Which of the following ions having following electronic structure would have maximum magnetic moment?
A \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 3 d^{3} \)
B . \( 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 3 d^{5} \)
\( \mathbf{c} \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 3 d^{7} \)
D \cdot \( 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 3 d^{9} \)


Find the direction cosines of vector \( \vec{r} \)
which is equally inclined to \( O X, O Y \)
and \( O Z \). Find total number of such
vectors.
A \( \cdot \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}} ; 6 \)
B. \( \frac{1}{\sqrt{3}}, \pm \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}} ; 8 \)
\( ^{\mathbf{C}} \pm \frac{1}{\sqrt{3}}, \pm \frac{1}{\sqrt{3}}, \pm \frac{1}{\sqrt{3}} ; 8 \)
D. None of these


Why covalent character of lithium
halides follow the following order? \( \boldsymbol{L} \boldsymbol{i} \boldsymbol{I}>\boldsymbol{L} \boldsymbol{i} \boldsymbol{B} \boldsymbol{r}>\boldsymbol{L} \boldsymbol{i} \boldsymbol{C l}>\boldsymbol{L} \boldsymbol{i} \boldsymbol{F} \)


Foe the electrochemical cell:
\[
\begin{array}{c}
\boldsymbol{Z} \boldsymbol{n}(\boldsymbol{s}) \mid \boldsymbol{Z} \boldsymbol{n}^{2+}(\boldsymbol{a} \boldsymbol{q}) \| \\
\boldsymbol{C l}^{-}(\boldsymbol{a} \boldsymbol{q})\left|\boldsymbol{C l}_{2}(\boldsymbol{g})\right| \boldsymbol{P} \boldsymbol{t}(\boldsymbol{s}) \\
\text { Given }: \boldsymbol{E}_{\boldsymbol{Z n}^{2+} / Z \boldsymbol{n}}^{o}=-\mathbf{0 . 7 6} \boldsymbol{V} \boldsymbol{o l t} \\
\boldsymbol{E}_{\boldsymbol{C l}^{\prime} / \boldsymbol{C l}_{2}(\boldsymbol{g})}=-\mathbf{1 . 3 6} \boldsymbol{V} \boldsymbol{o l t} \boldsymbol{t}
\end{array}
\]
From these data one can deduce that:
A \( \cdot Z n+C l_{2} \rightleftharpoons Z n^{2+}+2 C l^{-} \) is a non-spontaneous
reaction at standard conditions
B . \( Z n^{2+}+2 C l^{-} \rightleftharpoons C l_{2}+Z n \) is a spontaneous reaction at
standard conditions with \( E_{c e l l}^{o}=2.12 \) volt.
C. \( Z n+C l_{2} \longrightarrow Z n^{2+}+2 C l^{-} \) is a spontaneous reaction
at standard conditions with \( E_{c e l l}^{o}=2.12 \) volt.
D. \( Z n+C l_{2} \longrightarrow Z n^{2+}+2 C l^{-} \) is a spontaneous reaction
at standard conditions with \( E_{c e l l}^{o}=0.60 \) volt.


The mechanism of the reaction
\( \mathbf{2} N \boldsymbol{O}+\boldsymbol{O}_{2} \rightarrow \mathbf{2} \boldsymbol{N} \boldsymbol{O}_{2} \) is:
\( N O+N O \underset{k_{-1}}{\Gamma} N_{2} O_{2}(\text { fast }) ; N_{2} O_{2}+ \)
\( O_{2} \stackrel{k_{2}}{\longrightarrow} 2 N O_{2}(s l o w) \)
The rate constant of the reaction is :
\( A \cdot(A) k_{2} \)
B . (В) \( k_{2} k_{1}\left(k_{-1}\right) \)
c. (с) \( k_{2} k \)
D.
(D) \( k_{2}\left(\frac{k_{1}}{k_{-1}}\right) \)


In the hydrogen atom, the energy difference between the states \( n=2 \) and
\( n=3 \) is \( \mathrm{E} \) eV. The ionisation potential of \( \mathrm{H} \)
atom is:
A. 3.2
в. 5.6 Е
\( c \cdot 7.2 E \)
D. 13.2 E


A wave travels out in all directions from
a point source. Justify the expression \( \boldsymbol{y}=\left(\boldsymbol{a}_{0} / \boldsymbol{r}\right) \sin \boldsymbol{k}(\boldsymbol{r}-\boldsymbol{v} \boldsymbol{t}), \) at a distance
from the source. Find the speed,
periodicity and intensity of the wave.


The expansion of an ideal gas of mass \( \mathrm{m} \) at a constant pressure \( \mathrm{P} \) is given by
the straight line B. Then, the expanasion of the same ideal gas of mass \( 2 \mathrm{m} \) at a
pressure \( 2 P \) is given by the straight line
A.
B. A
\( c \cdot B \)
D. data insufficient


A square is placed with its centre at origin and having sides parallel to \( x \) and
\( y- \) axes. It has surface charge density
\( \sigma(x, y)=\sigma_{0} x y \) within its boundaries.
The charge of each side of square is \( Q \)
The total charge on the square is:
A \( \cdot 2 \sigma_{0} Q^{2} \)
в. \( 4 \sigma_{0} Q^{3} \)
c. \( \sigma_{0} Q^{2} \)
D. zero


I ne rectangular wıre trame, shown In
the figure has a width d, mass \( m \)
resistance \( R \) and a large length. \( A \) uniform magnetic field B exists to the left of the frame. A constant force \( F \)
starts pushing the frame into the
magnetic field at \( t=0 \)
(a)Find the acceleration of the frame
when its speed has increased to
(b how that after some time the frame
will move with a constant velocity till the whole frame enters into the
magnetic field. Find the velocity \( v_{0} \)
(c) Show that the velocity at time t is given byv \( =\boldsymbol{v}_{0}\left(\mathbf{1}-\boldsymbol{e}^{\frac{-F t}{m v_{0}}}\right) \)
\[
\begin{array}{ll}
x & x \\
x & x \\
x & x \\
x & x \\
x & x
\end{array}
\]


The ratio of number of lone pairs in
\( N H_{3}, H_{2} O \) and \( X e F_{2} \) is :
A .3: 2: 1
B. 2: 1: 3
\( \mathrm{c} \cdot 1: 2: 3 \)
D. 2: 3: 1


Assertion
Assertion: Liquids \( I F_{5} \) conducts
electricity
Reason
Reason: Liquid \( I F_{5} \) self ionizes as,
\( 2 I F_{5} \rightleftharpoons I F_{4}^{+}+I F_{6}^{-} \)
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


PAHs can break down by reacting with sunlight and other chemicals in the air over a period of days to weeks.
A. True
B. False


The weight of a body at the centre of the earth is
A. zero
B. Equal to its mass
c. Maximum
D. Infinite


Distinguish between 'intrinsic' and
extrinsic' semiconductors.


R.Q. is more than one in which of the
following case?
A. Fat
B. Fructose
c. Glucose
D. organic acid


toppr
Q Type your question_
\( \mathbf{A} \)
\( B \)
\( c \)
\( (c) \)
\( D \)


Predict if the solutions of the following salts are neutral, acidic or basic.
\( N a C l, K B r, N a C N, N H_{4} N O_{3}, N a \)
and \( \boldsymbol{K} \boldsymbol{F} \)


\( P \) is a point in the interior of \( a \)
parallelogram \( A B C D . \) Show that
\( \boldsymbol{a r}(\triangle \boldsymbol{A P B})+\boldsymbol{a r}(\triangle \boldsymbol{P C D})= \)
\( \frac{1}{2} a r(A B C D) \)


Teritary alcohol is obtained as major
product in
\( \mathbf{A} \cdot\left(C H_{3}\right)_{2} C H-C H=C H_{2}^{\text {oxymercution/demercution}} \)
\( \mathbf{B} \cdot\left(C H_{3}\right)_{3} C-C H=C H_{2} \stackrel{d i l H_{2} S O_{4}}{\longrightarrow} \)
\( \mathbf{C} \cdot\left(C H_{3}\right)_{2} C H-C H=C H_{2}^{H y d r o b o r a t i o n, O x i d a t i o n} \)
D. All of the above


An electric dipole of moment \( \vec{p} \) is placed normal to the lines of force of electric intensity \( \vec{E} \), then work done in
deflecting it through an angle of \( 180^{\circ} \) is:
A \( . p E \)
в. \( +2 p E \)
c. \( -2 p E \)
D. zero


0.0833 moles of the carbohydrate contain 1.0 g hydrogen. If the molecular
formula of the carbohydrate is \( C_{x} H_{y} O_{z} \) then the value of \( x, y \) and \( z \) are :
A. \( x=6, y=12, z=6 \)
в. \( x=4, y=8, z=4 \)
c. \( x=5, y=10, z=6 \)
D. none of these


Write electronic configurations of the Sodium.


Two liquids of specific heat ratio 1: 2
are at temperature \( 2 \theta \) and \( \theta \)
This question has multiple correct options
A. if equal amounts of them are mixed, then temperature of mixture is 1.56
B. if equal amounts of them are mixed,then temperature is \( \frac{4}{3} \theta \)
C. for their equal amounts, the ratio of heat capacities is 1: 1
D. For their equal amounts, the ratio of their heat capacities is 1: 2


Compound formed by \( s p^{3} d^{-} \) hybridization will have which of the following structure?
A. Trigonal bipyramidal
B. T-shaped
c. Linear
D. Either of these depending on the number of lone pair of electrons on central atom


A particle executing SHM has a
maximum speed of \( 30 \mathrm{cm} s^{-1} \) and a
maximum acceleration of \( 60 \mathrm{cms}^{-2} \). The
period of oscillation is:
A . \( \pi \)
в. \( \frac{\pi}{2} s \)
c. \( 2 \pi \)
D. \( \frac{2 \pi}{15} \)


Assertion
Millon's test is a test for identification
of proteins.
Reason Millon's reagent is a solution of mercurous nitrate and mercuric nitrate
in nitric acid containing little nitrous
acid.
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


Statement 1: Substances with hydrogen
bonding tend to have unusually low boiling points. Statement 2: Extra energy is necessary to break the hydrogen bonds.
A. Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation of Statement 1
B. Both the Statement 1 and Statement 2 are correct, but Statement 2 is not the correct explanation of Statement 1.
c. statement 1 is correct, but statement 2 is not correct
D. Statement 1 is not correct, but Statement 2 is correct


Plants exchange water with environment through structures by two cells
A . Lenticles
B. Hydathodes
c. Stomata
D. All the above


Assertion
In Rutherford's gold leaf experiment, most of the \( \alpha \) particles passed through the foil
Reason
The entire positive charge and nearly all of the mass of an atom is concentrated
in the nucleus
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A class has three teachers Mr. X, Ms. Y
and Mrs. Z and six students
\( A, B, C, D, E, F . \) Number of ways in
which they can be seated in a line of 9
chairs, If bwteen any two teachers there are exactly two students, is
A. \( 18(6 !) \)
в. \( 12(6 !) \)
c. \( 24(6 !) \)
D. \( 6(6 !) \)


A freely falling body converts:
A. kinetic energy into potential energy
B. potential energy into kinetic energy
C. chemical energy into kinetic energy
D. potential energy into chemical energy


\( P \) is any point inside the triangle \( A B C \)
Hence \( \angle B P C>\angle B A C \)
A. True
B. False
c. Ambiguous
D. Data insufficient


A metallic calorimeter of mass 100 g
contains 200 g of ice and the initial temperature of the calorimeter and the
ice is \( -10^{\circ} \mathrm{C} . \) Heat is supplied to the system containing calorimeter and ice
at a constant rate of 50 cals\( ^{-1} \). Find the
time required to raise the temperature
of the system to \( 50^{\circ} \mathrm{C} \). [Neglect the loss of heat to the surroundings]. Take specific heat capacity of calorimeter and ice as \( 0.2 c a l g^{-1 \circ} C^{-1} \) and \( \frac{1}{2} c a l g^{-1 \circ} C^{-1} \).Take latent heat of
fusion of ice as \( 80 \mathrm{calg}^{-1} \) and specific
heat capacity of water as 1 calg\( ^{-1 \circ} C^{-1} \)


Assertion
Ultrasonic waves are longitudinal
waves of frequency greater than 20,000 \( \mathrm{Hz} \)
Reason
The maximum frequency of audible sound waves is \( 20,000 \mathrm{Hz} \)
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


When water is added to \( H_{2} S O_{4}, \) the
reaction is exothermic. It is because of
formation of:
A. viscous nature of \( H_{2} S O_{4} \)
B. hydrates of \( H_{2} S O_{4} \)
c. corrosive nature of \( H_{2} S O_{4} \)
D. none of the above


Os Innominatum consist of
A. Pubis
B. Ischium
c. llium
D. All of the above


Which of the following factors affects
friction?
A. Nature of the surface
B. Weight of object placed over other
C. Amount of surface area in contact between the moving bodies
D. Both A and B


Two waves having same velocity enter electric and magnetic fields
respectively. If \( \lambda_{1} \) and \( \lambda_{2} \) are
their wavelengths as they move in the
fields, then
A \( \cdot \lambda_{1}, \lambda_{2} \) are constants
B. \( \lambda_{1} \) and \( \lambda_{2} \) are variable
c. \( \lambda_{1} \) is variable \( \lambda_{2} \) is constant
D. \( \lambda_{2} \) is variable, \( \lambda_{1} \) is constant


Prove that \( \frac{\sin x-\sin 3 x}{\sin ^{2} x-\cos ^{2} x}=2 \sin x \)


Number of lone pairs of electrons on Xe
atoms \( \mathrm{XeF}_{2}, \mathrm{XeF}_{4} \) and \( \mathrm{XeF}_{6} \)
molecules are respectively.
A. 3,2 and 1
B. 4,3 and 2
c. 2,3 and 1
D. 3,2 and 0


If the amplitude of waves at a distance
\( 10 \mathrm{cm} \) from a point source is \( A, \) the
amplitude at a distance \( 40 \mathrm{cm} \) will be
A. \( A / 2 \)
в. \( A / 4 \)
\( c . A \)
D. \( 2 A \)


If \( \sin ^{-1} x=\frac{\pi}{5}, \) for some \( x \in(-1,1) \)
then find the value of \( \cos ^{-1} x \)
A. \( -\frac{3 \pi}{10} \)
в. \( \frac{3 \pi}{10} \)
c. \( -\frac{7 \pi}{10} \)
D. \( \frac{7 \pi}{10} \)


\( \cot B=2 \tan (A-B)=>2 \tan B+ \)
\( \cot B \) is equal to
\( \mathbf{A} \cdot \tan A \)
B. \( \cot A \)
\( c \cdot 2 \tan A \)
D. \( 2 \cot A \)


A quantity of \( 1 g \) of metallic carbonate
\( X C O_{3} \) is completely converted into a
chloride. \( \boldsymbol{X} \boldsymbol{C l}_{2} \) weighing \( 1.11 g \). The
atomic mass of the element ' \( \boldsymbol{X}^{\prime} \) is
A . 10
B. 20
c. 30
D. 40


A planoconvex lens fits exactly into a planoconcave lens. Their plane surface are parallel to each other. If the lenses are made of different materials of
refractive indices \( \mu_{1} \) and \( \mu_{2} \) and \( R \) is
the radius of curvature of the curved
surface of the lenses, then focal length of combination is
A \( \cdot \frac{R}{\mu_{1}-\mu_{2}} \)
В. \( \frac{2 R}{\mu_{1}-\mu_{2}} \)
c. \( \frac{R}{2\left(\mu_{1}-\mu_{2}\right)} \)
D. \( \frac{R}{2-\left(\mu_{1}-\mu_{2}\right)} \)


State the following statement is True or False
Arithmetic mean of first five natural
numbers is 3
A . True
B. False


The pH of blood stream is maintained
by a proper balance of \( \boldsymbol{H}_{2} \boldsymbol{C O}_{3} \) and
\( N a H C O_{3} \) concentrations. What
volume of \( 5 M N a H C O_{3} \) solution
should be mixed with a \( 10 m L \) sample
of blood which is \( 2 M \) in \( H_{2} C O_{3} \) in
blood is \( 7.8 \times 10^{-7} ? \)


Find the least number which must be
added to the following number so as to get a perfect square:
6412
A .52
в. 149
\( c .63 \)
D. 112


What do you mean by noble metals?


