Choose the correct answer from the
alternatives given :

If Meselson and Stahls experiment is continued for four generations in bacteria, the ratio of \( N^{15}-N^{15}, N^{14}- \)
\( N^{15}, N^{14}-N^{14} \) containing DNA in the fourth generation would be
A . 1:1:10
B. 1:4:0
c. 0: 1: 3
D. 0:1:7


Find the volume of a sphere of radius
\( 2.1 \mathrm{cm}\left(\text { use } \pi=\frac{22}{7}\right) \)


A metal block has dimension \( 10 \mathrm{cm} \times \)
\( 5 c m \times 2 c m \).the ratio of maximum to
minimum resistance that can be
obtained from it is
\( \mathbf{A} \cdot 25: 1 \)
B. 1: 25
\( \mathbf{c} \cdot 10: 3 \)
D. 3: 10


In a nuclear reactor heavy water is used
as a
A. Moderate
B. Fuel
c. shield
D. Controlling element


A cannon fires successively two shells
with velocity \( v_{0}=250 m / s ; \) the first at
the angle \( \theta_{1}=60^{\circ} \) and the second at
the angle \( \theta_{2}=45^{\circ} \) to the horizontal, the
azimuth being the same. Neglecting the air drag, the time interval(in seconds) between firings leading to the collision of the shells is \( (10+x) \). Find the value of
x. (Take \( g=10 m / s^{2} \) and round-off your
answer to the nearest integer.)


Two iron rod \( A \) and \( B \) are taken. \( A \) is
dipped in dilute \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} . \boldsymbol{B} \) is first
dipped in conc. \( H N O_{3} \) and later in
dilute \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} . \) What will be the status
of iron rods after some time? Justify


f \( p=5+2 \sqrt{6} \) and \( q=\frac{1}{p}, \) find \( p^{2}+q^{2} \)
is :
A .49
B. 98
\( c .100 \)
D. None of these


A straight conductor \( 0.1 \mathrm{m} \) long moves in a uniform magnetic field ).1T. The velocity of the conductor is \( 15 \mathrm{m} / \mathrm{s} \) and is directed perpendicular to the field The e.m.f. induced between the two ends
of the conductors is.
A . \( 0.10 \mathrm{v} \)
B. 0.15 \( v \)
c. \( 1.50 v \)
D. 15.00


What is the result when \( 2 x^{2}+5 x-6 \) is
subtracted from \( 4 x^{2}-9 x+6 \)


Suggest four measures to check water pollution.


Which one is not correct about Krebs
cycle?
A. It is also called citric acid cycle.
B. The intermediate compound which links glycolysis with Krebs cycle is malic acid.
C. It occurs in mitochondria.
D. It start with six carbon compound.


A block of mass \( m \) slides down an
inclined plane of inclination \( \theta \) with
uniform speed. The coefficient of friction between the block and the plane
is \( \mu . \) The contact force between the
block and the plane is
\( \mathbf{A} \cdot m g \sin \theta \sqrt{1+\mu^{2}} \)
B. \( \sqrt{(m g \sin \theta)^{2}+(\mu m g \cos \theta)^{2}} \)
\( \mathrm{c} \cdot m g \sin \theta \)
D. \( m g \)


The sum of the length, breadth and depth of a cuboid is \( 19 \mathrm{cm} \) and the
length of its diagonal is \( 11 \mathrm{cm} \). Find the
surface area of the cuboid.


David wants to invest at most
Rs. 12,000 in bonds \( A \) and \( B \) According to the rule, he has to invest at
least \( R s .2,000 \) in Bond \( A \) and at least
Rs. 4,000 in Bond \( B \). If the rates of
interest on Bonds \( A \) and \( B \) respectively
are \( 8 \% \) and \( 10 \% \) perannum, formulate the problem as L.P.P. and solve it graphically for maximum interest. Also determine the maximum interest
received in a year.


If \( a-b=1 \) and \( a b=12, \) find the value
of \( \left(a^{2}+b^{2}\right) \)


A matrix having \( m \) rows and \( n \) columns
with \( m \neq n \) is said to be a
A. rectangular matrix
B. square matrix
c. identity matrix
D. scalar matrix


Antispasmodics are a group (class) of
medicines that can help to control some
symptoms that arise from part of the human body especially.
A . intestine
B. lungs
c. kidney
D. head


If the ratio of lengths, radii and Youngs
modulii of steel and brass wires in the
figure are a, b and c respectively. Then the corresponding ratio of increase in
their lengths would be:
A \( \cdot \frac{2 a}{h^{2}} \)
в. \( \frac{3 a}{2 b^{2} c} \)
c. \( \frac{3 c}{2 a b^{2}} \)
D. \( \frac{2 a^{2}}{b} \)


A beam of diameter \( d \) is incident on a
glass hemiphere as shown.If the radius
of curvature of the hemiphere is very large in composition to \( \mathrm{d} \), then the diameter of the beam at the base of the
hemiphere will be :


A moving coil galvanometer has a coil of area \( A \) and number of turns \( N . A \)
magnetic field \( \mathrm{B} \) is applied on it. The torque acting on it is given by \( \boldsymbol{\tau}=\boldsymbol{k} \boldsymbol{i} \)
where i is current through the coil. If moment of inertia of the coil is I about
the axis of rotation.
A charge \( Q \) is passed almost instantaneously through coil If the maximum angular deflection in it \( \mathbf{s} \boldsymbol{\theta}=\boldsymbol{Q} \sqrt{\frac{\boldsymbol{\pi} \boldsymbol{N} \boldsymbol{A} \boldsymbol{B}}{\boldsymbol{x} \boldsymbol{I} \boldsymbol{i}_{0}}} . \) Find \( \mathbf{x} \)


The coordinates of a particle moving in x-y plane at any instant of time t are \( x=4 t^{2} ; y=3 t^{2} . \) The speed of the
particle at that instant is :
A . 10
B. 5t
\( c \cdot 3 t \)
D. \( 2 t \)
E . \( \sqrt{13} t \)


Name the enzyme used in the inversion
of cane sugar.


The entropy \( \left(S^{o}\right) \) of the following
substances are:
\( \boldsymbol{C H}_{4}(\boldsymbol{g})=\mathbf{1 8 6 . 2} \boldsymbol{J} \boldsymbol{K}^{-1} \boldsymbol{m o l}^{-1} \)
\( \boldsymbol{O}_{2}(\boldsymbol{g})=\mathbf{2 0 5 . 0} \boldsymbol{J} \boldsymbol{K}^{-1} \boldsymbol{m o l}^{-1} \)
\( \boldsymbol{C O}_{2}(\boldsymbol{g})=\boldsymbol{2 1 3 . 6} \boldsymbol{J} \boldsymbol{K}^{-1} \boldsymbol{m o l}^{-1} \)
\( \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l})=\boldsymbol{6} \boldsymbol{9} . \boldsymbol{9} \boldsymbol{J} \boldsymbol{K}^{-1} \boldsymbol{m} \boldsymbol{o} \boldsymbol{l}^{-1} \)
The entropy change \( \left(\Delta S^{o}\right) \) for the
reaction \( \boldsymbol{C} \boldsymbol{H}_{4}(\boldsymbol{g})+\mathbf{2} \boldsymbol{O}_{2}(\boldsymbol{g}) \rightarrow \)
\( \boldsymbol{C O}_{2}(\boldsymbol{g})+\mathbf{2} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l}) \) is:
\begin{tabular}{l}
A. \( -312.5 \mathrm{JK}^{-1} \mathrm{mol}^{-1} \) \\
\hline
\end{tabular}
в. \( -242.8 \mathrm{JK}^{-1} \mathrm{mol}^{-1} \)
c. \( -108.1 \mathrm{JK}^{-1} \mathrm{mol}^{-1} \)
D. \( -37.6 J K^{-1} m o l^{-1} \)


\( \pi^{o} \) meson is exchanged between:
A. proton and neutron
B. proton and proton
c. neutron and neutron
D. may be between two protons or two neutrons


Draw a linear pair of angles. Bisect each of the two angles.Verify that the two bisecting rays are perpendicular to each other.


A scooterist travels at \( 30 \mathrm{km} / \mathrm{h} \) along
straight path for 20 min. What is distance?
A . \( 1.5 \mathrm{km} \)
B. \( 6 \mathrm{km} \)
\( c \cdot 10 \mathrm{km} \)
D. 90 km


If \( \boldsymbol{m}=\mathbf{2}(\mathbf{1 5}-\mathbf{4} \boldsymbol{x}), \boldsymbol{n}=\frac{\mathbf{5} \boldsymbol{x}+\mathbf{3}}{\mathbf{2}} \) and
\( \boldsymbol{m}: \boldsymbol{n}=\boldsymbol{2}: \boldsymbol{3} ; \) find \( \boldsymbol{n} \)
\( \mathbf{A} \cdot n=2 \)
В . \( n=7 \)
c. \( n=9 \)
D. \( n=12 \)


Given balanced chemical equation for the action of sulphuric acid on each of the following:
(1) Potassium hydrogen carbonate.
(2) Sulphur.


Assertion: Material used in the
construction of a standard resistance is
constantan or manganin Reason : Temperature coefficients of constantan and Magnanin are very
small
A. Both (A) and (R) are true and
(R) is the correct explanation of (A)
B. Both (A) and (R) are true but (R) is not the correct explanation of \( (A) \)
c. (A) is true but (R) is false
D. (A) is false but (R) is true


If \( \hat{a}, \hat{b} \) and \( \hat{c} \) are unit vectors satisfying \( |\hat{\boldsymbol{a}}-\hat{\boldsymbol{b}}|^{2}+|\hat{\boldsymbol{b}}-\hat{\boldsymbol{c}}|^{2}+|\hat{\boldsymbol{c}}-\hat{\boldsymbol{a}}|^{2}=\mathbf{9}, \) then
\( |2 \hat{a}+5 \hat{b}+5 \hat{c}| \) is
\( A \cdot 3 \)
B. 4
c. 5
D. 6


Why liquid fuel is better than solid fuel?
A. It is cheaper than solid fuel
B. It can be extracted easily
c. It does not leave any solid residue
D. All of these


Differentiating electron in inner transition elements enters the
orbital.(s/p/d/f)


Which of the following is not an application of wind energy?
A. Removing husk from grains
B. Propelling sail boats in rivers and seas
c. windmills
D. Cyclones


Given below are the two reactions of
\( H_{2} O_{2} . \) Mark the correct statement which follows:
\( (\mathrm{i}) 2 \mathrm{K} M n O_{4}+3 \mathrm{H}_{2} \mathrm{SO}_{4}+5 \mathrm{H}_{2} \mathrm{O}_{2} \rightarrow \)
\( \boldsymbol{K}_{2} \boldsymbol{S} \boldsymbol{O}_{4}+\boldsymbol{2} \boldsymbol{M} \boldsymbol{n} \boldsymbol{S} \boldsymbol{O}_{4}+\boldsymbol{8} \boldsymbol{H}_{2} \boldsymbol{O}+\boldsymbol{5} \boldsymbol{O}_{2} \)
(ii) \( 2 C r(O H)_{3}+4 N a O H+ \)
\( \mathbf{3} \boldsymbol{H}_{2} \boldsymbol{O}_{2} \rightarrow \boldsymbol{2} \boldsymbol{N} \boldsymbol{a}_{2} \boldsymbol{C r} \boldsymbol{O}_{4}+\boldsymbol{8} \boldsymbol{H}_{2} \boldsymbol{O} \)
A . (i) Shows oxidizing nature of \( H_{2} O_{2} \) and (ii) shows reducing nature of \( H_{2} O_{2} \)
B. \( \ln \left(\text { i) } H_{2} O_{2} \) acts as a reducing agent and in (ii) it acts \right. as an oxidizing agent
\( c \cdot \ln \operatorname{both}(i) \) and
(ii), \( H_{2} O_{2} \) acts as an oxidizing agent
D. In both (i) and
(i), \( H_{2} O_{2} \) acts as a reducing agent


When white light is incident on a prism,
which of the following ray will experience lesser deviation?
A. Black
B. Green
c. violet
D. Red


In the given figure, find the magnitude
and nature of zero error


What type of resource copper is?
A. Exhaustible
B. Non-exhaustible
C . Potential
D. National


Which of the following will exhibit
highest boiling point?
A. \( C H_{3} C H_{2} O C H_{2} C H_{3} \)
в. \( C H_{3} C H_{2} C H_{2} C H_{2} C H_{2} O H \)
c. \( C H_{3} C H_{2} C H_{2} C H\left(C H_{3}\right) O H \)
D. \( C H_{3} C H_{2} C\left(C H_{3}\right)_{2} O H \)


Which property is common between vinegar and curd?
A. Have sweet taste
B. Have bitter taste
c. Are tasteless.
D. Have sour taste


State whether True or False:
Bohr's model failed to explain atomic spectra of multi-electron atoms.
A. True
B. False


\( A B C \) is an isosceles triangle inscribed in a circle of radius \( r . \) If \( A B=A C \) and \( h \)
is the altitude from \( A \) to \( B C, \) then evaluate \( \lim _{h \rightarrow 0} \frac{\Delta}{P^{3}}, \) where \( \Delta \) is area of the triangle and \( P \) its perimeter.
A \( \cdot \frac{1}{128 r} \)
в. \( \frac{1}{64 r} \)
c. \( \frac{1}{32 r} \)
D. \( \frac{1}{256 r} \)


Find the areas of the triangles the whose coordinates of the points are respectively. (5,2),(-9,-3) and (-3,-5)


The positive terminal of \( 12 \mathrm{V} \) battery is connected to the ground. Then the negative terminal will be at :
A . - \( 6 v \)
B. +12 V
c. zero
D. -12 V


\( \lim _{x \rightarrow \frac{\pi}{2}} \frac{\tan 2 x}{x-\frac{\pi}{2}} \)


Energy spent in kilowatt-hour \( = \)
A. ampere, hour
B. ohm,min
c. ampere,min
D. joule,hour


The most ionic compound among the following is:
A . silica
B. aluminium fluoride
c. carborundum
D. aluminium chloride


Mark the correct statement the
magnitude of current induced in the
coil can be increased
A. by winding the coil on a soft iron core
B. by increasing the number of turns in the coil.
c. by increasing the strength of magnett
D. all


A stone is dropped from a rising balloon at a height of \( 300 \mathrm{m} \) above the ground and it reaches the ground in 10 s. The velocity of the balloon when the stone
was dropped is :
A \( \cdot 19 \mathrm{m} s^{-1} \)
B . \( 19.6 \mathrm{m} s^{-1} \)
c. \( 29 \mathrm{m} s^{-1} \)
D. o m \( s^{-1} \)


Benzene easily shows:
A. ring fission reactions since it is unstable.
B. addition reactions since it is unsaturated.
C. electrophilic substitution reactions due to stable ring and high \( \pi \) electron density.
D. nucleophilic substitution reactions due to stable ring and minimum electron density


Derive the condition of balance for
Wheatstone bridge.


