Ohm's law can be applied to
A. ohmic devices
B. non-ohmic devices
\( c . \) both (a) and (b)
D. none


Les-energetic electromagnetic radiations like X-rays are generated in
the
A. Radiation zone
B. Convection zone
c. Photosphere
D. chromosphere


If \( n \) is an integer between 0 and 21 , then
the minimum value of \( n !(21-n) ! \) is
attained for \( n= \)
A .
B. 10
c. 12
D. 20


One among the following is doping material in p-type of semiconductor:
A. carbon
B. Indium
c. Arsenic
D. Phosphorous


Nitrogen on reaction with hot calcium forms :
A. Calcium oxide
B. Nitrogen oxide
c. calcium hydride
D. Calcium nitride


During glycolysis, molecules of
NADH are formed.


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


Factorize:
\( 4 a^{2}-8 a b \)


Write the IUPAC names of the given
compounds:


When a p-n-p transistor is operated in
saturation region, then its
A. Base-emitter junction is forward biased and basecollector junction is reverse biased.
B. Both base-emitter and base-collector junctions are reverse biased
C. Both base-emitter and base-collector junctions are forward biased
D. Base-emitter junction is reverse biased and basecollector junction is forward biased.


The reference standard used for
defining atomic mass is:
A \( . H-1 \)
B. \( C-12 \)
c. \( C-13 \)
D. \( C-14 \)


A dishonest trader marks up his goods
by \( 80 \% \) and gives discount of \( 25 \% \)
Besides he gets \( 20 \% \) more amount per
kg from wholeseller and sells \( 10 \% \) less per kg to customer. What is the overall
profit percentage?


surface under the influence of a force \( \boldsymbol{P} \)
of the same magnitude in all the three
cases.
CoOefficient of friction is the same
between each block and the ground.
What possible relation holds between the magnitude of normal
reaction and friction forces? (Assume
that the block do not overturn about
edge.) Here, \( \boldsymbol{f}_{A}, \boldsymbol{f}_{B} \) and \( \boldsymbol{f}_{C} \) are frictional
forces and \( N_{A}, N_{B} \) and \( N_{C} \) are
reactions.

This question has multiple correct options
\( \mathbf{A} \cdot N_{A}>N_{C}>N_{B} \)
B . \( f_{A}>f_{C}>f_{B} \)
\( \mathbf{c} \cdot f_{C}>f_{A}=f_{B} \)
D. \( N_{C}>N_{A}=N_{B} \)


Draw the pressure-temperature and volume-temperature diagrams of an isochoric process of \( n \) moles of an ideal
gas from pressure \( P_{0}, \) volume \( V_{0} \) to
pressure \( 4 P_{0}, \) indicating the pressures and temperatures of the gas in the initial and the final states.


Sulphur dioxide gas turns lead acetate paper black.
A. True
B. False


A transformer having 4000 turns on its primary side and 500 turns on the secondary side. If the input voltage is
\( 240 V, \) find out the output voltage of the secondary side of the transformer?
A . \( 15 ~ V \)
в. \( 30 V \)
c. \( 60 V \)
D. \( 120 V \)
E . \( 240 \mathrm{V} \)


Which one is (a) Diploblastic (b)
Triploblastic?
Hydra, Centipede (Scolopendra), Liver fluke (Fasciola), Earthworm (Pheretima
posthuma)
A. Diploblastic - Hydra, Centipede (Scolopendra) Triploblastic - Liver fluke (Fasciola), Earthworm (Pheretima posthuma)
B. Diploblastic - Liver fluke (Fasciola), Centipede (Scolopendra), Earthworm (Pheretima posthuma) Triploblastic - Hydra
C. Diploblastic - Hydra; Triploblastic - Liver fluke (Fasciola), Centipede (Scolopendra), Earthworm (Pheretima posthuma)
D. Diploblastic - Hydra, Earthworm (Pheretima posthuma) Triploblastic - Liver fluke (Fasciola), Centipede (Scolopendra)


Which of the following processes will quadruple the pressure
a) Reduce V to half and double T
b) Reduce V to 1/8th and reduce T to half
c) Double \( \mathrm{V} \) and half \( \mathrm{T} \)
d) Increase both \( \mathrm{V} \) and \( \mathrm{T} \) to double the
values
\( A \cdot b, c \)
в. а,
c. \( c, d \)
D. a,d.


\( 298 \mathrm{K} \) is approximately what temperature in degrees Celsius?
A \( \cdot 25^{\circ} \mathrm{C} \)
B \( \cdot 24^{\circ} C \)
\( \mathbf{c} \cdot 29^{\circ} C \)
D. \( 27^{\circ} \mathrm{C} \)


A student secure \( 85 \%, 70 \% \) and \( 65 \% \)
marks in three test paper with
maximum marks 150,200 and 250
respectively. Find his aggregate percentage.


A given amount of a gas is heated till the
volume and pressure both increase by \( 2 \% \) each the percentage change in temperature of the gas is equal to nearly
A . \( 2 \% \)
B. 3\%
c. \( 4 \% \)
D. 1\%


Find the value of \( \int_{-\pi}^{\pi} \frac{\cos ^{2} x}{1+a^{x}}, a>0 \)
A . \( 1 \pi \)
в. \( \pi / 2 \)
c. \( \pi / 4 \)
D. \( 2 \pi \)


If you can change location of the point \( A \) on the wall and hence the orientation of
the string OA without altering the
orientation of the string \( 0 \mathrm{B} \) as shown in figure-II. What angle should the string
OA make with the wall so that a
minimum tension is developed in it?


The number of significant figures present in \( 4.50 \times 10^{3} \) is:
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. 5


The S.I. unit of specific heat capacity is
\( J k g^{-1} o C^{-1} \)
A. True
B. False


In a sequence of independent trials, the
probability of success is \( 1 / 4 . \) If \( p \) denotes the probability that the second
success occurs on the fourth trial or
later trial, find \( 32 p \)


Solve \( : 2 \tan ^{-1}(-3)= \)
This question has multiple correct options
\( \mathbf{A} \cdot-\cos ^{-1}(-4 / 5) \)
\( \mathbf{B} \cdot-\pi+\cos ^{-1}(4 / 5) \)
C \( \cdot-\frac{\pi}{2}+\tan ^{-1}(-4 / 3) \)
D. \( \cot ^{-1}(4 / 3) \)


A portion of a conductive wire is bent in
the form of a semicircle of radius r as
shown below in figure. At the centre of semicircle, the magnetic induction will
be:
A. zero
B. inifinite
C \( \cdot \frac{\mu_{0}}{4 \pi} \cdot \frac{\pi i}{2 r} \) tesla
D. \( \frac{\mu_{0}}{4 \pi} \cdot \frac{\pi i}{r} \) tesla


The hysteresis cycle curve for the
material of a permanent magnet is:
A. short and wide
B. tall and narrow
c. tall and wide
D. short and narrow


The energy of an electron in the first Bohr orbit of H atom is -13.6e \( V \). The
possible energy value(s) of the excited
state for electrons in Bohr orbits of \( L i^{2+} \)
is:
A. \( -61.2 e V \)
B. \( -13.6 e V \)
c. \( -122.4 e V \)
D. \( +6.8 e V \)


When \( N O \) and \( N O_{2} \) are mixed, the
following equilibrium are readily obtained, \( 2 N O_{2} \rightleftharpoons N_{2} O_{4}, K_{p}= \)
\( 6.8 a t m^{-1} \) and \( N O+N O_{2} \rightleftharpoons N_{2} O_{3} . \) In
an experiment when \( N O \) and \( N O_{2} \) are
mixed in the ratio of \( 1: 2, \) the final total
pressure was 5.05 at \( m \) and the partial
pressure of \( N_{2} O_{4} \) was \( 1.7 a t m \)
Calculate
(a) the equilibrium partial pressure of \( N O,(b) K_{p} \) for: \( N O+ \)
\( N O_{2} \rightleftharpoons N_{2} O_{3} \)
A \( .3 .43 a t m^{-1} \)
B. \( 5.63 a t m^{-1} \)
c. \( 7.43 a t m^{-1} \)
D. None of these


The IUPAC name of \( \boldsymbol{K}_{3}\left[\boldsymbol{V} \boldsymbol{F}_{6}\right] \) is
potassium hexafluorido vanadate (III).
A. True
B. False


Fuel efficiency is measured as
This question has multiple correct options
A. Its calorific value
B. Amount of heat produced by fuel per unit mass or volume
\( \mathbf{c} \cdot k J / K g \)
D. None of these


The correct order of reativity of PhMg Br towards given compounds. \( P h-\stackrel{0}{C}-P h \quad C H_{3}-\stackrel{0}{C}-H C H_{3}- \)
\( \stackrel{0}{N}-C H_{3} \)
(1)
(11)
A \( \cdot(I)>(I I)>(I I I) \)
B. \( (I I I)>(I I)>(I) \)
c. \( (I I)>(I I I)>(I) \)
D. \( (I)>(I I I)>(I I) \)


Show that the middle term in the
expansion of \( (1+x)^{2 n} \) is
\( \frac{1.3 .5 \ldots .(2 n-1)}{\mid \underline{n}} 2^{n} x^{n} \)


A body moves along circular path of radius \( 10 \mathrm{m} \) and the coefficient of friction is \( 0.5 . \) What should be its
angular velocity in rad/s if it is not to
slip from the surface? \( \left(\boldsymbol{g}=\mathbf{9 . 8 m} / \boldsymbol{s}^{2}\right) \)
A . 0.7
B. 0.28
c. 0.27
D. 2.7


Out of the following, select the correct
statements:
This question has multiple correct options
A. Mirage and looming take place in hot places
B. An object is not visible when its refractive index is unity
C. On increasing the angle of incidence, the angle of deviation also increases
D. During hot summer days, the trees and other tall objects seem to be quivering because the density of air changes in and irregular way


Large volume of air that a person can
wire after a forceful inspiration is called
A. inspiratory reserve volume
B. expiratory reserve volume
c. vital capacity
D. tidal volume


\( K_{P} \) for the reaction \( N_{2}+2 H_{2} \rightleftharpoons \)
\( 2 N H_{3} \) is \( 1.6 \times 10^{-4} a t m^{-2} \) at \( 400^{0} C \)
What will be \( K_{P} \) at \( 500^{0} C ? \) The heat of
reaction at this temperature is -25.14 kcal?
A \( \cdot K_{P_{2}}=1.428 \times 10^{-5} a t m^{-2} \)
B . \( K_{P_{2}}=15.55 \times 10^{-5} a t m^{-2} \)
C \( \cdot K_{P_{2}}=12 \times 10^{-4} a t m^{-2} \)
D. \( K_{P_{2}}=7.88 \times 10^{-5} a t m^{-2} \)


Find the square root of the following number by factorisation.
\( \mathbf{1 9 6} \)


Which of the following is an example of an open system?
A. a beaker full of water
B. an air-tight container
c. vacuum chamber
D. none of the above


In the following figure, \( A B C D \) is a rhombus and \( D C E F \) is a square.
If \( \angle A B C=56^{\circ} \), find
\( \angle D A E \)
\( \angle \boldsymbol{F} \boldsymbol{E} \boldsymbol{A} \)
\( \angle E A C \)
\( \angle A E C \)
+ Option


Why sugar turns black in presence of
conc. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} ? \)


Prove that: \( \sin ^{-1}\left(\frac{3}{5}\right)+\cos ^{-1}\left(\frac{12}{13}\right)= \)
\( \sin ^{-1}\left(\frac{56}{65}\right) \)


The magnitude of focal length of a concave mirror is \( f . \) An object is placed at a distance \( x \) from the focus and
forms a real image. The magnification is:
A \( \cdot-\frac{f}{x} \)
в. \( -\frac{x}{f} \)
\( c \cdot-\frac{f}{f-x} \)
D. \( \frac{x}{x-f} \)


If \( a=b, \) then \( a+x= \)
\( \mathbf{A} \cdot a+x \)
B. \( b x \)
c. \( b-x \)
D. \( b+x \)


\( \boldsymbol{P}=\boldsymbol{I}^{n} \times \boldsymbol{R}(\text { where } \mathrm{P}=\text { Power, } \mathrm{R}= \)
Resistane, I= Current)
The value of \( n \)
A .
B. -
c. 1
D.


When light goes from a denser to a rarer medium the angle of refraction is:
A. More than the angle of incidence
B. Less than the angle of incidence
c. Equal to the angle of incidence
D. critical angle


The number of solutions of \( [\sin x+ \) \( \cos x]=3+[-\sin x]+[-\cos x] \) in the
interval \( [\mathbf{0}, \mathbf{2} \boldsymbol{\pi}] \) is (where [.] denotes the greatest integer function.)
\( \mathbf{A} \cdot \mathbf{0} \)
B. 4
\( c .3 \)
D. Infinitely many


In a house, individual powers of two elements are \( \$ \$ 1001 \mathrm{W} 11001 \mathrm{W} \$ \$ . \) The effective power of their series combination will be :
A . \( 120 \mathrm{W} \)
B. \( 75 W \)
\( \mathbf{c} .50 W \)
D. \( 60 W \)


The variance of following:
\begin{tabular}{lllll}
\multirow{2}{*} { Age } & \multirow{2}{*} { \( \mathbf{2 0}- \) \( \mathbf{2 5} \)} & \( \mathbf{2 5}- \) & \( \mathbf{3 0}- \) & \( \mathbf{3 5}_{-} \) \\
& & \( \mathbf{3 0} \) & \( \mathbf{3 5} \) & \( \mathbf{4 0} \)
\end{tabular}
\begin{tabular}{l|c|c}
Number & \\
of & 170 \\
persons
\end{tabular} 15 80 45
\( \mathbf{A} \cdot 62.62 \)
B . 56.56
c. 7.93
D. 9.24


Which of the following statements is
not correct for the periodic
classification of elements?
A. The properties of elements are the periodic functions of their atomic numbers.
B. Non - metallic elements are lesser in number than
metalic elements
C. The first ionization energies of elements along a period do not vary in regular manner with increase in atomic number
D. For transition elements, the d-sub shells are filled with electrons monotonically with increase in atomic number.