\( \int \frac{1}{\left(x^{6}-1\right)} d x \)
A \( \cdot 1 / 2\left(\frac{1}{6} \ln \frac{(x-1)^{2}}{x^{2}+x+1}-\frac{1}{\sqrt{3}} \arctan \frac{2 x+1}{\sqrt{3}}-\frac{1}{6} \ln \frac{(x+1)^{2}}{x^{2}-x+1}-\right. \)
\( \left.\quad \frac{1}{\sqrt{3}} \arctan \frac{2 x-1}{\sqrt{3}}\right)+\mathrm{k} \)
B \( \cdot \)
\[
\begin{array}{l}\text { C } \mid / 2\left(\frac{1}{6} \ln \frac{(x+1)^{2}}{x^{2}-x+1}-\frac{1}{\sqrt{3}} \arctan \frac{2 x-1}{\sqrt{3}}-\frac{1}{6} \ln \frac{(x-1)^{2}}{x^{2}+x+1}-\right. \\ \left.\frac{1}{\sqrt{3}} \arctan \frac{2 x+1}{\sqrt{3}}\right)+\mathrm{k}\end{array}
\]
C \( \cdot 1 / 2\left(\frac{1}{6} \ln \frac{(x-1)^{2}}{x^{2}+x+1}-\frac{1}{\sqrt{3}} \operatorname{arccot} \frac{2 x+1}{\sqrt{3}}+\frac{1}{6} \ln \frac{(x+1)^{2}}{x^{2}-x+1}+\right. \)
\( \left.\frac{1}{\sqrt{3}} \operatorname{arccot} \frac{2 x-1}{\sqrt{3}}\right)+\mathrm{k} \)
D \( \cdot 1 / 2\left(\frac{1}{6} \ln \frac{(x-1)^{2}}{x^{2}+x+1}-\frac{1}{\sqrt{3}} \operatorname{arccot} \frac{2 x+1}{\sqrt{3}}-\frac{1}{6} \ln \frac{(x+1)^{2}}{x^{2}-x+1}-\right. \)
\( \left.\frac{1}{\sqrt{3}} \operatorname{arccot} \frac{2 x-1}{\sqrt{3}}\right)+\mathrm{k} \)


Fill in the blanks with suitable word:
All green plants are


The A.M. between two positive numbers
exceeds the GM by \( 5, \) and Gm exceed
the H.M. by 4. Then the numbers are
A .10,40
B. 10,20
c. 20,40
D. 10,50


A mass of \( 10 \mathrm{kg} \) is suspended vertically by a rope from the roof. when a horizontal force is applied on the rope at same points, the rope deviated at an
angle of \( 45^{0} \) at the roof point. if the
suspended mass is at equilibrium, the
magnitude of the force applied is \( (g= \)
\( \left.10 m s^{-2}\right) \)
A . 200 N
B. 100 N
c. 70
D. 140 N


An object is placed \( 50 \mathrm{cm} \) from a screen
as shown.

A converging lens is moved such that
line \( M N \) is its principal axis. Sharp
images are formed on the screen in two
positions of lens separated by \( 30 \mathrm{cm} \) Find the focal length of the lens in \( \mathrm{cm} \)


Answer the following question in one
word or one sentence or as per exact
requirement of the question. If \( \boldsymbol{f}(\boldsymbol{x})=|\boldsymbol{x}|+|\boldsymbol{x}-\mathbf{1}|, \) write the value of
\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}(\boldsymbol{f}(\boldsymbol{x})) \)


A bubble rises from the bottom of a lake,
90m deep. On reaching the surface, its volume becomes(take atmospheric pressure equals to \( 10 \mathrm{m} \) of water
A. 4 times
B. 8 times
c. 10 times
D. 3 times


If \( n \) is a positive integer and \( (5 \sqrt{5}+ \)
\( \mathbf{1 1})^{2 n+1}=I+f \) where I is an integer
and \( 0<f<1 \) then
This question has multiple correct options
A. I is an even integer
B. \( (I+f)^{2} \) is divisible by \( 2^{2 n+1} \)
c. lis divisible by 22
D. None of these


Why acquired characters are not
inherited?
A. Acquired characters do not produce change in the DNA of germ cells.
B. Acquired characters produce change in the DNA of germ cells.
C. Acquired characters do not produce change in the DNA of somatic cells.
D. All of the above.


Which type of relation does a fungus has with alga in lichens?
A. Epiphytic
B. Parasitic
c. symbiotic
D. Saprophytic


Photosynthesis (nourishment in light) was discovered by
A. Stephan Hales
B. Priestley
c. Ingenhousz
D. Van Mayer


Water is not used as a barometric
liquid because
A. it is difficult to have a barometer tube 11 m long
B. water vaporises under vacuum conditions
c. water sticks to the side of glass tube.
D. all the above


A random variable \( X \) has the following
probability distribution:
\[
\begin{array}{cccccc}
\boldsymbol{X} & \mathbf{1} & \mathbf{2} & \mathbf{3} & \mathbf{4} & \mathbf{5} \\
\hline P(X) & k^{2} & 2 k & k & 2 k & 5
\end{array}
\]
\[
5 k^{2}
\]
Then \( P(X>2) \) is equal to
\( \mathbf{A} \cdot \frac{1}{6} \)
B. \( \frac{7}{12} \)
c. \( \frac{1}{36} \)
D. \( \frac{23}{36} \)


A solenoid of length \( 0.4 m \) and diameter
\( 0.6 m \) consists of a single layer of 1000
turns of fine wire carrying a current of
\( \mathbf{5} \times \mathbf{1 0}^{-\mathbf{3}} \) A. Calculate the magnetic
field on the axis at the middle and at
the end of the solenoid:
A \( \cdot 8.7 \times 10^{-6} T, 6.28 \times 10^{-6} T \)
B . \( 6.28 \times 10^{-6} T, 8.7 \times 10^{-6} T \)
D. \( 8.7 \times 10^{-6} T, 8.28 \times 10^{-6} T \)


The cut part of sphere is coated outside with silver or similar material. What
kind of mirror does it form?
A. Convex mirror
B. Concave mirror
c. Plane mirror
D. None


A single wave is called
A. a wave pulse
B. a crest
c. a trough
D. a crest and a trough


Solve:
\( \int \frac{x^{2}+1}{x^{2}-4 x+6} d x \)


In Millikan's oil drop experiment, the charge of three oil drops \( X, Y, \) and \( Z \) have been found to be 2,0.04 and 0.8 respectively. What could be the probable charge of an electron and the number of electrons attached to these
oil drops?
A. \( 0.04 \mathrm{C}, 50,1,20 \)
B. \( 0.04 \mathrm{C}, 50,2,20 \)
c. \( 0.8 c, \) २०, 15, 50
D. 0.8, 1, 50, 23


Choose the correct answers from the
alternatives given. An example of selectively permeable membrane is
A. Plasmalemma
B. Cell wall
c. chloroplast membrane
D. Mitochondrial membrane


Spring wood (early wood) differs with autumn wood (late wood) in
A. Size of vessels and tracheids
B. Thickness of cell wall
c. Amount of wood
D. All the above


A narrow monochromatic beam of light
of intensity \( I \) is incident on a glass plate as shown in figure. Another identical glass plate is kept close to the first one and parallel to it. Each glass plate reflects \( 25 \% \) of the light incident on it and transmits the remaining. Find the ratio \( \sqrt{\frac{\boldsymbol{I}_{m a x}}{\boldsymbol{I}_{m i n}}} \) the interference
pattern formed by two beams obtained after one reflection at each plate.


Which scientist is most famous for his
work on the quantum physics along side with Albert Einstein?
A. Meghnad Saha
B. S.S. Abhyankar
c. Satyendra Nath Bose
D. Vikram Sarabhai


What is photophosphorylation? Distinguish between cyclic and noncyclic photophosphorylation. Give schematic sketches of both.


\( \frac{k}{k} \)


The cork cambium, cork and secondary
cortex are collectively called as
A. Phellem
B. Phelloderm
c. Phellogen
D. Periderm


If \( \vec{a} \) and \( \vec{b} \) are two unit vectors such that \( \vec{a}+2 \vec{b} \) and \( 5 \vec{a}-4 \vec{b} \) are perpendicular
to each other then the angle between \( \vec{a} \) and \( \vec{b} \) is
A . 45
B. \( 60^{\circ} \)
\( ^{\mathbf{c}} \cdot \cos ^{-1}\left(\frac{1}{3}\right) \)
D. \( \cos ^{-1}\left(\frac{2}{7}\right) \)


A step-up transformer works on \( 220 \mathrm{V} \) and gives 2 A to an external resistor. The
ratio of the number of turns between the
primary and secondary coils is 2: 25 Assuming \( 100 \% \) efficiency, find the secondary voltage, primary current and power delivered
A . 2750 \( \vee, \) 25 \( A, 5500 W \)
B. 2750 V, 20 A, 5000 W
c. 2570 V, 25 A, 550
D. 2750 V, 20 A, 55 W


What is the side product of soap industry?
A. Sodium Hydroxide
B. Esters
c. Ethanol
D. Glycerol


To measure
This question has multiple correct options
A. you will measure the potential drop across resistor till it is minimum on varying frequency
B. you will measure the voltage across \( L \) and \( C \) at various frequencies until \( V_{L}=V_{D} \)
C. you will measure the voltage across L and C at various frequencies until \( V_{L}=V_{C} \)
D. you will measure voltage across L until is minimum at a particular frequency


An ionic compound is a poor conductor
of electricity because:
A. ions do not conduct electricity
B. charge on the ions is uniformly distributed
C. ions occupy fixed positions in solids
D. ions have uniform field


Which of the following side chain reaction/s can be used to reduce the
activity of strongly activating groups like \( O H ? \)
A. Benzoylation
B. Acetylation
c. both A and B
D. none of the above


\( C O_{2} \) acceptor in \( C_{3} \) plants is
A. Xylulose-5-phosphate
B. 3-phosphoglyceric acid
c. Ribulose 1,5 -biphosphate
D. Phosphoenol pyruvic acid


Give the oxidation state of underlined.
\( N H 4 N O_{3} \)


Choose the correct answer from the
alternatives given

Closing of stomata are induced by:
A. axing
B. boxing
c. abscise acid
D. indole 3-acetic acid


A mechanical machine which is used to
lift or compress large loads.
A. hydraulic press
B. hydraulic lifts
c. hydraulic brakes
D. none


In racemic mixtures \( D \) -forms do not
exist.
A. True
B. False


When a transverse plane wave traverses a medium, individual particles execute periodic motion given by the equation \( \boldsymbol{y}=\mathbf{0 . 2 5} \cos (\mathbf{2} \boldsymbol{\pi} \boldsymbol{t}-\boldsymbol{\pi} \boldsymbol{x}) . \) The phase
difference for two position of same particle which are occupied by time intervals 0.4 second apart is


A charged \( 30 \mu \mathrm{F} \) capacitor is connected
to a \( 27 \mathrm{mH} \) inductor. What is the
angular frequency of free oscillations of the circuit?


The velocity-time graph for a body with non-uniform motion (assume non-
constant acceleration) is a:
A. straight line making some angle with the positive \( x \) axis.
B. straight line parallel to x-axis.
c. straight line parallel to y-axis
D. curved line


\( f f(x)=\left\{\begin{array}{ll}\frac{x-|x|}{x}, & x \neq 0 \\ 2, & x=0\end{array} \) show \right.
that \( \lim f(x) \) does not exist


Fill up the blanks.
When \( _{6} C^{14} \) isotope undergoes \( \beta \) -decay the resulting new element is


A radioactive nucleus has specific
binding energy' \( E_{1} \) '. It emits an \( \alpha \) particle. The resulting nucleus has
specific binding energy' \( E_{2} \) '. Then
A \( \cdot E_{2}=E_{1} \)
в. \( E_{2}<E_{1} \)
c. \( E_{2}>E_{1} \)
D. \( E_{2}=0 \)


Find \( \boldsymbol{x}+\boldsymbol{y}+\boldsymbol{z} \)
A \( \cdot x+y+z=180 \)
в. \( x+y+z=360^{\circ} \)
c. \( x+y+z=480^{\circ} \)
D. \( x+y+z=540 \)


Which is polymeric hydride?
A. \( C a H_{2} \)
в. \( M g H_{2} \)
\( \mathbf{c} \cdot B a H_{2} \)
D. \( \operatorname{SrH}_{2} \)


the net displacement and distance
travelled by the bolt, with respect to earth. (Take \( \left.g=9.8 m / s^{2}\right) \)


The ringing of an electric bell in an enclosed evacuated glass bell jar is not heard outside because


Solve: \( \boldsymbol{y}^{\prime}=\frac{\mathbf{3} \boldsymbol{x}-\boldsymbol{y}}{\boldsymbol{x}+\boldsymbol{y}} \)
\( \mathbf{A} \cdot(3 x+y)(x-y)=c_{0} \)
B \( \cdot(3 x-y)(x+y)=c_{0} \)
\( \mathbf{c} \cdot(x-3 y)(3 x+y)=c_{0} \)
\( \mathbf{D} \cdot(x+3 y)(x-y)=c_{0} \)


A paper weight is dropped from the roof of a block of multistorey flats, each storey being 3 meters high. It passes the ceiling of the \( 20^{t h} \) storey at \( 30 m / s \)
If \( g=10 m / s^{2}, \) how many storey
does the flat have?
A . 25
B. 30
c. 35
D. 40


Explain cumene process for the preparation of phenol or How would you prepare phenol from cumene?


