field
B. remains stationary
c. starts spinning
D. moves opposite to the direction of the field


There are 10 railway stations between a station \( x \) and another station \( y \)
Find the number of different tickets
that must be printed so as to enable a
passenger to travel from any one station
to any other


For a chemical reaction, \( \Delta G \) will always
be negative if
A. \( \Delta H \) and \( T \Delta S \) both are positive
B. \( \Delta H \) and \( T \Delta S \) both are negative
c. \( \Delta H \) is negative and \( T \Delta S \) is positive
D. \( \Delta H \) is positive and \( T \Delta S \) is negative


Which of the following is not a metallic element?
A. Nitrogen
B. Potassium
c. Magnesium
D. Calcium


Which alkyl halide can be formed with
the formula \( C_{5} H_{11} C l ? \)
A \( \cdot 1^{\circ} \)
в. \( 2^{\circ} \)
\( c \cdot 3^{0} \)
D. All of the above


Assertion
When \( 0.1 ~ M \) weak diprotic acid \( H_{2} A \) dissociates with its dissociation
constants \( \boldsymbol{K}_{\boldsymbol{a}_{1}}=\mathbf{1 0}^{-\mathbf{3}} \) and \( \boldsymbol{K}_{\boldsymbol{a}_{2}}=\mathbf{1 0}^{-\mathbf{8}} \)
then \( \left[A^{2-}\right] \) is almost equal to \( 10^{-3} M \)
Reason
\( \operatorname{since} K_{a_{2}} \ll K_{a_{1}} \) for \( 0.1 M H_{2} A, \) so
\( \left[\boldsymbol{A}^{2-}\right] \) is negligible \( \mathbf{w} . \mathbf{r . t .}\left[\boldsymbol{H} \boldsymbol{A}^{-}\right] \)
A. Both Assertion and Reason are correct and Reason 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


Name the method used for the refining
of Nickel metal.


Name two varieties of cloth materials
which are commonly used.


The correct order of boiling points of the
following isomeric amines is:
\( \boldsymbol{C}_{\mathbf{4}} \boldsymbol{H}_{\mathbf{9}} \boldsymbol{N} \boldsymbol{H}_{\mathbf{2}} \cdot\left(\boldsymbol{C}_{\mathbf{2}} \boldsymbol{H}_{\mathbf{5}}\right)_{\mathbf{2}} \boldsymbol{N} \boldsymbol{H}, \boldsymbol{C}_{\mathbf{2}} \boldsymbol{H}_{\mathbf{5}} \boldsymbol{N}\left(\boldsymbol{C} \boldsymbol{H}_{\mathbf{3}}\right. \)
\( \mathbf{A} \cdot C_{2} H_{5} N\left(C H_{3}\right)_{2}>\left(C_{2} H_{5}\right)_{2} N H>C_{4} H_{9} N H_{2} \)
\( \mathbf{B} \cdot\left(C_{2} H_{5}\right)_{2} N H>C_{2} H_{5} N\left(C H_{3}\right)_{2}>C_{4} H_{9} N H_{2} \)
\( \mathbf{c} \cdot C_{4} H_{9} N H_{2}>\left(C_{2} H_{5}\right)_{2} N H>C_{2} H_{5} N\left(C H_{3}\right)_{2} \)
D. \( \left(C_{2} H_{5}\right)_{2} N H>C_{4} H_{9} N H_{2}>C_{2} H_{5} N\left(C H_{3}\right)_{2} \)


Image obtained on a screen is called
image.


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


The rusting of iron takes place as follows \( 2 H^{+}+2 e+\frac{1}{2} O_{2} \rightarrow H_{2} O(l) ; E^{o}= \)
\( +1.23 V \)
\( F e^{2+}+2 e \rightarrow F e(s) ; E^{o}=-0.44 V \)
\( \Delta G^{o} \) for the net process is:
В. \( -161 k J \) mol \( ^{-1} \)
C. -152 kJ \( m o l^{-1} \)
D. \( -76 k J \) mol\( ^{-1} \)


If \( \chi \) stands for the magnetic
susceptibility of a substance, \( \mu \) for its
magnetic permeability and \( \mu_{0} \) for the permeability of free space, then This question has multiple correct options
A. For a paramagnetic substance: \( \chi>0, \mu>0 \)
B. For a paramagnetic substance: \( \quad \chi>0, \quad \mu>\mu_{0} \)
c. For a diamagnetic substance: \( \chi<0, \mu<0 \)
D. For a ferromagnetic substance: \( \quad \chi>1, \mu<\mu_{0} \)


Which of the following give good synergic bond with metal?
A. \( c o \)
в. \( N H_{3} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{O} \)
D. \( C l \)


What is an isomer? Write the isomer of
butane with structural formula.