Study the figures given below and mark
the correct statement
A. (i) Nitric acid + Water;
(i) Acetone + Ethyl alcohol
B. (i) Water + Ethyl alcohol
(ii) Acetone + Benzene
C. (i) Acetone + Ethyl alcohol;
(ii) Acetone + Chloroform
D. (i) Benzene + Chloroform
(ii) Acetone + Chloroform


Forces of attraction between particles in a pure substance are associated with physical properties. Additionally, specific trends are associated with a given group of elements. Of the following, which shows the greatest variation in physical properties for the given group of elements?
A. Alkali metals
B. Alkaline earth metals
c. Halogens
D. Noble gases


If four atoms of hydrogen combine to
form an \( 2^{4} H e \) atom, then the amount of
energy released is :
A. \( 26.7 \mathrm{MeV} \)
в. \( 25.3 \mathrm{MeV} \)
\( \mathrm{c} .22 \mathrm{MeV} \)
D. \( 24.5 \mathrm{MeV} \)


The emf of the cells obtained by combining zinc and copper electrodes of the Daniell cell with calomel
electrodes are 1.083 volt and
-0.018 volt respectively at \( 25^{\circ} \mathrm{C} . \) If the
reduction potential of normal calome electrode is +0.28 volt, find he emf of the Daniell cell.


Assertion
According to the Medical Termination of
Pregnancy act of \( 2017, \) pregnancy may be terminated on certain considered
grounds within the first 12 weeks of
pregnancy on the opinion of one registered medical practitioner.
Reason

The continuation of the pregnancy
would involve a risk to the life of the
pregnant woman or of grave injury of physical or mental health.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Which of the following is an advantage of a conventional circuit over integrated circuit?
A. They are fast.
B. They have higher power handling capability.
c. They are large in size.
D. All of the above


The distance between the straight lines \( \mathbf{7} \boldsymbol{x}+\mathbf{2 4} \boldsymbol{y}-\mathbf{1 3}=\mathbf{0}, \mathbf{7} \boldsymbol{x}+\mathbf{2 4} \boldsymbol{y}+\mathbf{1 2}=\mathbf{0} \)
is
\( A \cdot 1 \)
B . 2
\( c \cdot 25 \)
D. 50


Discuss the applicability of Rolle's theorem in the interval [-1,1] to the
function \( f(x)=|x| \)


The moment of inertia of a cylinder of
radius \( a, \) mass \( M \) and height \( h \) about
an axis parallel to the axis of the
cylinder and distance \( b \) from its centre
is
A \( \cdot \frac{3}{4} M(a-b)^{2} \)
в. \( \frac{2}{3} M(a+b)^{2} \)
c. \( \frac{3}{2} M a^{2} \)
D. \( \frac{M\left(a^{2}+2 b^{2}\right)}{2} \)


List the steps of preparation of temporary mount of a leaf peel to observe stomata.


The difference of the slopes of the lines
represented by \( 6 x^{2}-5 x y+y^{2}=0 \) is
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c .3 \)
D.


If the ratio of the concentration of
electrons to that of holes in a
semiconductor is \( \frac{7}{5} \) and the ratio of current is \( \frac{7}{4}, \) then what is the ratio of their drift velocities?
A \( \cdot \frac{5}{8} \)
B. \( \frac{4}{5} \)
\( c \cdot \frac{5}{4} \)
D. \( \frac{4}{7} \)


Find a unit vector normal to the plane
through the points (1,1,1),(-1,2,3) and (2,-1,3)


How do you convert the following:
(i) Prop-1-ene to 1-fluoropropane
(ii) Chlorobenzene to 2-chlorotoluene
(iii) Ethanol to propanenitrile
Write the main products when
(i) n-butyl chloride is treated with
alcoholic \( K O H \)
(ii) \( 2,4,6- \) trinitrochlorobenzene is
subjected to hydrolysis
(iii) methyl chloride is treated with
\( \boldsymbol{A} \boldsymbol{g} \boldsymbol{N} \)


Assertion
Atomicity of Phosphorus is 4
Reason
Atomicity is the number of atoms
present in 1 molecule.
A. Both Assertion and Reason are correct and the Reason
is the correct explanation of the Assertion
B. Both Assertion and Reason are correct but the Reason is not the correct explanation of the Assertion
C. Assertion is correct but the Reason is incorrect
D. Assertion is incorrect but the Reason is correct


What is the value of current \( I \) in given
circuits?


The reaction of zinc metal and \( H C l \)
produces which of the following?
¡. \( \boldsymbol{H}_{2}(\boldsymbol{g}) \)
¡¡¡. \( C l_{2}(g) \)
iii. \( Z n C l_{2}(a q) \)
A. ii only
B. iii only
c. i and ii only
D. i and iii only
E. i, ii and iii


Which of the following are diamagnetic? This question has multiple correct options
A \( \cdot C_{2} \)
B. \( O_{2}^{2} \)
\( \mathrm{c} \cdot \mathrm{L} i_{2} \)
D. \( N_{2}^{\text {th }} \)


Find the area of a quadrilateral piece of ground, one of whose diagonals is 60 metres long and the perpendiculars from
the other two vertices are 38 and 22
metres, respectively.
A \( \cdot 1800 m^{2} \)
В. \( 3600 m^{2} \)
c. \( 900 m^{2} \)
D. None of the above


The structure of the enolic form of
\( C H_{3}-C O-C H_{2}-C O-C H_{3} \) with
intra-molecular H-bonding is as given
above
f the given statement is correct
then enter 1 , else enter 0
\( A \)


To \( 500 m L \) of \( 0.150 M A g N O_{3} \) solution
were added \( 500 m L \) of \( 1.09 M F e^{2+} \)
solution and the reaction is allowed to
reach an equilibrium at 25
\[
\begin{array}{r}
\boldsymbol{A} \boldsymbol{g}^{+}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{F} \boldsymbol{e}^{2+}(\boldsymbol{a} \boldsymbol{q}) \rightleftharpoons \\
\boldsymbol{F} \boldsymbol{e}^{3+}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{A} \boldsymbol{g}(\boldsymbol{s})
\end{array}
\]
For \( 25 m L \) of the solution, \( 30 m L \) of
\( 0.0832 M K M n O_{4} \) were required for
oxidation. The equilibrium constant for
the reaction at \( 25^{\circ} \mathrm{C} \) is


Sodium chloride is an ionic compound
where as hydrogen chloride is mainly covalent because
A. sodium is less reactive
B. hydrogen is non-metal
C. hydrogen chloride is a gas
D. electronegativity difference in the case of Hydrogen and chlorine is less than 2.1


The fire extinguisher 'Pyrene' contains:
A. carbon dioxide
B. carbon disulphide
C. carbon tetrachloride
D. chloroform


The coefficient of mutual inductance of
the two coils is \( 5 H . \) The current through the primary coil is reduced to zero value
from \( 3 A \) in 1 millisecond. The induced
emf in the secondary coils is
A. zero
в. 1.67 Кル
c. \( 15 K V \)
D. \( 600 V \)


The equation of line passing through (1,-2,3) and having \( \operatorname{drs}(2,3,1) \) is
\( ^{\text {A }} \cdot \frac{x-1}{2}=\frac{y+2}{3}=\frac{z-3}{1} \)
B. \( \frac{x+1}{2}=\frac{y+2}{3}=\frac{z-3}{1} \)
c. \( \frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{1} \)
D. none of these


The ratio of incomes of Salim and Jawed
was \( 20: 11 . \) Three years later income of
Salim has increased by \( 20 \% \) and income of Jawed was increased by Rs.
500. Now ratio of their incomes
becomes \( 3: 2 . \) Find original incomes of
Salim and Jawed.


The term sericulture is used for which
of the following purpose?
A. Production of silk
B. Production of raw silk
c. Rearing of silkworm
D. Refinement of silk fibre


Mark the correct statement.
A. Blood has WBC while lymph has RBC
B. Blood has both RBC and WBC while lymph has none
C. Blood has RBC while Iymph has both RBC and WBC
D. Blood has RBC and WBC while Iymph has only WBC


Two parallel plate capacitors of
capacitances \( C_{1} \) and \( C_{2} \) such that
\( C_{1}=2 C_{2} \) are connected across a
battery of \( V \) volts as shown in the
figure. Initially the key ( \( k \) ) is kept closed
to fully charge the capacitors. The key is
now thrown open and a dielectric slab of
dielectric constant ' \( K^{\prime} \) is inserted in the
two capacitors to completely fill the gap between the plates. The ratio of the energies stored in the combination, before and after the introduction of the
dielectric slab:


What are represented by the equation \( \left(x^{2}-a^{2}\right)^{2}-y^{4}=0 \)


A metallic rod undergoes a strain of
\( 0.05 \% . \) The energy stored per unit volume is \( \left(Y=2 \times 10^{11} \mathrm{Nm}^{-2}\right) \)
A \( \cdot 0.5 \times 10^{4} \mathrm{Jm}^{-3} \)
B . \( 0.5 \times 10^{5} \mathrm{Jm}^{-3} \)
c. \( 2.5 \times 10^{5} \mathrm{Jm}^{-3} \)
D. \( 2.5 \times 10^{4} \mathrm{Jm}^{-3} \)


Two zinc rods are placed in contact with
dilute \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) and \( \operatorname{conc.} \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) in two
separate containers \( A \) and \( B \). The
characteristic gases evolved in the containers are respectively:
A. the gas in container' \( ^{2} \) ' turns \( K_{2} C r_{2} O_{7} \) green and the gas in container' \( B \) ' turns lead acetate black
B. \( A \rightarrow \) Pungent smelling gas, \( B \rightarrow \) colourless, odourless gas
C \( . A \rightarrow \) Inflammable gas, \( B \rightarrow \) Turns \( K_{2} C r_{2} O_{7} \) green
D. \( A \rightarrow \) Can react with \( O_{2} \) explosively, \( B \rightarrow \) No reaction with \( O_{2} \) at all


Let \( ^{*} \) be a binary operation on the set \( \boldsymbol{Q} \)
of rational numbers as follows:
\( \boldsymbol{a} * \boldsymbol{b}=\boldsymbol{a}^{2}+\boldsymbol{b}^{2} \)
Find which of the binary operations are commutative and which are
associative.


Two large parallel sheets having linear
current densities \( J \) and \( -J_{0} \) as shown
in figure, then magnetic field in region \( b \) is:-
\( \mathbf{b} \)
\begin{tabular}{|l|l|l|l|l|l|}
\hline & \( \mathrm{X} \) & \( \mathrm{X} \) & \( \mathrm{X} \) & \( \mathrm{X} \) & \( \mathrm{X} \) & \( -\mathrm{J} \) \\
\hline
\end{tabular}
A . zero
в. \( \frac{\mu_{0} J}{2} \)
c. \( \mu_{0} \).
D. None of these


An atom has electronic configuration
\( 2,8,7 . \) To which of the following elements would it be chemically similar? (Atomic numbers are given in parentheses)
A . N(7)
B. F(9)
c. \( P(15) \)
D. \( \operatorname{Ar}(18) \)


A sphere is released on a smooth
inclined plane from the top. When it
moves down its angular momentum is:
A. conserved about every point
B. conserved about the point of contact only
c. conserved about the centre of the sphere only
D. conserved about any point on a fixed line parallel to the inclined plane and passing through the centre of the ball


The coefficient of mean deviation from
median of observations 40,62,54,90
68,76 is
A . 2.16
B. 1.2
\( c \cdot 5 \)
D. none of these


Calculate the minimum size of a plane
mirror fixed on the wall of a room in
which an observer at the centre of the
room can see the full image of the wall behind him.


You are riding on your bicycle with
inflated tyres. Your friend asks for a lift and sits on the carrier behind you
A. The air pressure in the tyres increases
B. The air pressure in the tyres decreases
C. The air pressure in the tyres remains the same
D. Nothing inthe system changes except the reaction of the ground
E. Answer Required


At a particular height the velocity of an
ascending body is \( u \). The velocity at the same height while the body fall under
gravity is
\( A \)
B \( \cdot u^{2} \)
c. \( 2 u \)
D. \( u / 2 \)


A body of mass \( m \) is dropped freely from
a height \( h \). The de-Broglie wavelength of the body as it reaches the ground is:
A \( \cdot \frac{h}{\sqrt{g H}} \)
в. \( \frac{h}{m \sqrt{g H}} \)
c. \( \frac{h}{2 \sqrt{g H}} \)
D. \( \frac{h}{m \sqrt{2 g H}} \)


Therm is the unit of
A. heat
B. temperature
c. thermometry
D. work


Fill in the blank.
A rainbow is caused due to the
of white light. This question has multiple correct options
A. dispersion
B. refraction
c. propagation
D. intensity


Assertion. Stomata remain open during
the day time.
Reason. Stomata help in exchange of
gases.


DNA in the nucleus of rabbit egg is 1.8 picograms, its liver cell will have mass of DNA \( _{\text {一一一一一一火 }} \)
A. 7.2
B. 0.9
\( c \cdot 1.8 \)
D. 3.6


A steady electric current is flowing
through a cylindrical conductor.
This question has multiple correct options
A. The electric field at the axis of the conductor is zero.
B. The magnetic field at the axis of the conductor is zero.
C. The electric field in the vicinity of the conductor is zero.
D. The magnetic field in the vicinity of the conductor is zero.


In an examination \( A \) got \( 25 \% \) marks
more than \( \mathrm{B}, \mathrm{B} \) got \( 10 \% \) less than \( \mathrm{C} \) and \( \mathrm{C} \)
got \( 25 \% \) more that \( D \). If \( D \) got 320 marks out of \( 500, \) the marks obtained by \( A \)
were:
A . 450
B. 405
\( c .360 \)
D. 400


An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force. This statement is
known as:
A. Newton's first law of motion
B. Newton's second law of motion
c. Newton's third law of motion
D. Newton's law of gravitation


Correct sequence for Alanine code is
A . GCU, GCC, GCA
B. GAU, GAC, GAA
c. AGU, AGC, AGA
D. GUU, GUC, GUA


\( a \epsilon\{a, b, c\}, \) then \( \{a\} \) is a subset of
\( \{a, b, c\} .(\text { Enter } 1 \text { if true or } 0 \text { otherwise }) \)


The equilibrium constant for the
following reactions are \( \boldsymbol{K}_{\mathbf{1}} \) and \( \boldsymbol{K}_{\mathbf{2}} \)
respectively.
\( \mathbf{2} \boldsymbol{P}(\boldsymbol{g})+\mathbf{3} \boldsymbol{C} \boldsymbol{l}_{2}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{2} \boldsymbol{P} \boldsymbol{C l}_{3}(\boldsymbol{g}) \)
\( \boldsymbol{P C l}_{3}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{P} \boldsymbol{C l}_{5}(\boldsymbol{g}) \)
Then the equilibrium constant for the
reaction
\( \mathbf{2} \boldsymbol{P}(\boldsymbol{g})+\mathbf{5} \boldsymbol{C l}_{2}(\boldsymbol{g}) \rightleftharpoons \mathbf{2} \boldsymbol{P} \boldsymbol{C l}_{5}(\boldsymbol{g}) \) is:
A. \( K_{1} K_{2} \)
B. \( K_{1} K_{2}^{2} \)
\( \mathbf{c} \cdot K_{1}^{2} K_{2}^{2} \)
D. \( K_{1}^{2} K_{2} \)


The coefficient of \( x^{5} \) in the expansion of
\( \left(x^{2}-x-2\right)^{5} \) is
A. 351
в. -82
c. -86
D. -81


How is calcium oxide prepared?
A. Thermal decomposition of \( C a C O_{3} \)
B. Oxidation of \( C a C O_{3} \)
c. Reduction of \( C a C O_{3} \)
D. None of these


What is IUPAC name of \( \boldsymbol{C H}_{3}- \)
\( \boldsymbol{C}\left(\boldsymbol{C H}_{3}\right)(\boldsymbol{O H})-\boldsymbol{C}(\boldsymbol{O})-\boldsymbol{C H}_{3} ? \)
A. Heptane-1,3,5-tricarboxylic acid
B. Pentane-1,3,5-tricarboxylic acid
c. 3-Hydroxy-3-methylbutane-2-one
D. 3-buty|-1,4-hexadien-6-al


In the formation of electrovalent
compound \( M g C l_{2} \) name the substance that is oxidized and is reduced.


