Electric flux through a surface of area
\( 100 m^{2} \) lying in the xy plane is (in \( V \) -m) if \( \overrightarrow{\boldsymbol{E}}=\hat{\boldsymbol{i}}+\sqrt{\mathbf{2}} \hat{\boldsymbol{j}}+\sqrt{\mathbf{3} \hat{\boldsymbol{k}}} \)
A. 100
B. 141.4
c. 173.2
D. 200


Assertion
The conversion of fresh precipitate to colloidal state is called peptization.
Reason
It is caused by addition of common ions
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


In the diagram above which spot was
most soluble (i.e. dissolved best) in the
Solvent.
A. \( \operatorname{spot} A \)
B. Spot \( B \)
c. \( \operatorname{spot} C \)
D. All of the above


A man gives \( 40 \% \) of his money to his children and \( 20 \% \) of the remaining to a trust. If he is still left with \( \mathrm{Rs} .9,600 \) then what did he originally have?
A. Rs.14, 000
B . Rs.19, 845
c. Rs.20, 000
D. Rs.25, 409


The value of the determinant
\( \left|\begin{array}{ccc}\left(a^{x}+a^{-x}\right)^{2} & \left(a^{x}-a^{-x}\right)^{2} & 1 \\ \left(b^{x}+b^{-x}\right)^{2} & \left(b^{x}-b^{-x}\right)^{2} & 1 \\ \left(c^{x}+c^{-x}\right)^{2} & \left(c^{x}-c^{-x}\right)^{2} & 1\end{array}\right| \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B. 2abc
\( \mathbf{c} \cdot a^{2} b^{2} c^{2} \)
D. None of these


Select odd one(w.r.t. heterotrophic
bacteria)
A. Saprophytic bacteria
B. Chemosynthetic bacteria
c. Parasitic bacteria
D. symbiotic bacteria


Carbohydrates that, on attempted hydrolysis, are not cleaved to smaller
carbohydrates are called:
A. oligosaccharides
B. polysaccharides
c. disaccharides
D. monosaccharides


In an election between two candidates,
one got \( 55 \% \) of the total valid votes, \( 20 \% \) of the votes were invalid. If the total
number of votes was 7500 , the number
of valid votes that the other candidates
got, was?
A. 2700
B. 2900
\( c .3000 \)
D. 3100


To which of the following the oldest fossils belong?
A. Algae
B. Fungi
c. Blue green algae
D. Both A and C


The angular momentum of electron in hydrogen atom is proportional to
A \( \cdot \sqrt{r} \)
B. \( \frac{1}{r} \)
c. \( r^{2} \)
D. \( \frac{1}{\sqrt{r}} \)


Two identical metallic spheres \( A \) and \( B \) of exactly equal masses are taken. Sphere \( A \) is given positive charge \( Q \) columb and B is given an equal negative charge. So initially before the
charge is given. What will be the masses after the charging?


If a person sitting on a rotating stool with his hands outstretched, suddenly lowers his hands, then his :
A. Kinetic energy will decrease
B. Moment of inertia will decrease.
c. Angular momentum will increase.
D. Angular velocity will remain constant


Why do aldehydes and ketones have
high dipole moments?


Why do caesium \( (C s) \) and potassium
\( K \) ) find applications in photoelectric
cells?


The image of the point \( P(1,2,3) \) in the
plane \( 2 x-y+z+3=0 \) is
A \( \cdot(-3,4,1) \)
в. (3,5,2)
c. (-3,5,2)
D. (3,-5,2)


In the figure shown, the friction force
between the bead and the light string is
\( m g / 4, \) find the time which the bead
loses contact with string after the
system is released:
A. \( \sqrt{\frac{2 l}{7 a}} \)
в. \( \sqrt{\frac{4 l}{7 q}} \)
c. \( \sqrt{\frac{8 l}{7 q}} \)
D. \( \sqrt{\frac{7 l}{7 g}} \)


Compare and contrast the chemistry of group 1 metals with that of group 2 metals with respect to the following:
Polarizing power of cations increases on
going from group 1 to group 2.


If figure \( C E \) and \( D E \) are equal chords
of a circle with centre \( O \). If \( \angle A O B= \)
\( 90^{\circ}, \) find ratio of the area of \( \triangle C E D \) and
\( \triangle A O B \)


All terms of an arithmetic progression are natural numbers. The sum of its
nine successive terms, beginning with the first, is larger than 200 and smaller
than \( 220 . \) Find the progression if its
second term is 12


If \( \frac{x}{\cos \theta}=\frac{y}{\cos \left(\theta-\frac{2 \pi}{3}\right)}= \)
\( \frac{z}{\cos \left(\theta+\frac{2 \pi}{3}\right)}, \) then \( x+y+z \) is equal to
\( A \)
B.
\( c \cdot-1 \)
D. none of these


The inertial force acts in a
A. Opposite direction to that of acceleration force
B. Same direction as that of accelerating force
C. Perpendicular direction to that accelerating force
D. None of the above


By imparting heat to a body, its
temperature rises by \( 15^{\circ} \mathrm{C} \). What is the corresponding rise in temperature on kelvin scale?
A. \( 15 ~ K \)
B . \( 288 K \)
c. \( -15 ~ K \)
D. None of the above


Let \( f \) and \( g \) be functions satisfying
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{e}^{\boldsymbol{x}} \boldsymbol{g}(\boldsymbol{x}), \boldsymbol{f}(\boldsymbol{x}+\boldsymbol{y})=\boldsymbol{f}(\boldsymbol{x})+ \)
\( \boldsymbol{f}(\boldsymbol{y}), \boldsymbol{g}(\mathbf{0})=\mathbf{0}, \boldsymbol{g}^{\prime}(\mathbf{0})=\mathbf{4}, \boldsymbol{g} \) and \( \boldsymbol{g}^{\prime} \) are
continuous at 0
Then
A. \( f(x)=0 \) for all \( x \)
B. \( f(x)=x \) for all \( x \)
c. \( f(x)=x+4 \) for all \( x \)
D. \( f(x)=4 x \) for all \( x \)


Lightning quickly heats the air causing it to expand, which produces the sound
of thunder.

Sound travels approximately 1 mile in 5 seconds. Knowing \( \boldsymbol{X}=\boldsymbol{r} \cdot \boldsymbol{t} \) (where \( \boldsymbol{D}= \)
distance, \( r=\text { rate and } t=\text { time }), \) how
far away is a thunderstrom when you
notice a 3 -second delay between the
flash of lightning and the sound of
thunder?
\( \mathbf{A} \cdot 1 \) mile away
B. \( 3 / 5 \) mile away
c. \( 1 / 2 \) mile away
D. \( 1 / 5 \) mile away


In the raction \( S O_{2}+2 H_{2} S \rightarrow 3 S+ \)
\( 2 H_{2} O, \) the substance that is oxidized is
\( A \cdot S O_{2} \)
в. \( H_{2} \) О
\( c \cdot s \)
D. \( H_{2} S_{S} \)


Humus is an example of
A. Crystalloids
B. Organic colloids
C. Soil structure
D. None of the above


L.S.D causes hallucinations. The full
chemical name of this drug is:
A. dextro-lysine
B. Iysergic acid diethylamide
c. lithium sulphide
D. lanthanum sulphide


Peroxides of alkali metals are:
A. Paramagnetic
c. Acidic in nature
D. Amphoteric in nature


In an isosceles \( \triangle A B C, \) if \( A B=A C \)
and \( D \) is a point on \( B C, \) then prove that \( A B^{2}-A D^{2}=B D . C D \)


The force \( F \) acting on a particle of mass is indicated by force-time graph shown below.The change in momentum of the
particle over the time interval from zero
to 8 s is


Assertion
Let \( f \) and \( g \) be increasing and
decreasing functions respectively from \( [0, \infty] \) to \( [0, \infty] . \operatorname{Let} h(x)=f(g(x)) . \) If
\( h(0)=0, \) then \( h(x) \) is always zero
Reason
\( h(x) \) is an increasing function of \( x \)
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 radioactive sample at any instant has its disintegration rate 5000 disintegration per minute. After 5 minutes, the rate is 1250 disintegrations per minute. Then, the decay constant, per minute, is
A . \( 0.4 \ln 2 \)
B. \( 0.2 \ln 2 \)
c. \( 0.1 \ln 2 \)
D. \( 0.8 \ln 2 \)


The proteins found in the filaments of muscle fibres are
A. Actin and myosin
B. Myosin and elastin
c. Actin only
D. Myelin and tubulin


\( \ln \) an A.P. the first term is 2 , the last
term \( 29, \) the sum \( 155 ; \) find the
difference.


Alkynes occur in nature in:
\( \mathbf{A} \cdot \) free state
B. partially free state
c. combined state
D. none of these


\( \cos ^{-1}\left\{\frac{1}{2} x^{2}+\sqrt{1-x^{2}} \cdot \sqrt{1-\frac{x^{2}}{4}}\right\}= \)
\( \cos ^{-1} \frac{x}{2}-\cos ^{-1} x \) holds for
A. \( |x| \leq 1 \)
В. \( x \in R \)
c. \( 0 \leq x \leq 1 \)
D. \( -1 \leq x \leq 0 \)


Four identical plates each of area a are separated by a distance d. The connection is shown below. What is the
capacitance between \( \mathrm{P} \) and \( \mathrm{Q} \) ?
A \( \cdot 2 a \in_{0} / d \)
B \( \cdot a \epsilon_{0} /(2 d) \)
\( \mathrm{c} \cdot a \epsilon_{0} / d \)
D. \( 4 a \in_{0} / d \)


The r.m.s. value of potential difference
shown in the figure is :
\( A \cdot V_{0} / \sqrt{3} \)
в. \( V_{0} \)
\( c \cdot V_{0} / \sqrt{2} \)
D. \( V_{0} / 2 \)


\( \int e^{e^{x}+x} d x= \)
A \( \cdot e^{e^{x}}+x+c \)
B . \( e^{e^{x}}+c \)
\( \mathbf{c} \cdot e^{x}+c \)
\( \mathbf{D} \cdot e^{x}+x+c \)


Twelve cells, each having an e.m.f of \( \mathrm{E} \)
volt are connected in series and are
kept in a closed box. Some of these cells
are wrongly connected with positive and negative terminals reversed. This 12 cell battery is connected in series with
an ammeter, an external resistance \( \mathrm{R} \)
ohms and a two-cell battery (two cells of the same type used earlier, connected perfectly in series). The current in the
circuit when the 12 -cell battery and 2 cell battery aid each other is \( 3 A \) and is
2A when they oppose each other. Then the number of cells in 12-cells
battery that are connected wrongly is:
A . 14
B. 3
\( c \cdot 2 \)
D.


Bones become fragile due to
A. Arthritis
B. osteoporosis
\( c . \) Gout
D. None of the above


One megawatt is equivalent to
A \( \cdot 10^{2} W \)
B . \( 10^{6} W \)
\( \mathbf{c} \cdot 10^{4} W \)
D. \( 10^{8} W \)


Let \( \bar{a}, \bar{b}, \bar{c} \) be vectors of length 3,4,5
respectively. Let \( \bar{a} \) be perpendicular to \( \bar{b}+\bar{c}, \bar{b} \) is perpendicular to \( \bar{c}+\bar{a} \& \bar{c} \) is
perpendicular to \( \bar{a}+\bar{b} \). Then \( |\bar{a}+\bar{b}+\bar{c}| \)
is:
A \( .2 \sqrt{5} \)
B. \( 2 \sqrt{2} \)
c. \( 10 \sqrt{5} \)
D. \( 5 \sqrt{2} \)


If \( f(2)=4 \) and \( f^{\prime}(2)=1, \) then \( \lim _{x \rightarrow 2} \frac{x f(2)-2 f(x)}{x-2} \) equal to
A .2
B. -2
\( c \cdot 1 \)
D. 3


From a uniform disc of radius \( R, \) a
circular disc of radius \( \boldsymbol{R} / 2 \) is cut out. The centre of the hole is at \( R / 2 \) from the centre of the original disc. Locate the centre of gravity of the resultant flat body.
A \( \cdot \frac{R}{6} \) from the centre
в. \( \frac{R}{15} \) from the centre
c. \( -\frac{R}{5} \) from the centre
D. \( \frac{R}{20} \) from the centre


If \( a, b, c \) are in A.P. then \( \frac{a-b}{b-c} \) is equal to
A \( \cdot \frac{a}{b} \)
B. \( \frac{b}{c} \)
\( c \cdot \frac{a}{c} \)
D.


In the circuit shown in figure, ammeter
and voltmeter are ideal. If \( \boldsymbol{E}=\mathbf{4} \boldsymbol{V}, \boldsymbol{R}= \)
\( 9 \Omega \) and \( r=1 \Omega, \) then readings of
ammeter and voltmeter are
This question has multiple correct options
A \( \cdot A_{m}=1 A \)
B . \( A_{m}=2 A \)
c. \( V_{m}=3 V \)
D. \( V_{m}=4 V \)


For the function \( f(x)=x \cos \frac{1}{x}, x \geq 1 \)
which of the following is/are true??
This question has multiple correct options
A. There is at least one \( x \) in the interval \( [1, \infty) \) for which \( f(x+2)-f(x)<2 \)
\( \mathbf{B} \cdot \lim _{x \rightarrow \infty} f^{\prime}(x)=1 \)
C \( . f(x+2)-f(x)>2 \) for all \( x \) in the interval \( [1, \infty) \)
D. \( f^{\prime}(x) \) is strictly decreasing in the interval \( [1, \infty) \)


Which one of the following elements show different oxidation states?
A. Sodium
B. Fluorine
c. chlorine
D. Potassium


Trimerous condition of floral whorls is
characteristic of


A closed vessel contains some gas at
atmospheric pressure and room
temperature. It is then given a high speed
by placing it in a fast moving train. The
temperature of the gas
A. will increase
B. will decrease
c. will remain uncharged
D. increase or decrease depending on the chemical composition of gas


The rate of reaction is uniform
throughout the reaction.
A. True
B. False


The process of taking in \( C O_{2} \) by plants
and releasing \( O_{2} \) is component of
A. Transpiration
B. Respiration
c. Endosmosis
D. Photosynthesis


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


If the median of the data \( 6,7, x- \)
\( 2, x, 18,21 \) written in ascending order is
16, then the variance of that data is
A \( \cdot 30 \frac{1}{5} \)
в. \( 31 \frac{1}{3} \)
c. \( _{32} \frac{1}{2} \)
D. \( 33 \frac{1}{3} \)


Net energy gain from malic acid and succinic acid are
Malic acid: 3
Succinic acid: 5
Justify the mentioned values.


