Results of calculations for four different
designs of a fusion reactor using D-D reaction are given below.Which of these is most promising based on Lawson criterion?
A. deuteron density \( =2.0 \times 10^{12} \mathrm{cm}^{-3} \), confinement time \( =5.0 \times 10^{-3} \mathrm{s} \)
B. deuteron density \( =8.0 \times 10^{14} \mathrm{cm}^{-3} \), confinement time \( =9.0 \times 10^{-1} \mathrm{s} \)
C. deuteron density \( =4.0 \times 10^{23} \mathrm{cm}^{-3}, \) confinement time \( =1.0 \times 10^{-11} \mathrm{s} \)
D. deuteron density \( =1.0 \times 10^{24} \mathrm{cm}^{-3} \), confinement time
\[
=4.0 \times 10^{-12} \mathrm{s}
\]


If all the words, with or without
meaning, are written using the letters of the word QUEEN and are arranged as in English dictionary, then the position
of the word QUEEN is.
\( \mathbf{A} \cdot 45^{t h} \)
B. \( 46^{\text {th }} \)
\( \mathbf{c} \cdot 44^{t h} \)
D. \( 47^{t h} \)


The unit of thermal capacity is :
A \( \cdot c a l /^{\circ} C \)
в. \( c a l / g \)
c. \( \operatorname{cal} / g^{\circ} C \)
D. cal


A substance reacts according to order kinetic and rate constant for the
reaction is \( 1 \times 10^{-2} \)sec\( ^{-1} \). If the initial
concentration is \( 1 \mathrm{M} \)

Rate of the reaction after 1 minute is:
A \( .5 .49 \times 10^{-3} \) mol litre \( ^{-1} \) sec \( ^{-1} \)
B. \( 5.55 \times 10^{-3} \) mol litre \( ^{-1} \) sec \( ^{-1} \)
c. \( 7.49 \times 10^{-3} \) mol litre \( ^{-1} \) sec \( ^{-1} \)
D. None of these


Evaluate the following definite integrals
\( \int_{0}^{\pi / 2} \cos ^{2} x d x \)


Major product of above reaction:
A. \( C_{6} H_{5}-C H=C H-C O O H \)
в. \( C_{6} H_{5}- \) СООН
\( \mathrm{c} \cdot C_{6} H_{5}-C H=C H-C O O C H_{3} \)
\( \mathrm{D} \cdot C_{6} H_{5} C H_{2} C H O \)


For the following graph find:
Acceleration
Distance


Three weight \( W, 2 W \) and \( 3 W, \) are connected to identical springs suspended from rigid horizontal rod. The assembly of the rod and the weights fall freely. The positions of the weights from the rod are such that
A. \( 3 W \) will be farthest
B. \( W \) will be farthest
c. all will be at the same distance
D. \( 2 W \) will be farthest


A current carrying wire and a
rectangular loop are placed as shown in
figure then
A. The wire will be repelled by the rectangular loop
B. The wire will attracted by the rectangular loop
c. There will not be any change in position of wire
D. Loop will rotate


Why does micelle formation take place when soap is added to water? Will a
micelle be formed in other solvents like
ethanol also?


Assertion
cell constant is the EMF of a cell.
Reason
Cell constant is determined by using
saturated KCl solution.
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


Velocity of a bullet changes from \( u \) to \( v \) after passing through a board of thickness \( d \). Force of resistance is
directly proportional to the velocity. Time of motion of bullet in the board is
given by
A \( \frac{d(u-v)}{u v \log _{e} \frac{u}{v}} \)
\( ^{\mathrm{B}} \cdot \frac{d u}{v \log _{e} \frac{u}{v}} \)
\( ^{\mathbf{c}} \cdot \frac{d v}{u \log _{e} \frac{u}{v}} \)
D. \( \frac{d \log _{e} \frac{v}{u}}{v-u} \)


If \( \int x^{5} e^{-x^{2}} d x=g(x) \cdot e^{-x^{2}}+C \) then
the value of \( g(-1) \) is?
\( A \cdot \frac{3}{2} \)
в. \( \frac{5}{2} \)
\( c \cdot-\frac{5}{2} \)
D.


During sodium extract preparation for Lassaigne's test both \( N \) and \( S \) present
in an organic compound change to:
A. \( N a C N \) and \( N a_{2} S \)
В. \( \operatorname{NaNH}_{2} \) and \( N a_{2} S O_{4} \)
c. \( N a S C N \)
D. \( N a N O_{3} \) and \( N a_{2} S \)


The respiratory quotient (RQ) of carbohydrate is
A. Equal to 1
B. Less than 1
c. More than 1
D. None of the above


A particle executes SHM with an amplitude of \( 20 \mathrm{cm} \) and time period of 12 sec. The minimum time required for it to move between two points \( 10 \mathrm{cm} \) on either side of the mean position
A . 1 s
B. 2
\( c \cdot 3 s \)
D. 4 s


If \( \frac{a^{n}+b^{n}}{a^{n-1}+b^{n-1}} \) is the AM between a and
b, then the value of \( n \) is
A.
B.
\( c \cdot-1 \)
D. none of these


What is the action of the following reagent on ethanoic acid?
\( P C l_{3}, \) heat


IUPAC name of the compound
\( \left(\boldsymbol{C}_{2} \boldsymbol{H}_{5}\right)_{2} \boldsymbol{N} \boldsymbol{C} \boldsymbol{H}_{3} \) is:
A. 2, 2-diethylmethanamine
B. \( N, N \) - diethylmethanamine
c. \( N \) -ethyl- \( N \) -methylethanamine
D. \( N \) -methylbutanamine


Tubewell are used to pump out water
from :
This question has multiple correct options
A . tanks
B. ground
c. river
D. aquifer


Explain why kerosene doesn't catches fire easily whereas petrol does?


Let \( A=\{9,10,11,12,13\} \) and let \( f \) \( A \rightarrow N \) be defined by \( f(n)= \) the
highest prime factor of \( n \). Find the
range of \( \boldsymbol{f} \)


A positive charge \( +\mathrm{Q} \) is located at \( 5 \mathrm{cm} \)
on the positive y-axis. A negative charge
-Q is located at \( 5 \mathrm{cm} \) on the positive \( x \) -
axis. A positive test charge is at the origin where it feels a force "F" from the
positive charge above it. What is the net
force from both charges?
\( \mathbf{A} \cdot 2 F \)
B \( . F^{2} \)
\( c \cdot \frac{F}{2} \)
D. \( \sqrt{2} F \)


\( p^{t h}, q^{t h} \) and \( r^{t h} \) terms of an A.P. are
\( a, b, c \) respectively, then show that
(i) \( \boldsymbol{a}(\boldsymbol{q}-\boldsymbol{r})+\boldsymbol{b}(\boldsymbol{r}-\boldsymbol{p})+\boldsymbol{c}(\boldsymbol{p}-\boldsymbol{q})=\mathbf{0} \)
(ii) \( (a-b) r+(b-c) p+(c-1) q=0 \)


Assertion
Two bodies of different masses dropped from the same height reach the ground
at the same instant of time.
Reason
Time of flight depends upon the mass of
the bodies.
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 factors of \( 6-x-2 x^{2} \) are:
A. \( (x+2)(3-2 x) \)
В. \( (3-x)(3 x+2) \)
c. \( (x-2)(x+6) \)
D. None of these


The mean deviation from the mean for
the set of observations -1,0,4 is
A. Less than 3
B. Less than 1
c. Greater than 2.5
D. Greater than 4.9


\( (-3)^{-2}=\frac{1}{k} \) then value of \( k \) is


The base angles of an isosceles triangle
is \( 50^{\circ} . \) The size of vertical angle is
A \( .55^{\circ} \)
B. \( 35^{\circ} \)
\( c \cdot 70^{\circ} \)
D. \( 80^{\circ} \)


The minimum integral value of the sum of real numbers \( x^{11}, x^{3}, x^{7}, 1,4 x^{-5} \) and
\( x^{-1}, \) where \( x \) can take only those values for which \( f(x)=\ln (x) \) is well defined is
\( \mathbf{A} \cdot \mathbf{8} \)
B. 9
c. 10
D. 11


What is the correct sequence of the increasing effectiveness of the following electrolyte for the coagulation of ferric hydroxide sol? \( \boldsymbol{K}_{4}\left[\boldsymbol{F} e(\boldsymbol{C} \boldsymbol{N})_{6}\right. \)
\( A l P O_{4} \)
\( \boldsymbol{C a} \boldsymbol{S O}_{4} \)
\( \boldsymbol{S} \boldsymbol{n} \boldsymbol{C l}_{4} \)
Select the correct answer using the codes given below:
\( A \cdot d, b, a, c \)
B. \( \mathrm{d}, \mathrm{c}, \mathrm{b} \),
\( c \cdot a, b, c, d \)
D. \( c, d, b, a \)


Spiral valves are found in
A. Walls of cystic ducts (spleen)
B. Walls of cystic duct (gall bladder)
C . Hepatic duct (liver)
D. Common bile duct


The amplitude of a wave disturbance propagating in the positive y-direction is given by:
\( y=\frac{1}{1+x^{2}} \) at \( t=0 s a n d y= \)
\( \frac{1}{1+(x-1)^{2}} \) at \( t=2 s, \) then wave
velocity is
A. \( 1 m / s \)
в. \( 1.5 m / s \)
c. \( 0.5 m / s \)
D. \( 2 m / s \)


Prove that \( \tan ^{-1} \frac{63}{16}=\sin ^{-1} \frac{5}{13}+ \)
\( \cos ^{-1} \frac{3}{5} \)


On the axis and on the equator of an electric dipole for all points
A. On both of them \( V \neq 0 \)
B. On both of them \( V=0 \)
c. on the axis \( V=04 \$ a n d o \)nequatorv Vneq o\$s
D. on the axis \( V \neq 0 \) and on equator \( V=0 \)


Look at the measures shown in the
adjacent figure and find the area of \( \square P Q R S \)


The indication of the state of charge of a
battery is best given by:
A. specific gravity of electrolyte
B. temperature of electrolyte
c. colour of electrolyte.
D. level of electrolyte


The correct statement about
Neanderthal man is:
This question has multiple correct options
A. The first human like hominid
B. Started agriculture
c. Ate meat and walked erectly
D. Buried the deadd


Explain with reasons:
(i) Transition elements show variable
oxidation states
(ii) Transition elements form coloured
compounds.
(iii) The size of Lanthanide elements
decreases from La to Lu.


Probability of an event always greater
than or equal to
A \( \cdot \frac{1}{2} \)
B. 1
c. 0
D. -


Integrate the function \( \frac{1}{x-x^{3}} \)


If \( \boldsymbol{A}=\left(\begin{array}{ccc}4 & 1 & 2 \\ 1 & -2 & 3 \\ 0 & 3 & 2\end{array}\right), \boldsymbol{B}=\left(\begin{array}{ccc}2 & 0 & 4 \\ 6 & 2 & 8 \\ 2 & 4 & 6\end{array}\right) \) and \( \boldsymbol{C}= \)
\( \left(\begin{array}{ccc}1 & 2 & -3 \\ 5 & 0 & 2 \\ 1 & -1 & 1\end{array}\right), \) then
verify that \( \boldsymbol{A}+(\boldsymbol{B}+\boldsymbol{C})=(\boldsymbol{A}+\boldsymbol{B})+ \)
\( \boldsymbol{C} \)


If the global maximum value of \( \boldsymbol{f}(\boldsymbol{x})= \)
\( -x^{2}+a x-a^{2}-2 a-2 \) for \( x \epsilon[0,1] \) be
-5', then 'a' can take the value
This question has multiple correct options
\( ^{\mathrm{A}} \cdot \frac{-4+2 \sqrt{13}}{3} \)
B. \( \frac{-4-2 \sqrt{13}}{3} \)
c. 1
D. - 3


The shape of \( S C l_{4} \) is best described as
\( a: \)
A. square
B. tetrahedron
c. square pyramid
D. see-saw


If \( l=\lim _{n \rightarrow 3} \frac{x^{2}-9}{\sqrt{x^{2}+7}-4} \) and \( m= \)
\( \lim _{n \rightarrow-3} \frac{x^{2}-9}{\sqrt{x^{2}+7}-4}, \) then
\( \mathbf{A} \cdot l \neq m \)
B. \( l=2 m \)
c. \( l=-m \)
\( \mathbf{D} \cdot l=m \)


The friction that exists between a
surface sliding over another is called


When the number of turns in a solenoid
is doubled without any change in the length of the solenoid, its selfinductance becomes:
A . Half
B. Double
c. Four times
D. Eight times


For the gaseous reaction \( 2 A+B \rightarrow \)
\( C+D, \) the rate is given by \( k[A][B] . \) The
volume of the container containing the reaction mixture is suddenly reduced to one-fourth of its original volume. with respect to the original rate, now the rate would be:
A \( \cdot \frac{1}{16} \) times the original rate
B . \( \frac{1}{8} \) times the original rate
c. 16 times the original rate
D. 8 times the original rate


Which of the following is associated with biological amplification?
\( A \cdot S O_{4} \)
B. DDT
c. sewage
D. All of the above


A point charge of \( q \) mass \( m \) is placed at center of a fix ring of charge \( Q \) and radius \( R \) what is the
minimum velocity should be given by \( q \) so they would reach far away from ring.
A \( \cdot \frac{Q q}{5-\sqrt{5}} \)
в. \( \frac{Q q}{\sqrt{5}-1} \)
c. \( \sqrt{\frac{Q q}{2 \varepsilon \varepsilon R m}} \)
D. \( \frac{2 q}{5-\sqrt{5}} \)


A Si and a Ge diode has identical
physical dimensions. The band gap in \( \mathrm{Si} \)
is larger than that in Ge. An identical
reverse bias is applied across the
diodes
A. The reverse current in Ge is larger than that in Si
B. The reverse current in Si is larger than that in Ge
c. The reverse current is identical in the two diodes
D. The relative magnitude of the reverse currents cannot be determined from the given data only


A choke coil is needed to operate an arc \( \operatorname{lamp} \operatorname{at} 160 V(\mathrm{rms}) \) and \( 50 \mathrm{Hz} \). The arc
lamp has an effective resistance of \( 5 \Omega \) when running at \( 10 A(\mathrm{rms}) . \) Calculate
the inductance of the choke coil. If the
same arc lamp is to be operated on \( 160 V \) DC, what additional resistance
would be required. Compare the power losses in both the cases.


