In anaerobic respiration, the seeds
respire
A. In the presence of \( 0_{2} \)
B. In the presence of \( \mathrm{CO}_{2} \)
\( c . \) In the absence of \( 0_{2} \)
D. In the absence of \( \mathrm{CO}_{2} \)


For the equilibrium \( N_{2}+3 H_{2} \rightleftharpoons \)
\( \mathbf{2} N \boldsymbol{H}_{3}, \boldsymbol{K}_{6} \) at \( 1000 \mathrm{K} \) is \( \mathbf{2 . 3 7} \times \mathbf{1 0}^{-3} \)
Equilibrium \( \left[N_{2}\right]=2 . M\left[H_{2}\right]=3 M \) the
concentration of \( \boldsymbol{N} \boldsymbol{H}_{3} \) is:
A . 0.00358 M
в. 0.0358 М
c. 0.358 М
D. 3.58 м


Non combustible hydride is
A. \( \mathrm{PH}_{3} \)
в. \( \mathrm{SbH}_{3} \)
c. \( \mathrm{NH}_{3} \)
D. AsH \( _{3} \)


Balance the following equation.
\( \boldsymbol{P}_{2} \boldsymbol{H}_{4} \rightarrow \boldsymbol{P} \boldsymbol{H}_{3}+\boldsymbol{P}_{4} \boldsymbol{H}_{2} \)


Which of the following acid does not have - COOH group?
A . Picric acid
B. Ethanoic acid
c. Benzoic acid
D. Salicylic acid


\( \left(5 x^{2}-9 x+3\right),\left(10 x^{4}+17 x^{3}-\right. \)
\( \left.62 x^{2}+30 x-3\right) \)


Usually the process of photosynthesis is
A. Slower than respiration
B. Faster than respiration
c. Equal to respiration
D. None of the above


A die is rolled so that the probability of
face \( i \) is proportional to \( i,\{i= \) \( 1,2, \dots .6\} . \) The probability of an even number occurring when the die is rolled
is
\( A \cdot \frac{7}{4} \)
B. \( \frac{4}{7} \)
\( c \cdot \frac{5}{7} \)
D. None of these


Find the ratio in which the \( X Y \) - plane
divides \( A B \) if is (1,2,3) and \( B \) is (-3,4,-5)
Also find the positive vector of the point of division.


In distance-time graph, which of the following is plotted on the \( y \) -axis?
A. speed
B. distance
\( c . \) time
D. none of the above


Casparian strips occurs in
A. Cortex
B. Epidermis
c. Endodermis
D. Pericycle


Sugar and Salt solutions
a re


The probability of student \( A \) passing an examination is \( 2 / 9 \) and of students, \( B \) passing is \( 5 / 9 . \) Assuming the two
events: \( A \) passes'. \( B \) passes' as independent, find the probability of only
\( A \) passing the examination


The air pressure in the balloon is due to the air filled in it, striking the walls of the balloon.
A. True
B. False


Find the pressure in the circular water
pipe shown in the figure


Simplify using associative property :
\( \frac{7}{16} \times\left(\frac{-24}{49} \times \frac{28}{15}\right) \)
A \( \cdot \frac{28}{15} \)
B. \( \frac{2}{5} \)
c. \( \frac{-2}{5} \)
D. \( \frac{-3}{15} \)


Which of the following oxides of nitrogen is anhydride of nitric acid?
A \( \cdot \mathrm{N}_{2} \mathrm{O}_{3} \)
B. \( N_{2} O_{4} \)
\( \mathbf{c} \cdot \mathbf{N}_{2} \mathbf{O}_{\mathbf{5}} \)
\( D \cdot N_{2} O \)


Arrange the following elements in increasing order their Half life period, Uranium, Polonium, Radon, Strontium.


The reflection of the point \( P(1,0,0) \) in the İine \( \frac{x-1}{2}=\frac{y+1}{-3}=\frac{z+10}{8} \) is
A \( \cdot(3,-4,-2) \)
B \( \cdot(5,-8,-4) \)
c. (1,-1,-10)
D. (2,-3,8)


Chemical formula of corundum is
A \( \cdot A l_{2} O_{3} \cdot H_{2} O \)
B. \( S i C \)
c. \( A l_{2} O_{3} \cdot 2 H_{2} O \)
D. \( A l_{2} O_{3} \)


If \( \boldsymbol{\alpha}, \boldsymbol{\beta}, \boldsymbol{\gamma} \in[\mathbf{0}, \boldsymbol{2} \boldsymbol{\pi}], \) then the sum of all
possible values of \( \alpha, \beta, \gamma \) if \( \sin \alpha= \) \( -\frac{1}{\sqrt{2}}, \cos \beta=-\frac{1}{2}, \tan \gamma=-\sqrt{3}, \) is
A \( \cdot \frac{22 \pi}{3} \)
B. \( \frac{21 \pi}{3} \)
c. \( \frac{20 \pi}{3} \)
D. \( 8 \pi \)


Methyl orange gives red colour in
A. \( K O H \) solution
B. HCI solution
c. \( N a_{2} C O_{3} \) solution
D. \( N a C I \) solution


A particle is moving along a fixed
circular orbit with uniform speed. Then
the correct statement among the
following is:
A. Angular momentum of particle is constant only in magnitude but its direction changes from point to point
B. Angular momentum of particle is constant only in direction but its magnitude changes from point to point
C. Angular momentum of particle is constant both in magnitude and direction
D. Angular momentum of particle is not constant both in magnitude and direction


Which of the following structural formula represents cyclohexyl alcohol?
\( A \)
B.
\( c \)
D. None of the above


How much pressure would be required
to raise water to the top of a 416 ft. high
tree ?
\( \mathbf{A} \cdot 1 \mathrm{atm} \)
B. 13 atm
c. -77 bars
D. All of the above


The function \( f(x)=\sin ^{-1}(\cos x) \) is \( :- \)
A. discontinuous at \( x=0 \)
B. continuous at \( x=0 \)
C. differentiable at \( x=0 \)
D. none of these


Let \( V \) and \( E \) denote the gravitational potential and gravitational field at a point. It is possible to have This question has multiple correct options
A. \( V=0 \) and \( E=0 \)
B. \( V=0 \) and \( E \neq 0 \)
c. \( V \neq 0 \) and \( E=0 \)
D. \( V \neq 0 \) and \( E \neq 0 \)


The positive response of the plants towards the gravitation is called
A. Phototropism
B. Geotropism
c. Hydrotropism
D. chemotropism


For a reversible reaction \( \boldsymbol{a} \boldsymbol{A}+\boldsymbol{b} \boldsymbol{B} \rightleftharpoons \)
\( c C+d D ; \) the variation of \( K \) with
temperature is given by \( \log \frac{\boldsymbol{K}_{2}}{\boldsymbol{K}_{1}}=\frac{-\boldsymbol{\Delta} \boldsymbol{H}^{o}}{\mathbf{2 . 3 0 3} \boldsymbol{R}}\left[\frac{\mathbf{1}}{\boldsymbol{T}_{2}}-\frac{\mathbf{1}}{\boldsymbol{T}_{1}}\right] \) then
This question has multiple correct options
A \( \cdot K_{2}>K_{1} \) if \( T_{2}>T_{1} \) for an endothermic change
B. \( K_{2}<K_{1} \) if \( T_{2}>T_{1} \) for an endothermic change
C . \( K_{2}>K_{1} \) if \( T_{2}>T_{1} \) for an exothermic change
D. \( K_{2}<K_{1} \) if \( T_{2}>T_{1} \) for an exothermic change


External dimensions of a wooden
cuboid are \( 30 \mathrm{cm} \times 25 \mathrm{cm} \times 20 \mathrm{cm} . \) If
the thickness of wood is \( 2 \mathrm{cm} \) all round
find the volume of the wood contained in cuboid formed.


If the lines \( \boldsymbol{a} \boldsymbol{x}+\boldsymbol{y}+\mathbf{1}=\mathbf{0}, \boldsymbol{x}+\boldsymbol{b} \boldsymbol{y}+ \)
\( \mathbf{1}=\mathbf{0} \& \boldsymbol{x}+\boldsymbol{y}+\boldsymbol{c}=\mathbf{0} \) where \( \mathbf{a}, \mathbf{b} \& \mathbf{c} \)
are distinct real numbers different from
are concurrent, then the value of \( \frac{1}{1-a}+\frac{1}{1-b}+\frac{1}{1-c}= \)
\( A \cdot 4 \)
B. 3
\( c \cdot 2 \)
\( D \)


Ethers like ROR can be cleaved by concentrated HI but not by HCl because:
A . \( I^{-} \) is a weaker nucleophile than \( C l^{-} \)
B. \( I^{-} \) is stronger nucleophile than \( C l^{-} \)
c. \( S_{N} 1 \) mechanism carried out in this reaction is rapidly in presence of HI
D. None of the above


A coffee cup calorimeter initially contains
\( 125 g \) of water at a temperature of \( 24.2^{0} C \)
After (10.5gm) is added to the water at the
same temperature, the final temperature becomes \( 21.1^{0} \mathrm{C} \). The heat of solution is:
\( A \cdot 85 J / g \)
B. 110 J/g
c. 270 J/g
D. 167 J/g


If \( f(x)=\cos ^{2} x+\cos ^{2}\left(\frac{\pi}{3}+x\right) \)
\( \cos x \cos \left(\frac{\pi}{3}+x\right) \) then \( 4 f\left(\frac{\pi}{8}\right) \) is equal
to


Two metallic spheres \( A \) and \( B \) are made of same material and have got an identical surface finish. The mass of
sphere \( \mathbf{A} \) is four times that of \( \mathbf{B} . \) Both
the spheres are heated to the same
temperature and placed in a room having a lower temperature but thermally insulated from each other.
A. The ratio of heat loss of A to that of B is \( 2^{4 / 3} \)
B. The ratio of heat loss of A to that of B is \( 2^{2 / 3} \)
C. The ratio of the initial rate of cooling of A to that of B is \( 2^{2 / 3} \)
D. The ratio of the initial rate of cooling of \( A \) to that of \( B \) is \( 2^{-1 / 3} \)


A rubber ball of mass 250 g hits a wall normally with a velocity \( 10 m s^{-1} \) and bounces back with a velocity of \( 8 m s^{-1} . \) The impluse is \( -\dots-\dots--N \) s.
A. -0.5
в. +0.5
c. -4.5
D. +4.5


Starting from species, phylum comes
before
A. Genus
B. Kingdom
c. order
D. None of these


Write Ohm's law. Write name of devices
\( X \) and \( Y \) in the given circuit related to
Ohm's Law.


Let the instantaneous velocity of a rocket just after launching, be given by
the expression \( \boldsymbol{v}=2 \boldsymbol{t}+\boldsymbol{3} \boldsymbol{t}^{2} \) (where \( \boldsymbol{v} \) is
in \( m s^{-1} \) and \( t \) is in seconds). Find out
the distance travelled by the rocket
from \( t=2 s \) to \( t=3 s \)


If \( A_{2 \times 3}, B_{4 \times 3}, C_{2 \times 4} \) are three matrices,
then which of the following is/are defined ?
A \( . A C^{T} B \)
B . \( B^{T} C^{T} A \)
\( \mathbf{c} \cdot A B^{T} C \)
D. All of these


Which of the following is not an example of a heterogeneous catalysis?
This question has multiple correct options
A. Formation of \( S O_{3} \) In the chamber process.
B. Formation of \( S O_{3} \) in the contact process.
C. Hydrolysis of an ester in the presence of \( H^{+} \) ions.
D. Combination of \( H_{2} \) and \( C l_{2} \) in the presence of
moisture.


If the plates of a parallel plate capacitor are not equal in area, then quantity of charge
A. On the plates will be same but nature of charge will differ
B. On the plates as well as nature of charge will be different
c. on the plates will be different but nature of charge will be same
D. As well as nature of charge will be same


Derive Faradays law of induction from law of conservation of energy.


The diagram shows two circular loops a wire(A and B) centred on and
perpendicular to the \( x \) -axis, and
oriented with their planes parallel to
each other. The y-axis passes vertically through loop A(dashed line). There is a
current \( I_{B} \) in loop \( \mathrm{B} \) as shown. Possible
actions which we might perform on loop
\( \mathbf{A} \) are
A. Move A to the right along x axis closer to B
B. Move A to the left along x axis away from B
C. As viewed from above, rotate A clockwise about y-axis
D. As viewed from above, rotate A anticlockwise about y axis


The sum of the squares deviations for
10 observations taken from their mean
50 is \( 250 . \) The coefficient of variation is
A . \( 10 \% \)
B . \( 40 \% \)
c. \( 50 \% \)
D. none of these


Two different dice are tossed together.
Find the probability of the sum of no's appearing on two dice is 5
A \( \cdot \frac{1}{36} \)
в. \( \frac{1}{18} \)
c. \( \frac{1}{9} \)
D. \( \frac{1}{6} \)


The solubility of gases in water is
proportional to pressure
and \( _{-}---- \) proportional to
temperature.
A. directly
B. inversely
C . directly, inversely
D. inversely, directly


The refraction of light is commonly known as:
A. Bending
B. Scattering
c. Reflection
D. Interference


Green chemistry means such reactions
which -
A. are related to the depletion of ozone layer
B. study the reactions in plants
c. produce colour during reactions
D. reduce the use and production of hazardous
chemicals


Why there are two parallel plane mirrors
in a barber shop?
A. Two parallel plane mirrors form infinite images.
B. The customer can see the image of back of his head with the help of this setup.
C. The setup focusses light and helps the barber to cut the hair better.
D. None of the above.


When the p-njunction diode is reverse biased, the thickness of the depletion
layer
A . increases
B. decreases
c. becomes zero
D. remain constant


Among the following, the correct
statement is:
A. One would expect charcoal to adsorb chlorine more than hydrogen sulphide
B. Brownian movement is more pronounced for smaller particles than for bigger-particles
C. Hardy Schulze law states that bigger the size of the ions, the greater is its coagulating power
D. Sols of metal sulphides are lyophilic


What are meristmatic and permanent
tissue?