If the nuclei of masses \( X \) and \( Y \) are
fused together to form a nucleus of
mass \( m \) and some energy is released,
then
A. \( X+Y=m \)
B. \( X+Y<m \)
c. \( X+Y>m \)
D. \( X-Y=m \)


Diamond and graphite are good conductors of electricity.
A. True
B. False


How would you account for the following:
(i) Among lanthanoids, \( \ln (\| I) \) compounds are predominant. However, occasionally in solution or in solid compounds, +2 and +4 ions are also obtained.
(ii) The \( E_{M^{2+} / M}^{o} \) for copper is positive \( (0.34 \mathrm{V}) . \) Copper is the only metal in the first series of transition elements
showing this behavior.
(iii) The metallic radii of the third (5d)
series of transition metal are nearly the same as those of the corresponding members of the second series.


5 students of a class have an average
height \( 150 \mathrm{cm} \) and variance \( 18 \mathrm{cm}^{2} . \) A new student, whose height is \( 156 \mathrm{cm} \)
joined them. The variance \( \left(\operatorname{in} c m^{2}\right) \) of the height of these six students is
A . 22
B. 20
c. 16
D. 18


(a) State Gauss' law for magnetism.
(b) How this differs from Gauss' law for
electrostatics?
(c) Why is the difference in the two cases?


\( \lim _{x \rightarrow 1} \frac{1}{\sqrt{|x|-\{-x\}}}(\text { where }\{x\} \) denotes
the fractional part of \( x \) ) is equal to
A. does not exists
B. 1
\( c \cdot \alpha \)
D. \( \frac{1}{2} \)


The \( p H \) at which a \( 0.01 \mathrm{M} A l^{+3} \) solution
is \( 99.99 \% \) precipitated is:
\( \left(\boldsymbol{K}_{s p} \boldsymbol{A l}(\boldsymbol{O H})_{3}=\mathbf{1} \times \mathbf{1 0}^{-18} \boldsymbol{a t} \quad \mathbf{2 5}\right) \)
A . 6.67
B. 7.67
c. 8.67
D. 9.617


Given that \( \boldsymbol{K}_{s p} \) of \( \boldsymbol{C a} \boldsymbol{F}_{2} \) is \( \mathbf{1 . 7} \times \mathbf{1 0}^{-\mathbf{1 0}} \)
how many grams of its can be dissolved in


Alkyl halides are classified on the basis
of:
A. nature of halide atom
B. nature of carbon atom
c. nature of alkyl group
D. none of these


Bursting of contractile vacuole to throw
its contents is
A. Ephagy
B. systole
c. Diapause
D. Dehydration


Name the hormone which regulates the
blood calcium level


A man wishes to cross a river in a boat.
If he crosses the river in minimum time,
then he takes 10 minutes with a drift of
\( 120 m . \) If he crosses the river taking
shortest path, he takes 12.5 minutes. Velocity of boat w.r.t water is :
A. \( 40 \mathrm{m} / \mathrm{min} \)
в. \( 20 \mathrm{m} / \mathrm{min} \)
c. \( 10 m / \) min
D. \( 30 m / \) min


The absolute value of charge on the electron was determined by:
A. J.J. Thomson
B. R.A. Millikan
c. Rutherford
D. chadwick


Which one of the following correctly
explains the term 'chimera'
A. Spontaneously induced delections
B. Breaking a part of chromosome segment during mutation
C. Development of genetically diverse tissues in the same organism
D. During mutation at segregation, chromosome become equally distributed


What is the shape of this histogram?
A. Symmetrical
B. Skewed left
c. Skewed right
D. Rotational


In a charged spherical conductor id radius \( 10 \mathrm{cm} \) has potential \( V \) at point
distant \( 5 c m \) from its center, then the
potential at a point \( 15 \mathrm{cm} \) away from the
center will be then
A. \( 3 V \)
в. \( \frac{3}{2} V \)
c. \( \frac{2}{3} V \)
D. \( \frac{1}{3} v \)


One student uses a lens of focal length \( 50 \mathrm{cm} \) and another of \( -50 \mathrm{cm} . \) What is
the nature of the lens and its power
used by each of them?
A. Convex, \( 2 D ; \) Concave, \( -2 D \)
B. Concave, \( 2 D ; \) Convex, \( -2 D \)
c. Concave, \( -2 D ; \) Convex, \( 2 D \)
D. None of the above


Differentiate between passive transport and active transport.