Rhombic sulphur remains stable below
\( 95.6^{\circ} C \)
A. True
B. False


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


Hydrolysis of \( X e F_{6} \) in strongly alkaline solution is an auto-redox process.
If true enter 1 , else enter 0
\( A \)


The forward rate constant for the
elementary reversible gaseous reaction
\( C_{2} H_{6} \rightleftharpoons 2 C H_{3} \) is \( 1.57 \times 10^{-3} s^{-1} \) at
\( 100 K \)
What is the rate constant for the
backward reaction at this temperature
if \( 10^{-4} \) moles of \( C H_{3} \) and 10 moles of
\( C_{2} H_{6} \) are present in a 10 litre vessel at
equilibrium?
A \( .1 .57 \times 10^{9} \mathrm{L} \) mol\( ^{-1} s^{-1} \)
B. \( 1.57 \times 10^{10} L \quad \) mol \( ^{-1} s^{-1} \)
C \( \cdot 1.57 \times 10^{11} L \quad \) mol \( ^{-1} s^{-1} \)
D. \( 1.57 \times 10^{7} L \quad \) mol \( ^{-1} s^{-1} \)


A \( \ldots . . . . . . . . . . . . \) has 4 sides equal and 4 right
angles.
A . square
B. parallelogram
c. trapezium
D. rectangle


In a reavrsible process, \( \Delta S_{s y s}+\Delta S_{s u r r} \)
is
\( A \cdot>0 \)
B. <
\( c \cdot \geq 0 \)
\( D_{1}=0 \)


Fenestra ovalis is the opening of
A. Cranium
B. Tympanum
c. Tympanic cavity
D. Brain


Dialysis can separate which of the following in additions to the glucose from human blood?
A. Fructose
B. Starch
c. Proteins
D. sucrose


Galvanisation is a method of:
A. distillation
B. protection
c. corrosion
D. concentration


Oxidation means
oxygen and reduction means
of hydrogen.
A. gain, loss
B. loss, gain
c. gain, gain
D. loss, loss


Avena coleoptile auxin is
\( \mathbf{A} \cdot \mid B A \)
B. Indole 3-lactic acid
C. Indole 2-acetic acid
D. Indole 3-acetic acid


\( 25 t h \) term of the \( A . P: 5, \frac{5}{2}, 0,-\frac{5}{2}, \ldots \)


The figure shows a meter bridge with
null deflection in the galvanometer. The value of unknown resistance R is?
\( \mathbf{A} \cdot 158 \Omega \)
B . \( 151.67 \Omega \)
c. \( 128.65 \Omega \)
D. \( 130 \Omega \)


After examining the blood group of husband and wife, the doctor advised them not to have more than one child.
The blood groups of the couple are likely
to be
A. Male Rh" and female Rh
B. Female Rh - and male Rh
c. Male Rht and female Rht
D. Male Rh - and female Rh


If \( \sec \theta=\frac{25}{7}, \) then find the value of
\( \tan \theta ? \)


The complex number system, denoted
by \( C, \) is the set of all ordered pairs of
real numbers (that is, \( \boldsymbol{R} \times \boldsymbol{R} \) ) with the
operation (denoted by \( \times \) ) which satisfy
multiplication
\( \mathbf{A} \cdot(a, b) \times(c, d)=(a c+b d, b c-a d) \)
B. \( (a, b) \times(c, d)=(a c-b d, b c+a d) \)
C \( .(a, b) \times(c, d)=(a+c, b+d) \)
D. None of these


A \( 120 V A C \) line transformer is to supply \( 13000 V \) for a neon sign. To reduce shock hazard a \( 8.5 \mathrm{mA} \) fuse is inserted. Find the
maximum input power that can be given to the transformer.
\( \mathbf{A} \cdot 120 W \)
B. \( 121 W \)
\( c \cdot 110 W \)
D. \( 104 W \)


If two vectors \( 2 \hat{i}+3 \hat{j}+3 \hat{k} \) and \( -4 \hat{i}- \) \( 6 \hat{j}+\lambda \hat{k} \) are parallel to each other then
value of \( \lambda \) is
A . -6
B. -
\( c .-3 \)
D. -4


If \( |\overrightarrow{\boldsymbol{a}}|=\mathbf{5},|\overrightarrow{\boldsymbol{a}}-\overrightarrow{\boldsymbol{b}}|=\mathbf{8} \) and \( |\overrightarrow{\boldsymbol{a}}+\overrightarrow{\boldsymbol{b}}|= \)
\( \mathbf{1 0}, \) then \( |\overrightarrow{\boldsymbol{b}}| \) is equal to:
A .
в. \( \sqrt{57} \)
\( c \cdot 3 \)
D. 57


A chemical compound that contains 26 \( \% \) nitrogen and \( 74 \% \) oxygen has an atomic mass of \( 108 g / \) mol. What is the molecular formula of this compound?
в. \( N O_{2} \)
\( c \cdot N O_{6} \)
D. \( N_{2} O_{5} \)


If the moment of inertia of a circular
disc about an axis tangentially and
parallel to its surface be \( I \), then the moment of inertia about the axis
tangential but perpendicular to the surface will be :
A \( \cdot \frac{6}{5} I \)
в. \( \frac{3}{4} I \)
c. \( \frac{3}{2} I \)
D. \( \frac{5}{4} \)


Three small bodies of identical masses
can move along a straight line. The central body (2) is initially at rest and
bodies 1 and 3 are at a distance \( L \) and \( 2 L \)
from the central body respectively.
Bodies 1 and 3 move towards body 2
with speeds \( v_{0} \) each. The collision
between 1 and 2 is perfectly elastic and the collision between body 2 and 3 is perfectly inelastic. After all the collisions are over
A. all the bodies come to rest
B. the body 1 moves towards left, bodies 2 and 3 move towards right
c. body 2 remains at rest and other bodies 1 and 3 turn back
D. all the bodies move towards right.


What is an AC generator? Obtain an expression for the sinusoidal emf induced in the cell of ac generator,
rotating with a uniform angular speed in a uniform magnetic field.


Speed of light is maximum in:
A. glass
B. vaccumm
c. water
D. nylon


Use the given figure to find:
Given, \( n(\xi)=52, n(A)=43 \) and
\( \boldsymbol{n}(\boldsymbol{B})=\mathbf{2 7} \)
\( \boldsymbol{n}(\boldsymbol{A}-\boldsymbol{B}) \)


In nature, the photosynthesis should proceed up to the limit of
A. Light
B. Temperature
\( c \cdot C O_{2} \)
D. Moisture and wind


A body is first displaced by \( 5 \mathrm{m} \) and then by \( 12 \mathrm{m} \) in different directions. The minimum displacement it can have is
\( \mathrm{m} \)
\( A \cdot 7 \)
B. 13
\( c .0 \)
D. 17


Improper fraction of \( 12 \frac{1}{6} \) is
A \( \cdot \frac{72}{6} \)
в. \( \frac{73}{6} \)
c. \( \frac{108}{6} \)
D. \( \frac{85}{6} \)


The phenomenon of light coming back after hitting a smooth plane surface is:
A. reflection
B. refraction
c. dispersion
D. total internal reflection


A converging beam of light travelling in air converges at a point \( P \) as shown in the figure. When a glass sphere of refractive index 1.5 is introduced in
between the path of the beam, calculate
the position of the image. Also draw the ray diagram for the image formed


Mr. Kale (52 years old) has taxable income of Rs. 5,05,000 in financial year
\( 2012-13 . \) Calculate the net income tax
payable.


Assertion \( (A): \) If \( \frac{5 x+1}{(x+2)(x-1)}= \)
\( \frac{\boldsymbol{A}}{(\boldsymbol{x}+\mathbf{2})}+\frac{\boldsymbol{B}}{(\boldsymbol{x}-\mathbf{1})} \) and \( \sin \boldsymbol{\theta}=(\boldsymbol{A}+\boldsymbol{B}) \)
then \( \sin \theta \) does not exist
Reason \( (\mathrm{R}): \sin \theta \in[-1,1] \)
A. Both A and R are true and R is correct explanation of A
B. Both A and R are true and R is not correct explanation of A
c. A is true and R is false
D. A is false and R is true


fall the masses in the figure have a
mass of \( 2 k g \) and \( m_{2} \) has speed \( 2 m / s \)
and \( m_{3} \) has a speed of \( 4 m / s, \) what is
the \( x \) -component of the momentum of
the centre of mass of system?
A. 2 kg \( m / s \)
B. 4 kg \( m / s \)
c. \( 6 \mathrm{kg} \mathrm{m} / \mathrm{s} \)
D. \( 10 \mathrm{kg} \mathrm{m} / \mathrm{s} \)


Number of oxygen molecules utilized in
glycolysis is
\( \mathbf{A} \cdot \mathbf{0} \)
B. 2
\( c \cdot 4 \)
\( D \)


Draw a labelled diagram of a step-up transformer and explain how it works. State two characteristics of the primary coil as compared to its secondary coil.


We have two electric dipoles. Each dipole consists of two equal and opposite point charges at the ends of an insulating rod of length d. The dipoles sit along the \( x \) -axis a distance \( r \) apart, oriented as shown in figure. Their separation \( r>>d \). The dipole on the left:
This question has multiple correct options
A. wil feel a force to the left
B. will feel a force to the right
c. will feel a torque trying to make it rotate counterclockwis
D. will feel no torque


If \( A \) 's salary is \( 30 \% \) more than that of \( B \)
then how much percent is \( B \) 's salary less than that of \( A^{\prime} \) s?
A . \( 30 \% \)
B . 25\%
c. \( _{23} \frac{1}{3} \% \)
D. \( 33 \frac{1}{3} \% \)


If \( x \sqrt{1+y}+y \sqrt{1+x}=0 \) and \( x \neq y \)
show that \( \frac{d y}{d x}=\frac{-1}{(1+x)^{2}} \)


Which of the following gases probably least abundant in the early atmosphere?
A \( . H_{2} \)
в. \( 0_{2} \)
c. \( N H_{3} \)
D. co


Which of the following can't be taken as an example of parasympathetic stimulation:
A. Increase in the intestinal peristalsis
B. Increased secretion of gastric juice
c. contraction of the detrusor muscles of urinary bladder
D. Increase in ventricular force of contraction


Taking the gravitational potential at a
point infinte distance away as zero, the gravitational potential at a point \( \boldsymbol{A} \) is
-5 unit. If the gravitational potential at a point infinite distance away is taken as +10 units, the potential at a point \( A \)
is
A. - 5 unit
B . +5 unit
c. +10 unit
D. +15 unit


State the difference between laser light and ordinary light


The relation between an ac voltage source and time in Sl units is \( V= \)
\( 120 \sin (100 \pi t) \cos (100 \pi t) V \)
The value of peak voltage and frequency will be respectively:
A. \( 120 \mathrm{V} \) and \( 100 \mathrm{Hz} \)
B. \( \frac{120}{\sqrt{2}} \mathrm{V} \) and \( 100 \mathrm{Hz} \)
c. \( 60 \mathrm{V} \) and \( 200 \mathrm{Hz} \)
D. \( 60 \mathrm{V} \) and \( 100 \mathrm{Hz} \)


Assertion: The solubility product of hydroxide of \( F e^{2+} \) is higher than that of
\( \boldsymbol{F} \boldsymbol{e}^{\boldsymbol{3}+} \)
Reason: The lattice energy of \( \boldsymbol{F e}(\boldsymbol{O} \boldsymbol{H})_{2} \)
is lower than that of \( F e(O H)_{3} \)
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
E. Both Assertion and Reason are false


Convection cannot take place
in
A. solids
B. liquids
c. gases
D. None of the above


In shown diagram, tension in the cord is
A. Zero
B. 25 N
\( c \cdot 50 N \)
D. \( 100 \mathrm{N} \)
E. 200 N


Energy required to accelerate a car from
\( 10 m s^{-1} \) to \( 20 m s^{-1} \) compared with
that required to acceleration it from 0 to \( 10 m s^{-1} \) is
\( A \). twice
B. three times
c. four times
D. same


The length, breadth and height of a
glass slab are respectively \( 50 \mathrm{cm}, 20 \mathrm{cm} \)
and \( 25 c m . \) Find the order of
magnitude of volume of slab in Sl unit
A \( \cdot 10^{-2} m^{3} \)
В \( \cdot 10^{-4} m^{3} \)
\( \mathbf{c} \cdot 10^{-3} m^{3} \)
D. \( 10^{-3} \mathrm{cm}^{3} \)


Two closed vessel \( A \) and \( B \) of equal
volume of \( 8.21 L \) are connected by a
narrow tube of negligible volume with open valve. The left hand side container
id found to contain 3 mole \( C O_{2} \) and
2 mole of \( H e \) at \( 400 K . \) What is the
partial pressure of \( H e \) in vessel \( B \) at
\( \mathbf{5 0 0 K ?} \)
A. 2.4 atm
B. 8 atm
c. 12 atm
D. None of these


Consider a certain reaction \( \boldsymbol{A} \rightarrow \)
Products with, \( k=2.0 \times 10^{-2} s^{-1} \)
Calculate the concentration of \( \mathbf{A} \)
remaining after 100 s, if the initial
concentration of \( A \) is \( 1.0 m o l L^{-1} \)


Find the final product


Find whether the following function is
differentiable at \( x=1,2: \) \( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{cc}\boldsymbol{x}, & \boldsymbol{x} \leq \mathbf{1} \\ \boldsymbol{2}-\boldsymbol{x}, & \boldsymbol{1} \leq \boldsymbol{x} \leq \mathbf{2} \\ -\boldsymbol{2}+\boldsymbol{3} \boldsymbol{x}-\boldsymbol{x}^{2}, & \boldsymbol{x}>\boldsymbol{2}\end{array}\right. \)


