An element is placed in the 2 nd group and 3 rd period of the periodic table, burns in presence of oxygen to form a
basic oxide. The electronic
configuration of the element is
A. \( K, M, L(2,8,2) \)
B. \( K, L, M(2,6,4) \)
c. К, М, L (4,6,2)
D. K,L, M (2,8, 2)


The degree of the differential equation \( \boldsymbol{x}=\mathbf{1}+\left(\frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}\right)+\frac{\mathbf{1}}{\mathbf{2 !}}\left(\frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}\right)^{2}+ \)
\( \frac{1}{3 !}\left(\frac{d y}{d x}\right)^{3}+\dots \)
A . 3
B . 2
\( c \cdot 1 \)
D. not defined


If the system of linear equations
\( 2 x+2 a y+a z=0 \)
\( 2 x+3 b y+b z=0 \)
\( 2 x+4 c y+c z=0 \)
where \( a, b, c \epsilon R \) are non-zero and
distinct; has a non-zero solution, then:
A \( \cdot \frac{1}{a}, \frac{1}{b}, \frac{1}{c} \) are in A.P
B . \( a+b+c=0 \)
c. \( a, b, c \) are in A.P
\( \mathbf{D} \cdot a, b, c \) are in G.P


The Bernoulli's equation that is valid for non-viscous, incompressible fluids having laminar flow is a consequence of
A. Conservation of mass
B. Conservation of energy
c. conservation of momentum
D. conservation of kinetic energy


Match column A with column B


The values of \( \alpha, \) for which the system of
equation \( \boldsymbol{x}+\boldsymbol{y}+\boldsymbol{z}=\mathbf{1} \)
\( \boldsymbol{x}+\mathbf{2} \boldsymbol{y}+\mathbf{4} \boldsymbol{z}=\boldsymbol{\alpha} \)
\( x+4 y+10 z=\alpha \) is consistent, are
\( \mathbf{A} \cdot 1,-2 \)
в. -1,2
c. 1,2
D. None of these


A building has 8 right cylindrical pillars whose cross sectional diameter is \( 1 \mathrm{m} \)
and whose height is \( 4.2 \mathrm{m} \). Find the expenditure to paint these pillars at the
rate of Rs.24 per \( \boldsymbol{m}^{2} \)
A . Rs.2534.40
B. Rs.2506.13
c. Rs.2610.9
D. Rs.2514.5


The heat of combustion of ethane,
ethylene and hydrogen are \( 372.79 k c a l \)
\( 337.0 k c a l \) and \( 68.4 k c a l \) respectively
What is the heat evolved in the
reaction?
\( \boldsymbol{C}_{2} \boldsymbol{H}_{4}+\boldsymbol{H}_{2} \longrightarrow \boldsymbol{C}_{2} \boldsymbol{H}_{6} ? \)
A. \( -32.61 k c a l \)
B. \( +32 k c a l \)
c. \( 68.4 k c a l \)
D. None of these


Three cards are drawn at random
(without replacement) from a well shuffled pack of 52 cards. Find the probability distribution of number of red cards. Hence find the mean of the
distribution.


If \( \boldsymbol{f}(\boldsymbol{x})=(\boldsymbol{x}+\mathbf{1})(\boldsymbol{x}+\mathbf{2})(\boldsymbol{x}+\mathbf{3}) \dots . .(\boldsymbol{x}+ \)
\( \boldsymbol{n}), \) then find \( \boldsymbol{f}^{\prime}(\mathbf{0}) \)
A \( \cdot(n) !\left\{1+\frac{1}{2}+\frac{1}{3}+\ldots .+\frac{1}{n}\right\} \)
B . \( (n) ! \)
\( \mathbf{c} \cdot(n) !^{2}\left\{1+\frac{1}{2}+\frac{1}{3}+\ldots .+\frac{1}{n}\right\} \)
D. \( n(n+1) / 2 \)


Figure shows the strain-stress curve for
a given material. What are
(a) Young's
modulus and (b) approximate yield
strength for this material?


A cylinder has hemispherical ends having radius \( 7 \mathrm{cm} \) and total height of solid is \( 104 \mathrm{cm} \). If its outer surface is to
be polished and cost of polish is rs 100 per.sq.mtr find the total cost of polish.


A ray of light passes through a right
angled prism as shown in figure. State
the angles of incidence at the faces \( A C \)
and \( B C \).


The density of a cube is measured by measuring its mass ad length of its side. If the maximum errors in the
measurement of its mass and length are \( 3 \% \) and \( 2 \% \) respectively, the maximum error in the measurement of
density would be:
A . \( 12 \% \)
B. \( 14 \% \)
c. \( 7 \% \)
D. \( 9 \% \)


Given that \( \boldsymbol{R}=\{(\boldsymbol{a}, \boldsymbol{b}) \mid \boldsymbol{3} \text { divides } \boldsymbol{b}\} \)
is an equivalence relation in steel in the
set of integers \( Z \). What is the number of
partitions of \( Z ? \)


On adding \( H_{2} O \) to \( B i C l_{3} \) solution in \( H C l \) the compound produced is:
\( \mathbf{A} \cdot B i_{2} O_{3} \)
B \( \cdot B i(O H)_{3} \)
c. В гОС
D. \( B i O C l \)


\( 0.24 \mathrm{g} \) of a volatile gas upon vaporization gives 45 mL vapour at \( \mathrm{NTP} \) What will be the vapour density of the
substances? (density of \( \boldsymbol{H}_{2}=\mathbf{1} \) )
(a) 95.39
(b) 5.973
(c) 95.93
(d) 59.73


An engine has an efficiency of \( \frac{1}{3} . \) The
amount of work this engine can perform per kilocalorie of heat input is
A. 1400 cal
B. 700 cal
c. 700
D. 1400 J


Which one of the following belongs to representative group of elements in the periodic table?
A. Lanthanum
B. Tungston
c. Chromium
D. Aluminium


Sodium sulphate filtrate formed from the first step of oxidation test of sulphur is acidified with dilute hydrochloric acid and a solution of barium chloride to form a precipitate. The precipitate is :
A. Sodium chloride
B. Barium chloride
c. Barium sulphate
D. Barium oxide


(2) Explaıri clearly, wırn ex \( \mathbf{S}, \) Ine
distinction between:
(a) magnitude of displacement over an interval of time and the total length of
path covered by a particle over the same interval;
(b) magnitude of average velocity over an interval of time, and the average
speed over the same interval.
Show in both (a) and (b) that the second
quantity is either greater than or equal
to the first. When is the equality sign
true?
(ii) A man walks on a straight road
from his home to a market \( 2.5 k m \) away
with a speed of \( 5 k m h^{-1} \). Finding the
market closed, he instantly turns and walks back home with a speed of
\( 7.5 k m h^{-1} . \) What is the:
(a) magnitude of average velocity, and
(b) average speed of the man over the interval of time (i) 0 to 30 min, (ii) 0 to
\( \mathbf{5 0 m i n},(\text { iii) } 0 \text { to } 40 m i n ? \)


The characteristic(s) common to urea,
uric acid, and ammonia is/are
(i) They are nitrogenous wastes.
(ii) They all need a very large amount of water for excretion.
(iii) They are all equally toxic.
(iv) They are produced in the kidneys.
A. (i), (ii) and (iv)
B. (i) only
c. (i) and (iii)
D. (i) and (iv)


How many terms of the \( \boldsymbol{A} . \boldsymbol{P} \) \( -6,-\frac{11}{2},-5, \dots \) are needed to give the sum \( -25 ? \)


carrying current \( i_{0} \) lies in the \( x \) -y plane as shown in the figure. It is hinged at \( y^{-} \)
axis so that it can freely route about it. Moment of inertia of the loop about an
axis through its c.m. and normal to its
plane is equal to \( \gamma M a^{2} . A t t=0, \) an
external magnetic field of induction B is applied along +ve x axis. The initial angular acceleration of the loop is equal
to
A \( \cdot \frac{4 i_{0} B}{M(2 \gamma+1)} \)
В. \( \frac{i_{0} B}{M \gamma} \)
c. \( \frac{4 i_{0} \pi B}{M(2 \gamma+1)} \)
D. \( \frac{4 i_{0} B}{(2 \gamma+1)} \)


The vapour pressure of liquid methano
at \( 50^{0} C \) is \( 55.5 k P a . \) Which one is
correct for equilibrium reaction
attained in a vessel of 5 litres at \( 50^{0} C \)
for
\[
\boldsymbol{C H}_{3} \boldsymbol{O H}(\boldsymbol{l}) \rightleftharpoons \boldsymbol{C H}_{3} \boldsymbol{O H}(\boldsymbol{g}) ?
\]
This question has multiple correct options
\( \mathbf{A} \cdot K_{p}=55.5 k P a \)
B. \( K_{c}=2.067 \) mollitre \( ^{-1} \)
c. \( K^{0}=0.555 \)
D. \( K^{0}=0.555 k P a \)


Porters (coolies) place on their heads a round piece of cloth, to the
area of contact of the load with their
head.
A. increase
B. decrease
c. maintain the same
D. can not say


If \( z \neq 0 \), then \( \int_{0}^{50} \arg (-|z|) d x \) equals
A. 50
B. not defined
\( c \cdot 0 \)
D. \( 50 \pi \)


Sea-pansy, sea-pen and sea-fan are
A. Hydrozoans
B. Anthozoans
c. Scyphozoans
D. Annelids


Name of the following:
Appearance of a trait due to the presence of an allele exclusively on
either the \( X \) chromosome or on the \( Y \)
chromosome.


The floral formula belongs to the Family
\( \oplus \bigoplus K_{(5)} C_{(5)} A_{5} \underline{G}_{(2)} \)
A. Fabaceae
B. Asteraceae
c. Solanceae
D. Liliaceae


The eccentricity of the conic \( r^{2} \cos 2 \theta=a^{2} \) is
\( \mathbf{A} \cdot \mathbf{1} \)
B. \( \sqrt{2} \)
\( c \cdot 2 \)
D.


In which of the following pairs,
indicated bond has less bond
dissociation energy?
and
\( A \)
B. I
c. Both are equal
D. cannot determine


Which of the following safety features are used in vehicles to reduce the
negative effects of inertia?
(i)Safety seat belts
(ii)Automatic air bags
(iii)Absorber bumpers
A. Only (i) and (ii)
B. only (ii) and (iii)
c. Only (i) and (iii)
D. (i), (ii) and (iii)


Two closed bulbs of equal volume (v) containing an ideal gas initially at
pressure \( P_{4} \) and temperature \( T_{1} \) are connected through a narrow tube of negligible volume as shown in the
figure below. The temperature of one of
the bulbs is then raised to \( T_{2} \). What is
the final pressure \( \boldsymbol{P}_{f} ? \)


In the given (V T) diagram, what is the
relation between pressures \( P_{1} \) and \( P_{2} ? \)
\( (2) \mathrm{P}_{2}>\mathrm{P}_{1} \)
(4) cannot be predicted
A \( \cdot P_{2}=P_{1} \)
в. \( P_{2}>P_{1} \)
c. \( P_{2}<P_{1} \)
D. cannot be predicted


A force of \( 10 \mathrm{N} \) acts on a body for 3
microsecond \( (\mu s) . \) Calculate the impulse. If mass of the body is 5 g, calculate the change of velocity.
B . \( 3 \times 10^{-3} \mathrm{ms}^{-1} \)
\( \mathrm{c} \cdot 8 \times 10^{-3} \mathrm{ms}^{-1} \)
D. \( 16 \times 10^{-3} \mathrm{ms}^{-1} \)


\begin{tabular}{c}
\hline 0 \\
\hline \\
\hline 0 \\
\hline 0 \\
\hline 0 \\
\hline
\end{tabular}


A solid sphere is rolling purely on a rough horizontal surface with speed of center \( u=12 \mathrm{m} / \mathrm{s} \). It collides
inelastically with a smooth vertical wall at a certain moment, with the coefficient of restitution being \( \frac{1}{2} . \) How long (in sec) after the collision, does the sphere begin pure rolling? [coefficient of friction between the sphere and the ground is \( \frac{\mathbf{3}}{\mathbf{3 5}} \)


The equation of a wave disturbance is given as:
\( y=0.02 \sin \left(\frac{\pi}{2}+50 \pi t\right) \cos (10 \pi x) \)
where \( x \) and \( y \) are in metres and \( t \) is in
seconds.
Choose the correct statement(s):
This question has multiple correct options
A. the wavelength of wave is \( 0.2 m \)
B. displacement node occurs at \( x=0.15 \mathrm{m} \)
c. displacement antinode occurs at \( x=0.3 \mathrm{m} \)
D. the speed of constituent waves is \( 0.2 \mathrm{m} / \mathrm{s} \)


A neutron, a proton, an electron and an
\( \alpha \) particle enter perpendicular
uniform magnetic field, with the same uniform velocity. The path of electron in the following figure will be:
\( A \cdot 4 \)
B. 3
\( c \cdot 2 \)
D.


The acceleration produced in a body by a force of given magnitude depends on:
A. size of the body
B. shape of the body
c. mass of the body
D. none of these


What length of German silver wire, diameter \( 0.050 \mathrm{cm}, \) is needed to make a
28 resistor, if the resistivity of German silver is \( 2.2 \times 10^{-7} m ? \)
A . \( 20 m \)
B. \( 25 m \)
\( c .30 m \)
D. 35 m


Thomson proposed that:
A. an atom consists of a positively charged sphere and the electrons are embedded in it.
B. the negative and positive charges are equal in magnitude. So that atoms as a whole are electrically neutral.
\( c . \) both \( A \) and \( B \)
D. none of the above.


70 calories of heat are required to raise the temperature of 2 moles of an ideal
gas at constant pressure from \( 30^{\circ} \mathrm{C} \) to
\( 35^{\circ} \mathrm{C} . \) The amount of heat required to
raise the temperature of same gas
through the same range \( \left(30^{\circ} C t o 35^{\circ} C\right) \)
at constant volume \( (\boldsymbol{R}= \) \( 2 c a l / m o l / K) \) is:
A . 30
B. 50
c. 70
D. 90


Which set of \( d \) - orbitals of ion
experience more repulsion in tetrahedral field created by ligand?


In semiconductors, at a room
temperature
A. the valence band is partially empty and the conduction band is partially filled.
B. the valence band is completely filled and the conduction band is partially filled.
C. the valence band is completely filled.
D. the conduction band is completely empty.