The correct statement with respect to
CO is:
A. It combines with \( H_{2} O \)
to give carbonic acid
B. It reacts with hemoglobin in RBC
C. It is a powerful oxidizing agent
D. It is used to prepare aerated drinks


Which of the following quantities do not change when a resistor connected to a battery is heated due to the current?
A. Drift speed
B. Resistivity
c. Resistance
D. Number of free electrons


The term refraction of light is best
described by:
A. The bending of light rays when they enter from one medium to another medium
B. Splitting of white light into seven colours when it passes through the prism
C. Bending of light round corners of obstacles and
apertures
D. Coming back of light from a bright smooth surface


If \( \mathbf{S} \) and \( \mathbf{S}^{\prime} \) are the foci and \( \mathbf{B} \) is an
endpoint of the minor axis of an ellipse. If \( \angle S B S^{\prime}=120^{\circ} \) then its eccentricity
is:
A \( \cdot \frac{\sqrt{5}}{2} \)
B. \( \frac{\sqrt{3}}{2} \)
c. \( \frac{1}{\sqrt{2}} \)
D. \( \frac{1}{\sqrt{3}} \)


Three concentric conducting spherical
shells of radii \( \boldsymbol{R}, 2 \boldsymbol{R} \) and \( \boldsymbol{3} \boldsymbol{R} \) carry
charges \( Q,-2 Q \) and \( 3 Q, \) respectively
Find the electric potential at \( r=R \) and
\( \boldsymbol{r}=\boldsymbol{3} \boldsymbol{R}, \) where \( \boldsymbol{r} \) is the radial distance
from the centre
\( ^{\mathrm{A}} \cdot \frac{Q}{6 \pi \varepsilon_{0} R}, \frac{Q}{4 \pi \varepsilon_{0} R} \)
в. \( \frac{Q}{4 \pi \varepsilon_{0} R}, \frac{Q}{6 \pi \varepsilon_{0} R} \)
c. \( \frac{Q}{2 \pi \varepsilon_{0} R}, \frac{Q}{3 \pi \varepsilon_{0} R} \)
D. \( \frac{Q}{3 \pi \varepsilon_{0} R}, \frac{Q}{2 \pi \varepsilon_{0} R} \)


As the alkaline earth metals (except Be) tend to lose their valence electrons
readily they act as:
A. weak oxidising agent
B. weak reducing agent
C. strong oxidising agent
D. strong reducing agent


Consider the following statements and arrange in the order of true/false as given in the codes. \( S_{1}: \) Long form of periodic table completely helps in predicting the
oxidation state of elements.
\( S_{2}: \) Metallic and covalent radii of potassium are 203 pm and 230 pm respectively.
\( \boldsymbol{S}_{3}: \) Formation of \( \boldsymbol{S} \boldsymbol{e}^{2-} \) and \( \boldsymbol{A} \boldsymbol{r}^{-}, \) both
the absorption of energy.
A . FFT
в. गाग
c. \( \pi \mathrm{F} \)
D. TFT


Using the identity \( a^{2}-b^{2}= \)
\( (a+b)(a-b) \) solve \( \left(7 \frac{3}{4}\right)^{2}-\left(2 \frac{1}{4}\right)^{2} \)


A resistor of resistance \( 100 \Omega \) is
connected to an AC source \( \epsilon= \)
\( (12 V) \sin \left(250 \pi s^{-1}\right) t \)
Find the power consumed by the bulb.


Which of the following is not correct?
A \( . D(-) \) Fructose exists in furanose structure.
B. \( D(+) \) Glucose exists in pyranose structure.
C. In sucrose, the two monosaccharides are held together by peptide linkage.
D. Maltose is a reducing sugar.


Root mean square velocity of molecules of a diatomic gas is to be increased to 1.5 times, If the process is done adiabtically, the ratio of initial volume to the final volumes is :
A . 2.25
B. 4.6
\( c .5 .6 \)
D. 7.5


Find square root of 0.4225
A . 0.65
B. 6.5
c. 0.21
D. 0.021


A particle is executing SHM with amplitude \( A \) and has maximum velocity
\( V_{0} . \) Find its speed when it is located at
distance of A/2 from mean position.


\( \int_{0}^{1} \sqrt{\boldsymbol{x}(\mathbf{1}-\boldsymbol{x})} \boldsymbol{d} \boldsymbol{x} \)


The electric charge developed on glass
rod rubbed with silk cloth is different
from the charge developed on ebonite rod rubbed with fur
A. True
B. False


Which of the following statements is
NOT true in relation to a system that
has reached the critical temperature?
A. Substances can have more than one critical
temperature.
B. A surface between the liquid and vapour phases is no longer present.
C. The system can be described as a homogenous fluid
D. The system must a closed system


A mass \( m=20 \) g has a charge \( q=3.0 \)
mC. It moves with a velocity of \( 20 \mathrm{m} / \mathrm{s} \)
and enters a region of electric field of \( 80 \mathrm{N} / \mathrm{C} \) in the same direction as the
velocity of the mass. The velocity of the mass after 3 seconds in this region is:


The resultant resistance between \( A \) and
B is, given the galvanometer is ideal
with resistance 0
A . \( 4 \Omega \)
B. \( 2 \Omega \)
\( c .1 \Omega \)
D. \( 10 \Omega \)


Find the centre of mass of a uniform
solid cone.


Match List I (compounds) with List -II (used as) and select the correct answer
using the codes given below are the lists.


The process of making soap by the hydrolysis of fats and oils with alkalis is called:
A. hydrolysis
B. saponification
c. esterification
D. none of the above


Identify the correct statement about
light rays:
A. light propagate along a straight line
B. two light rays donot disturb each other upon intersection
C . object and its image are inter-changeable
D. none of these


If the value of the determinant
\( \left|\begin{array}{lll}\boldsymbol{a} & \boldsymbol{1} & \boldsymbol{1} \\ \boldsymbol{1} & \boldsymbol{b} & \boldsymbol{1} \\ \boldsymbol{1} & \boldsymbol{1} & \boldsymbol{c}\end{array}\right| \) is positive, then
A \( . a b c>1 \)
B . \( a b c>-8 \)
c. \( a b c<-8 \)
D. \( a b c>-2 \)


For the same mass, which one of the
following has the maximum thermal capacity?
A. wood
B. copper
c. water
D. Ice


In the figure given below, Find the
equivalent capacitance of the network between points \( A \) and \( B \)
Given \( : \boldsymbol{C}_{\mathbf{1}}=\boldsymbol{C}_{\mathbf{5}}=\mathbf{4} \boldsymbol{\mu} \boldsymbol{F}, \boldsymbol{C}_{\mathbf{2}}=\boldsymbol{C}_{\mathbf{3}}= \)
\( C_{4}=2 \mu F \)


The term tetanus refers to
A. The partial sustained contraction of major supporting muscles
B. A stronger contraction resulting from multiple motor unit summation
C. The result of wave summation, which produces a smooth and sustained contraction of a muscle
D. The state of muscle fatigue caused by depletion of ATP and accumulation of lactic acid


Which one of the following traits of garden pea, studied by Mendel, was a recessive feature?
A. Axial flower position
B. Green seed colour
c. Green pod colour
D. Round seed shape


Coagulation of blood is an important mechanism. Explain its mechanism.


\( \mathbf{f}\left[\begin{array}{cc}\boldsymbol{x}-\boldsymbol{y} & \boldsymbol{z} \\ \mathbf{2} \boldsymbol{x}-\boldsymbol{y} & \boldsymbol{w}\end{array}\right]=\left[\begin{array}{cc}-\mathbf{1} & \mathbf{4} \\ \mathbf{0} & \mathbf{5}\end{array}\right], \) find the
value of \( \boldsymbol{x}+\boldsymbol{y} \)


Assertion
In circular motion work done by all the
forces acting on the body is zero.
Reason

Centripetal force and velocity are
mutually perpendicular.
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


For the given square lamina, the
moment of inertia through EF and \( A C \) is


The rate of a reaction is
always
A. Positive
B. Negative
c. Both a and \( b \)
D. None of above


A uniform ring of mass \( m, \) with the
outside radius \( r_{2}, \) is fitted tightly on a
shaft of radius \( r_{1} . \) The shaft is rotated
about its axis with a constant angular
acceleration \( \beta . \) Find the moment
of elastic forces in the ring as a
function of the distance \( r \) from the
rotation axis.
A \( \cdot N=\frac{1}{2} \frac{m \beta}{\left(r_{2}^{2}-r_{1}^{2}\right)}\left(r_{2}^{4}-r^{4}\right) \)
B. \( N=\frac{1}{2} \frac{m \beta}{\left(r_{2}^{2}+r_{1}^{2}\right)}\left(r_{2}^{4}-r^{4}\right) \)
C \( \quad N=\frac{1}{2} \frac{m \beta}{\left(r_{2}^{2}+r_{1}^{2}\right)}\left(r_{2}^{4}+r^{4}\right) \)
D. None of these


In the formation of \( N_{2}^{+} \) from \( N_{2} \), the electron is removed from:
A. \( \sigma \) orbital
B . \( \pi \) orbital
\( \mathbf{c} \cdot \sigma^{*} \) orbital
D . \( \pi^{*} \) orbital


The total volume of air accommodated
in the lungs at the end of maximum forceful inspiration includes:-
(A) \( \boldsymbol{E} \boldsymbol{R} \boldsymbol{V}+\boldsymbol{R} \boldsymbol{V} \)
(B) \( \boldsymbol{T} \boldsymbol{R} \boldsymbol{V}+\boldsymbol{E} \boldsymbol{R} \boldsymbol{V} \)
(C) \( \boldsymbol{T} \boldsymbol{V}+\boldsymbol{I} \boldsymbol{R} \boldsymbol{V}+\boldsymbol{E} \boldsymbol{R} \boldsymbol{V}+\boldsymbol{R} \boldsymbol{V} \)
(D) \( \boldsymbol{V} \boldsymbol{C}+\boldsymbol{R} \boldsymbol{V} \)
A . A only
B. A \& B
c. conly
D. c and


If the current sensitivity of a galvanometer is doubled, then its voltage sensitivity will be
A. doubled
B. halvedd
c. unchanged
D. four times


Which of the following is a use of
\( A l(O H)_{3} ? \)
A. It is used in fire extinguisher as a foaming agent
B. It is used in the preparation of fertilizers
c. It is used in removing stains of grease from cloths
D. It is used as an antacid


The hyperbola \( \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1 \) passes
through the point \( (\sqrt{6}, 3) \) and the length
of the latusrectum is \( \frac{18}{5} . \) Then, the
length of the transverse axis is equal to
A . 5
B. 4
\( c \cdot 3 \)
D. 2
E . 1


what is the deviation factor for ideal
gas?
A . 1.0
B. 2.0
c. 1.9
D. 0.9


The number of neutrons in an atom \( \boldsymbol{X} \) of
atomic number \( Z \) and mass number \( \boldsymbol{A} \)
is
A . zero
в. \( Z \)
c. \( A-Z \)
D.


Which of the following is the atomic number of metal?
A . 32
B. 34
c. 36
D. 38


One cannot see through fog because
A. Fog absorbs light
B. Refractive index of fog is unity
C. Light suffers total internal reflection at the droplets in fog
D. Light is scattered by the droplets in fog


Why do food chains in an ecosystem do not have more than 4 to 5 trophic levels
\( ? \)


Which of the following combination should be selected for better turning of an L.C.R circuit used for
communication?
A. \( R=25 \Omega, L=1 \cdot 5 H, C=45 \mu F \)
в. \( R=25 \Omega, L=1 \cdot 5 H, C=35 \mu F \)
c. \( R=25 \Omega, L=2 \cdot 5 H, C=45 \mu F \)


(a)Account for the following:
(i)Acidic character increase from \( \boldsymbol{H} \boldsymbol{F} \)
to \( H I \)
(ii)There is a large difference between the melting and boiling points of oxygen and sulphur.
(iii) Nitrogen does not form pentahalide.
(b) Draw the structures of the following:
(i) \( C l F_{3} \)
(ii) \( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{\boldsymbol{4}} \)


Calculate the wavelength of radiation emitted when an electron in a hydrogen atom makes a transition from an energy level with \( n=3 \) to a level with \( n= \)
2:
A. 756 nm
B. 656 nm
\( c .556 \mathrm{nm} \)
\( D .663 \mathrm{nm} \)


Heat of reaction for the change \( Z n+ \)
\( \boldsymbol{C u}^{2+}(\mathbf{0 . 1} \boldsymbol{M}) \rightarrow \boldsymbol{Z} \boldsymbol{n}^{2+}(\mathbf{1} \boldsymbol{M})+\boldsymbol{C u} \mathbf{a t} \)
\( 27^{\circ} C \) is:
A. \( -2.17 \times 10^{5} \mathrm{J} \)
В. \( -2.29 \times 10^{5} \mathrm{J} \)
c. \( -2.24 \times 10^{5} J \)
D. \( -1.84 \times 10^{5} \mathrm{J} \)


Write the IUPAC name of the following compound:
\( o \)
\( \boldsymbol{C H}_{2}=\boldsymbol{C H}-\stackrel{\|}{\boldsymbol{C}}-\boldsymbol{C} \boldsymbol{H}_{3} \)


A card is drawn from a pack of 52 cards.
The probability of getting a queen of spade or a king of diamond is
A \( \cdot \frac{1}{56} \)
в. \( \frac{1}{26} \)
c. \( \frac{1}{52} \)
D. \( \frac{3}{56} \)


In aqueous solution 1 mole of
\( \boldsymbol{C o C l}_{3} \cdot \boldsymbol{4} \boldsymbol{N} \boldsymbol{H}_{3} \) gives 1 mole of \( \boldsymbol{A g C l} \)
precipitate with excess \( A g N O_{3}, \) then what is the secondary valency of metal?
\( A \cdot 3 \)
B. 4
\( c \cdot 5 \)
D. 6


Lower surface of a plank is rough and
lying at rest on a rough horizontal surface. Upper surface of the plank is smooth and has a smooth hemisphere placed over it through a light string as shown in the figure. After the string is burnt, trajectory of centre of mass of the sphere is:
A . a circle
B. an ellipse
c. a stright line
D. a parabola


How can you alter the frequency of ringing of an electric bell?