Climate of the world is threatened by.
A. Increasing concentration of atmospheric oxygen
B. Decreasing amount of atmospheric oxygen
C. Increasing amount of atmospheric carbon dioxide
D. Decreasing amount of atmospheric carbon dioxide


The ratio between total acceleration of
the electron is singly ionized Helium atom and doubly ionization Lithium atom (both in ground state) is
A .2
в. \( 4 / 9 \)
c. \( 8 / 27 \)
\( D \)


\( \boldsymbol{S} \boldsymbol{i} \boldsymbol{O}_{2}, \boldsymbol{G} \boldsymbol{e} \boldsymbol{O}_{2}, \boldsymbol{S} \boldsymbol{n} \boldsymbol{O} \) and \( \boldsymbol{P b O} \) are
respectively:
A. acidic, amphoteric, acidic, basic
B. acidic, amphoteric, amphoteric, acidicç
c. acidic, basic, amphoteric, basic
D. acidic, amphoteric, amphoteric, basic


The distance traveled by 5 identical particle is given below in the options \( A \) B, \( C, D \) and \( E \) respectively at specific time interval. Which object is moving with a constant velocity?
в. \( 2 m, 2 m, 4 m 4 m, 6 m \)
\( \mathbf{c} .2 m, 4 m, 6 m, 8 m, 10 m \)
D. \( 6 m, 11 m, 15 m, 18 m, 20 m \)
E. \( 4 m, 9 m, 15 m, 22 m, 29 m \)


When placenta forms a ridge along the
ventral suture of the ovary and the ovules are borne on this ridge forming two rows, the type of placentation is termed as
A. Marginal
в. Axile
c. Parietal
D. Free centra


When forces \( F_{1}, F_{2}, F_{3} \) are acting on a
particle of mass \( \mathrm{m} \) such that \( \boldsymbol{F}_{2} \) and \( \boldsymbol{F}_{3} \)
are mutually perpendicular, then the particle remains stationary. If the force
\( F_{1} \) is now removed then the acceleration
of particle the is
A. \( F_{1} / m \)
B . \( F_{2} F_{3} / m F_{1} \)
\( \mathbf{c} \cdot\left(F_{2}-F_{3}\right) / m \)
D. \( F_{2} / m \)


Explain the classification of hormones in detail.


The essential requirements of a fuse
wire are
A. High resistance and high melting point
B. High resistance and low melting point
C . Low resistance and low melting point
D. Low resistance and high melting point


Core of electromagnets are made of ferromagnetic material which have
A. low permeability and low retentivity
B. high permeability and high retentivity
c. high permeability and low retentivity
D. low permeability and high retentivity


Which of the following form is an ideal solution?
This question has multiple correct options
A. Ethyl bromide + Ethyl iodide
B. Ethyl alcohol + Water
c. chloroform + Benzene
D. Benzene + Toluene


A particle of mass \( 10 g \) is kept on the surface of a uniform sphere of mass
100 \( k g \) and radius \( 10 c m . \) Find the work
to be done against the gravitational force between them to take the particle far away from the
sphere
A \( \cdot 13.34 \times 10^{-10} \mathrm{J} \)
B . \( 13.33 \times 10^{-10} J \)
c. \( 6.67 \times 10^{-9} \mathrm{J} \)
D. \( 6.67 \times 10^{-10} J \)


Which of the following statements are not summarized within Dalton's Atomic
Theory?
A. Atoms cannot be created or destroyed.
B. Atoms are made of protons, neutrons and electrons
c. Atoms rearrange in chemical reactions
D. When atoms combine to form compounds, they combine in whole number ratios


A man slides down a snow covered hill
along a curved path and falls \( 20 m \) below his initial position. The velocity in \( \boldsymbol{m} / \boldsymbol{s e c}, \) with which he finally strikes the ground is \( ?\left(\boldsymbol{g}=\mathbf{1 0} \boldsymbol{m} / \boldsymbol{s e c}^{2}\right) \)
A . 20
в. 400
\( c \cdot 200 \)
D. 40


Consider a system of two identical particles. One of the particles is at rest and the other has an acceleration a. The
centre of mass has an acceleration
A . zero
B . \( \frac{1}{2} a \)
\( c \cdot a \)
D. 2a


How does the power of lens vary with its
focal length?


Find out the correct statement.
A. In lichens, the algal component is called phycobiont and fungal component is known as mycobiont, which are heterotrophic and autotrophic respectively.
B. Viroid contains RNA of low molecular weight and protein coat
C. A virus contains both RNA and DNA.
D. Viruses are obligatory parasites.
E. Viruses that infect plants have double stranded RNA.


Read below given tabular form and
answer the questions.
\begin{tabular}{llll}
Element & Electronic configuration & Element & Elec conf \\
\( \mathrm{He} \) & \( 1 s^{2} \) & \( \mathrm{Kr} \) & \( 4 s^{2} 4 \) \\
\( \mathrm{Ne} \) & \( 2 s^{2} 2 p^{6} \) & \( \mathrm{xe} \) & \( 5 s^{2} 5 \) \\
\( \mathrm{Ar} \) & \( 3 s^{2} 3 p^{6} \) & \( \mathrm{Rn} \) & \( 6 s^{2} 6 \) \\
\hline
\end{tabular}
Write the names of 'noble gas' elements


If \( \boldsymbol{x}=\mathbf{3}-\mathbf{2} \sqrt{\mathbf{2}}, \) find \( \boldsymbol{x}^{4}+\frac{\mathbf{1}}{\boldsymbol{x} \mathbf{4}} ? \)


The vertical component of earth's magnetic field at a place is \( \sqrt{3} \) times the horizontal component the value of angle of dip at this place is
A \( .30^{\circ} \)
В \( \cdot 45^{\circ} \)
\( c \cdot 60^{0} \)
D. \( 90^{\circ} \)


What will happen if there are no valves
in the heart?


A charged particle accelerated through a potential difference of \( 100 V \) passes through uniform electric and magnetic fields so as to experience no deflection. \( \boldsymbol{E}=\mathbf{1 5} \times \mathbf{1 0}^{6} \boldsymbol{V} \boldsymbol{m}^{-1} \) and \( \boldsymbol{B}=\mathbf{5} \times \mathbf{1 0}^{\mathbf{3}} \boldsymbol{T} \)
Then the specific charge \( \frac{e}{m} \) is :
A \( \cdot 4.5 \times 10^{4} \mathrm{C} / \mathrm{kg} \)
В . \( 9 \times 10^{7} C / k g \)
C \( .4 .5 \times 10^{3} C / k g \)
D. \( 9 \times 10^{5} C / k g \)


A convex lens is used to form an image
of an object on a screen, If the upper half of the lens is blackened so that it
becomes opaque.Then:
A. Only half of the image will be visible
B. The image position shifts towards the lens
c. The image position shifts away from the lens
D. The brightness of the image reduces


If \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{3}+\boldsymbol{b} \boldsymbol{x}^{2}+\boldsymbol{a} \boldsymbol{x} \) satisfies the
conditions of Rolles theorem on [1,3] with \( c=2+\frac{1}{\sqrt{3}} \) then \( (a, b)= \)
\( \mathbf{A} \cdot(11,6) \)
В \( \cdot(11,-6) \)
c. (-6,11)
D. (6,11)


Which of the following pair of vitamin participates as co factors in the cellular oxidation reduction reaction?
A. Pyridoxine and folate
B. Riboflavin and Cobalamine
c. Ascorbate and nicotinamide
D. Thiamine and pantothenate


Find the root of the quadratic equation
\( x^{2}+2 \sqrt{2 x}+6=0 \) by using the
quadratic formula
A . \( x=\sqrt{2} \pm 2 i \)
B. \( x=-\sqrt{2} \pm 2 i \)
c. \( x=-\sqrt{4} \pm 2 i \)
D. \( x=-\sqrt{2} \pm 4 i \)


Assertion
PhCOCOCOPh forms stable hydrate.
Reason
The compound in the hydrate from has intramolecular H-bonding.
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 incorrect but Reason is correct
D. Both Assertion and Reason are correct


\( \lim _{x \rightarrow 0^{-}}\left\{\sin ^{-1}[\tan x]\right\}=l \) then \( l \) is equal
to
where \( [\text { and }\{\} \) denotes greatest the integer and fraction part function
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( -\sin ^{-1}(1) \)
\( c \cdot \sin 1 \)
D. \( 2-\frac{\pi}{2} \)


Consider the nuclear reaction
\( \boldsymbol{X}^{200} \rightarrow \boldsymbol{A}^{110}+\boldsymbol{B}^{90}+ \)energy
If the binding energy per nucleon for \( X, A \) and \( B \) is \( 7.4 M e V, 8.2 M e V \) and
\( 8.2 M e V \) respectively. What is the
energy released?
A \( .200 \mathrm{MeV} \)
В. \( 160 \mathrm{MeV} \)
c. \( 110 M e V \)
D. 90 MeV


A solid sphere and a spherical shell roll down on inclined plane from rest from same height.The ratio of the times taken by them is.
A \( \cdot \sqrt{\frac{21}{25}} \)
B. 21/25
c. \( \sqrt{\frac{25}{21}} \)
D. 25/21


Which of the following is negation of the statement "All birds can fly".
A. "Some birds cannot fly"""""
B. "All the birds cannot fly""
c. "There is at least one bird which can fly".
D. All the above


The emission spectra of Sample \( \boldsymbol{A} \)
A. Must have 3 lines
B. Must have 2 lines
c. Must have 4 lines
D. It is not formed


\( \left[\begin{array}{cc}1 & 1 \\ 0 & 1\end{array}\right]\left[\begin{array}{cc}1 & 2 \\ 0 & 1\end{array}\right]\left[\begin{array}{cc}1 & 3 \\ 0 & 1\end{array}\right] \ldots \ldots\left[\begin{array}{cc}1 & n \\ 0 & 1\end{array}\right]= \)
\( A \cdot 27 \)
3.26
\( c .376 \)
D. 378


The equation of the hyperbola with vertices (0,±15) and foci (0,±20) is
A \( \cdot \frac{x^{2}}{175}-\frac{y^{2}}{225}=1 \)
В. \( \frac{x^{2}}{625}-\frac{y^{2}}{125}=1 \)
c. \( \frac{y^{2}}{225}-\frac{x^{2}}{125}=1 \)
D. \( \frac{y^{2}}{225}-\frac{x^{2}}{175}=1 \)


If \( \sin ^{-1}(1-x)-2 \sin ^{-1} x=\pi / 2, \) then
\( x \) is equals?
\( \mathbf{A} \cdot\{0,-1 / 2\} \)
B \cdot \( \{1 / 2,0\} \)
\( c \cdot\{0\} \)
D. (-1,0)


o-Xylene on ozonolysis will give:
\( A \)
B.
\( \& \)
\( c \)
\( D \)
0


What is the perimeter of the triangle with vertices \( \boldsymbol{A}(-\mathbf{4}, \mathbf{2}), \boldsymbol{B}(\mathbf{0},-\mathbf{1}) \) and
\( C(3,3) ? \)
A. \( 7+3 \sqrt{2} \)
B. \( 10+5 \sqrt{2} \)
c. \( 11+6 \sqrt{2} \)
D. \( 5+10 \sqrt{2} \)


Assertion
Heavy water is used as a moderator in
nuclear reactors.
Reason
Heavy water is made of an isotope of helium.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Alternate inverted prisms are placed in series. Choose correct options.
A. Even number of prisms does not produce a spectrum
B. Odd number of prisms produce a spectrum
c. More the number of prisms, less is the intensity of emergent ray/spectrum
D. All of above


Find the principal and general solutions of the following equation:
\( \sec x=2 \)
A ' principal solution \( =\frac{\pi}{6}, \frac{5 \pi}{6} \) and General solution \( = \)
\( n \pi \pm \frac{\pi}{6}, n \in Z \)
B. Principal solution \( =\frac{\pi}{3}, \frac{5 \pi}{3} \) and General solution \( = \)
\( n \pi \pm \frac{\pi}{3}, n \in Z \)
C ' principal solution \( =\frac{\pi}{6}, \frac{5 \pi}{6} \) and General solution \( = \)
\( 2 n \pi \pm \frac{\pi}{6}, n \in Z \)
D. principal solution \( =\frac{\pi}{3}, \frac{5 \pi}{3} \) and General solution \( = \)
\( 2 n \pi \pm \frac{\pi}{3}, n \in Z \)


What problem arises in using alitame
as artificial sweetener?


Solving \( \frac{\mathbf{2}}{\boldsymbol{x}}+\mathbf{3} \boldsymbol{y}=-\mathbf{3} \) and \( \boldsymbol{y}-\boldsymbol{4} \boldsymbol{x}=\frac{\mathbf{7}}{\mathbf{3}} \)
gives \( (\mathbf{x}, \mathbf{y}) \)
\( \mathbf{A} \cdot\left(-\frac{1}{2}, 3\right) \)
B \( \cdot\left(-1, \frac{1}{3}\right) \)
c. \( \left(-\frac{1}{2}, \frac{1}{3}\right) \)
D \( \cdot\left(-2, \frac{1}{3}\right) \)


Solve:
\( \int \frac{d x}{\sqrt{4-x^{2}}} \)


The shadow of the tower standing on a
level ground is found to be 60 meters
longer when the suns altitude is \( 30^{\circ} \)
than when it is \( 45^{\circ} . \) The height of the
tower is
\( A \cdot 60 m \)
в. \( 30 m \)
\( c \cdot 60 \sqrt{3} m \)
D. \( 20(\sqrt{3}+1) m \)


State whether true or false:
Alcohol and ether are conducting liquids of electricity.
A. True
B. False


What is an angle bisector?


What is the effect of soil erosion in our
country?