Find the principle value of \( \tan ^{-1}(-\sqrt{3}) \)
\( \mathbf{A} \cdot \pi / 3 \)
в. \( -\pi / 3 \)
c. \( \pi / 6 \)
D. \( -\pi / 6 \)


\( A \) follows the first-order reaction.
\( (A) \longrightarrow \) product.
The concentration of \( A \) changes from \( 0 . \)
M to \( 0.025 \mathrm{M} \) in 40 minutes. Find the
rate of reaction of \( A \) when concentration
of \( A \) is \( 0.01 \mathrm{M} ? \)
A \( \cdot 3.47 \times 10^{-4} \mathrm{M} \min ^{-1} \)
В. \( 3.47 \times 10^{-5} \mathrm{M} \min ^{-1} \)
c. \( 1.73 \times 10^{-4} \mathrm{M} \min ^{-1} \)
D. \( 1.73 \times 10^{-3} \mathrm{M} \min ^{-1} \)


Which of the following is free of salts?
A. Distilled water
B. Sea water
c. tap water
D. All of the above


For a first order reaction, to obtain a
positive slope, we need to plot:
\( \{[A] \text { is the concentration of reactant } A\} \)
\( \mathbf{A} \cdot \log _{10}[A] \) vs \( t \)
B. \( -\log _{e}[A] \) vs t
\( \mathbf{C} \cdot \log _{10}[A] \) vs \( \log t \)
D. \( [A] \) vs t


Effect of the day length duration on plant development and flowering is
A. Chemtropism
B. Phototropism
c. Photoperiodism
D. Photonasty


The percentage of sunlight utilized for photosynthesis by higher plants is
A . \( 100 \% \)
B. \( 110 \% \)
c. \( 50 \% \)
D. 1 - 2 \%


Higher order \( (>3) \) reactions are rare due
to:
A. low probability of simultaneous collision of all the reacting species
B. increase in entropy and activation energy as more molecules are involved
C. shifting of equilibrium towards reactants due to elastic collisions
D. loss of active species on collision


The set of all points where \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \sqrt[3]{x^{2}|x|}-|x|-1 \) is not differentiable is
\( A \cdot\{0\} \)
B \( \cdot\{-1,0,1\} \)
\( \mathbf{c} \cdot\{0,1\} \)
D. None of these


The value of \( x \) satisfying the equation \( \tan ^{-1} x+\tan ^{-1}\left(\frac{2}{3}\right)=\tan ^{-1}\left(\frac{7}{4}\right) \)
equal to
\( A \cdot \frac{1}{2} \)
в. \( -\frac{1}{2} \)
\( c \cdot \frac{3}{2} \)
D. \( -\frac{1}{3} \)
E


A solution is obtained by mixing \( 200 g \) of \( 30 \% \) and \( 300 g \) of \( 20 \% \) solution by weight What is the percentage of solute in the
final solution?
A . \( 50 \% \)
B . 28\%
c. \( 64 \% \)
D. 24\%


\( \operatorname{Let}\left(\frac{2 x^{2}+x+2}{x}\right)^{n}=\sum_{r=m}^{r=t} a_{r} x^{r} \)
then answer the following:
\( f\left(a_{p}=a_{q} \text { then } p+q=\dots\right. \)


In square PQRS. if \( \mathrm{PQ}=3 x-7 \) and
\( Q R=x+3 ; \) find PS
\( A \cdot 6 \)
B. 7
\( c \cdot 8 \)
D. 5


What charge do group IV A atoms have when they become ions?
A. Either +4 or - 4 but they don't usually become ions.
B. +4
\( c \cdot-4 \)
\( D \cdot+3 \)
E. - -


Electric potential of uniformly charged solid sphere at its surface
A. increases with increase in radius
B. decreases with increase in radius
c. remains constant
D. none of the above


7 is a factor of \( 2^{3 n}-1 \) for all natural
numbers n.
A. True
B. False


The number of covalent bonds formed
by Be is:


If \( \int \frac{\sqrt{4+x^{2}}}{x^{6}} d x= \)
\( \frac{\left(a+x^{2}\right)^{3 / 2} \cdot\left(x^{2}-b\right)}{120 x^{5}}+C \) then \( a+b \)
equals to


What would be the length of a sec. A pendulum at a planet (where acc, due to gravity is \( g / 4 \) ) if it's length on earth is \( l \)
A \( . l / 2 \)
в. \( 2 l \)
\( c \cdot l / 4 \)
D. 4


A biased coin with probability \( \boldsymbol{p}, \boldsymbol{0}< \) \( p<1, \) of heads is tossed until a head
appears for the first time. If the probability that the number of tosses required is even is \( 2 / 5, \) then \( p=\dots \)
A. \( 2 / 5 \)
B. \( 2 / 3 \)
c. \( 1 / 3 \)
D. \( 3 / 5 \)


A diatomic molecule has a dipole moment equal to 1.2 D. If the bond length
is \( 1 A^{0}, \) what fraction of electronic
charge \( ^{\prime} e^{\prime} \) exists on each atom.


g of sodium hydroxide is present in 1 litre of \( 1 \mathrm{M} \) solution.
A . 20
B. 40
\( c .30 \)
D. 10


The first use of quantum theory to explain the structure of atom was made
by:
A. Heisenbergg
B. Bohr
c. Planck
D. Einstein


Objects fall towards the earth because the earth pulls those. This pull is called force.
A. contact
B. muscular
c. gravitational
D. electrostatic


Define thermoplastics and thermosetting polymers with two examples of each.


In the reaction series:
\( \boldsymbol{C}_{\boldsymbol{6}} \boldsymbol{H}_{\boldsymbol{5}} \boldsymbol{C l} \frac{\boldsymbol{N H}_{\boldsymbol{3}}}{\boldsymbol{C u _ { 2 } \boldsymbol { O } , \mathbf { 2 0 0 } ^ { \boldsymbol { o } } \boldsymbol { C }}} \boldsymbol{X} ; \boldsymbol{X} \frac{\boldsymbol{H} \boldsymbol{N O}_{2}}{\boldsymbol{0}-\boldsymbol{5}^{0} \boldsymbol{C}} \)
\( Z ; X+Z \rightarrow A, \) the number of \( \sigma \) and \( \pi \)
bonds in \( A \) are:
\( \mathbf{A} \cdot 25 \sigma \) and \( 6 \pi \)
B . 25 \( \sigma \) and \( 7 \pi \)
c. \( 27 \sigma \) and \( 7 \pi \)
D. \( 27 \sigma \) and \( 6 \pi \)


Calculate the wavelength and energy of radiation emitted for the electronic
transition from infinite to stationary
state of hydrogen atom. (Given, \( \boldsymbol{R}= \) \( \mathbf{1} . \mathbf{0} \mathbf{9 6 7} \mathbf{8} \times \mathbf{1 0}^{\mathbf{7}} \mathbf{m}^{-\mathbf{1}}, \mathbf{h}=\mathbf{6 . 6 2 5 6} \times \)
\( 10^{-34} J-s \) and \( c=2.9979 \times 10^{8} m s^{-1} \)
)


The age distribution of 400 persons in a colony having median age 32 is given below
\[
\begin{array}{llll}
\text { Age } \sin & 20- & 25- & 30- \\
\text { Years) } & 25 & 30 & 35
\end{array}
\]
Frequency
75
Then, \( (x-y) \) is :
A .10
в. 20
c. -10
D. - 20


What is the total emf, when three cells
of emfs \( 2 V, 2 V, 2 V \) connected in
parallel?
A . \( 4 v \)
B. 1V
c. \( 2 v \)
D. \( 5 v \)


Analgesics have pain killing effect when consumed, is a classification based on
A. the basis of pharmacological effect
B. the basis of drug action
c. the basis of chemical structure
D. the basis of molecular targets


Fungi show sexual reproduction by all of the following processes except
A. oospores
B. Ascospores
c. Basidiospores
D. Aplanospores


The sides of a triangle are \( 3 x+ \)
\( 4 y, 4 x+3 y \) and \( 5 x+5 y \) units, where
\( \boldsymbol{x}, \boldsymbol{y}>0 . \) The triangle is
A. right angled
B. equilateral
c. obtuse angled
D. none of these


During fractional evaporation of liquid air, nitrogen comes out as a fraction along with:
\( \mathbf{A} \cdot \mathrm{Ar}, \mathrm{Kr}, \mathrm{Xe} \)
B. Only Ar
c. He and Ne
D. Kr, Xe


which is free to rotate about the smooth
vertical hinge passing through the center and perpendicular to the plate, is lying on a smooth horizontal surface. A
particle of mass \( m \) moving with speed
\( u^{\prime} \) collides with the plate and sticks to
it as shown in figure. The angular velocity of the plate after collision will
be:
\( A \cdot \frac{12}{5} \)
B. \( \frac{12}{19} \)
c. \( \frac{3}{-} \underline{u} \)
\( 2 a \)
D. \( \frac{3}{5} \)


Is \( P C l_{3} \) soluble in water?
A. Not Soluble
B. May be
c. Partially soluble
D. soluble


The displacement of a particle performing linear S.H.M is given by \( \boldsymbol{x}= \) \( 6 \sin (3 \pi t-5 \pi / 6) \) metre. Find the time
at which the particle reaches the extreme position towards the left:
A. \( 5 / 9 \) secs
B . 4/9 secs
c. \( 1 / 9 \) secs
D. 7/9 secs


Solve the equation for \( x, y, z \) and \( t \) if \( \mathbf{2}\left[\begin{array}{ll}\boldsymbol{x} & \boldsymbol{z} \\ \boldsymbol{y} & \boldsymbol{t}\end{array}\right]+\mathbf{3}\left[\begin{array}{cc}\mathbf{1} & -\mathbf{1} \\ \mathbf{0} & \mathbf{2}\end{array}\right]=\mathbf{3}\left[\begin{array}{ll}\mathbf{3} & \mathbf{5} \\ \mathbf{4} & \mathbf{6}\end{array}\right] \)


Which of the following is not Lewis acid?
A. \( B F_{3} \)
в. \( A l C l_{3} \)
c. \( F e C l_{3} \)
D. \( P H_{3} \)


Simplify: \( \left(a^{2}-b^{2}\right)^{2} \)


Prove that if chords of congruent circles subtend equal angles at their centre, then the chords are equal.


Ptyalin enzyme is secreted by
A. Salivary glands
B. Mouth
c. oesophagus
D. Stomach


A ship is travelling due east according to
mariner's compass. If the declination at
that place is \( 20^{\circ} \) east, the actual direction
of its motion is
A \( \cdot 40^{\circ} \) south of east
B. \( 20^{\circ} \) south of east
C \( \cdot 5^{\circ} \) south of east
D. \( 20^{\circ} \) north of east


Calculate the heat energy released by water in the experiment in cooling from
\( 70^{\circ} \mathrm{C} \) to \( 45^{\circ} \)


Explain why \( N_{2} \) has greater bond
dissociation energy than \( N_{2}^{+} \) whereas
\( O_{2} \) has lesser bond dissociation energy
\( \operatorname{than} O_{2}^{+} \)


is not unisexual flower.
A. coconnut
в. Papaya a
c. Gulmohar
D. watermelon


Consider a system of three charges \( \frac{\mathbf{q}}{\mathbf{3}} \)
\( \frac{\mathbf{q}}{\mathbf{3}} \) and \( -\frac{\mathbf{2 q}}{\mathbf{3}} \) placed at points \( \mathbf{A}, \mathbf{B} \) and
C, respectively, as shown in the figure.
Take 0 to be the centre of the circle of
radius \( \mathbf{R} \) and angle \( \mathbf{C A B}=\mathbf{6 0}^{\mathbf{0}} \)
A \( \cdot \) The electric field at point \( \mathrm{O} \) is \( \frac{\mathrm{q}}{8 \pi \epsilon_{0} \mathrm{R}^{2}} \) directed along the negative x-axis
B. The potential energy of the system is zero
C. The magnitude of the force between the charges at \( C \) and \( \mathrm{B} \) is \( \frac{\mathrm{q}^{2}}{54 \pi \epsilon_{0} \mathrm{R}^{2}} \)
D. The potential at point \( \mathrm{O} \) is \( \frac{\mathrm{q}}{12 \pi \epsilon_{0} \mathrm{R}} \)


A uniform cylinder has a radius R and
length L. If the moment of inertia of this cylinder about an axis passing through its centre and normal to its circular
face is equal to the moment of the same cylinder about an axis passing through its centre and perpendicular to its length, then
A \( . L=R \)
B. \( L=\sqrt{3} R \)
c. \( L=\frac{R}{\sqrt{3}} \)
D. \( L=\sqrt{\frac{3}{2}} R \)


For which of the following events will the resulting products have more mass than the mass of the stuff from which
the products came?
A. Alpha decay
B. Beta decay
c. An exothermic nuclear reaction
D. An endothermic nuclear reaction
E. Nuclear fission of uranium -235


A \( 0.5 g \) sample of \( K H_{2} P O_{4} \) is titrated with \( 0.1 M \) NaOH.The volume of base
required to do this is \( 25.0 m l \) The
reaction is represented as:
\( \boldsymbol{H}_{2} \boldsymbol{P} \boldsymbol{O}_{4}^{-}+\boldsymbol{O} \boldsymbol{H}^{-} \rightarrow \boldsymbol{H} \boldsymbol{P} \boldsymbol{O}_{4}^{2-}+\boldsymbol{H}_{2} \boldsymbol{O} \)
The percentage purity of \( K H_{2} P O_{4} \) is \( (\boldsymbol{K}=\mathbf{3 9}, \boldsymbol{P}=\mathbf{3 1}) \)
A . \( 68 \% \)
B. 34\%
c. \( 85 \% \)
D. 51\%


Explain, why dogs pant during hot summer days using the concept of evaporation?