A wheel rolls purely on the ground. If the
velocity of a point \( ^{\prime} \boldsymbol{P}^{\prime} \) as shown on the
periphery of a body has a velocity equal
to the velocity of the centre of mass of
the body. Find \( \theta=? \)


A N-pole of a very long magnetic needle is placed at a distance of \( 20 \mathrm{cm} \) from a
point P. If the pole strength of the magnetic needle is \( 40 \mathrm{Am} \), the magnetic induction at the point \( \mathrm{P} \) is
\( \mathbf{A} \cdot 10^{-3} \mathbf{T} \)
B . \( 10^{-4} \mathrm{T} \)
\( \mathbf{c} \cdot 10^{-6} \mathbf{T} \)
D. \( 10^{-8} \) T


A parallel beam of light travelling in water (refractive index \( =\mathbf{4} / \mathbf{3} \) ) is
refracted by a spherical air bubble of radius \( 2 \mathrm{mm} \) situated in water.

Assuming the light rays to be paraxial, find the position of image due to refraction at first surface and position of the final image.


Which source of energy is used in a nuclear power station to generate electrical energy?
A. Different types of atom regrouping
B. Heavy nuclei splitting
c. Radioactive isotopes decaying
D. Radioactive atoms emitting \( \beta \) -particles


Which one is the method of
contraception?
A. Barrier methods
B. Chemical methods
c. Intra Uterine Contraceptive Devices
D. All of the above


In Dahlia, the roots are
A. Fibrous
B. stilt
c. Moniliform
D. Fasciculated tuberous


The diameters of the front and the rear
wheels of a tractor are \( 63 \mathrm{cm} \) and
1.54 \( m \) respectively. Calculate their areas and circumference.


The class of diffraction in which
incident and diffracted wave fronts are
planar is called:
A. Fresnel diffraction
B. Fraunhofer diffraction
c. Huygens' diffraction
D. Newton's diffraction


A parallel narrow beam of light is
incident on the surface of a transparent
hemisphere of radius \( \boldsymbol{R} \) and refractive
index \( \mu=1.5 . \) The position of the image
formed by refraction at the spherical
surface only is
A. \( R / 2 \)
B. \( 3 R \)
\( c . R / 3 \)
\( \mathbf{D} \cdot 2 R \)


The press plungers of a Bramah
(hydraulic) press is \( 40 \mathrm{cm}^{2} \) in crosssection and is used to lift a load of
mass \( 800 k g . \) What minimum force is
required to be applied to the pump plunger if its cross-sectional area is
\( 0.02 m^{2} ? \)


The general methods of preparation of
Sulfuric acid are
A. By action of heat on nitric acid and sulphur
B. By dissolution of sulphur trioxide in water
C. By hydrolysis of sulphuryl chloride
D. All of the above


An arc of a circle of radius \( R \) subtends
an angle \( \frac{\pi}{2} \) at the centre. It carries a
current \( i . \) The magnetic field at the centre will :
A \( \cdot \frac{\mu_{0} i}{2 R} \)
в. \( \frac{\mu_{0} i}{8 R} \)
c. \( \frac{\mu_{0} i}{4 R} \)
D. \( \frac{\mu_{0} i}{5 R} \)


Which of the following factor is responsible for regulating the size of the potato slices during osmosis?
A. Increased salt concentration
B. Increased pressure
c. Increased temperature
D. Increased humidity


Which cells among the permanent tissue are impermeable to water?
A. Parenchyma
B. Collenchyma
c. Both A and B
D. Sclerenchyma


Cohesion-tension theory is related to
A. Respiration
B. Ascent of sap
c. Transpiration
D. Photosynthesis


The reaction of slaked lime with \( C l_{2} \) gas
gives:
\( \mathbf{A} \cdot \) only \( C a(O C l)_{2} \)
B. only \( C a C l_{2} \)
C . a mixture of \( C a(O C l)_{2}, C a(O H)_{2}, C a C l_{2}, H_{2} O \)
D. quick lime


If the perimeter of the square carpet is
\( 100 m, \) find the area covered by the
carpet.


Find the value of \( x \) for which the points
\( (x,-1),(2,1) \) and (4,5) are collinear.


In an arithmetic progression, \( a_{7}=9 . \) At
what value of its difference is the
product \( a_{1} a_{2} a_{7} \) the least?


If a Parrot starts flying upwards with an
acceleration in an air tight cage, then the boy will feel the weight of the cage:
A. Unchanged
B. Reduced
c. Increased
D. Nothing can be said


Construct an angle of \( 45^{\circ} \) from a
horizontal line and justify the
construction.


Write the expression for the common
difference of an \( A . P \) whose first term is
\( a \) and \( n t h \) term is \( b \)


A radioactive sample at any instant has its disintegration rate 5000 dpm. After 5 minutes, the rate is 1250 dpm.Then, the
decay constant (per minute) is
A \( .0 .4 \ln 2 \)
в. \( 0.2 \ln 2 \)
c. \( 0.1 \ln 2 \)
D. \( 0.8 \ln 2 \)


Identify the correct sequence of increasing number of \( \pi \) -bonds in the structures of the following molecules:
(I) \( \boldsymbol{H}_{2} \boldsymbol{S}_{2} \boldsymbol{O}_{6}(\|) \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{3}(\|) \boldsymbol{H}_{2} \boldsymbol{S}_{2} \boldsymbol{O}_{5} \)
A . ।, ॥।, ॥।
B. II, III,
c. ॥, ।, ॥।
D. I, III, II


A boy projects a ball up with an initial velocity of \( 80 \mathrm{ft} / \mathrm{s} \). The ball will be at a height of \( 96 \mathrm{ft} \) from the ground after
A. 2 s
B. 3
\( c \cdot 5 s \)
D. both (a) and (b)


In a galvanic cell, the positive ions of salt bridge migrate towards:
A . - ve electrode
B. + ve electrode
c. either anode or cathode
D. neither anode nor cathode


If \( A+B+C=180^{\circ}, \) then the value of
\( (\cot B+\cot C)(\cot C+ \)
\( \cot A)(\cot A+\cot B) \) will be
\( \mathbf{A} \cdot \sec A \sec B \sec C \)
B. \( \csc A \csc B \csc C \)
\( \mathbf{c} \cdot \tan A \tan B \tan C \)
D.


The retina is a delicate spot that
receives images through the eye lens and makes us see the world. If it gets
detatched, it is very difficult to join it back. Therefore, eye surgeons use
A. Laser-beams for welding the retina
B. Sound waves for joining
c. Micro-knives for surgery
D. Ultraviolet rays for surgery


Which among the following substances has the greatest specific heat?
A. Iron
B. Water
c. copper
D. Mercury


Which of the following substituted
carboxylic acids has the highest \( \boldsymbol{K}_{\boldsymbol{a}} \)
value?
\( A \)
в.
\( c \)
D.


What led to the failure of Dalton's
atomic theory?
A. Discovery of fundamental particle electron inside the atom
B. Discovery of fundamental particle proton inside the atom
c. Discovery of canal rays
D. Both A and B


\( P Q R S \) is a parallelogram. \( Q M \) is the
height from \( Q \) to \( S R \) and \( Q N \) is the height from \( Q \) to \( P S . \) If \( S R=12 c m \)
and \( Q M=7.6 \mathrm{cm} . \) Find:
the area of the parallelogram PQRS
\( Q N, \) if \( P S=8 c m \)


Mesomeric effect involves:
A. delocalisation of \( \pi \) -electrons
B. delocalisation of \( \sigma \) -electrons
C . partial displacement of electrons
D. delocalisation of \( \pi \) and \( \sigma \) electrons


In the following pair which is more
acidic?
\( \mathbf{C H}_{2} \mathbf{F C H}_{2} \mathbf{C O}_{2} \mathbf{H}, \mathbf{C H}_{3} \mathbf{C H M F C H C O}_{2} \mathbf{H} \)


If \( f \) is a real valued function defined by
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{3}+\mathbf{4} \boldsymbol{x}+\mathbf{3}, \) then find \( \boldsymbol{f}^{\prime}(\mathbf{1}) \) and
\( \boldsymbol{f}^{\prime}(\boldsymbol{3}) \)


It is observed that simple organisms like algae and fungi normally reproduce asexually but before the onset of adverse conditions they shift to sexual reproduction. It is so because sexual reproduction
A. Saves time
B. Is rapid
c. Produces variations
D. All of the above


In the hardening stage of plaster of paris, the compound formed is :
A. \( \operatorname{CaSO}_{4} \)
B. orthorhombic \( C a S O_{4} .2 H_{2} O \)
\( \mathrm{c} \cdot \mathrm{CaSO}_{4} \cdot \mathrm{H}_{2} \mathrm{O} \)
D. monoclinic \( C a S O_{4} .2 H_{2} O \)


In a particular process, the concentration of a solution that is
initially 0.24 M is reduced to 0.12 M in 10 hr and \( 0.06 \mathrm{M} \) in \( 20 \mathrm{hr} \)
\( 6.93 \times 10^{-x} h r^{-1} \) is the rate constant
for the reaction?
value of \( x \) is


Tertiary butyl methyl ether on treatment
with HI forms:
A. isobutane and methyl iodide
B. isobutanol and methanol
C . tertiary butyl iodide and methanol
D. tertiary butyl iodide and methyl iodide


\( D \) and \( F \) are mid-points of sides \( A B \)
and \( A C \) of a triangle \( A B C . \) A line
through \( F \) and parallel to \( A B \) meets
\( B C \) at point \( E . \) Then \( B D F E \) is a :
A. rhombus
B. parallelogram
c. rectangle
D. data insufficient


A uniform circular disc has radius \( \boldsymbol{R} \)
and mass \( m . \) A particle also of mass \( m \)
is fixed at a point \( A \) on the edge of the
disc as shown in the figure. The disc can rotate freely about a fixed
horizontal chord \( P Q \) that is at a
distance \( R / 4 \) from the centre \( C \) of the
disc. The line \( A C \) is perpendicular to
\( P Q . \) Initially the disc is held vertical
with the point \( A \) at its highest position.
If is then allowed to fall so that it starts
rotating about \( P Q . \) The linear speed of
the particle as it reaches its lowest position is \( \sqrt{n g R}, \) where \( n \) is an integer
Find the value of \( n \)


If resistance of the filament increases
with temperature, what will be power dissipated in a \( 220 \mathrm{V}-100 \mathrm{W} \) lamp when connected to 110 V power supply
\( A \cdot 25 W \)
B. <25 W
\( c \cdot>25 w \)
D. None of these


Water cycle refers to
A. Scientific management of water in areas excessively plagued with water logging.
B. Constant movement of water from ocean to land and
back to ocean again
C. An integrated attempt to recycle water in relatively arid regions
D. Planning of water distribution in relatively dry areas.


An aluminium rod (length \( l_{1} \) and
coefficient of linear expansion \( \alpha_{A} \) ) and
a steel rod (length \( l_{2} \) and coefficient of
linear expansion \( \alpha_{B} \) ) are joined
together. If the length of each rod increased by the same amount when
their temperatures are raised by \( t^{o} C \)
then \( l_{1} /\left(l_{1}+l_{2}\right) \) is:
A \( \cdot \alpha_{A} / \alpha_{B} \)
в. \( \alpha_{B} / \alpha_{A} \)
c. \( \alpha_{B} / \alpha_{A}+\alpha_{B} \)
D. \( \alpha_{A} / \alpha_{A}+\alpha_{B} \)


The equation of wave in string is \( y= \) \( 20 \sin \frac{\pi x}{2} \cos 40 \pi t \) in metre. The speed
of the wave is
A. Zero
в. \( 80 \mathrm{m} / \mathrm{s} \)
c. \( 320 m / s \)
D. \( 160 \mathrm{m} / \mathrm{s} \)


A fossil is a
A. Naturally preserved remains or traces of animals or plants
B. Dead animal of the past
C . Organic relic of the past
D. Stuffed animal


Which is correct in the case of carbon?
A. If forms complexes
B. It shows inert pair effect
C. It exhibits catenation property
D. Its tetra halides undergo hydrolysis


The ring \( B \) is coaxial with a solenoid \( A \)
as shown in figure. As the switch \( S \) is
closed at \( t=0, \) the ring \( B \)
A. is attracted towards \( A \)
B. is repelled by \( A \)
C. is initially repelled and then attracted
D. is initially attracted and then repelled


A bomb of \( 12 k g \) divides in two parts
whose ratio of masses is \( 1: 3 . \) If kinetic
energy of smaller part is \( 216 J \), then
momentum of bigger part in \( k g- \)
\( \boldsymbol{m} / \boldsymbol{s e c} \) will be
A . 36
B. 72
c. 108
D. Data is incomplete


Which of the following quantity decreases when a gas condenses into a liquid?
A. Standard voltaic potential
B. Entropy
c. Enthalpy
D. Reaction rate
E. Gibbs free energy


In a hydraulic lift, used at a service station the radius of the large and small piston are in the ratio of \( 20: 1 . \) What
weight placed on the small piston will be sufficient to lift a car of mass \( 1500 k g ? \)
A. \( 3.75 k g \)
в. \( 37.5 k g \)
c. \( 7.5 k g \)
D. \( 75 k g \)


A closed coil consists of 500 turns on a
rectangular frame of area \( 4.0 \mathrm{cm}^{2} \) and has a resistance of 50 ohms. The coil is
kept with its plane perpendicular to a uniform magnetic field of \( 0.2 \mathrm{wb} / \mathrm{m}^{2} \) the amount of charge flowing through the coil if it is turned over. (rotated
through \( 180^{0} \) ):
A \( \cdot 1.6 \times 10^{-3} \mathrm{c} \)
B. \( 16 \times 10^{-3} \mathrm{C} \)
c. \( 0.16 \times 10^{-3} \mathrm{c} \)
D. \( 160 \times 10^{-3} \mathrm{c} \)


Which cell organelle is not related with photorespiration?
A. Mitochondria
B. Chloroplast
c. Glyoxysome
D. Peroxysome


The impedance of a series L-C-R circuit
in an AC circuit is
A \( \cdot \sqrt{R+\left(X_{L}-X_{C}\right)} \)
B . \( \sqrt{R^{2}+\left(X_{L}^{2}-X_{C}^{2}\right)} \)
\( c \cdot c \)
D. None of these


\( \lim _{n \rightarrow \infty}\left(\frac{2 n^{3}}{2 n^{2}+3}+\frac{1-5 n^{2}}{5 n+1}\right) \) is equal to.
A . 0
B. 1
\( c \cdot 1 / 5 \)
D.


The function of villi in the intestine is
A. Digestion of food
B. To increase the absorption efficieny of the nutrients
c. control of intestinal movement
D. Hindrance in the movement of food


Name the fluid present in the joint capsule. What is its function?