Two convex lens of focal lengths \( f_{1} \) and
\( f_{2} \) form images with magnification \( m_{1} \)
and \( m_{2}, \) when used individually for an object kept at the same distance from
the lenses. Then \( \boldsymbol{f}_{1} / \boldsymbol{f}_{2} \)
A \( \cdot \frac{m_{1}\left(1+m_{1}\right)}{m_{2}\left(1+m_{2}\right)} \)
в. \( \frac{m_{1}\left(1-m_{2}\right)}{m_{2}\left(1-m_{1}\right)} \)
c. \( \frac{m_{2}\left(1+m_{1}\right)}{m_{1}\left(1+m_{2}\right)} \)
D \( \cdot \frac{m_{2}\left(1+m_{2}\right)}{m_{1}\left(1+m_{1}\right)} \)


Which bond is present in oxygen atom?
A. Ionic bond
B. Covalent bond
c. covalent divalent bond
D. covalent trivalent bond


Acid chlorides can be changed to
aldehydes by reaction with:
\( \mathbf{A} \cdot L i A l H_{4} \)
B. \( N a B H_{4} \)
C . Hydrogen and palladised \( B a S O_{4} \)
D. zinc amalgam and conc. \( H C l \)


A car travelling on a straight track
moves with uniform velocity of \( v_{1} \) for
some time and uniform velocity \( v_{2} \) for
the next equal time. The average of velocity of the car is :


The IUPAC name of the formic acid:
A. methanoic acid
B. ethanoic acid
C. propanoic acid
D. butanoic acid


The functional group in an alcohol is :
A. \( O \)
\[
-C-O-
\]
\( \begin{aligned} \text { в. } & O \\ &-C-O H \end{aligned} \)
\( \mathrm{c} .-O H \)
D. \( O \)
- \( C-H \)


The sum of 'n' terms of series \( 1^{2}+ \)
\( \left(1^{2}+2^{2}\right)+\left(1^{2}+2^{2}+3^{2}\right)+\left(1^{2}+\right. \)
\( \left.\mathbf{2}^{2}+\mathbf{3}^{2}+\mathbf{4}^{2}\right)+\ldots \ldots . \) will be
A \( \cdot \frac{1}{4} n(n+1)^{2}(n+2) \)
B \( \cdot \frac{1}{3} n(n+1)^{2}(n+2) \)
c. \( \frac{1}{12} n(n+1)(n+2)^{2} \)
D. \( \frac{1}{12} n(n+1)^{2}(n+2) \)


The radii of two spheres made of same metal are \( r \) and \( 2 r . \) These are heated to
the same temperature and placed in the
same surrounding. The ratio of rates of decrease of their temperature will be


Let \( \boldsymbol{A}=\{\mathbf{3}, \mathbf{6}, \mathbf{1 2}, \mathbf{1 5}, \mathbf{1 8}, \mathbf{2 1}\}, \boldsymbol{B}= \)
\( \{\mathbf{4}, \mathbf{8}, \mathbf{1 2}, \mathbf{1 6}, \mathbf{2 0}\}, \boldsymbol{C}= \)
\( \{\mathbf{2}, \mathbf{4}, \mathbf{6}, \mathbf{8}, \mathbf{1 0}, \mathbf{1 2}, \mathbf{1 4}, \mathbf{1 6}\} \) and \( \boldsymbol{D}= \)
\( \{\mathbf{5}, \mathbf{1 0}, \mathbf{1 5}, \mathbf{2 0}\} . \) Find \( \boldsymbol{A}-\boldsymbol{D} \)


\( \boldsymbol{C H}_{2}=\boldsymbol{C H}_{2}+\boldsymbol{B r}_{2} \rightarrow \boldsymbol{C H}_{2} \boldsymbol{B r}- \)
\( C H_{2} B r, \) is an example of
A. addition reaction
B. substitution reaction
c. elimination reaction
D. molecular rearrangement


Write present names of Eka-aluminium and Eka-silicon.


A loop and a disc roll without slipping
with same linear velocity \( v \). The mass of
the loop and the disc is same. If the total kinetic energy of the loop is \( 8 J \)
find the kinetic energy of the disc (in \( J) \)


A strip of copper and another of germanium are cooled from room
temperature to \( 80 \mathrm{K} \). The resistance of
A. Each of these increases
B. Each of these decreases
c. copper strip increases and that of germanium decreases
D. copper strip decreases and that of germaniumiumm increases


Let \( n \) be a positive integer and \( \Delta_{r}= \) \( \left|\begin{array}{ccc}2 r-1 & n & C_{r} & 1 \\ n^{2}-1 & 2^{n} & n+1 \\ \cos ^{2}\left(n^{2}\right) & \cos ^{2} n & \cos ^{2}(n+1)\end{array}\right| \) then
\( \sum_{r=0}^{n} \Delta_{r}=\dots \)
\( A \cdot 0 \)
B.
\( c \cdot 2 \)
\( D \)


Which colour of light is scattered the most(maximum) in the atmosphere?
A . Red
B. Yellow
c. Blue
D. Green


\( f\left(\begin{array}{ccc}1 & -1 & 2 \\ 3 & 0 & -2 \\ 1 & 0 & 3\end{array}\right], \) then verify that
\[
\boldsymbol{A}(\boldsymbol{a} \boldsymbol{d} \boldsymbol{j} \boldsymbol{A})=(\boldsymbol{a} \boldsymbol{d} \boldsymbol{j} \boldsymbol{A}) \boldsymbol{A}=\boldsymbol{I}|\boldsymbol{A}|
\]


Nucleic acids occur in
A. Viruses only
B. Bacteria only
C. Mammals only
D. All forms of life


Cards marked with the numbers 2 to
101 are put in a box and mixed thoroughly. One card is drawn from this box. Find the probability that the number on the card is an even prime
number less than 16 .
A \( \cdot \frac{5}{28} \)
B. \( \frac{3}{50} \)
\( c \cdot \frac{3}{25} \)
D. \( \frac{1}{100} \)


f \( a, b, c \) are real numbers such that \( \left|\begin{array}{ccc}\boldsymbol{b}+\boldsymbol{c} & \boldsymbol{c}+\boldsymbol{a} & \boldsymbol{a}+\boldsymbol{b} \\ \boldsymbol{c}+\boldsymbol{a} & \boldsymbol{a}+\boldsymbol{b} & \boldsymbol{b}+\boldsymbol{c} \\ \boldsymbol{a}+\boldsymbol{b} & \boldsymbol{b}+\boldsymbol{c} & \boldsymbol{c}+\boldsymbol{a}\end{array}\right|=0, \) then show
that either \( \boldsymbol{a}+\boldsymbol{b}+\boldsymbol{c}=\boldsymbol{0} \) or, \( \boldsymbol{a}=\boldsymbol{b}=\boldsymbol{c} \)


'F' block elements ae known as
elements.


An \( \alpha \) -particle is identical with:
A. proton
B. neutron
c. helium nucleus
D. electron


On reversing a reaction equilibrium \( (\Delta n=0), \) the numerical value of \( K_{c} \)
and its unit both are reversed.
A. True
B. False


Calgon used as water softner is:
\( \mathbf{A} \cdot N a_{2}\left[N a_{4}\left(P O_{3}\right)_{6}\right] \)
B. \( N a_{4}\left[N a_{2}\left(P O_{3}\right)_{6}\right] \)
\( \mathbf{c} \cdot N a_{2}\left[N a_{4}\left(P O_{4}\right)_{5}\right] \)
D. none of the above


Earth receives \( 1400 W / m^{2} \) of solar
power. If all the solar energy falling on a
lens of area \( 0.2 m^{2} \) is focussed onto a
block of ice of mass 280 grams, the time taken to melt the ice will be
minutes.(Latent heat of
fusion of ice \( =\mathbf{3 . 3} \times \mathbf{1 0}^{\mathbf{5}} \mathrm{J} / \mathrm{kg} \) ).
A . 6.5
B. 5.
\( c \cdot 8 \)
D.


In the image formed by a plane mirror, the left of the object appears on the right and the right appears on the left. This is called lateral inversion.
A . True
B. False


In a particle executing SHM, the following parameter at equilibrium will have its
A. Kinetic energy as maximum
B. Potential energy as maximum
C. Kinetic energy as minimum
D. None of the above


The focal lengths of the objective and eyepiece of a compound microscope are \( 2 \mathrm{cm} \) and \( 3 \mathrm{cm} \) respectively. The distance between the objective and eyepiece is \( 15 \mathrm{cm} . \) The final image formed is at infinity. The distances in cm of object and image from objective are going to be then:
\( A \cdot 2.4 \) and 12
B. 2.4 and 15
c. 2.3 and 3.0
D. 2.3 and 12


Amongst the following, the most stable
complex is:
\( \mathbf{A} \cdot\left[F e\left(H_{2} O\right)_{6}\right]^{3} \)
B . \( \left[F e\left(N H_{3}\right)_{6}\right]^{3+} \)
c. \( \left[F e\left(C_{2} O_{4}\right)_{3}\right]^{3} \)
D. \( \left[F e C l_{6}\right]^{3} \)


A parallel plate capacitor (fig.) made of circular plates each of radius \( \boldsymbol{R}= \)
\( 6.0 \mathrm{cm} \) has a capacitance \( C=100 \mu \mathrm{F} \)
The capacitor is connected to a \( 230 V \)
ac supply with a (angular) frequency of 300 rad \( s^{-1} . \) Determine the amplitude of
\( B \) at a point \( 3.0 \mathrm{cm} \) from the axis
between the plates.?


Check whether the first polynomial is a factor of the second polynomial by
applying the division algorithm. \( x^{3}- \)
\( \mathbf{3} \boldsymbol{x}+\mathbf{1}, \boldsymbol{x}^{\mathbf{5}}-\mathbf{4} \boldsymbol{x}^{\mathbf{3}}+\boldsymbol{x}^{\mathbf{2}}+\mathbf{3} \boldsymbol{x}+\mathbf{1} \)
A. Yes
B. No
c. Ambiguous
D. Data insufficient


Express each of the following without using decimals:
\( \mathbf{7 . 5 4} \boldsymbol{m} \)


If air resistance is not considered in
projectiles, the horizontal motion takes place with :
A. Constant velocity
B. Constant acceleration
c. constant retardation
D. Variable velocity


The phase space diagram for simple
Momentum harmonic motion is a circle
centered at the origin. In the figure, the
two circles represent the same oscillator but for different initia
conditions, and \( E_{1} \) and \( E_{2} \) are the total
mechanical energies respectively. Then:
\( \mathbf{A} \cdot E_{1}=\sqrt{2} E_{2} \)
\( \mathbf{B} \cdot E_{1}=2 E_{2} \)
\( \mathbf{c} \cdot E_{1}=4 E_{2} \)
\( \mathbf{D} \cdot E_{1}=16 E_{2} \)


What products are formed during, the electrolysis of a concentrated aqueous solution of \( N a C l ? \)
(I) \( C l_{2} \)
(II) \( N a O H(a q) \)
\( (\| I) H_{2}(g) \)
A. I only
B. I and II only
C. \( I \) and \( I I I \) only
D. I, II and III


Amplitude of \( \frac{1+i}{1-i} \) is :
A.
в. \( \pi \)
\( c \cdot \frac{\pi}{2} \)
D. -


Total number of electrons involved per
molecule in the oxidation of \( F e C_{2} O_{4} \) to
\( F e^{3+} \) and \( C O_{2} \) is :
\( \mathbf{A} \cdot \mathbf{3} \)
B. 2
\( c \cdot 4 \)
D. none of these


In a simultaneous throw of a pair of
dice, if the probability of getting a sum less then 6 is \( \frac{5}{a} . \) Find \( a \)


When 1 g of water at \( 100^{\circ} \mathrm{C} \) gets
converted into steam at the same
temperature, the change in volume is approximately
A \( .1 \mathrm{cc} \)
B. 1000 ç
\( c \cdot 1500 \mathrm{cc} \)
D. 1670 cc


For dilute solution, Raoult's law states
that:
A. the relative lowering of vapour pressure is equal to mole fraction of solute
B. the vapor pressure of the solution is equal to mole fraction of the solvent
C. the relative lowering of vapour pressure is proportional to amount of solute
D. the lowering of vapor pressure is equal to the mole fraction of solute in solution


Regarding a thermochemical equation a
Wrong statement is
A. It tells about the physical states of reactants and products
B. It tells whether the reaction is exothermic or
endothermic
C. It tells about the allotropic form (if any) of the reactant
D. It tells whether the reaction is possible or not


The position vectors of two points \( A \) and \( \mathrm{B} \) are \( i+j-k \) and \( 2 i-j+k \)
respectively. Then \( |\boldsymbol{A} \boldsymbol{B}|= \)
\( A \cdot 2 \)
B. 4
\( c .3 \)
D. 5


Which are true statements about \( s \)
block elements?
This question has multiple correct options
A. Metals are obtained by the electrolytic of fused chlorides.
B. Oxides are basic except Be0
C \( .+1 \) valency by alkali metals and +2 valency alkaline earth metals is shown
D. carbonates are thermally stable


An object 0 is placed in front of a mirror. Which is possible position of the image?
\( A \)
B. B
\( c \cdot c \)
D.


Which of the following statements are
correct for the above reaction?
This question has multiple correct options
A. The product is a mixture of (figure)
B. The product (II) is a cine-substitution product
C. The reaction proceeds via benzene intermediate
D. The reaction is \( A r S N \) (addition-elemination


A contraceptive is
A. Condom, cervical cap and diaphragm
B. Intrauterine device
c. Pill
D. All of the above


If we divide a positive integer by another positive integer, what is the resulting
number?
A. It is always a natural number
B. It is always an integer
c. It is a rational number
D. It is an irrational number


A \( 4 g \) bullet is fired horizontally with a speed of \( 300 m / s \) into \( 0.8 k g \) block of wood, which is at rest on a table. If the
coefficient of friction between the block
and the table is \( 0.3, \) how far will the
block slide approximately?
A. \( 0.20 \mathrm{m} \)
B. 0.375 m
c. \( 0.565 \mathrm{m} \)
D. 0.750 \( \mathrm{m} \)


A violet colour compound is formed in
detection of \( S \) in a compound:
A \( \cdot \operatorname{Na}_{4}\left[\mathrm{Fe}(\mathrm{CN})_{5} \mathrm{NOS}\right] \)
В \( \cdot \operatorname{Na}_{3}\left[\mathrm{Fe}(\mathrm{CN})_{5} \mathrm{NOS}\right] \)
c. \( \operatorname{Na}_{2}\left[\mathrm{Fe}(\mathrm{CN})_{5} \mathrm{NOS}\right] \)
D. \( \operatorname{Na}\left[\text {Fe}(\text {CN})_{5} \) NOS\right.


Match the List-I with List-II.
List-I List-II
\( A) \)
Liquid \( \rightarrow \) vapour
1) 32.8
В) \( H_{2}+C l_{2} \rightarrow 2 H C l-\Delta H=-44 \)
kcal
2) -22 Then, heat of formation \( H C l \) in kcal):
C) Heat of combustion of graphite
\[
\text { is }-393.5 \mathrm{kJ}
\]
3
Then its calorific value (kJ)
D) 4.184 Joules is equal to (in 4) calories): \( \quad \) endothermic
\( A \cdot A-1, B-2, C-3, D-4 \)
B. A-4, B-3, C-2, D-1
\( C \cdot A-4, B-2, C-1, D-3 \)
D. \( A-2, B-1, C-4, D-3 \)


The relative stability of +1 oxidation state of group 13 elements follows the order:
A. \( A l<G a<T l<I n \)
в. \( T l< \)In \( <G a<A l \)
c. \( A l<G a<I n<T l \)
D. \( G a<A l< \)In \( <T l \)


State whether the following statement
is True or False.