Find nth term of the
\( \boldsymbol{G} \cdot \boldsymbol{P} \cdot \sqrt{\boldsymbol{3}}, \frac{\mathbf{1}}{\sqrt{\mathbf{3}}}, \frac{1}{\mathbf{3} \sqrt{\mathbf{3}}}, \ldots \)


The equation of the plane which is equidistant from the two parallel planes \( 2 x-2 y+z+3=0 \) and \( 4 x-4 y+ \)
\( \mathbf{2} z+\mathbf{9}=\mathbf{0} \) is :
A. \( 8 x-8 y+2 z+15=0 \)
B. \( 8 x-8 y+4 z+15=0 \)
c. \( 8 x-8 y+4 z+3=0 \)
D. \( 8 x-8 y+4 z-3=0 \)
E \( .8 x-8 y+4 z+4=0 \)


A man of height \( 1.8 m \) is standing near a Pyramid. If the shadow of the man is of length \( 2.7 m \) and the shadow of the
Pyramid is \( 210 m \) long at that instant, find the height of the Pyramid


Statement I : An indicator will allow to
determine whether a solution is acidic
or basic.
Statement II : Indicator will change
colors in solutions with different pH.
A. Statement I is True, Statement II is True and statement I is correct explanation of statements
B. Statement lis True, Statement II is True and statement II is NOT correct explanation of statements
c. Statement lis True, Statement II is False
D. Statement I is False, Statement II is True
E. Statement lis False, Statement II is False


Which of the following is not artificial form of plastics?
A. Nylon
B. Teflon
c. Styrofoam
D. None of the above


Find the volume of a sphere whose
surface area is \( 154 \mathrm{cm}^{2} \)


Evaluate the given integral. \( \int x \cdot \sin ^{-1} x \)


\( \frac{3.24 \times 0.08666}{5.006} \)


\( _{1}^{2} \boldsymbol{H}+_{1}^{3} \boldsymbol{H} \rightarrow_{0}^{1} \boldsymbol{n}+\mathbf{X} \)
The product \( X \) in the nuclear reaction
represented is.
A \( \cdot \frac{1}{1} H \)
в. \( _{2}^{3} \mathrm{He} \)
\( \mathrm{c} \cdot_{2}^{4} \mathrm{He} \)
D. \( \frac{4}{3} L i \)
\( E \cdot_{3}^{5} L i \)


Two samples \( A \) and \( B \) of same radioactive nuclide are prepared Sample A has twice the initial activity of sample B. For this situation, mark out the correct statement(s):
This question has multiple correct options
A. The half-lives of both the samples would be same
B. The half-lives of the samples are different
C. After each has passed through 5 half-lives, the ratio of activity of A to B is 2:
D. After each has passed through 5 half-lives, ratio of activities of A to B is 64:


Two batteries of emf \( \boldsymbol{E}_{1} \) and \( \boldsymbol{E}_{2}\left(\boldsymbol{E}_{2}>\right. \)
\( E_{1} \) ) and internal resistance \( r_{1} \) and \( r_{2} \)
respectively are connected in parallel as shown in figure


If \( \boldsymbol{v}=\frac{\boldsymbol{A}}{\boldsymbol{t}}+\boldsymbol{B} \boldsymbol{t}^{2}+\boldsymbol{C} \boldsymbol{t}^{3} \) where \( \mathbf{v} \) is
velocity, t is time and \( A, B \) and \( C \) are constant then the dimensional formula
of B is?
\( \mathbf{A} \cdot\left[M^{0} L T^{0}\right] \)
\( \mathbf{B} \cdot\left[M L^{0} T^{0}\right] \)
\( \mathbf{c} \cdot\left[M^{0} L^{0} T\right] \)
\( \mathbf{D} \cdot\left[M^{0} L T^{-3}\right] \)


Evaluate \( \int_{0}^{1}\left(2 x^{2}+x+1\right) d x \)


Total world production of iron destroyed by rusting is about:
A . \( 10 \% \)
B. 50 \%
c. \( 15 \% \)
D. 40 \%


Assertion
Cell division is necessary because it is a physiological process bound to occur as a rule of nature.
Reason
Division of nucleus is followed by division of cytoplasm.
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


Which is characteristic to a Lewis
base?
A. React with metal to produce hydrogen gas
B. Donate an unshared electron pair
C. Always contain the hydroxide ion in its structure
D. Taste sour
E. Formed by the reaction of a nonmetal oxide and water


Let \( z_{1} \) and \( z_{2} \) be roots of the equation
\( z^{2}+p z+q=0, \) where the coefficients
\( p \) and \( q \) may be complex numbers. Let \( A \)
and \( B \) represents \( z_{1} \) and \( z_{2} \) in the
complex plane. If \( \angle A O B=\alpha \neq 0 \) and
\( \boldsymbol{O} \boldsymbol{A}=\boldsymbol{O} \boldsymbol{B}, \) where \( \boldsymbol{O} \) is the origin, then
\( p^{2}=k \cos ^{2} \frac{\alpha}{2}, \) where \( k= \)
\( \mathbf{A} \cdot \boldsymbol{q} \)
B. \( 2 q \)
c. \( 4 q \)
D. None of these


For a cell reaction \( 2 H_{2}(g)+O_{2}(g) \longrightarrow \)
\( 2 H_{2} O(l) ; \triangle_{r} S_{298}^{\circ}=-0.32 k J / K . \) What
is the value of \( \triangle_{f} H_{298}^{\circ}\left(H_{2} O, l\right) ? \)
Given \( \quad O_{2}(g)+4 H^{+}(a q .)+4 e^{-} \longrightarrow \)
\( 2 H_{2} O(l) ; \quad E^{0}=1.23 V \)
A. \( -285.07 k J / \) mol
в. \( -570.14 \mathrm{kJ} / \mathrm{mol} \)
c. \( 285.07 k J / \) mol
D. None of these


In isosceles triangle \( \boldsymbol{A B C}, \boldsymbol{A B}=\boldsymbol{A C} \)
The side \( B A \) is produced to \( D \) such that
\( \boldsymbol{B A}=\boldsymbol{A D} \)
Hence, \( \angle B C D=90^{\circ} \)
If the above statement is true then
mention answer as 1 , else mention 0 if
false


Consider the above sequence and
answer the following
Conversion \( \left(\boldsymbol{C H}_{3}-\boldsymbol{C H}_{3} \Rightarrow \boldsymbol{C H}_{3}-\right. \)
\( \left.C H_{2}-O H\right) \Rightarrow \) alcohol is achieved by:
A. \( B r_{2} / h v, \) alc. KOH
в. \( B r_{2} / h v, \) ая.КОН
c. \( B r_{2} / C C L_{4}, L i A l H_{4} \)
D. \( B r_{2} / C C l_{4}, N a B H_{4} \)


The value of \( p \) for which the function
\[
\left\{\begin{array}{ccc}
\boldsymbol{f}(\boldsymbol{x})= & & \\
& \left(\boldsymbol{4}^{\boldsymbol{x}}-\mathbf{1}\right)^{\mathbf{3}} & \\
\hline \multirow{2}{*} {\sin \frac{\boldsymbol{x}}{\boldsymbol{p}} \log \left(1+\frac{\boldsymbol{x}^{2}}{\mathbf{3}}\right)} & ; & \boldsymbol{x} \neq \mathbf{0} \\
& \mathbf{1 2}(\log \mathbf{4})^{\mathbf{3}} & ; \boldsymbol{x}=\mathbf{0}
\end{array}\right.
\]
continuous at \( \boldsymbol{x}=\mathbf{0}, \) is
A . 4
B. 2
\( c .3 \)
\( D \)


In which part of atmosphere, ozone layer is present?
A. Stratosphere
B. Troposphere
c. Mesosphere
D. Thermosphere


A parallel plate capacitor is to be designed with a voltage rating \( 1 k V \) using a material of dielectric constant
10 and dielectric strength \( 10^{6} V m^{-1} \) What minimum area of the plates is required to have a capacitoance of \( 88.5 p F ? \)


Q Type your question
in \( \mathrm{H}_{2} \mathrm{O} \longrightarrow \)
\( A \)
B.
\( c \)
\( D \)


The position vector of the foci of an ellipse are \( \vec{b} \) and \( -\vec{b}, \) and the length of
major axis is \( 2 a \), then the equation of
ellipse
A \( \cdot a^{4}-a^{2}\left(\vec{r}^{2}+\vec{b}^{2}\right)+\left(\vec{b}^{2} \times \vec{r}^{2}\right)=0 \)
\( ^{\text {В }} a^{4}-a^{2}\left(|\vec{r}|^{2}+|\vec{b}|^{2}\right)+\left(|\vec{b}|^{2} \cdot \vec{r}^{2}\right)=0 \)
c. \( a^{4}+\vec{a}^{2}\left(\vec{r}^{2}+\vec{b}^{2}\right)+\left(\vec{b}^{2} \cdot \vec{r}^{2}\right)=0 \)
D・ \( a^{4}-a^{2}\left(\vec{r}^{2}-\vec{b}^{2}\right)+\left(\vec{b}^{2} \cdot \vec{r}^{2}\right)=0 \)


In which of the following, sulphur has the highest oxidation state?
This question has multiple correct options
\( A \cdot S O_{2} \)
в. \( S O_{3} \)
c. \( H_{2} S O_{4} \)
D. \( H_{2} S_{S} \)


Correct statement regarding the given
reaction is:
\( \mathbf{A} \cdot \mathbf{B} \) is 2,5 -dimethylfuran
B. B is homocyclic aromatic compound
C. A is pyran
D. none of these


\( \operatorname{Points} \boldsymbol{A}(\boldsymbol{3}, \boldsymbol{2}, \boldsymbol{4}), \boldsymbol{B}\left(\frac{\boldsymbol{3} \boldsymbol{3}}{\boldsymbol{5}}, \frac{\boldsymbol{2} \boldsymbol{8}}{\boldsymbol{5}}, \frac{\boldsymbol{3} \boldsymbol{8}}{\boldsymbol{5}}\right), \) and
\( C(9,8,10) \) are given. The ratio in which
\( B \) divides \( \overline{A C} \) is
A . 5: 3
B . 2: 1
c. 1: 3
D. 3: 2


What is the trajectory of the charged particle if the initial velocity of the
particle is perpendicular to the direction of the magnetic field?


Same amount of heat is supplied to two liquids \( A \) and \( B \). The liquid \( A \) shows a greater rise in temperature. What can
you say about the heat capacity of A as compared to that of B?
A. Heat capacity of A is more than that of B
B. Heat capacity of A is less than that of B
c. Heat capacity of A is same as that of B
D. can't say


The time period of a particle executing \( \mathrm{SHM} \) is \( \frac{2 \pi}{\omega} \) and its velocity at a distance
\( b \) from mean position is \( \sqrt{3} b \omega \). Its
amplitude is
\( A \cdot b \)
B. 2b
\( c \cdot 3 b \)
D. 46


A bus starts from rest and moves with a
uniform acceleration of \( 1 ~ m s^{-2} . A \) boy
10 \( m \) behind the bus at the start runs
at a constant speed and catches the
bus in \( 10 s . \) Speed of the boy is :
A \( \cdot 10 m s^{-1} \)
B. \( 1 m s^{-1} \)
\( \mathrm{c} \cdot 6 \mathrm{ms}^{-1} \)
D. \( 4 m s^{-1} \)


Find the equation of the circle whose two end points of the diameter are
(4,-2) and (-1,3)


Fill the blank.
\( \$ \$ 2\{\text { Ca }\}_{-}\{3\}\left\{\text { lleft }\left(P\{0\}_{-}\{4\} \mid \text { right }\right)\right. \)
3. \( \{2\}+6 \operatorname{si}\{0\}_{-}\{2\}+10 C \) lrightarrow \( \{P \)
\( -\{4\}+\mid \) text \( \{-\} \operatorname{casi}\{0\}_{-}\{3 \)
\( 3+10 \cos \$ \)
\( A \cdot 2 \)
B. 4
\( c .5 \)
D. 6
E . 8


Which is the correct process-mineral matching in metallurgical extraction? This question has multiple correct options
A. Leaching : Ag
B. Zone-refining : Sn
c. Liquation: \( \operatorname{sn} \)
D. Van Arkel : zr


Male and female gametophytes are independent and free-living in
A. Sphagnum
B. Mustard
c. castor
D. Pinus


Which of the following will produce
sound through vibration.
A. A plastic scale when bent over the edge of a bench
B. Saying 'Ah' for few seconds
C. Plucking a rubber string by fingers
D. All of the above


A capillary tube when immersed vertically in a liquid rises to \( 3 \mathrm{cm} \). If the tube is held immersed in the liquid at
an angle of \( 60^{\circ} \) with the vertical,the length of the liquid column along the tube will be:
A. \( 2 \mathrm{cm} \)
B. 4.5 \( \mathrm{cm} \)
\( \mathrm{c} \cdot 6 \mathrm{cm} \)
D. 7.5 \( \mathrm{cm} \)


The main evolutionary feature of alternation of generations from algae to modern tracheophytes is
A. Elimination of sporophyte
B. Gradual elaboration of sporophyte
c. Gradual elaboration of gametophyte
D. Both B and C


For intensity \( I \) of a light of wavelength \( \mathbf{5 0 0 0} \boldsymbol{A} \) the photoelectron saturation current is \( 0.40 \mu A \) and stopping
potential is \( 1.36 V, \) the work function of metal is:
A . 2.47 ev
B. 1.36 ev
c. 1.10 ev
D. 0.43 ev


Identify \( \boldsymbol{x}, \boldsymbol{y} \) and \( \boldsymbol{z} \) for the following metallurgical process:
Metal sulphide \( \stackrel{x}{\rightarrow} \) Metal oxide \( \stackrel{y}{\rightarrow} \)
Impure metal
\( x, y \) and \( z \) are respectively:
A. roasting, smelting, electrolysis
B. roasting, calcination, smelting
c. calcination, auto-reduction, basemerisation
D. None of the above


The number of \( S-S \) bonds in
polythionic acid \( \boldsymbol{H}_{2} \boldsymbol{S}_{n} \boldsymbol{O}_{6} \) is :
\( A \)
B. \( n-1 \)
\( c \cdot n-2 \)
D. none of these


Form the differential equation from the following primitive, where constant is arbitrary. \( \boldsymbol{x} \boldsymbol{y}=\boldsymbol{a}^{2} \)


A current of i amp flows in a loop having circular arc of radius \( r \) subtending an
angle \( \theta \) as shown in the figure. The
magnetic field at the centre of the circle
is:
A \( \cdot \frac{\mu_{0} i}{4 \pi r} \)
B. \( \left(\frac{\mu_{0} i}{4 r}\right) \sin \theta \)
c. \( \left(\frac{2 \mu_{0} i}{2 r}\right) \sin \theta \)
D. \( \left(\frac{\mu_{0} i}{4 \pi r}\right) \sin \theta \)


Surgical removal of both the kidneys would result in death because
A. Water will accumulate in blood
B. Urea will not be excreted
c. Immune response will be suppressed
D. Glucose will be lost from the body


Heat of \( 20 \mathrm{Kcal} \) is supplied to the
system and \( 8400 J \) of external work is
done on the system so that its volume decreases at constant pressure. The change in internal energy is \( (J= \) \( 4200 J / k c a l) \)
A \( .9 .24 \times 10^{4} J \)
B. \( 7.56 \times 10^{4} J \)
c. \( 8.4 \times 10^{4} J \)
D. \( 10.5 \times 10^{4} J \)


Ribose sugar is not a component of
A. AMP
в. Атр
c. DNA
D. RNA


The probability that the value of certain stock will remain the same is \( 0.46 . \) The probability that its value will increase
by Rs. 0.50 or Re. 1 per share are respectively 0.17 and 0.23 and the probability that its value will decrease by Rs. 0.25 per share is 0.14 . The expected gain per share is
A . Rs. 0.75
B. Rs. 0.25
c. Rs. 0.28
D. Rs. 0.50


Two aeroplanes I and II bomb a target in succession. The probabilities of I and I scoring a hit correctly are 0.3 and 0.2 respectively. The second plane will bomb only if the first misses the target. The probability that the target is hit by the second plane is
A . 0.06
в. \( \frac{7}{22} \)
\( c .0 .2 \)
D. 0.7


Is used as a purple coloured antiseptic solution.
A. Bromine
B. Chlorine
c. lodine
D. Sulphur


Value of \( x \) in \( \frac{2}{3} x+6=12 \)
A . -
B. +27
\( c \cdot+9 \)
D. -27


A man fired a bullet against a wall and hears an echo after 2 s. He walks 80 m
towards the wall and fired bullet, such that he hears echo after 1 s. Find the
distance from wall to the second fired
place
A . \( 140 \mathrm{m} \)
B. 150 \( m \)
\( c .80 \mathrm{m} \)
D. 170 \( m \)


The main function of an antacid is:
A. to neutralize body acid
B. to neutralize body base
\( c . \) both a and \( b \)
D. none of these


If \( \mathrm{E} \) is the electric field intensity of an electrostatic field, then the
electrostatic energy density is proportional to:
\( A \cdot E \)
B . \( E^{2} \)
c. \( 1 / E^{2} \)
D. \( E^{3} \)


Perchloric acid is prepared by the action of concentrated sulphuric acid
on:
A \( \cdot \mathrm{NaClO}_{4} \)
в. \( \mathrm{KClO}_{3} \)
c. \( \left.\operatorname{ca}\left(\mathrm{ClO}_{3}\right) \mathrm{lO}_{3}\right) \)
D. Bac


Energy available from the oceans is:
A . OTE
B. sea-waves energy
c. tidal energy
D. all of the above


A decrease in blood pressure/ volume will not cause the release of
A. ADH
B. Renin
c. Atrial Natriuretic Factor
D. Aldosterone


Microorganisms can break down PAHs
in soil or water in a period of a week or a
month.
A. True
B. False


A car sometimes overturns while taking
a turn. When it overturns,:
A. the inner wheel leaves the ground first.
B. the outer wheel leaves ground first.
C. both the wheels leave the ground simultaneously.
D. either of the wheels leaves the ground first.