(A) Define the following terms:
(i) Limiting molar conductivity
(ii) Fuel cell
(B) Resistance of a conductivity cell filled with 0.1 mol \( L^{-1} \) KCl solution is
100\Omega. If the resistance of the same cell
when filled with 0.02 mol \( L^{-1} \) KCl
solution is \( 540 \Omega \), calculate the
conductivity and molar conductivity of 0.02 mol \( L^{-1} K C l \) solution. The
conductivity of 0.1 mol \( L^{-1} \) KCl solution is \( 1.29 \times 10^{-2} \Omega^{-1} \mathrm{cm}^{-1} \)


The correct relationship between free energy change in a reaction and the corresponding equilibrium constant \( \boldsymbol{K} \) is
\( \mathbf{A} \cdot-\Delta G=R T \ln K \)
B. \( \Delta G^{o}=R T \ln K \)
c. \( \Delta G=-R T \ln K \)
D. \( -\Delta G^{o}=R T \ln K \)


Solve: \( \sin ^{-1} \frac{5}{x}+\sin ^{-1} \frac{12}{x}=\frac{\pi}{2} \)


\( \int \frac{\boldsymbol{x}^{2}}{\boldsymbol{x}^{6}+\boldsymbol{2} \boldsymbol{x}^{3}-\boldsymbol{3}} \boldsymbol{d} \boldsymbol{x}= \)
A. \( \frac{1}{12} \log \left|\frac{x^{3}-1}{x^{3}+1}\right|+c \)
в. \( \frac{1}{12} \log \left|\frac{x^{3}-1}{x^{3}+3}\right|+c \)
c. \( \frac{1}{12} \log \left|\frac{x^{3}+3}{x^{3}-1}\right|+c \)
D. \( \frac{1}{12} \log \left|\frac{x^{3}-3}{x^{3}+1}\right|+c \)


A coin placed on a rotating turn table just slips if it is at a distance of \( 40 \mathrm{cm} \)
from the centre if the angular velocity of the turntable is doubled, it will just slip at a distance of:
\( \mathbf{A} \cdot 10 \mathrm{cm} \)
B. \( 20 \mathrm{cm} \)
c. \( 40 \mathrm{cm} \)
D. \( 80 \mathrm{cm} \)


Turnbull's blue is which of the following compound?
A. ferri cyanide
B. ferro ferricyanide
c. ferrous cyanide
D. ferri ferrocyanide


Scientific name of human is
A. Homo naled
B. Homo habilis
c. Homo erectus
D. Homo sapiens


A random variable \( \boldsymbol{X} \) has the following probability distribution:
\[
\begin{array}{ccccc}
\boldsymbol{X} & 0 & 1 & 2 & 3 \\
P(X) & 0.1 & k & 2 k & 2 k
\end{array}
\]
Determine:
(i) \( k \)
(ii) \( P(X \geq 2) \)


A positive ion having only one electron
ejects it if a photon of \( \gamma \leq 228 A^{0} \) is
abosrbed by it. The ion is
A \( . H e^{+} \)
B. \( L i^{+} \)
\( \mathbf{c} \cdot B e^{+3} \)
D. \( B^{+4} \)


A range of galavanometer is ' \( V \) ', when
\( 50 \Omega \) resistance is connected in series.
Its range gets doubled when \( 500 \Omega \) resistance is connected in series.
Galvanometer resistance is
\( \mathbf{A} \cdot 100 \Omega \)
в. 200\Omega
c. \( 300 \Omega \)
D. \( 400 \Omega \)


Measure of one angle of linear pair is
\( 108^{\circ}, \) then find the measure of another angle.


Define :
photoelectric work function.