You can see a rainbow only when your back is towards the sun
A. True
B. False


Find the chance of throwing at least one ace in a single throw with two dice.


Person living at sea level has lung capacity than a person living at high altitudes.
A. smaller
B. Higher
c. Equal
D. None of the above


A watch glass containing some powdered substance is placed between
the pole pieces of a magnet. Deep concavity is observed at the centre. The substance in the watch glass is
A. iron
B. chromium
c. carbon
D. woodd


Transfer of DNA bands from an agarose
gel to a nitrocellulose or nylon membrane is referred to as
A. western transfer
B. Northern transfer
c. Eastern transfer
D. Gene transfer
E. Southern blotting


The freezing point of mercury is:
\( A \cdot 100 K \)
в. 234.3 к
c. \( 123.5 \mathrm{k} \)
D. 450 K


n kidney, nephrostomes are functional
in
A. Tadpole
B. Adult Frog
c. cockroach
D. Rabbit


The value of \( k \) for which the function
\( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{ll}\frac{1-\cos 4 x}{8 x^{2}} & , x \neq 0 \\ k & , x=0\end{array}\right. \)
continuous at \( \boldsymbol{x}=\mathbf{0}, \) is
\( \mathbf{A} \cdot k=0 \)
B. \( k=1 \)
c. \( k=-1 \)
D. None of the above


Kirchhoff's first law is given by \( \sum \boldsymbol{I}=\mathbf{0} \) and Kirchhoff's second law is given by \( \sum I R=0, \) where the symbols have their
usual meanings. Choose the correct option.
A. Kirchhoff's first law is based on conservation of energy and second law is based on conservation of charge
B. Kirchhoff's second law is based on the conservation of energy and first law is based on conservation of charge
c. Both the laws based on the conservation of momentum
D. First law based on the conservation of momentumm and second law on the conservation of charge


A chemical signal that has both endocrine and neural roles is
A. Epinephrine.
B. Cortisol.
c. Melatonin.
D. Calcitonin.


A car is moving with speed 30 m/sec on
a circular path of radius 500 m. Its
speed is increasing at the rate of \( 2 m / s e c^{2} . \) What is the acceleration of
the car at that moment?


The flame of the candle has three zones.
The outer zone is blue, the middle zone
is yellow and the inner zone is black. Which is correct regarding this? This question has multiple correct options
A. The outer zone is hottest hot
B. The middle zone is hottest
c. The inner zone is least hot
D. All the zones have same temperature


Raj borrows Rs.8,000; out of which Rs.4,500 at 5\% and remaining at 6\%. Find the total interest paid by him in 4
years
A . Rs. 1,840
B. Rs. 1,170
c. Rs. 1,740
D. Rs. 1,890


A balloon in the form of a right circular cone surmounted by a hemisphere, having a diameter equal to the height of the cone, is being inflated. How fast is its volume changing with respect to its total height \( h, \) when \( h=9 \mathrm{cm} \)


Sir Isaac Newton's third law of motion is
called the action-reaction law. Which of
the following statements appropriately describes the action-reaction forces?
A. They act on different objects
B. They act on the same object
C. They are unequal in magnitude
D. They act at right angles to one another
E. They act in the same direction


Why must electrostatic field be normal
to the surface at every point of a charged conductor?


Synthesis of DNA ends in
A. s phase
B. Prophase
c. Premitotic gap phase
D. Post mitotic gap phase


A circular
the opening of the bladder into the
urethra


A \( 0.2 m l \) sample of a solution containing
\( 1 \times 10^{-7} \) curie of tritium \( _{1} H^{3} \) is injected
into the blood stream of a laboratory animal. After allowing sufficient time for circulation \( 0.1 m l \) of the blood is
found to have an activity of 20 disintegration per minute. What is the blood volume of the animal?
A. 1.1 litre
B . 0.55 litre
c. 0.65 litre
D. 1.65 litre


The shortest distance between the lines \( \frac{\boldsymbol{x}-\mathbf{5}}{\mathbf{4}}=\frac{\boldsymbol{y}-\mathbf{7}}{-\mathbf{5}}=\frac{\boldsymbol{z}+\mathbf{3}}{-\mathbf{5}} \) and \( \frac{\boldsymbol{x}-\mathbf{8}}{\mathbf{4}}= \)
\( \frac{y-7}{-5}=\frac{z-5}{-5} \) is
A . 45
B . 46
c. 47
D. 48


Write \( I U P A C \) name of the compound
given in the picture.


Assertion
The change in internal energy and change in heat enthalpy does not depend upon the path by which changes are brought in.
Reason
Both \( \Delta U \) and \( \Delta H \) are path independent as U and H are state functions.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect.
D. Assertion is incorrect but Reason is correct


Which of the following is weakly acidic?
В. \( 0.1 M \) NaCl
\( \mathrm{c} \cdot 0.1 \mathrm{M} \quad \mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2} \)
D. \( 0.1 M \quad C H_{3} O H \)
E. \( 0.1 M \) KOH


The distance between two consecutive
crests in a wave train produced in string is \( 5 \mathrm{m} \). If two complete waves pass through any point per second, the velocity of wave is:
A \( .2 .5 \mathrm{m} / \mathrm{s} \)
B. \( 5 \mathrm{m} / \mathrm{s} \)
c. \( 10 \mathrm{m} / \mathrm{s} \)
D. \( 15 \mathrm{m} / \mathrm{s} \)


The uses of bleaching powder are:
A. it is used for bleaching cotton
B. it is used as an oxidizing agent in chemical industries
C. it can be used for disinfecting water
D. all of the above


The actinoids exhibit more number of
oxidation states in general than the lanthanoids. This is because:
A. the \( 5 f \) orbitals are more buried than the \( 4 f \) orbitals
B. there is a similarity between 4 f and 5 f orbitals in their angular part of the wave function
c. the actinoids are more reactive than the lanthanoids
D. the 5 f orbitals extend further from the nucleus than the \( 4 f \) orbitals


Formal charge on nitrogen and oxygen
in \( N O_{3}^{-} \) ion are respectively:
A \( \cdot_{0, \frac{-1}{3}} \)
в. \( +1, \frac{-1}{3} \)
\( c \cdot+1, \frac{-2}{3} \)
D. \( _{0, \frac{-2}{3}} \)


If an electron in a hydrogen atom has moved from \( n=1 \) to \( n=10 \) orbit, the
potential energy of the system has:
A. increased
B. decreased
c. remained unchanged
D. become zero


Assertion(A): An inductor in a D.C.
circuit opposes both a steady current and a changing current. Reason(R): Induced emf is generated
only when the flux linked with the inductor remains unchanged.
A. Both A and R are individually true and R is the correct explanation of A
B. Both A and R are individually true but R is not the correct explanation of \( A \)
c. A is true but R is false
D. Both A and R are false


Assuming that 113 elements are there in the periodic table now, what would be the group and period to which newly added element belongs?
A. IVA group, 7th period.
B. VIA group, 7th period.
c. va group, 7th period.
D. VIIA group, 6th period.


Assertion
A cricket player while catching a bal lowers his hands to save himself from
getting hurt.
Reason
The impulsive force on hands is reduced by increasing the time of action.
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


There are two vessels of same
consisting same no of moles of two different gases at same temperature.
One of the gas is \( C H_{4} \& \) the other is
unknown X. Assuming that all the molecules of \( X \) are under random
motion whereas in \( C H_{4} \) except one all
are stationary. Calculate \( Z_{1} \) for \( X \) in
terms of \( Z_{1} \) of \( C H_{4} . \) Given that the collision diameter for both gases are same \( \&\left(U_{r m s}\right)_{x}=\frac{1}{\sqrt{6}}(U a v)_{C H_{4}} \)
A \( \cdot \frac{2 \sqrt{2}}{3 \sqrt{\pi}} Z_{1} \)
B \( \cdot \frac{3 \sqrt{2}}{2 \sqrt{\pi}} Z_{1} \)
c. \( \frac{2 \sqrt{3}}{2 \sqrt{\pi}} Z_{1} \)
D. \( \frac{4 \sqrt{2}}{3 \sqrt{\pi}} Z_{1} \)


Find the Median from the following
table-
\( \begin{array}{llll}\text { Class } & \mathbf{0}- & \mathbf{2 0 -} & \mathbf{4 0 -} \\ \text { Interval } & \mathbf{2 0} & \mathbf{4 0} & \mathbf{6 0}\end{array} \)
17
26
Frequency 10


If \( a<c<b \) then the roots of the
equation \( (a-b)^{2} x^{2}+2(a+b- \)
\( 2 c) x+1=0 \) are
A. Imaginary
B. Real
c. one real and one Imaginary
D. Equal and Imaginary


If the material has breaking point lies very close to elastic limit, the material
is
A. brittle
B. ductile
c. elastomer
D. diathermanous


Two metal wire 'P' and 'Q' of same length and material are stretched by same
load. Their masses are in the ratio \( \boldsymbol{m}_{1}: \)
\( m_{2} . \) The ratio of elongations of wire 'P' to
that of 'Q' is
A \( \cdot m_{1}^{2}: m_{2}^{2} \)
в. \( m_{2}^{2}: m_{2}^{1} \)
\( \mathrm{c} \cdot m_{2}: m_{1} \)
D. \( m_{1}: m_{2} \)


Verify whether \( x=3 \) is a zero of the
polynomial \( \boldsymbol{x}^{2}+\mathbf{2} \boldsymbol{x}-\mathbf{1 5} \)


\( \frac{x}{8} \)


A metal oxide \( M O_{(s)} \) can be reduced by carbon or carbon monoxide
successfully when the line in Ellingham
diagram for reaction (i):
A. lies above the line for one of the reactions (ii) to (iv)
B. intersects the line for one of the reactions
(ii) to (iv)
(ii) to (iv)
c. lies below the line for one of the reactions
D. may lie above or below the line for one of the reactions
(ii) to
(iv) depending upon the temperature


Explain allotropes of phosphorous.


What is the minimum height above the ground at which the rocketeer should
catch the student?
A . \( 92.1 \mathrm{m} \)
в. 460.9 т
c. \( 78.8 m \)
D. 82.3 m


Smoke is an example of:
A. gas dispersed in liquid
B. gas dispersed in solid
C. solid dispersed in gas
D. solid dispersed in solid


The lymph hearts in frog are
A. 1 pair
B. 2 pairs
c. 3 pairs
D. Absent


The slope of velocity \( (v) \) vs. time \( (t \)
curve at any instant of time gives:
A. displacement
B. velocity
c. acceleration
D. all of the above


For the formation of phosgene from
\( C O(g) \) and chlorine, \( C O(g)+ \)
\( C l_{2}(g) \longrightarrow C O C l_{2}(g), \) the
experimentally determined rate equation is, \( \frac{\boldsymbol{d}\left[\boldsymbol{C O C l}_{2}\right]}{\boldsymbol{d t}}= \)
\( \boldsymbol{k}[\boldsymbol{C O}]\left[\boldsymbol{C l}_{2}\right]^{3 / 2} \)
Is the following mechanism consistent with the rate equation?
\( (i) C l_{2} \rightleftharpoons 2 C l \quad \) (fast)
\( (i i) C l+C O \rightleftharpoons C O C l \)
\( (i i i) C O C l+C l_{2} \rightleftharpoons C O C l_{2}+C l \)
(slow)


Which of the following statement is
incorrect?
\( \mathbf{A} \cdot S O_{2}, \mathrm{CO}, \mathrm{Pb} \) and \( \mathrm{Hg} \) are pollutants
B. Methyl isocyanate and oil spills from ships are contaminants
C . Sea water is receptor for \( C O_{2} \)
D. Microorganisms is sink for dead animals and plants


Evaluate
\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}=\frac{\boldsymbol{e}^{\boldsymbol{x}} \boldsymbol{\operatorname { s i n }} \boldsymbol{x}}{\left(\boldsymbol{x}^{2}+\boldsymbol{2}\right)^{3}} \)


\( \frac{8}{6} \)


What is the function of enzyme
recombinase during meiosis
A. Formation of synaptonemal complex
B. Crossing over between nonsister chromatids
c. condensation of chromosomes
D. Alignment of bivalent chromosomes O equatorial plate


The Java man is considered to have
existed in
A. Java only
B. China only
c. Africa
D. Java and China


How many chlorine atoms are attached
to the carbon atom in chloral?
A . 1
B.
\( c \cdot 3 \)
\( D \)


Which of the following kingdoms is mismatched?
A. Protista - various modes of nutrition
B. Animalia - rarely ingestive
c. Plantae - usually photosynthetic
D. Fungi - usually saprotrophic


Which of the following changes will cause the free energy of the cell reaction to decrease:
\( \boldsymbol{Z} \boldsymbol{n}\left|\boldsymbol{Z n} \boldsymbol{S} \boldsymbol{O}_{4(\boldsymbol{a q})}(\boldsymbol{x}, \boldsymbol{M}) \| \boldsymbol{H} \boldsymbol{C l}_{(\boldsymbol{a q})}\left(\boldsymbol{x}_{\boldsymbol{2}} \boldsymbol{M}\right)\right| \boldsymbol{H} \)
This question has multiple correct options
\( 200 \mathrm{m} \)
B. Increase in pressure of hydrogen from 1 atm to 2 atm
c. Increase in molarity \( x_{2} \) from 0.1 to 1 M
D. Decrease in molarity \( x_{1} \) from 1 M to 0.1 M


The negative gradient of potential is
A. Electric force
B. Torque
C. Electric current
D. Electric field intensity


The active site of an enzyme is formed by
A. R group of aminoacids
B. Amino groups of aminoacids
c. coot group of aminoacids
D. Exposed sulfur bonds


The electric current is carried through the solution by:
A . acids
B. bases
\( c . \) ions
D. alkalis


The first organic pesticide to be used commercially was
A. Bordeaux mixture
B. Burgandy mixture
c. DDT
D. 2, \( 4- \) D


Calcination is the process of heating
the ore:
A. In inert gas
B. In the presence of air
c. In the absence of air or limited supply of air
D. In the presence of CaO and Mgo


The object distance \( u \) for a concave
mirror:
A. must be positive
B. must be negative
c. must not be negative
D. may be negative


Sodium hydroxide turns blue litmus red.
A . True
B. False


If \( P(A)=\frac{1}{3}, P(B)=\frac{1}{2} \) and \( A, B \) are
mutually exclusive, find \( \boldsymbol{P}\left(\boldsymbol{A}^{\prime} \cap \boldsymbol{B}^{\prime}\right) \)
A \( \cdot \frac{5}{6} \)
B.
\( c \cdot \frac{1}{5} \)
D.