Write the structures of the given compounds whose IUPAC names are given as:
2,7-dimethylocta-2,4,6-triene


\( \sin x+i \cos 2 x \) and \( \cos x-i \sin 2 x \) are
conjugate to each other for
A . \( x=n \pi \)
B. \( x=\left(n+\frac{1}{2}\right) \frac{\pi}{2} \)
c. \( x=0 \)
D. No value of \( x \)


The safest place during a thunderstorm is:
A. Under a tree
B. Near electricity poles
c. Inside a car
D. Lying on the ground


The hydride used as refrigerant in ice
plants is:
A . \( \mathrm{NH}_{3} \)
в. РНз \( _{3} \)
\( c \cdot \mathrm{N} \mathrm{Cl}_{3} \)
D. PCls


Find the value of \( \frac{i^{6}+i^{7}+i^{8}+i^{9}}{i^{2}+i^{3}} \)


The sum of two numbers is 45 and their
ratio is \( 7: 8 . \) Find the numbers.


If \( y^{2}=(x-c)^{3}, \) then find \( \frac{d y}{d x} \)


When one mole of \( P(g) \) is introduced in one litre closed rigid vessel maintained at constant temperature, the following equilibrium is established. \( \boldsymbol{P}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{Q}(\boldsymbol{g})+\boldsymbol{R}(\boldsymbol{g}) \quad \Longrightarrow \boldsymbol{K}\left(\boldsymbol{C}_{1}\right) \)
\( \boldsymbol{R}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{S}(\boldsymbol{g})+\boldsymbol{Q}(\boldsymbol{g}) \quad \Longrightarrow \boldsymbol{K}\left(\boldsymbol{C}_{2}\right) \)
f the final equilibrium pressure is 2 times of the initial pressure, then the value of \( \frac{\boldsymbol{K}\left(\boldsymbol{C}_{2}\right)}{\boldsymbol{K}\left(\boldsymbol{C}_{1}\right)} \) is
[Ratio of the equilibrium concentration of \( Q \text { and } R \text { is } 5] \)


If we increase the driving frequency in a circuit with a purely resistive load, then
amplitude \( V_{R} \)
A. remain in the same
B. increase
c. decrease
D. none


\( O_{3} \) acts as both oxidizing as well as
reducing agent.


A gas expands from volume \( V_{0} \) to \( 2 V_{0} \)
under three different processes. Process
is isobaric, 2 is isothermal and 3 is
adiabatic. Let \( \Delta U_{1}, \Delta U_{2} \) and \( \Delta U_{3} \) be
the change in internal energy of the gas
in these three processes. Then:
A \( \cdot \Delta U_{1}>\Delta U_{2}>\Delta U_{3} \)
B. \( \Delta U_{1}<\Delta U_{2}<\Delta U_{3} \)
\( \mathbf{c} \cdot \Delta U_{2}<\Delta U_{1}<\Delta U_{3} \)
D. \( \Delta U_{2}<\Delta U_{3}<\Delta U_{1} \)


A body executing \( S . H . M . \) along a
straight line has a velocity of \( 3 m s^{-1} \)
when it is at a distance of 4 m from its
mean position and \( 4 m s^{-1} \) when it is at
a distance of \( 3 m \) from its mean
position. Its angular frequency and amplitude are:
A \( \cdot 2 \) rad \( s^{-1} \) \& \( 5 m \)
B. 1 rad \( s^{-1} \) \& \( 10 m \)
c. 2 rad \( s^{-1} \) \& \( 10 m \)
D. 1 rad \( s^{-1} \) \& \( 5 m \)


The radius of a sphere is measured to be \( 5.3 \pm 0.1 \mathrm{cm} . \) Calculate the
percentage error in the measurement of
its volume.
A . \( 3.45 \% \)
B . \( 5.66 \% \) \%
c. \( 2.4 \% \)
D. 1.05\%\%\%\%


\( A B C D \) is a rectangle in which diagonal
\( A C \) bisects \( \angle A \) as well as \( \angle C . \) Show
that:
(i) \( A B C D \) is a square
(ii) diagonal \( B D \)
bisects \( \angle B \) as well as \( \angle D \)


There are 'mn' letters and n post boxes. The number of ways in which these
letters can be posted is:
A \( \cdot(m n)^{n} \)
B . \( (m n)^{m} \)
\( \mathrm{c} \cdot m^{m} \)
D. \( n^{m} \)


Adjoining figure shows a series \( R C L \) circuit connected to an ac source which
generates an alternating emf of frequency \( 50 H z . \) The reading of the
voltmeters \( V_{1} \) and \( V_{2} \) are \( 80 V \) and \( 60 V \)
respectively
Find:
The current in the circuit


When two dice are rolled :
List the outcomes for the event that
total is less than 5 .


For \( \mathbf{0} \leq \boldsymbol{x} \leq \mathbf{1}, \) the function \( \boldsymbol{f}(\boldsymbol{x})= \)
\( |\boldsymbol{x}|+|\boldsymbol{x}-\mathbf{1}| \) is
A. Monotonically increasing
B. Monotonically decreasing
c. constant function
D. Identity function


Which of the following has negative charge and pairs with opposite spin?
A. Proton
B. Neutron
c. Electron
D. Isotope
E. lon


A pair of compounds which is an illustration of law of multiple
proportions is:
A. \( H_{2} O \) and \( D_{2} O \)
в. \( N a O H \) and \( K O H \)
c. \( N a C l \) and \( N a B r \)
D. \( C O \) and \( C O_{2} \)


How many moles of \( N a O H \) are required to neutralize 1.2 moles of
\( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} ? \)
A. 0.6 mole
B. 1.2 mole
c. 2.4 mole
D. 3.6 mole
E . 4.8 mole


Plot \( A \& B \) represent variation of charge
with potential difference across the
combination (series and parallel) of two
capacitors. Then find the value of
capacitance of capacitors.
A \( .20 \mu F, 30 \mu F \)
B. \( 10 \mu F, 40 \mu F \)
с. \( 10 \mu F, 15 \mu F \)
D. \( 25 \mu F, 25 \mu F \)


Two concentric shells have radii \( \mathbf{R} \) and
2R, charges \( q_{A} \) and \( q_{B} \) and potentials \( 2 V \)
and \( (3 / 2) \vee \) respectively. Now shell \( B \) is
earthed and let charges on them
become \( \boldsymbol{q}_{\boldsymbol{A}}^{\prime} \) and \( \boldsymbol{q}_{\boldsymbol{B}}^{\prime} . \) Then:
This question has multiple correct options
\( \mathbf{A} \cdot q_{A} / q_{B}=1 / 2 \)
\( \mathbf{B} \cdot\left|q_{A}^{\prime}\right| /\left|q_{B}^{\prime}\right|=1 \)
C. Potential of A after earthing becomes (3/2)V
D. Potential difference between A and B after earthing becomes V/2


Find, in the given circuit, currents in
\( 10 \Omega \) and \( 100 \Omega \) resistors and the value
of R.


Explain law of multiple proportion.


The reaction in which reactants and the
catalyst have one phase is
1. heterogeneous catalysis
2. homogeneous catalysis
3. solid state catalysis
4. solution catalysis


Epimerase belongs to the class of
enzymes
A. Hydrolases
B. Ligases
c. Isomerases
D. Oxidoreductases


If the height of a triangle is decreased by \( 40 \% \) and its base is increased by \( 40 \% \). What will be the effect on its area?
A. Decreased by \( 16 \% \)
B. Increased by \( 16 \% \)
c. Decreased by \( 20 \% \)
D. Increased by \( 20 \% \)


\( _{\mathrm{H}_{3} \mathrm{C}}^{\mathrm{O}} \) 山 \( _{\mathrm{CH}_{3}} \frac{_{\mathrm{l}, \mathrm{NaBH}_{4}}}{2 . \mathrm{D}_{3} \mathrm{o}^{+}}>\mathrm{X} \)
\( \mathbf{X}=\mathbf{Y}=\quad \underset{\mathbf{H}_{3} \mathbf{C}}{\mathbf{C}} \stackrel{\mathbf{D}}{\mathbf{C}}_{\mathbf{C H}_{3}}^{\text {oD }} \)
\( \mathbf{X}=\mathbf{Y}=\underbrace{\mathbf{H}}_{\mathbf{H}_{3} \mathbf{C}}^{\mathbf{O} \mathbf{H}}_{\mathbf{C H}_{3}} \)


All straight wires are very long. Both \( \boldsymbol{A B} \)
and \( C D \) are arcs of the same circle,
both subtending right angles at the
centre \( O . \) Then the magnetic field at 0
is-
A \( \cdot \frac{\mu \text { is }}{4 \pi R R R} \)
B・ \( \frac{\mu_{\text {Di }}}{4 \pi} \sqrt{2} \)
c. \( \frac{\mu \text { li }}{2 \pi R_{R}} \)
D. \( \frac{\mu_{0} i}{2 \pi R}(\pi+1) \)


A given particle starts at \( x=1 \) on the
potential function \( U(x)=x^{2}-10 x+ \)
\( 25, \) where \( U \) is in Joules and \( x \) is in
meters. It then moves down the
potential gradient to \( x=3 \) where it has
\( 4 J \) of potential energy. If it started at rest, how much kinetic energy does it have as it passes through \( x=3 ? \)
A . 2.5
в. 45
\( c \cdot 8 J \)
D. 12.5
E .16 .5


An object is placed at a distance of 50 \( \mathrm{cm} \) from a concave lens of focal length
\( 20 \mathrm{cm} . \) Find the nature and position of the image.


Find the coordinates of the point \( \boldsymbol{P} \)
which divides the join of \( \boldsymbol{A}(-2,5) \) and \( B(3,-5) \) in the ratio 2: 3


n fig \( 10.49, \) ABCD is parallelogram
CE\perpAB,CF\perpAD and\angleBCE = 40^
Find the values of \( x, y \) and \( z \)


Deep black soil is considered to be
highly productive due to high proportion of
A. silt and earthworm
B. Clay and humus
c. Gravel and \( \mathrm{Ca}^{2} \)
D. sand and \( z n^{2+} \)


To use a transistor as an amplifier:
A. The emitter base junction is forward biased and the base collector junction is reverse biased
B. No bias voltage are required
C. Both junctions are forward biased
D. Both junction are reverse biased


The increasing order of specific charge of electron (e), proton (p), alpha partial
\( \alpha \) ) and neutron (n) is:
A. e, p, n, \( \alpha \)
B. n, p, e, \( \alpha \)
\( c \cdot n, \alpha, p, e \)
D. \( n, \) p, \( \alpha \), e


Which of the following are characteristics of ethene but not of
ethane
This question has multiple correct options
A. Carbon is \( s p^{3} \) hybridised
B. Carbon is \( s p^{2} \) hybridised
C. Allowed rotation through \( C-C \) bond and axis perpendicular to it
D. Forbidden rotation through \( C-C \) bond and axis
perpendicular to it


In 15 days, the earth picks up \( 1.2 \times 10^{8} \)
kg of dust from the atmosphere. In how many days it will pick up \( 4.8 \times 10^{8} \mathrm{kg} \)
of dust?


1.6 mole of \( \boldsymbol{P C l}_{5}(\boldsymbol{g}) \) is placed in \( \boldsymbol{4} \boldsymbol{d} \boldsymbol{m}^{3} \)
closed vessel. When the temperature is
raised to \( 500 K \), it decomposes and at
equilibrium 1.2 mole of \( P C l_{5}(g) \)
remains.What is the \( K_{c} \) value for the
decomposition of \( \boldsymbol{P} \boldsymbol{C l}_{\mathbf{5}}(\boldsymbol{g}) \) to \( \boldsymbol{P} \boldsymbol{C l}_{3}(\boldsymbol{g}) \)
and \( C l_{2}(g) \) at \( 500 K ? \)
\( \mathbf{A} \cdot 0.013 \)
B. 0.050
c. 0.033
D. 0.067


A card is drawn from a pack of 52 cards at random. The probability of getting neither an ace nor a king card is:
A \( \cdot \frac{2}{13} \)
в. \( \frac{11}{13} \)
c. \( \frac{4}{13} \)
D. \( \frac{8}{13} \)


Across the surface of a charged
conductor,

This question has multiple correct options
A. field is continuous
B. potential is continuous
C. field is discontinuous
D. potential is discontinuous


Find the following sum. \( \sum_{r=1}^{n}\left(6 r^{2}-2 r+6\right) \)


Two liquids \( A \) and \( B \) form ideal
solutions. At \( 300 K \), the vapour
pressure of a solution containing 1 mole of \( A \) and 3 moles of \( B \) is 550 mm
Hg. At the same temperature, if one
more mole of \( B \) is added to this
solution, the vapour pressure of the
solution increases by 10 mm \( H g \). The
vapour pressure of \( A \) and \( B \) in their
pure states are respectively:
A \( \cdot p_{A}^{o}=600 \mathrm{mm} \mathrm{Hg} \) and \( p_{B}^{o}=400 \mathrm{mm} \mathrm{Hg} \)
B . \( p_{A}^{o}=500 \mathrm{mm} \mathrm{Hg} \) and \( p_{B}^{o}=560 \mathrm{mm} \mathrm{Hg} \)
C \( \cdot p_{A}^{o}=450 \mathrm{mm} \mathrm{Hg} \) and \( p_{B}^{o}=650 \mathrm{mm} \mathrm{Hg} \)
D . \( p_{A}^{o}=400 \mathrm{mm} \mathrm{Hg} \) and \( p_{B}^{o}=600 \mathrm{mm} \mathrm{Hg} \)


Match the following and choose the
correct option.
\( \mathbf{A} \)
B. A- 4, B-1, C-2, D-3
C. \( A-4, B-1, C-3, D-4 \)
D. \( A-4, B-2, C-3, D-4 \)


For RNA-interference, two scientists got Nobel prize in \( 2006 . \) In which organism these scientists discovered this
process?
A. Paragonimus westermani
B. Hymenolepis nana
c. Echinococcus granulosus
D. caenorhabditis elegans


\( \boldsymbol{B}_{1}+\boldsymbol{B}_{2}+\ldots \ldots+\boldsymbol{B}_{49} \) is equal to
A. \( B_{0} \)
В. \( 7 B_{0} \)
\( \mathbf{c} \cdot 49 B_{0} \)
D. 49


A particle in S.H.M. has a period of 2
seconds and amplitude of \( 10 \mathrm{cm} \) Calculate the acceleration when it is at
\( 4 c m \) from its positive extreme position.