The \( r m s \) value of conduction current
will be:
\( \mathbf{A} \cdot 5.7 \mu A \)
в. \( 6.3 \mu A \)
\( \mathrm{c} .9 .6 \mu A \)
D. \( 6.9 \mu A \)


The value of \( \lim _{x \rightarrow \infty}\left(x \sin \left(\frac{3}{x}\right)\right) \)


\( (\overline{\mathbf{A}}+\overline{\mathbf{B}}) \times(\overline{\mathbf{A}}-\overline{\mathbf{B}}) \) is:
A \( \cdot\left(\bar{A}^{2}-\bar{B}^{2}\right) \)
в. \( 2 \overline{\mathrm{AB}} \)
c. \( 2(\overline{\mathrm{A}} \times \overline{\mathrm{B}}) \)
D. \( 2(\overline{\mathrm{B}} \times \overline{\mathrm{A}}) \)


The dimensions of \( \frac{\alpha}{\beta} \) in the equation \( \boldsymbol{F}=\frac{\boldsymbol{\alpha}-\boldsymbol{t}^{2}}{\beta \boldsymbol{v}^{2}}, \) where \( \boldsymbol{F} \) is force, \( \boldsymbol{v} \) is
velocity and \( t \) is time, is :
\( \mathbf{A} \cdot\left[M L T^{-1}\right] \)
B . \( \left[M L^{-1} T^{-2}\right] \)
\( \mathbf{c} \cdot\left[M L^{3} T^{-4}\right] \)
\( \mathbf{D} \cdot\left[M L^{2} T^{-4}\right] \)


There are three elements \( \mathrm{E}, \mathrm{F}, \mathrm{G} \) with
atomic number 19,8 and 17
respectively.Give molecular formula of the compound formed between \( \mathrm{E} \) and \( \mathrm{G} \)


Which of the following is valid name for Gramineae family?
A. Poaceae
B. Malvaceae
c. Fabaceae
D. Papilionaceae


A certain buffer solution contains equal
concentration of \( \boldsymbol{X}^{-} \) and \( \boldsymbol{H} \boldsymbol{X} . \) The \( \boldsymbol{K}_{\boldsymbol{b}} \)
for \( X^{-} \) is \( 10^{-10} . \) The \( p H \) of the buffer is:
A . 4
B. 7
c. 10
D. 14


A graph is plotted between the potential difference (applied across the ends of a conductor) and the current (following through the conductor). The graph is a straight line
A. having intercepts on both axes
B. having an intercept on the X-axis
c. having an intercept on the Y-axis
D. none of these


When ether is exposed to air for sometime an explosive substance
produced is:
A. peroxide
B. oxide
c. тNT
D. superoxide


Form the differential equation by eliminating the arbitrary constants from the equation \( y=a \cos (2 x+b) \) is
A \( \cdot \frac{d^{2} y}{d x^{2}}+4 y=0 \)
B. \( \frac{d^{2} y}{d x^{2}}-4 y=0 \)
c. \( \frac{d^{2} y}{d x^{2}}+2 y=0 \)
D. \( \frac{d^{2} y}{d x^{2}}+y=0 \)


The potential energy of a particle of mass \( 5 \mathrm{kg} \) moving in the \( \mathrm{x} \) -y plane is given by the equation, \( U=-7 x+24 y \)
Joule. Here \( x \) and \( y \) are in the meter at \( t=0, \) the particle is at the origin and moving with velocity \( (2 \hat{i}+3 \hat{j}) m / s . \) The
magnitude of acceleration of particle is
\( \mathbf{A} \cdot 3 m / s^{2} \)
B . \( 5 \mathrm{m} / \mathrm{s}^{2} \)
D. \( 15 \mathrm{m} / \mathrm{s}^{2} \)


Under whose leadership the Atomic Energy Department of India was established?
A. Homi Jahangir Bhabha
B. Vikram Sarabhai
c. Satish Dhawan
D. A.P.J. Abdul Kalam


If the pancreatic duct of a healthy dog is blocked an hour after it had its food,
which one of the following functions of the pancreas will not be affected?
A. Carbohydrate digestion
B. Neutralization of chyme
c. Break down of protein
D. None of the above


Select the option that correctly
identifies \( A \) to \( E \) in the given flow chart.
\( \mathbf{A} \cdot A-\alpha, B-\beta, C-G|u c a g o n, D-H y p e r g| y c a e m i a, E- \)
Hypoglycaemia
B. A- \( \beta \), B- \( \alpha \), C-Cortisol, D-Hypoglycaemia, EHyperglycaemia
C \( . A-\beta, B-\alpha, C \) -Cortisol, D-Hyperglycaemia, EHypoglycaemia
D. \( A-\beta, B-\alpha, C \) -Glucagon, D-Hypoglycaemia, EHyperglycaemia


\( \mathbf{2 4} \times \mathbf{2 7}= \)


The geometric mean between two numbers \( a \) and \( b \) is
A. \( \sqrt{a b} \)
B. \( \frac{1}{\sqrt{a b}} \)
c. \( \sqrt{2 a b} \)
D. \( 2 \sqrt{a b} \)


Ethers are isomeric with:
A. aldehydes
B. ketones
C. both aldehydes and ketones
D. alcohols


Nitrogen gas is very difficult to identify
because of its :
A. High dissociation energy
B. Characteristic colour
c. Unreactive nature
D. High electronegativity


A Toy cart attached to the end of an
unstretched string of length a, when received moves on a smooth horizontal
table in a circle of radius 2 s with a time
period T. Now the toy cart is speeded up until it moves in a circle of radius 3 a
with a period 'T'. If Hook's law holds then (Assume no friction)
A \( \cdot T^{\prime}=\sqrt{\frac{3}{2}} \pi \)
B \cdot \( T^{\prime}=\left(\frac{\sqrt{3}}{2}\right) T \)
\( \mathbf{c} \cdot \mathbf{T}^{\prime}=\left(\frac{3}{2}\right) \mathbf{T} \)
D. \( T^{\prime}=T \)


Assertion
When the ambient temperature is high and soil contains excess of water, the plants tend to lose water in the form of
droplets from lenticels.
Reason
Root pressure regulates the rate of loss of water form lenticels.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The smallest animal egg is that of
A . ostrich
B. Human female
c. Duck
D. Hen


Find the values of the following:
\( \sin 120^{\circ} \)


Two circular coils 1 and 2 are made from
the same wire but the radius of 1st coil
is twice that of the 2 nd coil. What
potential difference in volts should be
applied across them so that the magnetic magnetic field at the centres is the same
A. 4 times of first coil
B. 6 times of first coil
c. 2 times of first coil
D. 3 times of first coil


\( 75 g \) of water at \( 10^{\circ} C \) is heated by supplying \( 25200 J \) of heat energy. If the specific heat capacity of water is
\( 4.2 J / g^{o} C . \) Calculate the final temperature of water
\( \mathbf{A} \cdot 0^{\circ} C \)
B. \( 10^{\circ} \mathrm{C} \)
c. \( 100^{\circ} \mathrm{C} \)
D. \( 90^{\circ} \mathrm{C} \)


What are the constituents of
'Mischmetal'?
A. \( L a, F e \)
в. \( L a, C e \)
c. \( F e, C e \)
D. Ce.Cu


The geometry and the number of
unpaired electron(s) of \( \left[M n B r_{4}\right]^{2-} \) respectively, are:
A. tetrahedral and 1
B. square planarand
c. tetrahedral and 5
D. square planar and 5


To construct a triangle similar to given \( \Delta A B C \) with its sides \( \frac{4}{5} \) of that of
\( \Delta A B C . \) Locate points \( X_{1}, X_{2}, X_{3}, \dots \)
on ray \( B X \) at equal distances such that
\( \angle A B X \) is acute. The minimum number
of points to be located on \( B X \) is:
A . 14
B. 5
\( c .9 \)
D . 20


A particle falling under gravity
describes \( 80 f t \) in a certain sec. How
long does it take to describe next \( 112 f t \)
\( ?\left[\boldsymbol{g}=\boldsymbol{3} 2 \boldsymbol{f} \boldsymbol{t} \boldsymbol{s}^{-2}\right] \)
\( \mathbf{A} \cdot 1 s \)
B . \( 2 s \)
c. \( 3 s \)
D. \( 4 s \)


At \( 27^{\circ} \mathrm{C} \) two moles of an ideal
monoatomic gas occupy a volume \( V \) The gas expands adiabatically to a
volume \( 2 \mathrm{V} \). Calculate the final
temperature of the gas.
A \( \cdot T_{f}=388.99 \mathrm{K} \)
в. \( T_{f}=288.99 \mathrm{k} \)
c. \( T_{f}=188.99 \mathrm{k} \)
D. \( T_{f}=588.99 \mathrm{K} \)


\( \operatorname{lf}\left|\begin{array}{lll}\boldsymbol{x}_{1} & \boldsymbol{y}_{1} & \mathbf{1} \\ \boldsymbol{x}_{2} & \boldsymbol{y}_{2} & \mathbf{1} \\ \boldsymbol{x}_{3} & \boldsymbol{y}_{3} & \mathbf{1}\end{array}\right|=\left|\begin{array}{lll}\boldsymbol{a}_{1} & \boldsymbol{b}_{1} & \mathbf{1} \\ \boldsymbol{a}_{2} & \boldsymbol{b}_{2} & \mathbf{1} \\ \boldsymbol{a}_{3} & \boldsymbol{b}_{3} & \mathbf{1}\end{array}\right| \) then the
two triangles with vertices \( \left(x_{1}, y_{1}\right),\left(x_{2}, y_{2}\right),\left(x_{3}, y_{3}\right) \) and
\( \left(a_{1}, b_{1}\right),\left(a_{2}, b_{2}\right),\left(a_{3}, b_{3}\right) \) are
A . equal in area
B. similar
c. congruent
D. none of these


A particle (1) of mass m initially at A is at rest. The radius of circular path is 1
m. The particle (1), collides at bottom
with an other particle (2) of same mass
m. The distance travelled by the particle
(2) before coming at rest is
\( 4.1 .5 \mathrm{m} \)
B. 2.5
\( c .3 .5 \mathrm{m} \)
\( D \)


тре
(I) Quadrılateral MUKE
\( M O=6 \mathrm{cm} \)
\( \boldsymbol{O} \boldsymbol{R}=\mathbf{4 . 5} \boldsymbol{c m} \)
\( \angle M=60^{\circ} \)
\( \angle O=105^{\circ} \)
\( \angle R=105^{\circ} \)
(ii) Quadrilateral \( \boldsymbol{P} \boldsymbol{L} \boldsymbol{A} \boldsymbol{N} \)
\( \boldsymbol{P L}=\boldsymbol{4} \boldsymbol{c m} \)
\( \boldsymbol{L} \boldsymbol{A}=\mathbf{6 . 5} \boldsymbol{c m} \)
\( \angle \boldsymbol{P}=\mathbf{9 0}^{\circ} \)
\( \angle A=110^{\circ} \)
\( \angle N=85^{\circ} \)
(iii) Parallelogram \( \boldsymbol{H} \boldsymbol{E} \boldsymbol{A} \boldsymbol{R} \)
\( \boldsymbol{H} \boldsymbol{E}=\mathbf{5} \boldsymbol{c m} \)
\( \boldsymbol{E} \boldsymbol{A}=\boldsymbol{6} \boldsymbol{c m} \)
\( \angle \boldsymbol{R}=\mathbf{8} \mathbf{5}^{\circ} \)
(iv) Rectangle \( \boldsymbol{O} \boldsymbol{K} \boldsymbol{A} \boldsymbol{Y} \)
\( \boldsymbol{O} \boldsymbol{K}=\mathbf{7} \boldsymbol{c m} \)
\( \boldsymbol{K} \boldsymbol{A}=\mathbf{5} \boldsymbol{c m} \)


The resistance between \( A \) and \( B \) is
A \( \cdot \frac{288}{56} \Omega \)
В. \( 12 \Omega \)
\( c \cdot \frac{8}{3} \Omega \)
D. \( \frac{9}{4} \Omega \)


How many dead centres are there in one cycle of steam engine?
A . 4
B. 3
c. 2
\( D \)


Write balanced net ionic equation for
the following reactions in acidic
solution.
\[
\begin{array}{l}
\boldsymbol{S}_{4} \boldsymbol{O}_{6}^{2-}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{A l}(\boldsymbol{s}) \rightarrow \boldsymbol{H}_{2} \boldsymbol{S}(\boldsymbol{a} \boldsymbol{q})+ \\
\boldsymbol{A l}^{3+}(\boldsymbol{a} \boldsymbol{q})
\end{array}
\]
\( \mathbf{A} \cdot S_{4} O_{6}^{2-}(a q)+6 A l(s)+20 H^{+} \rightarrow 4 H_{2} S(a q)+ \)
\[
6 A l^{3+}(a q)+6 H_{2} O
\]
\( \mathbf{B} \cdot 2 S_{4} O_{6}^{2-}(a q)+6 A l(s)+20 H^{+} \rightarrow 4 H_{2} S(a q)+ \)
\[
2 A l^{3+}(a q)+6 H_{2} O
\]
\( \mathbf{c} \cdot S_{4} O_{6}^{2-}(a q)+5 A l(s)+20 H^{+} \rightarrow 4 H_{2} S(a q)+ \)
\[
3 A l^{3+}(a q)+6 H_{2} O
\]
D. None of the above


Photorespiration is also called as
A \( \cdot C_{2} \) cycle
B. \( C_{3} \) cycle
\( \mathbf{c} \cdot C_{4} \) cycle
D. None of the above


Why is \( I_{2} \) less reactive than \( I C l \) ?


Which of the following statement is
correct?
A. A person with myopia can see distant objects clearly
B. A person with hypermetropia can see nearby objects clearly
C. A person with myopia can see nearby objects clearly
D. A person with hypermetropia cannot see distant objects clearly


The limiting molar conductivity and molar conductivity of acetic acid are
\( 390.5 s . c m^{2} . m o l^{-1} \) and
\( 48.15 s . c m^{2} . m o l^{-1} \) respectively
Calculate the degree of dissociation of the weak acid?
\( \mathbf{A} \cdot 1.233 \)
B. 12.33
c. 0.1233
D. 0.01233


State the following statement is True or
False

A parabolic arch has a height 18 meters and span 24 meters. Then the height of the arch at 8 meters from the centre of the span is equal to 10
A. True
B. False


Is the name 2-methyl-3-buntanol correct? Explain.