When \( B a C l_{2} \) is added to an aqueous salt solution, a white precipitate is obtained. The anion among
\( C O_{3}^{2-}, S O_{3}^{2-} \) and \( S O_{4}^{2-} \) that was
present in the solution can be:
A \( \cdot C O_{3}^{2-} \) but not any of the other two
B. \( S O_{3}^{2-} \) but not any of the other two
c. \( S O_{4}^{2-} \) but not any of the other two
D. None of these


For a given reaction: \( \boldsymbol{M}^{(\boldsymbol{x}+\boldsymbol{n})}+ \)
\( \boldsymbol{n} e^{-} \rightarrow \boldsymbol{M}^{x+}, \boldsymbol{E}_{r e d}^{\ominus} \) is known along with
\( M^{x+n} \) and \( M^{x+} \) ion concentration.
Then:
A. \( n \) can be evaluated
B. \( x \) can be evaluated
c. \( (x+n) \) can be evaluated
D. \( n, x,(x+n) \) can be evaluated


flowers has trimerous
symmetry
A. Wheat
B. Maize
c. Both A and B
D. None of the above


Which of the following catalysts is not correctly matched with the reaction?
A. Vanadium (V) oxide in contact process for oxidation of \( S O_{2} \) to \( S O_{3} \)
B. Finely divided iron in Habers process in conversion of \( N_{2} \) and \( H_{2} \) to \( N H_{3} \)
C. \( P t C l_{2} \) catalyzes the oxidation of ethyne to ethanal in the Wacker process
D. Ni in presence of hydrogen for conversion of vegetable oil to ghee


Consider a planet in some system
which has a mass double the mass of
the earth and density equal to the average density of the earth. If an object weighs \( \mathrm{W} \) on the earth, then its weight on the planet is:
\( \mathbf{A} \cdot W \)
в. \( 2 W \)
c. \( \frac{w}{2} \)
D. \( 2^{1 / 3} W \)


Chlorination of methane proceeds by:
A. electrophilic substitution
B. nucleophilic substitution
c. free radical substitution
D. none of these


Which of the following is not a fundamental force ?
A. Gravitational force
B. Weak nuclear force
c. Strong nuclear force
D. Frictional force
E. Electromagnetic force


1 Parsec is:
A. 2.3 light years
B. 3.3 light years
C. 4.3 light years
D. 5.3 light years


\( \boldsymbol{H}_{2} \boldsymbol{S}<\boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{e}<\boldsymbol{H}_{2} \boldsymbol{T} \boldsymbol{e}<\boldsymbol{H}_{2} \boldsymbol{O} \) This is
the correct boiling point order. If true enter 1 else 0
A


Soaps are water soluble while
detergents are water insoluble.
A. True
B. False


Two elements have electronegativities
1.2 and 3.0 respectively, the bond formed between them would be:
A. ionic
B. covalent
c. coordinate
D. metallic


A uniform metre stick of mass 200 g is suspended from the ceiling through two vertical strings equal lengths fixed at the ends. A small object of mass 20 g is placed on the stick at a distance \( 70 \mathrm{cm} \)
from the left end. Find the tensions in
the two strings.


The value of the ionic product constant
for water \( \left(\boldsymbol{K}_{\boldsymbol{w}}\right) \) at \( \mathbf{6 0}^{\circ} \mathbf{C} \) is \( \mathbf{9 . 6} \times \mathbf{1 0}^{\mathbf{1 4}} \boldsymbol{M}^{\mathbf{2}} \)
What is the \( \left[\boldsymbol{H}_{3} \boldsymbol{O}^{+}\right] \) of a neutral
aqueous solution at \( 60^{\circ} \mathrm{C} \) and an
aqueous sol ion with a \( \mathrm{pH}=7.0 \) at \( 60^{\circ} \)
respectively?
A . \( 3.1 \times 10^{-7} \) acidic
B. \( 3.1 \times 10^{-7} \) neutral
c. \( 3.1 \times 10^{-8} \) basic
D. \( 3.1 \times 10^{-7} \) basic


If velocity ' \( V \) ', kinetic energy ' \( k \) ' and
time 'T" are taken as fundamental
quantities, then the dimensional
formula of surface tension is:
A \( \cdot K V^{2} T^{2} \)
B. \( K V^{-2} T^{-2} \)
c. \( K^{2} V^{2} T^{-2} \)
D. \( K^{2} V^{-2} T^{-2} \)


\( f x \neq 0 \) and \( \left|\begin{array}{ccc}1 & x & 2 x \\ 1 & 3 x & 5 x \\ 1 & 3 & 4\end{array}\right|=0, \) then \( x= \)
\( A \)
B. -
\( c \cdot 2 \)
\( D \ldots-2 \)


Which parameters of all the particles of rotating fan are same :-
A. Only angular \( (\theta, \omega, \alpha) \)
B. Only linear (s,v,a)
c. Both linear and angular
D. None of them


A radioactive material is in the form of
a sphere whose radius is \( 9 \times 10^{-3} \) m. If
\( 6.25 \times 10^{12} \beta^{-} \) particles are emitted per
second by it then in how much time will a potential of 1 volt be produced on the
sphere if it is isolated?
A . \( 1.1 \mathrm{ms} \)
B . \( 10^{-8} \mathrm{ms} \)
c. \( 1.0 \mu s \)
D. 11 \mus


Non zero digits are always Significant.
A. True
B. False


The solubility of \( A_{2} X_{5} \) is \( x \) mol \( d m^{-3} \)
Its solubility product is:
A \( \cdot 36 x^{6} \)
В. \( 64 \times 10^{4} x^{7} \)
c. \( 126 x^{7} \)
D. \( 1.25 \times 10^{4} x^{7} \)


toppr
\( 5 \tau . \) The decay products in both cases
are stable. A plot is made of the total number of radioactive nuclei as a
function of time. Which of the following figures best represents the form of this plot?
\( A \)
B.
\( c \)
\( D \)


Evaluate: \( \int_{\pi / 4}^{\pi / 2} \cos 2 x \log \sin x d x \)


Differentiate :
\( e^{e^{x}} \)


The compound having a tetrahedral geometry is :
\( A \cdot\left[N i\left(C N_{4}\right)\right]^{2-} \)
B. \( \left[P d\left(C N_{4}\right)\right]^{2} \)
\( c \cdot\left[\left.P d C\right|_{4}\right]^{2-} \)
D. [Nicl, ] \( ^{2} \)


After observing the graph, which
statement tells that the chemical
reaction is exothermic?
A. The potential energy at point 2
B. The energy difference between points 1 and 2
C. The time elapsed between points 2 and 3
D. The energy difference between points 1 and 3
E. The time needed to reach point 3


Distinguish between static friction, limiting friction and kinetic
friction.How do they vary with the applied force? Explain by diagram.


If the specific heat of lead is
\( 0.03 \operatorname{cal} g^{-1 o} C^{-1}, \) thermal capacity of 500 g of lead is
\( \mathbf{A} \cdot 5 \operatorname{cal}^{o} C^{-1} \)
B. \( 10 \mathrm{cal}^{\circ} \mathrm{C}^{-1} \)
c. \( 15 ~ c a l^{\circ} C^{-1} \)
D. \( 20 \mathrm{cal}^{\circ} \mathrm{C}^{-1} \)


A thin circular ring of mass \( M \) and
radius ' \( r^{\prime} \) is rotating about its axis with
a constant angular velocity \( \omega . \) Four
object each of mass \( m, \) are kept gently
to the opposite ends of two perpendicular diameters of the ring. The
angular velocity of the ring will be-


Three types of flowers occur in the inflorescence of
A. Raceme
B. Hypanthodium
c. Cyathium
D. Umbel


\( \ln K I O_{3}, \) what is the charge on \( K \) atom in lewis structure of molecule?
A \( .+1 \)
B. +2
\( c \cdot-1 \)
D. 0


For a given reaction:
\( \boldsymbol{F} \boldsymbol{e}+\boldsymbol{2} \boldsymbol{F} \boldsymbol{e}^{\boldsymbol{3}+} \rightarrow \boldsymbol{3} \boldsymbol{F} \boldsymbol{e}^{\boldsymbol{2}+} \)


(a) Show that the normal component of
electrostatic field has a discontinuity
from one side of a charged surface to another given by \( \$ \$\left(E_{-} 21,-\right. \)
\( \mathrm{~ I f r a c \{ s i g m a ~ \} \{ v a r e p s i l o n ~} \)
\( 03 \$ \$ \)
where \( \hat{n} \) is a unit vector normal to the
surface at a point and \( \sigma \) is the surface
charge density at that point. (The
direction of \( \hat{n} \text { is from side } 1 \text { to side } 2 .) \)
Hence show that just outside
a conductor, the electric field is \( \sigma \hat{n} / \epsilon_{0} \)
(b) Show that the tangential component of electrostatic field is continuous from
one side of a charged surface to another. [Hint: For (a), use Gauss's law. For, (b) use the fact that work done by
electrostatic field on a closed loop is zero.]


Three different circuits(I, II and III) are
constructed using identical batteries
and resistors of \( \mathrm{R} \) and \( 2 R \) ohm. What
can be said about current lin arm AB of
each circuit?
A \( \cdot I_{I I}<I_{I}<I_{I I} \)
в. \( I_{I}<I_{I I}<I_{I I} \)
c. \( I_{I}=I_{I I}=I_{I I} \)
D \( \cdot I_{I}>I_{I I}=I_{I I} \)


Mists are produced by:
A. smoke formed during combustion of organic matter
B. particles of spray liquids and by condensation of vapours in air
C. fine solid particles produced during crushing and grinding
D. condensation of vapours during chemical reactions


\( \tan 9-\tan 27-\tan 63+\tan 81= \)


In which of the following octahedral complexes of Co (atomic number 27),
will the magnitude of \( \Delta_{\mathrm{o}} \) be the highest?
\( \mathbf{A} \cdot\left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+} \)
B . [Co(NH3) \( _{6} \) ] \( ^{3} \)
c. \( \left[\mathrm{Co}(\mathrm{CN})_{6}\right]^{3-} \)
D \( \cdot\left[\mathrm{Co}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{3}\right]^{3} \)


A block body radiates heat at temperatures \( T_{1} \) and \( T_{2}\left(T_{2}>T_{1}\right) . \) The
frequency corresponding to maximum energy is
A. More at \( T_{1} \)
B. More at \( T_{2} \)
c. Equal for \( T_{1} \) and \( T_{2} \)
D. Independent of \( T_{1} \) and \( T_{2} \)


If errors of \( 1 \% \) each are made in the
base radius and height of a cylinder, then the percentage error in its volume is
A . \( 1 \% \)
B. 2\%
c. \( 3 \% \)
D. none of these


Active divisions occur in the cells of
A. Xylem
B. Phloem
c. Cambium
D. collenchyma


For 1 molal solution of each compound minimum freezing point will be
assuming complete ionisation in each
case:
\( \mathbf{A} \cdot\left[F e\left(\left(H_{2} O\right)_{6}\right] C l_{3}\right. \)
B. \( \mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{5} \mathrm{Cl} \) l \( \mathrm{Cl}_{2} \). \( \mathrm{H}_{2} \mathrm{O} \)
c. \( \left.F e\left(H_{2} O\right)_{4} C l_{2}\right] C l .2 H_{2} O \)
D. \( \operatorname{Fe}\left(H_{2} O\right)_{3} C l_{3} \) ]. \( H_{2} \) O


If \( \tan \left(2 \tan ^{-1}\left(\frac{1}{5}\right)-\frac{\pi}{4}\right)=-\frac{\lambda}{17}, \) then \( \lambda \) is
equal to


If a unit vector \( \vec{a} \) makes angles \( \frac{\pi}{3} \) with \( \hat{i} \)
\( \frac{\pi}{4} \) with \( \hat{j} \) and an acute angle \( \theta \) with \( \hat{k} \)
then find \( \theta \) and hence, the components of \( \overrightarrow{\boldsymbol{a}} \)


The value of a polynomial
A. changes with the change in variable
B. doesn"t change with the change in variable
C. many or may not change with the change in variable
D. all of the above


Chloroform when treated with
concentrated nitric acid yields:
A. chloropicrin
B. chloroprene
c. nitro picrin
D. nitro chloropicrin


BD is a median of a triangle ABC.F is a point on \( A B \) such that \( C F \) intersects \( B D \)
at \( \mathrm{E} \) and \( B E=B D . \) If \( B F=5 \mathrm{cm} . \) BA
is equal to
A . 10
B. 12
c. 15
D. 17


Metals in the middle of the activity series are generally present as
in nature.
A. carbonates, halides
B. oxides, chlorides
c. sulphides, carbonates
D. all of the above


The process of expelling of food in amoeba
A. Egestion
B. Digestion
c. Nutrition
D. None of the above


Give reasons to show that the following are chemical changes:
Burning of magnesium in the air.
Select the correct statements:
This question has multiple correct options
A. New substance is formed with different properties
B. New substance is formed and has the same properties
c. The reaction is reversible
D. The reaction is irreversible


Which of the following is not related to
the Darwin's theory of Evolution
A. All living organisms of a group are not identical.
B. Variations may be passed from parent to off-spring
C. Evolution is a slow and continuous process.
D. Population do not grow in geometrical progression


Jitubhai buys a T-shirt at Rs 500 and sold it to his friend at Rs \( 500 . \) profit \( =? \)
A. 0
B. 100
c. 200
D. 220


\( \left|\begin{array}{ccc}\boldsymbol{a} & \boldsymbol{a}+\boldsymbol{b} & \boldsymbol{a}+\boldsymbol{b}+\boldsymbol{c} \\ \mathbf{2} \boldsymbol{a} & \mathbf{3} \boldsymbol{a}+\mathbf{2} \boldsymbol{b} & \boldsymbol{4} \boldsymbol{a}+\boldsymbol{3} \boldsymbol{b}+\boldsymbol{2} \boldsymbol{c} \\ \boldsymbol{3} \boldsymbol{a} & \boldsymbol{6} \boldsymbol{a}+\boldsymbol{3} \boldsymbol{b} & \boldsymbol{1 0} \boldsymbol{a}+\boldsymbol{6 b}+\boldsymbol{3} \boldsymbol{a}\end{array}\right|=\boldsymbol{a}^{3} \)


For the A.P \( 45,41,37, \ldots \) find \( t_{10} \) and
\( \boldsymbol{t}_{\boldsymbol{n}+\mathbf{1}} \)


A metalloid of nitrogen family is:
A. \( N \)
в. \( A s \)
\( c . P \)
D. \( B i \)


The density of water is not same at all temperatures because of its anomalous expansion. The density is maximum at:
\( \mathbf{A} \cdot 0^{\circ} C \)
B. \( 4^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 40^{\circ} C \)
D. \( 100^{\circ} \mathrm{C} \)


Which law of motion is primarily involved during the gun recoil?
A. First law
B. Second law
c. Third law
D. cannot determine


Perform the division: \( 6 x^{3}-23 x+x^{2}+ \)
12 by \( 2 x-3 \)


A ball of mass \( m \) is fired vertically upwards from the surface of the earth
with velocity \( n \nu_{e}, \) where \( \nu_{e} \) is the
escape velocity and \( n>1 . \) To what height will the ball rise? Neglecting air resistance, take radius of the earth as
\( \boldsymbol{R} \)
A \( \cdot \frac{R}{n^{2}} \)
в. \( \frac{R}{\left(1-n^{2}\right)} \)
c. \( \frac{R n^{2}}{\left(1-n^{2}\right)} \)
D. \( R n^{2} \)


If BCI bond has a dipole moment,
explain why \( B C l_{3} \) molecule has
zero dipole moment


With the help of a diagram explain the
formation of rainbow in the sky. List two
essential conditions for observing a rainbow


Let \( \boldsymbol{f}: \boldsymbol{N} \rightarrow \boldsymbol{N} \) be defined by \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \boldsymbol{x}^{2}+\boldsymbol{x}+\mathbf{1}, \boldsymbol{x} \in \boldsymbol{N} . \) Then \( \boldsymbol{f} \) is
A. one-one onto
B. many-one onto
c. one-one but not onto
D. none of these


A ball of mass \( m \) moving at a speed \( v \)
collides with another ball of mass \( 3 \mathrm{m} \) at
rest. The lighter block comes to rest after collision. The coefficient of
restitution is-
A \( \cdot \frac{1}{2} \)
B. \( \frac{2}{3} \)
\( c \cdot \frac{1}{4} \)
D. None of these.