Water which gives lather with soap easily is called as hard water.
A. True
B. False


The measured potential for
\( M g^{2+}+2 e^{-} \rightleftharpoons M g(s) \)
does not depend upon:
A. raising the temperature
B. increasing the concentration of \( M g^{2+} \) ions
c. making the magnesium plate bigger
D. purity of magnesium plate


The general term of a sequence is given
by \( a_{n}=-4 n+15 . \) Is the sequence an
A.P? If so, find its 15 th term and the
common difference.


Among the following, the state
functions are:

This question has multiple correct options
A. Internal energy
B. Irreversible expansion work
C . Reversible expansion work
D. Molar enthalpy


The average weight of 15 Oarsmen in a
boat is increased by \( 1.6 \mathrm{kg} \) when one of the crew, who weigh \( 42 \mathrm{kg} \) is replaced
by a new man. Find the weight of the new man (in kg).
A . 65
B. 66
c. 43
D. 67


A chord of a circle of radius \( 12 \mathrm{cm} \)
subtends an angle of \( 120^{\circ} \) at the center
Find the area of the corresponding segment of the circle.


A capacitor 'C' is connected across a
D.C. source, the reactance of capacitor
will be
A . ZERO
в. Нाप्प
c. Low
D. INFINITE


The Kohlrausch law is realted to:
A. Conductance of ions at infinite dilution
B. Independent migration of ions
C. Both (a) and (b)
D. neither
(a) and (b)


Decreasing order of boiling point of \( I \) to
\( \boldsymbol{I} \boldsymbol{V} \) follow
Methylformate Ethylformate Iso-propylformate \[ _{I I I} \] n-Propylformtae
\( A \cdot|>||>|||>\mid V \)
B. ||| > IV > || > |
c. \( \mid V>\|>\|>1 \)


Find the typical de Broglie wavelength associated with a \( H e \) atom in helium
gas at room temperature \( \left(27^{\circ} C\right) \) and
1 atm pressure, and compare it with the mean separation between two atoms under these conditions.
A \( \cdot r_{0}=6.4 \times 10^{-9} \mathrm{m} \)
B . \( r_{0}=3.4 \times 10^{-9} \mathrm{m} \)
C \( \cdot r_{0}=4.4 \times 10^{-9} \mathrm{m} \)
D. \( r_{0}=5.4 \times 10^{-9} \mathrm{m} \)


A particle of mass \( \mathrm{M} \) at rest decays into
two masses \( m_{1} \) and \( m_{2} \) with non-zero
velocities. The ratio \( \lambda_{1} / \lambda_{2} \) of de Broglie
wavelengths of particles is
A \( \cdot m_{2} / m_{1} \)
в. \( m_{1} / m_{2} \)
c. \( \sqrt{m_{1}} / \sqrt{m_{2}} \)
in
D. 1:


The device that is used to protect
buildings from the effects of lightning is:
A. transformer
B. transducer
c. electrode
D. lightning conductor


Find the modulus and the argument of the complex number \( z=-1-i \sqrt{3} \)


What is the \( S_{\alpha} \) sulphur allotropes
called?
A. Rhombic
B. Monoclinic
c. Liquid
D. None of these


The equipotential surfaces corresponding to a single positive charge are concentric
spherical shells with the charge at its origin. The spacing between the surfaces for the same change in potential:
A. is uniform throughout the field
B. is getting closer as \( r \rightarrow \infty \)
c. is getting closer as \( r \rightarrow 0 \)
D. can be varied as one wishes to


If \( [\overrightarrow{\boldsymbol{a}} \overrightarrow{\boldsymbol{b}} \overrightarrow{\boldsymbol{c}}]=1 \) then \( \frac{\overrightarrow{\boldsymbol{a}} \cdot \overrightarrow{\boldsymbol{b}} \times \overrightarrow{\boldsymbol{c}}}{\overrightarrow{\boldsymbol{c}} \times \overrightarrow{\boldsymbol{a}} \cdot \overrightarrow{\boldsymbol{b}}}+\frac{\overrightarrow{\boldsymbol{b}} \cdot \overrightarrow{\boldsymbol{c}} \times \overrightarrow{\boldsymbol{a}}}{\overrightarrow{\boldsymbol{a}} \times \overrightarrow{\boldsymbol{b}} \cdot \overrightarrow{\boldsymbol{c}}}+ \)
\( \frac{\vec{c} \cdot \vec{a} \times \vec{b}}{\vec{b} \times \vec{c} \cdot \vec{a}} \) is equal to
\( A \cdot 3 \)
B. 1
\( c \cdot-1 \)
D. None of these


The time \( t, \) of a complete oscillation of a simple pendulum of length \( l \) is given by \( t=2 \pi \sqrt{\frac{l}{g}} \) where \( g \) is gravitational constant. Find the approximate percentage of errors in \( t \) when the
percentage of error \( l \) is \( 1 \% \)


An unknown composition of a mixture of carbon disulphide and hydrogen sulphide was burnt in sufficient
amount of oxygen. The resulting gases found to exert a pressure of 1.97 atm in a 20 I vessel at 400 K. The gaseous
mixture required 2.8 M iodine solution and \( 250 \mathrm{ml} \) of it was required to reach
the end point, forming \( \boldsymbol{I}^{-} \). Calculate the
mole fraction of \( \boldsymbol{C} \boldsymbol{S}_{2} \) in the original
mixture.
A. 0.2
B. 0.4
c. 0.6
D. 0.8


One diagonal of a square is the portion of \( \frac{x}{97}+\frac{y}{79}=1 \) intercepted between
the axes. \( \boldsymbol{p}_{1}, \boldsymbol{p}_{2} \) are the lengths of the perpendiculars from the vertices of the other diagonal on the axis of \( y \) then \( p_{1}^{2}+p_{2}^{2} \) is equal to


Determine the domain and range of the
following relations. \( \boldsymbol{S}=\{(\boldsymbol{a}, \boldsymbol{b}): \boldsymbol{b}=|\boldsymbol{a}-\mathbf{1}|, \boldsymbol{a} \in \boldsymbol{Z} \) and
\( |a| \leq 3\} \)


Which of the following can dissolve limestone?
A. \( C O_{2}+H_{2} O \)
в. \( N a O H_{2}+H_{2} O \)
c. \( N H_{3}+H_{2} O \)
D. None of these


Two waves of wavelengths \( 2 \mathrm{m} \) and 2.02 m respectively moving with the same velocity superpose to produce 2 beats
/s. The velocity of the wave is:
A. \( 400 \mathrm{m} / \mathrm{s} \)
B. 402 m/s
c. \( 404 \mathrm{m} / \mathrm{s} \)
D. \( 406 \mathrm{m} / \mathrm{s} \)


What is the range of molecular weight of cellulose?


Which of the given figures represents budding in hydra?
\( A \)
в.
\( c \)
D.


What are hormones? Give an example for each of the following:
(a) Steroid hormones
(b) Polypeptide hormones
(c) Amino acid derivatives


The valency of fluorine in \( C a F_{2} \) is :
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot-1 \)
D. - -


Mean of 10 observations is 50 and their
standard deviation is \( 10 . \) If each
observation is subtracted by 5 and then
divided by \( 4, \) then the new mean and standard deviation are
A \( .22 .45,2.5 \)
В. 11.25,2.5
c. 11.5,2.5
D. 11,2.5
E . 11.75,2.5


Biospecies concept was propounded by
A. Ernst Mayr
B. Darwin
c. simpson
D. Aristole


Hydrogen bomb is based on the
principle of:
A. nuclear fission
B. natural radioactivity
c. nuclear fusion
D. artificial radioactivity


Median of the odd divisors of 360 is
A. the mean of 3 rd and 4 th item
B. the mean of 4 th and 5 th item
c. the mean of 5 th and 6 th item
D. none of these


Which of the following is the correct
form of Schrodinger wave equation?
A \( \cdot \frac{\partial^{2} \Psi}{\partial^{2} x}+\frac{\partial^{2} \Psi}{\partial^{2} y}+\frac{\partial^{2} \Psi}{\partial^{2} z}+\frac{8 \pi^{2} m}{h^{2}}(E-V) \Psi=0 \)
B \( \cdot \frac{\partial^{2} \Psi}{\partial x^{2}}+\frac{\partial^{2} \Psi}{\partial y^{2}}+\frac{\partial^{2} \Psi}{\partial z^{2}}+\frac{8 \pi^{2} m}{h^{2}}(E-V) \Psi=0 \)
C \( \cdot \frac{\partial \Psi^{2}}{\partial x^{2}}+\frac{\partial \Psi^{2}}{\partial y^{2}}+\frac{\partial \Psi^{2}}{\partial z^{2}}+\frac{8 \pi^{2} m}{h^{2}}(E-V) \Psi=0 \)
D \( \cdot \frac{\partial^{2} \Psi}{\partial x^{2}}+\frac{\partial^{2} \Psi}{\partial y^{2}}+\frac{\partial^{2} \Psi}{\partial z^{2}}+\frac{8 \pi^{2} m^{2}}{h^{2}}(E-V) \Psi=0 \)


Two charges each of \( +Q \) units are
placed along a line. A third charge \( -q \) is
placed between them. At what position and for what value of \( q, \) will the system be in equilibrium?


Explain the laboratory method for preparation of hydrogen peroxide.


Which of the following statements has
the truth value \( ^{\prime} F^{\prime} ? \)
A. A quadratic equation has always a real root
B. The number of ways of seating 2 persons in two chairs out of \( n \) persons in \( P(n, 2) \)
C. The cube roots of unity are in GP
D. None of the above


The resistance of a heating element is
\( 99 \Omega \) at room temperature. What is the temperature of the element if the
resistance is found to be \( 116 \Omega ? \)
(Temperature coefficient of the material
of the resistor is \( 1.7 \times 10^{-4} o C^{-1} \) ).
A \( \cdot 9999^{\circ} \mathrm{C} \)
B . \( 1005.3^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 1020.2^{\circ} \mathrm{C} \)
D. \( 1037.1^{\circ} \mathrm{C} \)


If \( a, b \) are constants then, \( V a r(a+b X) \)
is
A. \( \operatorname{Var}(a)+\operatorname{Var}(X) \)
B. \( \operatorname{Var}(a)-\operatorname{Var}(X) \)
\( \mathbf{c} \cdot b^{2} \operatorname{Var}(X) \)
D. None of these


In a multiple choice question, there are
four alternative answer of which one or
more than one is correct. A candidate
will get marks on the question only if he ticks all the correct answer. The
candidate decides to tick all the correct
answer. The candidate decides to tick
answers at random. If he is allowed up to three chances to answer the
question, the probability that he will get marks on it is
\( A \cdot \frac{1}{2} \)
B.
\( c \cdot \frac{1}{4} \)
D. 5


If \( z_{1}=a+i b \) and \( z_{2}=c+i d \) are
complex numbers such tat \( \left|z_{1}\right|= \)
\( \left|z_{2}\right|=1 \& R e\left(z_{1} \overline{z_{2}}\right)=0, \) then the pair
of complex numbers \( \boldsymbol{w}_{1}=\boldsymbol{a}+\boldsymbol{i} \boldsymbol{c} \) and
\( \boldsymbol{w}_{2}=\boldsymbol{b}+\boldsymbol{i} \boldsymbol{d} \) satisfies -
This question has multiple correct options
\( \mathbf{A} \cdot\left|w_{1}\right|=1 \)
B \( \cdot\left|w_{2}\right|=1 \)
\( \mathbf{c} \cdot \operatorname{Re}\left(w_{1} \overline{w_{2}}\right)=0 \)
D. None of these


lonic hydride reacts with water to give:
A. hydride ions
B. acidic solution
c. protons
D. basic solution


The reptile which lacks penis belongs to
A. ophidia
B. crocodilia
c. Gymnophiona
D. Rhynchocephalia


In the Boolean algebra, the following one
is wrong
A . \( 1.0=0 \)
B. \( 0.1=0 \)
c. \( 1.1=0 \)
D. \( 1.1=1 \)


There are 3 balls of same shape and size made of wood, iron and plastic. Which one of them would have highest inertia?
A. wood
B. Iron
c. Plastic
D. None of these


toppr
Q Type your question
volume. I ne cyıınaer nas a cnarge per
unit length of \( \lambda \)

A Gaussian surface is imagined that is
also shown in the diagram. This
Gaussian surface is also a cylinder
having the same axis as the charged
cylinder. The Gaussian cylinder's radius
is \( a, \) where \( a<R, \) and its length is \( L \)
What is the charge enclosed in the
Gaussian cylinder?
\( ^{\mathbf{A}} \cdot Q_{e n c}=\lambda \frac{a}{R} \)
\( ^{\mathrm{B}} \cdot_{e n c}=\lambda L \frac{a}{R} \)
\( \mathrm{C}_{e n c}=\lambda L \frac{a^{3}}{R^{3}} \)
\( \mathrm{D} \cdot \mathrm{Q}_{e n c}=\lambda \frac{a^{3}}{R^{3}} \)
\( \mathrm{E} \cdot Q_{e n c}=\lambda L \frac{a^{2}}{R^{2}} \)


Assimilatory power refers to the
A. Generation of ATP and NADPH \( _{2} \)
B. Reduction of \( \mathrm{CO}_{2} \)
C . Splitting of water
D. Disintegration of plastids


Hypermetropia is due to the
of the eye.
A. low converging power
B. low diverging power
c. high converging power
D. high diverging power


Is sphere, a \( 2 D \) or a \( 3 D \) object?
A . \( 2 D \)
в. \( 3 D \)
c. Does not exist in both planes
D. None of the above


Removal of water molecule from the
substrate is called
A. Enolation
B. Phosphorylation
c. Decarboxylation
D. Oxidation


A ray passing with which part of a lens emerges undeviated ?
A. Focus
B. Centre of curvature
c. optical centre
D. Between focus and centre of curvature


Number of Bonds present in \( N_{2} O_{3} \)
molecule is :
\( A \cdot 2 \)
B. 4
\( c \cdot 6 \)
D. 8


Find the derivative of the following
function from first principle:
\( -x \)


Figure shows a composite system of
two uniform rods of lengths as
indicated. If both the rods are of same
density. Then the coordinates of the
centre of mass of the system of rods
are:
A \( \cdot\left(\frac{L}{2}, \frac{2 L}{3}\right) \)
B \( \cdot\left(\frac{L}{4}, \frac{2 L}{3}\right) \)
c. \( \left(\frac{L}{6}, \frac{2 L}{3}\right) \)
D. \( \left(\frac{L}{6}, \frac{L}{3}\right) \)


A particle of charge \( q \) and mass \( m \)
moves in a circular path of radius \( r \) in a
uniform magnetic field \( B \).

The particle is replaced with a particle
of identical charge and mass \( \frac{1}{2} m \) The radius of the new circular path the
particle makes is:
A \( \cdot \frac{1}{4} r \)
в. \( \frac{1}{2} r \)
c. \( r \)
D. \( 2 r \)
E . \( 4 r \)


What is incorrect about the given
structure?

This question has multiple correct options
\( A \). It has six D.U
B. It has ten \( s p^{2} \) hybrid C-atom
C. It has ten \( s p^{2}-s p^{2} \) C-C \( \sigma \) bond
D. All are correct.


Comet is an object with a head and a \( _{-}-_{-}-_{-}-_{-}- \) tail.
A. pale, long
B. bright, long
c. pale, short
D. bright, short


The terms order and molecularity are
common in chemical kinetics.
(a) What do you mean by order and molecularity?
(b) (i) Write two factors influencing rate of a reaction.
(ii) Write Arrhenius equation.


The voltage across the electrodes of a cathode ray tube is 500 V. Then the speed of the electron is
A \( \cdot 2.6 \times 10^{7} m s^{-1} \)
B. \( 1.33 \times 10^{7} m s^{-1} \)
\( \mathbf{c} \cdot 2.8 \times 10^{7} m s^{-1} \)
D. \( 1.9 \times 10^{7} \mathrm{ms}^{-1} \)


Very short answer type:
State one advantage and one disadvantage of cleistogamy.


When a constant potential difference is maintained between the ends of a
conductor
A. A steady current flows through the conductor
B. A current density is established at every point inside the conductor
c. An electric field is established inside the conductor
D. All are true


\( 7 / 8 \) fraction of a sample disintegrates in 't' time, how much time it will take to disintegrate \( 15 / 16 \) fraction?
\( \mathbf{A} \cdot \mathbf{t} \)
B. \( 4 / 3 t \)
\( c \cdot 5 / 3 t \)
D. 2t


How to divide the equation in algebraic expression


An electric charge of 5 Faraday's is passed through three electrolytes
\( A g N O_{3}, C u S O_{4} \) and \( F e C l_{3} \) solution
The grams of each metal liberated at cathode will be:
A. \( A g=10.8 g, C u=12.7 g, F e=1.11 g \)
в. \( A g=540 g, C u=367.5 g, F e=325 g \)
c. \( A g=108 g, C u=63.5 g, F e=56 g \)
D. \( A g=540 g, C u=158.8 g, F e=93.3 g \)


The diagram below shows a positively charged particle moving toward the right and about to enter a magnetic field whose direction is shown by the blue arrows. What is the direction of the
force on the positively charged particle (from our point of view) at the instant it
enters the magnetic field?
A . right
B. left
c. up
D. toward us
E. away from us


What is Quiescent stage in cell division
\( ? \)


\( \lim _{x \rightarrow 0} \frac{\tan ^{4} x-\sin ^{4} x}{x^{4}}= \)
A . 0
B.
\( c \cdot \frac{2}{3} \)
D.


Explain the cleansing action of soap.


The rate of the reaction \( \boldsymbol{A}+\boldsymbol{B}_{2} \rightarrow \)
\( A B+B ; \) is directly proportional to the
concentration of \( A \) and independent of
concentration of \( B_{2} \), hence, rate law is:
\( \mathbf{A} \cdot k[A]\left[B_{2}\right] \)
\( \mathbf{B} \cdot k[A]^{2}\left[B_{2}\right] \)
c. \( k[A] \)
D. \( k\left[B_{2}\right] \)


A uniform sphere of mass \( m \) and radius
\( r \) rolls without sliding over a horizontal
plane, rotating about a horizontal axle
OA. In the process, the centre of the sphere moves with a velocity \( v \) along a
circle of radius \( R \) Find the kinetic
energy of the sphere.


Which pair of following forces will never give resultant force of \( 2 \mathrm{N} \)
A. \( 2 \mathrm{N} \) and \( 2 \mathrm{N} \)
B. 1 N and 1 N
c. \( 1 \mathrm{N} \) and \( 3 \mathrm{N} \)
D. \( 1 \mathrm{N} \) and \( 4 \mathrm{N} \)


In optical fibre,which of the following principles is used?
A. scattering
B. refraction
c. successive reflections
D. total internal reflection


The ratio in which the line \( 3 x+4 y+ \)
\( 2=0 \) divides the distance between
\( 3 x+4 y+5=0 \) and \( 3 x+4 y-5=0 \)
A .7: 3
B. 3: 7
\( c \cdot 2: 3 \)
D. None of these


Heats of combustion of methane,
carbon and hydrogen are 212,94,68
kcal mol \( ^{-1} \)
The heat of formation of \( C H_{4} \) is:
B. +18 kcal mol \( ^{-1} \)
c. -9 kcal mol \( ^{-1} \)
D. None of these


The number of primary amines of
formula \( C_{4} H_{11} N \) is:
\( A \cdot 2 \)
B.
\( c \cdot 4 \)
D. 3


Carrot root phloem bioassay is a device for
A . Auxin
B. ABA
c. wound hormone
D. cytokinin


The direction cosines of a vector \( \hat{\boldsymbol{i}}+ \) \( \hat{\boldsymbol{j}}+\sqrt{\mathbf{2}} \hat{\boldsymbol{k}} \) are
A \( \cdot \frac{1}{2}, \frac{1}{2}, 1 \)
B. \( \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}, \frac{1}{2} \)
c. \( \frac{1}{2}, \frac{1}{2}, \frac{1}{\sqrt{2}} \)
D. \( \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}} \)


The distance \( x \) covered in time \( t \) by a
body having initial velocity \( v_{0} \) and
having constant acceleration \( a \) is given
by \( \boldsymbol{x}=\boldsymbol{v}_{0} \boldsymbol{t}+\mathbf{1} / \mathbf{2} \boldsymbol{a} \boldsymbol{t}^{2} . \) This result follows
from :
A. newton's Ist law
B. newton's IInd law
c. newton's IIIrd law
D. none of the above


Assertion (A): In the synthesis of ammonia by Haber's process, mixture of potassium and aluminium oxides
can be used as promoter. Reason (R): Promoter enhances the
activity of catalyst.
A. Both (A) and (R) are true and
(R) is the correct explanation of (A)
B. Both (A) and (R) are true and (R) is not the correct explanation of \( (A) \)
c. (A) is true and
(R) is false
D. (A) is false but (R) is true


The speed of transverse wave on a
stretched string is:
A. directly proportional to the tension in the string
B. directly proportional to the square root of the tension
C. inversely proportional to tension
D. inversely proportional to square root of tension


Three waves of equal frequency having amplitudes \( 10 m m, 4 m m \) and \( 7 m m \) arrive at a given point with successive phase difference \( \frac{\pi}{2} . \) The amplitude of the resulting wave (in \( \mathrm{mm} \) ) is given by:
A . 7
B. 6
c. 5
D. 4


Draw the graph of the equation \( 2 x+ \)
\( \mathbf{3} \boldsymbol{y}+\boldsymbol{6}=\mathbf{0} \)


When an object is placed between optical centre and focus of lens:
A. Inverted, real and enlarged image is formed
B. Virtual, erect and enlarged image is formed
c. Inverted, erect, diminished image is formed
D. Virtual, real, diminished image is formed


Chemical analysis of phloem shows the presence of
A. More amount of carbohydrates
B. organic nitrogenous compounds
c. Minerals
D. Both A and B


\( x \)
cnanges Its pıtch so that It IS rIyıng
\( 100 m / s \) in an area of the Earth's
magnetic field that is perpendicular to
the plane and equal to \( 5.010^{5} T \)

What is the emf induced between the
wing tips? Assume that the plane was previously flying parallel to the earths magnetic field.
A. \( 0.12 \mathrm{v} \)
B. 0.20
c. \( 1.2 v \)
\( D \)


In domestic sewage, suspended solids, colloidal and dissolved materials
constitute
A . \( 10 \% \)
B. \( 5.6 \% \)
\( c .2 .7 \% \)
D. \( 0.1 \% \)


If the value of \( 103.5 \mathrm{kg} \) is rounded off to three significant figures, then the value
is
A \( \cdot 103 \)
B. 103.0
\( c \cdot 104 \)
D. 10.3


'The specific latent heat of fusion of ice
is
A \( \cdot 136 . J g^{-1} \)
в. \( 236 . J g^{-1} \)
c. \( 336 J g^{-1} \)
D. \( 436 J g^{-1} \)


A species of an element \( A \) has a net charge of -1 and it has 18 electrons and
20 neutrons. Identify the correct
statements.

This question has multiple correct options
A . Its symbol will be \( _{17}^{3 \mathrm{A}} \)
B. Its atomic number is 18
c. The number of protons are 17
D. Its mass number is 38


The slope of plate characteristic and mutual characteristic curves of a triode
value is \( 0.02 \mathrm{mA} / \mathrm{V} \) and \( 1 \mathrm{mA} / \mathrm{V} \). The
amplification factor of triode value is:
A \( .2 \times 10^{8} \)
B. 20
c. 50
D. 40


Which of the following is incorrectly matched?
A . alkali metal \( \rightarrow \) cesium
B. alkali earth metal \( \rightarrow \) barium
c. chalcogens \( \rightarrow \) silicon
D. halogon \( \rightarrow \) iodine


The apparent molar mass of \( \boldsymbol{P C l}_{5} \) on dissociation shows lower value.
If true enter 1 , if false enter 0 .


Which of the following elements forms double or triple bonds involving \( \boldsymbol{p}-\boldsymbol{p} \)
bonding?
A. Carbon
B. Silicon
c. Germanium
D. Tin


In half wave rectifier, a p-n diode with internal resistance \( 20 \Omega \) is used. If the
load resistance of \( 2 K \Omega \) is used in the
circuit, then the efficiency of this half wave rectifier is (in percentage)


If the slope of the line passing through the points \( (2, \sin \theta) \) and \( (1, \cos \theta) \) is 0
then the general solution of \( \theta \), is
A \( \cdot n \pi+\frac{\pi}{4}, \forall n \in Z \)
B \( \cdot n \pi-\frac{\pi}{4}, \forall n \in Z \)
c. \( _{n \pi \pm} \frac{\pi}{4}, \forall n \in Z \)
D. \( n \pi, \forall n \in Z \)


If \( A \) is a skew-symmetric matrix, then
trace of \( \boldsymbol{A} \) is


The percentage of metals in a mine of
lead ore is \( 60 \% . \) Now the percentage of silver is \( \frac{3}{4} \% \) of metals and the rest is lead. If the mass of ore extracted from
this mine is \( 8000 k g \), the mass (in kg.) of lead is:
A. 4763
в. 4764
c. 4762
D. 476


A long silver tea spoon is placed in a cup filled with hot tea. After some time, the exposed end (the end which is not dipped in tea) of the spoon becomes hot even without a direct contact with the
tea. This phenomenon can be explained mainly by
A. conduction
B. reflection
c. radiation
D. thermal expansion


To make a p-njunction conducting
A. The value of forward bias should be more than the
barrier potenital
B. The value of forward bias should be less than the barrier potential
C. The value of revers bias should be more than the
barrier potential
D. The value of revers bias should be less than the barrier
potential


Arrange the following elements in increasing order of their size.
\( \mathbf{V}, \mathrm{Nb}, \mathrm{Ta}, \mathrm{Db} \)
A. \( v<\mathrm{Nb}=\mathrm{Ta} \approx \mathrm{Db} \)
B. \( D b<N b= \) Ta \( \approx V \)
c. \( \mathrm{Ta}<\mathrm{Nb}=\mathrm{v} \approx \mathrm{Db} \)
D. None of these


mole of \( \boldsymbol{P C l}_{5} \) is heated with 0.2 mole
of chlorine in a one litre vessel till
equilibrium is established.At equilibrium if 0.8 mole of chlorine is
present in the vessel, the equilibrium
constant for the dissociation of \( \boldsymbol{P C l}_{5} \) is:
A. 0.9
B. 1.8
c. 1.2
D. 0.5


An ideal gas is allowed to expand both reversibly and irreversibly in an isolated
system. If \( T_{i} \) is the initial temperature
and \( T_{f} \) is the final temperature, which of the following is correct?
\( \mathbf{A} \cdot T_{f}>T_{i} \) for reversible process but \( T_{f}=T_{i} \) for irreversible process
B . \( \left(T_{f}\right) \) rev \( =\left(T_{f}\right) \) irrev
C. \( T_{f}=T_{i} \) for both reversible and irreversible process
D. \( \left(T_{i}\right) \) irrev \( >\left(T_{f}\right) \) rev


In the figure given above, \( A B \) is paralle
to \( C D . \) If \( \angle D C E=x \) and \( \angle A B E=y \)
then what is \( \angle C E B \) equal to?
A \( \cdot y-x \)
в. \( \frac{(x+y)}{2} \)
c. \( x+y-(\pi / 2) \)
D. \( x+y-\pi \)


Choose the correct answer from the
alternative given.

Complete the following reactions.
\( (i) M n O_{4}^{-}+2 H_{2} O+3 e^{-} \rightarrow \)
\( +40 H^{-} \)
\( (i i) M n O_{4}^{-}+8 H^{+}+5 e^{-} \rightarrow \)
\( +4 H_{2} O \)
\( (i i i) M n O_{4}^{-}+e^{-} \rightarrow \)
\( \mathbf{A} \cdot M n O_{2}, M n^{2+}, M n O_{4}^{2} \)
B. \( M n^{2+}, M n O_{2}, M n O_{4}^{2} \)
c. \( M n O_{4}^{2-}, M n^{2+}, M n O_{4}^{2} \)
D. \( M n O_{2}, M n O_{4}^{2-}, M n^{2+} \)


Prabhani Kranti is
I) Okra variety resistant to shoot and fruit borer
II) Bhindi resistant to yellow mosaic
virus
III) A wild varity of bhindi
IV) Produced by sexual hybridization
A. I, I li and III only correct
B. II and IV only correct
c. III and IV only correct
D. I and II only correct


Q Type your question-
particle is attached to the cylinder by a
horizontal thread \( A B \) as shown in the
figure. The particle initially rest on
horizontal plane. A horizontal velocity \( \boldsymbol{v}_{0} \)
is imparted to the particle, normal to the threading during subsequent
motion. Point out the false statements:
This question has multiple correct options
A. Angular momentum of particle about \( O \) remains
constant
B. Angular momentum about \( B \) remains constant
c. Momentum and kinetic energy both remain constant
D. Kinetic energy remains consta


Formation of alkane by the action of zinc on alkyl halide is called:
A. Wurtz reaction.
B. Kolbe's reaction
c. UImann's reaction.
D. Frankland reaction


A chord is \( 8 \mathrm{cm} \) away from the centre of
a circle of radius \( 17 \mathrm{cm} . \) Find the length
of the chord.