The property between two charged
ebonite rods is :
fur
A. attraction
B. repulsion
\( c \cdot \) both
D. none


If the resistances I6R, 64R, ............ \infty
connected in series, their resultant will
be
A .
B . \( \infty \)
\( c \cdot 4 / 3 R \)
D. 3/4 R


The cell EMF is independent of the
concentration of the species of the cell
in:
A \( \cdot \operatorname{Fe}^{\ominus}|\operatorname{KOH}(a q)| N i O(s)\left|N i_{2} O_{3}(s)\right| N i \)
B \( \cdot P t\left|\left(H_{2}\right)\right| H C l \mid\left(C l_{2}\right) P t \)
\( \mathbf{c} \cdot Z n\left|Z n^{2+} \| C u^{2+}\right| C u \)
D. \( H g, H g_{2} C l_{2}\left|K C l \| A g N O_{3}\right| A g \)


Number of moles of sodium
thiosulphate reacted and unreacted after the reaction respectively is :
A. 3 and 2
B. 2 and 3
c. 2.2 and 1.8
D. 1.8 and 2.2


An a.c. supply of 100 volts is applied to a capacitor of capacitance \( 20 \mu \) F. If the current in the circuit is \( 0.628 \mathrm{A} \), the
frequency of a.c. must be
\( A \cdot 50 \mathrm{Hz} \)
B. 60 Н
c. 25 нz
D. \( 40 \mathrm{Hz} \)


The generic name of eel is
A. Anabas
B. Exocoetus
c. Anguilla
D. Clarias


When \( 0.2 M \) acetic acid is neutralised
with \( 0.1 M \) NaOH in 0.5 litre of water
the resulting solution is slightly alkaline. Calculate the pH of the
resulting solution. \( \boldsymbol{K}_{\boldsymbol{a}} \) for
\( \boldsymbol{C H}_{3} \boldsymbol{C O O H}=\mathbf{1 . 8} \times \mathbf{1 0}^{-\mathbf{5}} \)


\( \operatorname{Let} \sin ^{-1}\left(\frac{1-x^{2}}{1+x^{2}}\right), \) then \( \frac{d y}{d x} \) is
A \( \cdot \frac{2}{1+x^{2}} \)
в. \( \frac{1}{2\left(1+x^{2}\right)} \)
c. \( \frac{-2}{1+x^{2}} \)
D. \( \frac{2}{2-x^{2}} \)


The binding energy of \( _{17} C l^{35} \) nucleus is \( 298 \mathrm{MeV} . \) Find its atomic mass. The
mass of hydrogen atom \( \left(_{1} \boldsymbol{H}^{1}\right) \) is
1.008143 a.m.u. Given 1 a.m.u. \( =931 \)
\( \mathrm{MeV} \)


A train running at the speed of 60 km/hr crosses a pole in 9 seconds.
What is the length of the train?
A . 120 metres
B. 180 metres
c. 324 metres
D. 150 metres


Nitrogen gas turns moist blue litmus
paper red.
A. True
B. False


\( |f| \sin ^{-1} x|+| \cos ^{-1} x \mid=\frac{\pi}{2}, \) then \( x \in \)
A. \( R \)
в. [-1,1]
c. [0,1]
D.


\( A g N O_{3}(a q) \) was added to an aqueous
\( K C l \) solution gradually and the
conductivity of the solution was
measured. The plot of conductance \( (\boldsymbol{\Lambda}) \)
versus the volume of \( A g N O_{3} \) is :
\( A \cdot(P) \)
B . (Q)
c. (R)
\( D \cdot(S) \)


Who wrote the book 'Genetics and
Origin of Species'?
A. R.A. Fisher
B. G.L. stebbins
c. T.H. Dobzhansky
D. J.B.S. Haldane


A body dropped freely has covered \( (16 / 25)^{t h} \) of the total distance in the last second. Its total time of fall is
A . \( 2.5 s \)
B. \( 5 s \)
c. \( 7.5 s \)
D. \( 1 s \)


Which of the following order is correct for the IR vibrational frequency of CO?
\( ^{\mathbf{A}} \cdot\left[F e(C O)_{4}\right]^{2-}<\left[C o(C O)_{4}\right]^{-}<\left[N i(C O)_{4}\right] \)
\( ^{\mathrm{B}}\left[F e(C O)_{4}\right]^{2-}>\left[C o(C O)_{4}\right]^{-}>\left[N i(C O)_{4}\right] \)
\( ^{\mathbf{c}} \cdot\left[F e(C O)_{4}\right]^{2-}>\left[C o(C O)_{4}\right]^{-}<\left[N i(C O)_{4}\right] \)
D \( \cdot\left[F e(C O)_{4}\right]^{2-}<\left[C o(C O)_{4}\right]^{-}>\left[N i(C O)_{4}\right] \)


For which sequence below can we use
the formula for the general term of a geometric sequence?
A. \( 1,3,5,7,9, \ldots \)
.
в. \( 2,4,6,8,10 \ldots \)
c. \( 4,8,16,32,64 \dots \)
D. 1,-1,3,-2,4


If flux in a coil changes by \( \Delta \phi, \) and the resistance of the coil is \( R \), prove that the charge flown in the coil during the flux change is \( \frac{\Delta \phi}{R} . \) (Note: It is independent of the time taken for the change in flux)


The heat energy required to vaporize 5
kg of water at \( 373 \mathrm{K} \) is nearly (Latent
heat of vaporization \( \left.\boldsymbol{L}_{\boldsymbol{v}}=\mathbf{2 2 7 0} \boldsymbol{J}\right) \)
A . 2700 K.cal
B. 1000 K.cal
c. 27 к.са
D. 270 K.cal


A particle of mass \( \mathrm{M} \) is placed at origin
and a small mass \( \mathrm{m} \) is placed at \( \mathrm{A}, \) at a distance of \( r \) from M. A force F is applied
to \( m \) to make it move from \( A \) to a nearby point B. When the force becomes zero, it
is observed that the mass m moves
from B back to A. This is due to the
reason
A. Potential of B is larger than potential of A
B. objects starts moving in gravitational field until constant potential difference exist
c. The line B to A is equipotential surface
D. The mass moves from B to A, since A is nearer to origir


A wave travels in a medium according to the equation of displacement given by
\( \boldsymbol{y}(\boldsymbol{x}, \boldsymbol{t})=\mathbf{0 . 0 3} \sin \boldsymbol{\pi}(\boldsymbol{2} \boldsymbol{t}-\boldsymbol{0 . 0 1} \boldsymbol{x}) \)
where y and \( x \) are in meter and t in
second
The wavelength of the wave is
A. 200
B. 100 \( m \)
c. \( 20 \mathrm{m} \)
D. \( 10 \mathrm{m} \)


What is a constellation? Name any two
constellations.


A vendor purchased 40 dozen bananas for Rs.250.0ut of these,30 bananas were
rotten and could not be sold.At what
rate per dozen should he sell the remaining to make a profit of \( 20 \% \)


Generally, girls have a ............... voice whereas the voice in boys is
A. High pitched, low pitchedd
B. Low pitched, high pitched
c. sweet pitched, rough pitched
D. None of the above


Gravitational force can be repulsive.
A. True
B. False


Given below are the figures of blood
vessels. Identify them and select the
correct option.
A. A - Capillary
B - Vein
\( \mathrm{C}- \) Artery
B. A - Artery
B - Capillary
C - Vein
C. A - Vein
B - Capillary
C - Artery
D. A - Vein
\( \mathrm{B}- \) Artery
C - Capillary


The solubility product of lead iodide is \( 1.4 \times 10^{-8} . \) Calculate its molar
solubility in \( 0.1 M K I \) solution.


Assertion
Plastic is not responsible for utilising a major share of the world's oil or hydrocarbon resources
Reason
plastics use less than \( 4 \% \) of the world's hydrocarbon resources. Approximately
\( 90 \% \) is consumed for transportation,
power generation and heating.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


For which of the following values of \( m \) the area of the region bounded by the
curve \( y=x-x^{2} \) and the line \( y=m x \) equals \( \frac{\mathbf{9}}{\mathbf{2}} \)
A . -4
B. -
c. 2
D. 4


Simplify \( \frac{a}{x-a}+\frac{b}{x-b}=\frac{2 c}{x-c} \)


Specific conductance of a decinormal
solution of \( K C l \) is 0.0112 ohm \( ^{-1} c m^{-1} \)
The resistance of a cell containing the
solution was found to be \( 56 . \) Waht is the
cell constant?


In YDSE distance between slits and
screen is \( 1.5 \mathrm{m} \). When light of wavelength 500nm is used then 2nd bright fringe is
obtained on screen at a distance of
10mm from the central bright fringe. What will be the shift in the 2nd bright fringe of the light of wavelength 550nm is used?
\( A \cdot 2 m m \)
B. \( 1 \mathrm{mm} \)
c. \( 1.5 \mathrm{mm} \)
D. \( 1.1 \mathrm{mm} \)


A semiconductor has equal electron
and hole concentration of \( 2 \times 10^{8} m^{-3} \)
On doping with a certain impurity, the electron concentration increases to \( 4 x \)
\( 10^{10} m^{-3}, \) then the new hole
concentration of the semiconductor is
A \( \cdot 10^{6} m^{-3} \)
B . \( 10^{8} m^{-3} \)
D. \( 10^{12} m^{-3} \)


The amount of electrolytes required
coagulate a given amount of \( \boldsymbol{A} \boldsymbol{g} \boldsymbol{I} \) colloidal solution (-ve charge) will be in the order:
A \( \cdot \operatorname{NaNO}_{3}>\operatorname{Al}\left(\mathrm{NO}_{3}\right)_{3}>\mathrm{Ba}\left(\mathrm{NO}_{3}\right)_{2} \)
в. \( A l\left(N O_{3}\right)_{3}>B a\left(N O_{3}\right)_{2}>N a N O_{3} \)
c. \( A l\left(N O_{3}\right)_{3}>N a N O_{3}>B a\left(N O_{3}\right)_{2} \)
D. \( \operatorname{NaNO}_{3}>\operatorname{Ba}\left(\mathrm{NO}_{3}\right)_{2}>\operatorname{Al}\left(\mathrm{NO}_{3}\right)_{3} \)


Given
\( \boldsymbol{E}_{\boldsymbol{C r}^{3+} / \boldsymbol{C r}}^{\circ}=-\boldsymbol{0 . 7 4} \boldsymbol{V} ; \boldsymbol{E}_{M n O_{4}^{-} / M n^{2+}}^{\circ}= \)
\( +1.51 V \)
\( \boldsymbol{E}_{C r_{2} O_{7}^{2-} / C r^{3+}}^{\circ}=+\mathbf{1 . 3 3} \boldsymbol{V} ; \boldsymbol{E}_{C l / C l^{-}}^{\circ}= \)
\( +1.36 V \)
based on the data given above, strongest oxidizing agent will
be
A. \( M n^{2+} \)
в. \( M n O_{4}^{-} \)
c. \( C l \)
D. \( C r^{3} \)


The use of chemicals like CFCs has
endangered the ........ layer.


Compounds of carbon and hydrogen which from long chains or branched chains are :
A. Carbo hydrides
в. Hydrogen carbon
\( c \)
Hydrogen carbides
D. Hydrocarbon


Potassium on reacting with cold water catches fire and burns in a flame. Guess the colour of the flame.
A. Golden yellow
B. Lilac
c. Brick red
D. Blue


In the absence of air resistance, a ball
thrown horizontally from a tower with velocity v, will land after time T seconds.
If, however, air resistance is taken into account, which statement is correct?
A. The ball lands with a horizontal velocity less than v after more than T seconds
B. The ball lands with a horizontal velocity less than v after T seconds
c. The ball lands with a horizontal velocity v after more than \( T \) seconds
D. The ball lands with a horizontal velocity v after seconds


The length of the latus rectum of the
parabola \( \boldsymbol{x}^{2}-\mathbf{4} \boldsymbol{x}-\mathbf{8} \boldsymbol{y}+\mathbf{1 2}=\mathbf{0} \) is-
\( \mathbf{A} \cdot \mathbf{4} \)
B. 6
\( c \cdot 8 \)
D. 10


The image produced by the eye lens on the retina is
A. Real
B. Virtual
c. Inverted real
D. Inverted virtual


A two digit number is to be formed from the digits \( 0,1,3,4 . \) Repetition of the digits is allowed. Find the probability that number that formed is a -
(1) prime number
(2) multiple of 4
(3) multiple of 11.


The commercial catch is obtained from
the heart wood of
A. Acacia senegal
B. Acacia catechu
c. Acacia arabica
D. All of the above


In a battle \( 70 \% \) of the combatants lost
one eye, \( 80 \% \) an ear, \( 75 \% \) an arm, \( 85 \% \) a
leg, \( x \% \) lost all the four limbs the
minimum value of \( x \) is
A . 10
B. 12
c. 15
D.


\( N a_{2} C_{2} O_{4} \) and \( K H C_{2} O_{4} . H_{2} C_{2} O_{4} \) are
mixed in such a proportion by weight that the normality of the resulting
solution as a reducing agent is 3.62 times the normality as an acid. What is
the proportion? [Multiply your answer by 100].


Assertion
Atomic size increases down the group.
Reason

Since there are more filled energy levels
so the valence electrons are found
farther from the nucleus increasing the
atomic size.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is
not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Find the odd one out.
(i) Camphor, Ammonium Chloride,
Naphthalene balls, Sugar
(ii) Turmeric, Methyl Orange, Rose petals, Beetroot.


Feulgen test is unique for DNA which is
A. Gentian violet
B. Neutral red
c. Basic fuchsin
D. cotton blue


Name the three convenient units used
to measure length ranging from very short to very long value. How are they related to the S.I. unit?


Lagoon refers to
A. A full moon
B. A shallow body of water separated from a larger body of water by barrier islands or reefs.
C. A spot in a desert made fertile by presence of water
D. Horse shoe shaped coral reef


the value of \( x \) at which \( F_{x} \) is zero.
\( A \cdot x=2 m \)
B. \( x=4 \) m
\( c \cdot x=6 m \)
D. \( x=8 \) m


Hysterisis is the phenomenon of
lagging of
A. \( I \) behind \( B \)
B. \( B \) behind \( I \)
c. \( I \) and \( B \) behind \( H \)
D. \( H \) behind \( I \)


Bredig's arc method is used for the
preparation of colloidal solution of:
A. metals like silver, gold, etc
B. organic compounds
c. two liquids
D. inorganic compounds


If \( f(x)=\cos (\log x) \) then \( f(x) f(y)- \)
\( \frac{1}{2}\left[f\left(\frac{x}{y}\right)+f(x y)\right] \) has value
A . -1
B. 2
\( c .-2 \)
\( D \)


The necessary condition for an
interference by two sources of light is
that:
A. two light sources must have the same wavelength
B. two point sources should have the same amplitude and same wavelength
C. two sources should have the same wavelength, nearly the same amplitude and have a constant phase angle difference
D. the two point sources should have a randomly varying phase difference


What do you understand by electron
rich compounds of hydrogen.