The smog is essentially caused by the
presence of
\( \mathbf{A} \cdot \mathrm{O}_{2} \) and \( \mathrm{O}_{3} \)
B. \( O_{3} \) and \( N_{2} \)
C. Oxides of sulphur and nitrogen
\( D \cdot O_{2} \) and \( N_{2} \)


A bullet of mass \( 50 g \) travelling at \( 500 m / s \) penetrates \( 100 \mathrm{cm} \) into a
wooden block. Find the average force exerted on the block.
B . \( 62.5 \times 10^{4} N \)
c. \( 6.25 \times 10^{4} N \)
D. \( 2.65 \times 10^{4} N \)


Two students use same stock solution
of \( Z n S O_{4} \) and a solution of \( C u S O_{4} \). The
emf of one cell is \( 0.03 V \) higher than that of other. The concentration of
\( C u S O_{4} \) in the cell with higher emf value
is \( 0.5 M . \) Find out the concentration of
\( C u S O_{4} \) in the other cell. \( \left(\frac{2.303 R T}{F}=0.06\right) \)


What is the composition of Magnesia
mixture?
A. mixture of magnesium sulphate, ammonium chloride and ammonia
B. mixture of a solution magnesium chloride, ammonium phosphate and ammonia
C. mixture of a solution magnesium chloride, ammonium chloride and ammonia
D. mixture of a solution magnesium chloride and ammonium chloride


ff \( f(x)=x^{4}+10 x^{3}+39 x^{2}+76 x+65 \)
find the value of \( f(x-4) \)


Discuss the shape of the following molecule using VSEPR model:
\( A s F_{5} \) and \( P H_{3} \)


If two liquids \( A \) and \( B \) form minimum
boiling azeotrope at some specific
composition then:
A. \( A \) -B interactions are stronger than those between \( A-A \) or B-B
B. vapour pressure of solution increases because more number of molecules of liquids \( A \) and \( B \) can escape from the solution
C. vapour pressure of solution decreases because less number of molecules of liquids \( A \) and \( B \) can escape from the solution
D. show a large positive deviation from Raoult's law


Find the area of a square, the length of
whose diagonal is \( 25 \mathrm{cm} \)


The enzyme ptyalin used for digestion of food is present in:
A . saliva
B. blood
c. intestine
D. adrenal glands


\( 11^{t h} \) term of the \( A P \) is \( :-3,-\frac{1}{2}, 2, \dots \) is
A . 28
B. 22
c. -38
D. -48


Which of the following is approximately the rate of solar energy (in \( \mathbf{K W}) \)
falling per \( \mathbf{m}^{2} \) on the surface area of
the earth?
A .
в. 100
c. \( 0 . \)
D. 0.0001


A random variable \( X \) has the following
probability distribution:
\( \boldsymbol{X} \quad \mathbf{0} \quad \mathbf{1} \quad \mathbf{2} \)
\[
P(X) \quad 0 \quad k \quad 2 k
\]
Determine
(i) \( k \)
(ii) \( \boldsymbol{P}(\boldsymbol{X}<\mathbf{3}) \)
(iii) \( \boldsymbol{P}(\boldsymbol{X}>\boldsymbol{6}) \)
(iv) \( \boldsymbol{P}(\mathbf{0}<\boldsymbol{X}<\mathbf{3}) \)


What is meant by rms (effective) value
of alternating current?


Assertion
Aldehyde have lower boiling point than
ether.
Reason
Aldehydes are less polar than ether.
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


Assertion
The alkali metals are strong oxidizing
agents.
Reason
The one electron in their valence shell is
easily lost.
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


Using Ohm's law find out the current
through \( 25.0 \Omega \)
\( A \cdot 1 A \)
B. \( 1.5 \mathrm{A} \)
\( c \cdot 0.5 A \)
\( D \cdot 2 A \)


What is the net effect of the common
ion?
A. It reduces the solubility of the solute in the solution.
B. It reduces the increases of the solute in the solution.
C. It causes more product to be made.
D. It causes more ions to form.
E. There is no net effect overall.


Fill in the blanks.
Rotation turns an object about a \( P \) point. The fixed point is the centre of \( \underline{Q} \) The angle by which the object rotates is the \( R \)
Then, P Q R is:
A. fixed rotation angle of rotation
B. variable rotation central angle
c. fixed angle of rotation rotation
D. variable rotation angle of rotation


Which of the following area is created over land during land breeze?
A. High pressure
B. Low pressure
c. Low temperature
D. All of the above


The value of
\( \int_{0}^{\pi / 2} x(\sqrt{\tan x}+\sqrt{\cot x}) d x \) is?
\( \mathbf{A} \cdot \frac{\pi}{2 \sqrt{2}} \)
B. \( \frac{\pi^{2}}{2} \)
\( \frac{\pi^{2}}{2 \sqrt{2}} \)
D. \( \frac{\pi^{2}}{2 \sqrt{3}} \)


Although iron is only about two-third as abundant as aluminium in Earth's
crust but it costs only about onequarter as much as required to produce aluminium.
If true enter 1 , else 0


Evaluate: \( \left[i^{18}+\left(\frac{1}{i}\right)^{25}\right]^{3} \)


N methyl aniline is the stronger base
than pyridine.

If this is true enter 1 , if false enter 0 .


1 kgwt is equal to
A .980000 dynes
B. 9.80 dynes
c. 98 dynes
D. none of these


The molecular formula of phosphorous is:
\( A \cdot P_{1} \)
B. \( P_{4} \)
\( c \cdot P_{2} \)
D. \( P_{5} \)


Bharat stage emission standards is instituted in India to regulate
A. Air pollution
B. Soil pollution
c. water pollution
D. None of the above


n Fig. circuit section, \( A B \) absorbs energy at a rate of \( 50 \% \) W when a current \( i=1.0 \) A passes through it in the indicated direction. If device X does not
have internal resistance, what is its
emf?
A. 24 v
в. 48 v
\( c \cdot 32 v \)
D. 12 V


Which of the following is a true
property about \( C H_{3}^{+} ? \)
A. It is a non-planar species.
B. \( C^{+} \) is \( s p^{2} \) hybridised.
C. Electrophile can attack on \( C^{+} \) of \( C H_{3}^{+} \)
D. It is an example of carbene.


Assertion
Let \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) be a function defined by
\( \boldsymbol{f}(\boldsymbol{x})=\max \left\{\boldsymbol{x}, \boldsymbol{x}^{3}\right\} . \) Then, \( \boldsymbol{f}(\boldsymbol{x}) \) is not
differentiable at \( \boldsymbol{x}=-\mathbf{1}, \mathbf{0}, \mathbf{1} \)
Reason
\( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{l}\boldsymbol{x}, \boldsymbol{x} \leq-\mathbf{1} \\ \boldsymbol{x}^{3},-\mathbf{1}<\boldsymbol{x} \leq \mathbf{0} \\ \boldsymbol{x}, \mathbf{0}<\boldsymbol{x} \leq \mathbf{1} \\ \boldsymbol{x}^{3}, \boldsymbol{x}>\mathbf{1}\end{array}\right. \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A mass \( m \) moves with a velocity \( v \) and collides inelastically with another identical mass. After collision, the 1 st
mass moves with velocity \( \frac{v}{\sqrt{3}} \) in a
direction perpendicular to the initial direction of motion. Find the speed of the second mass after collision
A \( \cdot \frac{2 v}{\sqrt{3}} \)
B. \( \frac{v}{\sqrt{3}} \)
\( ^{c} \cdot \sqrt{\frac{2}{3}} \)
D. The situation of the problem is not possible without external impulse


One angle of a seven-sided polygon is
\( 114^{\circ} \) and each of the other six angles is
\( x^{\circ} . \) The value of \( x \) is?
A \( \cdot 114^{\circ} \)
B. 121
\( c \cdot 131^{\circ} \)
D. \( 151^{\circ} \)


How are the xylem vessels arranged in
dicot root?


What are the products obtained when excess ammonia is reacted with
chlorine?
A. \( \mathrm{N}_{2} \) and \( \mathrm{NCl}_{3} \)
B. \( \mathrm{N}_{2} \) and \( \mathrm{HCl} \)
c. \( \mathrm{N}_{2} \) and \( \mathrm{NH}_{4} \mathrm{Cl} \)
D. NCls and HCl


The monomeric repeating units of nylon
-6 are caprolactam. If true enter 1 , else enter 0 .
\( A \)


In the reaction, \( \boldsymbol{A}+\boldsymbol{B} \longrightarrow \boldsymbol{C}+\boldsymbol{D}, \) the
rate \( \left(\frac{d x}{d t}\right) \) when plotted against time \( t^{\prime} \) gives a straight line parallel to time axis and at some time \( ^{\prime} t^{\prime}, \frac{d x}{d t}=k . \) The order and rate of reaction will be:
A. \( 1, k+1 \)
в. \( 0, k \)
\( \mathbf{c} \cdot(1+k), 1 \)
D. \( k, k+1 \)


Algae have great economic importance
to man because
A. They can be grown in tanks.
B. They help to restore the fertility of the soil.
C. Of their high protein content, some algae may be used as future food.
D. Both B and C.


The formula of the hydride of nitrogen
that is acidic in nature is :
A . \( \mathrm{NH}_{3} \)
в. \( \mathrm{HN}_{3} \)
c. \( \mathrm{N}_{2} \mathrm{H}_{4} \)
D. \( \mathrm{NH}_{2} \mathrm{OH} \)


\( n \)
Fig., \( A B C \) is a quadrant of a circle of radius \( 14 \mathrm{cm} \) and a semicircle is drawn
with \( B C \) as diameter. Find the area of
the shaded region


The sum of the first 6 terms of a G.P. is 9
times the sum of the first 3 terms; find
the common ratio.


\( \frac{C_{0}}{1}+\frac{C_{2}}{3}+\frac{C_{4}}{5}+\frac{C_{6}}{7} \ldots \ldots= \)


Which of the following hydrogen bonds
are strongest in vapour phase?
A. HF...H
в. НF...нс
c. нсI...मС।
D. HF...H


If \( \overrightarrow{\boldsymbol{A}}=(1,1,1), \vec{C}=(0,1,-1) \) are given
vectors, then a vector \( \vec{B} \) satisfying the equation \( \overrightarrow{\boldsymbol{A}} \times \overrightarrow{\boldsymbol{B}}=\overrightarrow{\boldsymbol{C}} \) and
\( \vec{A} \cdot \vec{B}=3 \) is :
\( A \cdot(5,2,2) \)
B. \( \left(\frac{5}{3}, \frac{2}{3}, \frac{2}{3}\right) \)
c. \( \left(\frac{2}{3}, \frac{5}{3}, \frac{2}{3}\right) \)
D. \( \left(\frac{2}{3}, \frac{2}{3}, \frac{5}{3}\right) \)


The relative order of esterification of
alcohols is :-
A. \( 1<2<3 \)
В. \( 1>2>3 \)
c. \( 1>3>2 \)
D. \( 1<3<2 \)


Assertion
Acetic acid turns blue litmus turns red.
Reason
Acetic acid is acidic in nature.
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.


Calculate the gravitational force of
earth acting on an object weighting 10kg placed 1000km above the surface
of earth.
(Mass of earth \( =\mathbf{6} \times \mathbf{1 0}^{\mathbf{2 4}} \mathbf{k g} \) and radius
of earth \( \left.=\mathbf{6 . 4} \times \mathbf{1 0}^{6} \boldsymbol{m}\right) \)
A \( \cdot 0.84 \times 10^{3} N \)
В. \( 0.72 \times 10^{2} N \)
c. \( 0.65 \times 10^{6} N \)
D. \( 0.42 \times 10^{4} N \)


Tracer elements are
A. Micro elements
B. Macro-elements
C . Radio isotopes
D. Vitamins


Find the joint equation of lines passing through the origin, each of which
making angle of measure \( 150^{\circ} \) with the line \( \boldsymbol{x}-\boldsymbol{y}=\mathbf{0} \)


A ball of mass 20 gram hits a wall at an
angle of \( 45^{\circ} \) with a velocity of 15 m/s. If
the ball rebounds at \( 90^{\circ} \) to the direction
of incidence, calculate the impulse received by the ball.


The set of values of a for which the
equation \( \sin x(\sin x+\cos x)=a \) has
real solutions is
A \( \cdot[1-\sqrt{2}, 1+\sqrt{2}] \)
B. \( [2-\sqrt{3}, 2+\sqrt{3} \)
D. \( \left[\frac{1-\sqrt{2}}{2}, \frac{1+\sqrt{2}}{2}\right] \)


PQRS is a square E and F are points on the sides \( Q R \) and \( R S \) respectively show
that \( \boldsymbol{a r}(\boldsymbol{\Delta} \boldsymbol{P Q} \boldsymbol{E})=\boldsymbol{a r}(\boldsymbol{\Delta} \boldsymbol{P S F}) \)


The correct order of acidic strength of
oxides of nitrogen is :
A. \( N O<N O_{2}<N_{2} O<N_{2} O_{3}<N_{2} O_{5} \)
B. \( N_{2} O<N O<N_{2} O_{3}<N_{2} O_{4}<N_{2} O_{5} \)
c. \( N O<N_{2} \oslash<N_{2} O_{3}<N_{2} O_{5}<N_{2} O_{4} \)
D. \( N O<N_{2} O<N_{2} O_{5}<N_{2} O_{3}<N_{2} O_{4} \)


Solve the following simultaneous equations:
\( \frac{\mathbf{1 6}}{\boldsymbol{x}+\boldsymbol{y}}+\frac{\mathbf{2}}{\boldsymbol{x}-\boldsymbol{y}}=\mathbf{1} ; \quad \frac{\mathbf{8}}{\boldsymbol{x}+\boldsymbol{y}}- \)
\( \frac{12}{x-y}=7 \)
A \( . x=2, y=3 \)
B. \( x=6, y=1 \)
c. \( x=7, y=4 \)
D. \( x=3, y=5 \)


If \( \mathrm{M} \) is a reactive metal, then will
be evolved, when M reacts with dilute
sulphuric acid.
A. hydrogen
B. oxygen
c. helium
D. nitrogen


By which of the following, poisoning of lead in the body can be removed?
A \( . P t \)
c. \( O x^{2-} \)
D. \( P n \)


All members of a homologous series differ by a:
A. methyl group
B. methylene
c. methane
D. none of these


The degree of dissociation is 0.4 at
\( 400 K \& 1.0 a t m \) for the gaseous
reaction
\( \boldsymbol{P C l}_{5} \rightleftharpoons \boldsymbol{P C l}_{3}+\boldsymbol{C l}_{2}(\boldsymbol{g}) . \) Assuming
ideal behaviour of all gases. Calculate the density of equilibrium mixture at \( 400 K \)
\& 1.0 atm pressure.


If a car and a truck are moving with same momentum, the velocity of car is the velocity of truck.
A. Greater than
B. Lesser than
c. Equal to
D. might be lesser than


Find the sum of all \( 4- \) digit numbers
that can be formed using the digits 0,2,4,7,8 without repetition.