What is the percent ionization \( (\alpha) \) of \( a \)
\( 0.01 M H A \) solution?
(Given that \( \boldsymbol{K}_{\boldsymbol{a}}=\mathbf{1 0}^{-4} \) )
A \( .9 .5 \% \)
B. 1\%
c. \( 10.5 \% \)
D. \( 10 \% \)


A spherical balloon rises up and the
radius become twice that on the ground.
Assuming temperature to be constant
the pressure at that altitude is
A. \( 1 / 3 \) rd of that on the earth
B. \( 1 / \) 9th that on the earth's surface
C. \( 1 / 8 \) times of that on the earth's surface
D. 3 times of that on the surface of the earth


Select the correct match
\( \begin{array}{lll}\text { Hormone } & \text { Target Organ } & \text { Source } \\ \text { CCK-PZ } & \begin{array}{l}\text { Gallbladder and } \\ \text { pancreas }\end{array} & \begin{array}{l}\text { Small } \\ \text { intestine }\end{array} \\ \text { GIP } & \begin{array}{l}\text { Gastrointestinal } \\ \text { tract }\end{array} & \text { Pancreas } \\ \text { Gastrin } & \text { Liver and stomach } & \text { Duodenum } \\ \text { Secretin } & \begin{array}{l}\text { Liver and } \\ \text { gallbladder }\end{array} & \text { Duodenum }\end{array} \)


Simplify
\( \left(a^{3}-2 a^{2}+4 a-5\right)- \)
\( \left(-a^{3}-8 a+2 a^{2}+5\right) \)
A \( \cdot 2 a^{3}+7 a^{2}+6 a-10 \)
В. \( 2 a^{3}+7 a^{2}+12 a-10 \)
c. \( 2 a^{3}-4 a^{2}+12 a-10 \)
D . \( 2 a^{3}+4 a^{2}+6 a-10 \)


In an examination, 460 students
appeared. Out of these students; \( 23 \% \) got first division, \( 62 \% \) got second division and the remaining just passed. Assuming that no student failed. Find the number of students who just
passed
A . 69
B. 45
c. 55
D. 66


Assertion
Tetany is rapid spasm in muscle.
Reason
Tetany Is usually caused by an increase
in the blood calcium level.
A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true but reason is not
the correct explanation of assertion.
C. If assertion Is true but reason is false.
D. If both assertion and reason are false.


A stick of mass \( \mathrm{m} \) and length lis pivoted at one end and is displacement trough an angle \( \theta \). The increase in
potential energy is


An observer moves with a constant
speed along the line joining two stationary objects. He will observe that the two objects This question has multiple correct options
A. have the same speed
B. have the same velocity
c. move in the same direction.
D. move in opposite directions.


Which term of the G.P.: \( \sqrt{\mathbf{3}}, \mathbf{3}, \mathbf{3} \sqrt{\mathbf{3}}, \ldots \) is
729?


A polymeric sample in which \( 30 \% \) molecules have a molecular mass
\( 20,000,40 \% \) have 30,000 and the rest \( \mathbf{3 0 \%} \) have \( \mathbf{6 0}, \mathbf{0 0 0 .} \) The \( \left(\overline{\boldsymbol{M}}_{n}\right) \) and \( \left(\overline{\boldsymbol{M}}_{\boldsymbol{w}}\right) \)
of this sample are, respectively:
\( \mathbf{A} \cdot 36,000,43,333 \)
в. 43,000,36,000
c. 72,000,86,000
D. 86,000,72,000


Find the square root of the following number by Division method.
\( \mathbf{7 9 2 1} \)


The \( 10 \mathrm{kg} \) block is moving to the left
with a speed of \( 1.2 m / s \) at time \( t=0 . A \)
force \( F \) is applied as shown in the graph.
After 0.2 s the force continues at the
10 \( N \) level. If the coefficient of kinetic
friction is \( \mu_{k}=0.2 . \) Determine the time
\( t \) at which the block comes to a stop. \( (g= \)
\( \mathbf{1} \mathbf{0} \boldsymbol{m} / \boldsymbol{s}^{\mathbf{2}} \mathbf{)} \)
A . \( 0.333 s \)
B. \( 0.526 s \)
c. \( 0.165 s \)
D. None of the above


Assertion
Liquefaction of acetic acid leading to formation of glacial acetic acid.
Reason
Vinegar is roughly \( 3 \%-5 \% \) acetic acid by volume, making acetic acid the main component of vinegar apart from water
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


If \( f(x)=x^{3}-6 x^{2}+9 x+3 \) then \( f(2) \)
\( A \cdot 3 \)
B. 4
\( c \cdot 5 \)
D. None of these


The solubility of \( A g C N \) in a buffer solution of \( \boldsymbol{p} \boldsymbol{H}=\mathbf{3} \) is:
\( \left[\text { Given } \boldsymbol{K}_{s p} \text { of } \boldsymbol{A} \boldsymbol{g} \boldsymbol{C} \boldsymbol{N}=\mathbf{1 . 2} \times \mathbf{1 0}^{-\mathbf{6}} \) and \right.
\( \boldsymbol{K}_{a} \) for \( \boldsymbol{H} \boldsymbol{C} \boldsymbol{N}=\boldsymbol{4} . \boldsymbol{8} \times 10^{-10} . \) Assume
that no cyano complex is formed.
A \( \cdot a=1.67 \times 10^{-5} M \)
В. \( a=1.58 \times 10^{-5} M \)
C \( . a=1.51 \times 10^{-5} M \)
D. None of these


A current of \( 0.5 A \) flows through a resistance of \( 10 \Omega \) for \( \frac{1}{2} \) hour. And the amount of electrical energy consumed by the resistance.
\( \mathbf{A} \cdot 4500 J \)
в. \( 500 J \)
c. \( 250 k J \)
D. \( 2.6 k J \)


Find the number of different 8 letter
arrangements that can be made from the letters of the word "DAUGHTER "so
that
\( (A) \) All vowels occur together
\( (B) \) All vowels do not occur together


Which of the following numbers has 1 significant figure?
A . 0.060
B. 0.60
\( c \cdot 6.0 \)
D. 60


\( \tan ^{-1}(-2) \) is equal to
A \( \cdot-\cos ^{-1}\left(\frac{-3}{5}\right) \)
в. \( _{\pi}+\cos ^{-1} \frac{3}{5} \)
c. \( -\frac{\pi}{2}+\tan ^{-1} x\left(-\frac{3}{5}\right) \)
D. none of these


A synthetic indicator phenolphthalein
gives colour in basic
solution.
A . red
B. blue
c. pink
D. colourless


Photoelectric effect was successfully explained by
A. Planck
B. Hallwash
c. Hertz
D. Einstein


How is the angle of emergence 'e' related to the angle of incidence 'i'?


Calculate the amount of oxygen at 0.20 atm dissolved in 1 kg of water at 293 K. The Henry's law constant for oxygen is
\( 4.58 \times 10^{4} \) atmosphere at \( 293 \mathrm{K} \)
\( \mathbf{A} \cdot 7.07 \times 10^{-6} \mathrm{kg} \)
В. \( 7.27 \times 10^{-6} \mathrm{kg} \)
C \( .7 .57 \times 10^{-6} \mathrm{kg} \)
D. \( 7.77 \times 10^{-6} \mathrm{kg} \)


Eggs do not occur in archegonia in
A. Bryophyta
B. Pteridophyta
c. Angiosperms
D. spermatophyta


\( \lim _{x \rightarrow 1}\{1-x+[x+1]+[1-x]\}, \) where
\( x \) ] denotes greatest integer function, is
\( A \cdot 0 \)
B.
\( c .-1 \)
\( D .2 \)


A cloud is at a potential of \( 8 \times 10^{9} V \)
relative to the ground. A charge of \( 40 C \) is transferred in a lightning stroke
between the cloud and the earth. The
energy released is:
A \( \cdot 3.2 \times 10^{11} J \)
B . \( 5 \times 10^{9} J \)
c. \( 2 \times 10^{9} J \)
D. \( 32 \times 10^{12} J \)


Solve: \( \frac{|\boldsymbol{x}|-\mathbf{1}}{|\boldsymbol{x}|-\mathbf{3}} \geq \mathbf{0}, \boldsymbol{x} \in \boldsymbol{R}, \boldsymbol{x} \neq \pm \mathbf{3} \)


A spore producing plant is
A. Rose
B. Bread mould
c. Potato
D. Ginger


n \( X e F_{4} \) there are \( _{--}-_{-}- \) - lone pairs
of electron.


A spherical hole of radius \( \boldsymbol{R} / \mathbf{2} \) is
excavated from the asteroid of mass \( M \)
as shown in the figure. The gravitational acceleration at a point on the surface of the asteroid just above the excavation
is
A \( \cdot \frac{G M}{R^{2}} \)
в. \( \frac{G M}{2 R^{2}} \)
c. \( \frac{G M}{8 R^{2}} \)
D. \( \frac{7 G M}{8 R^{2}} \)


A \( 100 e V \) electron collides with a
stationary helium ion \( \left(H e^{+}\right) \) in its ground state and excites to a higher
level. After the collision, \( \boldsymbol{H} e^{+} \) ion emits
two photons in succession with wavelengths \( 1085 A \) and 304 A. Find the
principal quantum number of the excited state. Also, calculate the energy
of the electron after the collision. Given
\( \boldsymbol{h}=\mathbf{6 . 6 3} \times \mathbf{1 0}^{-\mathbf{3 4} \mathbf{J}} \boldsymbol{s} \)


Let \( x=\sin 1^{\circ}, \) then the value of the
\( \operatorname{expression} \frac{1}{\cos 0^{\circ} \cdot \cos 1^{\circ}}+ \)
\( \frac{1}{\cos 1^{\circ} \cdot \cos 2^{\circ}}+\frac{1}{\cos 2^{\circ} \cdot \cos 3^{\circ}}+\dots+ \)
\( \frac{1}{\cos 44^{\circ} \cdot \cos 45^{\circ}} \) is equal to
A . \( x \)
в. \( \frac{1}{x} \)
\( c \cdot \frac{\sqrt{2}}{x} \)
D. \( \frac{x}{\sqrt{2}} \)


A voltage of \( 1.1 \mathrm{V} \) is needed to stop the
photocurrent generated when a monochromatic light of wavelength
\( \lambda=4000 A \) is incident on it. Find the
work function of metal
\( A \cdot 2.3 \mathrm{ev} \)
B. 2 ev
c. 4.2 ev
D. None pf these


According to the five kingdom classification, bacteria belong to
A. Protista.
B. Monera.
c. Plantae.
D. Archaea.


Find the length of the perpendicular from the point (4,-7) to the line joining the origin and the point of intersection of the \( 2 x-3 y+14=0 \) and \( 5 x+5 y- \)
\( \mathbf{7}=\mathbf{0} ? \)


Two monatomic ideal gases 1 and 2 of
molecular masses \( m_{1} \) and \( m_{2} \)
respectively are enclosed in separate containers kept at the same temperature. The ratio of the speed of sound in gas 1 to gas 2 is given by
A. \( \frac{m_{1}}{m_{2}} \)
B. \( \sqrt{\frac{m_{1}}{m_{2}}} \)
c. \( \frac{m_{2}}{m_{1}} \)
D. \( \sqrt{\frac{m_{2}}{m_{1}}} \)


They does the mercury column in the barometer fall rapidly before a severe
storm?
A. It is due to the fall in atmospheric pressure
B. It is due to the rise in atmospheric pressure
c. It is due to decrease in humidity in air
D. It is due to the severe heat energy from the sun


By selling a bouquet for Rs \( 322, \) a florist
has a gain of \( 15 \% . \) At what price should
he sell it to gain \( 25 \% ? \)


The type of bond involved in the
formation of sodium chloride is:
A. ester bond
B. peptide bond
c. ionic bond
D. covalent bond
E. hydrogen bond


A force of \( 10 \mathrm{N} \) is applied to an object,
whose area is \( 5 \mathrm{cm}^{2} \) at an angle of 30
degrees with the vertical. What kind of stress can be found from this data
A. Normal and areal stress can be found
B. only normal stress can be found
c. only areal stress can be found
D. Stress cannot be found from this data, since applied force is neither along the horizontal or vertica


An \( \alpha \) - particle accelerated through volt is fired towards a nucleus. Its
distance of closest approach is \( r \). If a proton is accelerated through the same potential and fired towards the same nucleus, the distance of closest approach of proton will be:
\( A \)
B . \( 2 r \)
\( \mathrm{c} \cdot r / 2 \)
D. \( r / 4 \)


Match the column.


Can a non polar molecule have polar
covalent bonds?


Find the differential equation of family
of curves \( \boldsymbol{y}=\boldsymbol{e}^{\boldsymbol{x}}(\boldsymbol{A} \cos \boldsymbol{x}+\boldsymbol{B} \sin \boldsymbol{x}) \)
where \( A \) and \( B \) are arbitrary constants.


The equation of the line which is equidistant from the lines \( y=-\frac{13}{2} \) and \( y=\frac{17}{2} \) is :
\( \mathbf{A} \cdot y=2 \)
B. \( y=\frac{1}{2} \)
c. \( y=-1 \)
D. \( y=1 \)


A gaseous alkane is exploded with
oxygen. The moles of \( O_{2} \) for complete
combustion and \( C O_{2} \) formed is in the
ratio \( 7: 4 . \) Deduce the molecular
formula of alkane.
A \( \cdot C_{2} H_{6} \)
в. \( C H_{3} \)
\( \mathbf{c} \cdot C_{3} H_{6} \)
D. \( C_{2} H_{4} \)


\( N_{2} O \) is isoelectronic with \( C O_{2} \) and \( N_{3} \)
how many \( N-O-N \) linkages is/are
present in \( N_{2} \) O?


An article manufactured by a company
consists of two parts \( X \) and \( Y . \) In the
process of manufacture of the part \( \boldsymbol{X} . \mathbf{9} \)
out of 100 parts may be defective.
Similarly 5 out of 100 are likely to be
defective in part \( Y \). Calculate the
probability that the assembled product will not be defective.


Eusporangiate fern is produced from
A. Group of sporangial initial cell
B. single initial cell
c. Epidermal cells
D. Hypodermal cells


Assertion
The maximum refractive index of liquid for total internal reflection of the ray
passing through the prism should be \( \sqrt{2} \)
Reason
Here critical angle is \( 45^{\circ} \)
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


For which of the following particles will it be most difficult to experimentally verify the de-Broglie relationship?
A. an electron
B. a proton
c. an \( \alpha \) particle
D. a dust particle


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


The correct formula for the angular
frequency \( \omega_{0} \) of an \( L-C \) resonant
circuit is
A \( \cdot \frac{1}{\sqrt{L C}} \)
B . \( \sqrt{L C} \)
c. \( \frac{1}{2 \pi \sqrt{L C}} \)
D. \( \frac{1}{2 \pi L C} \)


Discuss briefly giving an example in each case the role of coordination
compounds in:
(i) biological systems
(ii) medicinal
chemistry and (iii) analytical chemistry (iv) extraction/metallurgy of
metals.