Which equation has the solution shown
on the number line?
\( \mathbf{A} \cdot 4>x \geq 1 \)
в. \( 0>x \geq-3 \)
c. \( x \neq 1 \)
D. \( x<0 \)


Which of the following molecule species has unpaired electron(s)?
A. \( N_{2} \)
в. \( F_{2} \)
\( c \cdot O_{2} \)
D. \( o_{2}^{2} \)


Fill in the blank:
The planet, which has no satellite, is
A. Mars
B. Mercury
c. Neptune
D. Jupiter


In diffraction pattern:
A. The fringe widths are equal
B. The fringe widths are not equal
C. The fringes can not be produced
D. The fringe width may or may not be equal


10 g ice at \%\%0^{lcirc } c \( \mathrm{~ i s c o n v e r t e d i n t o s t e a m a t l o o n \{ l c i r c \} ~} \)
.Findtotalheatrequired \( \left(\mathrm{L}_{-} \mathrm{f}=80\right. \)
cal/G, \( S_{-} w=1 \) cal/g \( \wedge\{\mid c \text { irc }\} C, L_{v}= \)
\( \mathbf{5 4 0} c a l / g) \)


If \( \boldsymbol{A}=[-\mathbf{1}, \mathbf{1}] \) then \( \boldsymbol{f}: \boldsymbol{A} \rightarrow \boldsymbol{A} \) defined
by \( f(x)=\sin \pi x \) is
A. one-one but not onto
B. onto but not one-one
c. neither one - one nor onto
D. bijective


What is the truth value of the statement
\( \mathbf{2} \times \mathbf{3}=\mathbf{6} \) or \( \mathbf{5}+\mathbf{8}=\mathbf{1 0} ? \)
A. True
B. False
C. Neither True nor False
D. Cannot be determined


The circular motion of a particle with
constant speed is
A. Periodic but not simple harmonic
B. Simple harmonic but not periodic
C. Periodic and simple harmonic
D. Neither periodic nor simple harmonic


Formaldehyde, is the first member of the aldehyde family is a at a
ordinary temperature
A . solid
B. liquid
c. gas
D. none of these


Which pair of functions is identical?
\( A \cdot \sin ^{-1}(\sin x) \) and \( \sin \left(\sin ^{-1} x\right) \)
B \( \cdot \log _{e} e^{x}, \log ^{\log _{x} x} \)
\( \mathbf{c} \cdot \log _{e} x^{2}, 2 \log _{e} x \)
D. none of these


Two identical balls of equal masses \( A \)
and \( \mathrm{B} \) are lying on a smooth surface as shown in figure. Ball A hits the ball B
(which is at rest) with a velocity \( \mathbf{v}=16 \) \( \mathrm{m} / \mathrm{s} . \) What should be the minimum
value of coefficient of restitution
between \( A \) and \( B \) so that \( B \) just reaches
the highest point of inclined plane:
\( \left(g=10 m / s^{2}\right) \)
\( A \cdot \frac{2}{3} \)
B. \( \frac{1}{2} \)
\( c \cdot \frac{1}{3} \)
D.


If Rolle's theorem is applicable to the
function, \( \boldsymbol{f}(\boldsymbol{x})=\frac{\ln \boldsymbol{x}}{\boldsymbol{x}} \) over the interval
\( [a, b], \) where \( a, b \in I^{+} \) then the value of
\( a+b \) is


A company which makes the cases for mobile phones requires a material that should be opaque, light, a bad conductor of heat and electricity, and which can be moulded into material
would the company prefer?
A. Mol
в. моз
\( c . \) мо4
D. моб


Starting with a sample of pure \( ^66 C u, 7 / 8 \) of its decays into \( Z n \) in
15 min. The corresponding half-life is
A . 10 min
B. 15 min
c. 5 min
D. \( 7 \frac{1}{2} \) min


Replace the blank with an integer to
make it a true statement.
\[
\times(-8)=-56
\]


Digestive system is complete where
A. All the digestive glands are present
B. Both anus and mouth are present
C. Digestion occurs in the cavity of digestive tract
D. Digestion occurs in the individual cells lining the digestive tract


Long-sightedness: Hypermetropia Short-sightedness:
A. Myopia
B. Focussing
c. Astigmatism
D. Accommodation


A 2 meter long aluminum pipe at \( 27^{\circ} \mathrm{C} \)
is heated until it is 2.0024 at \( 77^{\circ} \) C. The
coefficient of linear expansion of aluminum is :
A . \( 12 \times 10^{-6} /^{\circ} \mathrm{C} \)
B . \( 24 \times 10^{-6} /^{\circ} \mathrm{C} \)
c. \( 6 \times 10^{-6} /^{\circ} \mathrm{C} \)
D \( .20 \times 10^{-2} \)


Intermolecular forces between n-hexane
and n-heptane are nearly same as between hexane and heptane individually. When these two are mixed, which of the following is not true about the solution formed?
A \( \cdot \) It obeys Raoult's law, i.e, \( p_{A}=x_{A} p_{A}^{o} \quad \) and \( p_{B}= \)
\( x_{B} p_{B}^{o} \)
B. \( \Delta H_{\text {mixing }} \) is zero
c. \( \Delta V_{\text {mixing }} \) is zero
D. It forms minimum boiling azeotrope


What is the direction of Monsoon winds
in winter?
A. From oceans to land
B. From land to oceans
c. From equator to poles
D. From poles to equator


An organic compound with the
molecular formula \( C_{8} H_{8} O \) forms \( 2,4- \)
DN P derivative, reduces Tollen's
reagent and undergoes Cannizzaro reaction. On vigorous oxidation, it gives
1, 2-benzenedicarboxylic acid. The organic compounds is
A. 2 -ethylbenzaldehyde
B. 2-methylbenzaldehyde
c. acetophenone
D. 3-methylbenzaldehyde
E. henylacetaldehyde


In which of the following process, convection does not takes place
primarily?
A. Sea and land breeze
B. Boiling of water
c. Warming of glass of bulb due to filament
D. Heating air around a furnace


Correct order of dissociation energy of
\( N_{2} \) and \( N_{2}+ \) is:
A \( \cdot N_{2}>N_{2}^{+} \)
B. \( N_{2}=N_{2}^{+} \)
c. \( N_{2}<N_{2}^{+} \)
D. none of these


Assertion
Rate of reaction of alkyl halide in Williamson's synthesis reaction is
\( \mathbf{1}^{\circ} \boldsymbol{R} \boldsymbol{X}>\mathbf{2}^{\circ} \boldsymbol{R} \boldsymbol{X}>\mathbf{3}^{\circ} \boldsymbol{R} \boldsymbol{X} \)
Reason
It is a type of bimolecular substitution
reaction \( \left(\boldsymbol{S}_{N} \mathbf{2}\right) \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A man has a strange ability to jump from any height to another with ease. The manjumps to P then to Q, R, S, T and then into water. For which jump will he require the highest energy?
A. Land to P
в. s to \( T \)
\( c \cdot Q \) to \( R \)
D. R to


Select the correct option:
Stomata are distributed more on the
lower surface than on the upper surface in
A. Equifacial leaf
B. Bifacial leaf
c. Unifacial leaf
D. Both A and B


\( \sqrt{-35+12 i}-\sqrt{-35-12 i}=p \)
The value of \( p \) can be?
This question has multiple correct options
A .2
в. \( -12 i \)
\( c .12 i \)
D. -


The vapour density of \( N_{2} O_{4} \) and \( N O_{2} \)
mixture at a certain temperature is 30
Calculate the percentage dissociation
of \( N_{2} O_{4} \) at this temperature
\( N_{2} O_{4}(g) \rightleftharpoons 2 N O_{2}(g) \)
A . \( 53.33 \% \)
B. \( 58.56 \% \)
c. \( 62.43 \% \)
D. \( 67.67 \% \)


Mention any two applications of eddy
currents.


Chlorine does not exist in free state.
Give reason.


Materials used to reduce friction are
called \( _{\text {一一一一一一 }} \) (lubricants, beverages)


For a particle projected in a transverse direction from a height h above earth's surface, find the minimum initia
velocity so that it just grazes the surface of earth such that path of this particle would be an ellipse with centre of earth as the farther focus, point of projection as the apogee and a diametrically opposite point on earth's surface as perigee.


Molecule \( A B \) has a bond length of 1.617 A and a dipole moment of 0.38 D. The fractional charge on each atom (absolute magnitude) is :
\( \left(e_{0}=4.802 \times 10^{-10} \mathrm{esu}\right) \)
\( \mathbf{A} \cdot \mathbf{0} \)
B. 0.05
c. 0.5
D. 1.0


\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}\left[\log _{e}\left\{\left(\boldsymbol{e}^{\boldsymbol{x}}+\boldsymbol{2}\right)+\right.\right. \)
\( \sqrt{\boldsymbol{e}^{2 \boldsymbol{x}}+\boldsymbol{4} \boldsymbol{e}^{\boldsymbol{x}}+\boldsymbol{5}}\}]= \)
A. \( \frac{1}{\sqrt{e^{2 x}+4 e^{x}+5}} \) C. \( \frac{e^{x}}{\sqrt{e^{2 x}+4 e^{x}+5}} \)
D. \( \frac{e^{x}}{\sqrt{e^{2 x}+4 e^{x}+3}} \)
\( \sqrt{e^{2 x}+4 e^{x}+3} \)


A hot body, obeying Newton's law of cooling is cooling down from its peak
value \( 80^{\circ} C \) to \( 40^{\circ} C . \) How much time
will it take to cool down from \( 62^{\circ} \mathrm{C} \) to
\( \mathbf{3} \mathbf{2}^{o} \mathbf{C} ?(\operatorname{given} \ln \mathbf{2}=\mathbf{0 . 6 9 3}, \ln \mathbf{5}=\mathbf{1 . 6 0 9} \)
A. 8.6 minutes
B. 6.5 minutes
c. 9.6 minutes
D. 3.75 minutes


In a triangle \( A B C, \) a straight line parallel to BC intersects \( A B \) and \( A C \) at points \( D \) and E respectively. If the area of ADE is one fifth of the area of \( \mathrm{ABC} \) and \( \mathrm{BC}=10 \)
\( \mathrm{cm}, \) then DE equals.
A . \( 2 \mathrm{cm} \)
B . \( 2 \sqrt{5} \mathrm{cm} \)
\( c \cdot 4 \mathrm{cm} \)
D. \( 4 \sqrt{5} \mathrm{cm} \)


Which of the following element will
show almost same reactivity like \( C a ? \)
A \( . C r \)
в. \( M n \)
\( c . S c \)
D. Na


fthe binomial distribution whose mean
is 5 and variance \( \frac{10}{3} \) is \( P(X=r)= \)
\( ^{15} C_{r}\left(\frac{1}{a}\right)^{r}\left(\frac{2}{a}\right)^{15-r}, r=0,1,2, \dots, 15 \)
then the value of \( a \) is


The ionic conductances of \( A l^{3+} \) and
\( \boldsymbol{S} \boldsymbol{O}_{3}^{2-} \) ions at infinite dilution are \( \boldsymbol{x} \) and \( y \) oh \( m^{-1} c m^{2} m o l^{-1} \) respectively. If
Kohlrausch's law is valid, then molar
conductance of aluminium sulphate at infinite dilution will
be
A \( .3 x+2 y \)
в. \( 3 y+2 x \)
\( c \cdot 2 x+2 y \)
D. \( 3 x+3 y \)


Polycyclic aromatic hydrocarbons enter
our body via:
A. air contaminated by wild fire
B. air contaminated by coal tar
C. foods that have been grilled
D. all of these


Ancestors of colostomies are
A. Myxinoidea
B. Arthropods
c. ostracoderms
D. Urochordates


Select the correct statements:
This question has multiple correct options
A. Dissolution of \( K C l \) in water shows an increase in
entropy
B. Ionisation of acetic acid in water shows a decrease in
entropy
C. The solution containing ionised acetic acid is more ordered than molecular acetic acid
D. The solution containing ionised acetic acid is less ordered than molecular acetic acid


How many \( p- \) orbitals are parallel to
each other in the following conjugated system?


What could be the reasons for adopting
contraceptive methods?
A. To maintain the population size by preventing unwanted children
B. To maintain the distance between two children and to plan the family size
C. To prevent sexually transmitting diseases
D. All of the above


In the process of extraction of gold,
1.) Roasted Au ore \( +\boldsymbol{C} \boldsymbol{N}_{(a q)}^{-}+\boldsymbol{O}_{2} \longrightarrow \)
\( [\boldsymbol{X}]+\boldsymbol{N} \boldsymbol{a} \boldsymbol{O} \boldsymbol{H} \)
2.) \( [\boldsymbol{X}]+\boldsymbol{Z} \boldsymbol{n} \longrightarrow[\boldsymbol{Y}]+\boldsymbol{A} \boldsymbol{u} \)
A \( \cdot X=\left[A u(C N)_{2}\right]^{-}, Y=\left[Z n(C N)_{4}\right]^{2} \)
B . \( X=\left[A u(C N)_{4}\right]^{2-}, Y=\left[Z n(C N)_{4}\right]^{2} \)
c. \( X=\left[A u(C N)_{2}\right]^{-}, Y=\left[Z n(C N)_{6}\right]^{4-} \)
D. \( X=\left[A u(C N)_{4}\right]^{-}, Y=\left[Z n(C N)_{4}\right]^{2} \)


toppr
Q Type your question_
constant speed. The field deflects the
particle, a distance h above the original
line of flight as shown in the Figure. The
particle leaves the field region with
momentum, if \( h<<d, \) of about :
\( \frac{q B d^{2}}{2 h}, \) making an angle \( \frac{2 h}{d} \) with initial direction
B. \( \frac{q B h^{2}}{2 d}, \) making an angle \( \frac{2 h}{d} \) with initial direction
\( \frac{q B d}{2}, \) making an angle \( \frac{2 d}{h} \) with initial direction
\( \frac{q B h}{2}, \) making an angle \( \frac{2 d}{h} \) with initial direction


A vehicle sinks into soft ground. The vehicle is changed so that it does not sink as far. Which change is made?
A. A lower centre of mass
B. A more powerful engine
c. wheels that are further apart
D. Wider tyres


\( \operatorname{Let} h(x)=\min \left\{x, x^{2}\right\} \) for \( x \in R \) Then
which of the following is correct
A. \( h \) is continuous for all \( x \)
B. \( h \) is differentiable for all \( x \)
C \( \cdot h(x)=1 \) for all \( x>1 \)
D. \( h \) is not a differentiable at 2 values of \( x \)


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


Find the \( n^{t h} \) term of
\( 2,4,6,8,10, \dots \dots \dots \)


The allotrope of carbon used in nuclear
reactor is :
A. graphite
B. diamond
\( c \cdot \operatorname{coke} \)
D. sugar charcoal


State and prove mid point theorem.


Write the place value of 2 in the following decimal numbers:
\( \mathbf{9 . 4 2} \)


Pollution is:
A. removal of top soil
B. release of toxic/undesirable materials in environment
C. conservation of energy
D. all of the above


Nodes of Ranvier are
A. Joints occur between adjacent axons
B. Axon terminal forms synape with dendrites
C. Dendrites of one nerve cells to adjacent nerve cells
D. Non-myelinated areas of myelenated nerve fibre


A concave-convex glass (index \( =\mathbf{1 . 5} \) ) lens has radii of curvatures \( 60 \mathrm{cm} \) and
\( 40 \mathrm{cm} \) respectively. Its convex surface is silvered and it is placed on a horizontal table with concave surface
up. The concave is then filled with a
liquid of index \( 2.0 . \) The combination is
like a
A. concave mirror
B. convex mirror
c. flat mirror
D. convex lens


Write the expression for magnetic potential energy of a magnetic dipole kept in a uniform magnetic field and explain the terms.