Which one of the following statements
about lanthanides is false?
A. Lanthanides are separated from one another by ion exchange method
B. The ionic radii of trivalent lanthanides steadily increases with increase in atomic number
C. All lanthanides are highly dense metals
D. Most typical oxidation state of lanthanides is +3


A particular resistance wire has a resistance of 3.0 ohm per metre. The total resistance of three lengths of this wire each \( 1.5 \mathrm{m} \) long, joined in parallel
will be :
A \( .2 .5 \Omega \)
в. 3 \Omega
c. \( 4.5 \Omega \)
D. \( 1.5 \Omega \)


The concentration of \( C a\left(H C O_{3}\right)_{2} \) in a
sample of hard water is 486 ppm. The density of water sample is \( 1.0 \mathrm{g} / \mathrm{ml} \). The molarity of the solution is :
A . \( 3.0 \times 10^{-3} M \)
в. \( 5.0 \times 10^{-3} M \)
c. \( 2.0 \times 10^{-3} M \)
D. \( 6.0 \times 10^{-3} M \)


The angle of minimum deviation for
prism of angle \( \pi / 3 \) is \( \pi / 6, \) if the velocity
of light in vacuum is \( 3 \times 10^{8} m s^{-1}, \) then
the velocity of light in material of the prism is
A . \( 2.12 \times 10^{8} \mathrm{ms}^{-1} \)
B. \( 1.12 \times 10^{8} \mathrm{ms}^{-1} \)
c. \( 4.12 \times 10^{8} \mathrm{ms}^{-1} \)
D. \( 5.12 \times 10^{8} \mathrm{ms}^{-1} \)


Which one of the following sets is
infinite?
A. Set of all integers greater than 5
B. Set ofall integers between \( -10^{10} \) and \( +10^{10} \)
C. Set of all prime numbers between 0 and \( 10^{100} \)
D. Set of all even prime numbers


If the third term of a G.P. is 12 and its
sixth term is \( 96, \) find the sum of 9
terms.


A bullet gets embedded in a solid block resting on a frictionless surface. In this
process:
A. momentum is conserved
B. kinetic energy is conserved
c. potential energy is conserved
D. both (a) and (b)


Oxygen possesses high IE than krypton, although "Kr" having the stable electronic configuration. This is due to:
A. Poor shielding effect in krypton
B. Electron pair repulsion in krypton
c. Large size of oxygen
D. Very small size of oxygen respective of "Kr"


If \( \vec{a}, \vec{b}, \vec{c} \) are unit vectors, then \( |\vec{a}-\vec{b}|^{2}+ \)
\( |\vec{b}-\vec{c}|^{2}+|\vec{c}-\vec{a}|^{2} \) does not exceed :
A . 4
B. 9
\( c \cdot 8 \)
D.


Which one of waves cannot be seen
through electromagnetic spectrum?
A. radio waves
B. micro waves
c. infrared waves.
D. ultraviolet waves


Product formed on electrolysis of potassium salt of fumaric and maleic acid is:
A. Ethane
B. Ethene
c. Ethyne
D. Methane
E. All the above


Which type of floor does not allow rainwater to seep into the ground?
A. Cemented floor
B. Marble floor
c. limestone floor
D. None of the above


Consider the following statements for air molecules in an air tight container.
(I) The average speed of molecules is larger than root mean square speed.
(II) Mean free path of molecules is larger than the mean distance between molecules.
(III) Mean free path of molecules increases with temperature
(IV) The rms speed of nitrogen molecule is smaller than oxygen molecule. The
true statements are.
A. Only II
B. ॥ \& ॥ I
c. ॥ \& ।
D. I, II \& IV


A man's age is six times the age of his son. In six years, the father's age will be three times of the son's age. The age of
the father and the son are respectively:
A. 18 years and 3 years
B. 30 years and 5 years
c. 24 years and 4 years
D. 42 years and 7 years


Water from a tap, maintained at a constant potential \( V \), is allowed to fall by drops of radius \( r \) through a small hole into a hollow conducting sphere of radius R standing on an insulating stand until it fills the entire sphere. Find the potential of the hollow conductor after it is completely filled with water.


A rod lies across frictionless rails in
uniform magnetic field \( \vec{B} \) as shown in Fig. The rod moves to the right with
speed \( V . \) In order to make the induced
emf in the circuit to be zero, the
magnitude of the magnetic field should.
\begin{tabular}{|l|l|}
\hline & \\
\hline(8) & 8 \\
\hline & \( \bigotimes \) \\
\hline \\
\hline
\end{tabular}


Which of the following is most reactive
metal?
A . \( F e \)
в. \( Z \) и
\( c . C a \)
D. \( A l \)


General value of \( \theta \) satisfying equation
\( \tan ^{2} \theta+\sec 2 \theta=1 \) is
A \( . n \pi \)
B . \( n \pi+\frac{\pi}{3} \)
\( \mathbf{c} \cdot n \pi-\frac{\pi}{3} \)
D. All of these


A beam of light consisting of two
wavelengths, \( 650 \mathrm{nm} \) and \( 520 \mathrm{nm} \) is
used to obtain interference fringes in a Youngs double-slit experiment. What is the least distance from the central
maximum where the bright fringes due to both the wavelengths coincide?
A . \( 1.17 \mathrm{mm} \)
B. 2.52 mm
c. \( 1.56 \mathrm{mm} \)
D. 3.14 mm


Use Euclid's division algorithm to find
the HCF of the following number: 305
and 793


The direction cosines of the line which
is perpendicular to the lines with direction cosines proportional to
(1,-2,-2)\( \&(0,2,1) \) are
\( ^{\mathrm{A}} \cdot\left(\frac{2}{3},-\frac{1}{3}, \frac{2}{3}\right) \)
в. \( \left(\frac{2}{3}, \frac{1}{3}, \frac{2}{3}\right) \)
c. \( \left(\frac{2}{3}, \frac{1}{3}, \frac{-2}{3}\right) \)
D. \( \left(\frac{-2}{3}, \frac{1}{3}, \frac{2}{3}\right) \)


Which of the following effects of auxin is of wide application?
A. Induction of fruit development
B. Induction of root initiation
c. Prevention of abscission
D. All of the above


As shown in the figure, a bob of mass \( m \)
is tied by a massless string whose other
end portion is wound on a fly whee
(disc) of radius \( r \) and mass \( m . \) When
released from rest the bob starts falling
vertically. When it has covered a
distance of \( h, \) the angular speed of the
wheel will be:
\( \mathbf{A} \cdot r \sqrt{\frac{3}{4 g h}} \)
B. \( \frac{1}{r} \sqrt{\frac{4 g h}{3}} \)
\( c \cdot r \sqrt{\frac{3}{2 g h}} \)
D. \( \frac{1}{r} \sqrt{\frac{2 g h}{3}} \)


Draw a sketch showing the displacement of a body executing damped vibrations against time.


The direction cosines of the ray
\( \boldsymbol{P}(1,-2,4) \) and \( Q(-1,1,-2) \) are
A \( \cdot(-2,-3,-6) \)
B \( \cdot(2,-3,-6) \)
\( ^{C} \cdot\left(\frac{2}{7}, \frac{3}{7}, \frac{6}{7}\right) \)
D \( \cdot\left(-\frac{2}{7}, \frac{3}{7},-\frac{6}{7}\right) \)


If \( \boldsymbol{A}=\{\mathbf{1}, \mathbf{2}, \mathbf{3}\}, \boldsymbol{B}=\{\mathbf{1}, \mathbf{4}, \mathbf{6}, \mathbf{9}\} \) and \( \mathbf{R} \) is
a relation from \( A \) to \( B \) defined by \( ' x \) is
greater than \( y \) '. The range of R is
A \( \cdot\{1,4,6,9\} \)
в. \{4,6,9\}
c. \{1\}
D. \{4,6\}


Consider the following statements:
\( \frac{1}{22} \) can not be written as terminating decimal
2. \( \frac{2}{15} \) can be written as a terminating decimal
3. \( \frac{1}{16} \) can be written as a terminating decimal

Which of the statements given above is/are correct?
A. 1 only
B. 2 only
c. 1 and 3
D. 2 and 3


\( \boldsymbol{A} \cup(\boldsymbol{B} \cap \boldsymbol{C})=(\boldsymbol{A} \cup \boldsymbol{B}) \cap(\boldsymbol{A} \cup \boldsymbol{C}) \)
where \( \boldsymbol{A}= \)
\( \{1,2,4,5\}, B\{2,3,5,6\}, C= \)
\{4,5,6,7\} is \( A \cup(B \cap C)= \)
\( \{1,2, a, b, 6\} \) Find \( a+b \)


When a force is expressed in dyne, the number of significant figures is four. If it is expressed in newton, the number of significant figures will become:
(Given: \( \left.10^{5} \text { dyne }=1 N\right) \)
\( A \cdot 9 \)
B. 5
\( c \)
D.


Find the increase in pressure required to decrease the volume of a water
sample by \( 0.01 \% . \) Bulk modulus of
water \( =2.1 \times 10^{9} N m^{-2} \)


Which of the following is NOT a random experiment?
A. Rolling an unbiased dice
B. Tossing a fair coin
c. Drawing a card from a well shuffled pack of 52 card
D. None of these


calculate the angle of banking of a smooth curved road of radius \( 100 \mathrm{m} \) if
vehicles can safely travel along it with a speed of \( 108 k m / h \)


Which of the following option will complete the given series \( \mathbf{1}, \mathbf{6}, \mathbf{1 5}, ?, \mathbf{4 5}, \mathbf{6 6}, \mathbf{9 1} ? \)
A . 25
B . 26
c. 27
D . 28


Animals die in nitrogen because
A. It destroys haemoglobin
B. of the want of oxygen
C. It is heavier than air.
D. It is poisonous.


Assertion
Two persons on the surface of moon
cannot talk to each other
Reason

There is no atmosphere
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


f \( a, b, c, d \) are in G.P., show that
\( \mathbf{i}) \boldsymbol{a}^{2}+\boldsymbol{b}^{2}, \boldsymbol{b}^{2}+\boldsymbol{c}^{2}, \boldsymbol{c}^{2}+\boldsymbol{d}^{2} \) are in G.P


The order of rotational symmetry for the given figure is
A. 3
B. 4
\( c \cdot 6 \)
\( D \cdot 12 \)


Secondary valencies correspond to
of the metal atom
and are satisfied by ligands.
A. coordination number
B. valency
c. element
D. molecules


A dia-atomic gas undergoes adiabatic expansion as shown in the figure. Find
volume of gas when pressure of gas is
\( 2 \times 10^{5} N / m^{2} \)
A \( \cdot 14 \times 10^{4} m^{3} \)
B . \( 1.4 \times 10^{7} m^{3} \)
c. \( 28 \times 10^{4} m^{3} \)
D. \( 28 \times 10^{3} m^{3} \)


In a double slit experiment, the two slits
are \( 1 \mathrm{mm} \) apart and the screen is place 1 \( \mathrm{m} \) away. A monochromatic light of wavelength \( 500 \mathrm{nm} \) is used. What will
be the width of each slit for obtaining ten maxima of double slit within the
central maxima of single slit pattern?
A . \( 0.5 m m \)
В. \( 0.02 m m \)
\( c .0 .2 m m \)
D. \( 0.1 m m \)


An old T.V set was bought for Rs 1500
some repairs wee done for Rs \( 375 . \) Then
it was sold for Rs 2500 . find the profit or lost percentage


Centre of gravity is the point
A. where the weight of the object is supposed to be present or concentrated.
B. where the weight of the object is perpendicular to the surface area of the object
C. where maximum no of molecules presents
D. none of the above


Find the equation of the ellipse whose
vertices are \( (\pm \mathbf{7}, \mathbf{0}) \) and foci are
\( (\pm \mathbf{6}, \mathbf{0}) \)


In which of the following the corrosion of
iron will be most rapid?
A. In pure water
B. In pure oxygen
C. In air and moisture
D. In air and saline water


Which of the following represents the correct order of the acidity in the given compounds?
A \( \cdot F C H_{2} C O O H>C H_{3} C O O H>B r C H_{2} C O O H> \)
\( \mathrm{ClCH}_{2} \mathrm{COOH} \)
в. \( B r C H_{2} C O O H>C l C H_{2} C O O H>F C H_{2} C O O H> \)
\( C H_{3} C O O H \)
c. \( F C H_{2} C O O H>C l C H_{2} C O O H>B r C H_{2} C O O H> \)
\( C H_{3} C O O H \)
D. \( C H_{3} C O O H>B r C H_{2} C O O H>C l C H_{2} C O O H> \)
\( F C H_{2} C O O H \)


Non-conventional sources of energy are
This question has multiple correct options
A. pollution-free
B. renewable
C. inexhaustible
D. exhaustible


What are 'fuel cells'? Write cathode and
anode reaction in a fuel cell.


Monoclinic sulphur on cooling to 95.6
converts to
A. collodial sulphur
B. plastic sulphur
c. milk of sulphur
D. rhombic sulphur


One gram of ice (at \( 0^{\circ} \mathrm{C} \) ) is mixed with
one gram of steam (at \( 100^{\circ} \mathrm{C} \) ). After
thermal equilibrium, the temperature of the mixture is
\( \mathbf{A} \cdot 0^{\circ} C \)
B . \( 100^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 55^{\circ} C \)
D. \( 80^{\circ} \mathrm{C} \)


An insulated charged sphere of radius \( 5 c m \) has a potential of \( 10 V \) at the
surface. The potential at the centre will
be :
A. Same as that at \( 5 \mathrm{cm} \) from the surface
B. Same as that at \( 25 \mathrm{cm} \) from the surface
\( c .10 V \)
D. Zero


Find the mass of 200 steel spherical ball bearings, each of which has radius \( 0.7 \mathrm{cm}, \) given that the density of steel is \( 7.95 g / c m^{3} .(\text { Mass }=\text { Volume } \times \text { Density }) \)
A . \( 2.29 \mathrm{Kg} \)
в. \( 2.9 \mathrm{Kg} \)
\( \mathrm{c} .3 .29 \mathrm{Kg} \)
D. None of these


Give the answer in one word:
What is the differential coefficient of
\( \log \log \sin x ? \)


The wire shown in figure carries a
current of \( 40 A . \) If \( r=3.14 c m \) the
magnetic field at point p will be :
A \( .1 .6 \times 10^{-3} T \)
В. \( 3.2 \times 10^{-3} T \)
c. \( 6 \times 10^{-4} T \)
D . \( 4.8 \times 10^{-3} T \)


A 20 m deep well with diameter 7 m is
dug and the earth from digging is
evenly spread out to form a platform 22
\( \mathrm{m} \) by \( 14 \mathrm{m} . \) Find the height of the platform.