The larger of two supplementary angles exceeds the smaller by 18 degrees. Find
them.


One side of a square field is 92 m. Find the cost of raising a lawn on the field at
the rate of \( R s .1 .50 \) per \( s q . m \)


Find \( \frac{\boldsymbol{r}_{\mathbf{1}}}{\boldsymbol{r}_{2}} \)
\( \mathbf{A} \cdot 2^{1 / 6} \)
B. \( \frac{1}{2^{1 / 6}} \)
\( \mathbf{C} \cdot 2^{1 / 12} \)
D. \( 2^{-1 / 12} \)


Subtract
75 from \( 98-25+4 \)
\( A \cdot 2 \)
B. 5
\( c \cdot-2 \)
D.


Calculate the volume of \( C O_{2} \) evolved by the combustion of \( 50 \mathrm{ml} \) of a mixture
contains \( C_{2} H_{4} \) and \( 60 \% C H_{4} \) (by
volume)


A particle oscillating under a force \( \overline{\boldsymbol{F}}= \) \( -k \bar{x}-b \bar{v} \) is a (k and b are constants)
A. simple harmonic oscillator
B. linear oscillator
c. damped oscillator
D. forced oscillator


\( \left(x^{2} y-2 x y^{2}\right) d x=\left(x^{3}-3 x^{2} y\right) d y \)
A \( \cdot k y^{3} e^{x / y}=x^{2} \)
B. \( k x^{3} e^{x / y}=x^{2} \)
c. \( k x^{3} e^{x / y}=y^{2} \)
D. \( k y^{3} e^{x / y}=y^{2} \)


The \( P E \) of a \( 2 k g \) particle, free to move along \( x \) -axis is given by \( V(x)= \) \( \left(\frac{x^{3}}{3}-\frac{x^{2}}{2}\right) J . \) The total mechanical energy of the particle is \( 4 J . \) Maximum
speed \( \left(\operatorname{in} m s^{-1}\right) \) is
A \( \cdot \frac{1}{\sqrt{2}} \)
B. \( \sqrt{2} \)
c. \( \frac{3}{\sqrt{2}} \)
D. \( \frac{5}{\sqrt{6}} \)


Find the second term of the binomial
expansion of \( \left(\sqrt[13]{\boldsymbol{a}}+\frac{\boldsymbol{a}}{\sqrt{\boldsymbol{a}^{-1}}}\right)^{m}, \) if \( \boldsymbol{C}_{3}^{\boldsymbol{m}} \)
\( C_{2}^{m}=4: 1 \)


In vertical circle, can the motion be uniform circular motion?
A. yes
B. no
c. sometimes
D. none of these


Multicellular jacketed female sex organ of bryophytes is
A. Archegonium
c. Ascogonium
D. Trichogyne


In an auditorium the big curtain when falls suddenly then the reverberation
time
A . increases
B. decreases
c. Remains same
D. becomes zero


The resistance \( R \) of a conductor varies
with the temperature as shown in the
figure. If it is written as \( \boldsymbol{R}_{1}=\boldsymbol{R}_{0}(\mathbf{1}+ \)
\( \left.\boldsymbol{\alpha} \boldsymbol{t}+\boldsymbol{\beta} \boldsymbol{t}^{2}\right) \)
A \( \cdot \alpha \) and \( \beta \) are both negative
B. \( \alpha \) is positive and \( \beta \) is negative
c. \( \alpha \) and \( \beta \) are both positive
D. \( \alpha \) is negative and \( \beta \) positive


An axon terminal passes the electrical
stimulus to a dendrite of next neuron
through reaction.
A. Chemical
B. Electrical
c. Mechanical
D. None of the above


An ore contains \( 1.34 \% \) of the mineral
argentite, \( A g_{2} S \) by mass. How many gram of this ore would have to be
processed in order to obtain \( 1.00 g \) of pure solid silver, \( \boldsymbol{A} \boldsymbol{g} \) ?
A. \( 74.6 g \)
в. \( 85.7 g \)
c. \( 107.9 g \)
D. \( 134.0 g \)


Instrument that used to measure small
electric currents ?
A. Pipette
B. Manometer
c. Balance
D. Calorimeter
E. Galvanometer


Hydrogen gas is obtained from:
A . petroleum
B. coal tar
c. natural gas
D. coke


Which of the following will function as
buffer?
This question has multiple correct options
A. \( N a C l+N a O H \)
B. Borax+boric acid
c. \( N a H_{2} P O_{4}+N a H P O_{4} \)
D. \( N H_{4} C l+N H_{4} O H \)


In the reaction \( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H}=\boldsymbol{C H}_{2} \frac{1 . \boldsymbol{H g}(\boldsymbol{O A c})_{2}, \boldsymbol{H}_{2} \boldsymbol{O}}{2 . N a B D_{4}} \)
the product obtained is:
\( \mathbf{A} \cdot \mathbf{C H}_{3} \mathbf{C H}_{2} \) СНОНСН \( _{2} \mathbf{D} \)
в. \( \mathrm{cH}_{3} \mathrm{CH}_{2} \mathrm{CHDCH}_{2} \mathrm{OH} \)
c. \( \mathrm{cH}_{3} \mathrm{CH}_{2} \mathrm{CD}(\mathrm{OH}) \mathrm{CH}_{3} \)
D. \( \mathrm{cH}_{3} \mathrm{CH}_{2} \mathrm{CD}_{2} \mathrm{CH}_{2} \) O


Find \( A \) and \( B \)


Write the IUPAC name of the follwoing compounds?
b)


Find the values of \( c \) that satisfy the
Rolle's theorem for integrals on [-2,1]
\( \boldsymbol{f}(\boldsymbol{t})=\boldsymbol{2} \boldsymbol{t}-\boldsymbol{t}^{3}-\boldsymbol{t}^{2} \)
This question has multiple correct options
\( ^{\mathrm{A}} \cdot_{c}=\frac{1+\sqrt{7}}{-3} \)
B. \( c=\frac{1-\sqrt{7}}{-3} \)
\( c_{c}=\frac{-1+\sqrt{7}}{-3} \)
D. \( c=\frac{-1-\sqrt{7}}{-3} \)


Two parallel lines \( l \) and \( m \) are cut by a
transversal \( t . \) If the interior angles of the
same side of \( t \) are \( (2 x-8)^{\circ} \) and \( (3 x- \)
7)\( ^{\circ}, \) find the measure of each of these
angles.


\( 2 x^{2}+y^{2}-8 x-2 y+1=0 \)
Find the square of the Latus Rectum for
the given ellipse.


Form the differential equation
representing the family of curves \( y^{2}= \)
\( m\left(a^{2}-x^{2}\right), \) where \( a \) and \( m \) are
parameters.


A circuit containing resistance \( \boldsymbol{R}_{1} \)
Inductance \( L_{1} \) and capacitance \( C_{1} \)
connected in series resonates at the
same frequency \( n \) as a
second combination of \( \boldsymbol{R}_{2}, \boldsymbol{L}_{2} \) and \( \boldsymbol{C}_{2} . \) If
the two are connected in series, then the circuit will resonate at:
A . \( n \)
B. \( 2 n \)
c. \( \sqrt{\frac{L_{2} C_{2}}{L_{1} C_{1}}} \)
D. \( \sqrt{\frac{L_{1} C_{1}}{L_{2} C_{2}}} \)


Which of the following complexes is/are correctly matched with their geometries? This question has multiple correct options
A \( \cdot\left[\mathrm{CoCl}_{4}\right]^{2-}- \) tetrahedral
B . \( \left[\mathrm{Co}\left(\mathrm{PMe}_{3}\right)_{4}\right]- \) tetrahedral
C \( \cdot\left[C u(C N)_{4}\right]^{3-}- \) tetrahedral
D. \( \left[F e(C O)_{4}\right]^{2-}- \) square planar


Give reasons for the following:
No gas is released when sulphur is added to dilute HCI.


Which one is not the chain-growth
polymer?
A. Natural rubber
B. Polythene
c. Polypropylene
D. Terylene


A radioactive nuclide X decays into nuclei Y and Z by simultaneous disintegration as shown.Effective decay constant for the disintegration is
\( A \cdot \lambda_{1}+\lambda_{2} \)
B. \( \frac{\lambda_{1} \lambda_{2}}{\lambda_{1}+\lambda_{2}} \)
\( c \cdot \frac{\lambda_{1}+\lambda_{2}}{2} \)
D. \( \frac{2 \lambda_{1} \lambda_{2}}{\lambda_{1}+\lambda_{2}} \)


A uniform disc of mass \( \mathrm{m} \) and radius \( \mathrm{R} \)
is projected horizontally with velocity \( v_{0} \) on a rough horizontal floor so that it starts off with a purely sliding motion at
\( t=0 . \) After \( t_{0} \) seconds it acquires a pure rolling motion. Calculate the velocity of
the centre of mass of the disc at \( t_{0} \)
A \( \cdot v=(2 / 4) v_{0} \)
B. \( v=(2 / 3) v_{0} \)
\( c \cdot v=(3 / 3) v_{0} \)
\( D \cdot v=(4 / 3) v_{0} \)


Assertion
nm is not same as mN
Reason
\( \ln m=10^{-9} m \operatorname{and} 1 m N=10^{-3} N \)
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


A uniform meter rule is pivoted at its mid-point. A weight of 50gf suspended
at one end of it. Where should a weight
of \( 100 g f \) be suspended to keep the rule horizontal:
A. At distance \( 50 \mathrm{cm} \) from the pivoted end.
B. At distance \( 12.5 \mathrm{cm} \) from the other end
c. At distance \( 37.5 \mathrm{cm} \) from the other end.
D. At distance \( 25 \mathrm{cm} \) from the pivoted end.


One of the following is wrong for
comparison between dicot and monocot
stem. In dicot stem
A. Vascular bundles are arranged in ring and in monocots they are scattered
B. Vascular bundles are oval and in monocots wedge shaped
C. True pith is present and absent in monocot stem
D. There is no protoxylem lacuna


The process of seeping of water into the ground is called:
A. transpiration
B. evaporation
c. infiltration
D. None of the above


A copper rod is suspended a nonhomogeneous magnetic field region. The rod when in equilibrium will align
itself:
A. in the region where magnetic field is strongest
B. in the region where magnetic field is weakest and parallel to direction of magnetic field there
C. in the direction in which it was originally suspended
D. in the region where magnetic field is weakest and perpendicular to the direction of magnetic field there


Which of the following is the correct set
of elements to Dobereiner's triads?
A. Li-7, Na - 23, K -39
B. Br-80, CI-35.5,1-127
c. Fe \( -55.85, \) Ni \( -58.71, \) Co -58.93
D. All of these


Find the degree of the expression \( \left[x+\left(x^{3}-1\right)^{\frac{1}{2}}\right]^{5}+\left[x-\left(x^{3}-1\right)^{\frac{1}{2}}\right]^{5} \)


If \( A B \) is tangent to the circle at \( A \) and
\( O B=13 \mathrm{cm}, \) find the radius \( O A \)
\( 4.5 \mathrm{cm} \)
\( 3.7 \mathrm{cm} \)
\( c \cdot 8 c m \)
)


A coin is tossed three times. Find
\( P(A / B) \) in given cases:
\( A= \) Heads on third tossed, \( B= \) Heads
on first two tosses


The A.M. of first n even natural number
is
A \( . n(n+1) \)
в. \( \frac{n+1}{2} \)
\( c \cdot \frac{n}{2} \)
D. \( n+1 \)


Which of the following materials which lack permanent magnetic dipoles?
A. diamagnetic
B. ferromagnetic
c. semimagnetic
D. none of the above


Which of the following pairs is obtained on heating ammonium dichromate?
A. \( N_{2} \) and \( H_{2} O \)
B. \( N_{2} O \) and \( H_{2} O \)
c. \( N O_{2} \) and \( H_{2} O \)
D. \( N O \) and \( N O_{2} \)


Specialised epidermal cells surrounding the guard cells are called
A. Lenticels
B. Complementary cells
c. subsidiary cells
D. Bulliform cells.


Protein-free fluid is filtered from blood
plasma into the Bowmans capsule.
A. True
B. False


The General solution for the equation \( (2 \sqrt{x y}-x) d y+y d x=0 \) is?
A \( \cdot y=c e^{-\sqrt{x / y} / y} \)
B \( \cdot y=c e^{\sqrt{y / x}} \)
C \( \cdot x=c e^{\sqrt{y / x}} \)
D. None of these


solve
\( 4 \frac{2}{10} \)


From lyman series of Pfund series, frequency
A. increase
B. decrease
c. increase or decrease
D. no change


The energy gap in a semiconductor
A. Increases with temperature
B. Does not change with temperature
C . Decreases with temperature
D. Is zero


The equilibrium constant for a reaction
\( N_{2}(g)+O_{2}(G)=2 N O(g) \) is \( 4 \times 10^{-4} \)
at \( 2000 \mathrm{K} . \) In the presence of catalyst, the equilibrium constant is attained 10 times faster. The equilibrium constant in the presence of catalyst, at \( 2000 \mathrm{K} \) is
\( \mathbf{A} \cdot 40 \times 10^{-4} \)
В. \( 4 \times 10^{-4} \)
C \( .4 \times 10^{-2} \)
D. incomplete data


Reshma wishes to mix two types of food \( P \) and \( Q \) in such a way that the
vitamin contents of the mixture contain
at least 8 units of vitamin \( A \) and
11 units of vitamin B. Food \( P \) costs
Rs. \( 60 / k g \) and Food \( Q \operatorname{costs} R s .80 / k g \)
Food \( P \) contains 3 units/kg of Vitamin
\( A \) and 5 units / kg of Vitamin \( B \) while
food \( Q \) contains 4 units/kg of Vitamin
\( A \) and 2 units / kg of vitamin \( B \) Determine the minimum cost of the
mixture.