The side of a regular hexagon is \( \boldsymbol{p} \boldsymbol{c m} \)
then its area is
A \( \cdot \frac{\sqrt{3}}{2} p^{2} \mathrm{cm}^{2} \)
B. \( \frac{3 \sqrt{3}}{2} p^{2} \mathrm{cm}^{2} \)
c. \( 2 \sqrt{3} p^{2} c m^{2} \)
D. \( 6 p^{2} \mathrm{cm}^{2} \)


For ordinary terrestrial experiments, which of the observers below are inertial
and which are non-inertial?
a) a child revolving in a giant wheel
b) a driver in a sports car moving with a constant high speed of \( 200 \mathrm{km} / \mathrm{h} \) on a straight road
c) the pilot of an airplane which is taking off
d) a cyclist negotiating a sharp turn
e) the guard of a train which is slowing down to stop at a station


An air column in a pipe, which is closed at one end, will be in resonance with a
vibrating tuning fork of frequency \( 264 H z \) if the length of the column in
\( c m \) is:
A. 31.25
B. 62.50
c. 93.75
D. 125


Write the structure of Leucine.


\( A B \) and \( C D \) intersects each other at
point \( O . \) Measure of one angle formed by
intersection is \( 120^{\circ}, \) then the measure
of another three angles are \( 60^{\circ}, 120^{\circ}, 60^{\circ} \)
A. True
B. False


A particle having initial velocity \( u \) moves with a constant acceleration \( a \)
for a time \( t . \) Find the displacement of the particle in the last one second.
A \( \cdot u+\frac{a}{2}(t-1) \)
в. \( u+\frac{a}{2}(2 t-1) \)
c. \( u+\frac{a}{2}(4 t-1) \)
D. \( u t+\frac{1}{2} a t^{2} \)


A cricketer scored a total of 62 runs in
96 balls. He hits 3 sixes, 8 fours, 2 twos
and 8 singles, What highest percentage of the runs that came in:
A. Sixes
B. Fours
c. Twos
D. singles


Compound \( X\left(C_{5} H_{8} O_{2}\right) \) forms a
dioxime with \( N H_{2} O H . \) On

Clemmensen reduction it forms a
compound which forms only one monochloro derivative. 'X' can be :
\( A \)
в.
\( c \)
D. онс-снд \( -\mathrm{cH}_{2}-\mathrm{cH}_{2}- \) сно


Define venation


A batsman deflects a ball by an angle of
\( 90^{\circ} \) without changing its initial speed, which is equal to \( 54 \mathrm{km} / \mathrm{hr} \). What is the impulse imparted to the ball? (Mass of the ball is \( 0.15 k g \) ).


Minerals that have a relatively high concentration of metal and can be
extracted in an easy and cost-effective
process are called:
A. Metalloids
B. Gold crust
c. ores
D. None of above


Ammonium chloride is separated from
a mixture of sodium chloride and
ammonium chloride by the process of:
A. evaporation
B. sublimation
c. fractional distillation
D. filtration


A small body starts falling onto the Sun
from a distance equal to the radius of
the Earth's orbit. The initial velocity of the body is equal to zero in the heliocentric reference frame.
Making use of Kepler's laws, how long the body will be falling in days
A . 64.5
B. 65
c. 60
D. None of these


Atmospheric pressure is \( N m^{-2} \) at sea level.
A \( \cdot 2.026 \times 10^{5} \)
В. \( 1.013 \times 10^{5} \)
c. \( 3.039 \times 10^{5} \)
D. \( 1.013 \times 10^{6} \)


\( 18.4 \mathrm{g} \) of \( N_{2} O_{4} \) is taken in a 1 L closed vessel and heated till the equilibrium is
reached.
\( N_{2} O_{4(g)} \rightleftharpoons 2 N O_{2(g)} \)
At equilibrium it is found that \( 50 \% \) of
\( N_{2} O_{4} \) is dissociated. What will be the
value of equilibrium constant?
A . 0.2
B. 2
\( c .0 .4 \)
D. 0.8


Chemical change are characterised by
A. formation of new substance
B. release of energy
c. absorption of energy
D. reversible


If a ray makes angles \( \alpha, \beta, \gamma \) and \( \delta \) with the four diagonals of a cube and
\( \mathbf{A}: \cos ^{2} \boldsymbol{\alpha}+\cos ^{2} \boldsymbol{\beta}+\cos ^{2} \boldsymbol{\gamma}+\cos ^{2} \boldsymbol{\delta} \)
\( \mathbf{B}: \sin ^{2} \boldsymbol{\alpha}+\sin ^{2} \boldsymbol{\beta}+\sin ^{2} \boldsymbol{\gamma}+\sin ^{2} \boldsymbol{\delta} \)
\( \mathbf{C}: \cos 2 \boldsymbol{\alpha}+\cos 2 \boldsymbol{\beta}+\cos 2 \gamma+\cos 2 \boldsymbol{\delta} \)
Arrange \( A, B, C \) in descending order
A. \( B, A, C \)
в. \( A, B, C \)
c. \( C, A, B \)
D. \( B, C, A \)


If \( \boldsymbol{f}: \boldsymbol{I} \rightarrow \boldsymbol{I}, \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{3}+1, \) then \( \boldsymbol{f} \) is
A. one-one but not onto
B. onto but not one-one
c. one-one onto
D. none of these


Fuel cells are better than other cells.
Give any two reasons.