Sound travels the fastest in which
medium?
A. Gaseous
B. Liquid
c. Solid
D. Vacuum


One mole is defined as:
A. quantity having a mass equal to its atomic/molecular
mass
B. quantity having mass equal to half of its atomic/molecular mass
C. one gram of any quantity
D. one kilograms of any quantity


The chemical change in DNA molecule that could lead to synthesis of protein with an altered amino acid sequence is
called
A. replication
B. lipid formation
c. cellular membrane
D. mutation


Sodium hydrogen carbonate is used in fire extinguisher.
A. True
B. False


The number of peptide bonds in the
compound is :
\( A \)
B.
\( c \)
\( D \)


\( A, B, C \) are any three events. If \( P(S) \)
denotes the probability of \( S \) happening,
\( \operatorname{then} \boldsymbol{P}(\boldsymbol{A} \cap(\boldsymbol{B} \cup \boldsymbol{C}))= \)
A \( \cdot P(A)+P(B)+P(C)-P(A \cap B)-P(A \cap C) \)
B . \( P(A)+P(B)+P(C)-P(B) P(C) \)
C \( \cdot P(A \cap B)+P(A \cap C)-P(A \cap B \cap C) \)
D. None of these


Which of the following represent redox reactions?
\( \mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}+2^{\ominus} \boldsymbol{O} \boldsymbol{H} \longrightarrow 2 \boldsymbol{C r} \boldsymbol{O}_{4}^{2-}+ \)
\( \boldsymbol{H}_{2} \boldsymbol{O} \)
II. \( Z n+C u S O_{4} \longrightarrow Z n S O_{4}+C u \)
III. \( 2 M n O_{4}^{\ominus}+3 M n^{2+}+4 \stackrel{\theta}{O} H \longrightarrow \)
\( \mathbf{5} M n O_{2}+2 H_{2} O \)
IV. \( 2 C u^{\oplus} \longrightarrow C u+C u^{2+} \)
A . ।, । ।
в. ।, ॥
c. ॥ा, ।ा
D. ॥, ॥I, IV


Two similar cells, whether joined in series or in parallel, have the same current through an external resistance
of \( 2 \Omega . \) The internal resistance of each
cell is
A . \( 1 \Omega \)
B. 2\Omega
\( c .0 .5 \Omega \)
D. \( 1.5 \Omega \)


The relation "congruence modulo \( m " \) is:
A. reflexive only
B. symmetric only
c. transitive only
D. an equivalence relation


The leaf in which the stomata remains
confined to lower surface of the leaf is
known as
A. Amphistomatic
B. Hypostomatic
c. Epistomatic
D. All of the above


Urea synthesis occurs in
A. Kidney
B. Liver
c. Brain
D. Muscles


Twelve identical resistors of \( 6 \Omega \)
each are connected to form a cube as
shown above. The effective resistance
across the solid diagonal, AG is :
\( A .5 \Omega \)
B. \( 4.5 \Omega \)
\( c .3 .5 \Omega \)
\( \mathbf{D} \cdot 1.5 \Omega \)


Which of the following reaction is an example of a redox reaction?
A. \( X e F_{2}+P F_{5} \rightarrow[X e F]^{+}+P F_{6} \)
в. \( X e F_{6}+H_{2} O \rightarrow X e O F_{4}+2 H F \)
c. \( X e F_{6}+2 H_{2} O \rightarrow X e O_{2} F_{2}+4 H F \)
D. \( X e F_{4}+O_{2} F_{2} \rightarrow X e F_{6}+O_{2} \)


In fractionating colum:
A. vapours of high boiling point substance condense and fall back into a distillation flask
B. vapours of low boiling point substance condense and fall back into a distillation flask
C. vapours of high boiling point substance condense and evaporate
D. both \( B \) and \( C \)


When you hit a wall and sponge with equal force. Which case will hurt more?
A. Both equally
B. wall
c. sponge
D. No comparison


The sum of the solution of the equation \( 2 \sin ^{-1} \sqrt{x^{2}+x+1}+ \)
\( \cos ^{-1} \sqrt{x^{2}+x}=\frac{3 \pi}{2} \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B. - 1
\( c \cdot 1 \)
\( D \)


In barley stem vascular bundles are -
A. Closed and radial
B. Open and scattered
c. closed and scattered
D. open and in a ring


Give reason: we wear a number of
garments in winter rather than one
thick garment


Apes share \( \ldots \ldots . . . . . . . . \) blood groups with
man.
\( A \cdot A, B, A B \)
B. A, B, O
c. \( A B, O \)
D. A and B


Two wires are kept tight between the
same pair supports. The tensions in the wires are in the ration \( 2: 1, \) the radii are
in the ratio 3: 1 and the densities are in
the ratio \( 1: 2 . \) The ratio of their
fundamental frequencies is
A .2: 3
B. 2: 4
c. 2: 5
D. 2: 6


Which of the following is true with respect to crystal field splitting in complexes?
\( \mathbf{A} \cdot \Delta_{0}=\Delta_{t} \)
B. \( \triangle_{0}=\frac{9}{4} \Delta_{t} \)
c. \( \Delta_{t}=\frac{9}{4} \Delta_{0} \)
D. \( \triangle_{t}=\frac{2}{3} \Delta_{0} \)


Formation of nucleotide is a
A. Anabolic reaction
B. Catabolic reaction
c. Both A and B
D. None of the above


Find the electric field in the copper wire
of area of cross section \( 2 m m^{2} \) carrying
a current of 1 A. The resistivity of
copper is \( 1.7 \times 10^{-8} \Omega m \)
A . \( 4.25 \times 10^{-3} \mathrm{V} / \mathrm{m} \)
B . \( 8.5 \times 10^{-3} \mathrm{V} / \mathrm{m} \)
c. \( 8.5 V / m \)
D. \( 9.5 \times 10^{-3} \mathrm{V} / \mathrm{m} \)


Excessive release of \( C O_{2} \) into the
atmosphere results in:
A. polar vortex
B. depletion of ozone
\( c . \) formation of smog
D. global warming


A fair die is tossed 1620 times. If
getting a face with 6 points is considered as a success, then \( E(x)= \) \( \ldots \ldots ., V(x)=\dots \ldots . . \)
A .270,270
в. 270,225
c. 270,25
D. 27,250


A given ray of light suffers minimum
deviation in an equilateral prism \( P \)
Additional prism \( Q \) and \( R \) of identical
shape and of the same material as \( \boldsymbol{P} \)
are now added as shown in the figure. The ray will now suffer.
A. Greater deviation
B. No deviation
c. Same deviation as before
D. Total internal reflection


The armature of a DC motor has \( 20 \Omega \)
resistance. It draws a current of 1.5
amp when run by \( 200 V \) DC supply. The value of back emf induced in it will be
\( \mathbf{A} \cdot 150 V \)
в. \( 170 V \)
\( \mathbf{c} \cdot 180 V \)
D. \( 190 V \)


The ratio of thermal capacities of two aluminium spheres of radii \( 8 \mathrm{cm} \) and 16 \( \mathrm{cm} \) is
\( A \cdot 4: 1 \)
B. 1: 4
c. 1: 8
D. 8: 1


The periodic time of a particle doing simple harmonic motion is 4 s. The time taken for it to go from its mean position to half the maximum displacement (amplitude) is.
\( \mathbf{A} \cdot 2 s \)
B . \( 1 s \)
c. \( \frac{2}{3} s \)
D. \( \frac{1}{3} s \)


A positively charged disk is rotated clockwise as shown in the figure. The
direction of the magnetic field at point
\( A \) in the plane of the disk is
\( A \cdot \otimes \) into the page
B. \( \rightarrow \) towards right
\( \mathbf{c} . \leftarrow \) towards left
D. \odot out of the page


Which of the following animals are involved in the fluid feeding mode?
A. Honey bees
B. Amoeba
\( c . \) cow
D. None of the above


Which order of relative size among the following is incorrect?
A. \( L i<N a<K \)
в. \( C<S i<A l \)
c. \( M g>A l<N a \)
D. \( F<C l<B r \)


If \( \boldsymbol{\alpha} \boldsymbol{\epsilon}\left(-\frac{\boldsymbol{\pi}}{2}, \boldsymbol{0}\right), \) then find the value of
\( \tan ^{-1}(\cot \alpha)-\cot ^{-1}(\tan \alpha) \)


What is the use of kink near the bulb in
clinical thermometer
This question has multiple correct options
A. It prevents the level of the mercury from falling when taken out of the mouth
B. It allows the level of the mercury to fall when taken out of the mouth
C. It allows the level of the mercury to rise when taken out of the mouth
D. It prevents the level of the mercury from rising when taken out of the mouth


A solid sphere of radius \( \boldsymbol{R} \) has total charge \( 2 Q \) and volume charge density
\( \rho=k r \) where \( r \) is distance from centre.
Now charges \( Q \) and \( -Q \) are placed diametrically opposite at distance \( 2 a \) where \( a \) is distance form centre of
sphere such that net force on charge \( Q \) is zero then relation between \( a \) and \( R \) is
A \( \cdot a=R / 2 \)
В . \( a=R \)
c. \( a=2 R \)
D. \( a=3 R / 4 \)


The mass defect of \( _{2}^{4} H e \) is \( 0.03 u . \) The binding energy per nucleon of helium \( (\text { in } M e V) \) is
A . 69.825
B. 6.9825
c. 2.793
D. 27.93


The energy gap in case of which of the following is less than \( 3 e V ? \)
A. Aluminium
B. Iron
c. Germanium
D. copper


In a calorimeter of water equivalent 20
g, water of mass \( 1.1 \mathrm{kg} \) is taken at \( 288 \mathrm{K} \) temperature \( 373 \mathrm{K} \) is passed through it and temperature of water increases by
\( 6.5^{\circ} \mathrm{C} \) then the mass of steam
condensed is
A. \( 17.5 \mathrm{g} \)
в. \( 11.7 \mathrm{g} \)
c. \( 15.7 \mathrm{g} \)
D. \( 18.2 \mathrm{g} \)


An insect \( 8 m \) away from the foot of a lamp post which is \( 6 m \) tall, crawls towards it. After moving through a distance, its distance from the top of the lamp post is equal to the distance it has moved. How far is the insect away
from the foot of the lamp post? [Bhaskaracharya's Leelavathi]


Which element exhibits the greatest
number of oxidation states in its
compounds?
A. \( C a \)
в. \( V \)
c. \( C u \)
D. Na


Factorise the expression and divide them as directed.
\( \left(m^{2}-14 m-32\right) \div(m+2) \)


What are biodegradable and nonbiodegradable detergents ? Give one example of each.


How can you determine the focal length of a convex lens experimentally. Draw a
rough diagram.


Write any three uses of infrared
radiations.


The volume of \( O_{2} \) gas at S.T.P. obtained
by the decomposition of 1 c.c. of \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \)
solutionis known as its volume
strength. If this is true enter 1 , if false enter 0 .


Convert given percents to decimal fractions and also to fractions in
simplest forms:
\( \mathbf{2 5 \%} \)


The fraction of ice that melts by mixing
equal masses of ice at \( -10^{\circ} \mathrm{C} \) and
water at \( 60^{\circ} \mathrm{C} \) is :
A \( \cdot \frac{6}{11} \)
в. \( \frac{11}{16} \)
c. \( \frac{5}{16} \)
D. \( \frac{11}{15} \)


Two particles \( A \) and \( B \) are placed as
shown in Fig. A.12. The particle \( A \), on the top of tower, is projected horizontally with a velocity \( u \) and particle \( B \) is projected along the surface towards the
tower, simultaneously. If both particles
meet each other, then the speed of projection of particle \( \boldsymbol{B} \) is [ignore any friction]
A \( \cdot d \sqrt{\frac{g}{2 H}} u \)
в. \( d \sqrt{\frac{g}{2 H}} \)
\( c \)
\[
d \sqrt{\frac{g}{2 H}}-u
\]
D.


Electrons at rest are accelerated by a
potential of \( \boldsymbol{V} \) volt. These electrons enter the region of space having a uniform, perpendicular magnetic induction field \( B \). The radius of the path
of the electrons inside the magnetic field is:
A \( .1 / B \sqrt{m V / e} \)
B. \( \frac{\sqrt{2 m V / e}}{B} \)
c. \( m V / q B \)
D. \( 1 / B \sqrt{V / e} \)


The moon's distance from the earth is
\( 360000 \mathrm{km} \) and its diameter subtends
an angle of \( 42^{\prime} \) at the eye of the observer. The diameter of the moon is?
A. \( 4400 \mathrm{km} \)
B . \( 1000 \mathrm{km} \)
\( \mathbf{c} .3600 \mathrm{km} \)
D. \( 8800 \mathrm{km} \)


Which of the following examples is/are oil in water type emulsions?
\( A \cdot \ln k \)
B. Detergent
c. Soap
D. Milk


The voltage in the primary and the
secondary coils of a step up transformer are \( 200 \mathrm{V} \) and \( 4 \mathrm{KV} \) respectively. If the
current in the primary is 1 ampere then the current in the secondary coil will be
\( A \cdot 50 \mathrm{m} \) A
B. 500 \( \mathrm{m} \) A
\( c \cdot 5 A \)
\( D \cdot 5 m A \)


Which of the following is present in monocot flowers?
A. Sepals
B. Petals
c. Tepals
D. None of the above


A current of \( 1.0 A \) exists in a copper wire
of cross-section \( 1.0 \mathrm{mm}^{2} \). Assuming one
free electron per atom

Calculate drift speed of the free electron in the wire \( _{--}-_{-}-_{-} \) (the density of
copper is \( \left.9000 k g m^{2}\right) \)
A. \( 0.74 \mathrm{mms}^{-1} \)
B. \( 7.4 m m s^{-1} \)
\( \mathbf{c} \cdot 74 m m s^{-1} \)
D. \( 0.074 \mathrm{mms}^{-1} \)


This is known as heavy hydrogen:
A. protium
B. tritium
c. deuterium
D. proton


In summer, a mild wind is often found
on the shore of a calm river. This is due
to :
A. difference in thermal conductivity of water and soil
B. convection currents
c. conduction between air and the soil
D. radiation from the soil


\( (+)- \) Mandelic acid has a specific
rotation of \( +158^{\circ} . \) What would be the
observed specific rotation of a mixture of \( 25 \%(-)- \) mandelic acid and \( \mathbf{7 5 \%}(+)- \) mandelic acid:
A . \( +118.5^{\circ} \)
в. \( -118.5^{\circ} \)
\( \mathrm{c} .-79^{\circ} \)
D. +79


Which of following plant cells are without vacuoles and without nuclei?
A. Cambium cells
B. Xylem vessels
c. Root hairs
D. Companion cells