If India FDI from OPEC countries was
proportionately the same in 1992 and
1997 as the total FDI from all over the
world and if the FDI in 1992 from the
OPEC countries was Euro 2 million.
What was the amount of FDI from the
OPEC countries in \( 1997 ? \)
Trends of FDI in India
A . 1
в. 10.72
\( c \cdot 11.28 \)
D. 11.


An electric dipole of momentum \( \vec{p} \) is placed in a uniform electric field. The dipole is rotated through a very small angle \( \theta \) from equilibrium and is released, find the time period of simple harmonic motion


Prove that \( 3 \sin ^{-1}=\sin ^{-1}(3 x-1) \)
\( \left.4 x^{3}\right), x \epsilon\left[\frac{-1}{2}, \frac{1}{2}\right] \)


Figure shows three circular arcs, each of radius \( R \) and total charge as
indicated. The net electric potential at
the center of curvature is :
\( ^{A} \cdot \frac{Q}{2 \pi \varepsilon_{0} R} \)
\( B \)
c. \( \frac{3 Q}{32 \pi \varepsilon_{0} R} \)
D. none of these


If \( \vec{A} \times \vec{B}=\vec{C}, \) which of the following
options is wrong?
\( A \cdot \vec{C} \) is \( \perp \) to \( \vec{A} \)
B \cdot \( \vec{C} \) is \( \perp \) to \( \vec{B} \)
c. \( \vec{C} \) is \( \perp(\vec{A}+\vec{B}) \)
D \( \cdot \vec{C} \) is \( \perp \) to \( (\vec{A} \times \vec{B}) \)


If \( 2 \sin ^{-1} x=\sin ^{-1}(2 x \sqrt{1-x^{2}}), \) then
\( \boldsymbol{x} \in \)
A \( .[-1,1] \)
B. \( \left[-\frac{1}{\sqrt{2}}, 1\right] \)
\( c \cdot\left[-\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right] \)
D. none of these


Two astronauts are floating in gravitational free space after having lost contact with their spaceship. The
two will.
A. Will become stationary
B. Keep floating at the same distance between them
c. Move towards each other
D. Move away from each other


A gas under constant pressure of \( 4.5 \times \)
\( 10^{5} P a \) when subjected to \( 800 K J \) of
heat, changes the volume from \( 0.5 m^{3} \) to \( 2.0 m^{3} . \) The change in
the internal energy of the gas:
\( \mathbf{A} \cdot 6.75 \times 10^{5} J \)
B . \( 5.25 \times 10^{5} J \)
c. \( 3.25 \times 10^{5} J \)
D. \( 1.25 \times 10^{5} J \)


Change of orange color of chromium(VI) to green color of chromium(III)
indicates presence of a:
A. reducing agent
B. oxidizing agent
c. reagent
D. drying agent


A Truth table is given below. The logic gate having following truth table is
\( A \quad B \quad Y \)
\( \begin{array}{lll}0 & 1 & 1\end{array} \)
\( 0 \quad 0 \)
\( 0 \quad 1 \quad 0 \)
10
A. NAND gate
B. NOR gate
c. AND gate
D. OR gate


For the following reactions,write the rate of reaction expression in terms of reactants and products?
¡) \( \mathbf{4} \boldsymbol{N} \boldsymbol{H}_{3}(\boldsymbol{g})+\mathbf{5} \mathbf{0}_{2}(\boldsymbol{g}) \longrightarrow \mathbf{4} \boldsymbol{N} \boldsymbol{O}(\boldsymbol{g})+ \)
\( \mathbf{6} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \)
ii) \( \left.2 N_{2} O_{5}\right) \longrightarrow 2 N O_{2}+O_{2} \)


The mean deviation from mean of the
observation \( \boldsymbol{a}, \boldsymbol{a}+\boldsymbol{d}, \boldsymbol{a}+\boldsymbol{2} \boldsymbol{d}, \ldots, \boldsymbol{a}+ \)
\( 2 n d \) is


Density of a body depends on its shape and size. True or false.
A . True
B. False


At the time of Newlands, how many elements were known?
\( \mathbf{A} \cdot 50 \)
B. 52
c. 54
D. 56


A thin uniform rod of mass m moves
translationally with acceleration a due to two antiparallel force of lever arm \( I \)
One force is of magnitude \( F \) and acts at one extreme end. The length of the rod is:
A \( \cdot \frac{2(F+m a) I}{m a} \)
B. \( _{I\left(1+\frac{F}{m a}\right)} \)
c. \( \frac{(F+m a) I}{2 m a} \)
D. \( \frac{m a I}{m a+F} \)


De Broglie wavelength of neutrons in
thermal equilibrium is (given \( \boldsymbol{m}_{\boldsymbol{n}}= \)
\( \left.1.6 \times 10^{-27} k g\right) \)
A \( \cdot 30.8 / \sqrt{T}_{A}^{\circ} \)
B \( \cdot 3.08 / \sqrt{T}_{A}^{o} \)
c. \( 0.308 / \sqrt{T}_{A}^{\circ} \)
D \( \cdot 0.0308 / \sqrt{T}^{\circ} \)


Prove that:
\( \lim _{x \rightarrow 0} \frac{a x+x \cos x}{b \sin x} \)


The given image is a symbol of


Which has the highest freezing point?
A \( \cdot \operatorname{lm} K_{4}\left[F e(C N)_{6}\right] \quad \) solution
B. \( 1 m C_{6} H_{12} O_{6} \) solution
c. \( 1 m K C l \) solution
D. \( 1 m \) rock salt solution


The numerical value of \( d / D \) when \( \alpha=0 \)
for \( \boldsymbol{P} \boldsymbol{C l}_{5} \rightleftharpoons \boldsymbol{P} \boldsymbol{C l}_{3}+\boldsymbol{C l}_{2} ; \) where \( \boldsymbol{d} \) are
vapour density of equilibrium mixture
and \( D \) is vapour density of \( P C l_{5} \)


When we add a pinch of sodium hydrogen carbonate in a flask containing ethanoic acid a reaction
takes place. What will be the observation when we carry out the
reaction?
A. Milky solution
B. Bubble formation
c. Solution turns red
D. Brisk effervescence


Find the term of the expansion of \( (a+ \)
\( b)^{50} \) which is the greatest in absolute
value if \( |\boldsymbol{a}|=\sqrt{\mathbf{3}}|\boldsymbol{b}| \)


The coefficient of the term independent of \( x \) in the expansion of \( \left(\frac{x+1}{x^{\frac{2}{3}}-x^{\frac{1}{3}}+1}-\frac{x-1}{x-x^{\frac{1}{2}}}\right)^{10} \)
A . 210
в. 105
c. 70
D. 112


Penetration power of proton is
A. more than electron
B. less than electron
C. equal to electron
D. none of these


Write down all possible subsets of the following set. \{1,\{1\}\}


Molar heat capacity of water in equilibrium with the ice at constant pressure is
A. zero
B. Infinity
c. \( 40.45 k^{-1} \mathrm{mol}^{-1} \)
D. None


A current of \( 3 \mathrm{A} \) flows through the \( 2 \Omega \) resistor shown in the circuit. The power
resistant is the \( 5 \Omega \) resistor is?


Identify the metals will not react with
a solution of \( \boldsymbol{C} \boldsymbol{u} \boldsymbol{S} \boldsymbol{O}_{\boldsymbol{4}} \)
A . \( F e \)
в. \( Z n \)
\( c . A g \)
D. \( M g \)


If a wave completes 24 cycles in 0.8 s, then frequency of the wave is
\( A \cdot 30 \mathrm{Hz} \)
в. 8 н \( z \)
c. 24 нг
D. 12 Hz


Which of these are particulates?
A. Dust and fumes
B. Fly ash and smoke
c. Mist and fumes
D. All of these


For the following reaction:
\( C_{2} H_{4} \stackrel{H_{2} / P d}{\longrightarrow} C_{2} H_{6} \)
Which of the following options are
correct?
A. Carbon is reduced
B. Carbon is oxidised
C. Carbon is neither reduced nor oxidised
D. None of these


Without using tables, prove the following \( \sin 40^{\circ}-\cos 70^{\circ}=\sqrt{3} \)
\( \cos 80^{\circ} \)


A reversible engine converts one-sixth of the heat supplied into work. When the
temperature of the sink is reduced by
\( 62^{\circ} \mathrm{C}, \) the efficiency of the engine is
doubled. The temperature of the source and sink are:
A \( \cdot 99^{\circ} \mathrm{C}, 37^{\circ} \mathrm{C} \)
в. \( 80^{\circ} \mathrm{C}, 37^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 95^{\circ} C, 37^{\circ} C \)
D . \( 90^{\circ} \mathrm{C}, 37^{\circ} \mathrm{C} \)


The term independent of \( x \) in the expansion of
\( \left(x^{2}+\frac{1}{x}\right)^{9} \) is
\( A \)
B. -
c. 48
D. 84


In the given figure, find the value of \( x \)
\( A \cdot 25 \)
3.30
\( c .35 \)
2.4


A couple is acting on a two particle systems. The resultant motion will be
A. Purely rotational motion
B. Purely linear motion
c. Both \( A \) and \( B \)
D. None of these


A cell basically consists of conducting rods.
A. one
B. Two
c. Three
D. Four


Find the cube root of each of the
following numbers by prime factorisation method
512
\( A \cdot 6 \)
B. 8
\( c \cdot 7 \)
D.


A blind person after walking 10 steps in one direction, each of length \( 80 \mathrm{cm} \) turns randomly to the left or to the right
by \( 90^{0} \) each time moving 10 steps. After walking a total of 40 steps the maximum displacement of the person from his starting position could be :
A. 320 \( m \)
B. 32 \( m \)
c. \( 16 \sqrt{2} \mathrm{m} \)
D. none


If \( A=2 y^{2}+3 x-x^{2}, B=3 x^{2}-y^{2} \)
and \( C=5 x^{2}-3 x y \) then find
\( B-C \)


A Drosophila has \( X X X Y Y \) sex chromosomes. All the autosomal
chromosomes are normal. The sexual
phenotype will be.
A. Normal female
B. Super female
c. Intersexual
D. Male


The G.M. of numbers 4,5,10,20,25 is
A . 12.8
B. 10
\( c .7 .8 \)
D. none of these


A particle is thrown vertically upwards. Its velocity at half of the height is 10 \( \boldsymbol{m} / \boldsymbol{s} . \) The maximum height attained by
the particle is \( \left(\boldsymbol{g}=\mathbf{1 0} \boldsymbol{m} / \boldsymbol{s}^{2}\right) \)
\( A \cdot 8 m \)
B. 20m
\( c .10 m \)
D. \( 16 m \)


The angle between the incident ray and normal is known as:
A. glancing angle of reflection
B. glancing angle of incidence
c. angle of reflection
D. angle of incidence


Two particles of masses m and \( 2 \mathrm{m} \)
on an object are connected by a spring,
then with respect to the object's frame
of reference
A. the two particles are considered as rigid body, if the object moves with uniform velocity
B. the two particles are considered as rigid body, if the object moves with uniform acceleration
C. the two particles are considered as rigid body, if the object moves with uniform speed
D. the two particles are cannot be a rigid body, since deformation in the spring can bring about a change in the positions of the particles


If \( I_{n}=\int_{0}^{\pi / 4} \tan ^{n} x \times \sec ^{2} x d x, \) then
\( \boldsymbol{I}_{1}, \boldsymbol{I}_{2}, \boldsymbol{I}_{3}, \ldots . . . \) are in
A. A.P
в. G.
c. н.P
D. none


Kirchoff's junction law is equivalent to
A. Conservation of energy
B. conservation of charge
c. conservation of electric potential
D. Conservation of electric flux


A body initially at \( 60^{\circ} \mathrm{C} \) cools to \( 50^{\circ} \mathrm{C} \) in
10 min. What will be it's temperature at the end of the next 10 min. if the roc
temperature is \( 20^{\circ} \) C.Assume newton's
law of cooling.
A \( \cdot 42.50^{\circ} \mathrm{C} \)
B. \( 45^{\circ} \mathrm{C} \)
c. \( 40.46^{\circ} \mathrm{C} \)
D. \( 44.23^{\circ} \mathrm{C} \)


In presence of moisture \( \boldsymbol{H}_{2} \boldsymbol{S} \) can:
A. act as oxidant
B. lose electron
c. gain electron
D. none of these


How many electrons flow through a
metallic wire if a current of \( 0.5 A \) is
passed for 2 hours? (Given : \( 1 F= \)
\( \left.\mathbf{9 6}, \mathbf{5 0 0} \boldsymbol{C} \boldsymbol{m o l}^{-\mathbf{1}}\right) \)


A compound is non aromatic. Which of the following may be true?
A. No pi electrons are present.
B. Pi electrons are not delocalised
C. The compound has non planar structure
D. All of the above.


How can the rate of emission of
electrons in a cathode ray tube can be increased?
A. Increasing resistance of filament
B. Increasing filament current
c. Decreasing filament current
D. Increasing magnetic field inside tube


The circuit as shown in figure, the
equivalent gate is
A. NOR gate
B. oR gate
c. AND gate
D. NAND gate


Solve: \( x^{3}-(x+1)^{2}=2001 \)
\( A \cdot 13 \)
B. 16
c. 10
D. 21


Number of children in six different
classes are given below. Represent the data on a bar graph.
Class: \( \quad \) v \( \quad \) v। \( \quad \) vll \( \quad \) vı
Number of \( \begin{array}{llll}135 & 120 & 95 & 100\end{array} \)
children
Which class has the maximum number
of children?


The reaction can be aided by increasing the:
A. Time
B. Pressure
c. surface area of particle
D. All of above


The most widely used storage battery in cars, vehicles and domestic emergency lights is the :
A. Cadmium cell
B. Lead accumulator
C. Leclanche cell
D. Alkaline battery


Which is the correct order for the
processes involved in aerobic cellular respiration?
A. Krebs cycle, glycolysis, electron transport chain
B. Glycolysis, Krebs cycle, electron transport chain
c. Glycolysis, fermentation, electron transport chain,
D. Fermentation, Krebs cycle, electron transport chain.
E. Glycolysis, electron transport chain, fermentation


Two equal charges ' \( q \) ' of opposite sign are separated by a small distance '2a'. The electric intensity ' \( E \) ' at a point on the perpendicular bisector of the line joining the two charges at a very large distance
\( ^{\prime} r^{\prime} \) from the line is :
A \( \cdot \frac{1}{4 \pi \varepsilon_{0}} \frac{q a}{r^{2}} \)
В. \( \frac{1}{4 \pi \varepsilon_{0}} \frac{2 q a}{r^{3}} \)
c. \( \frac{1}{4 \pi \varepsilon_{0}} \frac{2 q a}{r^{2}} \)
D. \( \frac{1}{4 \pi \varepsilon_{0}} \frac{q a}{r^{3}} \)


The coordinates of the foot of the
perpendicular drawn from the point \( A(1,0,3) \) to the join of the points
\( B(4,7,1) \) and \( C(3,5,3) \) are
A \( \cdot(5,7,17) \)
B \( \cdot\left(\frac{-5}{7}, \frac{7}{3}, \frac{-17}{3}\right) \)
\( ^{\mathbf{c}} \cdot\left(\frac{5}{7}, \frac{-7}{3}, \frac{17}{3}\right) \)
D. \( \left(\frac{5}{7}, \frac{7}{3}, \frac{17}{3}\right) \)


Silk consists of
A. Central core of sericin.
B. Central core of fibroin.
C. Both (A) and (b).
D. A fine mixture of fibroin and sericin.