A coil having resistance \( 20 \Omega \) and inductance \( 2 H \) is connected to a
battery of emf \( 4.0 \% \). Find (a) the current
at \( 0.20 s \) after the connection is made
and
(b) the magnetic field energy in the
coil at the instant


Write down name, structural formula
and Hybridization of two Xenon compounds?


The value of the static dielectric
constant of any material is always
A. greater than 1
B. equal to 1
c. lesser than 1
D. None


The thickness of depletion layer is approximately
A . \( 1 \mu m \)
B. \( 1 \mathrm{mm} \)
\( c \cdot 1 c m \)
D. \( 1 m \)


The atom of an element has 10
electrons, 10 protons and 12 neutrons. Find the mass number of the element:
A . 10
B. 12
\( c \cdot 22 \)
D. 32


Brains can work 24 hours a day with no
rest.
A . True
B. False


Consider the two quadratic
polynomials:
\( C_{a}: y=\frac{x^{2}}{4}-a x+a^{2}+a-2 \) and
\( C: y=2-\frac{x^{2}}{4} \)
If the origin lies between the zeroes of
the polynomial \( C_{a}, \) then the number of
integral value(s) of \( ^{\prime} \boldsymbol{a}^{\prime} \) is
A.
B. 2
\( c .3 \)
D. more than 3


The variance of observations
112,116,120,125,132 is
A . 58.8
B. 48.8
c. 61.8
D. None of these


The van dar Waal's parameters for
gases \( W, X, Y \) and \( Z \) are:
\( \begin{array}{lll}\text { Gas } & \mathrm{a}\left(\mathrm{atm} l^{2} / \mathrm{mol}^{2}\right) & \mathrm{b}(\mathrm{l} / \mathrm{mol}) \\ \mathrm{w} & 4.0 & 0.027 \\ \mathrm{x} & 8.0 & 0.030 \\ \mathrm{Y} & 6.0 & 0.032 \\ \mathrm{z} & 12.0 & 0.027\end{array} \)
Which one of these gases has the
highest critical temperature?
\( A \cdot w \)
B. \( x \)
\( c \)
\( D . z \)


Rainbow is formed due to:
A. total internal reflection
B. scattering
c. refraction
D. dispersion and total internal reflection


The density of a gaseous substance at 1 atm pressure and \( 773 \mathrm{K} \) is \( 0.4 \mathrm{g} / \) lit. If the molecular weight of the substance is 30 the forces existing among gas molecules are?
A. repulsive
B. attractive
\( c . \) both
D. none


Which is the living component of xylem?
A. Tracheids
B. Xylem fibre
c. xylem parenchyma
D. Trachea


In two beakers \( (A \text { and } B) 50 m l \) water of
about \( 70^{\circ} \mathrm{C} \) each is taken. Then in
beaker \( A, 50 m l \) of water of about \( 30^{\circ} C \)
is added and after 5 minutes, in beaker
\( B, 50 m l \) of water of about \( 30^{\circ} C \) is
added. What would observe if the
temperatures of both beakers recorded immediately? Why?


Two isomer products are obtained in
(C). They are:
A. both \( \gamma \) -lactone
B. both \( \delta \) -lactones
C. one is \( \gamma \) -lactone and another is \( \delta \) -lactone
D. none


The composition of mischmetal is:
A. \( 5 \% \) of a lanthanoid metal, \( 95 \% \) of iron and traces of \( S, C, C a \) and \( A l \)
B. \( 95 \% \) of an actinoid metal, \( 5 \% \) of iron and traces of \( S, C, C a \) and \( A l \)
C. \( 95 \% \) of a lanthanoid metal, \( 5 \% \) of iron and traces of \( S, C, C a \) and \( A l \)
D. \( 95 \% \) of a transition metal, \( 5 \% \) of iron and traces of \( S, C, C a \) and \( A l \)