Two elements were elected by Mendeleev for studying the properties of compounds formed by other elements with the selected elements. What were
the selected elements?
A. Oxygen, Nitrogen
B. Hydrogen, Carbon
c. Hydrogen, Oxygen
D. Oxygen, Carbon


Two uniform rods of equal length but different masses are rigidly joined to
form an \( L \) shaped body, which is then
smoothly pivoted about \( O \) as shown.
If the body is in equilibrium in the
shown configuration, ratio \( M: m \) will
be :
\( A \)
B.
\( c \cdot \sqrt{2} \)
D. \( \sqrt{3} \)


After the capacitor gets fully charged,
\( \mathbf{S}_{1} \) is opened and \( \mathbf{S}_{2} \) is closed so that the
inductor is connected in series with the
capacitor. Then,
A \( . \) at \( t=0, \) energy stored in the circuit is purely in the form of magnetic energy
B. at any time \( t>0 \), current in the circuit is in the same
c. at \( t>0, \) there is no exchange of energy between the inductor and capacitor
D. at any time \( t>0 \), instantaneous current in the circuitt \( \operatorname{may} \mathrm{v} \sqrt{\frac{\mathrm{c}}{\mathrm{L}}} \)


A sound wave passes from a medium A to a medium B. The velocity of sound B is greater than that in A. Assume that
there is no absorption or reflection of the boundary. As the wave moves across
the boundary, the
A. Frequency of sound will increase
B. Wavelength of sound will increase
c. wavelength of sound will decrease
D. Intensity of sound will increase


Velocity of sound in vacuum is
A. equal to \( 330 \mathrm{m} / \mathrm{s} \)
B. greater than \( 330 \mathrm{m} / \mathrm{s} \)
c. less than \( 330 \mathrm{m} / \mathrm{s} \)
D. None of these


Solve:tan \( ^{-1} \mathbf{2} \boldsymbol{x}+\tan ^{-1} \mathbf{3} \boldsymbol{x}=\frac{\boldsymbol{\pi}}{\boldsymbol{4}} \)


The diagram shows the phenomenon of
a natural disaster. Which of the
following is an effect of the disaster?
A. Air pollution
B. Green house effect
c. water pollution
D. Sound pollution


At critical temperature of a liquid, surface tension is:
A . zero
B. infinite
c. varies liquid to liquid
D. can't be measured


The unit vector perpendicular to both the vectors \( \vec{a}=\vec{i}+\vec{j}+\vec{k} \) and \( \vec{b}=2 \vec{i}- \)
\( \vec{j}+3 \vec{k} \) and making an acute angle with the vector \( \vec{k} \) is
A \( \cdot-\frac{1}{\sqrt{26}}(4 \vec{i}-\vec{j}-3 \vec{k}) \)
B. \( \frac{1}{\sqrt{26}}(4 \vec{i}-\vec{j}-3 \vec{k}) \)
c. \( \frac{1}{\sqrt{26}}(4 \vec{i}-\vec{j}+3 \vec{k}) \)
D. None of these


10 g of an organic compound on complete combustion gives \( 17.6 \mathrm{g} \mathrm{CO}_{2} \)
\( 3.6 \mathrm{g} \) water and \( 6.4 \mathrm{g} \mathrm{SO}_{2 .} \) The
empirical formula of the compound is :
A. \( C_{4} H_{4} S O \)
в. \( C_{3} H_{4} \) SO
\( \mathbf{c} \cdot C_{4} H_{8} S O \)
D. \( C_{2} H_{4} S O \)


Radioactivity is a phenomenon.
A. nuclear
B. elustronic
c. atomic
D. all of the above


The sum of the ages of Anup and his
father is \( 100 . \) When Anup is as old as his father now, he will be five times as
old as his son Anuj is now. Anuj will be eight years older than Anup is now, when Anup is as old as his father.what are their ages right now.


In a upper triangular matrix \( n \times n \)
minimum number of zeroes is
A \( \cdot \frac{n(n-1)}{2} \)
в. \( \frac{n(n+1)}{2} \)
c. \( \frac{2 n(n-1)}{2} \)
D. None of these


Which of the following correctly
represent solubility of \( N_{2} \) in water (in
terms of mmole/litre) if \( N_{2} \) is bubbled
through water at \( 293 K \) at a pressure of
0.768 bar and Henry's constant is
\( \mathbf{7 6 . 8} K \) at \( \mathbf{2 9 3} \mathbf{K} ? \)
A \( \cdot 10^{-5} \)
5
В. \( 5.56 \times 10^{-4} \)
\( c \cdot 10^{-2} \)
D. \( 4.3 \times 10^{-4} \)


State the role of pancreatic juice in the digestion of proteins.


In charging a battery of motor car, which of the following effect of electric current is used?
A. heating
B. magnetic
c. chemical
D. induction


On moving down the group from \( \boldsymbol{F} \) to \( \boldsymbol{I} \) which of the properties decrease? This question has multiple correct options
A. Ionic radius
B. Ionization energy
c. oxidizing agent
D. Electronegativity


Consider the following molecules/ions:
\( \boldsymbol{S} \boldsymbol{O}_{2}, \boldsymbol{C} \boldsymbol{O}_{2}, \boldsymbol{N}_{2} \boldsymbol{O}, \boldsymbol{O} \boldsymbol{F}_{2}, \boldsymbol{I} \boldsymbol{C l}_{2}^{-}, \boldsymbol{I}_{3}^{-}, \boldsymbol{N} \boldsymbol{O}_{2}, \boldsymbol{N} \)
Among the above, the number of molecules/ions which are linear, is


Statement \( -1: P b O_{2} \) is an oxidising agent and reduced to Pbo.

Statement - 2 : Stability of Pb (II) > Pb
(IV) on account of inert pair effect.
A. Statement - - lis True, Statement - 2 is True; Statement 2 is a correct explanation for Stetement- -
B. Statement - 1 is True. Statement - 2 is True; Statement 2 is NOT a correct explanation for Statement-
c. Statement - - lis True, Statement - 2 is False
D. Statement-lis False, Statement- - 2 is True


\( \frac{\boldsymbol{x}-\boldsymbol{y}}{\sqrt{\boldsymbol{x}}+\sqrt{\boldsymbol{y}}}=\ldots \ldots \)
\( \mathbf{A} \cdot \sqrt{x-y} \)
B. \( \sqrt{x}+\sqrt{y} \)
c. \( -(\sqrt{x}+\sqrt{y}) \)
D. \( \sqrt{x}-\sqrt{y} \)


When a die is thrown, list the outcomes
of an event of getting:
A number greater than 5
\( \mathbf{A} \cdot \mathbf{5} \)
B. 4
\( c .6 \)
D. 3


We use \( Z n O \) in paints instead of \( P b^{2+} \)
salts.
If true enter 1 , else enter 0 .


\( \int_{0}^{\pi / 2} \frac{\cos x-\sin x}{1+\cos x \sin x} d x \) is equal to:
A.
в. \( \frac{\pi}{2} \)
c.
D. \( \frac{\pi}{6} \)


Ultraviolet radiation is absorbed by?
A. exosphere
B. ionosphere
c. ozonosphere
D. stratosphere


From the give options, which of the following compound will make best buffer solution?
A. \( H_{2} O, 1 M \) NaOH, 1 M \( H_{2} \) SO \( _{4} \),
в. \( H_{2} O, \) 1 \( M C H_{3} C O O H, 1 M N a^{+} C H_{3} C O O^{-} \)
c. \( H_{2} O, 1 M C H_{3} C O O H, 6 M N a^{+} C H_{3} C O O^{-} \)
D. \( H_{2} O, 1 M C H_{3} C O O H, 1 M N a O H \)


If the distance of a point \( (a, a, a) \) from the origin is \( \sqrt{108}, \) then the value of \( a \) is
This question has multiple correct options
\( A \cdot 9 \)
B. 6
\( c .-9 \)
D. - 6


Test cross is used to
A. Check heterozygosity in \( F_{1} \) generation
B. Check heterozygosity in \( F_{2} \) generation
C. Check independent assortment
D. Both A and B


ABCD is a trapeziumin which AB is parallel to DC. If the diagonals intersect at \( 0, \) then which one of the following is
correct?
A \( \cdot \frac{O A}{O C}=\frac{O B}{O D} \)
в. \( \frac{A D}{B C}=\frac{A B}{D C} \)
c. \( \frac{O B}{O D}=\frac{B C}{C D} \)
D. \( \frac{O A}{O C}=\frac{D A}{D C} \)


\( P H_{3} \) can be obtained by:
This question has multiple correct options
A. heating hypophosphorus acid.
B. heating orthophosphorus acid.
C. reacting white phosphorus with hot conc,NaOH.
D. hydrolysis of calcium phosphide.


Assertion
For the reaction
\( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{I}_{2}(\boldsymbol{g}) \rightleftharpoons 2 \boldsymbol{H} \boldsymbol{I}(\boldsymbol{g}), \) if the volume
of a vessel is reduced to half of its
original volume,equilibrium
concentration of all gases will be doubled.
Reason
According to Le Chatelier's principle, reaction shifts in a direction that tends
to minimize the effect of the stress.
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


Match the following


Permutit is the trade name of a mixture
of:
A. hydrated silicates of \( C a \) and \( M g \)
B. hydrated silicates of \( A l \) and \( N a \)
C. hydrated aluminates of \( C a \) and \( N a \)
D. hydrated aluminates of \( M g \) and \( N a \)


Water drops fall at regular intervals from a roof. At an instant when a drop is
about to leave the roof, the separations
between 3 successive drops below the
roof are in the ratio
A .1: 2: 3
B. 1: 4: 9
\( \mathrm{c} \cdot 1: 3: 5 \)
D. 1: 5: 13


\( \boldsymbol{A}=(-1,2,-\mathbf{3}), \boldsymbol{B}=(\mathbf{5}, \mathbf{0},-\mathbf{6}), \boldsymbol{C}= \)
(0,4,-1) are the vertices of a triangle.
The d.c's of the internal bisector of \( \angle \mathrm{BAC} \)
are?
\( ^{\mathbf{A}} \cdot\left(\frac{25}{\sqrt{714}}, \frac{-8}{\sqrt{714}}, \frac{-5}{\sqrt{714}}\right) \)
в. \( \left(\frac{5}{\sqrt{74}}, \frac{6}{\sqrt{74}}, \frac{8}{\sqrt{74}}\right) \)
\( ^{\mathbf{C}} \cdot\left(\frac{25}{\sqrt{714}}, \frac{8}{\sqrt{714}}, \frac{5}{\sqrt{714}}\right) \)
D. \( \left(\frac{-5}{\sqrt{74}}, \frac{6}{\sqrt{74}}, \frac{-8}{\sqrt{74}}\right) \)


Length of two sides of a \( \triangle A B C \) is \( A B=6 \mathrm{cm} \) and \( B C=7 \mathrm{cm} . \) Then
which of the following can represent the third side of the triangle ? Also, construct the triangle formed by these three sides
A. \( 8 \mathrm{cm} \)
в. \( 13 \mathrm{cm} \)
c. \( 14 \mathrm{cm} \)
D. \( 15 \mathrm{cm} \)


State whether the given set is finite or
infinite :Enter 1 for Finite and 0 for
infinite
\( A=\{x: x \in Z \text { and } x<10\} \)


In electromagnetic induction, the induced charge in a coil is independent
of
A . Time
B. Change in flux
c. Resistance in the circuit
D. None of the above


If \( \boldsymbol{y}=\tan \boldsymbol{x} . \tan 2 \boldsymbol{x} . \tan 3 \boldsymbol{x}, \) then \( \frac{d \boldsymbol{y}}{d \boldsymbol{x}} \) has
the value equal to
A \( \cdot 6 \sec ^{2} 3 x \cdot \tan x \cdot \tan 2 x+2 \sec ^{2} x \cdot \tan 2 x \cdot \tan 3 x+ \)
\( 4 \sec ^{2} 2 x \). \( \tan 3 x \cdot \tan x \)
B . \( 2 y(\operatorname{cosec} 2 x+2 \operatorname{cosec} 4 x+3 \operatorname{cosec} 6 x) \)
c. \( 3 s e c^{2} 3 x-2 \sec ^{2} 2 x-\sec ^{2} x \)
D. \( \sec ^{2} x+2 \sec ^{2} 2 x+3 \sec ^{2} 3 x \)


around a conducting wire connected to
a battery and a switch. As the switch is
closed, the free electrons in the wire
start moving along the wire. In any time interval, the number of electrons
entering the closed surface \( S \) is equal
to the number of electrons leaving it. On
closing the switch, the flux of the
electric field through the closed surface
(more than one option may be correct)
This question has multiple correct options
A. is increased
B. is decreased
C. remains unchanged
D. remains zerç


Choose the correct statement.
A. All bodies repel each other in this universe
B. Our earth does not behave like a magnet
C . Acceleration due to gravity is \( 8.9 \mathrm{m} / \mathrm{s}^{2} \)
D. All bodies have the same acceleration due to gravity at the surface of the earth


Which of the following is not effected by change in pressure?
A \( \cdot N_{2}+O_{2} \rightleftharpoons 2 N O \)
B. \( N_{2}+3 H_{2} \rightleftharpoons 2 N H_{3} \)
c. \( P C l_{5} \rightleftharpoons P C l_{3}+C l_{2} \)
D. \( 2 S O_{2}+O_{2} \rightleftharpoons 2 S O_{3} \)


Which one of the following undergoes reaction with \( 50 \% \) sodium hydroxide solution to give the corresponding alcohol and acid?
A. Phenol
B. Benzaldehyde
c. Butanal
D. Benzoic acid


Which of the following statements
about low density polythene is FALSE ?
A. It is a poor conductor of electricity
B. Its synthesis requires dioxygen or a peroxide initiator as a catalyst
C. It is used in the manufacture of buckets, dust-bins etc.
D. Its synthesis requires high pressure


A cycle wheel with 64 spokes is rotating with \( \mathrm{N} \) rotations per second at right angles to horizontal component of magnetic field. The induced emf generated between its axle and rim is E. If the number of spokes is reduced to 32 then the value of induced emf will be :
\( A \cdot E \)
B . 2E
c. \( \frac{E}{2} \)
D. \( \frac{E}{4} \)


There are two wires, \( A \) and \( B \), made of same material. Both the wires have the
same length. It is observed that the resistance of wire \( A \) is four times
the resistance of wire \( \mathrm{B} \), then find the
ratio of their cross sectional areas.
A . 4: 1
B. 1: 4
c. 1: 2
D. 2: 1


Find the sum: \( 1+2+4+\ldots \ldots \ldots+512 \)


Find \( \boldsymbol{P} \boldsymbol{M} \)
\( \mathbf{A} \cdot 3 c m \)
\( \mathbf{B} \cdot 4 c m \)
\( \mathbf{c} \cdot 5 c m \)
D. \( 8 \mathrm{cm} \)


Expansion in a substance is
A. directly proportional to rise in the temperature
B. inversely proportional to rise in the temperature
C. independent of rise in temperature
D. cannot say


Friction is much lesser in
in sliding.