The negative charge \( -q_{2} \) is fixed while
positive charge \( q_{1} \) as well as the
conducting sphere 'S' is free to move. If
the system is released from rest (the
total charge on \( \mathrm{S} \) being zero.
A. Both S and \( q_{1} \) move towards left
B. \( q_{1} \) moves towards right while \( S \) moves towards left.
C \( \cdot q_{1} \) remains at rest, \( S \) moves towards left
D. Both \( q_{1} \) and \( S \) remain at rest


A body of mass \( 2 k g \) is moving on a rough horizontal surface with an
acceleration of \( 5 m s^{-2} \) and when the
horizontal force is doubled, it gets an
acceleration of \( 18 m s^{-2} . \) Then the
coefficient of friction between the body and the horizontal surface is : (assume
\( \boldsymbol{g}=\mathbf{1 0 m} \boldsymbol{s}^{-2} \mathbf{)} \)
A . 0.2
B. 0.8
c. -0.4
D. 0.6


Find the shortest distance between the line \( \frac{x-3}{3}=\frac{y-8}{-1}=\frac{z-3}{1} \) and the
line of intersection of the planes \( 2 x+ \)
\( 5 y-z+47=0 \) and \( 2 x+y+z+7= \)
\( \mathbf{0} \)


A particle of mass \( 1 \mathrm{kg} \) is moving in a
S.H.M with an amplitude of \( 0.02 \mathrm{m} \) and a frequency of \( 60 \mathrm{Hz} \). The maximum force acting on the particle is :
A \( .2 .88 \times 10^{3} \mathrm{N} \)
B . \( 1.44 \times 10^{3} \) N
c. \( 5.67 \times 10^{3} \mathrm{N} \)
D. \( 0.75 \times 10^{3} \mathrm{N} \)


As the angle between the mirrors
decreases the number of images formed also decreases.
A. True
B. False


The safest and the most common
alternative of sugar is
A. glucose
B. aspartame
c. saccharine
D. cyclodextrin


Thirty percent of the members of a swim club have passed the life saving test. Among the members who have not passed the test, 12 have taken
the preparatory course and 30 have not
taken the course.How many members
are there in the swim club?
A . 60
B. 80
\( c .100 \)
D. 120
E . 140


Masses of two isobars \( _{29} C u^{64} \) and \( 30 Z n^{64} \) are \( 63.9298 u \) and \( 63.9292 u \)
respectively. It can be conclude from these data that
A. Both the isobars are stable
B . \( Z n^{64} \) is radioactive, decaying to \( C u^{64} \) through \( \beta- \) decay
C. \( C u^{64} \) is radioactive, decaying to \( Z n^{64} \) through \( \gamma \) decay
D. \( C u^{64} \) is radioactive, decaying to \( Z n^{64} \) through \( \beta- \) decay


Which of the following helps in differentiation of Iymphocytes?
A. cytosin
B. Thymosin
c. cyclin
D. None of the above


Give a brief account on human
excretory system. Add a note on vertica section of kidney.


The compouned interest, calculate
yearly, on a certain sum of money for the second year is Rs.1,089 and for the third year it is Rs. \( 1,197.90 . \) Calculate the rate of interest and the sum of money
\( A \cdot 11 \%, \) Rs. 800
B. 12\%, Rs. 400
c. 13\%, Rs. 700
D. None of these


The Sl unit of gravitational potential is
\( A . J \)
B. \( J k g^{-1} \)
c. \( J k g \)
D. \( J k g^{-2} \)


Prove that no matter what the real
numbers \( a \) and \( b \) are, the sequence with
\( n \) th term \( a+n b \) is always an A.P. What
is the common difference?


A hollow tube is carrying an electric current along its length distributed
uniformly over its surface. The magnetic field :
This question has multiple correct options
A. increases linearly from the axis to the surface
B. is constant inside the tube
c. is zero at the axis
D. is zero just outside the tube


The area of an equilateral triangle of
side \( 13 \mathrm{cm}, \) is
A. 74.079 sq.cm
в. 76.719 sq.cm
c. 63.917 sq.cm
D. 73.179 sq.cm


Which of the following element occurs in allotropic form?
A. lodine
B. Copper
c. sulphur
D. Silver


The smallest human cell is
A. Erythrocyte
B. Kidney cell
C. Liver cell
D. sperm


Which of the following transition in
\( H e^{+} \) ion emits light of wavelength
equal to the longest wavelength emitted in the Paschen series H-atom?
\( \mathbf{A} \cdot 9 \rightarrow 6 \)
B . \( 8 \rightarrow 6 \)
c. \( 8 \rightarrow 4 \)
D. none of these


Which of the following statements will not hold true if a plant is grown in only
sand \( (\mathrm{S}), \) only clay (C) and only humus
\( (H) ? \)
A. Water availability to the roots will be more in (C) and
(H) as compared to (S)
B. Ability of roots to penetrate (S) and (H) will be low as compared to (C).
C. Nutrient availability to roots will be less in (S) as compared to (C) and (H).
D. Oxygen availability to roots will be low in (C) as compared to (S) and (H).


A steel ball of diameter \( \boldsymbol{d}=\mathbf{3 . 0} \boldsymbol{m m} \)
starts sinking with zero initial velocity in olive oil whose viscosity is \( \eta= \)
\( 0.90 P . \) How soon after the beginning of
motion will the velocity of the ball differ from the steady-state velocity by \( \boldsymbol{\eta}=\mathbf{1 . 0 \%} ? \)


If \( A \) and \( B \) are acute angles such that
\( \sin A=\sin ^{2} B, 2 \cos ^{2} A=3 \cos ^{2} B \)
then
This question has multiple correct options
A \( \cdot A=\frac{\pi}{6} \)
B. \( A=\frac{\pi}{2} \)
c. \( B=\frac{\pi}{4} \)
D. \( B=\frac{\pi}{3} \)


Write down Snell's law of refraction and
explain


How would you describe J.J. Thomsons
model of the atom?
\( A . \) An atom is indivisible
B. The atom is composed of only negatively charged particles.
C. The atom is composed of a positive core with negatively charged particles orbiting the positive core.
D. The atom is composed of diffused ball of positive charge with negative particles dispersed throughout.


What is the electronic potential at the centre of square of side 1 m? The
charges \( 1 \times 10^{-8} C,-2 \times 10^{-8} C, 3 \times \)
\( 10^{-8} \) Cand \( 2 \times 10^{-8} C \) are placed at the
corners of the square.


Fill in the blank.
is a natural fibre,
with continuous filaments which can
stretch upto \( 1 \mathrm{km} \)


Solve the following equation: \( 3^{x-1} \times \)
\( \mathbf{5}^{2 y-3}=225 \)
A \( \cdot x=3, y=\frac{5}{2} \)
в. \( _{x}=-3, y=\frac{5}{2} \)
c. \( _{x}=3, y=\frac{-5}{2} \)
D. None of the above


A particle moves according to the equation \( \boldsymbol{x}=\boldsymbol{a} \sin ^{2}\left(\boldsymbol{\omega} \boldsymbol{t}-\frac{\boldsymbol{\pi}}{\boldsymbol{4}}\right) . \) Find the
amplitude and frequency of oscillations
\( \mathbf{A} \cdot a, \omega \)
в. \( \frac{a}{2}, \omega \)
c. \( \frac{a}{2}, \frac{\omega}{2} \)
D. \( \frac{a}{2}, 2 \omega \)


The value of a machine depreciates at
the rate of \( 10 \% \) every year. it was purchased 3 years ago. If its present value is Rs. 8748 , its purchase price
was
A. Rs. 10000
B. Rs. 11372
c. Rs. 12000
D. Rs. 12500


How to derive the Mode formula for
grouped data?


Find the magnitude of two vectors \( \vec{a} \) and \( \vec{b}, \) having the same magnitude and such that the angle between them is \( 60^{\circ} \) and their scalar product is \( \frac{1}{2} \)


State True or False.
The bond length decreases with increase in multiplicity of bonds between two atoms.
A. True
B. False


The alkaline earth metal which shows
some properties similar to aluminium
is:
A. \( C a \)
в. \( B e \)
\( c \cdot s r \)
D. \( B a \)


single Correct Answer Type A particle is moving along a circular path with uniform speed. Through what angle does its angular velocity change when it completed half of the circular
path?
\( \mathbf{A} \cdot 360 \)
B. 180
\( c \cdot 45 \)
D. 0


f the sides of a parallelogram touch a
circle. Prove that the parallelogram is a rhombus.


Range of data 7,8,2,1,3,13,18 is?
A . 10
B. 15
c. 17
D. None of the above


The direction cosines of \( \hat{i}+\hat{j}+\hat{k} \) are
\( \mathbf{A} \cdot 1,1,1 \)
B. 2,2,2
c. \( 1 / \sqrt{2}, 1 / \sqrt{2}, 1 / \sqrt{2} \)
D. \( 1 / \sqrt{3}, 1 / \sqrt{3}, 1 / \sqrt{3} \)


If Young's modulus of iron be \( 2 \times 10^{11} \)
\( \mathrm{N} / \mathrm{m}^{-2} \) and interatomic distance be \( 3 \mathrm{x} \)
\( 10^{-10} \mathrm{m}, \) the interatomic force constant
will be :
\( \mathbf{A} .60 N / m \)
в. \( 120 N / m \)
\( c .30 N / m \)
D. \( 180 N / m \)


Which of the following reactions does not take place during rusting?
A \( \cdot H_{2} C O_{3} \rightleftharpoons 2 H^{+}+C O_{3}^{2} \)
B. \( 4 F e^{2+}+O_{2(d r y)} \rightarrow F e_{2} O_{3} \)
C. \( 4 F e^{2+}+O_{2}+4 H_{2} O \rightarrow 2 F e_{2} O_{3}+8 H^{+} \)
D. \( F e_{2} O_{3}+x H_{2} O \rightarrow F e_{2} O_{3} \cdot x H_{2} O \)


The slope of a Normal stress vs Linear
strain in the linear region of the graph for a copper wire gives us
A. Young's modulus
B. Rigidity modulus
c. Bulk's modulus
D. Poisson's ratio


Aluminium is purified by :
A. roasting
B. sublimation
c. electrolytic refining
D. reduction with carbon


Consider the following two binary
relations on the set \( A=\{a, b, c\} \)
\( \boldsymbol{R}_{1}= \)
\( \{(c, a),(b, b),(a, c),(c, c),(b, c),(a, a)\} \)
and \( \boldsymbol{R}_{2}= \)
\( \{(a, b),(b, a),(c, c),(c, a),(a, a),(b, b) \)
Then
A. \( R_{2} \) is symmetric but it is not transitive
B. Both \( R_{1} \) and \( R_{2} \) are transitive
c. Both \( R_{1} \) and \( R_{2} \) are not symmetric
D. \( R_{1} \) is not symmetric but it is transitive


Temperature is generally increasing making the earth a hot plate. Mention
any two measures to control global warming.


\( z_{1} z_{2} \in C, z_{1}^{2}+z_{2}^{2} \in \)
\( \boldsymbol{R}, \boldsymbol{z}_{1}\left(\boldsymbol{z}_{1}^{2}-\boldsymbol{3} \boldsymbol{z}_{2}^{2}\right)=\boldsymbol{2} \) and
\( z_{2}\left(3 z_{1}^{2}-z_{2}^{2}\right)=11, \) then the value of
\( z_{1}^{2}+z_{2}^{2} \) is
A . 2
B. 3
\( c \cdot 4 \)
D. 5


Consider \( \boldsymbol{\alpha}- \) particles \( , \boldsymbol{\beta}- \) particles
and \( \gamma- \) rays, each having an energy of
\( 0.5 \mathrm{MeV} . \) In increasing order of penetrating powers, the radiations are
A. \( \alpha, \beta, \gamma \)
в. \( \alpha, \gamma, \beta \)
c. \( \beta, \gamma, \alpha \)
D. \( \gamma, \beta, \alpha \)


\[
f(x)=\left\{\begin{array}{ll}
\frac{1-\sin ^{2} x}{3 \cos ^{2} x}, & x<\frac{\pi}{2} \\
a, & x=\frac{\pi}{2} \\
\frac{b(1-\sin x)}{(\pi-2 x)^{2}} & x>\frac{\pi}{2}
\end{array}\right.
\]
then \( f(x) \) is continuous at \( x=\frac{\pi}{2} \)


A thin disc of mass \( \mathrm{M} \) and radius \( \mathrm{R} \) has
per unit area \( \sigma(r)=k r^{2} \) where \( r \) is the
distance from its centre. Its moment of
inertia about an axis going through its centre of mass and perpendicular ti its plane is :
\( \mathbf{A} \cdot 2 \frac{M R^{2}}{6} \)
B \( \cdot 2 \frac{M R^{2}}{3} \)
\( \mathbf{c} \cdot_{2} \frac{2 M R^{2}}{3} \)
D. \( 2 \frac{M R^{2}}{2} \)


A coil having 500 square loops each of side \( 10 \mathrm{cm} \) is placed normal to a magnetic field which increases at the rate of \( 1 T s^{-1} . \) The induced e.m.f. is
A . 0.1
B. 5.0 V
\( c \cdot 0.5 v \)
D. 1.0


In particular system of unit, if the unit of mass becomes twice and that of time
becomes half, then 8 Joules will be
written as
A . 16
B.
\( c \cdot 4 \)
D. 64


Electrons are present in the nucleus of
an atom.
A . True
B. False


Find the odd one out:
A. Nitrogen
B. Potassium
\( c . \) zinc
D. Phosphorus


1 amu is equal to
A \( \cdot 1.67 \times 10^{-27} k g \)
В. \( 1.67 \times 10^{27} k g \)
c. \( 1.67 \times 10^{-37} k g \)
D. \( 1.67 \times 10^{37} k g \)


\( ^{16} O \) and \( ^{17} O \) can be said as :
A. allotropes
B. amphiprotic
c. isoelectronic
D. isomers
E. isotopes


Which one of the following codes for an amino acid?
A. Cistron
B. Exon
c. codon
D. Intron