Largest number of molecules are
present in-
A. \( 44 g m \) of carbon dioxide
B. \( 28 g m \) of carbon monoxide
c. \( 36 g m \) of water
D. \( 64 g m \) of sulphur dioxide


Which of the following term does not represent electrical power in a circuit? This question has multiple correct options
\( \mathbf{A} \cdot I^{2} R \)
B . \( I R^{2} \)
c. \( v \)
D. \( V^{2} I R \)


Name the process involved in preparation of sulphuric acid.
A. Electrolysis
B. Decomposition
c. Photolysis
D. contact process


The treatment of \( \left(\boldsymbol{C H}_{3}\right)_{2} \boldsymbol{C}=\boldsymbol{C H} \boldsymbol{C H}_{3} \)
with boiling \( K M n O_{4} \) produces :
A. \( C H_{3} C O C H_{3}+C H_{3} C O O H \)
B. \( C H_{3} C O C H_{3}+C H_{3} C H O \)
c. \( C H_{3} C H O+C O_{2} \)
D. \( C H_{3} C O C H_{3} \) only


Match the enzymes in column I with
their respective biochemical reactions
in column II. Choose the correct
combination from.
Column I
(P)
(i) removal of phosphory Transaminases
acid group from a specific amino
(Q) Protein
(ii) removal of \( \alpha \) -amino group Kinases acid \( \quad \) from a specific amino
(R) Protein
(iii) addition of phosphoryl Phosphatases froup to a specific amino acid
\( (s) \)
(iv) interconversion of optical Dehydrogenases isomers
(v) oxidation and reduction of substrates
A. P-iv, Q-ii, R-iii, S-v
B. P-ii, Q-i, R-ii, S-iv
c. P-ii, Q-iii, R-i, S-v
D. P-v, Q-ii, R-iii, S-i


Write the steps to construct \( \triangle A B C, \) in which \( B C=5.2 c m, \angle A C B=45^{\circ} \) and
perimeter of \( \triangle \boldsymbol{A B C} \) is \( 10 \mathrm{cm} \)


Zinc react with aqueous sodium hydroxide to form dihydrogen and
A. zinc oxide
B. sodium zincate
c. zinc hydroxide
D. sodium precipitate


Proximal convoluted tubule is lined by a single layer of ............ cells.
A. Brush bordered cubical
B. Columnar
c. Squamous
D. cubical


If a set contains \( n \) elements then
number of elements in its power set is
A \( \cdot 2^{n}-n \)
B . \( 2^{n}-2 \)
\( c \cdot 2^{n} \)
\( \mathbf{D} \cdot n^{2} \)


In mechanism, photophosphorylation is
very similar to
A. substrate-level phosphorylation
B. oxidative phosphorylation
c. calvin cycle
D. glycolysis


Which of the following is least? (All angles have been measured in radians)
\( A \cdot \sin 3 \)
B. \( \sin 2 \)
\( c \cdot \sin 1 \)
D. \( \sin 7 \)


An object of mass, \( m \) is moving with a
constant velocity, \( \boldsymbol{v} \). How much work
should be done on the object in order to bring the object to rest?


A reduction in atomic size with
increase in atomic number is a
characteristic of elements of:
A. d-block
B. f-block
c. radioactive series
D. high atomic masses


The mean of the following distribution
is
15. Find the value of a
\( \begin{array}{lll}\text { C.I. } & \text { 5 } & \text { 10 }\end{array} \) 15 \( \mathbf{2 0} \) \( \mathbf{2 5} \)
Freq 6 a 6 5 10


Write the following in increasing energy orders \( : 3 \mathrm{d}, 5 \mathrm{s}, 6 \mathrm{s}, 4 \mathrm{f}, 4 \mathrm{d} \)
A. \( 4 f<6 s<4 d<5 s<3 d \)
B. 4f > 6s > 4d > 5s > 3d
\( c \cdot 4 f>4 d>6 s>5 s>3 d \)
D. \( 4 f>6 s>5 s>4 d>3 d \)


Assertion
\( N H_{4} N O_{3} \) undergoes a redox reaction
to give \( N_{2} O \) and \( H_{2} O \)
Reason
It is a disproportionation 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. Assertion is incorrect but Reason is correct


The number of even numbers with three
digits such that if 3 is one of the digit
then 5 is the next digit are
A . 959
B. 285
c. 365
D. 512