The most stable conformation of
ethylene glycol and but-2-ene are respectively.
A. anti and anti
B. gauche and anti
c. gauche and gaushe
D. partially eclipsed and anti


Which selection correctly shows units for specific heat capacity?
A \( \cdot \) Cal \( \cdot g \cdot^{\circ} C \)
в. \( C a l \cdot g /^{\circ} C \)
\( \mathbf{c} \cdot J /\left(g \cdot^{o} C\right) \)
D. \( g / J \). \( ^{\circ} C \)


Q Type your question
the following information carefully and
answer the questions given below. The sub divided bar diagram given below depicts the result of Class XII students of a school for three years.
The number of students passed with
second class in 2000 is what percent of
number of students passed with first
class in 2002?
A. 50\%
B. 62.5\%
c. \( 45 \% \)
D. 70.5


Liquid benzene \( \left(C_{6} H_{6}\right) \) burns in oxygen
according to \( 2 C_{6} H_{6}(I)+15 O_{2}(g) \rightarrow \)
\( 12 C O_{2}(g)+6 H_{2} O(g) . \) How many litres
of \( O_{2} \) at STP are needed to complete the
combustion of 39 g of liquid benzene?
A . \( 74 L \)
B. \( 11.2 L \)
c. \( 22.4 \mathrm{L} \)
D. 84L


Formula of the hydrocarbon
is
A \( \cdot C_{3} H_{8} \)
в. \( C_{3} H_{6} \)
\( \mathbf{c} \cdot C_{3} H_{4} \)
D. \( C_{2} H_{6} \)


Show that \( \frac{2 \tan 30^{\circ}}{1-\tan ^{2} 30^{\circ}}=\sqrt{3} \)


Which group elements are the most reactive among the non-metals?
A . 15 th
B. 16th
c. 17 th
D. 18th


Microorganisms commonly causing
diarrhoeal diseases are
A. Escherichia coli, Shigella, Campylobacter and Bacillus pertussis
B. Clostridium tetani, Giardia, Entamoeba histolytica, Salmonella, Shigella and Escherichia coli
C. Escherichia coli, Giardia, Shigella, Campylobacter and Salmonella
D. Neisseria, Treponema, Escherichia, Giardia, Shigella, Campylobacter and Salmonella


Fire extinguisher pyrene is:
A \( \cdot C O_{2} \)
в. \( C C l_{4} \)
c. \( C H C l_{3} \)
D. \( H_{2} C O_{3} \)


A ball of 100 g mass is thrown with a velocity of \( 100 m s^{-1} . \) The wavelength of
the de Broglie wave associated with the ball is about:
A. \( 6.63 \times 10^{-35} \mathrm{m} \)
В \( \cdot 6.63 \times 10^{-30} \mathrm{m} \)
c. \( 6.63 \times 10^{-33} \mathrm{cm} \)
D. \( 6.63 \times 10^{-33} \mathrm{m} \)


Find the fraction of 25 paise to \( R s 2 \)
A \( \cdot \frac{9}{8} \)
B. \( \frac{3}{8} \)
\( c \cdot \frac{5}{8} \)
D.


White phosphorus can be removed from
red phosphorus by:
This question has multiple correct options
A. sublimation
B. dissolving in \( C S_{2} \)
c. distillation
D. heating with alkali solution


To draw a pair of tangents to a circle which are at right angles to each other it is required to draw tangents at end points of two radii which are inclined at an angle of
\( \mathbf{A} \cdot 60^{\circ} \)
B. \( 90^{\circ} \)
\( c \cdot 120^{\circ} \)
D. \( 45^{\circ} \)


Find the differentiation of \( \sec \left(\tan ^{-1} x\right) \)
w.r.t. \( \boldsymbol{x} \)


In the laboratory, \( M n O_{2} \) is made by:
A. heating \( M n \) in \( O_{2} \)
B. oxidising \( M n^{2+} \)
C. electrolytic oxidation of \( M n S O_{4} \)
D. titration of \( K M n O_{4} \) in alkaline medium


\( 12 x y\left(9 x^{2}-16 y^{2}\right) \div 4 x y(3 x+4 y) \)


The values of \( A \) and \( B \) represented on
the number line are
\begin{tabular}{cccccccccc}
\hline & & & & & & & & & \\
\( \frac{-6}{1} \) & \( \frac{-5}{1} \) & \( \frac{-4}{1} \) & \( \frac{-3}{\mathrm{A}} \) & \( \frac{-2}{1} \) & \( \frac{-1}{1} \) & \( \frac{0}{1} \) & \( \frac{1}{\mathrm{B}} \) & \( \frac{2}{1} \) & \( \frac{3}{1} \)
\end{tabular}
A . 1,1
B. -1,1
\( c \cdot 1,-1 \)
D. -1,-1


Which acids/ bases are used for the
following?
(i) To neutralize sting of wasps
(ii) In alkaline batteries
(iii) Manufacturing of soap
A \( \cdot \) (i) \( C H_{3} C H O \) (ii) \( C s O H \) (iii) \( C a(O H)_{2} \)
B . (i) \( C H_{3} C O O H \) (ii) \( C u S O_{4} \) (iii) \( B a(O H)_{2} \)
c. \( \left(\text { i) } C H_{3} \text { COOH (ii) } K O H \text { (iii) } N a O H\right. \)
D. None of these


The electronegativites of the following
elements \( H, O, F, S \) and \( C l \) increase in
the order:
A. \( H<O<F<S<C l \)
в. \( S<H<C l<O<F \)
c. \( H<S<O<C l<F \)
D. \( H<S<C l<O<F \)


A weak electrolyte having the limiting equivalent conductance of \( 400 S \mathrm{cm}^{2} g \)
equiv \( ^{-1} \) at \( 298 K \) is \( 2 \% \) ionized in its \( 0.1 N \) solution. The resistance of this
solution (in ohm) in an electrolytic cell of cell constant \( 0.4 \mathrm{cm}^{-1} \) at this
temperature is:
A . 200
в. 300
c. 400
D. 500
E. 600


If \( \sin \theta=\frac{8}{17} \) and \( 90^{\circ}<\theta<180^{\circ}, \) then
the value of the expression \( \frac{2 \sin \theta+\cos \theta}{3 \cos \theta+5 \sin \theta} \) is :
\( A \cdot \frac{1}{5} \)
B. \( -\frac{1}{5} \)
c. \( \frac{31}{85} \)
D. \( -\frac{31}{85} \)


Let \( \vec{a}=\hat{j}-\hat{k} \) and \( \vec{c}=\hat{i}-\hat{j}-\hat{k}, \) then
the vector \( \overrightarrow{\boldsymbol{b}} \) satisfying \( \overrightarrow{\boldsymbol{a}} \times \overrightarrow{\boldsymbol{b}}+\overrightarrow{\boldsymbol{c}}=\mathbf{0} \)
and \( \vec{a} \cdot \vec{b}=3 \) is
\( \mathbf{A} \cdot-\hat{i}+\hat{j}-2 \hat{k} \)
B . \( 2 \hat{i}-\hat{j}+2 \hat{k} \)
c. \( \hat{i}-\hat{j}-2 \hat{k} \)
D. \( \hat{i}+\hat{j}-2 \hat{k} \)


Bryophytes resemble algae in which of the following aspects?
A. Filamentous body, presence of vascular tissues and autotrophic nutrition
B. Differentiation of plant body into root, stem and leaves and autotrophic nutrition
c. Thallus like plant body, presence of root and autotrophic nutrition
D. Thallus-like plant body, lack of vascular tissues and autotrophic nutrition


Given a parallelogram \( \boldsymbol{A B C D} \). If \( |\overrightarrow{A B}|=a,|\overrightarrow{A D}|=b \&|\overrightarrow{A C}|=c, \) then
\( \overrightarrow{D B} \cdot \overrightarrow{A B} \) has the value
\( ^{\text {A } \cdot} \frac{3 a^{2}+b^{2}-c^{2}}{2} \)
B. \( \frac{a^{2}+3 b^{2}-c^{2}}{2} \)
c. \( \frac{a^{2}+b^{2}-3 c^{2}}{2} \)
D. None


Two concentric co-planar circular loops
of radii \( r_{1} \) and \( r_{2} \) carry currents of
respectively \( i_{1} \) and \( i_{2} \) in opposite
directions (one clockwise and the other
anticlockwise.) The magnetic induction
at the centre of loops is half that due to
\( i_{1} \) alone at the centre. If \( r_{2}=2 r_{1} . \) the
value of \( i_{2} / i_{1} \) is
\( \mathbf{A} \cdot 2 \)
B. \( \frac{1}{2} \)
\( c \cdot \frac{1}{4} \)
D.


A lead ball of radius \( 24 \mathrm{cm} \) is melted down and recast into smaller balls of
radius \( 6 \mathrm{cm} . \) Assuming that no metal is lost in this process, number of complete smaller balls that can be made, is -
A . 4
B . 16
\( c .36 \)
D. 64


Select incorrect statement.
A. Mellitic acid is benzene hexa-carboxylic acid.
B. \( P b \) dissolves in conc. \( H C l \) forming \( P b C l_{2} \)
C \( . P b \) dissolves in hot \( N a O H \) forming \( N a_{2}\left[P b(O H)_{6}\right] \)
D. Diamond is unreactive but graphite forms \( (C H)_{n} \) with
\( F_{2} \)


Evaluate \( \int_{0}^{5}(2-x) d x \)


The increase in length of a wire on stretching is \( 0.025 \% \). If its Poisson's ratio is \( 0.4, \) then the percentage
decrease in diameter is:
A . \( 0.01 \% \)
B . 0.02\%
c. \( 0.03 \% \)
D . 0.04\%


State true or false.
Soft soaps are potassium salts of higher fatty acids.
A. True
B. False


Which of the following diseases is cured by sulpha drug?
A. Diptheria
B. Dysentry
c. Tuberculosis
D. all of these


The value of \( \int_{1 / 2}^{1} \frac{d x}{x \sqrt{3 x^{2}+2 x-1}} \) is?
\( \mathbf{A} \cdot \pi / 2 \)
в. \( \pi / 3 \)
c. \( \pi / 6 \)
D. \( \pi / \sqrt{2} \)


Select the correct statement.
A. Carbon-carbon bond order in graphite is more than diamond
B. Carbon-carbon bond order in graphite is less than diamond
C. Hybridization of each carbon in diamonds is \( S p_{3} \)
D. Hybridization of each carbon in graphite is \( S p_{3} \)


A body of mass \( 60 k g \) is dragged with
just enough force to start moving on a rough surface with coefficients of static
and kinetic friction 0.5 and 0.4
respectively. On applying the same force what is the acceleration?
A \( \cdot 0.98 m / s^{2} \)
в. \( 9.8 m / s^{2} \)
\( \mathbf{c} \cdot 0.54 m / s^{2} \)
D. \( 5.292 \mathrm{m} / \mathrm{s}^{2} \)


Prove that: \( \sin \left(\frac{\pi}{2}-\theta\right)=\cos \theta \)


The extent of the ionization depends on
the
A. nature of the solvent
B. temperature of the solution
c. concentration of the solution
D. nature of the solute
E. all of the above


Ozone is a rare gas found in the outer reaches of the atmosphere. Small quantities are sometimes produced by:
A. Electrical heaters
B. Electric sparks of electric trains
c. Heating rusted iron
D. Melting ice from glaciers


Which of the following is a satellite of Neptune?
\( A \). Titon
B. Phobos
c. Deimos
D. Triton


The high boiling point water is due to the presence of:
A. dative bond
B. covalent bond
c. hydrogen bond
D. vander waals bond


While keeping area of cross-section of a solenoid same, the number of turns and length of solenoid one both doubled. The
self inductance of the coil will be?
A. Halved
B. Doubled
c. \( 1 / 4 \) times the original value
D. Unaffected


A projectile is thrown in the upward
direction making an angle of \( 60^{\circ} \) with the horizontal direction with a velocity
of \( 147 m s^{-1} . \) Then the time after which
its inclination with the horizontal is \( 45^{\circ} \)
is (Take \( \boldsymbol{g}=\mathbf{9 . 8} \boldsymbol{m} / \boldsymbol{s}^{2} \) )
A . \( 15 s \)
B. \( 10.98 s \)
c. \( 5.49 s \)
D. 2.745 \( s \)


Distinguish between Phellem and phelloderm.


The orbital that has one radial node is:
A \( .2 p \)
в. \( 3 p \)
c. \( 4 p \)
D. \( 5 p \)


Whether Photorespiration is present at low light intensities.


Rate law for the reaction, \( \boldsymbol{A}+\boldsymbol{B} \longrightarrow \)
product is rate \( =\boldsymbol{k}[\boldsymbol{A}]^{2}[\boldsymbol{B}] . \) What is the
rate constant; if rate of reaction at a
given temperature is \( 0.22 M s^{-1}, \) when
\( [\boldsymbol{A}]=\mathbf{1} \boldsymbol{M} \) and \( [\boldsymbol{B}]=\mathbf{0 . 2 5} \boldsymbol{M} ? \)
\( \mathbf{A} \cdot 3.52 M^{-2} s^{-1} \)
B . \( 0.88 M^{-2} s^{-1} \)
c. \( 1.136 M^{-2} s^{-1} \)
D. \( 0.05 M^{-2} s^{-1} \)


Assertion
The rate of reaction increases generally
by 2 to 3 times for every \( 10^{\circ} \mathrm{C} \) rise in temperature.
Reason
An increase in temperature increases the coliision frequency.
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


\( 5 \% \) solution of cane sugar is isotonic
with \( 0.877 \% \) of \( X . \) The molecular weight
of substance \( \boldsymbol{X} \) is:
A . 126.98
B. 119.96
c. 95.5
D. 59.98


Write the balanced equations for the reaction occurring when gold is dissolved in aqua regia.
A \( \cdot 2 A u+3 H N O_{3}+11 H C l \rightarrow 2 H A u C l_{4}+3 N O C l+ \)
\( 6 H_{2} O \)
B . \( 2 A u+3 H N O_{3}+13 H C l \rightarrow 2 H A u C l_{4}+2 N O C l+ \)
\( 8 H_{2} O \)
c. \( 2 A u+5 H N O_{3}+11 H C l \rightarrow 2 H A u C l_{4}+2 N O C l+ \)
\( 8 H_{2} O \)
D. None of these


Let \( z_{1} \) and \( z_{2} \) be complex numbers, then
\( \left|z_{1}+z_{2}\right|^{2}+\left|z_{1}-z_{2}\right|^{2} \) is equal to
A \( \cdot\left|z_{1}\right|^{2}+\left|z_{2}\right|^{2} \)
B \( \cdot 2\left(\left|z_{1}\right|^{2}+\left|z_{2}\right|^{2}\right) \)
c. \( 2\left(z_{1}^{2}+z_{2}^{2}\right) \)
D. \( 4 z_{1} z_{2} \)


If the \( m^{t h} \) term of an \( A . P . \) is \( \frac{1}{n} \) and \( n^{t h} \) term is \( \frac{1}{m}, \) then the sum of first \( m n \)
terms is
A \( . m n+1 \)
в. \( \frac{m n+1}{2} \)
c. \( \frac{m n-1}{2} \)
D. \( \frac{m n-1}{3} \)


Assertion
The force exerted by the fluid is due to
the collisions of molecules with their
surroundings.
Reason
The normal force exerted by the fluid
particles on the walls of the container
results pressure.
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 incorrect


Which of the following process is/are irreversible?
This question has multiple correct options
A. Combustion reaction of a mixture of petrol and air ignited by a spark
B. Diffusion of cooking gas in air
c. Temperature change in atmosphere
D. None of these


A simple telescope used to view distant objects has eyepiece and objective lens
of focal lengths \( f_{e} \) and \( f, \) respectively.
Then


Compare the traditional water harvesting system with portable system in hilly/mountains areas or plains or plateau regions.