The ratio in which the plane \( \bar{r} .(\bar{i}-2 \bar{j}+ \) \( \mathbf{3} \bar{k})=17 \) divides the line joining the points \( -2 \bar{i}+4 \bar{j}+7 \bar{k} \) and \( 3 \bar{i}-5 \bar{j}+8 \bar{k} \)
is
A. 1: 10
B. 3: 10
\( c .3: 5 \)
D. 1: 5


A bomb of mass 9 kg explodes into two pieces of masses \( 3 \mathrm{kg} \) and 6 kg. The velocity of mass \( 3 \mathrm{kg} \) is \( 16 \mathrm{ms}^{-1} \). The
kinetic energy of mass \( 6 \mathrm{kg} \) is
A . 96 J
B. 384 J
c. 192 J
D. 768 J


A photon of \( 300 \mathrm{nm} \) is observed by a gas and then re-emits two photons.one reemitted photon has wavelength \( 496 \mathrm{nm} \) the wavelength of second re-emitted photons is:
A. 759 nm
B. 857 nm
\( c .957 \mathrm{nm} \)
D. 657 nm


A particle of charge \( q \) and mass \( m \) starts moving from origin under the action of an electric field \( \vec{E}=E_{0} \vec{i} \) and magnetic field \( \vec{B}=B_{0} \vec{k} \). Its velocity at
\( (x, 3,0) \) is \( (4 i+3 i), \) the value of \( x \) is:
A \( \cdot \frac{36 E_{o} B_{0}}{q m} \)
В. \( \frac{25 m}{2 q E_{0}} \)
c. \( \frac{10 m}{q E_{o}} \)
D. \( \frac{25 E_{0} B_{0}}{m} \)


Prove that the coefficient of \( x^{n} \) in the
expression of \( (1+x)^{2 n} \) is twice the
coefficient of \( x^{n} \) in the expression of
\( (1+x)^{2 n-1} \)


A ball weighing 15 g is tied to a string 10 cm long. Initially the ball is held in position such that the string is
horizontal. The ball is now released. A
nail \( N \) is situated vertically below the
support at a distance \( L \)

The minimum value of \( L \) such that the
string will be wound round the nail is
\( A \cdot 2 \mathrm{cm} \)
B. \( 4 \mathrm{cm} \)
\( \mathbf{c} .6 \mathrm{cm} \)
\( \mathbf{D} \cdot 8 \mathrm{cm} \)


In the given circuit the current through
Zener Diode is close to :
\( \mathbf{A} \cdot 6.0 m \)
в. \( 4.0 \mathrm{m} \) А
\( c .6 .7 m A \)
D. \( 0.0 \mathrm{mA} \)


The broadest category of organism in biological taxonomy is
A. Phylum
B. Class
c. kingdom
D. Family


The value of \( \tan 75^{\circ} \) is
A \( \cdot 1+\frac{1}{\sqrt{3}} \)
B. \( 2-\sqrt{3} \)
\( c \cdot 2+\sqrt{3} \)
D. \( 1+\sqrt{3} \)


The maximum kinetic energy of
photoelectrons ejected from a metal, when it is irradiated with radiation of
frequency \( 2 \times 10^{14} s^{-1} \) is \( 6.63 \times 10^{-20} J \)
Find the threshold frequency of the
metal.


\( 1 g \) of ice at \( 0^{0} C \) is converted to steam
at \( 100^{0} C . \) The amount of heat required
will be:
\( \left(L_{\text {steam}}=536 c a l / g\right) \)
A . 756 call \( l \)
B. 12000 cal
c. 716 call \( l \)
D. 450 call \( l \) and


Consider three points \( \boldsymbol{P}=(-\sin (\boldsymbol{\beta}- \)
\( \boldsymbol{\alpha}),-\cos \beta), \boldsymbol{Q}=(\cos (\beta-\boldsymbol{\alpha}), \sin \beta) \)
and \( \boldsymbol{R}=(\cos (\boldsymbol{\beta}-\boldsymbol{\alpha}+\boldsymbol{\theta}), \sin (\boldsymbol{\beta}-\boldsymbol{\theta})) \)
where \( 0<\alpha, \beta, \theta<\frac{\pi}{4} . \) Then
A. \( P \) lies on the line segment \( R Q \)
B. \( Q \) lies on the line segment \( P R \)
c. \( R \) lies on the line segment \( Q P \)
D. \( P, Q, R \) are non-collinear


Find the fifth term of the G.P.
\( \frac{3}{2}, \frac{3}{4}, \frac{3}{8} \)


Fill in the blanks:
An interaction of one object with
another object results in a between the two objects.
A. pressure
B. attraction
c. force
D. repulsion


A metal ball of radius \( 1 m m \) and density \( 10^{4} \mathrm{kg} \mathrm{m}^{-3} . \) falls freely in air through a height 'h' before falling in a tank full of
water. If on falling in water its velocity remains unchanged, then the value of h will be (Coefficient of viscosity of
water \( =10^{-3} \) Pa.s and \( g=10 m s^{-2} \)
A . \( 10 m \)
B. \( 15 \mathrm{m} \)
\( c .25 m \)
D. \( 20 m \)


\( N_{2}+O_{2} \leftrightharpoons 2 N O, K_{1} ; \quad \frac{1}{2} N_{2}+ \)
\( \frac{1}{2} O_{2} \leftrightharpoons N O, K_{2} \)
\( \mathbf{2} N \boldsymbol{O} \rightleftharpoons \boldsymbol{N}_{2}+\boldsymbol{O}_{2}, \boldsymbol{K}_{3} ; \quad \boldsymbol{N} \boldsymbol{O} \rightleftharpoons \)
\( \frac{1}{2} N_{2}+\frac{1}{2} O_{2}, K_{4} \)
Correct relation(s) between \( \boldsymbol{K}_{1}, \boldsymbol{K}_{2}, \boldsymbol{K}_{3} \)
and \( \boldsymbol{K}_{4} \) is/are:
This question has multiple correct options
A \( \cdot K_{1} \times K_{3} \)
в. \( \sqrt{\left(K_{1}\right)} \times K_{4}=1 \)
c. \( \sqrt{\left(K_{3}\right)} \times K_{2}=1 \)
D. None of the above


For the compounds,
I) HCOOH
॥) \( C H_{3} C O O H \)
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C O O H} \) IV \( \boldsymbol{C}_{6} \boldsymbol{H}_{5} \boldsymbol{C O O H} \)
The correct order of decreasing acidity is :
\( A \cdot|>||>|||>\mid V \)
B. IV >1>||>111
c. ।>IV> || > II
D. IV> || > || > |


\( \begin{array}{ll}\text { Column-I } & \text { Column-II } \\ \text { (1) Planet nearest to the sun } & \text { (a) Jupiter } \\ \text { (2) Largest planet } & \text { (b) Saturn } \\ \text { (3) Lightest planet } & \text { (c) Neptune } \\ \text { (4) Farthest planet } & \text { (d) Mercury }\end{array} \)


The two equilibria \( A B \rightleftharpoons A^{+}+B^{-} \) and
\( A B+B^{-} \rightleftharpoons A B_{2}^{-} \) are simultaneously
maintained in a solution with
equilibrium constants, \( \boldsymbol{K}_{1} \) and \( \boldsymbol{K}_{2} \)
respectively. The ratio of \( \boldsymbol{A}^{+} \) to \( \boldsymbol{A} \boldsymbol{B}_{\mathbf{2}}^{-} \) in the solution is:
A. directly proportional to the concentration of \( B \)
B . inversely proportional to the concentration of \( B \)
c. directly proportional to the square of the concentration of \( B^{-} \)
D. inversely proportional to the square of the concentration of \( B \)


If point \( C(\bar{c}) \) divides the segment joining the point \( \boldsymbol{A}(\overline{\boldsymbol{a}}) \) and \( \boldsymbol{B}(\overline{\boldsymbol{b}}) \)
internally in the ratio \( m: n \), then prove
\( \operatorname{that} \bar{c}=\frac{m \bar{b}+n \bar{a}}{m+n} \)


A hoop of mass \( 500 g \) and radius \( 10 c m \)
is placed on a nail, then the moment of
inertia of the hoop, when is rotated
about the nail will be \( _{--}-_{--} k g m^{2} \)
A . 0.05
B. 0.02
c. 0.01
D. 0.03


The non-existence of \( \boldsymbol{P b I}_{4} \) is due to:
This question has multiple correct options
A . highly oxidising nature of \( P b^{4+} \)
B. highly reducing nature of \( P b^{4+} \)
C. sufficiently large covalent character
D. highly reducing power of \( I^{-} \)


\( \ln \operatorname{an} A \cdot P \) if \( a_{1}=2, a_{3}=26 \) Find \( a_{2} \)


Complete the following, so as to make a
true statement:
A quadrilateral has diagonals


(a) How long will a stone take to fall to the ground from the top of a building \( 80 m \) high and (b) what will be the velocity of the stone on reaching the
ground? (Take \( \left.g=10 m s^{-2}\right) \)
B . (a) \( 4 s \), (b) \( 30 m s^{-1} \)
C \( \cdot \) (a) \( 10 s, \) (b) \( 40 \mathrm{m} \mathrm{s}^{-1} \)
D. (a) \( 4 s, \) (b) \( 40 \mathrm{m} \mathrm{s}^{-1} \)


The difference between the wave
number of \( 1^{s t} \) line of Balmer series and
last line of paschen series for \( L i^{2+} \) ion
is :
A \( \cdot \frac{R}{36} \)
в. \( \frac{5 R}{36} \)
c. \( 4 R \)
D. \( \frac{R}{4} \)


If a point lies at a distance \( ^{\prime} x^{\prime} \) from the
mid point of the dipole along its axis, the electric potential at this point is proportional to :
A \( \cdot \frac{1}{x^{2}} \)
B. \( \frac{1}{x^{3}} \)
c. \( \frac{1}{x^{4}} \)
D. \( \frac{1}{x^{3 / 2}} \)


An electron and a proton are separated by a distance \( r \) so that the potential
energy between them is \( U=k \log r \)
where \( k \) is a constant. The expression for various energy levels of the above said hypothetical atom is:
\( ^{\mathbf{A}} \cdot \frac{k}{2}\left[1+\log \frac{n^{2} h^{2}}{4 \pi^{2} m k}\right] \)
в. \( 2 k\left[2+\log \frac{n^{2} h^{2}}{4 \pi^{2} m k}\right] \)
\( c \cdot k\left[2+\log \frac{n^{2} h^{2}}{4 \pi^{2} m k}\right] \)
D. \( \frac{k}{2}\left[1+\log \frac{n^{2} h^{2}}{2 \pi^{2} m k}\right. \)


If \( \left(\tan ^{-1} x\right)^{2}+\left(\cot ^{-1} x\right)^{2}=\frac{5 \pi^{2}}{8}, \) then
\( \boldsymbol{x}= \)
A . -1
B.
\( c \cdot 0 \)
D.


Commercial name of permonosulphuric acid is :
A. Marshall's acid
B. Oleum
c. Fuming sulphuric acid
D. Caro's acid


Explain why:
Zr and Hf exhibit similar properties.
(At. no. of \( \mathrm{Zr}=40, \mathrm{Hf}=72) \)


\( \int_{\pi / 4}^{3 \pi / 4} \frac{d x}{1+\cos x} \) is equal to:
A .2
B. -2
\( c \cdot \frac{1}{2} \)
D. \( -\frac{1}{2} \)


Remains of Neanderthal man were
found in Neander Valley of
A. Germany
B. France
c. England
D. Egypt


In \( \Delta A B C, \angle A=100^{\circ}, \angle B=30^{\circ} \) and
\( \angle C=50^{\circ}, \) then
\( \mathbf{A} \cdot A B>A C \)
B. \( A B=A C \)
c. \( A B<A C \)
D. None of these


Which one of the following is incorrect for 'atherosclerosis'?
A. Constriction of arterial lumen reduces the blood flow
B. Loss of dilation ability of the arterial wall and its rupture
C. Cholesterol deposition at the inner wall of the artery
D. None of these


Upward movement of water through xylem is best explained by
A. Cohesion tension theory
B. Pulsation theory
c. capillarity theory
D. Root pressure theory


What volume of hydrogen at NTP will be liberated when 3.25 g of zinc completely dissolve in dilute HCI?
[At. mass of \( \mathrm{Zn}=65 \)
A . 1.12 litre
B. 11.20 litre
c. 224 litre
D. 22.40 litre


At \( 373 \mathrm{K} \), steam and water are in
equilibrium and \( \Delta H=40.98 \mathrm{kJ} \) mol\( ^{-1} \)
What will be \( \Delta S \) fro conversion of
water into steam?
\( \boldsymbol{H}_{2} \boldsymbol{O}_{(l)} \rightarrow \boldsymbol{H}_{2} \boldsymbol{O}_{(g)} \)
A \( \cdot 109.8 \) J \( K^{-1} m o l^{-1} \)
B . 31 J \( K^{-1} \) mol \( ^{-1} \)
c. 21.98 J \( K^{-1} m o l^{-1} \)
D. 326 J \( K^{-1} \) mol \( ^{-1} \)


toppr
Q Type your question
the blood with
iodine using the reaction
\( \boldsymbol{H} \boldsymbol{C} \boldsymbol{N}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{I}_{3}^{-}(\boldsymbol{a} \boldsymbol{q}) \rightarrow \boldsymbol{I} \boldsymbol{C} \boldsymbol{N}(\boldsymbol{a} \boldsymbol{q})+ \)
\( \mathbf{2} \boldsymbol{I}-(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{H}^{+}(\boldsymbol{a} \boldsymbol{q}) \)
A diluted blood sample of volume 15.00
mL was titrated to the endpoint with
\( 5.21 \mathrm{mL} \) of a \( I_{3}^{-} \) solution. The molar
concentration of the \( I_{3}^{-} \) solution was
determined by titrating it against arsenic(III)oxide, \( A s_{4} O_{6}, \) which in solution forms arsenous acid,
\( \mathrm{H}_{3} \mathrm{As} \mathrm{O}_{3} \) via the following equation:
\( \mathbf{6} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l})+\boldsymbol{A} \boldsymbol{s}_{4} \boldsymbol{O}_{6}(\boldsymbol{s}) \rightarrow \boldsymbol{4} \boldsymbol{H} \boldsymbol{3} \boldsymbol{A} \boldsymbol{s} \boldsymbol{O}_{3}(\boldsymbol{a} \boldsymbol{q}) \)
A volume of \( 10.42 \mathrm{mL} \) of the triiodide
I3 \( ^{-} \) ) solution was needed to reach the
endpoint on a 0.122 g sample of \( \$ \$ A s 406 \) in the reaction
\( \boldsymbol{H}_{3} \boldsymbol{A} \boldsymbol{s} \boldsymbol{O}_{3}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{I}_{3}^{-}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l}) \rightarrow \)
\( \boldsymbol{H}_{3} \boldsymbol{A} \boldsymbol{s} \boldsymbol{O}_{4}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{3} \boldsymbol{I}^{-}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{2} \boldsymbol{H}^{+}(\boldsymbol{a} \boldsymbol{q}) \)
What is the molar concentration of HCN
in the blood sample?
A. \( 0.04 \mathrm{M} \)
\( B \)
\( c \)
D. 0.36 M


Can you say, whether the compound
numbered as 10 is E or \( Z \) isomer?
A. \( E \) isomer
B. \( Z \) isomer
\( c . \) Both
D. None


Acetal or ketal is:
A. Vic dialkoxy compound
B. \( \alpha, \omega \) - dialkoxy compound
C. \( \alpha \) -alkoxy alcohol
D. Gem dialkoxy compound


Dialysing unit (artificial kidney) contains a fluid which is almost same
as plasma except that it has
A. High glucose
B. High urea
c. No urea
D. High uric acid


Mark out the correct options.
A. The total charge of the universe is constant
B. The total positive charge of the universe is constant.
C. The total negative charge of the universe is constant
D. The total number of charged particles in the universe is constant


Which of the following best describes why purely metallic mixtures are
created?
Note: These do not include metalloid
elements.
A. To reduce the damaging effects of rusting of the substance when exposed to air
B. To allow for conduction of electricity without any conduction of heat
c. To allow a solid to have high tensile strength without being ductile.
D. To easily dissolve in water that allows for very rapid decomposition in the environment reducing the amount of metals that wind up in landfills


If \( s \) represents the sum of \( n \) terms of G.P whose first term and common ratio are
\( a \) and \( r \) respectively, then \( s_{1}+s_{2}+ \)
\( \boldsymbol{s}_{3}+\ldots+\boldsymbol{s}_{\boldsymbol{n}} \)


\( \int \sin x \cdot \cos x d x \)


Acidified water is electrolysed by using carbon electrodes.What is produced at negative carbon electrode?


\( \ln K H, \) the oxidation number of
hydrogen is:
A \( .+2 \)
B. +1
c. 0
D. -
E. -2


Find the sum of first 32 multiples of 4
\( \mathbf{A} \cdot 2,112 \)
B. 2,712
\( c \cdot 2,110 \)
D. 2,111


Assertion
The Joule-Thomson coefficient for an
ideal gas is zero.
Reason
There are no intermolecular attractive
forces in an ideal gas.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


A ball falls freely under gravity from rest. Name the kind of energy it will possess at the point from where it falls:
A. Maximum energy
B. Heat energy
c. Potential energy
D. Kinetic energy


Choose the correct option
This question has multiple correct options
A. Temperature of a water kept inside a beaker is measured when the laboratory thermometer is held inside the water
B. Temperature of a water kept inside a beaker is measured when the laboratory thermometer is removed from the water
C. Temperature of our body is measured when the clinical thermometer is kept inside the mouth
D. Temperature of our body is measured when the clinical thermometer is removed from the mouth


How many moles of electrons will weigh
one kilogram?
\( \mathbf{A} \cdot 6.023 \times 10^{23} \)
B. \( \frac{1}{9.108} \times 10^{31} \)
C \( \cdot \frac{6.023}{9.108} \times 10^{54} \)
D. \( \frac{1}{9.108 \times 6.023} \times 10^{8} \)


Tes
\( x \)
18.
\( \infty \)


Product of \( n \) positive numbers is unit.
The sum of these numbers can not be
less than
A . 1
в. \( n \)
c. \( n^{2} \)
D. None of these


Given mean \( =12, \) mode \( =3 . \) Find
median.
A \( \cdot 12 \)
B. 2
\( c \cdot 9 \)
D.


Work done by a fielder in catching a ball
is
A . zero
B. positive
c. negative
D. none of these


Match the names of the phytohormones
with the roles listed.
\( A \cdot A-t, B-p, C-s, D-q \)
B. A-t, B- p, C- q, D-s
C. \( A-t, B-p, C-q, D-r \)
D. A- t, B- s, C- p, D- q


na \( \Delta A B C \), the sides \( A B, B C \) and \( C A \) are
\( \mathbf{1 0 c m}, \mathbf{8 c m} \) and \( \mathbf{7 c m} \) respectively. In AB
a point \( P \) is taken such that \( A P=4 c m \).
If \( P Q \) is drawn parallel to \( B C \), then its
length is equal to
A. \( 4.0 \mathrm{cm} \)
В. \( 3.8 \mathrm{cm} \)
\( c .3 .5 \mathrm{cm} \)
\( 0.3 .2 \mathrm{cm} \)


An object with mass \( 2 \mathrm{kg} \) moves with a velocity of \( 10 \mathrm{m} / \mathrm{s} \). What is the net force
on the body?
A. 20
B. on
\( c \cdot 5 N \)
D. 25 N


The time period of a particle executing
\( \boldsymbol{S H} \boldsymbol{M} \) is \( \boldsymbol{8} \boldsymbol{s} . \) At \( \boldsymbol{t}=\boldsymbol{0} \) it is at the mean
position. The ratio of distance covered
by the particle in \( 1^{s t} \) second to the \( 2^{n d} \) second is
A \( \cdot\left(\frac{1}{\sqrt{2}-1}\right) \)
B. \( \sqrt{2} \)
c. \( (\sqrt{2}+1) \)
D. \( \frac{1}{\sqrt{2}} \)


In which part uriniferous tubule, \( \boldsymbol{N} \boldsymbol{a}^{+} \)
passes out
A. Descending loop of Henle
B. Collecting tubule
c. Ascending loop of Henle
D. None of the above


If \( \boldsymbol{x}_{1}=\sqrt{\mathbf{3}} \) and \( \boldsymbol{x}_{\boldsymbol{n}+1}=\frac{\boldsymbol{x}_{\boldsymbol{n}}}{\mathbf{1}+\sqrt{\mathbf{1}+\boldsymbol{x}_{\boldsymbol{n}}^{2}}} \)
\( \forall n \epsilon N, \) then \( \lim _{n \rightarrow \infty} 2^{n} x_{n} \) equal to
A \( \cdot \frac{3}{2 \pi} \)
в. \( \frac{2}{3 \pi} \)
c. \( \frac{2 \pi}{3} \)
D. \( \frac{3 \pi}{2} \)


What is the correct order of covalent
size of the following?
\( \mathrm{Nb} \)
A. \( \mathrm{Nb}= \) Ta
B. Nb < Ta
c. \( \mathrm{Nb}>\mathrm{T} \)
D. None of these.


The experiment which led to the discovery of nucleus was performed by :
A. Goldstein
B. J.J. Thomson
c. Dalton
D. Rutherford


\( \boldsymbol{O} \)
\( \boldsymbol{C} \boldsymbol{H}_{3}-\stackrel{\|}{\boldsymbol{C}}-\boldsymbol{C} \boldsymbol{H}-\boldsymbol{C} \boldsymbol{H}-\boldsymbol{C} \boldsymbol{H}-\boldsymbol{C} \boldsymbol{H}_{3} \)
\( \boldsymbol{C H}_{3} \quad \boldsymbol{C H O} \quad \boldsymbol{C H}_{3} \)
The IUPAC name of compound is:
A. 3,5-dimethyl-4-formylpentanone
B. 1-isopropy|-2-methy|-4-oxobutanal|
c. 2-isopropyl-3-methyl-4-oxopentanal
D. none of the above


Let \( A=\{1,2,3\} . \) Then, the number of
equivalence relations containing (1,2) over set \( A \) is
A . 1
B . 2
\( c .3 \)
D. 4


A form of combustion reaction where
there is a release of high amount of a heat and light energy in a small interval of time is
A. spontaneous combustion
B. rapid combustion
c. fast combustion
D. instant combustion


The conclusion that may be drawn from
the experiment which demonstrated radioactivity (A.R) is
A. \( A l \) is artificial radioactive substance
B. positrons are essential for the production of A.R
c. Exponential decay led to the discovery of A.R.
D. In A.R., only positrons are produced


In an elastic collision, kinetic energy of
the relative motion is converted into the
energies of two momentarily compressed bodies, and then is
converted back into the \( _{--}- \) - energy.
Fill in the blanks.
A. kinetic,kinetic
B. elastic,kinetic
c. elastic,elastic
D. kinetic,elastic


A transverse wave is passing through a medium. The maximum speed of the vibrating particle occurs when the displacement of the particle from the mean position is
A. zero
B. half of the amplitude
c. equal to the amplitude
D. none of the above


If the equation of a standing wave is given by \( y=6 \sin \pi x \cos 100 \pi t, \) the
equation of the component waves are
A \( . y=3 \sin (\pi x+50 \pi t) \) and \( 3 \sin (\pi x-50 \pi t) \)
B. \( y=3 \sin (\pi x+100 \pi t) \) and \( 3 \sin (\pi x-100 \pi t) \)
c. \( y=6 \sin (\pi x+100 \pi t) \) and \( 6 \sin (\pi x-100 \pi t) \)
D. \( y=6 \sin (\pi x+50 \pi t) \) and \( 6 \sin (\pi x-50 \pi t) \)


The figure shows a metre-bridge circuit, with \( A B=100 c m, X=12 \Omega \) and \( R= \)
\( 18 \Omega, \) and the jockey \( J \) in the position of
balance. If \( R \) is now made \( 8 \Omega \), through
what distance will \( J \) have to be moved
to obtain balance?
A . \( 10 \mathrm{cm} \)
B. 20 cm
\( c .30 \mathrm{cm} \)
D. \( 40 \mathrm{cm} \)


The sum of the oxidation numbers of all
the carbons in \( C_{6} H_{5} C H O \) is :
\( A \cdot O \)
\( B \cdot+2 \)
\( c \cdot+4 \)
D. - -


What will happen if our eyes are exposed to very dim light?
A. Causes eye strain and headache
B. Causes vomiting
c. causes stomach pain
D. None of the above


Which is a free living nitrogen fixing bacterium?
A. Pseudomonas
B. Azotobacter
c. Nitrosomonas
D. Rhizobium


In one shop, an article is marked 75\% above the cost price but the purchaser is allowed a discount of \( 20 \% \) on the
marked price. In another shop, a similar article is sold for \( \mathrm{Rs} .58 \) at a gain of \( 45 \% \) What did the purchased pay for this article in the first shop?
A . \( R s .69 \)
B. \( R s .56 \)
c. \( R s .62 \)
D. Rs.65


For the cube-rod-sphere combination shown, the density of the material is uniform throughout the object. A thin rod of length, \( d \), connects the centers of the two objects. Where is the center of mass?
A. Inside the cube
B. closer to the cube than to the sphere
c. At the midpoint between the cube and the sphere
D. closer to the sphere than to the cube
E. Inside the sphere


If \( a+b=1 a n d a^{2}+b^{3}+3 a b=k, \) then
the value of k is
\( \mathbf{A} \cdot \mathbf{1} \)
B. 3
\( c .5 \)
D.


The image of an object placed on the principal axis of a concave mirror of focal length \( 12 \mathrm{cm} \) is formed at a point which is \( 10 c \) more distance from the
mirror than the object. The magnification of the image is
\( A \cdot 8 / 3 \)
B . 2.
\( c \cdot 2 \)
D. -1.5.


Which is the correct combination
\begin{tabular}{ll|l|l|}
& & \multicolumn{2}{l} { change } \\
& & in \\
Emission & Atomic number & mass number \\
\hline (a) & \( \alpha \) & -2 & -2 \\
(b) & \( \beta^{-} \) & +1 & 0 \\
(c) & \( \gamma \) & 0 & 0 \\
(d) & \( \beta^{+} \) & -1 & 0 \\
\hline
\end{tabular}


Which moon is also referred to as "Dark
Moon'!
A. Full Moon
B. Waning Crescent
c. New Moon
D. waning Gibbous


\( \left(\begin{array}{l}n \\ 0\end{array}\right)+2\left(\begin{array}{l}n \\ 1\end{array}\right)+2^{2}\left(\begin{array}{l}n \\ 2\end{array}\right)+\ldots .+2^{n}\left(\begin{array}{l}n \\ n\end{array}\right) \)
is equal to
A \( \cdot 2^{n} \)
B.
\( c \cdot 3^{n} \)
D. None of these


PQRS is a parallelogram. If \( L, M \) are
the midpoints of \( Q R \) and \( P S \)
respectively, and \( O \) is any point on \( L M \)
then the area of triangle \( O P Q \) is equal
to
A \( \cdot\left(\frac{1}{3}\right)^{r d} \) of the parallelogram \( P Q R S \)
B \( \cdot\left(\frac{1}{4}\right)^{t h} \) of the parallelogram \( P Q R S \)
C \( \cdot\left(\frac{1}{2}\right) \) of the parallelogram \( P Q R S \)
D \( \left(\frac{1}{6}\right)^{t h} \) of the parallelogram \( P Q R S \)


If \( \int_{a}^{b} x^{3} d x=0 \) and \( \int_{a}^{b} x^{2} d x=\frac{2}{3}, \) then
what are the values of \( a \) and \( b \)
respectively?
A. -1,1
в. 1,1
c. \( 0, \)
D. 2,-2


Write a balance chemical equation of
the following:
\( \boldsymbol{F} \boldsymbol{e} \boldsymbol{S} \boldsymbol{O}_{4}(\boldsymbol{s}) \stackrel{\text {heat}}{\longrightarrow} \boldsymbol{F} \boldsymbol{e}_{2} \boldsymbol{O}_{3}(\boldsymbol{s})+\boldsymbol{S} \boldsymbol{O}_{2}(\boldsymbol{g})+ \)
\( \boldsymbol{S} \boldsymbol{O}_{3}(\boldsymbol{g}) \)


Range of \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2}+\frac{\mathbf{1}}{\boldsymbol{x}^{2}+\boldsymbol{4}} \)


Simplify:
Find \( \boldsymbol{x}(\boldsymbol{x}+\mathbf{1})(\boldsymbol{x}+\mathbf{2})(\boldsymbol{x}+\boldsymbol{3}) \div \boldsymbol{x}(\boldsymbol{x}+\mathbf{1}) \)
A \( \cdot(x+2)(x+3) \)
B. \( x+2 \)
c. \( x+3 \)
D. None of these


A passenger in an aeroplane shall
A. never see a rainbow.
B. may see a primary and a secondary rainbow as concentric circles.
C. may see a primary and a secondary rainbow as concentric arcs.
D. shall never see a secondary rainbow.


A circular disc is rotating about its own
axis at constant angular acceleration. If its angular velocity increases from
210 rpm to 420 rpm during 21 rotations then the angular acceleration of disc is :
A. \( 5.5 \mathrm{rad} / \mathrm{s}^{2} \)
B. 11 rad / \( s^{2} \)
c. \( 16.5 \mathrm{rad} / \mathrm{s}^{2} \)
D. 22 rad / \( s^{2} \)


The metal extracted by leading with a cyanide is:
A . \( A l \)
в. \( N a \)
\( c . A g \)
D. \( C u \)


The IUPAC name(s) of the following
compound is (are):
This question has multiple correct options
A. 4 - methylchlorobenzene
B. 4 - chlorotoluene
C. I - chloro-4-methylbenzene
D. I - methyl - 4- chlorobenzene


The forward characteristic curve of a
junction diode is shown in Figure.
Calculate the resistance of the diode at:
(1) \( V=0.5 V \)
(2) \( \mathrm{I}=60 \mathrm{mA} \)


'Greater the valency, the higher is the coagulating power of ion'. This rule was introduced by:
A. Hardy-Schulze
B. Graham
c. Kossel and Lewis
D. Faraday


Which of the following quantities can only be a whole number?
A. Atomic radius
B. Atomic number
c. Mass number
D. Equivalent weight


If \( f(x)=x+5 \) and \( g(x)=\sqrt{x^{2}-9} \) then find the domain of \( \operatorname{gof}(x) \)
A \( \cdot(-8,-2) \)
В \( \cdot(-\infty,-8) \cup(-2, \infty) \)
c. \( (-\infty,-8] \cup[-2, \infty) \)
D. \( (-(-\infty,-8] \cup[-2, \infty) \)


Which of the following
statements about bonding is correct?
A. Only van der Waals forces exist between polar molecules
B. Dipoles are the result of the equal sharing of electrons
C \( . C u(s) \) is a network covalent solid
D. Hydrogen bonds exist between the molecules of \( H C l \)
E . \( N a C l(a q) \) has attraction between the molecules and the ions


Which of the following is the smallest unit?
A. millimetre
B. angstrom
c. fermi
D. metre


Addition of phosphates and
nitrates/fertilizers into water leads to
A. Increased algal growth
B. Nutrient enrichment/ eutrophication
c. Increased growth of decomposers
D. Reduced algal growth


Let \( z_{1}, z_{2} \in C \) and \( x=\left|z_{1} z_{2}\right|- \)
\( \boldsymbol{\operatorname { R e }}\left(\boldsymbol{z}_{1} \boldsymbol{z}_{2}\right)-\frac{\mathbf{1}}{\mathbf{2}}\left|\overline{z_{2}}-\boldsymbol{z}_{1}\right|^{2}+\frac{\mathbf{1}}{\mathbf{2}}\left(\left|\boldsymbol{z}_{2}\right|-\right. \)
\( \left.\left|z_{1}\right|\right)^{2} \) then
\( \mathbf{A} \cdot x<0 \)
B. \( x=0 \)
c. \( x \geq 1 \)
D. \( 0<x<1 \)


The equilibrium constant for the reaction is:
\( \boldsymbol{P}_{4}(\boldsymbol{s})+\mathbf{5} \boldsymbol{O}_{2}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{P}_{4} \boldsymbol{O}_{10}(\boldsymbol{s}) \)
\( ^{\mathbf{A}} \cdot_{K_{c}}=\frac{1}{\left[O_{2}\right]^{5}} \)
В \( \cdot K_{c}=\left[O_{2}\right]^{5} \)
\( \mathbf{c} \cdot_{K_{c}}=\frac{\left[P_{4} O_{10}\right]}{5\left[P_{4}\right]\left[O_{2}\right]} \)
D. \( _{K_{c}=\frac{\left[P_{4} O_{10}\right]}{\left[P_{4}\right]\left[O_{2}\right]^{5}}} \)


In crystalline form sulphur existing in
\( \boldsymbol{S}_{8} \) molecule has:
A. crown shaped structure
B. tetrahedral structure
c. pyramidal structure
D. angular structure


What is corrosion?


Solid calcium oxide was taken in a
container and water was added slowly
to it-
(i) State two observations made in the
experiment.
(ii) Write the name and the chemical
formula.


Which of the following parameters of a wave undergoes a change when wave is reflected from a boundary?
A. Intensity
B. Phase
c. Speed
D. Frequency


Identify the type of \( \operatorname{set} A^{\prime}=\{1,2,6,7\} \)
and \( \boldsymbol{B}=\{\mathbf{6}, \mathbf{1}, \mathbf{2}, \mathbf{7}, \mathbf{7}\} \)
A. Overlapping Sets
B. Unequal Sets
c. Equal sets
D. None of these


A rod of length \( 10 \mathrm{cm} \) lies along the principal axis of a concave mirror of focal length \( 10 \mathrm{cm} \) in such away that the end closer to the pole is \( 20 \mathrm{cm} \) away
from it. Find the length of the image.
A . \( 2 \mathrm{cm} \)
B. \( 4 \mathrm{cm} \)
\( c \cdot 5 \mathrm{cm} \)
D. \( 6 \mathrm{cm} \)


Arytenoid cartilage is found in
A . Hyoid
B. Sternum
c. Larynx
D. Nose


Pure water is:
A. colourless and opaque
B. colourless and transparent
C . coloured and transparent
D. colourless, odourless and transparent


If analytical chemist found approximately 12 moles of oxygen in a sample of \( \left(\mathrm{Al}_{2} \mathrm{O}_{3}\right) \) and she also knows
that the atomic mass of aluminum is
27 g/mol and the atomic mass of
oxygen is \( 16 \mathrm{g} / \mathrm{mol} \) then what total mass
of this \( A I_{2} O_{3} \) is :
A. 102 g
B. 192 \( g \)
c. \( 3672 \mathrm{g} \)
D. 408 g
E. \( 1224 \mathrm{g} \)


A virtual image larger than the object can be obtained by
A. Concave mirror
B. Convex mirror
c. Plane mirror
D. concave lens


How can the brightness of the pattern on the screen of cathode ray tube be changed?
A. Changing the target
B. By changing the current on gridd
c. By changing the negative potential on gridd
D. can't be changed


Excess \( F_{2}(g) \) reacts at \( 150^{0} \mathrm{C} \) and 1.0
\( \operatorname{atm} \) pressure with \( B r_{2}(g) \) to give a
compound \( B r F_{n} . \) What is n? [Atomic mass \( \mathrm{Br}=80, \mathrm{F}=19] \)


Masses of three wires of copper are in
the ratio of 1: 3: 5 and their lengths are
in the ratio of 5: 3: 1

The ratio of their electrical resistances
is.
A. 1: 3: 5
B. 5: 3: 1
c. 1: 15: 125
D. 125: 15: 1


From the following given statements
i) \( 0-\dots \) Hydrogen bond length is more than covalent "O-H" bond length
ii) The ionic bond strength of \( C s F \) is more than that of \( N a F \)
iii) The number of electrons present in all shells of sodium atom is 10
The correct combination is:
A. only (i) is correct
B. only (i) and (ii) are correct
c. only (ii) and (iii) are correct
D. all are incorrect


Carbon dioxide formed after reaction
with cupric oxide is tested by :
A. caustic soda
B. quick lime
c. lime water
D. baking soda


Which of these waves can be polarised?
A. Sound waves
B. Longitudinal waves on a string
C. Transverse waves on a string
D. Light waves


Mention the limitations of ohm law.


Given the structural formula for the
following:
Ethanal


When the electronjumps from \( n=5 \) to \( n \)
= 2 level, the spectral line observed in
the hydrogen spectrum belongs to:
A. Balmer series
B. Lyman series
c. Brackett series
D. Pfund series


\( \boldsymbol{I}=\boldsymbol{6} \cos \boldsymbol{w} \boldsymbol{t}+\boldsymbol{8} \sin \boldsymbol{w} \boldsymbol{t} \) is
applied across a resistor of \( 40 \Omega \). Find the potential difference across
the resistor
A . \( 660 v \)
B. 80
c. \( 330 v \)
D. 400


\( \boldsymbol{o}-\boldsymbol{B r}-\boldsymbol{C}_{6} \boldsymbol{H}_{4}-\boldsymbol{N} \boldsymbol{H}_{2} \) is :
A . aliphatic \( 1^{0} \) - amine
B. aromatic \( 1^{0} \) - amine
c. aliphatic \( 2^{0} \) - amine
D. aromatic \( 2^{0} \) - amine


Trace of \( A^{50} \) equals
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D. 3


What is the gravitational potential energy of the mass \( m ? \)
\( ^{\mathbf{A}} \cdot \frac{2}{\sqrt{3}} \frac{G M m}{l}(1-2 \sqrt{3}) \)
B. \( -\frac{2}{\sqrt{3}} \frac{G M m}{l}(1+2 \sqrt{3}) \)
\( ^{\mathbf{c}}-\frac{\sqrt{3}}{2} \frac{G M m}{l}(1-2 \sqrt{3}) \)
D. \( -\frac{\sqrt{3}}{2} \frac{G M m}{l}(1+2 \sqrt{3}) \)


A spaceship moves in a circular orbit of
radius \( 7200 \mathrm{km} \) round the earth. How
far does it travel while sweeping an
angle of \( 100^{\circ} ? \)


Consider the line \( x=\sqrt{3} y \) and the
circle \( x^{2}+y^{2}=4 \)
What is the area of the region in the first quadrant enclosed by the y-axis, the line \( x=\sqrt{3} \) and the circle?
A \( \cdot \frac{2 \pi}{3}+\frac{\sqrt{3}}{2} \)
B \( \cdot \frac{\pi}{2}-\frac{\sqrt{3}}{2} \)
c. \( \frac{\pi}{3}-\frac{1}{2} \)
D. None of the above


Which of the following is a largest source of formaldehyde vapour pollution in a room?
A. Utensil
B. Furniture
c. cooking range
D. Books


If \( P(A \cup B)=\frac{3}{4} \) and \( P(\bar{A})=\frac{2}{3}, \) then
find the value of \( \boldsymbol{P}(\overline{\boldsymbol{A}} \cap \boldsymbol{B}) \)
A \( \cdot \frac{3}{2} \)
B. \( \frac{1}{2} \)
c. \( \frac{5}{12} \)
D. None of these


Find the mean deviation about the following continuous distribution:
\( \begin{array}{llll}\text { Marks } & 0- & 10- & 20- \\ \text { obtained } & 10 & 20 & 30\end{array} \)
No. of
boys 1 6 8 14


A transverse wave is travelling along a
string from left to right. The figure
represents the shape of the string (snap-shot) at a given instant. At this
instant how many points will have downward magnitude of velocity.


Explain the sex determination in humans.


\( \boldsymbol{P}(\boldsymbol{A}-\boldsymbol{B})=\boldsymbol{P}(\boldsymbol{A})-\boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B})= \)
\( \boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B})-\boldsymbol{P}(\boldsymbol{B})=\boldsymbol{P}(\boldsymbol{A} \cap \overline{\boldsymbol{B}})=1- \)
\( \boldsymbol{P}(\overline{\boldsymbol{A}} \cap \boldsymbol{B}) \)
A. True
B. False


The line represented by the equation \( y= \) \( x \) is the perpendicular bisector of line segment AB. If A has the coordinates
\( (-3,3), \) what are the coordinates of \( \mathrm{B} \) ?
A \( \cdot(6,-3) \)
в. (3,-6)
c. (3,-3)
D. (6,3)


An uncharged conductor can be charged by
A. rubbing
B. positively
c. diverge
D. induction


A car travelling at \( 60 \mathrm{km} / \mathrm{h} \) overtake
another car traveling at \( 42 \mathrm{km} / \mathrm{h} \)
Assuming each car to be \( 5.0 m \) long,
find the time taken during the overtaking and the total road distance
used for the overtake.


A vessel contains \( N \) molecules of a gas
at temperature \( T . \) Now the number of
molecules is doubled, keeping the total energy in the vessel constant. The
temperature of the gas is.
A. \( T \)
в. 27
c. \( \frac{T}{2} \)
D. \( \sqrt{2} T \)


A page is opened at random from a book containing 90 pages. Then probability of a page number is a perfect square, is


Which is right combination?
(a) Hydrate isomerism\( \left[\boldsymbol{C o}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{3} \boldsymbol{C l}_{3}\right] \boldsymbol{3} \boldsymbol{H}_{2} \boldsymbol{O} \) and
\( \left[\boldsymbol{C o}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{6}\right] \boldsymbol{C l}_{3} \)
(b) lonisation isomerism-
\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{5} \boldsymbol{B r}\right] \boldsymbol{S O}_{4} \) and
\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{5} \boldsymbol{S} \boldsymbol{O}_{4}\right] \boldsymbol{B} \boldsymbol{r} \)
(c) Geometrical isomerism- \( M C l_{2} B r_{2} \)
\( A \cdot a \) and \( b \)
B. b and c
c. a and c
D. a , b and c


Electron transition in \( H e^{+} \) ion takes
from \( n_{2} \) to \( n_{1} \) shell such that:
\( 2 n_{2}+3 n_{1}=18 \)
\( 2 n_{2}-3 n_{1}=6 \)
What will be the total number of
photons emitted when electrons transit
to \( n_{1} \) shell?
A . 21
B . 15
c. 20
D. 10


What type of force is exerted on our body during respiration?
A. Magnetic force
B. Non-contact force
c. Muscular force
D. Gravitational force


Assertion
Natural rubber becomes stiff by the vulcanization with sulphur
Reason
Sulphur forms cross links at the reactive sites of double bonds in
vulcanization.
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


Why do the electrostatic field lines not
form closed loops?


Type of isomerism shown by
\( \left[\boldsymbol{C r}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{5} \boldsymbol{N} \boldsymbol{O}_{2}\right] \boldsymbol{C l}_{2} \) is
A. optical
B. ionisation
c. geometrical
D. linkage


Assertion
A simple has undivided. lamina
Reason
Leaves showing pinnate and palmate
venation have various type of incision.
A. If both the assertion and the reason are true and the
reason is a correct explanation of the assertion
B. If both the assertion and reason are true but the
reason is not a correct explanation of the assertion
C. If the assertion is true but the reason is false
D. If both the assertion and reason are false


If the equal sides of an isosceles
triangle \( A B C \) are produced, prove that the exterior angles so formed are obtuse,say ext \( \angle B, \) and find \( e x t \angle B- \)
\( \angle A \)


ff \( \alpha, \beta \) are the roots of \( \left|\begin{array}{lll}x & 1 & 2 \\ 0 & 1 & 1 \\ 1 & x & 2\end{array}\right|=0 \)
\( \operatorname{then} \boldsymbol{\alpha}^{\boldsymbol{n}}+\boldsymbol{\beta}^{\boldsymbol{n}}=? \)
A.
в.
\( c \cdot 2 \)
D. 2n


The electronic configuration of transition elements is:
A \( \cdot n s^{1} \)
B . \( n s^{2} n p^{5} \)
c. \( n s^{2}(n-1) d^{10} \)
D . \( (n-1) d^{1-10} n s^{0}-2 \)


Which of the following order is true regarding the acidic nature of phenol?
A. Phenol> 0 -cresol > O-nitrophenol
B. Phenol> 0 -nitrophenol > 0-cresol
c. o-cresol < phenol < 0- nitrophenol
D. Phenol < O-cresol < O-nitrophenol


Alkenes and alkynes are unsaturated
compounds
A. True
B. False


An aqueous solution freezes at
\( -\mathbf{0 . 1 8 6}^{\circ} \boldsymbol{C}\left(\boldsymbol{K}_{\boldsymbol{f}}=\mathbf{1 . 8 6}^{\boldsymbol{o}} ; \boldsymbol{K}_{\boldsymbol{b}}=\mathbf{0 . 5 1 2}^{\boldsymbol{o}}\right) \)
What is the elevation in boiling point?
A. 0.186
в. 0.512
c. \( \frac{0.512}{1.86} \)
D. 0.0512


Which of the following does not electrical power in circuit?
\( \mathbf{A} \cdot I^{2} R \)
B . \( I R^{2} \)
c. \( V I \)
D. \( \frac{V^{2}}{R} \)


Solve :
\( \mathbf{3} \boldsymbol{x}-\mathbf{2} \boldsymbol{y}=\mathbf{1} \)
\( 2 x+y=3 \)


Q Type your question
and \( (D) \) are respectively:
4
\( B \)
\( c \)
\( D \)
of


The displacement from the position of
equilibrium of a point \( 4 \mathrm{cm} \) from a source of sinusoidal oscillations is half
the amplitude at the moment \( t=\frac{T}{6}(T \) is the time period). Assume that the
source was at mean position at \( t=0 \)
The wavelength of the running wave is
A \( .0 .96 m \)
B. \( 0.48 m \)
c. \( 0.24 \mathrm{m} \)
D. \( 0.12 \mathrm{m} \)


The oxidation state of sulphur in its octahedral
halide is:
\( A \cdot+4 \)
\( B .+6 \)
\( c \cdot+5 \)
\( D \cdot+2 \)


During unloading beyond \( B \), say \( C \), the
length at zero stress is now equal to:
A. less than original length
B. greater than original length
c. original length
D. can't be predicted


\( L \)
\( L \)
\( L \)
\( L \)


Write IUPAC names of following
alcohols.
\( \boldsymbol{C H}_{3}-\underset{\boldsymbol{C}_{2} \boldsymbol{H}_{5}}{\boldsymbol{C H}}-\boldsymbol{C H}-\boldsymbol{C H}_{3} \)
\( \boldsymbol{o} \boldsymbol{H} \)


\( \ln \) a reaction \( \boldsymbol{A} \longrightarrow \boldsymbol{B}+\boldsymbol{C}, \) The
following data were obtained:
t in seconds
\( \begin{array}{lll}0 & 900 & 1800\end{array} \)
conc. of \( \mathbf{A} \)
\[
\begin{array}{lll}
50.8 & 19.7 & 7.62
\end{array}
\]
Prove that it is a first order reaction.