A coil having \( n \) turns and resistance \( \boldsymbol{R} \) \( \Omega \) is connected with a galvanometer of
resistance \( 4 R \Omega \). This combination is
moved in time \( t \) seconds from a
magnetic flux \( W_{1} \) to \( W_{2} \). The induced
current in the circuit is
A. \( -\frac{W_{2}-W_{1}}{5 R n t} \)
в. \( \frac{n\left(W_{2}-W_{1}\right)}{5 R t} \)
c. \( -\frac{\left(W_{2}-W_{1}\right)}{R n t} \)
D. \( -\frac{n\left(W_{2}-W_{1}\right)}{R n t} \)


A uniform heavy disc of moment of
inertia \( I_{1} \) is rotating with constant
angular velocity \( \omega_{1} . \) Then, a second
nonrotating disc of moment of inertia \( I_{2} \)
is dropped on it. The two discs rotate together. The final angular velocity of the
system becomes
\( \mathbf{A} \cdot \frac{I_{1} \omega_{1}}{I_{2}} \)
B. \( \sqrt{\frac{I_{1}}{I_{2}} \omega_{1}} \)
C. \( \frac{I_{1} \omega_{1}}{I_{1}+I_{2}} \)
D. \( \frac{\left(I_{1}-I_{2}\right) \omega_{1}}{I_{1}+I_{2}} \)


The number of Glucose molecules
present in 10 ml of decimolar solution
is:
A \( .6 .0 \times 10^{20} \)
В . \( 6.0 \times 10^{19} \)
c. \( 6.0 \times 10^{21} \)
D. \( 6.0 \times 10^{22} \)


Form the expression for: "Sum of number \( a \) and \( b \) subtracted from their
product-


Why are cimetidine and ranitidine
better antacids than sodium hydrogen carbonate or magnesium or aluminium hydroxide?


Which statements are correct about
sucrose?
This question has multiple correct options
A. IUPAC name of sucrose is \( \alpha \) -D-glucopyranosyl- \( \beta \) -Dfructofuranside
B. IUPAC name of sucrose is \( \beta \) -D-fructofuranosyl- \( \alpha \) -Dglucopyranoside
C. It is hydrolysed both by emulsin and amylase
D. On hydrolysis, the solution is laevorotatory


Phenol-water system is a/an
A. element
B. compound
c. homogeneous system
D. heterogeneous system


Cell division is tightly regulated, which of the following is true regarding mitosis or meiosis.
I. Mitosis shows no homologous pairing.
II. There is no S phase between meiosis
and II
III. Meiosis centromeres do not divide at
anaphase I.
A. I and III only
B. I and II only
c. ॥ only
D. I, II and III


The final product formed when silica reacts with hydrogen fluoride is :
A . \( S i F \)
в. \( H_{2} \) s \( s F_{6} \)
\( \mathrm{c} . \mathrm{H}_{2} \mathrm{SiF}_{4} \)
D. \( H_{2} \) sio \( _{3} \),


A thin lens with focal length \( f \) to be used as magnifying glass. Which of the following statements regarding the situation is true?
A. A converging lens may be used, and the object be placed at a distance greater than 2 from the lens.
B. A diverging lens may be used, and the object be placed between \( f \) and \( 2 f \) from the lens
c. A converging lens may be used, and the object be placed at a distance less than f from the lens
D. A diverging lens may be used, and the object be placed at any point other than the focal point


Which one of the following ores is best concentrated by froth-floatation method?
A . Magnetite
B. Cassiterite
c. Galena
D. Malachite


The arithmetic mean of \( 1,8,27,64, \dots \) up to n terms is given by
A \( \cdot \frac{n(n+1)}{2} \)
B. \( \frac{n(n+1)^{2}}{2} \)
c. \( \frac{n(n+1)^{2}}{4} \)
D. \( \frac{n^{2}(n+1)^{2}}{4} \)


If the body is moving in a circle of
radius \( r \) with a constant speed \( V \), its angular velocity is
A \( \cdot V^{2} / r \)
в. \( V r \)
c. \( V / r \)
D. \( r / V \)


If \( \boldsymbol{A}=\{\mathbf{0}, \mathbf{1}, \mathbf{2}, \mathbf{3}, \mathbf{4}, \mathbf{5}\} \) and relation \( \boldsymbol{R} \)
defined by \( a R b \) such that \( 2 a+b=10 \)
then \( R^{-1} \) equals
A \( \cdot\{(4,3),(2,4),(5,0)\} \)
B - \{(3,4),(4,2),(5,0)\}
c. \{(4,3),(2,4),(0,5)\}
D \( \cdot\{(4,3),(4,2),(5,0)\} \)