Let \( \boldsymbol{f}(\boldsymbol{x})=(\boldsymbol{x}-\boldsymbol{p})^{2}+(\boldsymbol{x}-\boldsymbol{q})^{2}+(\boldsymbol{x}- \)
\( \boldsymbol{r})^{2} . \) Then \( \boldsymbol{f}(\boldsymbol{x}) \) has a minimum at \( \boldsymbol{x}=\boldsymbol{\lambda} \)
where \( \lambda \) is equal to
A. \( \frac{p+q+r}{3} \)
B. \( \sqrt[3]{p q r} \)
c. \( \frac{3}{\frac{1}{p}+\frac{1}{q}+\frac{1}{r}} \)
D. none of these


Why the compounds of \( T l^{+} \) are much
more stable than those of \( \boldsymbol{T l}^{\mathbf{3}+} \) ?


The final image formed by an astronomical telescope is:
A. real and erect
B. virtual and erect.
c. real and inverted.
D. virtual and inverted.


An epistomatic leaf is?
A. Sunflower
B. Maize
c. Nymphaea
D. calotropis


Baking powder used to make a cake is a
mixture of \( \operatorname{starch}, N a H C O_{3} \) and
\( \boldsymbol{C} \boldsymbol{a}\left(\boldsymbol{H}_{2} \boldsymbol{P} \boldsymbol{O}_{4}\right)_{2} . \) The function of
\( \boldsymbol{C a}\left(\boldsymbol{H}_{2} \boldsymbol{P} \boldsymbol{O}_{4}\right)_{2} \) is:
A \( \cdot \) to slow down the release of \( C O_{2} \)
B. being acidic in nature and give \( C O_{2} \) when moistened with \( N a H C O_{3} \)
\( c . \) to act as a fille
D. none of these


Which allotrope of carbon is good conductor of electricity?
A. charcol
B. coal
c. Gas carbon
D. graphite


f \( (k, 2-2 k),(-k+1,2 k),(-4- \)
\( k, 6-2 k) \) are collinear, then \( k= \)
\( A \cdot+1 \)
B. -
\( c \cdot-2 \)
\( D .2 \)


If Anil's salary is \( 20 \% \) less than Raju's
salary, then by what percentage is Raju's salary more than that of Anil?


What is the pH value of base?
\( A \cdot>7 \)
B. \( <7 \)
\( c \cdot=7 \)
D. None


Assertion
Nylon wire is stronger than steel wire.
Reason

Nylon is a fibre while steel is an alloy.
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 particle is executing S.H.M. on a line \( 4 \mathrm{cms} \) long. If its velocity at its mean position is \( 12 \mathrm{cm} / \mathrm{sec}, \) its frequency in Hertz will be :
A \( \cdot \frac{2 \pi}{3} \)
в. \( \frac{3}{2 \pi} \)
c.
D. \( \frac{3}{\pi} \)


Which of the following is a bad conductor of heat?
A. woodd
B. Aluminium
c. Iron
D. Bronze


Upper molars in human dentition have
A. Four roots
B. Three roots
c. Two roots
D. single root


Integrate \( \int \frac{1}{x^{1 / 2}+x^{1 / 3}} d x \)


Which one of the following is specific function of the liver?
A. Excretion
B. Glycogenolysis
c. Digestion
D. Histolysis


Diagonals of a rectangle are:
A. equal to each other
B. not equal
C. one is double of other
D. none


Nitrogen is liberated by the thermal decomposition of :
A. \( N H_{4} N O_{2} \)
в. \( \operatorname{NaN}_{3} \)
c. \( \left(N H_{4}\right)_{2} C r_{2} O_{7} \)
D. All of these


Which of the following pair will form an ideal solution?
A. Chlorobenzen, chloro ethane
B. Benzene, Toluene
c. Acetone, chloroform
D. water, HCl


Assertion
Equivalent mass of \( K M n O_{4} \) is equal to
one-third of its molecular mass when it
acts as an oxidising agent in an alkaline medium.
Reason
Oxidation number of \( M n \) is +7 in
\( \boldsymbol{K} \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{4} \)
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 frequency of sound waves can be
expressed in
A . \( \mathrm{Hz} \)
B. Cycles
\( c \cdot s^{-1} \)
D. All of these


The ratio of time taken by an electron in revolution around the H-nucleus in 2nd
and 3 rd orbits is:
A .2: 3
B . 4: 8
\( \mathbf{c} \cdot 8: 27 \)
D. 27: 8


A clock pendulum having coefficient of linear expansion \( \boldsymbol{\alpha}=\mathbf{9} \times \mathbf{1 0}^{-\mathbf{7}} /^{\circ} \mathbf{C} \) has
a period of \( 0.5 s \) at \( 20^{\circ} \mathrm{C} . \) If the clock is
used in a climate where the
temperature is \( 30^{\circ} \mathrm{C} \), how much times
does the clock lose in each oscillation?
\( (g=\text { constant }) \)
A \( \cdot 2.5 \times 10^{-7} \mathrm{s} \)
B . \( 5 \times 10^{-7} \) s
D. \( 2.25 \times 10^{-6} \mathrm{s} \)


Plastic can be used for:
A. polythene bags
B. food packaging
C . electrical appliances
D. All of the above


Find the value of \( 64.75-75.97+36.82 \)
A . 25.60
B. 23.98
c. 29.76
D. 21.96


\( A B C \) is an equilateral triangle of side 6 cm. If a circle of radius \( 1 \mathrm{cm} \) is moving inside and along the sides of the triangle, then locus of the centre of the circle is an equilateral triangle of side
A. \( 5 \mathrm{cm} \)
B. \( 4 \mathrm{cm} \)
c. \( (6-2 \sqrt{3}) \) ст
D. \( (3+\sqrt{3}) \) cm


Identify the true statement.
A. The \( X \) -axis is a vertical line
B. The \( Y \) -axis is a horizontal line
C. The scale on both the axes must be the same in a
Cartesian plane
D. The point of intersection between the \( X \) -axis and \( Y \) axis is called the origin


A coil of metal wire is kept stationary in a non-uniform magnetic field. An emf is induced in the coil.
A. True
B. False


A ship sends a longitudinal wave towards the bottom of the sea. The wave
returns from the bottom of the sea after
\( \mathbf{2 . 0} s . \) The bulk modulus of the sea water
is \( 2.2 \times 10^{9} N m^{-2} \) and the density of
water is \( 1.1 \mathrm{g} \mathrm{cm}^{-3} . \) The depth of the sea is about
A . \( 2200 m \)
в. 2000 \( m \)
c. \( 1400 m \)
D. \( 1100 m \)


For the following electrochemical cell at
\( 298 K \)
\( \boldsymbol{P t}(s)\left|\boldsymbol{H}_{2}(\boldsymbol{g}, \mathbf{1} \boldsymbol{b a r})\right| \boldsymbol{H}^{+}(\boldsymbol{a} \boldsymbol{q}, \mathbf{1} \boldsymbol{M}) \| \boldsymbol{M}^{4+} \)
\( \boldsymbol{E}_{c e l l}=\mathbf{0 . 0 9 2 V} \) when \( \frac{\left[\boldsymbol{M}^{2+}(\boldsymbol{a} \boldsymbol{q})\right]}{\left[\boldsymbol{M}^{4+}(\boldsymbol{a q})\right]}=\mathbf{1 0}^{x} \)
Given \( : \boldsymbol{E}_{M^{4+} / M^{2+}}^{0}= \)
\( \mathbf{0 . 1 5 1} V ; \mathbf{2 . 3 0 3} \frac{\boldsymbol{R T}}{\boldsymbol{F}}=\mathbf{0 . 0 5 9} \boldsymbol{V} \)
The value of \( x \) is :
A . -2
B. -
\( c \cdot 1 \)
D.


A glass rod is rubbed with silk, is found positively charged. This is because.
A. Electrons are transferred from glass rod to silk.
B. Electrons are transferred from silk to glass rod.
c. Protons are transferred from glass rod to silk.
D. Protons are transferred from silk to glass rod.


A reaction involving an aromatic nucleus is usually initiated by:
A. free radicals
B. molecules possessing a lone pair of electrons
c. nucleophiles
D. electrophiles


A solid cube has volume \( (1000 \pm 0.3) \)
\( c m^{3} . \) The side of the cube is
A \( \cdot(10 \pm 0.1) \) ст
в. \( (10 \pm 0.01) \) ст
c. \( (10 \pm 0.001) \mathrm{cm} \)
D. \( (10 \pm 0.003) \) с \( m \)


A ball is released from the top of a tower
of height h metres. It takes T seconds to reach the ground. What is the position of the ball in \( T / 3 \)
seconds?
A. h/9 metre from the ground
B. 7h/9 metre from the ground
c. \( 8 \mathrm{h} / 9 \) metre from the ground
D. 17h/18 metre from the ground


Which of the following options does not
show instantaneous rate of reaction at
\( 40^{t h} \) second?
A \( \frac{V_{5}-V_{2}}{50-30} \)
3. \( \frac{V_{4}-V_{2}}{50-30} \)
\( c \cdot \frac{V_{3}-V_{2}}{40-30} \)
D. \( \frac{V_{3}-V_{1}}{40-20} \)


Assertion
Red phosphorus is preferred to white phosphorus in the manufacture of
matches.
Reason
Red phosphorus is non-poisonous in
nature.
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


A small block slides with velocity
\( 0.5 \sqrt{g} r \) on the horizontal friction less
surface as shown in the figure. The
block leaves the surface at point \( C . \) The
angle \( \theta \) in the figure is:
\( \mathbf{A} \cdot \cos ^{-1}(4 / 9) \)
B \( \cdot \cos ^{-1}(3 / 4) \)
\( \mathbf{C} \cdot \cos ^{-1}(1 / 2) \)
D. none of the above


Thermodynamically, in which form of carbon is the most stable?
A. coal
B. Fullerenes
c. Diamond
D. Graphite


A planet was suddenly stooped in its orbit supposed to be circular. The time it will fall on to the sun is, if time period
of planet's revolution is \( T \)
A \( \cdot \frac{T}{2} \)
в. \( \frac{\sqrt{2} T}{4} \)
c. \( \frac{\sqrt{2} T}{8} \)
D. \( \sqrt{2} T \)


\( \boldsymbol{A} \boldsymbol{g} \mid \boldsymbol{A} \boldsymbol{g}^{\oplus}(\boldsymbol{1} \boldsymbol{M})\left\|\boldsymbol{A} \boldsymbol{g}^{\oplus}\right\| \boldsymbol{A} \boldsymbol{g} \)
\( 0.5 \mathrm{F} \) electricity is first passed in this LHS (anode) and 1 F of electricity is passed in the RHS (cathode) making them independent electrolytic cells at 298 K. EMF of the cell after electrolysis
will:
A. increase
B. decrease
c. not change
D. none of the above


The equation of a line passing through
(2,-3) and inclined at an angle of \( 135^{\circ} \)
with the positive direction of \( x \) -axis is.
A. \( x+y-1=0 \)
в. \( x+y+1=0 \)
c. \( x-y-1=0 \)
D. \( -x+y+1=0 \)


Show that \( f(x)=e^{2 x} \) is increasing on \( R \)


The diagrams show different resistor
arrangements.

Which arrangement has the smallest
combined resistance?
\( A \)
B.
\( c \)
\( D \)


Match the names of the parts listed
with the names of the organs.
\begin{tabular}{lll|l}
List I (Parts) & \multicolumn{3}{c} { List II } \\
& (Organs) & \\
A & Bicuspid valve & p & Brain \\
B & Nephron & q & Liver \\
C & Alveoli & r & Heart \\
D & Cerebrum & s & Kidney \\
& t & Lungs
\end{tabular}
\( \mathbf{A} \)
\( A-r, B-t, C-s, D-R \)
B. \( A-r, B-s, C-t, D-B \)
\( c \cdot A-s, B-q, C-p, D-t \)
D. A-s, B-r, C- p, D-


A square yard has area \( 1764 \mathrm{m}^{2} \). From a
corner of this yard, another square part
of area \( 784 \mathrm{m}^{2} \) is taken out for public
utility. The remaining portion is divided in to 5 equal square parts. What is the perimeter of each of these equal parts?


Very short answer type. What is the function/role of bulliform
cells in grasses?