A force of 5 N acts on a 15 kg particle initially at rest. What will be
instantaneous power due to the force at
the end of \( 6^{t h} \) second.
A. 10 watt
B. 5 watt
c. 20 watt
D. 25 watt


Factorise \( 2 x^{2}-9 x+9 \)


A coral island in a central shallow lake
is known as
A. Coral reef
B. Atoll
c. corallite
D. Diatomaceous sheath


Assuming \( \boldsymbol{g}_{(m o o n)}=\left(\frac{1}{6}\right) g_{e a r t h} \) and
\( D_{(m o o n)}=\left(\frac{1}{4}\right) D_{e a r t h} \) where \( g \) and \( D \)
are the acceleration due to gravity and diameter respectively, the escape velocity from the moon is:
A \( \cdot \frac{11.2}{24} k m s^{-1} \)
B . \( 11.2 \times \sqrt{24} \mathrm{kms}^{-1} \)
c. \( \frac{11.2}{\sqrt{24}} k m s^{-1} \)
D. \( 11.2 \times 24 \mathrm{kms}^{-1} \)


The weight of an object depends on
A. Mass of the object
B. Acceleration due to gravity acting on the object
c. Both A and B
D. None of the above


In a semiconductor
A. There are no free electrons at any temperature
B. The number of free electrons is more than in a
conductor
C. There is no free electrons at OK
D. None of these


Phototropism is due to the hormone
A . IAA
в. яА
\( c \cdot 2-4 D \)
D. Cytokinin


Give the IUPAC name of the following compound.


Assertion
Molecularity greater than three is not
observed.
Reason
The overall molecularity of a complex
reaction is equal to molecularity of the
Slowest step.
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


An excess of \( A g_{2} C r O_{4}(s) \) is added to a
\( \mathbf{5} \times \mathbf{1 0}^{-\mathbf{3}} \boldsymbol{M} \boldsymbol{K}_{\mathbf{2}} \boldsymbol{C r} \boldsymbol{O}_{\mathbf{4}} \) solution. The
concentration of \( A g^{+} \) in the solution is closest to.[Solubility product for \( \left.A g_{2} C r O_{4}=1.1 \times 10^{-12}\right] \)
B . \( 1.5 \times 10^{-5} \) М
c. \( 1.0 \times 10^{-6} \mathrm{M} \)
D. \( 5.0 \times 10^{-3} \) М


If \( 7 \cos ^{2} \theta+3 \sin ^{2} \theta=4 \) and \( \theta \) is in first
quadrant .Show that \( \boldsymbol{\theta}=\mathbf{6 0}^{\circ} \)


\( N_{2}(g)+3 H_{2}(g) \rightleftharpoons 2 N H_{3}(g) \)
\( \Delta H^{o}=-18 \quad k J \)
According to Le-Chateliers principal the favourable condition for good yield of
\( N H_{3} \)
A. Low pressure and low temperature
B. High pressure and low temperature
c. Low pressure and High temperature
D. High pressure and High temperature


Assertion
If \( \boldsymbol{x}<\mathbf{0}, \tan ^{-1} \boldsymbol{x}+\tan ^{-1} \frac{\mathbf{1}}{\boldsymbol{x}}=\frac{\boldsymbol{\pi}}{\mathbf{2}} \)
Reason \( \tan ^{-1} x+\cot ^{-1} x=\frac{\pi}{2} \forall x \in R \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


The side view of the pentagonal prism is
A. pentagon
B. square
c. rectangle
D. parallellogram


If \( \boldsymbol{A}^{-1}=\left[\begin{array}{cc}1 & -2 \\ -2 & 2\end{array}\right], \) then what is
\( \operatorname{det}(A) \) equal to \( ? \)
\( A \cdot 2 \)
B. -2
c. \( 1 / 2 \)
D. \( -1 / 2 \)


The \( n t h \) term of the series \( 3, \sqrt{3}, 1, \ldots . \) is \( \frac{1}{243}, \) then \( n \) is
A . 12
B. 13
c. 14
D. 15


Which of the following statements are
correct?
This question has multiple correct options
A. Diastereomers have different physical properties and similar but not identical chemical properties
B. Enantiomers have the same physical and chemical properties but different physiological properties
C. Polarimeter is used in measuring the optical rotation of a compound.
D. Only organic molecules show optical isomerism.


Assertion:
In the periodic table, the atomic radius increases from left to right.
Reason:
The number of protons is increasing
from left to right.
\( A \)
Both Assertion and Reason are true and the Reason is the correct explanation of the Assertion.
B. Both Assertion and Reason are true, but Reason is not the correct explanation of the Assertion.
c. Assertion is true, but the Reason is false.
D. Assertion is false, but the Reason is true
E. Both assertion and reason is incorrect


A wire shaped as a circle of radius \( \mathrm{R} \)
rotates about the axis \( 00^{\prime} \) with an
angular velocity \( \omega \) as shown in figure.
Resistance of the circuit is \( R \). Find the
mean thermal power generated in the
loop during a period of a rotation.
A \( \cdot \frac{\left(B \pi a^{2} \omega\right)^{2}}{4 R} \)
B. \( \frac{\left(B \pi a^{2} \omega\right)^{2}}{2 R} \)
\( ^{\mathbf{C}} \cdot \frac{\left(3 B \pi a^{2} \omega\right)^{2}}{2 R} \)
D. None of these


Bakelite is formed by the reaction of:
A. phenol and formaldehyde
B. formaldehyde and aniline
c. adipic acid and ethylene glycol
D. phthalic acid and ethylene glycol


State which pairs of triangles in Fig. are
similar. Write the similarity criterion
used by you for answering the question and also write the pairs of similar
triangles in the symbolic form:


If two straight lines intersect, the measures of the vertically opposite angles are
A. equal
B. not equal
c. cannot be determined
D. Nont of these


Select the false statement.
A. Scientists who study and contribute to the classification of organisms are known as systematists.
B. Carolus Linnaeus developed the first scientific system of naming species.
C. A five kingdom arrangement of organisms was introduced by R. H. Whittaker.
D. Genus is a group of species which are related and have less characters in common as compared to species.
E. Phycomycetes are called club fungi because of a club shaped end of mycelium known as basidium.


If \( \int \frac{3 x+4}{x^{3}-2 x-4} d x=\log |x-2|+ \)
\( \boldsymbol{K} \log \boldsymbol{f}(\boldsymbol{x})+\boldsymbol{C}, \) then
This question has multiple correct options
A. \( K=-1 / 2 \)
B . \( f(x)=x^{2}+2 x+2 \)
C \( . f(x)=\left|x^{2}+2 x+2\right| \)
D. \( K=1 / 4 \)


The height of the cylinder of maximum volume that can be inscribed in a
sphere of radius R is?
A \( \cdot \frac{2 R}{3} \)
в. \( \frac{R}{3} \)
c. \( \frac{2 R}{\sqrt{3}} \)
D. \( \frac{R}{\sqrt{3}} \)


The IUPAC name of the compound is:
A. 1 -bromo-1chloro-4, \( 4^{\prime} \) -bicyclobutane
B. \( 4-\left(4^{\prime}-\text { chlorocyclobutyl }\right)-1 \) -bromocyclobutane
c. 3 -Bromo-3'-chloro-1, 1'-bicyclobutane
D. 4-(4'-bromocyclobutyl)-1-chlorocyclo butane


The process of burning wood in limited supply of oxygen to obtain charcoal as a resultant product is called:
A. Destructive distillation
B. Simple distillation
c. Fractional distillation
D. Azeotropic distillation


A man, sitting firmly over a rotating stool has his arms stretched. If he folds
his arms, the work done by the man is :
A. zero
B. positive
c. negative
D. may be positive or negative


If a wire of resistance \( 20 \Omega \) is covered
with ice and a voltage of \( 210 \mathrm{V} \) is applied across the wire, then the rate of melting of ice is
A. \( 8.85 g s^{-1} \)
В . \( 1.92 g s^{-1} \)
c. \( 6.56 g s^{-1} \)
D. none


A square plate of mass \( M \) and edge \( L \)
is shown in the fig. The moment of
inertia of the plate about the axis in the
plane of plate and passing through one
of its vertex making an angle \( 15^{0} \) with the horizontal is
A. \( \frac{M L^{2}}{12} \)
B. \( \frac{11 M L^{2}}{24} \)
\( c \cdot \frac{7 M L^{2}}{12} \)
D. none of these


A parallel plate capacitor of capacitance \( 6 \mu F \) in air and \( 60 \mu F \) When dielectric is introduced. What is
the dielectric constant of the medium.?
A . 0.4
в. 0.1
c. 0.77
D. 0.25


A virtual Image cannot be taken on the
screen.
A . True
B. False


state \( \quad \) Minimum Wage per Hour
daho \( \$ 7.25 \)
Montana
\[
\$ 7.90
\]
Orego \( \$ 9.10 \)
Wahington \( \quad \$ 9.32 \)
The table above shows the 2014 minim
wages for several states that share a
border. Assuming an average workweek of between 35 and 40 hours, which
inequality represents how much more a worker who earns minimum wages can
earn per week in Oregon than in Idaho?
A \( . x \geq 1.85 \)
в. \( 7.25 \leq x \leq 9.10 \)
c. \( 64.75 \leq x \leq 74 \)
D. \( 253.75 \leq x \leq 364 \)


A plane meet the co-ordinate axes in
\( A, B, C \) such that the centroid of
triangle \( A B C \) is \( (a, b, c) . \) If equation of plane \( \frac{x}{a}+\frac{y}{b}+\frac{z}{c}=k(k \neq 0), \) then the
value of \( k \) equals
A . 2
B. 3
\( c \cdot 4 \)
D. 5


The D.E whose signature is \( y= \)
\( C_{1} e^{3 x}+C_{2} e^{5 x} \) is:
A \( \cdot y_{2}+2 y_{1}+15 y=0 \)
в. \( y_{2}+8 y_{1}+15 y=0 \)
c. \( y_{2}+8 y_{1}-15 y=0 \)
D. \( y_{2}-8 y_{1}+15 y=0 \)


A person brings amass of \( 1 k g \) from
infinity to a point A Initially, the mass was at rest but it moves at a speed of \( 3 m / s \) as it reaches A. The work done by
the person on the mass is \( -5.5 J \) The
gravitational potential at \( \boldsymbol{A} \) is
A. \( -1 J / k g \)
в. \( -4.5 J / k g \)
\( \mathbf{c} .-5.5 J / k g \)
D. \( -10 J / k g \)


If \( R \) is a relation from a finite \( \operatorname{set} A \)
having \( m \) elements to a finite set \( B \)
having \( n \) elements, then the number of relations from \( A \) to \( B \) is:
\( A \cdot 2^{m n} \)
B . \( 2^{m n}-1 \)
\( c \cdot 2 m n \)
D. \( m^{n} \)


The washing away or removal of soil
from land is called
A. Soil formation
B. Soil erosion
c. crop rotation
D. Recycling


The slipper shaped organism that reproduces by binary fission is
A. Amoeba
B. Paramoecium
c. Plasmodium
D. Salmonella


n an L-C-R circuit as shown both
switches are open initially. Now switch \( S_{1} \) and \( S_{2}, \) are closed. \( (q \) is the charge on the capacitor and \( r=R C \) is
capacitance time constant). What is the charge on the capacitor at \( t=2 \tau ? \)


A jar filled with two non mixing liquids
1 and 2 having densities \( \rho_{1} \) and \( \rho_{2} \) respectively. A solid ball, made of a
material of density \( \rho_{3}, \) is dropped in the jar. It comes to equilibrium in the
position shown in the figure
A \( \cdot \rho_{3}<\rho_{1}<\rho_{2} \)
B . \( \rho_{1}<\rho_{3}<\rho_{2} \)
\( \mathbf{c} \cdot \rho_{1}<\rho_{2}<\rho_{3} \)
D. \( \rho_{3}<\rho_{2}<\rho_{1} \)


Find the upper limit of the median class
from the given frequency distribution
table
\( \begin{array}{cccc}\mathbf{0}- & \mathbf{6}- & \mathbf{1 2}- & \mathbf{1 8}- \\ \mathbf{5} & \mathbf{1 1} & \mathbf{1 7} & \mathbf{2 3}\end{array} \) Class
Frequency 8 \( 03 \quad 10 \quad 15 \)
\( \mathbf{A} \cdot 17 \)
B . 17.5
\( \mathbf{c} \cdot 18 \)
D. 18.5


Wave number of spectral line for a given
transition is \( x c m^{-1} \) for \( H e^{+}, \) then its
value for \( B e^{3+} \) (isoelectronic of \( \boldsymbol{H} \boldsymbol{e}^{+} \) )
for same transition is:
A \( \cdot \frac{x}{4} c m^{-1} \)
B. \( x \mathrm{cm}^{-1} \)
\( c \cdot 4 x c m^{-1} \)
D. \( 16 x \mathrm{cm}^{-1} \)


The value indicated by Fermi energy
level in an intrinsic semiconductor is
A. the average energy of electrons and holes.
B. the energy of electrons in conduction band
C. the energy of holes in valence band
D. the energy of forbidden region


Factorize \( (\boldsymbol{a} \boldsymbol{x}+\boldsymbol{b} \boldsymbol{y})^{2}+(\boldsymbol{b} \boldsymbol{x}-\boldsymbol{a} \boldsymbol{y})^{2} \) by
the grouping method
A \( \cdot\left(x^{2}+y^{2}\right)\left(a^{2}+b^{2}\right) \)
В - \( \left(2 x^{2}+y^{2}\right)\left(a^{2}+b^{2}\right) \)
c. \( \left(2 x^{2}+y^{2}\right)\left(2 a^{2}-b^{2}\right) \)
D. \( \left(x^{2}+2 y^{2}\right)\left(a^{2}-b^{2}\right) \)


\( 1+5 x \) is a quadratic polynomial
A. True
B. False


The amount of silver deposited on passing \( 2 \mathrm{F} \) of electricity through
aqueous solution of \( A g N O_{3} \) is
A. 548
B. \( 108 g \)
c. \( 216 g \)
D. 324g


The radii of curvature of a double
concave lens are \( 30 \mathrm{cm} \) and \( 60 \mathrm{cm} \) and
the refractive index of its glass is 1.5 Calculate the focal length of the lens.