Which of the following row is giving the
correct combination of all the three
column?
\( \begin{array}{lll}\text { Column I } & \text { Column II } & \begin{array}{l}\text { Column } \\ \text { II }\end{array} \\ \text { (1) Myopia } & \begin{array}{l}\text { Long } \\ \text { sightedness }\end{array} & \begin{array}{l}\text { Convex } \\ \text { lens }\end{array} \\ \begin{array}{l}\text { (2) } \\ \text { Hypermetropia }\end{array} & \begin{array}{l}\text { Near } \\ \text { sightedness }\end{array} & \begin{array}{l}\text { Concave } \\ \text { lens }\end{array} \\ \text { (3) Presbyopia } & \begin{array}{l}\text { Old age } \\ \text { problem }\end{array} & \begin{array}{l}\text { Bifocal } \\ \text { lens }\end{array}\end{array} \)


Maximum oxidation state shown by
sulphur in its compounds is


The various phases of the cell cycle will be affected by limiting growth factors like
A. Sufficient nucleotides
B. Temperature
c. Nutrients
D. All of the above


Two rings each of mass ' \( m^{\prime} \) and radius
\( r^{\prime} \) are placed such that their centres
are at a common point and their planes
are normal to each other. The moment of
inertia of the system about an axis passing through the centre and perpendicular to plane of one of ring is:
A \( \cdot 2 m r^{2} \)
B. \( m r^{2} \)
c. \( \frac{1}{2} m r^{2} \)
D. \( \frac{3}{2} m r^{2} \)


\( \lim _{x \rightarrow 0} \frac{3 \sin x-4 \sin ^{3} x}{x}= \)


Which is aminated hormone?
A. Progesterone
B. Epinephrine
C. Estrogen
D. Relaxin


Nutation is shown by
A. Root
B. Stem
c. Leaves
D. Both A and B
E. Root, Stem, and Leaves


toppr
Q Type your question
diagram for it is:
\( A \)
\( B \)
\( c \)
\( D \)


The equation of the ellipse whose equation of directrix is \( 3 x+4 y-5=0 \)
coordinates of the focus are (1,2) and the eccentricity is \( \frac{1}{2} \) is \( 91 x^{2}+84 y^{2}- \)
\( 24 x y-170 x-360 y+475=0 \)
A. True
B. False


Which statement is wrong from the
following?
Statement-1: METSAT is useful for
weather forecasting. Statement -2: INSAT is useful for
Direct to Home (DTH) transmission
Statement-3: CARTOSAT is useful for
astronomical observation.
A. Statement -1
B. Statement -3
c. Statement-1 and 2
D. Statement -2


Pallavi got PUC certificate for her vehicle which indicates which of the
following criteria for the vehicle?
A. It has low rate of emission
B. It is equipped with new technology
c. It has greater fuel capacity
D. None of the above


Simplify the polynomial and write it in
standard form:
\( (-2 x-5)(2 x-8)-(2 x-5)(3 x+7) \)


If \( \tan ^{2} \) la \( \tan ^{2} \beta+\tan ^{2} \beta \cdot \tan ^{2} \gamma+ \)
\( \tan ^{2} \gamma \cdot \tan ^{2} \alpha+2 \tan ^{2} \alpha \cdot \tan ^{2} \beta \cdot \tan ^{2} \gamma= \)
1, then the value of \( \sin ^{2} \alpha+\sin ^{2} \beta+ \)
\( \sin ^{2} \gamma \) is :
A .
B. -
\( c \)
\( D \cdot \frac{1}{2} \)


Mothers present age is 6 times the age
of her son, After 5 years the mothers age will be 4 times that times the age of her
son. What will be the presents age of a
son?


Assertion
The ferromagnetic substance do not obey Curie's law.
Reason
At Curie point a ferromagnetic substance start behaving as a paramagnetic substance.
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


During transcription, holoenzyme RNA
polymerase binds to a DNA sequence and the DNA assumes a saddle like
structure at that point. What is that
sequence called?
A. CAAT box
B. GGTT box
C. AAAT box
D. TATA box


A negative charge is placed at some point of the joining the two \( +Q \) charges at rest. The direction of motion of
negative charge will depend upon the:
A. Position of negative charge alone
B. magnitude of negative charge alone
c. both on the magnitude and positive of negative charge
D. magnitude of positive charge