A charge is projected with a velocity of \( 10^{5} m / s . \) In a perpendicular magnetic field. Find the magnetic of a transverse electric field if if moves undeflected
\( \left(B=4 * 10^{-5} T\right) \)
A . \( 4 \mathrm{N} / \mathrm{C} \)
в. \( 4 \times 10^{-2} \mathrm{N} / \mathrm{C} \)
c. \( 24 \times 10^{-2} N / C \)
D. not possible


Prove that \( : \sum_{i=1}^{n}\left(x_{i}-\bar{x}\right)=0 \)


The equation of the plane passing through \( (a, b, c) \) and parallel to the plane \( r \cdot(\hat{i}+\hat{j}+\hat{k})=2 \) is
A. \( x+y+z=1 \)
B . \( a x+b y+c z=1 \)
c. \( x+y+z=a+b+c \)
D. None of these


A particle of mass \( M \) is placed at the centre of a uniform spherical shell of mass \( 2 M \) and radius The gravitational potential on the surface of the shell is:
A. \( -\frac{G M}{R} \)
в. \( -\frac{3 G M}{R} \)
c. \( -\frac{2 G M}{R} \)
D. zero


\( -84 \times \dots \dots=+84 \)
A .
\( B .+ \)
\( c \cdot+84 \)
D. -


Amino acids are an example of:
A. an acid
B. a base
\( c . \) an acidic sal
D. an amphoteric substance


Use Euclids division algorithm to find
the HCF of:
(i) 135 and 225
(ii) 196 and 38220
(iii) 867 and 225


The \( \beta \) - particles emitted by the
radioactive substances are
A. positively charged
B. negatively charged
C. charge less
D. positively charged in some substances and negatively charged in others


Evaluate the integral \( \int_{0}^{a} \sqrt{a^{2}-x^{2}} d x \)
A \( \cdot \frac{a^{2}}{4} \)
B \( \cdot \pi a^{2} \)
c. \( \frac{\pi a^{2}}{2} \)
D. \( \frac{\pi a^{2}}{4} \)


Express as kilogram (kg) using decimals:
\( 5 k g 750 g \)


\( \mathbf{A}=\left[\begin{array}{cc}\mathbf{1 1} & \mathbf{1} \\ \mathbf{0} & \mathbf{1 1}\end{array}\right], \mathbf{B}=\left[\begin{array}{cc}\mathbf{0} & -\mathbf{2} \\ -\mathbf{3} & \mathbf{4}\end{array}\right], \mathbf{I}=\left[\begin{array}{cc}\mathbf{1} & \mathbf{0} \\ \mathbf{0} & \mathbf{1}\end{array}\right] \)
Find \( \boldsymbol{A}+\mathbf{3} \boldsymbol{B}+\boldsymbol{4} \boldsymbol{I} \)
A \( \cdot\left[\begin{array}{cc}0 & 2 \\ -3 & 0\end{array}\right] \)
B \( \cdot\left[\begin{array}{cc}15 & 2 \\ -13 & -16\end{array}\right] \)
c. \( \left[\begin{array}{cc}15 & -5 \\ -9 & 27\end{array}\right] \)
D. \( \left[\begin{array}{cc}11 & 2 \\ -4 & -5\end{array}\right] \)


Responsible for most helium found on Earth:
A. Gamma decay
B. Nuclear fusion
c. Alpha decay
D. Positron emission
E. Nuclear fission


From below which are the good
conductors of heat?
A. Metals
B. Plasticç
c. Paper
D. woodd


Find \( \boldsymbol{x}, \boldsymbol{y} \) if \( \left[\begin{array}{cc}\mathbf{0} & \mathbf{4} \\ \boldsymbol{x}^{2} & \boldsymbol{y}^{2}\end{array}\right]=\left[\begin{array}{ll}\mathbf{0} & \mathbf{4} \\ \boldsymbol{4} & \mathbf{9}\end{array}\right] \)


Select and write the most appropriate
answer from the given alternatives
for question:
The cartesian equation of the line passing through the points \( \boldsymbol{A}(\mathbf{4}, \mathbf{2}, \mathbf{1}) \) and \( \boldsymbol{B}(\mathbf{2},-\mathbf{1}, \mathbf{3}) \) is
A. \( \frac{x+4}{2}=\frac{y-2}{3}=\frac{z-1}{-2} \)
в. \( \frac{x-4}{-2}=\frac{y-2}{-3}=\frac{z-1}{-2} \)
c. \( \frac{x-4}{2}=\frac{y-2}{3}=\frac{z-1}{-2} \)
D. \( \frac{x-4}{-2}=\frac{y-2}{3}=\frac{z-1}{-2} \)


Sulphur dioxide can be used as:
This question has multiple correct options
A. bleaching agent
B. antichlor
c. disinfectant
D. none of these


The sum of squared deviations of a set
of \( n \) values from their mean is
A. Minimum
B. Least
c. Maximum
D. zero


The first of two samples has 100 items with mean 15 and \( S . D .3 . \) If the whole
group has 250 items with mean 15.6 and \( s . d=\sqrt{13.44}, \) find the standard
deviation of the second group.
A . 5
B. 4
\( c \cdot 6 \)
D. 3.52


Nylon has high elasticity and tensile strength.
A . True
B. False


Which statement is wrong?
This question has multiple correct options
A. In polar aprotic solvents such as DMSO, DMF, and DMA, the fugacity order is \( I^{\ominus}>B r^{\ominus}>C l^{\ominus}>F^{\ominus} \)
B. Strong bases are good leaving groups
C - The leaving group order of the following is : \( \stackrel{\ominus}{O H}> \) \( R O^{\ominus}>C H \equiv C^{\ominus}>\stackrel{\ominus}{N} H_{2} \)
D. Charged species are good leaving groups than neutral species


Ammonia gas dissolves in water to give
\( N H_{4} O H . \) In this reaction. water acts as
:-
A. An acid
B. A base
c. \( A \) salt
D. \( A \) conjugate base


\( \boldsymbol{A}_{1}\left(\boldsymbol{x}_{1}, \boldsymbol{y}_{1}\right), \boldsymbol{A}_{2}\left(\boldsymbol{x}_{2}, \boldsymbol{y}_{2}\right), \boldsymbol{A}_{3}\left(\boldsymbol{x}_{3}, \boldsymbol{y}_{3}\right) \)
are \( n \) points a plane such that
\( A_{1} A_{2} \) is bisected at \( G_{1}, G_{2}, A_{2} \) is
divided in the ration 1: 2 at \( G_{2}, G_{2}, A_{4} \)
is divided in the ratio 1: 3 at \( G_{3} \). The
process is continued until all \( n \) points are exhausted, then find the co-
ordinates of the final point \( G_{n} \)


In a school the mark distribution of 25
students in a mathematics
examination is given below. Calculate it's mode.
\( \begin{array}{cccc}30- & 40- & 50- & 6 \\ 40 & 50 & 60\end{array} \) Marks
2 No. of
students
A. 65
в. 32
c. 34
D. 31


Glucagon is produced in the islets of Langerhans by
\( \mathbf{A} \cdot \beta \) cells
B. \( \alpha \) cells
c. Delta cells
D. Both A and B


Which of the following is not used as SI prefixes:
A. Deca
B. Kilo
c. Femto
D. Mica


Factorise: \( (\boldsymbol{a}+\mathbf{2 b}-\mathbf{3 c})^{\mathbf{3}}-\boldsymbol{a}^{\mathbf{3}}-\mathbf{8 b}^{\mathbf{3}}+ \)
\( \mathbf{2 7 c}^{\mathbf{3}} \)


\( \lim _{x \rightarrow \infty} x^{2}\left(1-\cos \frac{2}{x}\right) \)


How many pair of vertically opposite
angles are formed?


In alternative current generator, \( A C \)
current reverses its direction:
A. 20 times per second
B. 50 times per second
c. once per second
D. twice per second


Express which of the following setups
can be used to verify Ohms law?
\( A \)
\( B \)
\( c \)
\( D \)


The mean of the cubes of the first \( n \)
natural numbers is :
A \( \cdot \frac{n(n+1)^{2}}{4} \)
B \( \cdot n^{2} \)
c. \( \frac{n(n+1)(n+2)}{8} \)
D. \( \left(n^{2}+n+1\right) \)


Write the name and structure of one of
the common initiators used in
free radical addition polymerisation.


When equilibrium is attained, the concentration of each of the reactants
and products become equal.
A. True
B. False
c. Ambiguous
D. None of these


When \( 100 \mathrm{ml} \) of a \( O_{2}-O_{3} \) mixture was
passed through turpentine, there was the reduction of volume by \( 20 \mathrm{ml} \). If 100ml of such a mixture is heated, what
will be the increase in volume?
A. \( 10 \mathrm{ml} \)
B. \( 20 \mathrm{ml} \)
c. \( 30 m l \)
D. \( 25 \mathrm{ml} \)


\( \int_{0}^{\frac{\pi}{2}} \frac{\sqrt{\sin x}}{\sqrt{\sin x}+\sqrt{\cos x}} d x \) is equal to
\( \mathbf{A} \cdot \mathbf{0} \)
в. \( -\pi \)
c. \( \frac{3 \pi}{2} \)
D. \( \frac{\pi}{2} \)
E. \( \frac{\pi}{4} \)


If \( z_{1}=2-i, z_{2}=1+i, \) find
\( \left|\frac{z_{1}+z_{2}+1}{z_{1}+z_{2}+i}\right| \)


The velocity of electromagnetic waves
in a dielectric medium \( \left(\varepsilon_{r}=2\right) \) is:
A \( \cdot 3 \times 10^{8} \) meter/second
B . \( 1.5 \times 10^{8} \) meter/second
C. \( 6 \times 10^{8} \) meter/second
D. \( 7.5 \times 10^{7} \) meter/second


Olefin, which gives \( C H_{3} C H O \) and
\( C H_{3} C H_{2} C H O \) on ozonization and hydrolysis is :
A. 1butene
B. 2butene
c. 1pentene
D. 2pentene


Which of the following do have \( \boldsymbol{p}_{\boldsymbol{\pi}}-\boldsymbol{d}_{\boldsymbol{\pi}} \)
bonding?
A \( . N O_{3}^{-} \)
B. \( S O_{3}^{-2} \)
\( \mathrm{c} \cdot B O_{3}^{-3} \)
D. \( C O_{3}^{-2} \)


If \( A \) has 2 elements and \( B \) has 2
elements, then the number of elements
in \( A \times B \) is :


In the given figure
\( O A \times O B=O C \times O D, \) then which of
the following is correct.
\( \mathbf{A} \cdot \angle A=\angle B \)
B. \( \angle A=\angle C \)
c. \( \angle D=\angle C \)
D. none of these


Two particles of equal masses have velocities \( \vec{V}_{1}=2 \hat{i} m / s . \) The first
particle has an acceleration \( \overrightarrow{a_{1}}=(3 \hat{i}+ \)
\( 3 \hat{j}) \frac{m}{s^{2}}, \) while the acceleration of the
other particle is zero. The center of
mass of the particles moves in a :
A. Circle
B. Parabola
c. Straight line
D. Ellipse


Solve \( \left|\begin{array}{ccc}\mathbf{1} & \mathbf{1} & \mathbf{1} \\ \mathbf{1} & \mathbf{1}+\boldsymbol{x} & \mathbf{1} \\ \mathbf{1} & \mathbf{1} & \mathbf{1}+\boldsymbol{y}\end{array}\right| \)
\( A \)
B.
\( c \)
D. \( x y \)


toppr
Q Type your question
the conductor, is correctly represented
by the figure:
\( A \)
B.
\( c \)
\( D \)


Assertion
If a pure enantiomer of the following
ester is hydrolysed in dilute alkaline
medium, a pure enantiomer of alcohol
is obtained.
Reason
Under the given condition of hydrolysis, acyl oxygen heterolysis always takes
place.
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


Organisms that cannot prepare their own food are called as
A. Autotrophs
B. Heterotrophs
c. Algae
D. None of the above


The electric field components due to a
charge inside the cube of side \( 0.1 \mathrm{m} \) are
shown in figure.
where, \( \boldsymbol{E}_{\boldsymbol{x}}=\boldsymbol{\alpha}, \) where \( \boldsymbol{\alpha}=500 \mathrm{N} / \mathrm{C}-\mathrm{m} \)
\( \boldsymbol{E}_{\boldsymbol{y}}=\mathbf{0}, \boldsymbol{E}_{\boldsymbol{z}}=\mathbf{0} \)
Calculate
(a) the flux through the cube and
(b) the charge inside the cube.


Which term of the A.P. \( 121,117,113, \ldots . \) is its first negative term?


Which of the following arrangements does not represent the correct order of
the property stated against it?
A \( \cdot V^{2+}<C r^{2+}<M n^{2+}<F e^{2+}: \) Paramagnetic behavior
B. \( N i^{2+}<C o^{2+}<F e^{2+}<M n^{2+}: \) lonic size
C. \( C o^{3+}<F e^{3+}<C r^{3+}<S c^{3+}: \) Stability in aqueous solution
D. \( S c<T i<C r<M n \) : Number of oxidation states


Match the items of Column-I with its
proportional term in the items of
Column-II:
Column-I
(a) Kinetic energy
(p) Mole fraction
(b) Partial pressure of a
(q) Density
gas
(c) Rate of diffusion
(r) Molar mass
(d) Vapour pressure of a
(s) Absolute liquid \( \quad \) temperature


The breakdown electric intensity for air is
\( 3 \times 10^{6} \mathrm{V} / \mathrm{m} . \) The maximum charge that
can be held by a sphere of radius \( 1 \mathrm{mm} \) is
A \( .0 .33 C \)
в. 0.33 пС
\( c .3 .3 C \)
D. \( 3.3 \mu C \)


Pressure \( 3 \mathrm{m} \) below the free surface of a
liquid is \( 15 ~ K N / m^{2} \) in excess of
atmosphere pressure. Determine its density and specific gravity. \( [\mathrm{g}=10 \) \( \left.\boldsymbol{m} / \boldsymbol{s e c}^{2}\right] \)


Evaluate \( : \lim _{x \rightarrow \infty} \frac{5 x^{2}+1}{x^{2}+10} \)


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


Correct order of acidic strength.
\( (I) \)
\( (\|) \)
\( \mathbf{A} \cdot I>I I>I I I \)
B. \( I I>I I I>I \)
\( \mathbf{c} \cdot I>I I I>I I \)
D. \( I I I>I I>I \)


A spherical solid ball of volume \( V \) is
made of a material of density \( \rho_{1} \) It is
falling through a liquid of density
\( \rho_{1}\left(\rho_{2}<\rho_{1}\right) . \) Assume that the liquid
applies a viscous force on the ball that
is Proportional to the square of its
speed \( \mathbf{v}, \) i.e., \( \boldsymbol{F}_{\boldsymbol{v} i \text {scous}}=-\boldsymbol{k} \boldsymbol{v}^{2}(\boldsymbol{k}>\mathbf{0}) \)
The terminal speed of the ball is:
A \( \cdot \sqrt{\frac{V g\left(\rho_{1}-\rho_{2}\right)}{k}} \)
в. \( \frac{V g \rho_{1}}{k} \)
c. \( \sqrt{\frac{V g \rho_{1}}{k}} \)
D. \( \frac{V g\left(\rho_{2}<\rho_{1}\right)}{k} \)


Which of the following are alicyclic compounds?
A. cyclopropane
B. ethane
c. benzene
D. pyridine


When speed of a moving object is doubled its:
A. acceleration is doubled
B. momentum becomes four times more
c. kinetic energy is increased to four times
D. potential energy is increased


If a simple harmonic motion is represented by \( \frac{d^{2} x}{d t^{2}}+\alpha x=0, \) its time period is then
A. \( 2 \pi \sqrt{\alpha} \).
. \( \sqrt{\sqrt{\alpha}} \). \( \alpha \).
в. \( 2 \pi \alpha \)
c. \( \frac{2 \pi}{\sqrt{\alpha}} \)
D. \( \frac{2 \pi}{\alpha} \)


How many 6 digits odd numbers greater than 60,0000 can be formed from the
digits 5,6,7,8,9,0 if Repetitions are not allowed:
A . 60
B. 120
c. 240
D. 480


The atomic mass of \( _{11}^{23} \mathrm{Na} \) in amu is :


The number of 160 ohms resistors to
be connected in parallel to produce 5 A current on a \( 100 \mathrm{V} \) line is:
\( A \cdot 2 \)
B. 4
\( c \cdot 8 \)
D. 10


Which one of the following has a potential more than zero?
A \( \cdot P t, \frac{1}{2} H_{2}(\operatorname{latm}) \mid H C l(1 M) \)
в. \( P t_{2} \frac{1}{2} H_{2}(1 a t m) \mid H C l(2 M) \)
c. \( \quad P t, \frac{1}{2} H_{2}(1 a t m) \mid H C l(0.1 M) \)
D \( \cdot \operatorname{Pt}, \frac{1}{2} H_{2}(1 \text { at } m) \mid H C l(0.5 M) \)


toppr
Q Type
solutıon (C). Lıthıum Is reacted with (B)
yielding a solid product (D) which effervescence with water to give a
strongly basic solution (E). When \( C O_{2} \) gas is bubbled through the solution (C), a white ppt (F) is formed but this redissolved forming solution (G) when
more \( C O_{2} \) is passed. The precipitate (F) effervesced when moistened with conc.
\( H C l \) and give deep red coloration to the Bunsen burner flame. (F) on heating
with an excess of carbon at \( 2000^{\circ} C \)
give (H).

Solution (G) contains a salt which:
(i) causes permanent hardness of water
(ii) can not be obtained in solid-state
(iii) causes temporary hardness of
water
(iv) can be obtained in solid-state
Identify the salt with correct options.
A. (i) and (ii)
B. (i) and (iv)
c. (ii) and (iii)
D. (ii) and (iv)


One milliwatt of light of wavelength \( \lambda=4560 A \) is incident on a cesium
metal surface. Calculate the electron
current liberated. Assume a quantum efficiency of \( \boldsymbol{\eta}=\mathbf{0 . 5 \%} \). [Work function
for cesium \( =1.89 e V] \) take \( h c= \)
\( 12400 e V-A \)


Solve: Value of \( \boldsymbol{D}=\left|\begin{array}{ccc}\mathbf{1} & \mathbf{1} & \mathbf{1} \\ \boldsymbol{a} & \boldsymbol{b} & \boldsymbol{c} \\ \boldsymbol{a}^{2} & \boldsymbol{b}^{2} & \boldsymbol{c}^{2}\end{array}\right| \) is


Suppose \( X \) has a binomial distribution \( B \) of \( 6, \frac{1}{2} . \) Show that \( X=3 \) is the most likely outcome
(Hint \( : P(X=3) \) is the maximum
among all \( \left.\boldsymbol{P}\left(\boldsymbol{x}_{i}\right), \boldsymbol{x}_{i}=\mathbf{0}, \mathbf{1}, \mathbf{2}, \mathbf{3}, \mathbf{4}, \mathbf{5}, \boldsymbol{6}\right) \)


The maximum value of \( f(x)=100- \) \( |45-x| \) is
A . 100
в. 145
c. 55
D. 45


The molar specific heat of oxygen at
constant pressure \( \mathrm{C}_{p}=7.03 \mathrm{cal} / \mathrm{mol}^{o} \mathrm{C} \)
and \( \mathrm{R}=8.31 \mathrm{J} / \mathrm{mol}^{o} \mathrm{C} \). the amount of
heat taken by 5 mol of oxygen when
heated at constant volume from \( 10^{\circ} \mathrm{C} \) to
\( 20^{\circ} \mathrm{C} \) will be approximately
A \( .25 \mathrm{cal} \)
B. 50 cal
c. \( 250 c a l \)
D. 500 call


The \( 9^{t h} \) term of an A.P.is equal to 6
times its second term. If its \( 5^{t h} \) term is
\( 22, \) then find the A.P.


A \( 500 \mathrm{mL} \) solution is prepared by dissolving 20 g sodium hydroxide in water. This is mixed in another \( 200 \mathrm{mL} \)
solution of \( N a O H \) having molarity 0.2
M. The molarity of resulting solution is:
A. 0.66 M
в. 0.77 М
c. \( 1.80 \mathrm{M} \)
D. 1.97 М


When \( 2 s-2 s, 2 p-2 p \) and \( 2 p-2 s \)
orbitals overlap, the bond strength decreases in the order:
A. \( p-p>s-s>p-s \)
в. \( p-p>p-s>s-s \)
c. \( s-s>p-p>p-s \)
D. \( s-s>p-s>p-p \)


Determine the electrostatic potential energy of a system consisting of two charges \( 7 \mu C \) and \( -2 \mu C \) (and with no
external field) placed at \( (-9 c m .0 .0) \) and \( (9 c m, 0.0) \) respectively.


In which of the compounds oxygen does not exhibit oxidation state (-2)\( ? \)
This question has multiple correct options
A \( \cdot C s O_{2} \)
в. \( K_{2} O_{2} \)
c. \( O F_{2} \)
D. \( C l_{2} O \)


Define factorisation


By simply looking at the pair of angles
given in figure. State which of the angle
in the pairs is greater.


Find the gain or loss.
C.P. \( = \) Rs. \( 550.75 ; \) S.P. \( = \) Rs. 475.30


Volume of a gas at \( t^{\circ} \mathrm{C} \) is 20 litre when
temperature of gas increases by \( 50^{\circ} \mathrm{C} \)
at constant pressure than volume of
gas increased by \( 25 \% \) than calculate value of it?


The number of roots of the equation \( 2^{x}+2^{x-1}+2^{x-2}=7^{x}+7^{x-1}+7^{x-2} \)
is-


Butylated hydroxy toluene as a food
additive acts as:
A . antioxidant
B. flavouring agent
c. coloring agent
D. emulsifier


Assertion
In case of uniform linear motion,
acceleration remains zero.
Reason Velocity remains constant in uniform
linear motion.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


If \( \vec{a}=2 \hat{m}+\hat{n}, \vec{b}=\hat{m}-2 \hat{n} \) and angle
between the unit vectors \( \hat{m} \) and \( \hat{n} \) is \( 60^{\circ} \)
\( a, b \) are the sides of a
parallelogram,then the lengths of the diagonals are
A \( . \sqrt{7}, \sqrt{5} \)
B. \( \sqrt{13}, \sqrt{5} \)
C \( . \sqrt{7}, \sqrt{13} \)
D. \( \sqrt{11}, \sqrt{13} \)


Plot the following points on a graph paper and find out in which quadrant do
they lie?
(i) \( A(3,5) \)
(ii) B (-2, 7)
(iii) \( C(-3,-5) \) \( D(2,-7)(v) 0(0,0) \)


The membrane which covers the brain
and the spinal cord is
A. White matter
B. Grey matter
c. Peritonium
D. Meninges


Which of the following statement is
correct for \( \boldsymbol{C s B r _ { 3 }} \) ?
A. It is a covalent compound
B. It contains \( C s^{3+} \) and \( B r^{-} \) ions
c. It contains \( C s^{+} \) and \( B r_{3}^{-} \) ions
D. It contains \( C s^{+}, B r_{3}^{-} \) and lattice \( B r_{2} \) molecul


State whether the given statement is true or false:
Hydrogen peroxide acts both as an oxidizing and as a reducing agent in alkaline solution towards certain first-
row transition metal ions.


Do we apply a force on the ground while walking? (Yes/No)


When mass is rotating in a plane about a
fixed point, its angular momentum is directed along
A. the axis of rotation
B. line at an angle of \( 45^{\circ} \) to the axis of rotation
c. the radius
D. the tangent to the orbitt


Find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}: \sin \boldsymbol{x}+\mathbf{7} \boldsymbol{x}^{2}+\boldsymbol{y}^{2}=\mathbf{5} \)


There are \( x^{4}+57 x+15 \) pens to be
distributed in a class of \( x^{2}+4 x+2 \)
students. Each student should get the minimum possible number of pens. Find the number of pens received by each student and the number of pens
left undistributed \( (\boldsymbol{x} \epsilon \boldsymbol{N}) \)
в. \( 9 x-15 \)
c. \( 9 x-20 \)
D. \( 9 x+13 \)


A gas expands adiabatically from a
temperature \( T_{1} \) to a temperature
\( \boldsymbol{T}_{2}\left(\boldsymbol{T}_{1}>\boldsymbol{T}_{2}\right) . \) The work done in this
process is
A. \( C_{p}\left(T_{1}-T_{2}\right) \)
в. \( C_{v}\left(T_{1}-T_{2}\right) \)
c. \( R\left(T_{1}-T_{2}\right) \)
D. zero


Why it is said that evolution is a
progressive development of plants and animals.


The instrument which can be used to
detect a charged body is :
A. Electroplate
B. Leaf electroscope
c. Capacitor
D. Galvanometer


Rohit's family is planning to build a
concrete basketball court in their
backyard. How many square metres will be left in the backyard for grass?
A. 60 sq. \( \mathrm{cm} \)
B. 35 sq. \( \mathrm{cm} \)
c. 31 sq. \( \mathrm{cm} \)
D. 24 sq. \( \mathrm{cm} \)


is represented by
the given structure.
A. Prontosil
B. Sulphapyridine
C. Chloramphenicol
D. Chloroxylenol


In the figure given, the measure in
degrees of \( \angle A B C \) is \( 72^{\circ} . \) Find the value
of \( \boldsymbol{x} \)
\( \mathbf{A} \cdot 18^{\circ} \)
B. \( 24^{\circ} \)
\( c \cdot 27^{\circ} \)
\( \mathbf{D} \cdot 30^{\circ} \)


In a meter bridge, the balance point is
found at a distance \( l_{1} \) with resistances
\( \mathrm{R} \) and \( \mathrm{S} \) as shown in the figure
An unknown resistance \( X \) is now
connected in parallel to the resistance and the balance point is found at a
distance \( l_{2} \). Obtain a formula for \( X \) in
terms of \( l_{1}, l_{2} \) and \( S \)


If Youngs modulus of the material of a rod is \( 2 \times 10^{11} \mathrm{Nm}^{-2} \) and density is
\( 8000 \mathrm{kg} \mathrm{m}^{-3}, \) the time taken by a sound wave to traverse \( 1 \mathrm{m} \) along the rod is
A. \( 1.11 \times 10^{-4} s \)
В. \( 3 \times 10^{-4} s \)
c. \( 2 \times 10^{-4} s \)
D. \( 1 \times 10^{-4} s \)


A chelating agent has two or more than two donor atoms to bind a single metal
ion. Which of the following is not a chelating agent?
A. Thiosulphato
B. Glycinato
c. oxalato
D. Ethane-1, 2-diamine


Vessels and companion cells are found
in
A. Angiosperm
B. Pteridophytes
c. Bryophytes
D. Thallophytes


\( \boldsymbol{n}(\boldsymbol{A} \cap \boldsymbol{B}) \)


Find \( n \) if the given value of \( x \) is the \( n^{t h} \) term of the \( A P: 5 \frac{1}{2}, 11,16 \frac{1}{2}, 22, \dots ; x= \)
\( \mathbf{5 5 0} \)
A . 100
в. 110
\( c \cdot 200 \)
D. 220


Determine the standard emf of the cell
and standard free energy change of the cell reaction.
\( Z n / Z n^{2+} \| N i^{2+} / N \)
\( \boldsymbol{E}^{o} \boldsymbol{Z} \boldsymbol{n}^{2+} / \boldsymbol{Z} \boldsymbol{n}=-\mathbf{0 . 7 6} \boldsymbol{V} \)
\( \boldsymbol{E}^{o} \boldsymbol{N} \boldsymbol{i}^{2+} / \boldsymbol{N} \boldsymbol{i}=-\mathbf{0 . 2 5} \boldsymbol{V} \)


The ratio of radii of two spheres is 2: 3
Find the ratio of their surface areas and
volumes.


Statement 1: Atom \( A \) with 7 valence
electrons forms \( A B, \) with atom \( B \) with
two valence electrons.

Statement \( 2: B \) donates its electrons to
fill the outer shell of \( \boldsymbol{A} \)
A. Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation of Statement 1.
B. Both the Statement 1 and Statement 2 are correct, but Statement 2 is not the correct explanation of Statement 1.
c. statement 1 is correct, but statement 2 is not correct
D. Statement 1 is not correct, but Statement 2 is correct


Which of the following is an ionic compound?
\( A \cdot S O_{3} \)
в. \( I C l \)
c. \( K I \)
D. \( C H C l_{3} \)


Two identical thin rings each of radius
\( \boldsymbol{R} \) metre are kept on the same axis at a
distance of \( \boldsymbol{R} \) metre apart. If the
charges on them are \( 10 C \) and \( 5 C \)
respectively. Calculate the work done in
moving charge \( q \) coulomb from the
centre of one ring to that of another
A \( \cdot \frac{5 q}{4 \pi \varepsilon_{0} R}\left[1-\frac{1}{\sqrt{2}}\right] J \)
В. \( \frac{5 q}{4 \pi \varepsilon_{0} R}\left[\frac{\sqrt{2}-1}{2}\right] J \)
\( ^{\mathbf{C}} \cdot \frac{15 q}{4 \pi \varepsilon_{0} R}\left[\frac{\sqrt{2}-1}{\sqrt{2}}\right] J \)
\( ^{\mathrm{D}} \frac{10 q}{4 \pi \varepsilon_{0} R}\left[\frac{\sqrt{2}-1}{\sqrt{2}}\right] J \)


Ampere rule is used to find the
A. direction of current
B. direction of magnetic field
C. direction of motion of the conductor
D. magnitude of current


Which of the following is an acidic amino acid ?
A. Glycine
B. Valine
c. Leucine
D. Glumatic acid


Which one of following is employed as a tranquilizer?
A. Chlorpheninamine
в. Equanil
c. Naproxen
D. Tetracycline


The compound which does not exist as hydrate form:
A. ferrous sulphate
B. copper sulphate
c. magnesium sulphate
D. sodium chloride


Explain seld induction and mutual
induction.