The type of bond formed by \( C a \) with \( O \) is:
A. ionic
B. covalent
c. coordinate
D. none of these


A spherical ball of mass \( 1 k g \) moving
with a uniform speed of \( 1 \mathrm{m} / \mathrm{s} \) collides symmetrically with two identical spherical balls of mass \( 1 k g \) each at rest touching each other. If the two balls move with \( 0.5 m / s \) in two directions at
the same angle of \( 60^{\circ} \) with the direction of the first ball, the loss of kinetic
energy on account of the collision is:
в. \( 0.5 \mathrm{J} \)
c. \( 1.0 \mathrm{J} \)
D. \( 0.75 J \)


A radioactive sample has \( 8.0 \times 10^{18} \)
active nuclei at a certain instant. How
many of these nuclei will still be in the
active state after two half-lives (in
\( \left.\times 10^{18}\right) ? \)


Nitrolim is a mixture of :
A. \( C a C_{2} \) and graphite
B. \( C a C N_{2} \) and graphite
c. \( C a(C N)_{2} \) and graphite
D. \( C a C N_{2}+N_{2} \)


In a sewage plant, BOD is indicated as high. After sometime it shows a
decrease then
A. There is increase in bacterial growth but decrease in oxygen.
B. There is decrease in bacterial growth but increase in oxygen.
c. There is increase in bacterial growth but increase in oxygen
D. There is decrease in bacterial growth but decrease in oxygen


Malleolus is a
A. Prominence between metacarpal and proximal phalanges.
B. Knee prominence.
C. Prominence of femur
D. Prominence at end of tibia and fibula.


The oscillations represented by curve 1
in the graph are expressed by equation
\( x= \) Asinwt. The equation for the
oscillations represented by curve 2 is expressed as:
A. \( x=2 A \sin (\omega t-\pi / 2) \)
B. \( x=2 A \sin (\omega t+\pi / 2) \)
c. \( x=-2 \operatorname{Asin}(\omega t-\pi / 2) \)
D. \( x=\operatorname{Asin}(\omega t-\pi / 2) \)


What is angular displacement in radian
of a second hand of a clock in 10 second
\( ? \)


Circinate vernation is seen in
A. Equisteum, Nephrolepis, Psilotum
B. Nephrolepis, Adiantum, Pteris
C . Lycopodium, Nephrolepis
D. Psilotum, Nephrolepis, Adiantum


Resistor is coloured as green - orange -
yellow - gold,its resistance will be:
A. \( 53 \times 10^{4} \pm 10 \% \)
В. \( 54 \times 10^{4} \pm 10 \% \)
c. \( 42 \times 10^{4} \pm 10 \% \)
D. \( 53 \times 10^{4} \pm 5 \% \)


Assertion
The maximum value of
\( (\sqrt{-3+4 x-x^{2}}+4)^{2}+(x-5)^{2} \)
(where \( 1 \leq x \leq 3 \) ) is 36
Reason
The maximum distance between the
point (5,-4) and the point on the circle
\( (x-2)^{2}+y^{2}=1 \) is 6
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


Define angiosperms.


Among the following the most basic compound is :
A. p-nitroaniline
B. acetanilide
c. aniline
D. benzylamine


Find the coordinate of the points which trisect the line segment joining the points \( \boldsymbol{A}(\mathbf{2}, \mathbf{1},-\mathbf{3}) \) and \( \boldsymbol{B}(\mathbf{5},-\mathbf{8}, \mathbf{3}) \)


Which condition favours the bond format
ion?
A. Maximum attraction and maximum potential energy
B. Minimum attraction and minimum potential energy
C. Minimum potential energy and maximum attraction
D. None of the above


A \( 10 g \) bullet is fired at a plank of wood
with a speed of \( 200 m s^{-1} . \) After passing
through the plank, which is \( 1 m \) thick, the speed of the bullet reduces to
\( 100 m s^{-1} . \) Find the average resistance offered by the plank.


Which of the hydrated species can
exist?
\( \boldsymbol{I}: \boldsymbol{H}_{5} \boldsymbol{O}_{2}^{+} \boldsymbol{I I}: \boldsymbol{H}_{3} \boldsymbol{O}^{+} \boldsymbol{I I I} \)
\( \boldsymbol{H}_{3} \boldsymbol{O}_{2}^{-} \quad \boldsymbol{I} \boldsymbol{V}: \boldsymbol{H}_{7} \boldsymbol{O}_{3}^{+} \)
Select alternate from:
A . II only
B. \( I \) and \( I I \)
c. \( I, I I \) and \( I V \)
D. \( I, I I, I I I \) and \( I V \)


\( 10^{t h} \) term of \( \mathrm{AP}: 2,7,12, \ldots . . \) is
A . 35
B. 47
c. 55
D. None of the above


In the reaction given below, the product \( \boldsymbol{X} \) is:
\( 4 H N O_{3}+P_{4} O_{10} \rightarrow 4 H P O_{3}+X \)
A. \( N_{2} O_{5} \)
в. \( N_{2} O_{3} \)
\( c \cdot N O_{2} \)
D. \( H_{2} O \)


Explain why the deflection occurs in
the galvanometer


In a series \( L C R \) circuit the frequency of
a \( 10 V, A C \) voltage source id adjusted in such a fashion that the reluctance of
the inductor or measures \( 15 \Omega \) and that
of the capacitor \( 11 \Omega . \) If \( R=3 \Omega, \) the
potential difference across the series combination of \( L \) and \( C \) will be:
\( A \cdot 8 V \)
B. \( 10 V \)
\( c \cdot 22 V \)
D. \( 52 V \)


The major product of the reaction of 2 butene with alkaline \( K M n O_{4} \) solution
is
\( A \)
в.
\( c \)
D.


Which of the following does not result in an increase in entropy?
A. crystallisation of sucrose from solution
B. rusting of iron
c. conversion of ice to water
D. vapourisation of camphor


In a cyclic process, which of the following statement is correct?
A. Change in internal energy is not zero.
B. The system returns to its initial state and it is is is reversible
c. The total heat absorbed by the system is not equal to work done by the system
D. Change in internal energy is zero.


If \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R}, \boldsymbol{g}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) are defined by
\( f(x)=x^{2}, g(x)=\cos x \) then
\( (g o f)(x)= \)
\( \mathbf{A} \cdot \cos 2 x \)
B. \( x^{2} \cos x \)
\( \mathbf{c} \cdot \cos x^{2} \)
D. \( \cos ^{2} x^{2} \)


A coin is tossed until a head appears or
it has been tossed 3 times. Given that
head does not appear on the first toss, the probability that the coin is tossed 3 times is
A \( \cdot \frac{1}{4} \)
B. \( \frac{3}{8} \)
\( c \cdot \frac{1}{8} \)
D.


In a group, if \( 60 \% \) of people drink tea and \( 70 \% \) drink coffee. What is the
maximum possible percentage of people drinking either tea or coffee but
not both?
\( \mathbf{A} \cdot 100 \% \)
B. \( 70 \% \)
\( c .30 \% \)
D. \( 10 \% \)


In a metal, the separation between conduction band and valence band is of
the order
A . 100 eV
B. 10 eV
\( c \cdot 0 e V \)
D. 1 eV


The experimental curve obtained when the rate of a reaction is plotted against
time, appeared parallel to the time axis
some time after the reaction started.
This indicates that:
A. the reaction has stopped
B. the equilibrium is established
c. the concentration of the reactants is negligible
D. the reaction is complex


One integer is greater than the other by \( +4 . \) If one number is \( -16, \) then the other
will be
A. +12
B. 0
c. -1
D. -12


State whether the following statement is true or false.
If \( Z_{r}=\cos \frac{\pi}{3^{r}}+i \sin \frac{\pi}{3^{r}}, r= \)
\( \mathbf{1}, \mathbf{2}, \mathbf{3}, \dots \dots \operatorname{then} z_{1} z_{2} z_{3} \dots \dots \dots=i \)
A. True
B. False


Sonar is an instrument used for finding
the depth of sea. State true or false.
A. True
B. False


Assertion
When monochromatic light falls on a photosensitive material, the number of
photo electrons emitted per second is \( n \)
and their maximum kinetic energy is
\( K_{m a x} . \) If the intensity \( I \) of the incident
light is doubled, \( n \) is doubled but \( K_{m a x} \)
remains the same.
Reason
The value of \( n \) is directly proportional to
\( I \) but \( K_{\max } \) is independent of \( I \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Evaluate \( -12 \times 21 \)
A \( .-2412 \)
B . -242
\( \mathbf{c} .-252 \)
D. +252


In three test tubes \( P, Q, \) and \( R \) iron
nails, water, oil and anhydrous calcium
chloride is taken. Among these test
tubes, in which test tubes corrosion of
nails will not take place?
\( A \cdot P, Q \) and \( R \)
B. \( P \) and \( R \)
\( c . P \) and \( Q \)
D. \( Q \) and \( R \)


State which surface of a plane mirror reflects most of the light incidents on it:
the front smooth surface or the back
silvered surface?
A. Back silvered surface
B. Front smooth surface
c. Both refract equally
D. Both reflect no light


The rate of interest


Which of the following statement is/are true for \( _{1} \boldsymbol{H}^{1},_{1} \boldsymbol{H}^{2} \) and \( _{1} \boldsymbol{H}^{3} \)
respectively? This question has multiple correct options
A. They are isotopes of each other
B. They have similar electronic configuration
c. They exist in the nature in the ratio 1: 2: 3
D. Their atomic masses are in the ratio 1: 2: 3


The boiling point of the hydrochloric acid varies with its concentration.
A. True
B. False


Among the VA(15) group elements one of them forms a compound sold under the name 'Pearl White'. the element
used is :
A .
B. P
\( c \cdot s b \)
D. Bi


On acid hydrolysis, propane nitrile gives
A. Propanal
B. Acetic acid
c. Propionamide
D. Propanoic acid


The gravitational force acting on a
particle of \( 1 g \) due to a similar particle is
equal to \( 6.67 \times 10^{-11} \). Calculate the
seperation between the particles.


solve
\( x y \frac{d y}{d x}=x^{2}+2 y^{2} \)


Write down name of functional group
\( -\boldsymbol{X} \)


The water is reabsorbed under the
influence of ADH. it is
A. Active reabsorption
B. obligatory reabsorption
c. Facultative
D. All of the above


A emulsifier is a substance which:
A. stabilises the emulsion
B. homogenises the emulsion
C . coagulates the emulsion
D. accelerates the dispersion of liquid in liquid


Consider the following statements:
(a) High blood pressure is an infectious disease.
(b) Penicillin is effective against
bacteria because it inhibits their wall
formation.
(c) AlDS spreads, through sex, blood to blood contact and from mother to child.
Which of the above statements are
correct?
\( A \cdot(a) \) and \( (b) \)
B. (b) and (c)
\( c \cdot(a),(b) \) and \( (c) \)
D. None of the above


A particle moving in straight line
diverse a distance \( x \) in that straight line
from a fixed point in time \( t . \) If \( \boldsymbol{x}= \) \( a \cos \sqrt{\mu} t\{\text { Where } \mu>0) . \) Find the
acceleration of the particle in time \( t \)
A. \( -\mu x \)
B. \( \mu x \)
c. \( -\sqrt{\mu} x \)
D. \( \sqrt{\mu} x \)


Thermal radiations are similar to
A . \( \alpha \) rays
B. X-rays
c. cathode rays
D. none of these


What is the area of the region bounded
by the lines \( x=y, y=0 \) and \( x=4 ? \)
A. 4 square units
B. 8 square units
c. 12 square units
D. 16 square units


The total magnification produced by a compound microscope is \( 20 . \) The magnification produced by the eye piece along is \( 5 . \) The microscope is focused on a certain object. The distance between the objective and
eyepiece is observed to be \( 14 \mathrm{cm} . \) Then the focal lengths of the objective and eyepiece are respectively, if final image formed at near point \( (D=20 \mathrm{cm}) \)
A. \( 2 \mathrm{cm}, 5 \mathrm{cm} \)
B. \( 5 \mathrm{cm}, 10 \mathrm{cm} \)
\( \mathrm{c} \cdot 3 \mathrm{cm}, 9 \mathrm{cm} \)
D. \( 4 \mathrm{cm}, 12 \mathrm{cm} \)


Which of the following is called
Westron?
A \( . C H_{3} C l \)
в. \( C H C l_{3} \)
c. \( C H C l_{2} . C H C l_{2} \)
D. \( C C l_{2}=C H C l \)


The term that would apply to \( ^{16} \mathrm{O} \) and \( 170 ? \)
A. Isotopes
B. Isobars
c. Isoelectronics
D. Isotones


If the angle of projection is \( 60^{\circ}, \) the height of the projectile when it has travelled a distance \( \frac{3 R}{4} \) is \( (R \) is the range)
A \( \cdot \frac{3 \sqrt{3} R}{16} \)
в. \( \frac{2}{3} R \)
c. \( \frac{\sqrt{3} R}{16} \)
D. \( \frac{4}{5} R \)


Write down the set represented by the
shaded region in figure (ii)


Moment of any force is equal to the algebraic sum of the components of that force. This is known as:
A. Principle of moments
B. Principle of combination
c. Law of inflution
D. All


The interior of a building is in the form of a right circular cylinder of a diameter \( 4.2 \mathrm{m} \) and height \( 4 \mathrm{m}, \) surmounted by a cone. The vertical height of the cone is 2.1 \( \mathrm{m} \). Find the outer surface area and
volume of the building.(Take \( \pi=22 / 7) \)
A. Outer surface area \( =72.4 \mathrm{m}^{2} ; \) Volume \( =68.142 \mathrm{m}^{3} \)
B. Outer surface area \( =72.4 \mathrm{m}^{2} ; \) Volume \( =65.142 \mathrm{m}^{3} \)
c. outer surface a rea \( =75.4 m^{2} ; \) volume \( =68.142 m^{3} \)
D. Outer surface area \( =75.4 \mathrm{m}^{2} ; \) Volume \( =65.142 \mathrm{m}^{3} \)