The Doppler effect is applicable for
A . Light waves only
B. Sound waves only
c. Both light and sound waves
D. None of the above


In optical instruments, the lenses are
used to form images by :
A. Reflection
B. Refraction
c. Dispersion
D. Scattering


\( \boldsymbol{x}+\boldsymbol{y}+\boldsymbol{z}=\mathbf{1} \)


Q Type your question
made to reaci with anute nul tads r is
evolved in the reaction which is made to
pass through the delivery tube into test
tube 2 having solution \( Z \) and a milky
solution is obtained What are \( X, Y \) and \( Z \)
respectively?
A. \( N a O H, C O_{2}, N a_{2} C O_{3} \)
в. \( \operatorname{Ca}(O H)_{2}, H_{2}, C a\left(H C O_{3}\right)_{2} \)
c \( \cdot \operatorname{ca}(O H)_{2}, C O_{2}, C a C O_{3} \)
D \( \cdot \) \( _{C a} \) a \( C \) O \( _{3}, \) C \( O_{2}, C a(O H)_{2} \)


A line with direction cosines
proportional to 2,1,2 meets each of the line \( \boldsymbol{x}=\boldsymbol{y}+\boldsymbol{a}=\boldsymbol{z} \) and \( \boldsymbol{x}+\boldsymbol{a}=\boldsymbol{2} \boldsymbol{y}= \)
2 \( z \). The co-ordinates of each of the
points of intersection are given by:
A. \( (3 a, 3 a, 3 a),(a, a, a) \)
в. \( (3 a, 2 a, 3 a),(a, a, a) \)
c. \( (3 a, 2 a, 3 a),(a, a, 2 a) \)
D. \( (2 a, 3 a, 3 a),(2 a, a, a) \)


The least count of a stop watch is 0.2 second. The time of 20 oscillations of a
pendulum is measured to be 25 seconds. The percentage error in the time period is
A . \( 16 \% \)
B. 0.8 \%
c. \( 1.8 \% \)
D. 8\%


A point charge \( Q \) is located at the center of the hollow spherical conductor of
inner radius \( \boldsymbol{R}_{1} \) and outer radius \( \boldsymbol{R}_{2} \)
the conductor being uncharged initially The potential at the inner surface will
be
A \( \cdot K Q\left[\frac{1}{R_{1}}+\frac{1}{R_{2}}\right] \)
В \( \cdot K Q\left[\frac{1}{R_{1}}-\frac{1}{R_{2}}\right] \)
c. \( K Q\left[\frac{1}{R_{2}}-\frac{1}{R_{1}}\right] \)
D. None of these


One conducting U tube can slide inside another as shown in figure, maintaining electric contacts between the tubes. The
magnetic field B is perpendicular to the plane of the figure. If each tube moves
towards the other at a constant speed \( v \)
then the emf induced in the circuit in
terms of \( \mathrm{B}, l \) and \( \mathrm{v} \) where \( l \) is the width of
each tube, will be
A . -Blv
в. Вlv
c. 2 вlv
D. zero


A ball is dropped from a height \( h \) on a
floor of coefficient of restitution \( e \). The
total distance covered by the ball just before second hit is
A \( \cdot h\left(1-2 e^{2}\right) \)
B \( \cdot h\left(1+2 e^{2}\right) \)
c. \( h\left(1+e^{2}\right) \)
\( D \cdot h e^{2} \)


An electron gun with its collector at a potential of \( 100 \mathrm{V} \) fires out electrons in a spherical bulb containing hydrogen gas at low pressure \( \left(\sim 10^{-2} \mathrm{mm} \text { of } \mathrm{Hg} \text { ). } \mathrm{A}\right. \)
magnetic field of \( 2.83 \times 10^{4} T \)
curves the path of the electrons in a
circular orbit of radius 12.0 cm.
(The path can be viewed because the
gas ions in the path focus the beam by attracting electrons, and emitting light by electron capture; this method is known as the fine beam tube method.) Determine e/m from the data.


Which of the following forms a homologus series?
A. Ethane, ethylene, acetylene
B. Ethane, propane, butanol
c. Methanal, ethanol, propanoic acid
D. Butane, 2 - Methylbutane, 2, 3 - Dimethyl butane


In a moving coil galvanometer a radial magnetic field is applied with concave magnetic poles, to have
A) uniform magnetic field
B) the plane of the coil parallel to field Choose the correct option among the following
A. both A and B are true
B. both A and B false
c. A is true, B is false
D. A is false, B is true


The Van't Hoff factor of \( 0.1 \mathrm{M} \mathrm{Ba}\left(\mathrm{NO}_{3}\right)_{2} \)
solutions is \( 2.74 . \) The degree of dissociation will be
A . 91.3\%
B. 87\%
c. \( 100 \% \)
D. 74\%


The minimum height required to convert the stored potential energy of water into electric energy is
\( \mathbf{A} \cdot 54 M \)
B. \( 34 M \)
c. \( 100 M \)
D. \( 5 ~ M \)


A generator with a circular coil of 100
turns of area \( 2 \times 10^{-2} m^{2} \) is immersed
in a \( 0.01 T \) magnetic field and rotated at a frequency of \( 50 H z . \) The maximum emf which is produced during a cycle is
\( \mathbf{A} \cdot 6.28 V \)
B . \( 3.44 V \)
\( c \cdot 10 V \)
D. \( 1.32 V \)


Carbon dioxide acceptor in \( C_{3} \) plants is
A. PEP
B. RuBP.
c. PGA
D. NADP.


Two neutral conducting spheres are next to each other and touching each
other, They are also each separated from the table with an insulating stand.
Then, a negatively charged rod is brought near, but not touching, sphere
A. The two spheres are then separated
by touching only their insulating base Finally, the charged rod is removed. What are the charges of sphere \( A \) and
sphere B?
A. Sphere A is positive while sphere B is negative
B. Sphere A is negative while sphere B is positive
c. Both spheres are positively charged.
D. Both spheres are negatively charged


The chemical substances used to bring down body temperature in a high fever
are known as:


What happens to the current in the external circuit when a battery ages?
A. Remain the same
B. Polarize
c. Reverse direction
D. Increase
E. Decrease


\( A B C D \) is parallelogram. \( L \) and \( M \) are points on \( A B \) and \( D C \) respectively such that \( A L=C M . \) The diagonal \( B D \)
intersects \( L M \) at point \( O . \) If \( A B= \) \( 14 c m, A D=9 c m \) and \( L O=5 c m, \) find
the length of \( M O \)


Which of the following has the highest
mass?
A. 1 mole of \( C \) atoms
в. \( \frac{1}{2} \) mole of \( C H_{4} \)
c. \( 10 \mathrm{ml} \) of water
D. \( 3.011 \times 10^{23} \) a toms of oxygen


If the quotient is terminating decimal, the division is complete only when
A. we get the remainder 1
B. we get the remainder zero
c. we get the remainder as the repeated numbers
D. All of the above


Through the process of photosynthesis plants absorb from the
atmosphere and release into it.
A. Carbon dioxide, oxygen
B. Exhaustible
c. Non-renewable
D. Natural


The vapour pressure of two miscible liquids \( A \) and \( B \) are 300 and 500 mm of
Hg respectively. In a flask, 10 moles of \( A \)
is mixed with 12 moles of \( B \). However,
as soon as \( B \) is added, \( A \) starts
polymerizing into a completely insoluble solid. After 100 minutes,
0.525 moles of a non-volatile solute is
dissolved which arrests the polymerization completely. The final vapour pressure of the solution is 400 mm of Hg. Assume negligible volume
change on mixing, polymerization and ideal behaviour for the final solution.
If a number of moles of \( \boldsymbol{A} \) polymerized
in 100 minutes are expressed as \( x, \) then
a value of \( 10 x \) is:
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c .3 \)
D. 4


Evaluate the following:
\( \left|\begin{array}{ccc}1 & a & b c \\ 1 & b & c a \\ 1 & c & a b\end{array}\right| \)


A uniform rod of mass \( M \) and length \( L \) hinged at centre is rotating in
horizontal plane with angular speed \( \omega_{0} \)
Now two objects each of mass \( m \) are kept on rod near the hinge on both sides. They starts sliding towards ends.
Find \( \omega \) of rod finally.
A \( \frac{M \omega_{0}}{6 M+m} \)
в. \( \frac{M \omega_{0}}{M+6 m} \)
c. \( \frac{6 M \omega_{0}}{M+m} \)
D. \( \frac{M \omega_{0}}{M+2 m} \)


A particle is moving in a straight line with initial velocity and uniform
acceleration \( a \). If the sum of the
distance travelled in \( t^{t h} \) and \( (t+1)^{t h} \)
seconds is \( 100 \mathrm{cm}, \) then its velocity
after \( t \) seconds, in \( \mathrm{cm} / \mathrm{s}, \) is
A . 80
B. 50
c. 20
D. 30


In figure given below, find the value of
resistance \( X \) for which points \( A \) and \( B \) are at the same potential:


If the mass ratio of non-reacting gases
\( O_{2} \) and \( N_{2} \) in a vessel is \( 2: 7, \) then the
ratio of their molecules will be:
A \( \cdot 1: 2 \)
B. 3:5
c. 2: 7
D. 1: 4


A candle is placed \( 20 \mathrm{cm} \) from the surface of a convex mirror and a plane mirror is also placed so that the virtual images in the two mirrors coincide. If the plane mirror is \( 12 \mathrm{cm} \) away from the object, what is the focal length of the convex mirror?
\( \mathbf{A} \cdot 20 \mathrm{cm} \)
B. \( 15 \mathrm{cm} \)
\( \mathbf{c} \cdot 10 \mathrm{cm} \)
D. \( 5 \mathrm{cm} \)


Earthworm has no special sense organs, still they are sensitive to
A. Light and sound
B. touch and sound
c. Touch, taste and light
D. Touch, taste, light and vibrating


The area of the shaded region in the diagram below where the given triangle is isoceles with vertices of base lying on
axis of the radius perpendicular to the diameters of the two small semicircles,
is
в. \( 16(\pi-1) \)
c. \( 32(\pi-1) \)
D. \( 32(\pi+1) \)


The oil used as frothing agent in froth floatation process is?


In how many different orders can five boys stand on a line?
A . 40
B. 50
\( c \cdot 80 \)
D. 120


In the figure shown in thin parallel beam of light is incident on a plane
mirror \( \boldsymbol{m}_{1} \) at small angle \( ^{\prime} \boldsymbol{\theta}^{\prime} \boldsymbol{m}_{2} \) is a
concave mirror of focal length ' \( f^{\prime} \). After
three successive reflections of this
beam the \( x \) and \( y \) coordinates of the
image is:
A \( . x=f-d, y=f \theta \)
B. \( x=f+d, y=f \)
c. \( x=f-d, y=-f \theta \)
D. \( x=d-f, y=-f \theta \)


Consider the situation shown in the
figure . The tension in the string connecting the 1.0 kg blocks.


An electrical heater and a capacitor are joined in series across a \( 220 V, 50 H z \)
\( A C \) supply. The
potential difference across the heater is
\( 90 V . \) The potential difference across the
capacitor will be about
\( \mathbf{A} \cdot 200 V \)
B. \( 130 V \)
\( \mathrm{c} \cdot 110 \mathrm{V} \)
D. \( 90 V \)


\( N H_{4} C l, N H_{4} N O_{3} \) and \( \left(N H_{4}\right)_{2} C O_{3} \)
gives \( N H_{3} \) gas on heating.
A. True
B. False


Rapid water absorption takes place by :
A. Osmosis
B. Active absorption
c. Both \( A \& B \)
D. None of this


A student writes the equation of an angular \( \mathrm{SHM} \) as \( \boldsymbol{\pi} / \mathbf{3}=\boldsymbol{\pi} / \mathbf{6} \sin (\boldsymbol{\omega} \boldsymbol{t}) . \) Is
this correct?
A. This equation is correct as it is of the form \( \theta= \) \( \phi \sin (\omega t) \)
B. This equation is incorrect as instantaneous angular displacement is more than the angular amplitude
C. This equation is incorrect as the equation lacks a phase factor
D. This equation is correct since the SHM has a sin factor in it


Identify the correct option amongst the following:
An \( \alpha \) particle is :
A. a hydrogen molecule
B. a helium nucleus
c. an electron
D. a proton


In plant nutrition elements are classified as major or minor depending
on
A. Their availability in the soil.
B. Their relative production in the ash obtained after burning the plants.
c. Their relative amounts required by the plants.
D. Their relative importance in plant growth


In a single slit diffraction experiment,
the width of the slit is made half the
original width
A. the width of the central maxima becomes double
B. the width of the central maxima becomes half
c. the width of the central maxima becomes one fourth
D. the width of the central maxima becomes four times


Without expanding, show that the value
of the following determinant is zero:
\( \left|\begin{array}{ccc}\mathbf{0} & \boldsymbol{x} & \boldsymbol{y} \\ -\boldsymbol{x} & \boldsymbol{0} & \boldsymbol{z} \\ -\boldsymbol{y} & -\boldsymbol{z} & \boldsymbol{0}\end{array}\right| \)


Non-metals combine with oxygen to
form usually:
A. basic oxides
B. neutral oxides
c. acidic oxides
D. amphoteric oxides


When a bullet is fired from a gun
a) Kinetic Energy of bullet is more than
that of gun
b) acceleration of bullet is more than
that of gun
c) momentum of bullet is more that of
gun
d) velocity of bullet is more than that of
gun
A. only a \( \& \) b are true
B. only b \& c are true
\( \mathrm{c} \cdot \mathrm{a}, \mathrm{b} \& \mathrm{d} \) are true
D. a, b, c \& d are true


Assertion : Current is passed through a metallic wire, heating it red. When cold water is poured on half of it, the rest
becomes more hot.

Reason: Resistance decreases due to
the decrease in temperature and then
current through wire increases.
A. Both (A) and (R) are true and (R) is the correct explanation of A
B. Both (A) and (R) are true but (R) is not the correct explanation of A
c. (A) is true but (R) is false
D. (A) is false but (R) is true


\( \mathrm{g}_{2} U^{235} \) nucleus absorbs a neutron and disintegrates into \( _{54} X e^{139},_{38} S r^{94} \) and
X. What will be the product \( X ? \)
A. 2 neutrons
B. 3 neutrons
c. \( \alpha \) -particle
D. \( \beta \) -particle


When the intermolecular distance
decreases due to compressive force,
there is :
A. zero resultant force between molecules
B. Repulsive force between molecules
c. Attractive force between molecules
D. No force between molecules


Atomslions needed in very small
amounts function mainly as ............. of enzymatic reactions.


Which name is associated with the
chemical substances produced in endocrine ductless glands?
A. Vitamins
B. Antigens
c. Bile acids
D. Hormones


Atomic weight of boron is 10.81 and it
has two isotopes \( _{5} B^{10} \) and \( _{5} B^{11} . \) Then
ratio of \( _{5} B^{10}:_{5} B^{11} \) in nature would be
A . 19: 81
B. 10: 11
c. 15: 16
D. 81: 19


Which of the following radiations has the least wavelength?
A. \( \gamma \) -rays
B. \( \beta \) -rays
c. \( \alpha \) -rays
D. X-rays


If \( x \) and \( y \) vary inversely as each other, and \( x=10 \) when \( y=6 . \) Find \( y \) when
\( \boldsymbol{x}=\mathbf{1 5} \)
A . 2
B. 4
c. 8
D.


If the escape speed of a projectile on Earth's surface is \( 11.2 k m s^{-1} \) and \( a \)
body is projected out with thrice this speed, then determine the speed of the body far away from the Earth:
A \( .56 .63 k m s^{-1} \)
B. \( 33 k m s^{-1} \)
\( \mathbf{c} \cdot 39 k m s^{-1} \)
D. \( 31.7 k m s^{-1} \)


Assertion
Permanent hardness of water can be
removed by using washing soda
Reason

Washing soda reacts with soluble calcium and magnesium chlorides and sulphates in hard water to form
insoluble carbonates
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


For \( \frac{\boldsymbol{x}^{\mathbf{3}}+\mathbf{2} \boldsymbol{x}+\mathbf{1}}{\mathbf{5}}-\frac{\mathbf{7}}{\mathbf{2}} \boldsymbol{x}^{2}-\boldsymbol{x}^{\mathbf{6}}, \) write
i) the degree of the polynomial
ii) the coefficient of \( x^{3} \)
iii) the coefficient of \( x^{6} \)
iv) the constant term


In what ways lithium shows similarities to magnesium in its chemical behaviour?


Find an expression for \( \boldsymbol{y} \) given \( \frac{d y}{d x}=7 x^{5} \)


Q Type your question
volume. This is strictly true only if there are no external influences. A gas
column under gravity, for example, does not have uniform density (and
pressure). As you might expect, its density decreases with height. The precise dependence is given by the socalled law of atmospheres
\( \boldsymbol{n}_{2}=\boldsymbol{n}_{1} \exp \left[-\boldsymbol{m} \boldsymbol{g}\left(\boldsymbol{h}_{2}-\boldsymbol{h}_{1}\right) / \boldsymbol{k}_{B} \boldsymbol{T}\right] \)
where \( n_{2}, n_{1} \) refer to number density at
heights \( h_{2} \) and \( h_{1} \) respectively. Use this
relation to derive the equation for sedimentation equilibrium of a suspension in a liquid column:
\( \boldsymbol{n}_{2}=\boldsymbol{n}_{1} \exp \left[-\boldsymbol{m} \boldsymbol{g} \boldsymbol{N}_{\boldsymbol{A}}\left(\boldsymbol{\rho}-\boldsymbol{\rho}^{\prime}\right)\left(\boldsymbol{h}_{2}-\right.\right. \)
\( \left.\left.\boldsymbol{h}_{1}\right) /(\boldsymbol{\rho} \boldsymbol{R} \boldsymbol{T})\right] \)
where \( \rho \) is the density of the suspended
particle and \( \rho^{\prime} \) that of surrounding
medium. \( \left[\mathrm{N}_{A} \) is Avogadro's number, and \right. \( \mathrm{R} \) the universal gas constant. [Hint : Use Archimedes principle to find
the apparent weight of the suspended particle.]


Galileos law of odd numbers:
"The distances traversed, during equal intervals of time, by a body falling from rest, stand to one another in the same
ratio as the odd numbers beginning with unity [namely,1 : 3 : 5 : 7..]". Prove
it


Define the term 'electrical conductivity of a metallic wire. Write its S.I. unit.


The dual nature of radiation was
proposed by :
A. De Broglie
B. Heisenberg
c. JJ Thomson
D. Einstein


Which pressure is NOT standard
pressure?
A. 760 torr
B. 1 atm
c. \( 101.325 k P a \)
D. \( 70 \mathrm{mm} \mathrm{Hg} \)


The addition of two numbers \( 6.75 \times 10^{3} \)
\( \mathrm{cm} \) and \( 4.52 \times 10^{2} \mathrm{cm} \) with regard to
significant figures is:
A \( \cdot 7.20 \times 10^{3} \mathrm{cm} \)
В. \( 7.20 \times 10^{3} \mathrm{mm} \)
c. \( 7.20 \times 10^{4} \mathrm{cm} \)
D. None of these


Choose the correct statement from the
following?
This question has multiple correct options
A. Pressure is same at all points in the horizontal plane
B. A liquid seeks its own level
C. The lateral pressure exerted by a liquid decreases with the increase in depth of the liquid
D. The upper surface of a stationary liquid is always horizontal


The differential equation which
represents the family of curves \( \mathbf{y}= \)
\( \mathbf{c}_{1} \mathbf{e}^{\mathbf{c}_{2} \mathbf{x}} \) where \( \mathbf{c}_{1} \) and \( \mathbf{c}_{2} \) are arbitrary
constants, is:
A \( \cdot y^{\prime}=y^{2} \)
B. \( \mathrm{y}^{\prime \prime}=\mathrm{y}^{\prime} \mathrm{y} \)
\( \mathbf{C} \cdot \mathbf{y y}^{\prime \prime}=\mathbf{y}^{\prime} \)
D・yy" = (y') 2


The acceleration due to gravity at a depth of \( 1600 k m \) inside the earth is
\( \mathbf{A} \cdot 6.65 \mathrm{ms}^{-2} \)
B. \( 7.35 \mathrm{ms}^{-2} \)
c. \( 8.65 \mathrm{ms}^{-2} \)
D. \( 4.35 \mathrm{ms}^{-2} \)


Explain the different types of adaptations in plants with suitable examples.


Which one is not a co-factor?
A. Coenzyme
B. Apoenzyme
c. Prosthetic group
D. Metal ion


A series LCR circuit with \( \mathrm{R}=22 \Omega, \mathrm{L}=1.5 \)
\( \mathrm{H} \) and \( \mathrm{C}=40 \mu \mathrm{F} \) is connected to a variable frequency \( 220 \mathrm{V} \) ac supply.
When the frequency of the supply equals the natural frequency of the circuit, what is the average power transferred to the circuit in one
complete cycle?
A. 2000
B. 2200 W
c. 2400 \( w \)
D. 2500 W


\( P Q, Q R \) and \( R S \) are three consecutive
sides of a regular polygon. If \( <Q P R= \)
\( 20^{\circ} \) find the number of side in the
polygon.


Functional unit of kidney is
A. Neuron
B. Nephorn
c. Glomerulous
D. Bowman's capsule


Describe an experiment to demonstrate the thermal expansion in a gas.


Equal lengths of magnesium ribbons are taken in two test-tubes \( X \) and \( Y \)
Hydrochloric acid is added to test-tube
\( X \) and acetic acid is added to test-tube
\( \boldsymbol{Y} \)
In which test-tube, the reaction will be
more vigorous ? Why?


Assertion
Boiling point of \( H F \) is lesser than
water
Reason
Hydrogen bonding in water is weaker
than \( \boldsymbol{H} \boldsymbol{F} \)
A. Assertion is true, Reason is true and Reason is correct explanation for Assertion
B. Assertion is true, Reason is true and Reason is not the correct explanation for Assertion
C. Assertion is true, Reason is false
D. Assertion is false, Reason is true


After \( n p \) -orbitals are filled, the next orbital filled will be:
A \( \cdot(n+1) s \)
B \( \cdot(n+2) p \)
\( \mathbf{c} \cdot(n+1) d \)
D. \( (n+2) s \)


A ball strikes a horizontal floor at
\( 45^{\circ} .25 \% \) of its kinetic energy is lost
collision. Find the coefficient of
restitution
A .
в. \( \frac{1}{\sqrt{2}} \)
c. \( \frac{1}{\sqrt{4}} \)
D.


Radio active carbon \( C^{14} \) in a wood
sample, decays with a half life of 5700 years. The fraction of the radio active
carbon \( C^{14}, \) that remains after a decay
period of 17,100 years is :
A. \( 1 / 4 \)
B. 3/4
\( c \cdot 1 / 8 \)
D. \( 7 / 8 \)


Each of the urns contains 4 white and 6
blackballs. The \( (n+1) \) th urn contains 5
white and 5black balls. One of the \( (n+1) \)
urns is chosen atrandom and two balls
are drawn from it withoutreplacement and both the balls turn out to beblack.
Then the probability that the \( (n+1) \) th urn was chosen to draw the balls is \( 1 / 16 \) the value of \( n \) is
A . 10
в. 11
c. 12
D. 13


At the molecular level what can be said
about Heat energy?
A. Heat energy is equal to total mechanical energy of all its molecules
B. Heat energy is equal to total potential energy of all its molecules
C. Heat energy is equal to total kinetic energy of all its molecules
D. Heat energy is equal to total heat energy of all its molecules


Describe the factors that effects the
season.


What is the minimum energy required
to lunch a satellite of mass \( m \) from the
surface of a planet of mass \( M \) and radius \( R \) In a circular orbit at an
altitude of \( 2 R ? \)
A \( \cdot \frac{2 G m M}{3 R} \)
в. \( \frac{G m M}{2 R} \)
c. \( \frac{G m M}{3 R} \)
D. \( \frac{5 G m M}{6 R} \)


For a pair production, the minimum
frequency of the gamma ray must be:
A \( \cdot 2.5 \times 10^{14} \mathrm{Hz} \)
B. \( 2.5 \times 10^{20} \mathrm{Hz} \)
C \( \cdot 2.5 \times 10^{28} \mathrm{Hz} \)
D. \( 2.5 \times 10^{34} \mathrm{Hz} \)


Q Type your question
consisting or two semıcircles eacn of
radius \( r \) is placed in such a way that
the centre \( C \) of the conducting wire is at
a distance \( 2 r \) from the end of
the wire.The rod AB moves with velocity
of \( 5 m s^{-1} \) along the direction of the
current flow as shown in the figure. If
the line joining the ends of the rod
makes an angle \( 30^{\circ} \) with the wire then,
This question has multiple correct options
A. the emf induced between the ends of the rod is
\( \ln 4) \mu V \)
B. the end \( A \) is at higher potential than end \( B \).
C. the end \( A \) is at lower potential than end \( B \)
D. the emf induced between the ends of the rod is \( \ln 3) \mu V \)


Given \( \boldsymbol{A}=\{\mathbf{5}, \mathbf{6}, \mathbf{7}\} \) and \( \boldsymbol{B}=\{\mathbf{3}, \mathbf{4}\} \)
Form all possible ordered pairs and write the total number of ordered pairs formed. So that the first component is from \( \mathrm{B} \) and second is from \( \mathrm{A} \)

Find the total number of such pairs.


of green plants are called factories
of food production.
A. Mitochondria
B. Chloroplasts
c. Endoplasmic reticulum
D. Nucleus


According to law of conservation of
energy, heat energy is transformed into which two types of energy?
A. Kinetic and potential energy
B. Mechanical and potential energy
c. Kinetic and thermal energy
D. Nuclear and potential energy


What is the correct sequence of the
following in a heart attack?
1. Narrowing of the inner orifice of the vessel
2. 'Plaque' from fibrous tissue and high cholesterol
3. Inadequate supply of blood and
oxygen
4. Clots of blood carried Into the
coronary arteries
A .2,3,1,4
B. 2, 4, 1, 3
\( c \cdot 1,2,3,4 \)
D. 4,2,1,3


Mamta knitted a circular pattern and
then she put a handle around it and
used it as a hand fan. Find the area of
the design she has made, if outer circle
radius is \( 17.5 \mathrm{mm} \) and inner circle
radius is \( 7.5 \mathrm{mm} .\left[\boldsymbol{U} \boldsymbol{s e} \boldsymbol{\pi}=\frac{22}{7}\right] \)


The foci of the ellipse \( 4 x^{2}+9 y^{2}=1 \) are
\( ^{\mathbf{A}} \cdot\left(\pm \frac{\sqrt{3}}{2}, 0\right) \)
B. \( \left(\pm \frac{\sqrt{5}}{2}, 0\right) \)
\( ^{\mathbf{c}} \cdot\left(\pm \frac{\sqrt{5}}{3}, 0\right) \)
D \( \cdot\left(\pm \frac{\sqrt{5}}{6}, 0\right) \)
E \( \cdot\left(\pm \frac{\sqrt{5}}{4}, 0\right) \)


ff \( \boldsymbol{A}=\left[\begin{array}{cc}\cos \boldsymbol{x} & \sin \boldsymbol{x} \\ -\sin \boldsymbol{x} & \cos \boldsymbol{x}\end{array}\right], \) then find \( \boldsymbol{x} \)
satisfying \( \mathbf{0}<\boldsymbol{x}<\frac{\boldsymbol{\pi}}{\mathbf{2}} \) when \( \boldsymbol{A}+\boldsymbol{A}^{\boldsymbol{T}}=\boldsymbol{I} \)


Which is more hazardous to human
health?
A. Pyrethrum
B. DDT
c. Rotenone
D. Humulin


In the case of plane mirror. from the
mirror distance of the image \( = \) distance of the
A. Second image
B. object
c. both
D. none


Which of the following compounds gives
acetone \( \left(C H_{3}\right)_{2} C=o \) as one of the
product of its ozonolysis?
\( A \)
B.
\( c \)
\( D \)


How many factors of 1080 a
A .32
B. 36
c. 8
D. 25


In the depletion layer of p-njunction diode, these are presents.
A. Only holes
B. Only electrons
c. Electrons and holes both
D. Neither electron nor hole


Find the variance of first 10 multiples of
3
\( \mathbf{A} \cdot 72.65 \)
B. 74.05
c. 74.25
D. 73.85


The approximate concentration of \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) in perhydrol is :
A. 30 gm/litre
B. \( 300 \mathrm{gm} / \mathrm{ml} \)
c. \( 10 \mathrm{gm} / \) /litre
D. 300 gm/litre


Kinetic energy of the liquid per unit mass is
\( \mathbf{A} \cdot \frac{1}{2} m v^{2} \)
B \( \cdot \frac{1}{2} v^{2} \)
C \( \cdot \frac{1}{2} m^{2} v \)
D. \( m v^{2} \)