The diagram shows the graphs of
pressure vs density for a given mass of
an ideal gas at two temperatures \( T_{1} \) and \( T \)
2
\( A \cdot T_{1}>T_{2} \)
B. \( T_{1}=T_{2} \)
\( c \cdot T_{1}<T_{2} \)
D. Any of the three are possible


Find the principal value of \( \operatorname{cosec}^{-1}\left(\frac{2}{\sqrt{3}}\right) \)


Assertion
Both Be and Al can form complexes
\( \operatorname{such} \operatorname{as} B e F_{4}^{-2} \) and \( A I F_{6}^{3-} \)
respectively, \( B e F_{6}^{-3} \) is not formed.
Reason
In the case of Be, no vacant d-orbitals
are present in its outermost shell.
These questions consist of two statements each, printed as assertion
and reason. While answering these questions you are required to choose any one of the following four responses.
A. If both Assertion and Reason are true and the Reason is the correct explanation of the Assertion, then mark
B. If both Assertion and Reason are true but the Reason is not the correct explanation of the Assertion, then mark
C. If Assertion is true statement but Reason is false, then mark
D. If both Assertion and Reason are false statements, then mark


Incomplete breakdown of glucose in
muscles results in the formation of
A. Alcohol and water
B. Alcohol and lactic acid
c. \( C O_{2} \) and water
D. Lactic acid


The frequency \( f \) of vibration of mass \( m \)
suspended from a spring of spring
contact \( k \) is given by \( \boldsymbol{f}=\boldsymbol{c} \boldsymbol{m}^{\boldsymbol{x}} \boldsymbol{k}^{\boldsymbol{y}} \)
Where \( c= \) dimensionless constant
then find the values of \( x \) and \( y \)


Which one of the following statements
is false?
A. Work is a state function
B. Temperature is a state function
C. Work appears at the boundary of the system
D. Change in the state is completely defined when the initial and final states are specified


When a glass rod is rubbed with silk,
both become charged due to:
A. migration of protons
B. exchange of electrons and protons
c. migration of electrons
D. migration of neutrons


A radioactive sample can decay by two different processes. The half-life for the
first process is \( T_{1} \) and that for the
second process is \( T_{2} \). The effective half-
life \( T \) of the radioactive sample is
A \( \cdot T=T_{1}+T_{2} \)
в. \( \frac{1}{T}=\frac{1}{T_{1}}+\frac{1}{T_{2}} \)
c. \( T=\frac{T_{1}+T_{2}}{T_{1} T_{2}} \)
D. \( T=\frac{T_{1}-T_{2}}{T_{1} T_{2}} \)


\( A \) and \( B \) are two identical spherical
charged bodies which repel each other with force \( F, \) kept at a finite distance apart A third uncharged sphere of the same size is brought in contact with sphere \( \mathrm{B} \) and removed. It is then kept at mid-point of \( A \) and \( B \) find the magnitude of force on \( \mathbf{C} \)
\( A \cdot F / 2 \)
B. F/8
\( c \cdot F \)
D. zero


Assertion
The reactions taking place in the sun
are nuclear fusion reactions.
Reason
The main reason for nuclear fusion
reactions in the sun is that \( \boldsymbol{H}_{2} \) is
present in the sun's atmosphere so that
hydrogen nuclei can fuse to form helium.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The property to restore the natural shape or to oppose the deformation is called:
A. elasticity
B. plasticity
c. ductility
D. none of the above


If the angle of incidence is \( 80^{\circ}, \) what will be the angle of reflection with respect to the normal drawn perpendicular at the point of reflection?
\( A \cdot 80 \)
B. 100
\( c \cdot 160 \)
D. 20


Q Type your question
orgamisıng nis graduated cymnaers In the hopes of keeping his office tidy and setting a good example for his students. He has beakers with diameters, in inches, of \( \frac{1}{2}, \frac{3}{4}, \frac{4}{5}, 1 \) and \( \frac{5}{4} . \) With his original five cylinders, professor Buckingham realises that he is missing a cylinder necessary for his upcoming lab demonstration for Thursday's class. He remembers that the cylinder he needs when added to the original five, will create a median diameter value of
for the set of six total cylinders. He
\( \overline{\mathbf{1 0}} \)
also knows that the measure of the
sixth cylinder will exceed the value of the range of the current five cylinders by a width of anywhere from \( \frac{1}{4} \) inches to \( \frac{1}{2} \) inches, inclusive. Based on the data, what is one possible value of \( y \), the diameter of this missing sixth cylinder?
A \( .1 \leq y \leq 1.25 \)
в. \( 2 \leq y \leq 2.25 \)
c. \( 3 \leq y \leq 3.25 \)
D. \( 4 \leq y \leq 4.25 \)


Assertion
faraday is the charge that liberates 1 eq. of metal at cathode.
Reason
Passsage of 1 faraday charge through
aq. \( \mathrm{MgCl}_{2} \) liberates 12 g Mg at cathode.
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 structural gene which synthesizes mRNA that translates the permease protein is
A. Y-gene
B. \( P^{53} \) gene
c. A- gene
D. z-gene


Refer to the given figure of human
urinary system and select the option
that correctly identifies the labelled
parts \( A \) to \( E \)
A. Superior vena cava Inferior vena cava Dorsal aorta Urethra Pelvis
B. Inferior vena cava Superior vena cava Dorsal aorta Urinary bladder Cortex
c. Ureter Inferior vena cava Dorsal aorta Urinary bladder Pelvis
D. Dorsal aorta Inferior vena cava Superior vena cava Urinary bladder Cortex


Two resistors \( \boldsymbol{R}_{1}(\mathbf{2 4} \pm \mathbf{0 . 5}) \mathbf{\Omega} \) are
joined in series. The equivalent
resistance is
A . \( 32 \pm 0.33 \Omega \)
B \( .48 \pm 1 \Omega \)
c. \( 32 \pm 0.2 \Omega \)
D. \( 32 \pm 0.9 \Omega \)


and \( m_{3} \) are connected to the ends of a
mass-less rod of length \( L \) which lies at rest on a smooth horizontal plane. At
\( t=0, \) an explosion occurs between \( m_{2} \)
and \( m_{3}, \) and as a result, mass \( m_{3} \) is
detached from the rod, and moves with
a known velocity \( v \) at an angle of \( 30^{\circ} \)
with the y-axis. Assume that the
masses \( m_{2} \) and \( m_{3} \) are unchanged
during the explosion.

What is the velocity of the centre of
mass of the system consisting of three masses after the expulsion?
A \( \cdot \frac{v}{4}(\hat{i}-3 \hat{j}) \)
B \( \cdot \frac{v}{4}(-\hat{i}+\sqrt{3} \hat{j}) \)
c. \( -v \)
D. none of the above


Choose the correct option which describe the magnetic field produced by a current in a long, straight wire?
A. The field in uniform
B. The field increases in strength as the distance from the wire increases
c. The field lines are directed parallel to the wire, but opposite to the direction of the current
D. The field lines are directed radially outward from the wire
E. The field lines form circles about the wire


Hard water is unfit for laundries
because:

This question has multiple correct options
A. consumes much soap
B. leaves dirty strains of ' \( C a \) ' and ' \( M g^{\prime} \)
C. causes irritation on skin
D. water is very hard to handle


If 1 and 2 are the wavelengths of characteristic X-ray and gamma rays respectively, then the relation between
them is :
\( A \cdot 1<2 \)
B \( .1=2 \)
\( c \cdot 1>2 \)
D. None of these


Striations in the striated muscles are
due to
A. Projections of myosin
B. Absence of myofilaments
c. Presence of myofilaments
D. specilaized arrangement of myofilaments


Explain the appropriate reason for the following statement:
(a)Size of \( M g^{2+} \) is less than Mg.
(b) Electron gain enthalpy of Cl is more than that of F.


A charge of \( 10^{-9} C \) moves from \( X \) to \( Z \)
Find the work done by the electric field due to the charge \( Q=2 C \) in moving the
charge from \( X \) to \( Z \). The value of
coulomb's constant is \( 9 \times 10^{9} N m^{2} C^{-2} \)
A . \( 0 . J \)
В. \( 150 J \)
\( c .300 J \)
D. \( 560 J \)
E. \( 1,000 J \)


The random variable \( x \) follows normal
distribution
Then the value of \( C \) is
A \( \cdot \sqrt{2 \pi} \)
в. \( \frac{1}{\sqrt{2 \pi}} \)
c. \( 5 \sqrt{2 \pi} \)
D. \( \frac{1}{5 \sqrt{2 \pi}} \)


\( \Delta A B C \sim \Delta L M N \cdot \ln \Delta A B C, A B= \)
\( 5.1 \mathrm{cm}, \angle B=55^{\circ}, \angle C=65^{\circ} \) and
\( \frac{A C}{L N}=\frac{3}{5}, \) then construct \( \Delta L M N \)


The most electronegative element
belongs to:
A. group 1
B. group 18
c. group 17
D. group 15


If \( P(E) \) denotes the probability of an event \( \mathrm{E} \), then
A. \( P(E)<0 \)
В. \( P(E)>1 \)
c. \( 0 \leq P(E) \leq 1 \)
D. \( -1 \leq P(E) \leq 1 \)


The significant result deduced from the
Rutherford's scattering experiment is
that
A. whole of the positive charge is concentrated at the centre of atom
B. there are neutrons inside the nucleus
C . \( \alpha \) -particles are helium nuclei
D. electrons are embedded in the atom
E. electrons are revolving around the nucleus


From the prices of shares \( X \) and \( Y \) below find out which is more stable in
value:
35 54 52 53 56 \( x \)
108 \( Y \) 107 \( \quad 105 \) 105 106


The auto reduction process is not used in the metallurgy of
A. \( H g \)
в. \( C u \)
\( c \cdot P b \)
D. \( F e \)


The net external force acting on the disk
when its centre of mass is at
displacement x with respect to its equilibrium position is
4. \( k x \)
3. \( 2 k x \)
\( c \cdot-\frac{2 k x}{3} \)
D. \( -\frac{4 \mathrm{kx}}{3} \)


A concave mirror of focal length \( f, \) in vacuum, is placed in a medium of refractive index \( 2 . \) Its focal length in the medium is :
\( A \cdot \frac{f}{2} \)
B. \( f \)
\( c \cdot 2 f \)
D. \( 4 f \)


Write the valencies of \( X, Y \) in the
chemical compound having the following lewis notation.


Identify the correct order of solubility in aqueous medium:
A \( \cdot C u S>Z n S>N a_{2} S \)
в. \( Z n S>N a_{2} S>C u S \)
c. \( N a_{2} S>C u S>Z n S \)
D. \( N a_{2} S>Z n S>C u S \)


Which of the following is the \( A \) in the
given reaction
A. Benzene diazonium chloride
B. Benzene
c. Nitro benzen
D. Amino benzene


In an experiment with a beam balance,
an unknown mass \( m \) is balanced by two
known masses of \( 16 \mathrm{kg} \) and \( 4 \mathrm{kg} \) as
shown in fig. Find \( \boldsymbol{m} \)
A . \( 10 \mathrm{kg} \)
B. \( 6 k g \)
\( c .8 k g \)
D. \( 12 \mathrm{kg} \)


The diagonals of a parallelogram
\( A B C D \) intersect at \( O . A \) line through
intersect \( A B \) at \( X \) and \( D C \) at \( Y \). Identify
the correct option
A. \( O X=O Y \)
в. \( O X>O Y \)
c. \( O X<O Y \)
\( \cdot O X-O Y=0 \)
0


Which of the following is not a complex?
A. Potassium ferricyanide
B. Ferrous ammonium sulphate
C . Potassium ferrocyanide
D. Tetraaminecopper
(II) sulphate


Among the following which one is the formula for noncyclic, saturated
hydrocarbon?
\( \mathbf{A} \cdot C_{6} H_{12} \)
в. \( C_{7} H_{14} \)
с \( . C_{7} H_{16} \)
D. \( C_{7} H_{18} \)
E \( . C_{7} H_{12} \)


electric field is along negative \( x \) direction and it is constant. A particle having mass \( m \) and charge \( q \) is projected along \( x \) -direction with speed \( V_{0} . \) An additional force \( \overrightarrow{\boldsymbol{F}}=\overrightarrow{\boldsymbol{C}} \times \overrightarrow{\boldsymbol{V}} \) is
acting on the charge where \( \vec{V} \) is velocity vector and \( \vec{C} \) is a constant vector. The
charge comes out of region with speed \( \boldsymbol{V}_{0} \)
\( 2^{\text {as shown in figure, then the }} \)
magnitude of electric field is :
A \( \cdot \frac{3}{8} \frac{m V_{0}^{2}}{q d} \)
B. \( \frac{4}{3} \frac{m V_{0}^{2}}{q d} \)
c. \( \frac{8}{3} \frac{m V_{0}^{2}}{q d} \)
D. Can't be determined


Answer the question in the limit of
maximum 50 words.
Describe the dispersion of light by glass prism with neat figure.


According to Hooke's law of elasticity, if stress is increased, the ratio of stress to
strain
A . decreases
B. increases
c. becomes zero
D. remains constant


Fertilisation is defined as the process
by which
A. a diploid spermatozoan unites with a haploid ovum to form a triploid zygote
B. a haploid spermatozoan unites with a haploid ovum to form a diploid zygote
C . a diploid spermatozoan unites with a diploid ovum to form a diploid zygote
D. a diploid spermatozoan unites with a haploid ovum to form a diploid zygote.


Find the equation of the tangent and the normal to the following curve at the indicated point. \( c^{2}\left(x^{2}+y^{2}\right)=x^{2} y^{2} \) at \( \left(\frac{x}{\cos \theta}, \frac{c}{\sin \theta}\right) \)


Two isosceles triangles have equal
vertical angles and their areas are in the ratio \( 36: 25 . \) Find the ratio of their
corresponding heights.


Milk is an example of water in oil emulsions.
A. True
B. False
c. Ambiguous
D. Data insufficient


For the coagulation of \( 100 m L \) of
arsenious sulphide solution, \( 5 m L \) of
\( 1 M N a C l \) is required. What is the
coagulating power of \( N a C l ? \)


Define the terms:
¡) Declination
ii) Inclination or Dip.


Acetabulum is located in:
A. collar bone
B. hip bone
c. shoulder bone
D. thigh bone


Hydroponics is growing plants
A. Without soil
B. Without organic matter
C. In water
D. All the above


A reduction of \( 12.5 \% \) in the price of dining table brought down its price at Rs. \( 4375 . \) What is the original price of
the dining table?
\( \mathbf{A} \cdot 8,000 \)
в. 5,000
c. 5,500
D. 6,080


The correct equation of nuclear fusion
reaction is
\( \mathbf{A} \cdot_{1} H^{1}+_{1} H^{1} \rightarrow H_{2} \)
\( \mathbf{B} \cdot_{1} H^{2}+_{1} H^{1} \rightarrow_{2} H e^{4}+_{0} n^{1} \)
\( \mathbf{C} \cdot_{1} H^{2}+_{1} H^{2} \rightarrow_{2} H e^{4}+ \)energy
\( \mathbf{D} \cdot 2 H_{2}+3 H_{2} \rightarrow 5 H_{2} \)


A vessel, whose bottom has round holes
with diameter 0.1 mm, is filled with
water. The maximum height up to
which water can be filled without
leakage is
A. \( 100 \mathrm{cm} \)
B. \( 75 \mathrm{cm} \)
\( c .50 \mathrm{cm} \)
D. \( 30 \mathrm{cm} \)


How many moles of \( C O_{2} \) are in 1.53 g
\( C O_{2} ? \)
A. \( 1.807 \times 10^{-24} \)
4 \( 47 \times 10^{77} \) ?
В. \( 3.476 \times 10^{-2} \)
c. \( 1.717 \times 10^{-2} \)
D. \( 1.204 \times 10^{24} \)
E . \( 2.414 \times 10^{-1} \)


A box contains 100 cards marked with
numbers 1 to \( 100 . \) If one card is drawn
randomly from the box. Find the probability that it bears.
(1) Even prime number.
(2) A number divisible by 7.
(3) The number at unit place is 9


The unit vector in the direction of \( \overrightarrow{\boldsymbol{a}} \) is
A \( \cdot \frac{\vec{a}}{|\vec{a}|} \)
в. \( \vec{a}|\vec{a}| \)
\( c \cdot a^{2} \)
D.


Obtain the probability distribution of
the number of sixes in two tosses of a
fair die


A ball is dropped from a tower. In the
last second of its motion it travels a
distance of 15 m. Find the height of the tower. [take \( \left.g=10 m / s e c^{2}\right] \)


A simple pendulum oscillates freely between points \( A \) and \( B \) We now put a peg (nail) at some point \( C \)
as shown. As the pendulum moves from
At to the right, the string will bend at \( C \) and the pendulum will go to its extreme point D. Ignoring friction, the point D.
A. Will lie on the line AB
B. Will lie above the line AB
c. will lie below the line \( A B \)
D. Will concide with B


A \( 2 k g \) block is placed over a \( 4 k g \) block
and both are placed on a smooth horizontal surface. The coefficient of
friction between the blocks is \( 0-20 \)
Find the acceleration of the two blocks
if a horizontal force of \( 12 N \) is applied to
(a) the upper block, (b) the lower
block. Take \( g=10 m / s^{2} \)


The membranes that suspend
vertebrate organs in the body cavity are
called:
A . visceral muscle
B. coelomic membranes
c. ligaments
D. visceral membranes


'Origin of Species' was written by :
A. Oparin
B. Weismann
c. Lamarck
D. Darwin


Young's double slit experiment is carried out by using green, red and blue light, one color at a time. The fringe
widths recorded are \( \beta_{G}, \beta_{R}, \beta_{B} \) respectively. Then
\( \mathbf{A} \cdot \beta_{G}>\beta_{B}>\beta_{R} \)
в. \( \beta_{B}>\beta_{G}>\beta_{R} \)
c. \( \beta_{R}>\beta_{B}>\beta_{G} \)
D. \( \beta_{R}>\beta_{G}>\beta_{B} \)


At constant temperature, specific resistance of a conductor material
increases with:
A. increase in area of cross section
B. decrease in length
c. decrease in area of cross section
D. none of the above


Twenty four cells each of emf \( 1.5 \mathrm{V} \) and internal resistance 0.5 ohms are to be
connected to a 3 ohm resistance. For
maximum current through this resistance the number of rows and
number of columns that you connect
these cells is?
A. 12 cells in series 2 rows in parallel
B. 8 cells in series 3 rows in parallel
c. 4 cells in series 6 rows in parallel
D. 6 cells in series 4 rows in parallel


An atomic orbital is represented by:
\( \mathbf{A} \cdot \psi^{2} \)
B. \( \psi \) mod \( \psi \)
\( c \cdot \psi \)
D. \( \psi \) !


If \( \triangle_{1}, \triangle_{2} \) be the areas of two triangles with vertices \( (b, c),(c, a),(a, b), \) and \( \left(a c-b^{2}, a b-c^{2}\right),\left(b a-c^{2}, b c-\right. \)
\( \left.a^{2}\right),\left(c b-a^{2}, c a-b^{2}\right), \) then \( \frac{\triangle_{1}}{\triangle_{2}}= \)
\( (a+b+c)^{2} \)
A. True
B. False


Using the information, given in each of the following figures, find the valuesof
\( a \)
\( [\text { Given }: \boldsymbol{C} \boldsymbol{E}=\boldsymbol{A C}] \)
A . \( 136^{\circ} \)
B. \( 124^{\circ} \)
\( c \cdot 110^{\circ} \)
D. none of the above


Molecule obtained by \( s p^{3} d^{2} \) hybridisation has bond angle of:
A \( \cdot 90^{\circ} \)
B \( .109^{0} 28 \)
\( c \cdot 120^{\circ} \)
D. \( 72^{\circ} \)


If a hydrocarbon has a carbon-carbon
double bond, it is:
A. alkyne
B. alkane
c. alkene
D. all the above


Show that \( e=B v 1 \) where e is emf v is
velocity of rods and 1 is length of rods


In which year the first ozone hole was
discovered?
A . 1980
в. 1983
\( c \cdot 1985 \)
D. 1990


Chords of the circle \( x^{2}+y^{2}+2 g x+ \)
\( 2 f y+c=0 \) subtends a right angle at
the origin. The locus of the feet of the perpendiculars from the origin to these chords is
A \( \cdot x^{2}+y^{2}+g x+f y+c=0 \)
B . \( 2\left(\mathrm{x}^{2}+\mathrm{y}^{2}\right)+\mathrm{gx}+\mathrm{fy}+\mathrm{c}=0 \)
C \( \cdot 2\left(\mathrm{x}^{2}+\mathrm{y}^{2}+\mathrm{gx}+\mathrm{fy}\right)+\mathrm{c}=0 \)
D. \( x^{2}+y^{2}+2(g x+f y+c)=0 \)


A jet airplane travelling from east to
west at a speed of \( 500 \mathrm{km} h^{-1} \) eject out gases of combustion at a speed of
\( 1500 k m h^{-1} \) with respect to the jet
plane. What is the velocity of the gases with respect to an observer on the ground?
A. \( 1000 \mathrm{km} h^{-1} \) in the direction west to east.
B. \( 1000 \mathrm{km} h^{-1} \) in the direction east to west.
c. \( 2000 k m h^{-1} \) in the direction west to east.
D. \( 2000 \mathrm{km} h^{-1} \) in the direction east to west.


Match the column I with column II and
mark the appropriate choice.
and \( \begin{array}{ll}\text { column } & \text { column I } \\ 1\end{array} \)
Interstitial
hydride \( A \) 4 A Nat
\[
C H_{4}
\]
ii Molecular
hydride В
\( C \)
\( V H_{0.56} \)
\( B_{2} H_{6} \) iii lonic hydride Electron
deficient
hydride iv
A. \( (A) \rightarrow(i i i),(B) \rightarrow(i v),(C) \rightarrow(i i)(D) \rightarrow(i) \)
B. \( (A) \rightarrow(i i),(B) \rightarrow(i v),(C) \rightarrow(i i i)(D) \rightarrow(i) \)
c. \( (A) \rightarrow(i),(B) \rightarrow(i i),(C) \rightarrow(i v)(D) \rightarrow(i i i) \)
D. \( (A) \rightarrow(i i i),(B) \rightarrow(i i),(C) \rightarrow(i)(D) \rightarrow(i v) \)


A uniform thin rod of Length L and Mass M is bent at the middle point 0
Consider an axis passing through its middle point 0 and perpendicular to the plane of the bent rod. The moment of inertia about this axis is:
A \( \cdot \frac{2}{3} m L^{2} \)
B. \( \frac{1}{3} m L^{2} \)
c. \( \frac{1}{12} m L^{2} \)
D. Dependent on \( \theta \)


The percentage of deuterium in heavy
water is:
A . 22.2
в. 11.2
c. 44
D. 20


Which of the following contains isoprene units?
A. Natural rubber
B. Nylon - 6, 6
c. Polyethylene
D. Dacron


Apoplast is the system of adjacent cell walls that is continuous throughout the plant except at the
A. Plasmodesmata
B. Vessel element
c. casparian strips of endodermis
D. Tracheids


A rubber ball of mass \( 10 g m \) and volume
\( 15 c m^{3} \) dipped in water to a depth of
10m. Assuming density of water
uniform throughout the depth, find
(a) the acceleration of the ball, and
(b) the time taken by it to the surface if it is released from rest. take \( g= \)
\( 980 \mathrm{cm} / \mathrm{s}^{2} \)
(b) \( 2.02 \sec \)
B . (a) \( 4.9 \mathrm{m} / \mathrm{s}^{2} \)
(b) \( 2.02 \sec \)
c. (a) \( 4.9 \mathrm{m} / \mathrm{s}^{2} \)
(b) \( 12.02 \mathrm{sec} \)
D. (a) \( 8.9 m / s^{2} \)
(b) \( 2.02 \sec \)


limiting friction is of the area of
contact.fill in the blank
A. directly proportional
B. indirectly proportional
c. independent
D. none


Runs scored by Rahul in a match are 38
more than that faced by Virat. If together they have scored 144 runs and
the runs scored by Rahul are 18 more
than those faced by Virat. Find the number of runs scored by Rahul


Write uses of Fullerene.


The atomic weight of an element is 23 and its atomic number is \( 11 . \) The
number of proton, electrons and neutrons respectively, present in the atom of the element are
A. 11,11,12
В. 12,12,11
c. 11,12,11
D. 12,11,12


Armoured fishes belongs to class
A. Placodermi
B. Osteichytes
c. Elasmobranchi
D. Chondrichthyes


The small oval depression found on
inter auricular septum in adult human
is termed as
A. Foramen ovale
B. Fossa ovalis
c. Foramen of monro
D. Foramen of magnum


In two separate collisions, the
coefficients of restitution are \( e_{1} \) and \( e_{2} \)
are in the ratio \( 3: 1 . \) In the first collision
the relative velocity of approach is twice the relative velocity of separation, then
the ratio between relative velocity of approach and the relative velocity of separation in the second collision is :
A .1: 6
B . 2: 3
c. 3: 2
D. 6: 1


Join properly Column-I and Column-II.
Column I Column II
\( (A) \)
(1)
Lysin A) UUU \( 6^{G C} \)
(B)
(2)
Stop codon
\( (C) \)
(3) Phenyl Alanine AAA
(D)
(4)
UAA Glycine ne
\( A \cdot a-2, b-3, c-4, d-1 \)
B. \( a-4, b-3, c-1, d-2 \)
c. \( a-1, b-4, c-3, d-2 \)
D. \( a-3, b-4, c-1, d-2 \)


The scores of 10 students in a class test
are given as
44,54,46,63,55,42,34,48,70,38
Calculate the mean deviation about the
median.
A . 8.6
B. 6.6
\( c .7 .6 \)
D. 8.8
E . None of these


Light in air is incident at an angle of \( 45^{\circ} \)
on the surface of glass plate having Refractive index 1.526 through what angle is light deviated upon refraction at top of surface.


Lens which diverges light from a single point is
A. concave lens
B. convex lens
c. biconvex lens
D. both B and C


If \( V_{e} \) is the escape velocity of a body from a planet of mass \( M \) and radius \( R \) Then, the velocity of satellite revolving at height \( h \) from the surface of planet
will be
A \( \cdot V=V_{e} \sqrt{\frac{R}{(R+h)}} \)
B \( \cdot V=V_{e} \sqrt{\frac{2 R}{(R+h)}} \)
\( ^{\mathbf{c}} \cdot_{V}=V_{e} \sqrt{\frac{(R+h)}{R}} \)
D. \( V=V_{e} \sqrt{\frac{R}{2(R+h)}} \)


Root pressure helps in
Continuous flow of water in plants
ii Pulling force iii Replacement of lost water
B. ii, ii
c. i, ii i
D. All of the above


Q Type your question_
木政
,
Classification of representative
mammals.
\( \begin{array}{lll}\text { Kingdom } & \text { Animalia } & \text { Animalia } \\ \text { Phylum } & \text { Chordata } & \text { Chordata } \\ \text { Class } & \text { Mammalia } & \text { Mammalia } \\ \text { Order } & \text { Cetacea } & \text { Carnivora } \\ \text { Family } & \text { Mysticeti } & \text { Felidae } \\ \text { Genus } & \text { Balenopora } & \text { Felis } \\ \text { Species } & \text { B. physaius } & \text { F. catus } \\ \text { Common name } & \text { Blue Whale } & \text { Cat }\end{array} \)
\( A \)
Family
B. Kingdom
c. Species
D. Order
E. Class


Evaluate: \( \int \frac{d x}{\left(x^{2}+1\right)\left(x^{2}+4\right)} \)


A solution of saturated \( C a F_{2} \) is found to
contain \( 4.1 \times 10^{-4} M \) fluoride ion.
Calculate the \( \boldsymbol{K}_{s p} \) of \( \boldsymbol{C} \boldsymbol{a} \boldsymbol{F}_{2} . \) Neglect
hydrolysis.


The common mode of reproduction in Rhizopus is by
A. Sporangiospores
B. Oidia
c. Plasmospores
D. Zoospores


Anhydrous \( M g C l_{2} \) can be prepared by
heating \( M g C l_{2} \cdot 6 H_{2} O: \)
A. In a current of dry HCl gas
B. With carbon
c. Until it fuses
D. With lime


If statement \( \boldsymbol{p} \rightarrow(\boldsymbol{q} \vee \boldsymbol{r}) \) is true then
the truth values of statements \( p, q, r \)
respectively
\( \mathbf{A} \cdot \mathbf{T}, \mathbf{F}, \mathbf{T} \)
в. F, Т, F
\( \mathrm{c} \cdot \mathrm{F}, \mathrm{F}, \mathrm{F} \)
D. all of these


Assertion
Secreting hypotonic urine is effective in reducing urinary loss of water.
Reason
Hypotonic urine is more concentrated and higher in osmotic pressure than the blood.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The value of the determinant \( \mid \begin{array}{ccc}1+a^{2}-b^{2} & 2 a b & -2 b \\ 2 a b & 1-a^{2}+b^{2} & 2 a \\ 2 b & -2 a & 1+a^{2}-b^{2}\end{array} \)
is equal to
\( A \)
B \( \cdot\left(1+a^{2}+b^{2}\right) \)
c. \( \left(1+a^{2}+b^{2}\right)^{2} \)
D. \( \left(1+a^{2}+b^{2}\right)^{3} \)


Bond dissociation enthalphies of \( \boldsymbol{H}_{2}(\boldsymbol{g}) \)
and \( N_{2}(g) \) are \( 436.0 \mathrm{kJ} \) mol \( ^{-1} \) and 941.8
kJ mol \( ^{-1} \) respectively and enthalpy of
formation of \( \boldsymbol{N} \boldsymbol{H}_{3}(\boldsymbol{g}) \) is \( -46 \mathrm{kJ} \boldsymbol{m o l}^{-1} \)
What is enthalpy of atomization of
\( N H_{3}(g) ? \)
A. 390.3 kJ \( m o l^{-1} \)
B . 1170.9 kJ \( m o l^{-1} \)
c. 590 k \( \operatorname{mol}^{-1} \)
D. 720 kJ \( m o l^{-1} \)


In triangle \( A B C, \) medians \( A D \) and \( B E \) are drawn.lf \( \boldsymbol{A D}=\mathbf{4}, \angle \boldsymbol{D A B}=\frac{\boldsymbol{\pi}}{\mathbf{6}} \) and
\( \angle A B E=\frac{\pi}{3}, \) then the area of the
\( \triangle A B C \) is
A \( \cdot \frac{8}{3} \)
в. \( \frac{16}{3} \)
c. \( \frac{32}{3 \sqrt{3}} \)
D. \( \frac{64}{3} \)


Naphthalene, a white solid used to
make moth balls has a vapour pressure
of \( 0.10 \mathrm{mm} \) Hg at \( 27^{\circ} \mathrm{C} . \) Hence
\( \boldsymbol{K}_{\boldsymbol{p}} \) and \( \boldsymbol{K}_{\boldsymbol{c}} \) for the equilibrium are:
\( \mathbf{C}_{\mathbf{1 0}} \mathbf{H}_{\mathbf{8}}(\mathbf{s}) \rightleftharpoons \mathbf{C}_{\mathbf{1 0}} \mathbf{H}_{\mathbf{8}}(\mathbf{g}) \)
A. 0.10,0.10
B . \( 0.10,4.1 \times 10^{-3} \)
c. \( 1.32 \times 10^{-4}, 5.34 \times 10^{-6} \)
D. \( 5.36 \times 10^{-6}, 1.32 \times 10^{-4} \)


Pericardial fluid is secreted by
A. Myocardium
B. Perietal peritoneum
c. Visceral peritoneum
D. Pericardium


Regeneration is carried out by specialized cells.
A. True
B. False


Let \( \triangle_{1}, \triangle_{2}, \triangle_{3}, \dots, \triangle_{k} \) be the set of
third-order determinants that can be
made with the distinct nonzero real
numbers \( a_{1}, a_{2}, a_{3}, \dots a_{9}, \) and \( \Sigma a_{i}=0 \)
Then
This question has multiple correct options
\( \mathbf{A} \cdot k=9 ! \)
B . \( \sum_{i=1}^{k} \Delta_{i}=0 \)
C . at least one \( \Delta_{i}=0 \)
D. none of these


Identify the incorrect statement.
\( \mathbf{A} \cdot \operatorname{In} N_{2} O_{4} \) the \( \mathrm{N}-\mathrm{N} \) bond length is longer than the usual N-N single bond distance.
B. \( N O_{2} \) molecule is angular with \( N \) -O distance equal to the intermediate distance between a single and a double bond
\( \mathrm{C} \cdot N_{2} \mathrm{O} \) is a linear molecule and has a small dipole moment.
D. None of the above


If the door of a refrigerator is kept open
in a room, will it make the room warm or
cool?