There exists ........ number of rational numbers between \( \frac{2}{5} \) and \( \frac{4}{5} \)
A. 0
B. 1
c. 5
D. infinite


A road runs midway between two parallel rows of buildings. A motorist moving with a speed of \( 36 \mathrm{km} / \) hour sounds the horn. He hears the echo one
second after he has sounded the horn. The distance between the 2 rows of
buildings is (Velocity of sound is 330 \( \mathrm{m} / \mathrm{s}) \)
A. 300 \( m \)
B. 150 \( m \)
\( c \cdot 1080 m \)
D. 330 m


Match the items in Column I with as
many items as possible in Column \( \begin{array}{llll} & \text { Column I } & & \text { Column II } \\ \text { (a) } & \text { Deer } & \text { (i) } & \text { Autotroph } \\ \text { (b) } & \text { Parrot } & \text { (ii) } & \text { Ecosystem } \\ \text { (c) } & \text { Cobra } & \text { (iii) } & \text { Pond } \\ \text { (d) } & \text { Pine tree } & \text { (iv) } & \begin{array}{l}\text { Deciduous } \\ \text { forests }\end{array} \\ \text { (e) } & \text { Grasshopper } & \text { (v) } & \text { Parasite } \\ & \text { (vi) } & \text { Carnivore } \\ & \text { (vii) } & \text { Producer }\end{array} \)


The monomer of Natural Rubber is:
\( \mathbf{A} \cdot C H_{2}=C \quad-\quad C H=C H_{2} \)
\( C H_{3} \)
B. \( C l \)
\[
C H_{2}=C \quad-\quad C H=C H_{2}
\]
\( \mathbf{c} \cdot C H_{2}=C H-C H=C H_{2} \)
D. None of these


If either vector \( \vec{a}=\overrightarrow{0} \) or \( \vec{b}=\overrightarrow{0}, \) then \( \vec{a} \) \( \vec{b}=0 . \) But the converse need not be true
Justify your answer with an example.


Correct statement regarding Mitochondria and Chloroplast
A. ATP synthesis is seen in both
B. Outer membrane has more surface in
both
C. Circular naked DNA, RNA and 70
ribosomes are seen in both
D. Oxidative phosphorylation occurs in both
A . A and B
B. B and C
c. A and \( c \)
D. A and D


The process of obtaining salt by evaporation of seawater is known as:
A. crystallisation
B. sedimentation
c. galvanization
D. amalgamation


Assertion
For \( \boldsymbol{n} \in \boldsymbol{N},(\boldsymbol{n} !)^{3}<\boldsymbol{n}^{\boldsymbol{n}}\left(\frac{\boldsymbol{n}+\mathbf{1}}{\mathbf{2}}\right)^{2 \boldsymbol{n}} \)
Reason
\( \boldsymbol{n}>\boldsymbol{6},\left(\frac{\boldsymbol{n}}{\boldsymbol{3}}\right)^{\boldsymbol{n}}<\boldsymbol{n} !\left(\frac{\boldsymbol{n}}{2}\right)^{\boldsymbol{n}} \)
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 three vertices of a parallelogram \( A B C D \) are \( A(3,-4), B(-1,-3) \) and
\( C(-6,2) . \) Find the coordinates of vertex
\( D \) and find the area of \( A B C D \)


Value(s) of \( \mathrm{m} \) for which system remains at rest (pulleys and strings are ideal)
\( \left[\boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{2}\right] \)
This question has multiple correct options
\( A \cdot 1 k g \)
B. \( 2 k g \)
\( c .18 k g \)
D. \( 20 k g \)


Which of the following statements
applies to light?
A. Light can only be described as particles.
B. Light can only be described as waves.
C. Light can be described as rays, waves and particles.
D. Light can only be described as rays.


How do antiseptics differ from disinfectants ? Name a substance
which can be used as a disinfectant as
well as an antiseptic.


In the network shown, the sources of
emf \( 2 \vee, 12 \) V and 16 V are taken to be
ideal. Select incorrect statements from
the following:
This question has multiple correct options
A \( \cdot \) The potential drop across \( 4 \Omega \) is \( \frac{28}{13} \vee \)
B. The current through 2 v battery is \( \frac{17}{13} \) A, discharging.
C ' the current through 2 V battery is \( \frac{17}{13} \) A, charging.
D. The potential drop across \( 8 \Omega \) is \( \frac{60}{13} \vee \)


Which of the following is a measurement of water pollution?
A . PSC
в. РСВ
\( c . \) во
D. coo


If \( \vec{i}, \vec{j}, \vec{k} \) be the position vectors of the vertices of a triangle, then its area is
A \( \cdot \sqrt{3} \) sq. units
B. \( \frac{1}{2} \sqrt{3} \) sq. units
c. 3 sq. units
D. \( 3 \sqrt{3} \) sq. units


Elements \( A, B, C, O \) and \( E \) having the following electronic configuration
(i) \( 1 s^{2}, 2 s^{2}, 2 p^{1} \)
(ii) \( 1 s^{2}, 2 s^{2}, 2 p^{6}, 3 s^{2}, 3 p^{1} \)
(iii) \( 1 s^{2}, 2 s^{2}, 2 p^{6}, 3 s^{2}, 3 p^{3} \)
(iv) \( 1 s^{2}, 2 s^{2}, 2 p^{6}, 3 s^{2}, 3 p^{5} \)
\( (v) 1 s^{2}, 2 s^{2}, 2 p^{6}, 3 s^{2}, 3 p^{6} \)
Electronic configurations belonging to
the same group are:
A. (i) and (iii)
B. (i) and (iv)
c. (i) and (ii)
D. (i) and (v)


Evaluate \( a^{2}-b^{2}-(a+b)^{2} \)


Identify a metalloid from the following list of elements.
A. carbon
B. Neon
c. sodium
D. Tellurium


A metallic rod of length \( L \) and mass \( M \) is moving under the action of two
unequal forces \( F_{1} \) and \( F_{2} \) (directed opposite to each other) acting at its ends along its length. lgnore gravity and any external magnetic field. If specific charge of electrons is \( (e / m), \) then the
potential difference between the ends of the rod is steady state must be:
A \( \cdot\left|F_{1}-F_{2}\right| m L / e M \)
B . \( \left(F_{1}-F_{2}\right) m L / e M \)
\( \mathbf{c} \cdot[m L / e M] \ln \left[F_{1} / F_{2}\right] \)
D. None


Two poles of same strength attract each other with a force of magnitude \( F \) when
placed at the corners of an equilateral triangle. If a north pole of the same
strength is placed at the third vertex, it experiences a force of magnitude
A. \( F \sqrt{3} \)
в. \( F \)
c. \( F \sqrt{2} \)
D. \( 2 F \)


\( \boldsymbol{X}- \) ray falling on a material
A. Exerts a force on it
C. Transfers momentum to it
D. Transfers impules to it


Like charges each
other and unlike
charges each other:
A . repel, attract
B. attract, repel
c. repel, repel
D. attract, attract


The maximum sum of the series \( 20+ \) \( 19 \frac{1}{3}+18 \frac{2}{3}+18+\ldots \) is
A . 310
в. 290
\( c \cdot 320 \)
D. None of these


For a common emitter amplifier,
current gain is \( 60 . \) If the emitter current is \( 6.6 m A \), the base current is
\( \mathbf{A} \cdot 1.08 \mathrm{mA} \)
B . \( 10.8 \mathrm{mA} \)
c. \( 0.108 m A \)
D. \( 8.01 \mathrm{mA} \)


Q Type your question_
\( A \)
B
\( \mathbf{C} \)
D.


The lateral petals of vexillary corolla are called
A. Vexilla
B. Alae
c. Carina
D. Both B and C


A solid cylinder of uniform density of
radius \( 2 c m \) has mass of \( 50 g . \) If its
length is \( 10 \mathrm{cm} \). Calculate its moment
of inertia about.
(i) its own axis of rotation passing through the centre,
(ii) an axis passing through its centre and perpendicular to its length.


Early African
man was discovered in 1948 by Leakey.
t was
A. Homo habilis
B. Gigantopithecus
c. Proconsul
D. Homo erectus


Mention the shape and draw a diagram
of \( \boldsymbol{X} \boldsymbol{e} \boldsymbol{O}_{3} \)


Group of two or more than two plant species is called as
A. Plant community
B. Animal ecosystem
c. Plant ecosystem
D. Ecological niche


Which one is a conjugate enzyme?
A. succinate dehydrogenase
B. Urease
c. Trypsin
D. Both A and B


When Cu and Ge are cooled to \( -150^{\circ} \mathrm{C} \)
then resistance of \( \mathrm{Cu} \).... and that of Ge
A. increases, increases
B. decrease, increases
c. decrease, decreases
D. increases, decreases


The general solution of the differentia equation \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\frac{\boldsymbol{x}+\boldsymbol{y}+\mathbf{1}}{\mathbf{2} \boldsymbol{x}+\mathbf{2} \boldsymbol{y}+\mathbf{1}} \) is:
A \( \cdot \log _{e}|3 x+3 y+2|+3 x+6 y=C \)
B . \( \log _{e}|3 x+3 y+2|-3 x+6 y=C \)
\( \mathbf{c} \cdot \log _{e}|3 x+3 y+2|-3 x-6 y=C \)
D \( \cdot \log _{e}|3 x+3 y+2|+3 x-6 y=C \)


Which of the following is not an artificial sweetener?
A. Sucralose
B. Alitame
c. saccharin
D. sucrose


The statement 'Sucrose has \( C_{1}-C_{2} \)
glycosidic linkage between \( \beta \) -D-Glucose
\& \( \alpha \) -D-Fructose' is
A. True
B. False


What is the difference between feeding and nutrition?


The slope of a velocity-time graph for the free fall of a body under gravity, starting from rest is (Take \( \boldsymbol{g}=\mathbf{1 0} \boldsymbol{m} \boldsymbol{s}^{-2} \)
.)
A \( \cdot 10 m / s^{2} \)
В. \( -10 m / s^{2} \)
c. \( 0 m / s^{2} \)
D. \( 1 m / s^{2} \)


Q Type your question
Inglictic ilciu I mu
paper.Wire \( C D \) is in the shape of an arc
and is fixed. \( O A \) and \( O B \) are the wires
rotating with angular velocity \( \omega \) as
shown in the figure in the same plane
as that of the arc about point \( O . \) If at
some instant, \( O A=O B=1 \) and each
wire makes angle \( \theta=30^{\circ} \) with \( y \) -axis,
then the current through resistance \( \boldsymbol{R} \)
is (wire \( O A \) and \( O B \) have no
resistance)
A . 0
B. \( \frac{B \omega l^{2}}{R} \)
c. \( \frac{B \omega l^{2}}{2 R} \)
D. \( \frac{B \omega l^{2}}{4 R} \)
E . answer


Assertion
An electric bell is a mechanical bell that
functions by means of an electromagnet. When an electric current is applied, it produces a repetitive buzzing or clanging sound. Electric bells have been widely used at railroad crossings, in telephones, fire and burglar alarms, as school bells,
doorbells, and alarms in industrial
plants.
Reason
Electromagnetic force is the force of
attraction between the north and south
poles of magnets
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 variation of the instantaneous
current (I) and the instantaneous emf(E) in a circuit is as shown in figure.
Which of the following statements is
correct?
A. The voltage lags behind the current by \( \pi / 2 \)
B. The voltage leads the current by \( \pi / 2 \)
c. The voltage and the current are in phase
D. The voltage leads the current by \( \pi \)


A proton travels few distance in an
electric field, then it enters a crossed
magnetic field of \( 1 \mathrm{T} \) and radius \( 0.2 \mathrm{m} \) Find the velocity of proton.
A \( \cdot 0.2 \times 10^{8} \mathrm{ms}^{-1} \)
В. \( 0.2 \times 10^{7} \mathrm{ms}^{-1} \)
\( c \cdot 0.2 \times 10^{6} m s^{-1} \)
\( - \)
D. \( 2 \times 10^{8} \mathrm{ms}^{-1} \)


Rutherford experiment of scattering of \( \alpha \) particles showed for the first time
that the atom has


A variable line is such that its distance
from origin always remains 2 units. Minimum value of the length of intercept made by it between coordinate axis is
A . 2
B. 4
c. 8
D. 16


With reference to human respiration,
which is correct?
A. Pulmonary ventilation is equal to alveolar ventilation.
B. Alveolar ventilation is less than pulmonary ventilation.
C. Alveolar ventilation is more than pulmonary ventilation
D. Pulmonary ventilation is less than alveolar ventilation.