In copper, each atom releases one electron. If a current of \( 1.1 \mathrm{A} \) is flowing in the copper wire of diameter 1mm then
the drift velocity of electrons, will a pproximately be (density of copper \( = \) \( 9 \times 10^{3} \mathrm{Kgm}^{-3} \) and its atomic weight
\( =\mathbf{6 3}) \)
A. \( 10.3 \mathrm{mm} / \mathrm{s} \)
B. \( 0.1 \mathrm{mm} / \mathrm{s} \)
c. \( 0.2 \mathrm{mm} / \mathrm{s} \)
D. \( 0.2 \mathrm{cm} / \mathrm{s} \)


A point \( P \) is such that its perpendicular
distance from the line \( \boldsymbol{y}-\mathbf{2 x + 1}=\mathbf{0} \)
is equal to its distance from the
origin,then the locus of the point \( \boldsymbol{P} \)
A \( \cdot x^{2}+4 y^{2}+4 x y+4 x-2 y-1=0 \)
B. \( x^{2}+y^{2}+4 x y+x-y-1=0 \)
c. \( x^{2}+4 y^{2}-1=0 \)
D. None of these


if \( \boldsymbol{f} \) and \( \boldsymbol{g} \) are real function defined by
\( \boldsymbol{f}(\boldsymbol{x})=\mathbf{2} \boldsymbol{x}-\mathbf{1} \) and \( \boldsymbol{g}(\boldsymbol{x})=\boldsymbol{x}^{2}, \) then
A. \( (3 f-2 g)(1)=1 \)
В. \( (f g)(2)=10 \)
C \( \cdot g^{3}(2)=128 \)
D \( \cdot\left(\frac{\sqrt{f}}{g}\right)(2)=\frac{\sqrt{3}}{2} \)


Algae are not associated with diseases
unlike many fungi and bacteria. What is
the reason for this?


Volume of air inspired or expired with each normal breath is called as
A. Tidal volume
B. Inspiratory capacity.
c. Total lung capacity
D. Residual volume.


The locus of the mid points of the chord
of the circle \( x^{2}+y^{2}=4, \) which
subtended a right angle at the origin is
A. \( x+y=1 \)
B . \( x^{2}+y^{2}=1 \)
c. \( x+y=2 \)
D. \( x^{2}+y^{2}=2 \)


The population of a city in \( J a n .1987 \) was \( 20,000 . \) It increased at the rate of
\( 2 \% \) per annum. Find the population of the city in \( j a n .1997 \)


A ray of light suffers refraction through equilateral prism. The deviation produced by the prism does not depend on the :
A. angle of incidence
B. colour of light.
c. material of prism.
D. size of prism


Infant mortality rate in India has declined to \( _{-}-_{-}-_{-} \) per thousand as
per Census 2011
A . 32
B. 47
\( c \cdot 5 \)
D. 66


An ideal coil of \( 10 \mathrm{H} \) is joined in series
with a resistance of \( 5 \Omega \& \) a battery of \( 5 V . \) Two seconds after the connection is
made, the current flowing in amperes in the circuit is:
A \( \cdot e^{-1} \)
В \( \cdot\left(1-e^{-1}\right) \)
\( \mathbf{c} \cdot 1-e \)
D. \( e \)


bricks each. Aswin arranged his four
bricks as shown in figure A. Anwar arranged his bricks as shown in figure
B, in order to be a taller one.
Now let us complete the following
sentences by choosing the right option
below
(equal to, less than, more than)
a) The force of \( A \) on the ground is the force of \( B \) on the
ground.
b) The area that \( A \) occupies is
\( B \) on the ground.
c) The pressure exerted by \( A \) is the pressure exerted by B.


Assertion
In an adiabatic process change in internal energy of a gas in equal to work done on or by the gas in the process.
Reason
Temperature of gas remains constant in
an adiabatic process.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The compound \( X \) formed by the
reaction of furfural \( Y \) with ethanol is :
A. an aldol
B. an acetal
c. a ketal
D. a hemiacetal


From a solid cylinder whose height is \( 4 \mathrm{cm} \) and radius \( 3 \mathrm{cm}, \) a conical cavity of height \( 4 \mathrm{cm} \) and base radius \( 3 \mathrm{cm} \) is
hollowed out. What is the volume of the
remaining solid?
\( \mathbf{A} \cdot 9 \pi c m^{3} \)
В. \( 15 \pi c m^{3} \)
\( \mathrm{c} \cdot 21 \pi c m^{3} \)
D. \( 24 \pi c m^{3} \)


The order of basic strength of the given
basic nitrogen atoms is :
A \( . I I I>I I>I>I V \)
В. \( I I I>I>I I>I V \)
c. \( I>I I I>I I>I V \)
D. \( I I>I I I>I>I V \)


Find the matrix \( A \) such that
\( \left[\begin{array}{cc}2 & -1 \\ 1 & 0 \\ -3 & 4\end{array}\right] A=\left[\begin{array}{cc}-1 & -8 \\ 1 & -2 \\ 9 & 22\end{array}\right] \)


In a cassette player, material used for
coating magnetic tapes is :
A . cobalt
в. \( \operatorname{CoFe}_{2} \mathrm{O}_{4} \)
c. \( \operatorname{NiFe}_{2} O_{4} \)
D. nickel


A gas \( x \) at 1 atm is bubbled through a solution containing a mixture of \( 1 \mathrm{M} \) \( Y^{\ominus} \) and \( 1 \mathrm{M} Z^{\ominus} \) at \( 25^{\circ} \mathrm{C} . \) If the reduction
potential is \( \mathbf{Z}>Y>\mathbf{X}, \) then :
This question has multiple correct options
A. Y will oxidize X only
B. Y will oxidize Z only
c. z will oxidize \( x \) and \( Y \)
D. zwill reduce both \( x \) and \( y \)


The velocity of a body moving with a uniform acceleration of \( 2 m / \sec ^{2} \) is 10 \( m / \) sec. Its velocity after an interval of \( 4 \sec \) is
\( A \cdot 12 \mathrm{m} / \mathrm{sec} \)
B. \( 14 \mathrm{m} / \mathrm{sec} \)
c. \( 16 \mathrm{m} / \mathrm{sec} \)
D. 18 m/sec


Find the hydrolysis product of maltose:
A . \( \alpha-D- \) glucose \( +\alpha-D- \) glucose
B. \( \alpha-D- \) glucose \( +\alpha-D- \) fructose
c. \( \alpha-D-g l u c o s e+\alpha-D-g a l a c t o s e \)
D. \( \alpha-D- \) fructose \( +\alpha-D- \) galactose


Ecological succession begins with species and end with \( \ldots \). .......stage.


A heating coil is rated \( 100 W, 220 V \)
The coil is cut in half and two pieces are joined in parallel to the same source. Now what is the energy (in
\( \times 10^{2} J \) ) liberated per second?


The value of \( \sec ^{-1}\left(\frac{1}{1-2 x^{2}}\right)+ \)
\( 4 \cos ^{-1} \sqrt{\frac{1+x}{2}} \) is equal to
\( A \cdot A P \)
в. G.P.
c. н.P
D. None of these


The wavelength of the radiation emitted
by Hydrogen when compared to \( \boldsymbol{H} \boldsymbol{e}^{+} \) is:
A. 2 times that of \( H e^{+} \) ion
B. 3 times that of \( H e^{+} \) ion
c. 4 times that of \( H e^{+} \) ion
D. same as \( H e^{+} \)


A double convex lens of focal length 6 \( \mathrm{cm} \) is made of glass of refractive index
1.5. The radius of curvature of one
surface which is double that of the
other surface will be
\( A .3 c m \)
B. 9 cm
\( \mathbf{c} \cdot 12 c m \)
D. \( 24 \mathrm{cm} \)


Which of the following is/are the
properties of moment of a couple?
This question has multiple correct options
A. It tends to produce pure rotation.
B. It is different about any point in the plane of lines of action of the forces.
C. It can be replaced by any other couple of the same moment
D. The resultant of set of two or more couples is equal to the sum of the moments of the individual couples.


Raindrops of radius 1 mm and mass
4 mg are falling with a speed of \( 30 m / s \)
on the head of a bald person. The drops splash on the head and come to rest. Assuming equivalently that the drops cover a distance equal to their radii on the head, estimate the force exerted by each drop on the head.


Which of the following molecular formulas corresponds to that of an unsaturated fatty acid?
A. \( C_{18} \mathrm{H}_{35} \mathrm{COOH} \)
в. \( C_{16} H_{33} \) СООН
c. \( C_{19} \mathrm{H}_{39} \mathrm{COOH} \)
D. \( C_{17} H_{35} \) COOH


Draw an Ellingham diagram for metal oxides and explain what information can be obtaines from it.ln addition
explain why why most of the lines slope upwards from left 10 right,why the lines change in slope, and what happens when a line crosses the \( \Delta G=0 \) axis


In which of the following we see the phenomena of total internal reflection?
A. Rainbows
c. camera
D. Both a and


Why is the distance between stars
expressed in light years? What do you understand by the statement that a star is eight light years away from the Earth
\( ? \)


A rocket of mass \( 5700 k g \) ejects mass at
a constant rate of \( 15 k g / s \) with constant
speed of \( 12 k m / s . \) The acceleration of the rocket 1 minute after the blast is
\( \boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{2} \)
A \( \cdot 34.9 m / s^{2} \)
В. \( 27.5 m / s^{2} \)
c. \( 3.50 m / s^{2} \)
D. \( 13.5 m / s^{2} \)


Write the full form of BOD.


If the dipole is place in a non-uniform
electric field an angle \( \theta, \) in addition
tarque
A. Experiences a force
B. Experiences a repulsive force
c. No any kind of force
D. Neither attractive nor repulsive force


The eccentricity of the ellipse \( x^{2}+ \)
\( 4 y^{2}+8 y-2 x+1=0 \) is
\( A \cdot \frac{\sqrt{3}}{2} \)
в. \( \frac{\sqrt{5}}{2} \)
\( c \cdot \frac{1}{2} \)
D.


Identify the correct order of lattice energies.
A. \( C s C l<R b C l<K C l<N a C l \)
в. \( K C l>C a C l_{2}>A l C l_{3} \)
c. \( N a C l<L i C l<M g C l_{2}<A l C l_{3} \)
D. \( L i C l>N a C l<M g C l_{2}<A l C l_{3} \)


An emf of 100 millivolts is induced in a
coil when the current in another nearby coil becomes \( 10 A \) from zero to 0.1 sec
The corfficient of mutual induction
between the two coils will be
\( \mathbf{A} \cdot 1 m H \)
в. \( 10 \mathrm{mH} \)
c. \( 100 \mathrm{mH} \)
D. \( 1000 m H \)


Given the velocity-time graph. How can it be used to find the displacement of the body in a given time:
A. The net area of the colored region, under velocity-time \( \operatorname{graph} \)
B. The total area under velocity-time graph
c. Slope of velocity-time graph
D. None of the above


Study the bar graph representing the
number of persons in various age
groups in a town shown in the above fig.
Observe the bar graph and answer the
following questions:

What is the number of persons in the
age-group \( 60-65 ? \)


There are no base cations. If true write 1
else write 0


Assertion
The electronic configuration of nitrogen atom is represented by the given figure.
Reason
The electronic configuration of the
ground state of an atom is the one
which has the greatest multiplicity.
\( \|\quad\| \quad \uparrow \quad \uparrow \quad \uparrow \)
and not as
\( \|\quad\| \quad \| \quad \uparrow \)
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


Given that \( 2 a-3 b=c ;-3 a+5 b=d \)
expressing \( a \) and \( b \) as linear
combinations of \( c \) and \( d \) we get \( a= \)
\( k c+m d \) and \( b=h c+r d . \) Find \( k+ \)
\( \boldsymbol{m}+\boldsymbol{h}+\boldsymbol{r} ? \)


The temperature of the substance remains constant when it is melting
and boiling though some quantity of heat is supplied. What happens to this
energy?
A. It is dissipated as sound energy
B. It is consumed to increase the energy of the molecules
C. It is used to change the state of the substance
D. It is still an unsolved problem in science


Find the inverse of the matrix
\( \$ \$ \mathrm{~ l l e f t [ l b e g i n ~ \{ a r r a y \} ~} \mid 5 \& 11 \backslash 14 \& 9 \)
\( \mathrm{~ l e n d ~ \{ a r r a y \} l r i g h t ] \$ \$ ~ b y ~ e l e m e n t a r y ~} \)
transformations.


limiting friction is also celled as


Iron obtained from blast furnace is:
A. Wrought iron
B. Cast iron
c. Pig iron
D. steel


Which is the principal cation in the plasma of the blood?
A. Calcium
B. Sodium
c. Potassium
D. Magnesium


Sound is produced when your school bell in struck with hammer. Why?


Suppose, the torque acting on a body is \( \operatorname{given} \) by \( \boldsymbol{\tau}=\boldsymbol{K} \boldsymbol{L}+\boldsymbol{M} \boldsymbol{I} / \boldsymbol{w} . \) Where \( \boldsymbol{L}= \)
angular momentum, \( I= \) moment of
inertia, \( \boldsymbol{w}= \) angular speed. The
dimensional formula for \( \boldsymbol{K} \boldsymbol{M} \) is same
as that for:
A \( \cdot \) time \( ^{2} \)
B . time \( ^{4} \)
\( \mathrm{c} \cdot \operatorname{time}^{-2} \)
D. time \( ^{-4} \)


Movement of alimentary canal does not help in slipping down of food is
A. Peristalsis movement
B. Pendular (segmentary) movement
c. Both
D. None


For which of the species, Bohrs theory is not applicable?
\( \mathbf{A} \cdot B e^{+3} \)
B. \( L i^{+2} \)
\( \mathbf{c} \cdot H e^{+2} \)
D. \( H \)


(a) The conductivity of \( 0.001 \mathrm{mol} \mathrm{L}^{-1} \)
solution of \( \boldsymbol{C H}_{3} \boldsymbol{C O O H} \) is \( 3.905 \times 10^{-5} \)
Scm \( ^{-1} \). Calculate its molar conductivity and degree of dissociation. Given: \( \left(H^{+}\right)=349.6 \mathrm{S} \mathrm{cm}^{2} \mathrm{mol}^{-1} \) and
\( \left(C H_{3} C O O^{-}\right)=40.9 S \mathrm{cm}^{2} m o l^{-1} \)
(b) Define electro chemical cell. What
happens if external potential
applied becomes greater than \( \boldsymbol{E}_{\text {cell}} \) of
electro chemical cell?