Suppose \( \boldsymbol{f}:[-\mathbf{2}, \mathbf{2}] \rightarrow \boldsymbol{R} \) is defined by
\( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{l}-1 \text { for }-2 \leq x \leq 0 \\ x-1 \text { for } 0 \leq x \leq 2\end{array}\right. \)
then the \( \{x \in(-2,2): x \leq \)
\( \operatorname{Oand} f(|x|)=x\}= \)
A . \{-1\}
в. \{0\}
c. \( \left\{\frac{-1}{2}\right\} \)
D.


When \( 20 g \) of \( C a C O_{3} \) were put into 10
litre flask and heated to \( 800^{\circ} \mathrm{C}, 35 \% \) of
\( \mathrm{CaCO}_{3} \) remained unreacted at
equilibrium. \( K_{P} \) for decomposition of
\( \boldsymbol{C a C O}_{3} \) is:
A. 1.145 atm
B. 0.145 atm
c. 2.145 atm
D. 3.145 atm


State whether true or false.
A magnetic field is a region around a magnet where magnetic lines of force
act
A. True
B. False


Which is not a reversible reaction?
A. Base-promoted ester hydrolysis
B. Claisen condensation
c. Acid catalyst ester hydrolysis
D. Acetal formation


Why colloidal system in gas in gas does not exist?


Find the value of \( (1+i)^{3}+(1-i)^{6} \)


Out of the following four nets there are two correct nets to make a tetrahedron.
ldentify them.


Which of the following deplete ozone
layer?
\( A \cdot S O_{2} \)
в. \( C O_{2} \)
c. \( c o \)
D. NO and freons


\( f\left(\frac{1}{3}\right)+\cos ^{-1} x=\frac{\pi}{2}, \) then find \( x \)


Is every diameter of a circle also a
chord?


Specific heat of one mole of hydrogen at
constant pressure and at constant volume are \( 450 J K^{-1} \) and \( 300 J K^{-1} \)
respectively. Then what is the density of the gas at S.T.P?
\( \left(P_{a t m}=1.013 \times 10^{5} N m^{-2}\right) \)
A \( .2 .47 \mathrm{kg} / \mathrm{m}^{3} \)
В. \( 3.0 \mathrm{kg} / \mathrm{m}^{3} \)
c. \( 3.58 \mathrm{kg} / \mathrm{m}^{3} \)
D. \( 4.0 \mathrm{kg} / \mathrm{m}^{3} \)
E. No solution


Tickets numbered 1 to 20 are mixed up
and then a ticket is drawn at random.
What is the probability that the ticket drawn has a number which is a multiple
of 3 or \( 5 ? \)
A \( \cdot \frac{7}{20} \)
в. \( \frac{8}{20} \)
c. \( \frac{6}{20} \)
D. \( \frac{9}{20} \)


For a transistor, the current
amplification factor is \( 0.8 . \) The transistor is connected in
common emitter configuration, the change in collector current when the
base current changes by \( 6 m A \) is
\( \mathbf{A} \cdot 6 m A \)
в. \( 4.8 \mathrm{mA} \)
c. 24 m
D. \( 8 m A \)


A coil of inductance \( 0.50 \mathrm{H} \) and
resistance \( 100 \Omega \) is connected to a 240
V, 50 Hz ac supply.
(a) What is the maximum current in the
coil?
(b) What is the time lag between the
voltage maximum and the current maximum?


Two copper spheres of the same radii,
one hollow and the other solid, are
charged to the same potential, then
A. hollow sphere holds more charge
B. solid sphere holds more charge
c. both hold equal charge
D. we cant say


If the matrix \( \left[\begin{array}{ccc}\mathbf{0} & \mathbf{2} \boldsymbol{\beta} & \mathbf{\Upsilon} \\ \boldsymbol{\alpha} & \boldsymbol{\beta} & -\mathbf{\Upsilon} \\ \boldsymbol{\alpha} & -\boldsymbol{\beta} & \mathbf{\Upsilon}\end{array}\right] \) is
orthogonal, then
A \( \cdot \alpha=\pm \frac{1}{\sqrt{2}} \)
в. \( \beta=\pm \frac{1}{\sqrt{6}} \)
c. \( _{\gamma}=\pm \frac{1}{\sqrt{3}} \)
D. all of these


Which is the amount of energy
that must be added to raise
the temperature of 1 gram of
a substance by \( 1^{\circ} \mathrm{C} ? \)
A. Enthalpy change
B. Entropy change
c. Gibbs free energy change
D. Activation energy
E. Specific heat capacity


In a Kundt's tube experiment, the heaps of Iycopodium powder are collected at \( 20 \mathrm{cm} \) separations. The frequency of
tuning fork used is
A \( .660 H z \)
B. \( 825 \mathrm{Hz} \)
\( \mathrm{c} .775 \mathrm{Hz} \)
D. \( 915 ~ H z \)


Shearing strain is expressed by
A. angle of shear
B. angle of twist
c. decrease in volume
D. increase in volume


Write the polynomial in standard form and also write down their degree. \( \left(\frac{5}{6} z-\frac{3}{4} z^{2}-\frac{2}{3} z^{3}+1\right) \)


Roots-respire through.
A. Stomata
B. Lenticels
c. Spiracles
D. Air spaces


Fill in the blank.
Static electricity produced by charged particles in the atmosphere is known
as
A. Atmospheric electricity
B. Atmospheric charge
c. cloud electricity
D. Wind electricity


The refracting angle of a prism is \( A \). The refractive index of the prism is \( \cot \frac{A}{2} \) Find angle of minimum deviation.
\( \mathbf{A} \cdot 180^{\circ}+2 A \)
B \( \cdot 180^{\circ}-3 A \)
D. \( 90^{\circ}-A \)


Which of the following statements is true for the electrochemical Daniel cell?
A. Electrons flow from copper electrode to zinc electrode
B. Current flows from zinc electrode to copper electrode
c. Cations move toward copper electrode
D. Cations move toward zinc electrode


\( D \) and \( E \) are the mid-points of the sides
\( A B \) and \( A C \) of \( A B C \) and \( O \) is any point
on side \( B C . O \) is joined to \( A . \) If \( P \) and \( Q \)
are the mid-points of \( O B \) and \( O C \)
respectively, then \( D E Q P \) is:
A . a square
B. a rectangle
c. a rhombus
D. a parallelogram


Differentiate with respect to \( x \)
\( \boldsymbol{y}=\sin 2 \boldsymbol{x}-\boldsymbol{4} \boldsymbol{e}^{\boldsymbol{3}} \boldsymbol{x} \)


Write the principal value of \( \cos ^{-1}\left(\frac{1}{2}\right)- \) \( 2 \sin ^{-1}\left(-\frac{1}{2}\right) \)


A particle starts moving from rest from a fixed point in a fixed direction. The
distance \( s \) from the fixed point at a time
\( t \) is given by \( s=t^{2}+a t-b+17, \) where
\( a, b \) are real numbers. If the particle
comes to rest after 5 sec at a distance
of \( s=25 \) units from the fixed point
then values of \( a \) and \( b \) are respectively.
A .10,-33
B. -10,-33
c. -8,33
D. -10,33


\( 25.0 \mathrm{g} \) of \( F e S O_{4} .7 H_{2} O \) was dissolved in
water containing dilute \( H_{2} S O_{4} \) and the
volume was made up to 1.0 L. 25 mL of
this solution required 20 mL of an \( \frac{N}{10} K M n O_{4} \) solution for complete oxidation. The percentage of
\( F e S O_{4} \cdot 7 H_{2} O \) in the acid solution is:
A . \( 78 \% \)
B. \( 98 \% \)
c. \( 89 \% \)
D. \( 79 \% \)


A liquid A has specific heat capacity higher than the liquid B. Which liquid can be used as a coolant in car
radiators?
\( A \cdot A \)
B. B
c. Both can be used
D. Data insufficient


In which direction from Saptarshi (or Ursa Major,or Great bear) shown in the figure do we search for the pole star?
\[
\begin{array}{c}
\delta \\
\star \\
\dot{\gamma}
\end{array}
\]
SAPTARSHI
\( \mathbf{A} \cdot \alpha \) to \( \beta \)
B. \( \gamma \) to \( \delta \)
\( c \cdot \beta \) to \( \alpha \)
\( \mathbf{D} \cdot \delta \) to \( \gamma \)


Find the cube root of \( \frac{125}{216} \)


The gases evolved in the decomposition of lead nitrate are:
A. \( N_{2} O_{3}, N O \)
в. \( N O_{2}, O_{2} \)
\( \mathrm{c} \cdot \mathrm{N}_{2} \mathrm{O}_{3}, \mathrm{O}_{2} \)
D. \( N_{2} O, O_{2} \)


The IUPAC name is:
A. 2-ethyl-2-butanol
B. 3-Methyl-3-pentanol
c. 3-ethyl-3-methyl-3-pentanol
D. 1,1-diethyl ethanol


Construct two tangent to a circle of
radius \( 3.5 \mathrm{cm} \) from a point \( 4.5 \mathrm{cm} \) away from the circle.


Susceptibility is positive and large for a
A. paramagnetic substance
B. ferromagntic substance
c. diamagnetic substance
D. non magnetic substance


What is the frequency of A.C. in India?


With what speed should a bus travel so that it can cover a distance of \( 10 \mathrm{km} \) in 5
\( \min ? \)
\( A \cdot 60 \mathrm{km} / \mathrm{hr} \)
B. 10 km/hr
c. \( 12 \mathrm{km} / \mathrm{hr} \)
D. 120 km/hr


Why metal gets deposited at the negative pole when electric current is passed through a metal salt??
A. Metal is negatively charged.
B. Metal is positively charged.
c. Metal does not have any charges.
D. Both a and c.


Which of the following represents isostructural pairs?
\( \mathbf{A} \cdot\left[N F_{3}, N O_{3}^{-}\right] \) and \( \left[B F_{3}, H_{3} O^{+}\right] \)
B \cdot \( \left[N F_{3}, H N_{3}\right] \) and \( \left[N O_{3}^{-}, B F_{3}\right] \)
\( \mathbf{c} \cdot\left[N F_{3}, H_{3} O^{+}\right] \) and \( \left[N O_{3}^{-}, B F_{3}\right] \)
D・ \( \left[N F_{3}, H_{3} O^{+}\right] \) and \( \left[H N_{3}, B F_{3}\right] \)


Name the first organic compound that is prepared in laboratory?


If the function \( g(x) \) is defined by \( \boldsymbol{g}(\boldsymbol{x})=\frac{\boldsymbol{x}^{200}}{200}+\frac{\boldsymbol{x}^{199}}{199}+\frac{\boldsymbol{x}^{198}}{198}+\ldots .+ \)
\( \frac{x^{2}}{2}+x+5, \) then \( g^{\prime}(0)= \)
\( A \)
в. 200
\( c .100 \)
D. 5


Out of A-T, G-C pairing, bases of DNA may exist in alternate valency state owing to arrangement called as
A. Tautomerisational mutation
B. Analogue substitution
c. Point mutation
D. Frameshift mutation


ff \( P(x) \) is a polynomial of degree 3 such that \( P(i)=\frac{1}{i+1} \forall i=\{1,2,3,4\} \) then find \( P(5) \)


Which of the following reactions does not involve oxidation-reduction?
This question has multiple correct options
A \( \cdot 2 R b+2 H_{2} O \rightarrow 2 R b O H+H_{2} \)
в. \( 2 C u I_{2} \rightarrow 2 C u I+I_{2} \)
c. \( N H_{4} C l+N a O H \rightarrow N a C l+N H_{3}+H_{2} O \)
D. \( _{4 K C N}+F e(C N)_{2} \rightarrow K_{4}\left[F e(C N)_{6}\right] \)


\( (A) \) and \( (B) \) are:
\( A \)
\[
\mathbf{A} \text { and } \mathbf{B} \Rightarrow \mathbf{N} \equiv \mathbf{C} \ \prod_{\mathbf{O}}
\]
в.
\[
\mathbf{A} \text { and } \mathrm{B} \Rightarrow \mathbf{N} \equiv \mathrm{C} \overbrace{\mathrm{M}_{\mathrm{e}}}^{\mathrm{OH}} \mathbf{M}_{\mathrm{e}}
\]
\( c \)
\[
\begin{array}{c}
\mathbf{A} \Rightarrow \mathbf{N} \equiv \mathbf{C} \widehat{\|} \mathbf{N} \\
\mathbf{O} \\
\mathbf{B} \Rightarrow \mathbf{M} \mathbf{e}
\end{array}
\]
D.
\[
\mathbf{A} \Rightarrow \mathbf{N} \equiv \mathbf{C} \widehat{\mathbf{O}}
\]
\[
\mathrm{B} \Rightarrow \mathrm{Me} \overbrace{\mathrm{o}}^{\mathrm{OH}} \overbrace{\mathrm{Me}}^{\mathrm{M}}
\]


Salivary glands are modified into
poison glands in
A. Snakes
B. Lizard
c. Both A and B
D. None of the above


Assertion
If \( a>0 \) and \( b^{2}-4 a c<0 . \) then the
value of the integral \( \int \frac{d x}{a x^{2}+b x+c} \) will be of the type \( \mu \tan ^{-1}\left(\frac{x+A}{B}\right)+ \)
\( C ; \) where \( A, B, C, \mu \) are constant.
Reason
\( f\left(a>0, b^{2}-4 a c<0, \text { then } a x^{2}+b x+\right. \)
\( c \) can be written as sum of two squares.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


In the touch-me-not plant the leaves
show movements. What type of movement have you observed? Discuss.