Muscular force can
A. change the state of motion of an object
B. change the shape of an object
C. both A and B
D. neither A nor B


Complete hydrolysis of cellulose gives:
A . D-fructose
B. D-ribose
c. D-glucose
D. L-glucose


If the electric field is given by \( (5 i+ \) \( 4 j+9 k), \) the electric flux through a
surface of area 20 unit lying in the \( Y-Z \) plane will be :
A. 100 unit
B. 80 unitt
c. 180 unit
D. 20 unit


For the determination of Iron and Copper from their mixure, which titration is
used?
A. Back titration
B. complexometric titration
c. lododmetric titration
D. Acid-base titration


Write the structures and IUPAC names
of possible isomers of \( C_{5} H_{11} B r \) and
classify them as \( 1^{0} / 2^{0} / 3^{0} \)


A cloudy or milky appearance characterizes:
A. soft water
B. hard water
c. chlorinated water
D. both a and c


A vector \( \vec{p} \) is making \( 45^{\circ} \) and \( 60^{\circ} \) with
+ve \( x \) and \( y \) axes respectively. Then
angle made by this vector with +ve z axis is
A . 255 \( ^{\circ} \)
B . 75
\( c \cdot 30^{0} \)
D. \( 60^{\circ} \)


Two man 'A' and 'B' are standing on opposite edge of a \( 6 \mathrm{m} \) long platform which is further kept on a smooth floor.
They starts moving towards each other and finally meet at the midpoint of platform. Find the displacement of platform. Find the displacement of platform if mass of \( A, B \) and platform \( \operatorname{are} 40 \mathrm{kg}, 60 \mathrm{kg} \) and \( 50 \mathrm{kg} \) respectively.


The wavelength of radiation emitted, when in \( H e^{+} \) electron falls from infinity
to ground state would be:
\( \left(R=1.097 \times 10^{7} m^{-1}\right) \)
A \( .2 .2 \times 10^{-8} m \)
th
B. 2.2 \( \times 10^{-9} \mathrm{m} \)
c. \( 120 m \)
D. \( 22 \times 10^{7} \mathrm{m} \)


When an ideal diatomic gas is heated at constant pressure, the fraction of the heat energy supplied which increased the internal energy of the gas is:
A \( \cdot \frac{2}{5} \)
B. \( \frac{3}{5} \)
\( c \cdot \frac{3}{7} \)
D.


When a permanent magnet is moved towards a coil, current is induced in the
coil by faraday's law. What is the source
of energy associated with the current produced?


A block of mass \( 3 k g \) is released from
the rest at top of the inclined plane. If length and height of the inclined plane is \( 6 \mathrm{m} \) and \( 4 \mathrm{m} \) respectively. Calculate its speed at the bottom of inclined plane. Assume the force of friction 16 \( \mathrm{N} \)
on the block is a constant.
A. \( 2 \mathrm{m} / \mathrm{s} \)
B. 3 \( \mathrm{m} / \mathrm{s} \)
\( c \cdot 4 m / s \)
\( D \cdot 5 m / s \)
E. \( 6 \mathrm{m} / \mathrm{s} \)


ff \( y=m \log x+n x^{2}+x \) has its
extreme values at \( x=2 \) and \( x=1 \)
then \( 2 m+10 n \) is equal to
A . -1
B. -4
c. -2
D.
E. -3


Which of the following is an example of network polymer?
A. Polyethylene
B. PVC
c. Bakelite
D. All


\( \left\{\mathbf{x} \in \mathbb{R}: \cos 2 x+2 \cos ^{2} x-2=0\right\}= \)
A \( \cdot\left\{2 n \pi+\frac{\pi}{3}, n \in Z\right\} \)
в \( \cdot\left\{n \pi \pm \frac{\pi}{6}, n \in Z\right\} \)
с \( \cdot\left\{n \pi+\frac{\pi}{3}, n \in Z\right\} \)
D \( \cdot\left\{2 n \pi-\frac{\pi}{3}, n \in Z\right\} \)


Electromagnetic radiation of wavelength \( 242 \mathrm{nm} \) is just sufficient to ionise the sodium atom. Calculate the
ionisation of sodium \( \mathrm{kn} \mathrm{kJ} \mathrm{mol}^{-1} \)
A. \( 8.8266 \times 10^{-35} \mathrm{m} \)
B. 8.8266 \( \times 10^{35} \mathrm{m} \)
c. \( 8.8266 \times 10^{-36} \mathrm{m} \)
D. 8.8266 \( \times 10^{-34} \mathrm{m} \)


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


The isomer(s) of \( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4} \boldsymbol{C l}_{2}\right] \) that
has/have a \( C l-C o-C l \) angle of \( 90^{\circ} \)
is/are:
A. trans only
B. meridional and trans
c. cis and trans
D. cis only


The speed at which the current travels
in a conductor, is nearly.
A \( .3 \times 10^{4} m s^{-1} \)
В. \( 3 \times 10^{5} \mathrm{ms}^{-1} \)
c. \( 4 \times 10^{6} m s^{-1} \)
D. \( 3 \times 10^{8} \mathrm{ms}^{-1} \)


Define autotrophic nutrition


If \( 2^{x}+2^{y}=2^{x+y}, \) then \( \frac{d y}{d x} \) has the value
equal to
This question has multiple correct options
A \( \cdot-\frac{2^{y}}{2^{x}} \)
B. \( \frac{1}{1-2^{x}} \)
\( \mathbf{C} \cdot 1-2^{y} \)
D \( \cdot \frac{2^{x}\left(1-2^{y}\right)}{2^{y}\left(2^{x}-1\right)} \)


Rank the following alkenes in order of decreasing heats of hydrogenation:
(largest first)
A \( .2>34>1 \)
в. \( 2>4>3>1 \)
c. \( 1>3>4>2 \)
D. \( 1>4>3>2 \)


The angular momentum of the electron in hydrogen atom in the ground state is
\( \mathbf{A} \cdot 2 h \)
в. \( \frac{h}{2} \)
c. \( \frac{h}{2 \pi} \)
D. \( \frac{h}{4 \pi} \)


Two vectors, each of magnitude \( A \) have
a resultant of same magnitude \( A \). The angle between the two vectors is
\( A \cdot 30 \)
B. \( 60^{\circ} \)
\( c \cdot 120^{\circ} \)
D. 150


\( S^{-2} \) is isoelectronics with \( x^{+2} . \) If an
atom of \( x \) contain \( (z+2) \) neutrons then
find no. of \( e^{-}, p \) and \( n \) in \( x \) and \( x^{+2} .(z= \)
Atomic no)


Two long straight wires, each carrying an electric current of 5 A, are kept
parallel to each other at a separation of \( 2.5 \mathrm{cm} . \) Find the magnitude of the magnetic force experienced by \( 10 \mathrm{cm} \) of
a wire.
A \( .4 .0 \times 10^{-4} N \)
В. \( 3.5 \times 10^{-6} N \)
c. \( 2.0 \times 10^{-5} N \)
D. \( 2.0 \times 10^{-9} N \)


Obtain the resonant frequency and \( Q \) factor of a series LCR circuit with \( L=3.0 \)
\( \mathrm{H}, \boldsymbol{C}=\mathbf{2 7} \boldsymbol{\mu} \boldsymbol{F}, \) and \( \boldsymbol{R}=\mathbf{7 . 4} \mathbf{\Omega} . \) It is
desired to improve the sharpness of the resonance of the circuit by reducing its full width at half maximum' by a factor
of \( 2 . \) Suggest a suitable way.


Which of the following compounds possesses zero dipole moment?
A. \( H_{2} O \)
в. \( C H_{3} F \)
c. \( C C l_{4} \)
D. \( B F_{3} \)


The total solid angle subtended by the sphere is
\( \mathbf{A} \cdot 0.25 \pi \)
в. \( 0.5 \pi \)
c. \( 4 \pi \)
D . \( 2 \pi \)
E . \( 1 \pi \)


Three point charges \( Q_{1}=25 \mu C, Q_{2}= \)
\( 50 \mu C \) and \( Q_{3}=100 \mu C, \) are kept at the
corners \( A, B \) and \( C \) respectively of an
equilateral triangle ABC having each side equal to \( 7.5 \mathrm{m} \). Calculate the total electrostatic potential energy of the
system


Rusting is a special term, given to the corrosion of which metal?
A. zinc
в. copper
c. Nickel
D. Iron


What is \( X \) in the equation? \( \boldsymbol{C a O}+\boldsymbol{3 C} \rightarrow \boldsymbol{X}+\boldsymbol{C O} \)
A \( \cdot C a C O_{3} \)
в. \( C a C_{2} \)
\( c \cdot C O_{2} \)
D. None of these


What is meant by the white fleece of the lamb?


When chlorine gas is passed through an aqueous solution of \( K B r, \) the solution
turns orange brown due to the
formation of:
A. \( K C l \)
в. \( H C l \)
\( \mathrm{c} . \) НВт
D. \( B r_{2} \)


Solve : \( \int e^{x} \cdot \sin 3 x d x \)


Equation of the tangent at (4,4) on \( x^{2}= \)
4y is
A. \( 2 x+y+4=0 \)
В. \( 2 x-y-4=0 \)
c. \( 2 x+y-12=0 \)
D. \( 2 x+y+12=0 \)


The precipitate of \( \boldsymbol{C a} \boldsymbol{F}_{2}\left(\boldsymbol{K}_{\boldsymbol{s} \boldsymbol{p}}=\mathbf{1 . 7} \times\right. \)
\( \left.10^{-10}\right) \) is obtained when equal volumes
of the following are mixed:
A \( \cdot 10^{-4} M C a^{2+}+10^{-4} M F^{-} \)
B . \( 10^{-2} M C a^{2}+10^{-3} M F^{-} \)
\( \mathbf{c} \cdot 10^{-5} M C a^{2}+10^{-3} M F^{-} \)
D. \( 10^{-3} M C a^{2}+10^{-5} M F^{-} \)


Conversion of vapour into solid on cooling is called:
A. desublimation
B. vapour deposition
c. Both A and B
D. None of the above


The link between successive generation
is provided by
A. Nucleus
B. Cytoplasm
c. Lysosome
D. Nucleic acid


A body projected vertically up travels a
height \( h \) in the \( n^{t h} \) second. The distance
travelled by it in the next two seconds is
\( A \cdot h+2 g \)
в. \( 2 h+g \)
c. \( 2 h+2 g \)
D. \( 2 h+3 g \)


Two resistors are joined in series, then their equivalent resistance is \( 90 \Omega \) When the same resistors are joined in parallel, the equivalent resistance is \( 20 \Omega \)
The resistances of the two resistors will
be :
A. \( 70 \Omega, 20 \Omega \)
в. \( 80 \Omega, 10 \Omega \)
\( \mathbf{c} \cdot 60 \Omega, 30 \Omega \)
D. \( 50 \Omega, 40 \Omega \)


The value of \( \sec ^{3} \theta, \) where \( \theta \) is the acute
angle between the plane faces of a regular tetrahedron, is


If \( \mathbf{A}=\left[\begin{array}{cc}\mathbf{2} & \mathbf{2} \\ -\mathbf{3} & \mathbf{2}\end{array}\right], \mathbf{B}=\left[\begin{array}{cc}\mathbf{0} & \mathbf{- 1} \\ \mathbf{1} & \mathbf{0}\end{array}\right] \) then
\( \mathbf{B}^{-\mathbf{1}} \mathbf{A}^{-\mathbf{1}} \)
A \( \cdot \frac{1}{10}\left[\begin{array}{cc}2 & 2 \\ -3 & 2\end{array}\right] \)
в. \( \frac{1}{10}\left[\begin{array}{cc}2 & -2 \\ 2 & 3\end{array}\right] \)
c. \( \frac{1}{10}\left[\begin{array}{cc}2 & 2 \\ -2 & 3\end{array}\right] \)
D. \( \cdot \frac{1}{10}\left[\begin{array}{cc}-2 & 2 \\ 2 & 3\end{array}\right] \)


\( (\mathbf{1}) \boldsymbol{C}_{6} \boldsymbol{H}_{5}-\stackrel{\mathbf{0}}{\boldsymbol{C}}-\boldsymbol{C}_{\mathbf{6}} \boldsymbol{H}_{\mathbf{5}} \)
\( (2) C_{6} H_{5}-C H O \)
\( (\mathbf{3}) \boldsymbol{p}-\boldsymbol{C} \boldsymbol{H}_{3}-\boldsymbol{C}_{6} \boldsymbol{H}_{4}-\boldsymbol{C} \boldsymbol{H} \boldsymbol{O} \)
\( (4) p-C H_{3} O-C_{6} H_{4}-C H O \)
Correct order for nucleophilic addition reaction.
A \( .2>1>3>4 \)
4 \( 4>1>3>1>3>1>3>2 \) 4
в. \( 4>3>2>1 \)
c. \( 2>3>4>1 \)
D. \( 4>2>3>1 \)


A satellite is revolving in a circular
equatorial orbit of radius \( \boldsymbol{R}=\mathbf{2} \times \mathbf{1 0}^{\mathbf{4}} \)
\( \mathrm{km} \) from east to west. Calculate the
interval after which it will appear at the same equatorial town. Given that the
radius of the earth \( =6400 \mathrm{km} \) and
g(acceleration due to gravity) \( =10 \mathrm{m} \) \( s^{-2} \)


Assertion \( P h N_{2} B r^{\ominus} \) on reaction with \( N a O H \)
gives benzene diazohydroxide.
Reason
\( \theta \)
\( O H \) is a strong nucleophile, attacks the terminal \( \mathrm{N} \) atom, and forms a covalent
bond.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A man pushes a \( 10 k g \) box at a constant
velocity over a distance of \( 4 m \) on a
rough horizontal surface. The coefficient of kinetic friction between
the box and the floor is \( 0.3 . \) Calculate
the work done by the person on the box?
A . \( 12 J \)
B. \( 40 J \)
c. \( 75 J \)
D. \( 120 J \)
E . \( 400 J \)


Cube of 1.3 is:
A . 2197
B. 219.7
c. 21.97
D. 2.197


n the given Haber process, find out \( A \)
A. сао
в. \( C a(O H)_{2} \)
\( c \cdot C a C O_{3} \)
D. None of these


Magnetic flux passing through a coil of
resistance \( 2 \Omega \) is as shown in figure.
Match the following two columns. In
column II all physical quantities are in
SI units


The external or internal framework
which provides support to the body is called
A. Supportive chord
B. Tendons
c. skeleton
D. Muscles


Solve:
\( \int_{0}^{1} x+x^{2} d x \)


Velocity of the planet is minimum at
A \( . C \)
в. \( D \)
\( c . A \)
\( D \)


The hysteresis cycle for the material of permanent magnet is
A. Short and wide
B. Tall and narrow
c. Tall and wide
D. short and narrow


Match list 1 and list 2 .
List - List
A) \( C O+H_{2} \)
1. Producer
gas
B) \( C O+N_{2} \)
2. Semi
water gas
C) \( \boldsymbol{C O}+\boldsymbol{H}_{2}+\boldsymbol{N}_{2} \)
3. Water gas
D) \( \boldsymbol{H}_{2}+\boldsymbol{C} \boldsymbol{H}_{4}+\boldsymbol{C O} \)
4. Coal gas
\( A \cdot 1342 \)
B. 2 4 13
\( c .3124 \)
D. 1432


Two balls of mass \( m \) and \( 2 m \) are
connected by a light inextensible string The string is initially slack. The heavier
ball is given velocity \( v_{0} \) towards the right. Find impulse by the string on the ball of mass \( \mathrm{m} \) when the string becomes tight


What is the value of \( \Delta S^{\ominus} \) for the fuel
cell at \( 25^{\circ} C \) ?
В. \( -160 J K^{-1} \)
c. \( 160 J K^{-1} \)
D. \( 1600 J K^{-1} \)


In a moving cell galvanometer, we use a radial magnetic field so that the galvanometer scale is
A. logarithmic
B. exponential
c. linear
D. none of the above


White colour of the cloud is due to
A. reflection of seven colors of light
B. refraction of seven colors of light
C. scattering of seven colors of light
D. absorption of seven colors of light


Which of these types of cells is most likely to divide?
A. Meristem
B. Parenchyma
c. xylem
D. Epidermis


When salt is dissolved in distilled
water, we obtain salt solution which is a
I an:
A. conductor of electricity
B. insulator of electricity
c. motor of electricity
D. filament of electricity


State whether true or false:
Square root of 121 is 11 and (-11)
A. True
B. False


If \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}+\frac{1}{\boldsymbol{x}} \)
prove that \( [\boldsymbol{f}(\boldsymbol{x})]^{3}=\boldsymbol{f}\left(\boldsymbol{x}^{3}\right)+\boldsymbol{3} \boldsymbol{f}\left(\frac{1}{x}\right) \)


The \( S I \) unit of the coefficient of
viscosity is:
A \( \cdot N s^{-1} m^{-2} \)
B. \( N s m^{-2} \)
c. \( N s^{-2} m^{-2} \)
D. \( N s^{-1} m^{-3} \)


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


Find \( s_{30} \) for an AP, where \( a_{10}=20 \) and
\( \boldsymbol{a}_{20}=\mathbf{5 8} \)


Assertion
Smaller drops of liquid resist deforming forces better than the larger drops.
Reason

Excess pressure inside a drop is directly proportional to surface area.
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 speed of sound in air is \( v . \) Both the
source and observer are moving towards each other with equal speed \( u \)
The speed of wind is \( w \) from source to
observer. Then, the ratio \( \left(\frac{f}{f_{0}}\right) \) of the
apparent frequency to the actual frequency is given by
A \( \cdot \frac{v+u}{v-u} \)
в. \( \frac{v+w+u}{v+w-u} \)
c. \( \frac{v+w+u}{v-w-u} \)
D. \( \frac{v-w+u}{v-w-u} \)


Arrange the following in correct sequence with reference to sexual reproduction in Rhizopus
I. Formation of germ tube.
II. Formation of zygophores.
III. Formation of warty wall layer of
zygospore.
IV. Secretion of trisporic acid.
The correct sequence is
\( \mathbf{A} \cdot \mid \mathbf{V}, \) ॥ᅵ, И, 1
B. IV, II, III, I
c. ॥, ।, ।V, ॥॥
D. I, III, II, IV


\( \frac{\sqrt{3}-1}{\sqrt{3}+1}=a+b \sqrt{3} ; \) then what is the
value of \( \boldsymbol{a}+\boldsymbol{b} ? \)
A . -3
B.
\( c \cdot 3 \)
D. -


The average power transmitted through a given point on a string supporting a sine wave is 0.40 watt when the
amplitude of wave is 2 mm. What average power will transmitted through this point its amplitudes is increased
to 4 mm?
A. 0.40 watt
B. 0.80 watt
c. 1.2 watt
D. 1.6 watt


Find the quadratic function \( \boldsymbol{f}(\boldsymbol{x}) \boldsymbol{i} \boldsymbol{f} \boldsymbol{f}(\boldsymbol{0})=\mathbf{1}, \boldsymbol{f}(1)=\mathbf{0}, \boldsymbol{a} \boldsymbol{n} \boldsymbol{d} \boldsymbol{f}(\boldsymbol{3})= \)
\( \mathbf{5} \)


Find out a suitable term from the
following for the various components of
cells.
A . Tissue
B. Cell organelles
c. chromosomes
D. Genes


The gaseous fuels
(A) burn without producing smoke
(B) has low calorific value
(C) are easy to ignite
(D) have high calorific value. Select the correct alternatives.
A. A and B
B. B and C
\( c \cdot c \) and \( D \)
D. D and B


Unpaired external naris occurs in
A. Petromyzon
B. Torpedo
c. Anabas
D. Solea


A \( 100 m \) long train at \( 15 m / s \) overtakes a man running on the platform in the same direction in \( 10 s . \) How long the
train will take top cross the man if he
was running in the opposite direaction?
A . \( 7 s \)
B. 5 s
\( c .3 s \)
D. \( 1 s \)


Which of the following is not a use of benzoic acid?
A. Food preservative
B. Anticeptic
c. In manufacture of dye
D. In metal polish


\( \boldsymbol{H} \boldsymbol{C l}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{Z} \boldsymbol{n}(\boldsymbol{s}) \rightarrow \boldsymbol{Z} \boldsymbol{n} \boldsymbol{C l}_{2}(\boldsymbol{a q})+ \)
\( \boldsymbol{H}_{2}(\boldsymbol{g}) \)
In the reaction above, which term best
describes the role of \( \boldsymbol{H} \boldsymbol{C l}(\boldsymbol{a} \boldsymbol{q}) ? \)
A. Bronsted acid
B. Oxidizing agent
c. Reducing agent
D. Precipitate
E. Cathode


A small signal voltage \( V(t)=V_{0} \sin \omega t \)
is applied across an ideal capacitor \( \boldsymbol{C} \)
Then:
A . current \( I(t) \), lags voltage \( V(t) \) by \( 90^{\circ} \)
B. over a full cycle the capacitor \( C \) does not consume any energy from the voltage source
c. current \( I(t) \) is in phase with voltage \( V(t) \)
D. current \( I(t) \) leads voltage \( V(t) \) by \( 180^{\circ} \)


What will be the ratio of the distances
moved by a freely falling body from rest in 4 th and 5 th seconds of journey
A .4: 5
B. 7: 9
c. 16: 25
D. 1: 1


The pteridophytes with high content of silica is
A. Club moss
B. Ferns
c. Horsetails
D. Lycopodium


Weightlessness experienced while orbiting the earth in a spaceship is the result of
A. Inertia
B. Accelaration
c. zero gravity
D. Centre of gravity


"Chipko movement" by Sunderlal Bahuguna was started in
A . 1965
B. 1973
\( c \cdot 1983 \)
D. 1947


A current of \( 1 \times 10^{-5} A \) is passed
through a solution of single atom thick
layer of \( A g N O_{3} \) for 16 min \( 5 s, \) using plantinum electrodes. A uniform single atom thick layer of Ag is deposited covering \( 90 \% \) of cathode surface. The
total surface area \( \left(\text { in } c m^{2}\right) \) of cathode if
each silver atom covers an area of
\( \mathbf{5 . 6} \times \mathbf{1 0}^{-\mathbf{1 6}} \mathbf{c m}^{\mathbf{2}} \mathbf{i s} \)


Calculate the neutrons ratio for the
isotopes \( \boldsymbol{O}^{\mathbf{1 6}} \) and \( \boldsymbol{O}^{\mathbf{1 8}} \)
This question has multiple correct options
\( A \cdot 8: 10 \)
B. 4: 5
\( c \cdot 9: 8 \)
\( D \cdot 1: 1 \)


Complete the given balanced equation and find out the missing term.
\( _{6}^{14} C \rightarrow_{4}^{10} B e+? \)
B . \( _{1}^{0} \)
\( \mathrm{c} \cdot_{2}^{4} \mathrm{He} \)
\( D \cdot_{0}^{0} \)
E \( . \quad \begin{array}{l}n \\ n\end{array} \)


Let \( A=\{1,2,3\} \) and \( R= \)
\{(1,2),(2,3),(1,3)\} be a relation on \( A \)
Then \( \boldsymbol{R} \) is
A. neither reflexive nor transitive
B. neither symmetric nor transitive
c. transitive
D. none of these


Ellingham diagram is used for:
A. Reduction
B. Electrolysis
c. zone refining
D. van-Arkel


Which of the following statements is correct for an electron having azimuthal
quantum number \( l=2 ? \)
A. The electron may be in the lowest energy shell
B. The electron is in a spherical orbital
C . The electron must have spin \( m_{s}=+\frac{1}{2} \)
D. None


The volume of a sphere of diameter \( 2 p \) cm is given by
A \( \cdot \pi p^{2} c m^{3} \)
В \( \cdot \pi p^{3} c m^{3} \)
\( \mathbf{c} \cdot 4 \pi p^{3} c m^{3} \)
D. \( \frac{4}{3} \pi p^{3} c m^{3} \)


What will be the molarity of a solution which contains \( 5.85 g \) of \( N a C l(s) \) per \( \mathbf{5 0 0} \mathrm{ml} ? \)
A. 4 mol \( L^{-1} \)
B. 20 mol \( L^{-1} \)
c. 0.2 mol \( L^{-1} \)
D. 2 mol \( L^{-1} \)


A ball is dropped from height 5 m. The
time after which ball stops rebounding if coefficient of restitution between ball
and ground \( e=1 / 2, \) is
This question has multiple correct options
A. 1 sec
B. 2 sec
\( \mathrm{c} \cdot 3 \mathrm{sec} \)
D. infinite


Palisade parenchyma and spongy parenchyma are the two components of
A. Cortex of hydrophytic stem
B. cortex of monocot root
c. Mesophyll of the leaf
D. cortex of a dicot stem


Silver reacts with hydro chloric acid to give
A. \( A g C l \)
в. \( H_{2} \)
c. \( A g H \)
D. no reaction


Which of the following are neurotransmitters that affect a
person's mood?
This question has multiple correct options
A. Dopamine
B. Argenine
c. Insulin
D. Serotonin


If an A.P is given by \( 7,12,17,22, \) then \( n \) th term is
A \( .2 n+5 \)
B. \( 4 n+3 \)
\( c \cdot 5 n+2 \)
D. \( 3 n+4 \)


Find the values of \( a \) and \( b \) so that the
function, \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{l}\frac{1-\sin ^{2} x}{3 \cos ^{2} x}, \quad x<\pi / 2 \\ a, \quad x=\pi / 2 \\ \frac{b(1-\sin x)}{(\pi-2 x)^{2}}, \quad x>\pi / 2\end{array}\right. \)
continuous


The first stable compound formed
during the photosynthesis of \( C_{3} \) plants
is
A. Phosphoglyceric acid.
B. Starch
c. Pyruvic acid
D. Ribulose diphosphate


A concave lens forms the image of an
object such that the distance between
the object and image is \( 10 \mathrm{cm} \) and the
magnification produced is \( 1 / 4 . \) The focal length of the lens will be
\( \mathbf{A} \cdot 8.6 \mathrm{cm} \)
B. \( 6.2 \mathrm{cm} \)
c. \( 10 \mathrm{cm} \)
D. \( 4.4 \mathrm{cm} \)


In the given figure, find the area of the
path (shaded portion) which is \( 2 m \)
wide all round.


What is the role of switch in an electric
circuit ?


Calculate the amount of \( C a C l_{2} \) (molar
mass \( =111 \mathrm{g} / \mathrm{mol} \) ) which must be added to \( 580 g \) of water so that freezing point
lower by \( 2 \mathrm{K}, \) assuming \( \mathrm{CaCl}_{2} \) is completely dissociated:
\( \left[K_{f} \text { for water }=1.86 \mathrm{K} \mathrm{kg} / \mathrm{mol}\right] \)


Match the items given in list I with those in list II.


A radioactive sample has 5000 disintegration per minute initially and 1250 disintegration per minute after 5
seconds. Then the decay constant is
A \( .0 .4 \ln 2 \)
B. \( 0.2 \ln 2 \)
c. \( 0.1 \ln 2 \)
D. \( 0.8 \ln 2 \)


Find the smallest number that such
must be
subtracted from 220 to make it a
perfect cube


At absolute zero, Si acts as
A. non-metal
B. metal
c. insulator
D. semiconductor


Desert can be converted into green land by planting
A. Oxylophytes
B. Psammophytes
c. Halophytes
D. Green trees


Citric acid cycle is \( \ldots \). step in carbohydrate metabolism.
A. First
B. second
c. Third
D. Fourth


Draw the appropriate Venn diagram for
\( A^{\prime} \cap B^{\prime} \)


The number of molecules of water of
crystallisation present in one molecule of ferrous sulphate is
\( \mathbf{A} \cdot \mathbf{5} \)
B. 7
\( c .6 \)
D. 10


When a coil of cross-sectional area \( A \)
and number of turns N is rotated in a
uniform magnetic field B with angular velocity \( \omega, \) then the maximum emf
induced in the coil will be
A. BNA
в. \( \frac{B a \omega}{N} \)
c. BNA\omega
D. zero


The dimensional formula for viscosity is
\( \left[M L^{-1} T^{-1}\right] . \) One poise, i.e, C.G.S. unit of viscosity is:
A \( \cdot 10^{-1} \) M.K.S.
B. \( 10^{0} \) M.K.S.
c. \( 10^{1} \) M.K.S.
D . \( 10^{-2} \) M.K.S


Find a two-digit number which exceeds
by 12 the sum of the squares of its digits and by 16 the doubled product of its digits.


The atomic number \( (A) \) and mass
number \( (M) \) of the nuclide formed
where three alpha \( \alpha \) and two \( \beta \)
particles are emitted from \( 238_{92}^{238} U \)
A. \( A=87, M=233 \)
В. \( A=86, M=226 \)
c. \( A=88, M=227 \)
D. \( A=88, M=226 \)


What is a tropic movement?
A. The directional growth movements of plants.
B. The directional growth movements of plants due to external stimuli.
C. The directional growth movements of plants due to internal stimuli.
D. The random growth movements of plants due to external stimuli.


A particle of charge \( q \) and mass \( m \)
moves in a circular orbit of radius \( r \)
with angular speed \( \omega . \) The ratio of the
magnitude of its magnetic moment to that of its angular momentum depends
on
A. \( \omega \) and \( q \)
B. \( \omega, q \) and \( m \)
c. \( q \) and \( m \)
D. \( \omega \) and \( m \)


A bag contains 4 balls.Two balls drawn at random without replacement and are
found to be white. What is the
probability that all balls are white?


A ball is dropped from a height of \( 1 \mathrm{m} \). if coefficient of restitution between the
surface and the ball is \( 0.6, \) the ball
rebounds to a height of
\( A \cdot 0.6 m \)
B. 0.4 \( m \)
\( c \cdot 1 m \)
D. 0.31 \( m \)


During collision
a) There is a change in momenta of individual bodies
b) The change in total momentum of the system of colliding particle is zero
c) The change in total energy is zero
d) The law of conservation of
momentum is not valid
A. only a \( \& \) b are true
B. only b \& c are true
\( c \cdot a, b \& c \) are true
D. b, c \& d are true


The kinetic energy of particles is maximum in
A . gas
B. liquid
c. solid
D. Same in all the states


The minimum value of \( 2^{\left(x^{2}-3\right)^{3}+27} \) is
\( A \cdot 2^{27} \)
B.
\( c \cdot 2 \)
D. None of the above


Triangles \( A B C \) and DEF are similar. If their areas are \( 64 \mathrm{cm}^{2} \) and \( 49 \mathrm{cm}^{2} \) and
if \( A B \) is \( 7 \mathrm{cm}, \) then find the value of DE.
\( A \cdot 8 \mathrm{cm} \)
в. \( \frac{49}{8} \mathrm{cm} \)
c. \( \frac{8}{49} \mathrm{cm} \)
D. \( \frac{64}{7} \mathrm{cm} \)


An ideal gas \( \left(C_{v}=\frac{3}{2} R\right) \) is maintained
in a vessel of volume \( 83 \times 10^{-4} m^{3} \) at
pressure \( 1.6 \times 10^{6} N m^{-2} \) and
temperature \( 300 K . \) If \( 2.49 \times 10^{4} J \)
heat is given to this vessel, then its
final temperature will be
\( \mathbf{A} \cdot 600 K \)
B. \( 625 K \)
\( \mathbf{c} .650 K \)
D. \( 675 K \)


Aspartame, the artificial sweetener is made by a dipeptide of the amino acid,
A. aspartic acid and phenylalanine
B. aspartic acid and phenylhydrazine
c. alanine and glycine
D. aspartic acid and glutamic acid


In the sequence of reaction,the product
B is ?
\( \langle\square\rangle-\mathrm{MgBr}+\mathrm{CH}_{2}-\mathrm{CH}_{2} \longrightarrow \mathrm{A} \frac{\mathrm{H}_{2} \mathrm{O} / \mathrm{H}^{+}}{\mathrm{o}^{\prime}} \)
A. Benzyl alcohol
B. 2-phenyl ethanol
c. 1-phenyl ethanol
D. Quinol


The catalyst used in Kjeldahl's method for the estimationof nitrogen is :
A. copper
B. Magnesium
C. Mercury
D. Sodium


Weight in g of \( N i \) plated per hour is:


What is the value of \( (\vec{P}+\vec{Q}) \times(\vec{P}-\vec{Q}) \)
\( ? \)
\( A \cdot O \)
B. \( P^{2}-Q^{2} \)
c. \( P^{2}+Q^{2}+2 P Q \)
D. none of these


Consider the reactions:
\( \mathbf{2} S_{2} O_{3}^{2-}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{I}_{2}(\boldsymbol{s}) \rightarrow \boldsymbol{S}_{4} \boldsymbol{O}_{6}^{2-}(\boldsymbol{a} \boldsymbol{q})+ \)
\( 2 I^{-}(a q) \)
\( \boldsymbol{S}_{2} \boldsymbol{O}_{3}^{2-}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{2} \boldsymbol{B} \boldsymbol{r}_{2}(\boldsymbol{l})+\boldsymbol{5} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l}) \rightarrow \)
\( \mathbf{2} \boldsymbol{S} \boldsymbol{O}_{\mathbf{4}}^{\mathbf{2}-}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{4} \boldsymbol{B} \boldsymbol{r}^{-}(\boldsymbol{a} \boldsymbol{q})+\mathbf{1 0} \boldsymbol{H}^{+}(\boldsymbol{a} \boldsymbol{q}) \)
Why does the same reductant,
thiosulphate react differently with iodine and bromine?


A mammal excretes nitrogen in the
form of
A. Ammonium ions
B. Amino acids
c. urea
D. Uric acid


Median is independent of change of
A . only origin
B. only scale
c. origin and scale
D. neither origin nor scale


Select the incorrect statement.
A. If the orbitals differ largely in energy, the cost of hybridization energy becomes large
B. The hybridization in phosphorus between \( 3 s \) and \( 3 p- \) orbitals any be possible and the participation of \( 3 d \) orbitals in the hybridization with the \( 3 s \) and \( 3 p- \) orbitals in not expected because of their (i.e, \( 3 d \) orbital) much higher energy
C. The orbital participation generally requires to bond with highly electronegative elements
D. \( P H_{5} \) does not exist but \( P C l_{5}, P F_{5} \) exist through the formation of \( s p^{3} d^{2} \) hybridization


10 g of ice at \( 0^{\circ} \mathrm{C} \) absorbs \( 5460 \mathrm{J} \) of heat energy to melt and change to water at
\( 50^{\circ} \mathrm{C} . \) Calculate the specific latent heat of fusion of ice. Specific heat capacity of water is \( 4200 \mathrm{J} \mathrm{kg}^{-1} \mathrm{K}^{-1} \)
A \( \cdot 136 \) J \( g^{-1} \)
В. 236 J \( g^{-1} \)
c. 336 J \( g^{-1} \)
D. 436 J \( g^{-1} \)


Which one of the following scientists showed that if electrodes are immersed
in water and a current was passed, bubbles of oxygen and hydrogen were produced?
A. William Thomson
B. William Nicholson
c. william watson
D. William Harvey


Resistance of 6 ohm each are connected
in the manner shown in adjoining
figure.With the current 0.5 ampere as
shown in figure, the potential difference
\( \boldsymbol{V}_{\boldsymbol{p}}-\boldsymbol{V}_{\boldsymbol{Q}} \) is:
\( A \cdot 3.6 V \)
B. 6.0 \( v \)
c. \( 3.0 \mathrm{V} \)
D. 7.2 \( v \)


In which of the following \( K_{p} \) is less than
\( \boldsymbol{K}_{c} ? \)
A \( \cdot N_{2} O_{4}(g) \rightleftharpoons 2 N O_{2}(g) \)
B . \( 2 H I(g) \rightleftharpoons H_{2}(g)+I_{2}(g) \)
c. \( 2 S O_{2}(g)+O_{2}(g) \rightleftharpoons 2 S O_{3}(g) \)
D. \( P C l_{5}(g) \rightleftharpoons P C l_{3}(g)+C l_{2}(g) \)


When rain is accompanied by
a thunderstorm, the collected rain water
will have a pH value:
A. slightly lower than that of rain water without thunderstorm
B. slightly higher than that when the thunderstorm is not there
C. uninfluenced by occurrence of thunderstorm
D. which depends on the amount of dust in air


The redox process involves the complete transfer of electrons in the formation in
ionic bonds or partial transfer or shift of electrons in the formation of covalent
bonds.
If true enter 1 , else enter 0 .
\( A \)


Dative bond is present in:
\( A \cdot S O_{3} \)
в. \( N H_{3} \)
c. \( B a C l_{2} \)
D. \( B F_{3} \)


Identify the incorrect statement?
A. Energy can be converted into matter
B. Matter can be converted into energy
C. Energy can be converted into matter, and matter can be converted into energy
D. Matter can be converted into energy, but energy cannot be converted into matter
E. Energy can be measured in units of joules and calories


Values of magnetic orbital quantum number for an electron of \( M \) -shell can
be:
\( \mathbf{A} \cdot 0,1,2 \)
в. -2,-1,0,+1,+2
c. 0,1,2,3
D. -1,0,+1


The displacement current will be
A. \( 6.9 \mu A \)
B. \( 9.6 \mu A \)
c. \( 6.3 \mu A \)
D. \( 5.7 \mu A \)


In Brassica oleracea var. capitata, the edible part is
A. Inflorescene
B. Flower budd
c. vegetative bud
D. Stem


Find the equation of the circle which
passes through the points (2,-2) and \( (3,4) . \) And whose centre lies on the line
\( \boldsymbol{x}+\boldsymbol{y}=\mathbf{2} \)
A. \( x^{2}+y^{2}+7 x+3 y+16=0 \)
B . \( x^{2}+y^{2}+7 x-3 y-16=0 \)
c. \( x^{2}+y^{2}+4 x+5 y-16=0 \)
D. \( x^{2}+y^{2}+5 x+8 y+30=0 \)


\( x=\tan \left(\frac{1}{a} \log y\right) \) prove :
\( \left(1+x^{2}\right) y_{2}+(2 x-a) y_{1}=0 \)


The valve \( V \) in the bent tube is initially
kept closed. Two soap bubbles \( \boldsymbol{A} \)
(smaller) and \( B \) (larger) are formed at
the two open ends of the tube. \( V \) is now
opened and air can flow freely between
the bubbles.
A. There will be no change in the size of the bubbles
B. The bubbles will become of equal size
c. \( A \) will become smaller and \( B \) will become larger
D. The sizes of \( A \) and \( B \) will be interchanged


The size of the iso-electronic species
\( C l^{-}, A r \) and \( C a^{2+} \) is affected by:
A. principle quantum number of valence shell
B. nuclear charge
C. azimuthal quantum number of valence shell
D. electron-electron interaction in the outer orbitals


Which of the following is true about \( \boldsymbol{f}(\boldsymbol{x}) ? \)
A. \( f(x) \) decreases for \( x \epsilon[2 n \pi,(2 n+1) \pi], n \epsilon Z \)
в.
\( f(x) \) decreases for \( x \epsilon\left[(2 n-1) \frac{\pi}{2},(2 n+1) \frac{\pi}{2}\right], n \epsilon Z \)
c. \( f(x) \) is non-monotonic function.
D. \( f(x) \) increases for \( x \in R \)


Ebonite handles would not permit heat
to be conducted from hot utensil to
hand.


Zinc-copper couple that can be used as a reducing agent is obtained by:
A. mixing zinc dust and copper gauze
B. zinc coated with copper.
c. copper coated with zinc.
D. zinc and copper wires welded together


The converse of "If \( x \) has courage, then \( x \)
will win", is
A. If \( x \) wins, then \( x \) has courage.
B. If \( x \) has no courage, then \( x \) will not win.
C. If \( x \) will not win, then \( x \) has no courage.
D. If \( x \) will not win, then \( x \) has courage.


An electron moves on a straight line path XY as shown. The abcd is a coil
adjacent to the path of electron. What will be the direction of current, if any,
induced in the coil?
A. No current induced
B. abcd
\( c \cdot \) adcb
D. The current will reverse its direction as the electron
goes past the


The intrinsic semiconductor behaves as
insulator at
\( \mathbf{A} \cdot 0^{0} C \)
B . \( 100^{\circ} \mathrm{C} \)
c. \( 100 K \)
D. \( 0 K \)


Assertion
AgI does not dissolve in \( N H_{3} \)
Reason
This does not dissolve due to ionic
character of \( \boldsymbol{A} \boldsymbol{g} \boldsymbol{I} \)
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


Formation of polyethylene from calcium carbide taken place as follows:
\( \boldsymbol{C a C}_{2}+\mathbf{2 H _ { 2 }} \boldsymbol{O} \rightarrow \boldsymbol{C a}(\boldsymbol{O H})_{2}+\boldsymbol{C}_{2} \boldsymbol{H}_{2} \)
\( \boldsymbol{C}_{2} \boldsymbol{H}_{2}+\boldsymbol{H}_{2} \rightarrow \boldsymbol{C}_{2} \boldsymbol{H}_{4} \)
\( \boldsymbol{n} \boldsymbol{C}_{2} \boldsymbol{H}_{4} \rightarrow\left(\boldsymbol{C} \boldsymbol{H}_{2}-\boldsymbol{C} \boldsymbol{H}_{2}\right) \boldsymbol{n} \)
The amount of polyethylene obtained from \( 64.0 \mathrm{kg} \) of \( \mathrm{CaC}_{2} \) is:
\( A \cdot 27 \mathrm{kg} \)
в. \( 24 \mathrm{kg} \)
c. \( 22 \mathrm{kg} \)
D. \( 28 \mathrm{kg} \)


State if True or False
Check whether the polynomial \( p(y)= \)
\( 2 y^{3}+y^{2}+4 y-15 \) is a multiple of
\( (2 y-3) \)
A .
B. can not say
\( c \)
D. can not be determine


A body lying initially at point (3,7) starts moving with a constant acceleration of 4i. Its position after 3 s is given by the co-ordinates:
\( A \cdot(7,3) \)
B. (7,18)
c. (21, 7)
D. (3,7)


If \( S= \)
\( \left\{x \in N: 2+\log _{2} \sqrt{x+1}>1-\log _{1 / 2}\right. \)
then
\( \mathbf{A} \cdot S=1 \)
B. \( S=Z \)
c. \( S=N \)
D. none of these


If \( \{(7,11),(5, a)\} \) represents a constant
function, then the value of 'a' is :
\( A \cdot 7 \)
B. 11
\( c .5 \)
D.


What is the minimum possible amount of charge?
A. Electronic charge \( e \)
B. Electronic charge \( 2 e \)
C . Electronic charge \( \frac{e}{2} \)
D. Electronic charge \( \frac{e}{\sqrt{2}} \)


Two block of mass \( m_{1} \) and \( m_{2} \) are
connected with the help of a spring
constant \( k \) initially the spring in its natural length as shown. A sharp
impulse is given to mass \( m_{2} \) so that it
acquires a velocity \( v_{0} \) towards right. If the system is kept on smooth floor then find
(a) the velocity of the centre of
mass,
(b) the maximum elongation that the spring will suffer?


Number of integers in the domain of the
function \( \boldsymbol{f}(\boldsymbol{x})=\log _{(6-x)}\left(7 x-x^{2}\right) \) is
A. 6
B. 5
\( c \cdot 4 \)
D. infinite


What is the maximum number of
emission lines when the excited electron
of an \( \mathrm{H} \) atom in \( \mathrm{n}=4 \) drops to the ground
state?
A \( \cdot 14 \)
B. 6
c. 15
D. 10


Consider points \( A, B, C, D \) on a horizontal cardboard equidistant from center \( \boldsymbol{O} \) as shown in the figure. \( \mathbf{A} \) copper wire perpendicular to the
cardboard passes through the center \( O \) and carries an electric current
flowing upwards. Deflection of magnetic needle will be maximum when it is kept
at the point
A . \( A \)
в. \( B \)
\( c . c \)
\( D \)


Identity the most favourable conditions
for the melting of ice.
A. high temperature, low pressure
B. low temperature, Iow pressure
c. low temperature, high pressure
D. high temperature, high pressure


How many structural isomer are
possible with the molecular \( C_{8} H_{10} ? \)