The order and degree of the differential equation \( \left(\boldsymbol{y}^{\prime \prime \prime}\right)^{2}+\left(\boldsymbol{y}^{\prime \prime}\right)^{3}-\left(\boldsymbol{y}^{\prime}\right)^{4}+\boldsymbol{y}^{5}= \)
0 is
A. 3 and 2
B. 1 and 2
\( c \cdot 2 \) and 3
D. 1 and 4
E. 3 and 5


Choose the correct answer from
alternatives given

The mixture of a pure liquid and a
solution in a long vertical column (i.e, horizontal dimensions
A \( -\frac{1}{d}\left(\frac{d u}{d y}\right) \mu \)
B \( \cdot \frac{d}{h}\left(\frac{d u}{d y}\right) \)
c. \( \left(\frac{d u}{d y}\right) \)
" \( -\frac{1}{\mu}\left(\frac{d u}{d y}\right) d \)


When a ray of light strikes a plane
mirror at an angle of \( 15^{\circ} \) with the mirror, what will be the angle of reflection with respect to the normal?
A . 15
B. 30
\( c \cdot 75 \)
D. None of these


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


The reaction of alkyl halide with benzene in presence of anhydrous
\( A l C l_{3} \) gives alkyl benzene.This reaction is known as:
A. Friedel-craft's reaction
B. carbylamine reaction
c. Gattermann reaction
D. Wurtz reaction


According to Bohr's theory, the energy required for the transition of H-atom from \( n=6 \) to \( n=8 \) state is:
A. equal to the energy required for the transition from \( n= \) 5 to \( n=6 \) state
B. larger than the energy required for the transition from \( n=7 \) to \( n=9 \) state
c. less than the energy required for the transition from n \( =7 \) to \( n=9 \) state
D. equal to the energy required for the transition from \( n= \) 7 to \( n=9 \) state


The vital capacity of lungs is
A. \( 4-5 L \)
B. 3.5-4.5 L
c. \( 5-6 L \)
D. 4-7L


\( \mathrm{Cl}, \mathrm{Br}, \mathrm{I} \) follows Dobereiner's triads, the atomic masses of \( \mathrm{Cl} \) and I are 35.5 and
127 respectively. The atomic mass of Br is :
A . 162.5
B. 91.5
c. 81.25
D. 45.625


Derive an expression for the refractive index of the material of a prism.


\( \operatorname{Let} A=\{1,2,3, \dots \dots 50\} \) and \( B= \)
\( \{2,4,6 \dots \dots .100\} \). The number of
elements \( (x, y) \in A \times B \) such that \( x+ \)
\( \boldsymbol{y}=\mathbf{5 0} \)
A .24
B . 25
c. 50
D. 75


initial speed with which water strikes
the ground.


If Poisson's ratio \( \sigma \) for a material is \( -\frac{1}{2} \) then the material is
A. Elastic fatigue
B. Incompressible
c. compressible
D. None of the above


Buckminster fullerene is:
A. isotope of carbon
B. isobar of carbon
c. allotrope of carbon
D. none of these


\( X e F_{4} \) reacts violently with water to
give:
A. \( X e+O_{2} \)
в. \( X e O_{3}+O_{2}+H F \)
c. \( X e+O_{2}+H F+X e O_{3} \)
D. \( X e O F_{4} \)


Rusting of iron is catalysed by :
This question has multiple correct options
\( A \cdot H^{+} \) ions
B. dissolved \( C O_{2} \) in water
\( c \cdot O_{2} \)
D. impurities present


What is weight?


The IUPAC name of \( \boldsymbol{K}_{4}\left[\boldsymbol{F} e(\boldsymbol{C} \boldsymbol{N})_{6}\right] \) is:
A. potassium ferricyanide
B. potassium ferrocyanide
c. potassium hexacyanoferrate (II)
D. potassium hexacyanoferrate (III)


Consider \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{3}+\boldsymbol{a} \boldsymbol{x}^{2}+\boldsymbol{b} \boldsymbol{x}+\boldsymbol{c} \)
Parameters \( a, b, c \) are chosen,
respectively, by throwing a die three times. Then the probability that \( f(x) \) is
an increasing function is
A \( .5 / 12 \)
в. \( 2 / 9 \)
c. \( 4 / 9 \)
D. \( 1 / 3 \)


The formula of Auxin-A is
A. \( \mathrm{C}_{18} \mathrm{H}_{30} \mathrm{O}_{7} \)
the
в. \( \mathrm{c}_{10} \mathrm{H}_{9} \mathrm{NO}_{2} \)
\( \mathbf{c} \cdot \mathbf{c}_{12} \mathbf{H}_{30} \mathbf{O}_{6} \)
D. \( \mathrm{c}_{20} \mathrm{H}_{30} \mathrm{O}_{5} \)


For \( i=1,2,3,4 \) let \( T_{i} \) denote the event
that the students \( S_{i} \) and \( S_{i+1} \) do NOT sit adjacent to each other on the day of the examination. Then the probability of the
event \( \boldsymbol{T}_{\mathbf{1}} \cap \boldsymbol{T}_{\mathbf{2}} \cap \boldsymbol{T}_{\mathbf{3}} \cap \boldsymbol{T}_{\mathbf{4}} \) is?
A \( \cdot \frac{1}{15} \)
в. \( \frac{1}{10} \)
c. \( \frac{7}{60} \)
D.


Obtain balancing condition of
Wheatstone's bridge Kirchoff's rules electrical circuit.


A person cannot see objects clearly
which are nearer than \( 75 \mathrm{cms} \) from his
eyes, the disease he is suffering from is:
A. Astigmatism
B. Myopia
c. Hypermetopia
D. Presbyopia


In case of uniform circular motion
which of the following physical quantity do not remain constant
A. Speedd
B. Momentum
c. Kinetic energy
D. Mass


If a line has direction ratio 2,-1,-2
determine its direction cosines.


During extraction of silver from silver glance by cyanide process,
\( N a_{2}\left[Z n(C N)_{4}\right] \) becomes soluble and
\( A g \) is precipitated

If the statement is true enter 1 , else
enter 0


fibres are obtained
from plants and animals.
A. Natural
B. Plant
c. Animal
D. Synthetic


Assertion
Most of the secretions released by
laticiferous tissue is of no use to plants.
Reason
They are by products of physiological reactions useful for mankind.
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


Wires \( A \) and \( B \) have resistivities \( \rho_{A} \) and
\( \boldsymbol{\rho}_{B},\left(\rho_{B}=2 \rho_{A}\right) \) and have lengths \( l_{A} \) and
\( l_{B} . \) If the diameter of the wire \( B \) is twice
that of \( A \) and the two wires have same
resistance, then \( \frac{l_{B}}{l_{A}} \) is:
\( A \cdot 2 \)
B.
c. \( 1 / 2 \)
D. \( 1 / 4 \)


2
\( \boldsymbol{N} \equiv \boldsymbol{C}-\boldsymbol{C H}=\boldsymbol{C H}_{2} \)
What is the hybridization of carbons
marked as 1 and \( 2 ? \)
\( \begin{array}{lll}\text { A } \cdot s p^{2} & \text { and } & s p^{2}\end{array} \)
B . sp \( ^{3} \) and sp
c. sp and \( s p^{2} \)
D. sp and sp


Calculate the concentration of \( C O_{2} \) in a
soft drink that is bottled with a partial
pressure of 4 atm over the liquid at
\( 25^{\circ} \mathrm{C} . \) The Henry's law constant for \( C O_{2} \)
in water at \( 25^{\circ} \mathrm{C} \) is \( 3.1 \times \)
\( 10^{-2} \) atm / mole \( - \) litre.
A. 0.129 mol/litre
в. 129.03 mol/litre
c. 0.224 mol / litre
D. 224.3 mol/litre


Nonmetals react with hydrogen to form:
A. covalent compounds
B. ionic compounds
C. electrovalent compounds
D. coordinate compounds


Find the In the circuit shown in Fig,
switch \( S_{1} \) was closed for a long time. At
time \( t=0 \) the switch is
opened. Angular frequency of oscillation of the charge on the capacitor:
A \( \cdot 100 \operatorname{rad} s^{-1} \)
B. 200 rads\( ^{-1} \)
c. 300 rads\( ^{-1} \)
D. 400 rads\( ^{-1} \)


Four particles each of mass \( M, \) are located at the vertices of a square with
side \( L . \) The gravitational potential due
to this at the centre of the square is
A \( \cdot-\sqrt{32} \frac{G M}{L} \)
в. \( -\sqrt{64} \frac{G M}{L^{2}} \)
c. zero
D. \( \sqrt{32} \frac{G M}{L} \)


Draw the histogram for the following
frequency distribution
\( \begin{array}{ll}\text { Class-Interval } & \text { Frequency } \\ 0-5 & 5 \\ 5-10 & 8 \\ 10-15 & 15 \\ 15-20 & 4 \\ 20-25 & 10\end{array} \)


Taking \( \boldsymbol{\pi}=\mathbf{3 . 1 4}, \) find the
circumference of a circle whose radius
is \( 8 \mathrm{cm} \)


Solution of the differential equation \( \frac{d y}{d x}+y \sec x=\tan x\left(\leq x<\frac{\pi}{2}\right) \) is
A \( \cdot y(\sec x-\tan x)=(\sec x+\tan x)-x+C \)
B \cdot \( y(\sec x+\tan x)=(\sec x-\tan x)-x+C \)
C \( \cdot y(\sec x+\tan x)=(\sec x+\tan x)-x+C \)
D. noneofthese


Sound wave is travelling along positive x-direction. Displacement (y) of
particles from their mean positions at
position \( x \) is shown in figure. Choose the correct alternative(s):
This question has multiple correct options
A. particle located at E has its velocity in negative x direction
B. particle located at D has zero velocity
C. particles located near C are under compression
D. change in pressure at D is zero


Contractile vacuole of Amoeba placed in
salt water will
A. Burst
B. Disappear
c. Enlarge
D. Multiply


It is easy to stop a tennis ball than a cricket ball moving with the same velocity. This is because:
A. tennis ball has less momentum than cricket ball
B. tennis ball is soft and offers less friction
c. cricket ball is hard and offers more friction
D. none of these


There is an electric field \( \boldsymbol{E} \) in \( \boldsymbol{X} \)
=direction. If work done in moving a
charge \( 0.2 C \) through a distance of \( 2 m \)
along a line making an angle of 60 degree with \( X \) -axis is 4.0 joule, what
is the value of \( \boldsymbol{E} \) ?
A. \( \sqrt{3} \) newton per coulomb
B. 4 newton per coulomb
c. 5 newton per coulomb
D. None of these


In which of the following process the system and surrounding does not comes back to original state after
the process is complete?
A. Isothermal process
B. Adiabatic process
c. Reversible process
D. Irreversible process


If vectors \( i+2 j+2 k \) is rotated through
an angle of \( 90^{\circ} \) so as to cross positive
direction of \( y \) -axis, then the vector in the new positive is?
A \( \cdot-\frac{2}{\sqrt{5}} i+\sqrt{5} j-\frac{4}{\sqrt{5}} k \)
B. \( \frac{2}{\sqrt{5}} i-\sqrt{5} j+\frac{4}{\sqrt{5}} k \)
c. \( 4 i-j-k \)
D. None of these


The marks scored by students in Mathematics in a certain examination
are given below:
\( \begin{array}{lll}\text { Marks Scored } & \text { Number of Students } \\ 0-20 & 3 \\ 20-40 & 8 \\ 40-60 & 15 \\ 60-80 & 17 \\ 80-100 & 7\end{array} \) Draw histogram for the above data.


Evaluate :
(i) \( (1.2)^{3} \)
(ii) \( (3.5)^{3} \)
(iii) \( (0.8)^{3} \)
\( (i v)(0.5)^{3} \)


Which of the following changes decreases the vapour pressure of water kept in a sealed vessel?
A. Decreasing the quantity of water
B. Increasing the quantity of water
c. Decreasing the volume of vessel to one-half
D. Decreasing the temperature of water


Find the number of ion(s) which are
having ionizable hydrogen from the following:
\( \boldsymbol{H}_{2} \boldsymbol{P} \boldsymbol{O}_{2}^{-}, \boldsymbol{H} \boldsymbol{P} \boldsymbol{O}_{3}^{2-}, \boldsymbol{H}_{2} \boldsymbol{P}_{2} \boldsymbol{O}_{7}^{2-} \)


Select the correct statement.
A. During the decomposition of an oxide into oxygen and metal vapour, entropy increases.
B. Decomposition of an oxide is an endothermic change.
C . To make \( \triangle G^{0} \) negative, temperature should be high enough so that \( T \triangle S^{0}>\triangle H^{0} \)
D. All are correct answers.


\( 4.48 L \) of an ideal gas at S.T.P requires
12 calories to raise its temperature by
\( 15^{\circ} \mathrm{C} \) at constant volume. The \( C_{p} \) of the gas is:
A . 3 call \( l \)
в. 4 са \( l \)
c. \( 7 c a l \)
D. \( 6 c a l \)


Quantum theory was postulated by:
A. Rutherford
B. Maxwell
c. Max Planck
D. Becquerel


If \( \boldsymbol{f}: \boldsymbol{A} \rightarrow \boldsymbol{B} \) is a bijective function then
\( \boldsymbol{f}^{-1} \circ \boldsymbol{f}= \)
A \( \cdot f \circ f^{-1} \)
B. \( f \)
\( c \cdot f^{-1} \)
D. \( I_{A} \) (Identity map of the set \( A \) )