Define:
a) Mitosis and
b) Meiosis


Salvarsan is the medicine used for
which disease?
A. Maleria
B. Syphilis
c. Acidity
D. all of these


If \( x=y \sqrt{1-y^{2}}, \) then \( \frac{d y}{d x} \) equals to?


Identify the electronic components from
the following symbols.

Write any one difference between them.
\( \mathbf{a} \)


What is the primary characteristic on
which the broad division of animal is
made?


Assertion
To protect iron from rusting it is coated
with a thin layer of zinc.
Reason
The zinc forms a barrier against
corrosion in that the steel underneath
does not come into contact with water
moisture in the air
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 given object taken \( n \) times more time
to slide down a \( 45^{\circ} \) rough inclined plane
as it takes to slide down a perfectly
smooth \( 45^{\circ} \) incline. The coefficient of
kinetic friction between the object and the incline is :
A \( \cdot \sqrt{1-\frac{1}{n^{2}}} \)
в. \( _{1-\frac{1}{n^{2}}} \)
c. \( \frac{1}{2-n^{2}} \)
D. \( \sqrt{\frac{1}{1-n^{2}}} \)


The production of ATP through chemiosmosis is known to occur in
which of the following organisms?
A. All cells (prokaryotic and eukaryotic) are capable of respiration using either oxygen or other electron acceptors.
B. All cells (prokaryotic and eukaryotic), but only in the presence of oxygen.
C. Eukaryotic cells only, and only when oxygen is present.
D. All cells that possess mitochondria, and only when oxygen or other electron acceptors are present.


The time(s) taken by a group of students to walk across their college is
given in the table below. Find the average time using direct method.
A. 12.02 sec
B. 39.12 sec
c. 40.20 sec
D. 31.90 sec


dentify correct reactivity order for \( \boldsymbol{S}_{N} \mathbf{2} \)
reaction.
(ii)
A . i > iì ii i
B. ii > jii >
D. None of these


A wave is represented by the equation \( \boldsymbol{y}=\boldsymbol{A} \sin \left(\mathbf{1 0} \boldsymbol{\pi} \boldsymbol{x}+\mathbf{1 5} \boldsymbol{\pi} \boldsymbol{t}+\frac{\boldsymbol{\pi}}{\mathbf{3}}\right), \) where \( \boldsymbol{x} \)
is in meters and \( t \) is in seconds. The
expression represents This question has multiple correct options
A. a wave travelling in the positive x-direction with a velocity \( 1.5 \mathrm{m} / \mathrm{s} \)
B. a wave travelling in the negative x-direction with a velocity \( 1.5 \mathrm{m} / \mathrm{s} \)
c. a wave travelling in the negative x-direction with a wavelength \( 0.2 m \)
D. a wave travelling in the positive x-direction with a wavelength \( 0.2 m \)


The range of the function \( f(x)= \)
\( \sin ^{-1}\left(x^{2}-2 x+2\right) \)
\( A \cdot \phi \)
B. \( \left[-\frac{\pi}{2}, \frac{\pi}{2}\right] \)
c. \( \frac{\pi}{2} \)
D. none of these


A highly ionic compound is formed by the combination of elements belonging
to:
A. I A group and VII A group
B. II A group and VI A group
c. III A group and V A group
D. o group and VII A group


The position vector of a particle is determined by the expression \( \vec{r}= \) \( 3 t^{2} \hat{i}+4 t^{2} \hat{j}+7 \hat{k}, \) The distance
traversed in first 10 sec is
\( \mathbf{A} \cdot 500 m \)
B. \( 300 m \)
\( c \cdot 150 m \)
D. \( 100 m \)


State whether given statement is True or False.
An object thrown upwards has a constant acceleration but zero velocity at the maximum height.
A. True
B. False


The correct order for decreasing atomic radius of the five atoms \( \boldsymbol{H}, \boldsymbol{B r}, \boldsymbol{I}, \boldsymbol{H} \boldsymbol{e} \)
and \( S \) is :
A \( . I>B r>S>H e>H \)
В. \( I>S>B r>H>H e \)
c. \( I>S>B r>H e>H \)
D. \( B r>I>S>H e>H \)


Unit matrix is a diagonal matrix in which all the diagonal elements are unity. Unit matrix of order 'n' is denoted
by \( I_{n}(\text { or } I) \) i.e. \( A=\left[a_{i j}\right]_{n} \) is a unit
matrix when \( \boldsymbol{a}_{\boldsymbol{i} j}=\mathbf{0} \) for \( \boldsymbol{i} \neq \)
\( \boldsymbol{j} \boldsymbol{a} \boldsymbol{n} \boldsymbol{d} \boldsymbol{a}_{i j}=\mathbf{1} \)
A . True
B. False


If \( \boldsymbol{x}<\mathbf{0}, \) then \( \tan ^{-1} \boldsymbol{x} \) is equal to
This question has multiple correct options
A \( \cdot-\pi+\cot ^{-1} \frac{1}{x} \)
B. \( \sin ^{-1} \frac{x}{\sqrt{1+x^{2}}} \)
c. \( -\cos ^{-1} \frac{1}{\sqrt{1+x^{2}}} \)
D. \( -\operatorname{cosec}^{-1} \frac{\sqrt{1+x^{2}}}{x} \)


Assertion
The magnetic field produced by a
current carrying solenoid Is
independent of its length and cross-
sectional area.
Reason
The magnetic field inside the solenoid
is uniform.
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 statements is
true?
A. A convex lens has 4 dioptre power having a focal length \( 0.25 \mathrm{m} \)
B. A convex lens has 4 dioptre power having a focal length \( 0.125 \mathrm{m} \)
C. A concave lens has 4 dioptre power having a focal length \( 0.25 \mathrm{m} \)
D. A concave lens has 4 dioptre power having a focal length \( 0.125 \mathrm{m} \)


An \( \ldots \) employed in an electric bell.
A. steel
B. electromagnet
c. permanent
D. right angles


Consider the reaction at \( 300 K \)
\( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g}) \rightarrow 2 \boldsymbol{H} \boldsymbol{C l}(\boldsymbol{g}) \)
\( \Delta H^{o}=-185 k J / m o l \)
If 3 mole of \( H_{2} \) completely react with 3
mole of \( C l_{2} \) to form \( H C l . \) What is \( \Delta U^{\circ} \)
for this process?
A. \( 0 k J \)
\( J \)
в. \( 185 k J \)
c. \( 555 k J \)
D. \( -553.8 k J \)


A slab of glass, of thickness \( 6 \mathrm{cm} \) and
refractive index \( \mu=1.5 \) is placed in
front of a concave mirror as shown in
the figure. If the radius of curvature of
the mirror is \( 40 \mathrm{cm} \) and the reflected
image coincides with the object, then
the distance of the object from the
mirror is :
\( A .30 \mathrm{cm} \)
B. 22 \( \mathrm{cm} \)
c. \( 42 \mathrm{cm} \)
D. 38 cm


With respect to Eichorrnia:
Statement \( X: \) It drains off oxygen from
water and is seen growing in standing
water.
Statement Y : It is an indigenous species of our country.
A. Both statements \( x \) and \( Y \) are correct
B. Both statements X and Y are wrong
c. only statement \( x \) is correct and \( Y \) is wrong
D. only statement Y is correct and X is wrong


Under the influence of air and light, chloroform decomposes into:
A. \( C C l_{4} \)
в. \( \left(C H_{3}\right)_{2}^{O H} C-C C l_{3} \)
c. \( \operatorname{cocl}_{2} \)
D. \( C C l_{3} C H O \)


Find the values of the unknown \( x \) and \( y \)
in the following diagram.


find \( 1+\frac{1}{1+2}+\frac{1}{1+2+3}+ \)
to n terms.


Which of the following represents the IUPAC names of the compounds 0 dinitrobenzene, m-dinitrobenzene, and
p-dinitrobenzene respectively.
A. 1,2 -dinitrobenzene, 1,3 -dinitrobenzene and \( 1,4- \) dinitrobenzene
B. 1,2-dinitrobenzene, 1,4-dinitrobenzene and 1,3dinitrobenzene
c. 1.3 -dinitrobenzene, 1,2 -dinitrobenzene, and \( 1,4- \) dinitrobenzene
D. 1.3-dinitrobenzene, 1,4-dinitrobenzene and 1,2dinitrobenzene


Find the induced emf. Will the induced
emf be time dependent?


When light ray bends away from normal then which angle is larger?
A. Angle of incidence
B. Angle of Refraction
c. Angle of deviation
D. Angle of normal


Charge \( +q \) placed at point \( A \) is a distance \( 2 L \) apart from \( B \) and \( C \) is the
midpoint between A and B. The work
done in moving charge \( +\mathrm{Q} \) along the
semicircle CRD is
\( \mathbf{A} \cdot \frac{\mathrm{q} Q}{2 \pi \varepsilon_{\mathrm{U}}} \)
B. \( \frac{9 Q}{6 \pi \varepsilon_{0}} \)
\( \mathbf{c} \cdot-\frac{q Q}{6 \pi \varepsilon L} \)
D. \( \frac{q Q}{4 \frac{q Q}{4 \varepsilon_{0} L}} \)


The pH of the solution at 25 which has twice as many hydroxide ion as in pure
water at \( 25, \) will be:
A \( \cdot 14 \)
в. 9
c. 6.699
D. 7.301


Is the given sequence 2,4,8,16 form an
A.P. If it forms an AP, find the common
difference \( d \)


In an endothermic process, solubility increases with
temperature.
\( A \). increase
B. decrease
c. no change in temperature
D. none of the above


For construction of a quadrilateral \( A B C D, \) where \( A B=4.2 \mathrm{cm}, B C=3.8 \)
\( \mathrm{cm}, C D=4.9 \mathrm{cm}, A D=5.4 \mathrm{cm} \) and
\( \angle B=72, \) its steps for construction is given injumbled form. Identify the third step from the following
1) From \( B \), set off \( B C=3.8 \mathrm{cm} \)
2) Draw \( A B=4.2 \mathrm{cm} \) and : Make
\( \angle A B X=72 \)
3) With \( A \) as center and radius equal to
\( 5.4 \mathrm{cm} \) draw an arc.
4) With \( C \) as center and radius equal to
\( 4.9 \mathrm{cm}, \) draw another arc, cutting the previous arc at \( D \). Join \( A D \) and \( C D \)
A. 3
в.
\( c \)
D.


What do you understand by the 'order of a reaction'? Identify the reaction order from each of the following units of reaction
rate constant:
(i) \( L^{-1} \) mol \( s^{-1} \)
(ii) \( L m o l^{-1} s^{-1} \)


The type of muscle fibre present in the wall of alimentary canal is
A. smooth muscle fibre
B. striped muscle fibre
c. cardiac muscle fibre
D. both (a) and (b)


Assertion
In case of oscillatory motion the average speed for any time interval is always greater than or equal to its average velocity
Reason
Distance travelled by a particle cannot be less than its displacement.
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 nail has \( 2 c m^{2} \) at one end and \( \frac{1}{100} c m^{2} \) at the other end. A force of 1000 gwt is applied on the first end. Calculate the
pressure acting on the wall?
A \( \cdot 78 \times 10^{6} \) dunecm\( ^{-2} \)
B. \( 88 \times 10^{6} \) dynecm\( ^{-2} \)
c. \( 98 \times 10^{6} \) dynecm \( ^{-2} \)
D. \( 95 \times 10^{6} \) dynecm \( ^{-2} \)


The value of \( \frac{(\boldsymbol{n}+\mathbf{2}) !-(\boldsymbol{n}+\mathbf{1}) !}{\boldsymbol{n} !} \) is:
A \( \cdot(n+2) ! \)
в. \( (n+1) ! \)
c. \( (n+2)^{2} \)
D. \( (n+1)^{2} \)
\( E \)


on or of of


\( \ln 2 s p^{2} \) orbital, character of \( 2 p_{z} \) orbital
will be
A. always \( 33.33 \% \)
B. always \( 0 \% \)
c. always \( 66.66 \% \)
D. always \( 33.33 \% \) or \( 0 \% \)


ATP ase activity occur in
A. Head of \( F_{1} \) particle.
B. Stalk of \( F_{1} \) particle.
C. Base of F particle.
D. All of the above.


Express the following as improper fractions:
\( \mathbf{7} \frac{\mathbf{3}}{\mathbf{4}} \)
\( \mathbf{5} \frac{\mathbf{6}}{\mathbf{7}} \)
\( 2 \frac{5}{6} \)
\( 10 \frac{3}{5} \)


The order of electronegativity of carbon
in \( s p, s p^{2} \) and \( s p^{3} \) hybridized states follows:
\( \mathbf{A} \cdot s p>s p^{2}>s p^{3} \)
B \( \cdot s p^{3}>s p^{2}>s p \)
\( \mathbf{c} \cdot s p>s p^{3}>s p^{2} \)
D \( \cdot s p^{2}>s p>s p^{3} \)


According to the adsorption theory of catalysis,the speed of the reaction increase because:
A. The concentration of reactant molecules at the active centers of the catalyst becomes high due to adsorption
B. In the process of adsorption, the activation energy of the molecules becomes large
c. Adsorption produces heat which increases the speed of the reaction
D. Adsorption lowers the activation energy of the reaction.


Dryopithecus is considered to be
A. Ancestral form of ape
B. Ancestral form of monkeys
C. Connecting links between ape and man
D. Common ancestor of ape and man


If \( \boldsymbol{a}_{\mathbf{1}} \in \boldsymbol{R}-\{\mathbf{0}\}, \boldsymbol{i}=\mathbf{1}, \mathbf{2}, \mathbf{3}, \boldsymbol{4} \) and \( \boldsymbol{x} \in \boldsymbol{R} \)
and \( \left(\sum_{i=1}^{3} a_{i}^{2}\right) x^{2}- \)
\( \mathbf{2} \boldsymbol{x}\left(\sum_{i=1}^{3} \boldsymbol{a}_{i} \boldsymbol{a}_{i+1}\right)+\sum_{i=2}^{4} \boldsymbol{a}_{i}^{2} \leq \mathbf{0}, \) then
\( a_{1}, a_{2}, a_{3}, a_{4} \) are in
A . A.
в. G.
c. н.
D. A.G.