A long solenoid has 200 turns per cm
and carries a current I. The magnetic field at its centre is \( 6.28 \times \)
\( 10^{-2} W b / m^{2} . \) Another long solenoid has
100 turns per \( \mathrm{cm} \) and it carries a
current i/3. The value of the magnetic
field at its centre is
A \( \cdot 1.05 \times 10^{-2} \mathrm{Wb} / \mathrm{m}^{2} \)
B . \( 1.05 \times 10^{-5} \mathrm{Wb} / \mathrm{m}^{2} \)
c. \( 1.05 \times 10^{-3} \mathrm{Wb} / \mathrm{m}^{2} \)
D. \( 1.05 \times 10^{-4} \mathrm{Wb} / \mathrm{m}^{2} \)


HeLa cells used for the study of cell division, are
A. Human skin cancer cells
B. Human uterine cancer cells
c. Human heart cells
D. Rat uterine cancer cells


The atomic radii of the elements across
the second period of ihe periodic table:
A. decrease due to increase inatomic number
B. decrease due to increase in effective nuclear charge
C. decrease due to increase in atomic weights
D. increase due to increase in the effective nuclear
charge


The most vast dicot family is
A. Fabaceae
B. Compositae
c. orchidaceae
D. Loranthaceae


Which of the following is used as \( \mathrm{S} \) I prefixes:
A . Micro
B. Mica
c. Mikro
D. Maca


Find the distance between the following pairs of point. \( \boldsymbol{P}(-\mathbf{5}, \mathbf{7}), \boldsymbol{Q}(-\mathbf{1}, \mathbf{3}) \)


In a triangle \( A B C \)
\( \boldsymbol{b} \cos (\boldsymbol{C}+\boldsymbol{\theta})+\boldsymbol{c} \cos (\boldsymbol{B}-\boldsymbol{\theta})= \)
A \( . a \cos \theta \)
B. \( a \sin \theta \)
c. \( a \tan \theta \)
D. a cot \( \theta \)


The type of bond formed between two electronegative atoms would be:
A . covalent
B. ionic
c. coordinate
D. all of these


Moist hydrogen peroxide cannot be
dried over conc. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) because:
A. it can catch fire
B. it is reduced by \( H_{2} S O_{4} \)
C . it is oxidised by \( H_{2} S O_{4} \)
D. it is decomposed by \( H_{2} S O_{4} \)


\( 25.3 g \) of sodium carbonate, \( N a_{2} C O_{3} \) is dissolved in enough water to make \( 250 m L \) of solution. If sodium cabonate
dissociates completely, molar
concentration of sodium ion, \( N a^{+} \) and
carbonate ion \( C O_{3}^{2-} \) are respectively:
(Molar mass of \( \boldsymbol{N} \boldsymbol{a}_{2} \boldsymbol{C} \boldsymbol{O}_{3}= \)
\( \left.106 g \quad m o l^{-1}\right) \)
A. \( 0.955 M \) and \( 1.910 M \)
в. \( 1.910 M \) and 0.955 М
c. \( 1.90 M \) and \( 1.910 M \)
D. \( 0.477 M \) and \( 0.477 M \)


The chemical formula of king of chemicals, sulphuric acid is :
A \( \cdot H_{2} S_{2} O_{3} \)
в. \( H_{2} S O_{3} \)
c. \( H S O_{4} \)
D. \( H_{2} S O_{4} \)


A circular coil of mean radius of \( 7 \mathrm{cm} \)
and having 4000 turns is rotated at the rate of 1800 revolutions per minute in
the earth's magnetic field \( (\mathrm{B}=\mathbf{0 . 5} \) gauss), the peak value of emf induced in coil will be?
A . \( 1.158 \mathrm{v} \)
B. \( 0.58 \mathrm{V} \)
c. \( 0.29 v \)
D. \( 5.8 v \)


The number of solutions of \( \cos x= \)
\( |1+\sin x|, 0 \leq x \leq 3 \pi, \) is
A. 3
B. 2
\( c \cdot 4 \)
D. none of these


The impedance of a pure anti-resonant
circuit at resonance is
A . zero
B. infinity
\( c \cdot 1 \)
D. \( \frac{1}{2} \)


A wheel is rotating with an angular speed 20 rad \( / \) s. It is stopped to rest by applying constant torque in \( 4 s \). If the moment of inertia of the wheel about is
axis is \( 0.20 k g / m^{2}, \) then the work done
by the torque in two seconds will be :
A . \( 10 J \)
B. \( 20 J \)
c. \( 30 J \)
D. \( 40 J \)


Assertion
No three consecutive binomial
coefficient can be in G.P. \& H.P.
Reason
Three consecutive binomial coefficients
are in A.P.
A. Both Assertion \& Reason are individually true \& Reason is correct explanation of Assertion,
B. Both Assertion \& Reason are individually true but Reason is not the correct (proper) explanation of Assertion,
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true


Which is a homopolysaccharide?
A. Pectin
B. Heparin
c. Hyaluronic acid
D. Inulin


An animal is taken to polar region. Which of the following adaptive characteristic may help it to survive in
the new environment?
A. Growth of thick and less hairy skin
B. Sharp beaks and strong claws
c. Growth of thick fur on its skin
D. Light weight wings to fly


Draw Venn diagrams to illustrate \( \boldsymbol{C} \cap \)
\( (B \backslash A) \)


Assertion
For an observer looking out through the window of a fast moving train, the
nearby objects appear to move in the opposite direction to the train, while the
distant objects appear to be stationary.
Reason
If the observer and the object are
moving at velocities \( \bar{V}_{1} \) and \( \bar{V}_{2} \)
respectively with reference to a laboratory frame the velocity of the
object with respect to the observer is \( \bar{V}_{2}-\bar{V}_{1} \)
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 area of the triangle formed by joining the mid point of the triangle whose vertices are (0,-1),(2,1) and (0,3)
Find the ratio of area of the triangle formed to the area of the given triangle.


Consider the given halogen-containing compounds:
The compounds with a net zero dipole
moment are:
\[
\text { I. } \mathrm{CHCl}_{3}
\]
II. \( \mathrm{CCl}_{4} \). \( \quad \) III. \( \mathrm{CH}_{2} \mathrm{Cl}_{2} \)
IV. \( \mathrm{CH}_{3} \mathrm{Cl} \)
v.
A. \( (I I),(V) \)
в. \( (I I I) \)
c. \( (I I I),(I V) \)
D. \( (I),(I V) \)
E. None


What is the IUPAC name of the above
compound?


Bird females have chromosome
arrangement as
A. \( x y \)
B. xo
\( c \cdot w z \)
D. ww


solve :
\( \frac{x^{2}-5 x+6}{|x|+7}<0 \) then \( x \epsilon(\alpha, \beta) \quad \alpha+\beta= \)


If \( \boldsymbol{x} \boldsymbol{y}+\boldsymbol{y}^{2}=\tan \boldsymbol{x}+\boldsymbol{y}, \) then \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \) is equa
to
A \( \frac{\sec ^{2} x-y}{(x+2 y-1)} \)
B. \( \frac{\cos ^{2} x+y}{(x+2 y-1)} \)
C \( \frac{\sec ^{2} x-y}{(2 x+y-1)} \)
D. \( \frac{\cos ^{2} x+y}{(2 x+2 y-1)} \)


Look at the given figure and suggest in
which of the vessels \( A, B, C \) or \( D \) the
rate of evaporation will be the highest? Explain


A coil of self inductance \( 10 m H \) and
resistance \( 0.1 \Omega \) is connected through a switch to a battery of internal resistance \( 0.9 \Omega \) After the switch is closed, the time taken for the current to attain \( 80 \% \) of the saturation value is :
(Take \( l n 5=1.6) \)
A . \( 0.103 s \)
B. \( 0.016 s \)
c. \( 0.002 s \)
D. \( 0.324 s \)


Show that \( |\vec{a}| \vec{b}+|\vec{b}| \vec{a} \) is perpendicular to \( |\vec{a}| \vec{b}-|\vec{b}| \vec{a}, \) for any two nonzero vectors \( \vec{a} \) and \( \vec{b} \)


The value of resistivity of super conductor is
A . zero
B. unity
c. infinity
D. none of these


Find the terminal velocity of a steel ball of diameter \( 0.2 \mathrm{cm} \) when it falls through
a tube filled with glycerin. \( \left(\boldsymbol{g}=\mathbf{9 . 8 m} / \boldsymbol{s}^{2}\right. \)
,density of steel \( =8000 k g / m 63 \)
,density of glycerin \( =1.33 g / c m^{3}, \eta= \)
8.33 poise \( =0.833 N s / m^{2} \)


Which of the following is a mixed acid anhydride :
A. Nitrogen (III) Oxide
B. Nitrogen (II) Oxide
c. Nitrogen (V) Oxide
D. Nitrogen (IV) Oxide


Find the value of \( \tan \frac{\mathbf{1 9} \pi}{\mathbf{3}} \)


Show that the differential equation \( x \frac{d y}{d x} \sin \frac{y}{x}+x-y \sin \frac{y}{x}=0 \) is
homogeneous. Find the particular solution of this differential equation given that \( x=1 \) when \( y=\frac{\pi}{2} \)


\( \lim _{x \rightarrow 0} \frac{\sin x^{0}}{x}= \)
\( \mathbf{A} \cdot \mathbf{1} \)
В . \( \frac{\pi}{180} \)
c. 180
D.


Huygen's concept of wavelets is useful
in
A. explaining polarisation
B. determining focal length of lenses
c. determining chromatic aberration
D. geometrical reconstruction of a wavefront


Among the following the compounds
which can undergo an \( S_{N} 1 \) reaction in
an aqueous solution, are:
A. I and IV only
B. II and IV only
c. Il and III only
D. II, III and IV only


An inventor claims to have developed an
engine that takes in \( 1000 J \) of heat and
produces \( 1500 J \) of work during each
cycle. Comment on the validity of this
claim.
A. The proposed engine claims to produce more work in a cyclic process than the amount of heat that is supplied, so it is in violation of the first law of thermodynamics.
B. The statement is completely valid as it increases the efficiency by increasing the work output.
C. The proposed engine claims to produce more work in a cyclic process than the amount of heat that is supplied, so it is in violation of the zeroth law of thermodynamics.
D. None of these


The curve \( y=a x^{3}+b x^{2}+c x+5 \)
touches the \( x \) -axis at \( P(-2,0) \) and
cuts the \( y \) -axis at a point \( Q, \) where its
gradient is \( 3 . \) Find \( a, b, c \)
A \( \cdot a=-\frac{1}{5}, b=1, c=3 \)
B. \( a=-\frac{1}{4}, b=-1, c=4 \)
c. \( _{a=-\frac{1}{4}, b=0, c=3} \)
D. \( a=-\frac{1}{3}, b=1, c=-3 \)


A metal M which is one of the best
conductor of heat and electricity used in making electric wires is found in the
nature as sulphide ore, \( M_{2} S \). Name the
metal M.
A. cu
B. Al
c. \( F e \)
D. Ag


toppr LoGin Jolv Now
0
Q Type your question
functions.
What is and
\( \begin{array}{lll}\text { Functions of } & \text { Functions of } \\ \text { growth promoters } & \begin{array}{l}\text { growth } \\ \text { inhibitors }\end{array} \\ \text { (a) } & \text { (i), (ii), (vii), (ix) } & \begin{array}{l}\text { (iii), (iv), (v), (vi), } \\ \text { (viii), (x) }\end{array} \\ \begin{array}{ll}\text { (b) } & \text { (viii), (ix), (x) } & \begin{array}{l}\text { (i), (ii), (ii)), (iv), } \\ \text { (v), (vi), (vii) }\end{array} \\ \text { (c) } & \begin{array}{l}\text { (i), (ii), (ii), (iv), (v), } \\ \text { (vi), (vii) }\end{array} & \text { (viii), (ix), (x) } \\ \text { (d) } & \begin{array}{l}\text { (i), (ii) (ii), (iv), (v), } \\ \text { (vi), (vii), (ix), (x) }\end{array} & \text { (viii) }\end{array}\end{array} \)


Equations of the two straight lines
passing through the point (3,2) and
making an angle of \( 45^{\circ} \) with the line
\( x-2 y=3, \) are
A. \( 3 x+y-7=0 \) and \( x+3 y+9=0 \)
B. \( 3 x-y-7=0 \) and \( x+3 y-9=0 \)
C \( . x+3 y-7=0 \) and \( x+3 y-9=0 \)
D. none of these


Prove
\[
\tan \Theta+\sec \theta=\frac{1}{\sec \Theta-\tan \Theta}
\]


Calcium bicarbonate in water makes it
permanently hard.
A. True
B. False


Name the three organelles involved in
photorespiration.


Diode can work as
A. Modulator
B. Demodulator
C. Rectifier
D. Amplifier


\( \int \frac{3 x^{2}}{x^{6}+1} d x \)
A \( \cdot \frac{1}{2} \tan ^{-1} x^{3} \)
B. \( \tan ^{-1} x^{3} \)
\( \mathbf{c} \cdot \tan ^{-1} x^{6} \)
D. \( \sec ^{-1} x^{3} \)


For two triangles, if one angle of a triangle is equal to one angle of the other triangle and the sides including these angles are proportional, then the two triangles are similar. This is called
similarity.
\( A \cdot A A A \)
B. SSS
c. sas
D. none of these


If \( \boldsymbol{y}=\frac{\boldsymbol{x}}{\boldsymbol{x}+\mathbf{1}}+\frac{\boldsymbol{x}+\mathbf{1}}{\boldsymbol{x}}, \) then \( \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}} \) at \( \boldsymbol{x}= \)
1 is equal to
\( A \cdot \frac{7}{4} \)
B. \( \frac{7}{8} \)
\( c \cdot \frac{1}{4} \)
D. \( \frac{-7}{8} \)
E \( \frac{-7}{4} \)


Without doing any actual division, find which of the following rational numbers have terminating decimal representation:
(i) \( \frac{7}{16} \)
(ii) \( \frac{23}{125} \)
(iii) \( \frac{\mathbf{9}}{\mathbf{1 4}} \)
(iv) \( \frac{32}{45} \)
\( (v) \frac{43}{50} \)
(vi) \( \frac{17}{40} \)
(vii) \( \frac{61}{75}(\text { viii }) \frac{123}{250} \)
A \( . \) (i), (iii), (v), (vi) and (vii)
B. (i), (ii), (v), (vi) and (viii)
C . (i), (iii), (v), (vi) and (viii)
D. (i), (ii), (v), (vi) and (vii)


\( S O_{2} \) can act as both oxidant and
reductant.


At STP, a container has 1 mole of \( A r, 2 \)
moles of \( C O_{2}, 3 \) moles of \( O_{2} \) and 4
moles of \( N_{2} . \) Without changing the total
pressure of \( \boldsymbol{O}_{2} \) is removed, the partial
pressure of \( \boldsymbol{O}_{2} \) is:
A. changed by about \( 16 \% \)
B. halvedd
c. changed by \( 26 \% \)
D. unchanged.


The unit of ebullioscopic constant is?
A . \( K \) kg mol \( ^{-1} \) or \( K(\text { molality })^{-1} \)
B . mol kg \( K^{-1} \) or \( K^{-1} \) (molality)
c. \( k g \) mol \( ^{-1} K^{-1} \) or \( K^{-1} \) (molality) \( ^{-1} \)
D. \( K \) mol \( k g^{-1} \) or \( K(\text { molality }) \)


Which of the following term can be related to the opening of guard cell?
A. Turgidity
B. Flaccidity
c. Transpiration
D. None of the above