At \( t=0, \) a transverse wave pulse in wire is described by the function; \( \boldsymbol{y}=\frac{\boldsymbol{6}}{\boldsymbol{x}^{2}+\boldsymbol{3}} \)
Where \( x \) and \( y \) are in meters. Write the function \( y(x, t) \) that describes this wave if it travelling in the positive \( x \) -direction with a speed of \( 4.50 \mathrm{m} / \mathrm{s} \)
A \( \cdot y=\frac{12}{\left[(x-4.5 t)^{2}+3\right]} \)
B. \( y=\frac{6}{\left[(x-4.5 t)^{2}+9\right]} \)
c. \( y=\frac{16}{\left[(x-4.5 t)^{2}+3\right]} \)
D. \( y=\frac{6}{\left[(x-4.5 t)^{2}+3\right]} \)


Draw the Venn diagram of \( \boldsymbol{A} \cap \boldsymbol{B} \)


A charge \( q_{0} \) is brought from infinity to the centre of dipole. Find work done?
в. \( 0 . \)
\( c \cdot 3 J \)
D. \( 4 J \)


Heptane and octane form ideal solution.
At \( 373 \mathrm{K} \), the vapour pressures of the two liquids are \( 105.2 \mathrm{kPa} \) and \( 46.8 \mathrm{kPa} \) respectively. What will be the vapour
pressure, in bar, of a mixture of 25 g heptane and 35 g of octane?


Figure represents a metre scale balancing on a knife edge at \( 20 \mathrm{cm} \)
mark. When a weight of 60 N is suspended from 10 cm mark. Calculate
the weight of the ruler(in N).
A . 30
B. 60
\( c \cdot 15 \)
D. 20


If a beam of metal supported at the two ends is loaded at the centre, then the depression at the centre will be proportional to
A \( \cdot \gamma^{2} \)
B. \( \gamma \)
\( c \cdot \frac{1}{\gamma} \)
D. \( \frac{1}{\gamma^{2}} \)


The disposal of waste produced in a nuclear power plant is difficult because they are:
A. highly inflammable
B. highly radioactive
c. highly poisonous
D. extremely heavy


\( \Delta H_{c o m b} \) of \( C H_{4}, C_{2} H_{6} \) and \( C_{3} H_{8} \) are
-210,-368.4 and \( -526.3 k c a l m o l^{-1} \)
Hence \( \Delta \boldsymbol{H}_{c o m b} \) of \( \boldsymbol{C}_{4} \boldsymbol{H}_{10} \) is
approximately:
A . \( -684.0 \mathrm{kcal} \)
в. -368.4 kcal
c. \( -842.0 \mathrm{kcal} \)
D. - 600.0 k call \( l \)


People use bases called antacids due
to:
A. get rid of stomach pain
B. irritation
c. both \( (A) \) and \( (B) \)
D. none of the above


A long horizontal slit is place 1 mm above a horizontal plane mirror. The interference between the light coming directly from the slit and that after reflection is seen on a screen 1 m away
from the slit. If the mirror reflects only
\( 64 \% \) of the light falling on it, the ratio of
the maximum to the minimum
intensity in the interference pattern
observed on the screen is:
\( \mathbf{A} \cdot 8: 1 \)
B . 3: 1
c. 81: 1
D. 9: 1


Assertion
In the reaction, \( C_{12} H_{22} O_{11}(a q)+ \) \( \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l}) \stackrel{d i \boldsymbol{l} \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4}}{\longrightarrow} \boldsymbol{C}_{6} \boldsymbol{H}_{12} \boldsymbol{O}_{6}(\boldsymbol{a} \boldsymbol{q})+ \)
\( C_{6} H_{12} O_{6}(a q), H_{2} S O_{4} \) is called as a
homogeneous catalyst.
Reason
\( H_{2} S O_{4} \) is in the same phase as the reactants and products.
A. If both Assertion and Reason are correct and Reason the correct explanation of Assertion
B. If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion
c. If Assertion is correct, but Reason is incorrect
D. If Assertion is incorrect, but Reason is correct


A pipe's lower end is immersed in water such that the length of air column from
the top open end has a certain length
\( 25 \mathrm{cm} . \) The speed of sound in air is
\( 350 m / s . \) The air column is found to
resonate with a tuning fork of frequency
\( 1750 H z . \) By what minimum distance
should the pipe be raised in order to make the air column resonate again
with the same tuning fork?
\( \mathbf{A} \cdot 7 \mathrm{cm} \)
B. \( 5 \mathrm{cm} \)
c. \( 35 \mathrm{cm} \)
D. \( 10 \mathrm{cm} \)


The six most common atoms in organic
molecules are
A. \( c, H, 0, \) He, \( \operatorname{ca} \) and \( s \)
B. C, H, 0, N, P and S
c. \( c, H, 0, c a, M g, \) and \( s \)
D. C, 0, N, S, P and Mg


3 geometric means between \( \frac{1}{9} \) and 9 is
A \( \cdot \frac{2}{3}, 1,3 \)
в. \( \frac{1}{3}, 2,3 \)
c. \( \frac{1}{3}, 1,6 \)
D. \( \frac{1}{3}, 1,3 \)


Which of the following is/are disproportionation reaction(s)? This question has multiple correct options
A \( \cdot 2 C C l_{3} C H O+N a O H \rightarrow C C l_{3} C O O N a+ \)
\( C C l_{3} C H_{2} O H \)
в. \( N H_{4} N O_{3} \rightarrow N_{2} O+2 H_{2} O \)
c. \( 2 K C l O_{3} \rightarrow 2 K C l+3 O_{2} \)
D. \( 5 C l_{2}+6 O H^{-} \rightarrow C l O_{3}^{-}+5 C l^{-}+3 H_{2} O \)


Which of the statements are correct?
This question has multiple correct options
\( \mathbf{A} \cdot B e_{2} C+H_{2} O \rightarrow \) Marsh gas
B. \( A l_{4} C_{3}+H_{2} O \rightarrow \) Gas is a content of CNG
\( \mathbf{C} \cdot C a C_{2}+H_{2} \rightarrow \) Gas is used for welding purpose with
\( O_{2} \) gas
D. \( C a_{3} P_{2}+H_{2} O \rightarrow \) Gas is used in Holme signals with
\( \mathrm{CaC}_{2} \)


Neuroglial cells are associated with the
A . Heart
B. Kidney
c. Brain
D. Eyes


Direction cosines \( l, \boldsymbol{m}, \boldsymbol{n} \) of two lines are
connected by the equation \( l-5 m+ \)
\( \mathbf{3} n=\mathbf{0} \) and \( \mathbf{7 l}^{2}+\mathbf{5 m}^{\mathbf{2}}-\mathbf{3 n}^{\mathbf{2}}=\mathbf{0 .} \) The
direction cosines of one of the lines are
в. \( 2 / \sqrt{6}, 1 / \sqrt{6},-1 / \sqrt{6} \)
D. \( 1 / \sqrt{6}, 1 / \sqrt{6}, 2 / \sqrt{6} \)


Find the depth of a cylindrical tank of
radius \( 28 m, \) if its capacity is equal to
that of a rectangular tank of size
\( 28 m \times 16 m \times 11 m \)


suitable common differences given in
column B.
Column A
Column B
A. \( -2,2,6,10, \dots \)
1. \( \frac{2}{3} \)
B. \( a=18, n=10, a_{n}=0 \)
2. -5
\( \mathbf{C} \cdot \boldsymbol{a}=\mathbf{0}, \boldsymbol{a}_{\mathbf{1 0}}=\mathbf{6} \)
3. 4
D. \( \boldsymbol{a}_{\mathbf{2}}=\mathbf{1 3}, \boldsymbol{a}_{\boldsymbol{4}}=\mathbf{3} \)
4. -4
\( 5 .-2 \)
6. \( \frac{1}{2} \)
7. 5
A. A-3, B-5, C-1, D-2
B. A-4, B-1, C-3, D-2
C. A-2, B-7, C-5, D-6
D. \( A-7, B-4, C-2, D-2 \)


Blood which leaves liver and passes
towards heart has concentration of
A . Bile
B. Oxygen
c. RBCs
D. urea


Select the odd one out w.r.t. conduction
of heat (wood, paper, plastic, silver)
A . silver
B. woodd
c. paper
D. plastic


If \( z \) is a complex number such that
\( |z|=1, \) then \( \left|\frac{1}{z}\right| \) is
\( \mathbf{A} \cdot \mathbf{0} \)
в. -1
\( c \cdot \sqrt{2} \)
D.


The van't Hoff factor of
\( 0.1 M L a\left(N O_{3}\right)_{3} \) solution is found to
be 2.74 , the percentage dissociation of the salt is:
A. \( 85 \% \)
в. \( 58 \% \)
c. \( 65.8 \% \)
D. \( 56.8 \% \)


For a given number, find the smallest whole number by which it should be
divided so as to get a perfect square. 2925


Fill in the blank:
To increase the effective resistance in a
circuit the resistors are connected in


Which of the following compounds do
not contain covalent bond?
A \( . C H_{4} \)
в. \( M g C l_{2} \)
c. \( \operatorname{sicl}_{4} \)
D. \( N H_{3} \)


When the load applied to a suspended wire is increased from 3 kg-wt to 5 kgwt; the elongation increases from 0.6 \( \mathrm{mm} \) to \( 1 \mathrm{mm} . \) How much work is done
during the extention of the wire.


In an ecosystem undergoing succession, replacement of a plant community takes place due to
A. Pollution
B. Herbivory
c. Parasitism
D. Abiotic factors
E. Intraspecific competition


How can the conversion of (i) to (ii) be
brought about?
\( \mathbf{A} \cdot K B r \)
\( \mathbf{B} \cdot K B r+C H_{3} O N a \)
\( \mathbf{c} \cdot K B r+K O H \)
\( \mathbf{D} \cdot B r_{2}+K O H \)


Using molar concentrations what is
unit of \( K_{c} \) for the reaction
\( \mathbf{C H}_{3} \mathbf{O H}(\mathbf{g}) \rightleftharpoons \mathbf{C O}(\mathbf{g})+\mathbf{2} \mathbf{H}_{2}(\mathbf{g}) \)
\( A \cdot M^{-2} \)
B. \( \mathrm{M}^{2} \)
\( c \cdot M^{-1} \)
D.


Which of the following departments prepare weather reports?
A. Pollution department
B. Health department
c. Meteorological department
D. Environment department


Susceptibility is large and positive for
A. para magnetio
B. diamagnetic
C. ferro magnetic
D. electromagnetic


The shadow of a tower standing on a
level plane is found to be \( 50 m \) longer
when sun's elevation is \( 30^{\circ} \) than when
it is \( 60^{\circ} . \) Find the height of the tower.


If \( \sqrt{\boldsymbol{x}}+\sqrt{\boldsymbol{y}}=10, \) find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \) at \( \boldsymbol{y}=\boldsymbol{4} \)
\( A \cdot 4 \)
в. -3
c. -4
D. 3


\( Z n+H_{2} S O_{4} \rightarrow \) a gas
If we bring a burning splinter near the gas produced in the given reaction, it burns with a pop sound. The gas is:
\( A \cdot O_{2} \)
в. \( N_{2} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \)
D. \( C O_{2} \)


If \( \boldsymbol{x}+\boldsymbol{i} \boldsymbol{y}=\frac{\boldsymbol{3}}{\boldsymbol{2}+\cos \boldsymbol{\theta}+\boldsymbol{i} \sin \boldsymbol{\theta}}, \) then
\( x^{2}+y^{2} \) is equal to
A \( .3 x-4 \)
B. \( 4 x-3 \)
c. \( 4 x+3 \)
D. None of these


Assertion
The proton gradient results in
movement of protons across the
membrane to stroma through the
transmembrane channel of the \( F_{0} \) of the
ATPase.
Reason
This proton gradient leads to release of
energy
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The adjoining sketch shows a running
tract \( 3.5 ~ m \) wide all around which of two
straight paths and two semicircular rings. Find the area of the track.


In redox reaction:
A. energy is absorbed.
B. energy is released.
C. transfer of electrons takes place between species.
D. catalyst increases the rate of reaction.


The magnetic moment of
\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{6}\right] \boldsymbol{C l}_{3} \) is:
A . 1.73
в. 2.83
c. 6.6
D. zero


Which of the following statement is true
statement?
A. Aldehydes and ketones have lower boiling points than alcohols and carboxylic acids of comparable molecular masses.
B. Aldehydes and ketones have higher boiling points than alcohols and carboxylic acids of comparable molecular masses.
C. Aldehydes and ketones have lower boiling points than alcohols but higher boiling points than carboxylic acids of comparable molecular masses.
D. Aldehydes and ketones have higher boiling points than alcohols but lower boiling points than carboxylic acids of comparable molecular masses.


A trivalent Metal "M" occurs in nature in
the form of its oxide \( M_{2} 0_{3} \). The metals
is widely used in making household
utensils and bodies of aircraft.
(i) Identify the metal
(ii) Name the chief ore of metal
(iii) Write down the reaction involved
during the extraction of metal with
figure.


State whether the following statement
is True or False.

Ampere's swimming rule describes the direction of magnetic lines of force in a straight conductor.


Shoot-apex protected by
A. Root cap
B. Shoot cap
c. Calyptra
D. Primordial leaves


The sum of the squares of deviations of 10 items about mean 50 is 250 .The
coefficient of variation is
A . 10\%
B. 50\%
c. 30\%
D. none of these


The carbonyl compound producing an optically active product by reaction with
\( \boldsymbol{L} \boldsymbol{i} \boldsymbol{A} \boldsymbol{l} \boldsymbol{H}_{4} \) is:
A. propanone
B. butanone
c. 3-pentanone
D. benzophenone


Graph of position of image versus
position of point object from a convex lens is shown. Then, focal length of the
lens is
A. \( 0.50 \pm 0.05 \mathrm{cm} \)
B. \( 0.50 \pm 0.10 \mathrm{cm} \)
\( c .5 .00 \pm 0.05 c m \)
D. \( 5.00 \pm 0.10 \mathrm{cm} \)


Name the different pigments found in algae


Main function of leaf is
A. Transpiration
B. Exchange of gases
C. Photosynthesis
D. Cooling


The maximum intensity in Young's
double slit experiment is \( I_{0} . \) Distance
between the slits is \( d=5 \lambda \), where \( \lambda \) is
the wavelength of monochromatic light used in the experiment. What will be the intensity of light in front of one of the
slits on a screen at a distance \( D=10 d \)
\( ? \)
A \( . I_{0} \)
в. \( I_{0} / 4 \)
c. \( _{\overline{4}_{l_{0}}^{I_{0}}} \)
D. \( I_{0} / 2 \)


If one of the zeroes of the
quadratic polynomial \( (k-1) x^{2}+ \)
\( k x+1 \) is \( (-3), \) then \( k \) equals to
A \( \cdot \frac{4}{3} \)
в. \( -\frac{4}{3} \)
\( c \cdot \frac{2}{3} \)
D. \( -\frac{2}{3} \)