Evaluate the following using suitable identity:
\( (10 x-1)^{2} \)
\( (x-8 y)^{2} \)


A parallel plate condenser is immersed
in an oil of dielectric constant 2. The
field between the plates is :
A \( \cdot \) increased, proportional to \( \frac{1}{2} \)
B. decreased, proportional to - 2
c. increased, proportional to - 2
D. decreased, proportional to \( -\frac{1}{2} \)


find the \( n^{t h} \) term of G.P G.P: \( 2,6,18,54 \dots \)


If the direction of the current changes in the current carrying loop placed in some magnetic field perpendicular to loop, then Potential energy of loop is not effected because current is a scalar
quantity.Enter 1 if true and 0 if False.


Chloretone is:
A. \( C C l_{3} N O_{2} \)
в. \( C H_{3} C O C H_{2} C H C l_{2} \)
c. \( \left(C H_{3}\right)_{2} \) СОСНС\( l_{2} \)
D \( \cdot\left(C H_{3}\right)_{2} C(O H) C C l_{3} \)


\( \lim _{x \rightarrow a} \frac{x^{m}-a^{m}}{x-a}= \)
\( \mathbf{A} \cdot m a^{m-1} \)
B. \( m a^{m} \)
c. \( \frac{1}{m} a^{n} \)
D. \( a^{m-1} \)


Metal sols are negatively charged.
A. True
B. False


Draw \( \angle L M N=165^{\circ} \) and divide in into
four equal parts.


Parallel rays of light of intensity \( l= \)
\( 912 W m^{-2} \) are incident on a spherical
black body kept in surroundings of temperature 300 K. Take Stefan-
Boltzmann constant \( \sigma=5.7 \times \)
\( 10^{-5} W m^{-2} K^{-4} \) and assume that the
energy exchange with the surroundings is only through radiation. The final
steady state temperature of the black body is close to:
\( A \cdot \) 330 \( K \)
B. 660 K
c. \( 990 \mathrm{k} \)
D. \( 1550 \mathrm{K} \)


ff \( \boldsymbol{f}: \boldsymbol{A} \rightarrow \boldsymbol{B} \) is bijective function such
\( \operatorname{that} n(A)=10, \operatorname{then} n(B) \)


(a) In reference of Freundlich adsorption isotherm, write the expression for adsorption of gases on solids in the form of an equation.
(b) Write an important characteristic of lyophilic solutions.
(c) Based on type of particles of dispersed phase, give one example each of associated colloid and
multimolecular colloid.


Assertion: o-phenol sulphonic acid on heating at \( 100^{0} C \) changes to \( \mathrm{p} \)
phenol sulphonic acid. Reason: Sulphonation of phenol is a reversible process.
A. If both Assertion and Reason are correct and Reason is the correct explanation of Assertion
B. If both Assertion and Reason are correct but Reason is not the correct explanation of Assertion
C. If Assertion is correct but Reason is incorrect
D. If Assertion is incorrect but Reason is correct


The degree of tbe differential equation whose primitive is \( c^{2}+2 c y+a^{2}- \)
\( x^{2}=0, \) where \( c \) is an arbitrary and a is
definite constant is:


For electrolytic solution, the Van't Hoff
factor (i) is always equals to unity.
A. True
B. False


A rotating wheel has a speed of 1200 rpm and the it is made to slow down at
a constant rate at 2 rad\( / s^{2} \). The number of revolution it makes before coming to rest will be:


If \( \alpha \) and \( \beta \) are the roots of the equation
\( x^{2}-p x+q=0, \) then find the equation whose roots are \( \frac{\boldsymbol{q}}{\boldsymbol{p}-\boldsymbol{\alpha}} \) and \( \frac{\boldsymbol{q}}{\boldsymbol{p}-\boldsymbol{\beta}} \)


In which of three media; air, water and steel, does sound travel the fastest?
A . air
B. water
c. steel
D. none of these


\( \lim _{x \rightarrow \infty}\left(\frac{x^{2}+2 x-1}{2 x^{2}-3 x-2}\right)^{\frac{2 x+1}{2 x-1}} \) is equal
to
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( \infty \)
\( c \cdot \frac{1}{2} \)
D. None of these


If \( A \) is matrix of order \( m \times n \) and \( B \) is a
matrix of order \( n \times p, \) then the order of
\( A B \) is
\( \mathbf{A} \cdot p \times m \)
в. \( p \times n \)
c. \( n \times p \)
D. \( m \times p \)


Two waves of sound \( \boldsymbol{y}_{1}= \)
\( \mathbf{1 0} \sin (\mathbf{4 0 4} \boldsymbol{\pi} \boldsymbol{t}-\mathbf{0 . 2 x}) \) and \( \boldsymbol{y}_{\mathbf{2}}= \)
\( 8 \sin (400 \pi t-0.2 x) \) superpose. As a
result
A. at several places maximum intensity and at other places minimum intensity will be heard
B. 4 beats will be heard in a second
c. 2 beats will be heard in a second
D. there will be no change in intensity of the sound rather two separate waves would be heard


Identify \( \boldsymbol{X} \)
\( A \)
в.
\( c \)
\( D \)


The reaction \( M n O_{4}^{-}+M n^{2+} \rightarrow \)
\( M n O_{2} \) is an example of:
A. disproporitonation
B. oxidation
c. reduction
D. comproportionation


Common oxidation state of Scandium
¡<__ACCDOTABOVE__>s/are:
\( A \cdot+4 \)
B. +1
\( c \cdot+3 \)
D. +4 and +1


The lightest element in the periodic table is
A. lithium
B. fluorine
c. hydrogen
D. helium


Which of the following is colorless and odorless?
A. Propyne
B. 1-butyne
c. 2-butyne
D. All of the above


What happens when fused sodium
metal reacts with ammonia?


Slime moulds in the division
Myxomycota (true slime moulds) have
A. Feeding stages consisting of solitary individual cells
B. Spores that develop into free living amoeboid cells
c. spores that develop into flagellated gametes
D. None of the above


Density of water in the solid state is.............. than the density of water in the liquid
state
A. higher
B. lower
c. same
D. none of these


Evaluate : \( \int \frac{\boldsymbol{d} \boldsymbol{x}}{\mathbf{3} \sin ^{2} \boldsymbol{x}+\sin \boldsymbol{x}} \cos \boldsymbol{x}+\mathbf{1} \)
A \( \cdot \frac{2}{\sqrt{15}} \tan ^{-1}\left(\frac{2(\cot x-2)}{\sqrt{15}}\right) \)
в. \( \frac{2}{\sqrt{3}} \tan ^{-1}\left(\frac{3 \tan x-1}{\sqrt{15}}\right)+c \)
c. \( \frac{2}{\sqrt{3}} \tan ^{-1}\left(\frac{3 \tan x+1}{\sqrt{15}}\right)+c \)
D. \( \frac{2}{\sqrt{15}} \tan ^{-1}\left(\frac{2(\cot x-2)}{\sqrt{15}}\right) \)


Which is not a buffer solution:
A \( . N H_{4} C l+N H_{4} O H \)
в. \( C H_{3} \)СООН\( + \)СН\( _{3} \)СОО Na
c. \( C H_{3} C O O N H_{4} \)
D. \( N H_{4} N O_{3} \)


Coulomb's law states that the electric
force becomes weaker with increasing distance, Suppose that instead, the
electric force between two charged particles were independent of distance. In this case, would a neutral insulator
still be attracted towards the comb.


The following intramolecular redox
reaction shows a loss and gain of how much electrons?
\( \left(N H_{4}\right)_{2} C r_{2} O_{7} \rightarrow N_{2}+C r_{2} O_{3}+ \)
\( 4 H_{2} O \)
A. Six
B. Seven
c. Eight
D. None of these


A body with an initial temperature \( \theta_{1} \) is allowed to cool in a surrounding which
is at a constant temperature of \( \boldsymbol{\theta}_{0}\left(\boldsymbol{\theta}_{0}<\right. \)
\( \theta_{1} \) ). Assume that Newton's law of
cooling is obeyed. The temperature of the body after time \( t \) is best expressed
by, Let \( k= \) constant.
A \( \cdot\left(\theta_{1}-\theta_{0}\right) e^{-k t} \)
B \( \cdot\left(\theta_{1}-\theta_{0}\right) \ln (k t) \)
c. \( \theta_{0}+\left(\theta_{1}-\theta_{0}\right) e^{-k t} \)
D. \( \theta_{1} e^{-k t}=\theta_{0} \)


If the vertices of an equilateral triangle
have integral co-ordinates, then
A. Such a triangle is not possible
B. The area of the triangle is irrational
C. The area of the triangle is an integer
D. The area of the triangle is rational but not an integer


The mixture that forms maximum
boiling azeotrope is :
A. Water + Nitric acid
B. Ethanol + Water
c. Acetone + Carbon disulphide
D. Heptane + octane


The decreasing order of boiling points of alkyl halides is:
A. \( R F>R C l>R B r>R I \)
B. \( R B r>R C l>R I>R F \)
c. \( R I>R B r>R C l>R F \)
D. \( R C l>R F>R I>R B r \)
E \( . R I>R F>R C l>R B r \)


Find the value of \( y, \) if \( \left[\begin{array}{cc}x-y & 2 \\ x & 5\end{array}\right]= \)
\( \left[\begin{array}{ll}2 & 2 \\ 3 & 5\end{array}\right] \)


In which of the following the final image
is erect?
A. Compound microscope
B. Astronomical telescope
c. simple microscope
D. All of the above


The number of completed transitional series in the periodic table is / are:
A . 2
B. 3
\( c \cdot 4 \)
\( D \)


Define sericulture


\( \boldsymbol{p} \boldsymbol{H} \) of \( \mathbf{1 0}^{-8} \mathbf{M} \boldsymbol{B} \boldsymbol{a}(\boldsymbol{O} \boldsymbol{H})_{2} \) solution will
be:
A . 6.96
B. 6.31
c. 7.04
D. 7.08


Factorize:
\( \left(2 x^{3}+54\right) \)


Differentiate the following functions
with respect to \( \boldsymbol{x} \)
If \( y=\cos ^{-1}(2 x)+ \)
\( 2 \cos ^{-1} \sqrt{1-4 x^{2}}, 0<x<\frac{1}{2}, \) find \( \frac{d y}{d x} \)


Evaluate: \( \lim _{n \rightarrow \infty} \sum_{r=0}^{n-1} \frac{1}{n+r} \)
\( A \cdot \log 2 \)
B. \( 2 \log 2 \)
c. \( \frac{1}{2} \log 2 \)
D. \( \frac{1}{4} \log 2 \)


What is Hypermetropia? How can it be
corrected?


\( \boldsymbol{p} \wedge(\sim \boldsymbol{p}) \Rightarrow \boldsymbol{p} \) is
A. a tautology
B. a contradiction
C. neither tautology nor contradiction
D. none of these


The main fuse is connected in:
A. live wire.
B. neutral wire.
c. both the live and earth wires.
D. both earth and neutral wire.


Annual growth rings are formed due to activity of
A. Extra-stelar cambium
B. Intra-stelar cambium
c. Inter-stelar cambium
D. All of the above


Prakash peddles a stationary bicycle, the pedals of which are attached to a
100 turn coil of area \( 0.1 m^{2} . \) The coil
rotates at half a revolution per second
and it is placed in a uniform magnetic field of \( 0.01 T \) perpendicular to the axis
of rotation of the coil. Determine the
maximum voltage generated in the coil.


The percentage of marks obtained by a student in a unit test are given below:
Unit II
II IV \( t \) est
\( \% \) of 70 \( \quad \) 72
\( 65 \quad 68 \)
marks
What is the probability that the student gets more than \( 70 \% \) marks
A \( \cdot \frac{1}{5} \)
в. \( \frac{2}{5} \)
\( c \cdot \frac{3}{5} \)
D.


A farmer has enough food to feed 20
animals in his cattle for 6 days. How long would the food last if there were 10
more animals in his cattle?


For the reaction, \( 2 N O+C l_{2} \longrightarrow \)
\( 2 N O C l, \) the following mechanism has
been proposed:
\( N O+C l_{2} \rightleftharpoons N O C l_{2} \)
\( N O C l_{2}+N O \longrightarrow 2 N O C l \)
(slow)
The rate law for the reaction is:
A \( \cdot \) Rate \( =k[N O]^{2}\left[C l_{2}\right] \)
B・Rate \( =k[N O]\left[C l_{2}\right]^{2} \)
c. Rate \( =k\left[N O C l_{2}\right] \)
D・Rate \( =k[N O C l]^{2} \)


Solve: \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}+\mathbf{1}=\boldsymbol{e}^{\boldsymbol{x}+\boldsymbol{y}} \)


In an estimation of sulphur by Carius
method 0.2175 g of the substance gave 0.5825 g of barium sulphate. Calculate then percentage of sulphur in the compound.
A . \( 30.12 \% \)
B. \( 42.22 \% \)
c. \( 36.78 \% \)
D. 45.36\%


\( \operatorname{Let}\left|\frac{z_{1}-2 z_{2}}{2-z_{1} \bar{z}_{2}}\right|=1 \) and \( \left|z_{2}\right| \neq 1, \) where
\( z_{1} \) and \( z_{2} \) are complex numbers. Find
the value of \( \left|z_{1}\right| \)


Suppose the point with coordinates (-12,5) is on the terminal side of angle
\( \theta, \) the value of the sine trigonometric function of \( \theta . \) is \( \frac{a}{13} \) Find \( a \)


The number of arbitrary constant in the particular solution of a differential equation is
\( A \cdot 3 \)
B. 4
c. infinite
D. zero


Integrate: \( \int \frac{x}{x^{4}-x^{2}+1} d x \)


Draw a graph for the following pair of
linear equations in two variables and find their solution from the graph.
\( 2 x+y=5 \)
\( 3 x-2 y=4 \)


Solve :
\[
\tan ^{2} \theta-2 \sin \theta=0
\]


A number is 27 more than the number
obtained by reversing its digits. If its unit's and ten's digits are \( x \) and \( y \)
respectively, write the linear equation representing the above statement


Chipko movement was launched for the protection of
A. Grasslands
B. Forests
c. Livestock
D. Wet lands


Is 402 a term of the sequence:
\( 8,13,18,23, \dots \dots \dots \dots \dots \)


What is chemical change?


Each codon consists of how many nitrogen bases?
A. four
B. twenty
c. three
D. sixty four


Electric charge \( Q, Q \) and \( -2 Q \)
respectively are place at the three corner of an equilateral triangle of side
a. Magnitude of the electric dipole moment of the system is: