Right aortic arch is found in
A. Mammals
B. Birds
c. Mammals and birds
D. Reptiles


Q Type your question
\( X \) from 2 -butanone, 1 -chloro-propane
and methyl iodide?
\( A \)
B.
\( c \)
\( D \)


The number of solutions of the equation \( 2 \cos \left(\frac{x}{2}\right)=5^{x}+5^{-x} \) is
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c .3 \)
D. None of these.


When gas (A) is passed through dry
KOH at low temperature, a deep red coloured compound (B) and a gas (C) are obtained. The gas \( A, \) on reaction with but-2-ene, followed by treatment
with \( Z n / H_{2} O \) yields acetaldehyde. \( (A) \)
(B) and
(C) are identified as \( \boldsymbol{O}_{\boldsymbol{x}}, \boldsymbol{K} \boldsymbol{O}_{\boldsymbol{y}} \)
and \( O_{z} . \) What is \( x+y+z ? \)


The domain of the function \( f(x)= \)
\( \frac{\sqrt{5-x}}{(x+1)(x-2)(x-3)}+ \)
\( a \sin ^{-1}\left[\frac{2 x-5}{3}\right] ; a \neq 0 \) and \( [\cdot] \) denotes
greatest integer function, is:
A \( \cdot[1,5]-\{2,3\} \)
3
B . [1,2)\( \cup(3,5] \)
c. \( \left[1, \frac{11}{2}\right) \)
D・ [1,5]


The equivalent capacitance between
the terminals \( X \) and \( Y \) in the figure
shown will be -
A \( .100 p F \)
в. \( 200 p F \)
c. \( 300 p F \)
D. \( 400 p F \)


\( x^{2}=x y \) is a relation (defined on set \( R \) )
which is
A. Symmetric
B. Reflexive
c. Transitive
D. None of these


The slope of a curve at each of its points is equal to the square of the abscissae of the point. Find the particular curve through the point (-1,1)


The reduction of benzoyl chloride with
\( P d \) and \( B a S O_{4} / C a S O_{3} \) produces :
A. benzyl chloride
B. benzoic acid
c. benzaldehyde
D. All of the above


A rocket starts vertically upward with
speed \( v_{0} . \) Show that its speed \( v \) at height \( h \) is given by \( v_{0}^{2}-v^{2}=\frac{2 g h}{1+\frac{h}{R}} \)
hence \( R \) is the radius of the Earth.


The major product in the following
reaction is:
\( A \)
в.
\( c \)
D.


The bisectors of interior angles of a parallelogram forms a
This question has multiple correct options
A. square
B. rectangle
c. parallelgram
D. rhombus


Which of the following is known as hydronium ion?
A \( . H^{+} \)
в. \( H_{2} O^{+} \)
c. \( H_{3} O^{+} \)
D. \( H_{2} O_{2}^{+} \)


Polystyrene is an example of
A. elastomer
B. fibre
C . cation polymerisation polymer
D. thermosetting polymer


If \( \left(x_{1}, y_{1}, z_{1}\right) \) and \( \left(x_{2}, y_{2}, z_{2}\right) \) are two vertices and \( (\alpha, \beta \gamma) \) is the centroid of a triangle, find the third vertex of the triangle.


A charged particle, initially at rest at 0 when released follows a trajectory as
shown. Such a trajectory is possible in
the presence of.
A. Electric field of constant magnitude and varying direction
B. Magnetic field of constant magnitude and varying direction
C. Electric filed of constant magnitude and constant direction
D. Electric and magnetic fields of constant magnitudes and constant directions which are parallel to each other


The ratio of radii of spheres of metal is
1 : 2. The ratio of the amounts of
radiation emitted by them at same temperature will be :
A .1: 4
B. 1: 8
c. 2: 1
D. 8: 1


In the manufacture of ammonia by
Haber's process, write the flow chart and chemical equations with optimum conditions.


If a compound has "n" asymmetric carbon atoms with different terminal groups, the number of stereoisomers is
given by the formula:
A \( \cdot\left(\frac{1}{2}\right)^{n} \)
B . \( 2^{n} \)
\( c \cdot 2 \sqrt{n} \)
D. \( \sqrt{2} n \)


What acts as an inducer in lac operon? How does it switch on the operon?


According to \( -\ldots-\ldots- \) the power of coagulation of an ion depends upon
Valency.
A. Brownian motion
B. Hardy-Schulze rule
c. Tyndall effect
D. None of these


Instead of using two slits, if we use two separate identical sodium lamps in Young's experiment, which of the following will occur?
A. General illumination
B. Widely separate interference
c. very bright maxima
D. Very dark minima


Phenoxide ion has \( _{-} \) number
of resonating structures than benzoate ion and benzoic acid is a
acid than phenol.
A. more, stronger
B. more, weaker
c. less, stronger
D. less, weaker


In a quadrilateral \( P Q R S, \overrightarrow{P Q}= \) \( \vec{a}, \overrightarrow{Q R}=\vec{b}, \overrightarrow{S P}=\vec{a}-\vec{b} . M \) is the mid-
point of \( Q R \) and \( X \) is a point on \( S M \) such that \( \overrightarrow{S X}=\frac{4}{5} S \vec{M}, \) then \( \overrightarrow{P X} \) is
A \( \cdot \frac{1}{5} \overrightarrow{P R} \)
В. \( \frac{3}{5} \overrightarrow{P R} \)
c. \( \frac{2}{5} \overrightarrow{P R} \)
D. None of these


\( \mathrm{E}, \mathrm{F}, \mathrm{G} \) and \( \mathrm{H} \) are the midpoints of
quadrilateral ABCDas shown in the
figure. If \( \mathrm{BD}=8 \mathrm{cm}, \) then EH is:
\( A \cdot 6 c m \)
B. 4 cm
\( c .5 \mathrm{cm} \)
D. cannot be found


The equation of displacement of a particle executing SHM is \( \boldsymbol{x}= \) \( 0.40 \cos (2000 t+18) . \) The frequency of
the particle is
\( \mathbf{A} \cdot 10^{3} \mathrm{Hz} \)
B. \( 20 \mathrm{Hz} \)
c. \( 2 \times 10^{3} \mathrm{Hz} \)
D. \( \frac{10^{3}}{\pi} \mathrm{Hz} \)


Radius of curvature of a road is \( 60 \mathrm{m} \). It
is a to be banked so that no friction
force is required for a car travelling on the road at \( 25 \mathrm{mt} / \mathrm{sec} \). Find the angle of
banking?
A \( .47^{\circ} \)
B . \( 45^{\circ} \)
\( c .90 \)
D. \( 180^{\circ} \)


An organic compound contains \( C, H \) and \( O . \) If \( C(\%): H(\%)=6: 1, \) what is the
simplest formula of the compound given that one mole of the compound contains half as much oxygen as would
be required to burn all the \( C \) and \( H \)
atoms in it to \( C O_{2} \) and \( H_{2} O ? \)
\( \mathbf{A} \cdot C H_{2} O \)
в. \( C_{2} H_{4} O_{3} \)
\( \mathbf{c} \cdot C_{3} H_{6} \)
D. \( C_{3} H_{6} O_{2} \)


Formalin is the commercial name of :
A. formic acid
B. fluoroform
c. \( 40 \% \) aqueous solution of methanal
D. paraformaldehyde


If \( y=\sin ^{-1} \frac{x-1}{x+1}+\log (2-x), \) then
its domain is:
A. (1,2)
(i) 5,(1,2)
в. (-1,2)
D. none


Figure shows the position-time \( (x-t) \)
graph of one dimensional motion of a
body mass 500 g. What is the time interval between two consecutive
impulses received by the body?
\( A \cdot 2 s \)
B. 4 s
\( c \cdot 6 s \)
\( D \cdot 8 s \)


In Youngs double slit experiment using monochromatic light, the fringe pattern
shifts by a certain distance on the
screen when a mica sheet of \( R . l . \) and
thickness 1.964 micron is introduced in
the path of one of the interfering waves.
The mica sheet is then removed and the
distance between the slits and the
screen is doubled, it is found that the distance between successive maxima
(or minima) now is the same as the
observed fringe shift upon the introduction of the mica sheet.
Calculate the wavelength of monochromatic light used in the experiment.


When molecules of type A react with molecules of type B in one-step process
to give \( A B_{2} \), then the rate law is?
A \( \cdot \) rate \( =K[A]^{1}[B]^{2} \)
B . rate \( =K[A]^{2}[B]^{1} \)
c. rate \( =K[2 A][B] \)
D. rate=K [A][B]


Which shells are called penultimate and prepenultimate shells?


Fill in the blank:
The impression of an image lasts on the retina for of a second


The number of solution of the equation \( \tan ^{-1}(x-1)+\tan ^{-1}(x)+\tan ^{-1}(x+ \)
1) \( =\tan ^{-1}(3 x) \) is
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c .3 \)
D. 4


f \( \boldsymbol{x}_{\boldsymbol{i}}>\mathbf{0}, \boldsymbol{i}=\mathbf{1}, \mathbf{2}, \dots, \mathbf{5 0} \) and \( \boldsymbol{x}_{\mathbf{1}}+ \)
\( \boldsymbol{x}_{2}+\ldots+\boldsymbol{x}_{50}=\mathbf{5 0} \) then the minimum
value of \( \frac{1}{x_{1}}+\frac{1}{x_{2}}+\ldots+\frac{1}{x_{50}} \) equals to
A . 50
B. \( (50)^{2} \)
\( c \cdot(50)^{3} \)
D. \( (50)^{4} \)


Tanya's grandfather was 8 times older to her 16 years ago. He would be 3 times
of her age 8 years from now. Eight years ago, what was the ratio of tanya's age to that of her grandfather?
A .1: 2
B. 1: 5
c. 3: 8
D. 11: 53


A bullet of mass m traveling at velocity v strikes a block of mass \( 2 \mathrm{m} \) that is
attached to a rod of length \( \mathrm{R} \). The bullet collides with the block at a right angle and gets stuck in the block. The rod is free to rotate. What is the centripetal acceleration of the block after the
collision?
A \( \cdot v^{2} / R \)
B . \( (1 / 2) v^{2} / R \)
C \( \cdot(1 / 3) v^{2} / R \$ \)
D. \( (1 / 9) v^{2} / R \)


Why it is not recommended to touch
water metal-pipe lines, electric wires during thunderstorm?
A. They are good conductors thus may carry charges.
B. They are insulators and never carry charges.
c. They may store charges
D. This is a myth.


A solid cylindrical rod of radius \( 3 m m \) gets depressed under the influence of a load through \( 8 m m . \) The depression produced in an identical hollow rod with
outer and inner radii of \( 4 m m \) and \( 2 m m \)
respectively, will be
A. 2.7mm
B. \( 1.9 \mathrm{mm} \)
c. \( 3.2 \mathrm{mm} \)
D. 7.7mm


The energy per unit volume of a
dielectric medium is proportional to
square of
A . relative permittivity
B. charge
c. energy
D. electric intensity


\( \boldsymbol{x}+\frac{\mathbf{4}}{\mathbf{3}}=\mathbf{3} \frac{\mathbf{1}}{\mathbf{2}} \)


Two numbers are selected at random
(without replacement) the first six
positive integers. Let \( X \) denote the
larger of the two numbers obtained.
Find \( \boldsymbol{E}(\boldsymbol{X}) \)


When the convex lens acts as a
magnifying glass, the object is between the \( \ldots \ldots \ldots . . \) and the optical centre of lens.


Choose the correct answers from the
alternatives given.
Facultative anaerobes:
A. require a constant supply of oxygen
B. are killed in an oxygenated environment
c. do not always need oxygen
D. are photosynthetic but do not give off oxygen


Surface density of charge on a sphere of radius \( R \) in terms of electricity intensity \( E \) at a distance \( r \) in free space
is
\( \left(\epsilon_{0}=\text { permittivity of free space }\right) \)
\( ^{\mathrm{A}} \cdot_{\epsilon_{0} E}\left(\frac{R}{r}\right)^{2} \)
в. \( \frac{\epsilon_{0} E R}{r^{2}} \)
\( ^{\mathbf{C}} \epsilon_{0} E\left(\frac{r}{R}\right)^{2} \)
D. \( \frac{\epsilon_{0} E r}{R^{2}} \)


The matrix A satisfies the matrix
equation if \( A=\left[\begin{array}{lll}1 & 2 & 2 \\ 2 & 1 & 2 \\ 2 & 2 & 1\end{array}\right] \)
\( \mathbf{A} \cdot A^{2}-4 A-5 I=0 \)
B \( \cdot A^{2}-4 A-5=0 \)
C \( \cdot A^{2}+4 A-5 I=0 \)
D \( \cdot A^{2}+4 A-5=0 \)


Which of the following sentences are
NOT a statement?
\( A \cdot 9 \) is less than 7
B. The sun is a star.
c. There is no rain without clouds
D. Mathematics is fun.


Statement:-Tangent at any point of a circle is perpendicular to the radius through the point of contact
If yes enter \( 1, \) else 0


When Carbon monoxide is passed over heated copper oxide it gives:
A. \( C O_{2} \)
в. \( C O \)
\( c \cdot O_{2} \)
D. all of these


Evaluate \( (2 x+3 y+5 z)^{2} \)


In Brassica oleracea var. capitata
(cabbage), the edible part is
A. Infloresence
B. Flower budd
c. vegetative bud
D. Stem


Draw the structures of the following
compounds.
(i) 3-Methylbutanal
(ii)
Nitropropiophenone
(iii) p-Methylbenzaldehyde 4-Methylpent-3-en-2-one
(v) 4 -Chloropentan-2-one
\( (\mathbf{v} \mathbf{i}) \)
Bromo-4-phenylpentanoic acid
(vii) p,p-Dihydroxybenzophenone Hex-2-en-4-ynoic acid


The 2 nd, 3 rd and 4 th terms in the
expansion of \( (x+y)^{n} \) are 240,720,1080 respectively; find \( x, y, n \)


Find \( \frac{d y}{d x} \) if
(a) \( x^{3}+2 x^{2} y+3 x y^{2}+4 y^{3}=5 \)
(b) \( x=2 \cos ^{3} \theta, y=2 \sin ^{3} \theta \)
(c) \( y=\sin ^{-1}(2 x \sqrt{1-x^{2}}) ;-1 \leq x \leq 1 \)


An isosceles triangle contains three
angles that measure \( 40^{\circ}, x^{\circ}, \) and \( y^{\circ} \)
Which of the following CANNOT be true?
A \( . x=y \)
B. \( x=50 \)
c. \( x-y=60 \)
D. \( x=70 \)
E . \( x=100 \)


You are told to prepare a closed experimental environment (a box) for student mice. The box volume will be
294 litres (about \( 10 f t_{3} \) ) and the entire
air volume will be changed every
minute. The relative humidity of the air entering the box is to be controlled at 40
per at \( 21^{\circ} \mathrm{C} \). What weight of \( \mathrm{H}_{2} \mathrm{O} \) (in
grams) must be added to the flow of dry air per minute?
[Equilibrium vapour pressure for \( \boldsymbol{H}_{2} \boldsymbol{O} \) at \( \left.21^{\circ} \mathrm{C} \simeq 19 \text { torr }\right] .[\mathrm{R}=0.082 \) liter atm
mole \( ^{-1} \mathrm{deg}^{-1}, \) molecular weight
\( \left.\boldsymbol{H}_{2} \boldsymbol{O}=\mathbf{1 8}\right] \)
[Write your answer to the nearest integer].


Which functional group is present in a
molecule of \( \boldsymbol{C H}_{3} \boldsymbol{O H} \) ?
A. Ketone
B. Aldehyde
c. Ester
D. Alcohol
E. Halide


In S-phase of the cell cycle
A. Amount of DNA doubles in each cell
B. Amount of DNA remains same in each cell
c. Chromosome number is increased
D. Amount of DNA is reduced to half in each cell


A block of mass \( m \) has initial velocity \( u \) having direction \( +x \) axis. The block stops after covering distance \( S \) causing
an extension in the spring of spring
constant \( K \) holding it. If \( \mu \) is the kinetic
friction between the block and the
surface on which it was moving, the distances \( \boldsymbol{S} \) is :
A \( \cdot \frac{1}{K} \mu^{2} m^{2} g^{2} \)
B. \( \frac{1}{K}\left(m K u^{2}-\mu^{2} m^{2} g^{2}\right)^{\frac{1}{2}} \)
c. \( \frac{1}{K}(\sqrt{\mu^{2} m^{2} g^{2}+m K u^{2}}-\mu m g) \)
D \( \cdot \frac{1}{K}\left(\mu^{2} m^{2} g^{2}-m K u^{2}+\mu m g\right)^{\frac{1}{2}} \)


A bicycle is sold at a gain of \( 16 \% \). If it
had been sold for Rs. 20 more, \( 20 \% \)
would have been gained. The C.P. of the bicycle is
A . Rs. 350
B. Rs. 400
c. Rs. 500
D. Rs. 600


Assertion
In an elastic collision of two bodies, the momentum and energy of the system are conserved.
Reason
If two bodies stick to each other, after
colliding, the collision is said to be perfectly inelastic.
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


Draw the structure of \( O_{3} \) and \( N O_{2} \)


State whether the given statement is True or False.

The magnetic lines of force are always parallel to a straight conductor carrying an electric current.


Among the following compounds, the one which does NOT produce nitrogen gas upon heating is?
A \( \cdot\left(N H_{4}\right)_{2} C r_{2} O_{7} \)
в. \( \operatorname{NaN}_{3} \)
\( \mathbf{c} \cdot N H_{4} N O_{2} \)
D. \( \left(N H_{4}\right)_{2}\left(C_{2} O_{4}\right) \)


Electric circuit provides a complete
path for:
A. solution to flow
B. metal to flow
c. neutron to flow
D. current to flow


Potassium alum, \( K A l\left(S O_{4}\right)_{2} \cdot 12 H_{2} O \)
is obtained in the form of octahedral
crystals when a solution of \( K_{2} S O_{4} \) and
\( A l_{2}\left(S O_{4}\right)_{3} \) is concentrated by
evaporation. Suggest specific experiments to specify whether it is a complex or double salt.
A. One can determine conductance
B. One can determine freezing points
c. one can detect \( A l^{3+}, S O_{4}^{2-}, K^{+} \)
D. All of these


Calculate \( \Delta H^{o} \) for the reaction,
\( N a_{2} O(s)+S O_{3}(g) \rightarrow N a_{2} S O_{4}(g) \)
using the following:
\( N a(s)+H_{2} O(l) \rightarrow N a O H(s)+ \)
\( \frac{1}{2} H_{2}(g) ; \Delta H^{o}=-146 k J \)
\( N a_{2} S O_{4}(s)+H_{2} O(l) \rightarrow \)
\( 2 N a O H(s)+S O_{3}(g) ; \Delta H^{o}= \)
\( +418 k J \)
\( \mathbf{2} N \boldsymbol{a} \boldsymbol{O}(\boldsymbol{s})+\mathbf{2} \boldsymbol{H}_{2}(\boldsymbol{g}) \rightarrow \boldsymbol{4} \boldsymbol{N} \boldsymbol{a}(\boldsymbol{s})+ \)
\( 2 H_{2} O(l) ; \Delta H^{o}=+259 k J \)
A \( .+823 \mathrm{kJ} \)
B. - 581 k
\( c \ldots-435 k J \)
\( D \cdot+531 \mathrm{k} \)


The total number of lone pairs in chlorate ion is :
\( A \cdot 8 \)
B. 6
\( c \cdot 4 \)
\( D \)


For two events \( A \) and \( B \), if \( P(A)= \) \( \boldsymbol{P}(\boldsymbol{A} \mid \boldsymbol{B})=\mathbf{1} / \mathbf{4} \) and \( \boldsymbol{P}(\boldsymbol{B} \mid \boldsymbol{A})=\mathbf{1} / 2, \) then
This question has multiple correct options
A. A and B are independent
B. A and B are mutually exclusive
c. \( P\left(A^{\prime} \mid B\right)=3 / 4 \)
D. \( P\left(B^{\prime} \mid A^{\prime}\right)=1 / 2 \)


Standard reduction potential of most of the transition elements is generally:
A. negative
B. positive
c. zero
D. none of the above


The probability of a radioactive nucleus to survive one mean life is \( \frac{1}{e+x}, \) then \( x \) is


Electronic configuration of element T is 2,8,7
How many valence electrons are there in an atom of T?
\( A \)
B. 5
\( c \cdot 3 \)
D. 7


What is \( \int(x \cos x+\sin x) d x \) equal to?
Where \( c \) is an arbitrary constant
\( \mathbf{A} \cdot x \sin x+c \)
B. \( x \cos x+c \)
\( c \cdot-x \sin x+c \)
D. \( -x \cos x+c \)


The constant ratio of the sine of angle of incidence to the sine of angle of refraction is also known as:
A. Snell's law
B. Optical density
c. Relative density
D. None of these


The most stable carbonate among the following is :
A \( \cdot L i_{2} C O_{3} \)
в. \( N a_{2} C O_{3} \)
\( \mathbf{c} \cdot R b_{2} C O_{3} \)
D. \( C s_{2} C O_{3} \)


Gibberellins promote
A. Seed dormancy
B. Leaf fall
c. Seed germination
D. Root elongation


In an oscillating \( L-C \) circuit in which
\( C=4.00 \mu F, \) the maximum potential
across the capacitor during the oscillations is \( 1.50 V \) and the maximum
current through the inductor is \( 50.0 m A \)
How much time does the charge on the capacitor take to rise from zero to its maximum value?
A. \( 0.238 \mathrm{ms} \)
B. \( 0.788 \mathrm{ms} \)
c. \( 0.488 \mathrm{ms} \)
D. \( 0.188 \mathrm{ms} \)


Find the Quotient and the Remainder when the first polynomial is divided by the second.
\( \left(6 x^{2}-31 x+47\right) \) by \( (2 x-5) \)
A. Quotient \( =3 x-8, \) Remainder \( =7 \)
B. Quotient = 3x + 8, Remainder = 7
c. Quotient \( =-3 x-8, \) Remainder \( =7 \)
D. Quotient \( =-3 x+8, \) Remainder \( =7 \)


Which of the following materials is an electrical insulator?
A. Aluminium
B. Gold
c. Rubber
D. all of these


Solute \( A \) is a ternary electrolyte and solute B is a non-electrolyte. If \( 0.1 \mathrm{M} \) solution of solute B produces an
osmotic pressure of \( 2 P, \) then 0.05
M solution of \( A \) at the same
temperature will produce an osmotic
pressure equal to:
A . \( 1.5 P \)
B. 2P
\( c \cdot 3 P \)
D.


Find the derivative of the following
functions:
\( 5 \sec x+4 \cos x \)


Discuss the reactivity of an isolated alkene \( (C=C) \) and a carbonyl group
\( (C=O) \) with a nucleophilic agent in
terms of MO theory.


Which of the following enzymes
hydrolyse proteins to \( \alpha \) - amino acids?
A. trypsin
B. pepsin
c. chymotrypsin
D. all of the above


toppr
Q Type your question-
number of different amino acids in the
beta hemoglobin chain of various
organisms compared to the human beta chain.

Organism Name of different amino acids
Human
Mouse 27
Frog 68
Monkey 11
Lamprey 125
Chicken
Gibbon
Which of the following organisms are closely related to humans, based on hemoglobin amino acid sequence?
A. Mouse
в. Monkey
c. chicken
D. Gibbon
E. Lampre


Two charges \( +q \) and \( -q \) are placed at a distance a in a uniform electric field.
The dipole moment of the combination is \( 2 q a(\cos \theta \hat{i}+\sin \theta \hat{j}), \) where, \( \theta \) is the
angle between the direction of the field and the line joining the charges. Which of the following statement(s) is are correct?
This question has multiple correct options
A. The torque exerted by the field on the dipole vanishes
B. The net force on the dipole vanishes
c. The torque is independent of the choice of coordinates
D. The net force is independent of a


At high temperatures, the enzymes of photosynthesis gets deactivated
because
A. They get denatured
B. They are proteinous in nature
c. They have optimum range of temperature at which they are functional
D. All of the above


Laws of reflection hold good for:
A. only plane mirrors
B. only concave mirrors
c. only convex mirrors
D. all types of mirrorrs


A bank pays \( 5 \% \) rate of interest semiannually, interest being calculated half yearly. A sum of Rs. 400 is deposited in the bank. The amount at the end of
year will be
A. Rs. 440
B. Rs. 439
c. Rs. 441.00
D. Rs. 442


Convert each part of ratio to percentage
(a) 3: 1
(b) 2: 3: 5
(c) 1: 4
\( (d) 1: 2: 5 \)


The image of an object is formed by a convex lens. When that object is placed beyond the focal length is -
A. Virtual and inverted
B. Virtual and magnified
c. Real and inverted
D. Real and magnified


When \( _{3} L i^{7} \) nuclei are bombarded by
protons and the resultant nuclei are
\( 4 B e^{8}, \) the emitted particles will be:
A. alpha particles
B. beta particles
c. gamma particles
D. neutrons


What is the method for the formation of
calcium oxide called?
A. Reduction
B. Oxidation
c. calcination
D. Carbonation


Information about the solubility in water of four oxides is shown. Which oxide, when added to water,
gives a solution with a \( p H \) less than
\( p H 7 ? \)
Name of oxide - nitrogen dioxide, solubility in water - soluble Name of oxide - copper(II) oxide, solubility in water - insoluble
Name of oxide - silicon(IV) oxide,
solubility in water - insoluble Name of oxide - barium oxide, solubility
in water - soluble
A. Nitrogen dioxide
B. Copper (II) oxide
c. silicon(IV) oxide
D. Barium oxide


If the radius of the earth reduces by \( 4 \% \) density remaining the same, then the escape velocity will:
A. increases by \( 4 \% \)
B. increases by \( 2 \% \)
c. decreases by \( 4 \% \)
D. decreases by \( 2 \% \)


Let \( f \) and \( g \) be continuous function on
\( a \leq x \leq b \) and \( \operatorname{set} p(x)=\max \)
\( \{f(x), g(x)\} \) and \( q(x)=\min \)
\( \{f(x), g(x)\}, \) the area bounded by the
curves \( \boldsymbol{y}=\boldsymbol{p}(\boldsymbol{x}), \boldsymbol{y}=\boldsymbol{q}(\boldsymbol{x}) \) and the
ordinates \( \boldsymbol{x}=\boldsymbol{a} \) and \( \boldsymbol{x}=\boldsymbol{b} \) is given by
This question has multiple correct options
A \( \cdot \int_{a}^{b}(f(x)-g(x)) d x \)
B \( \cdot \int_{a}^{b}(p(x)-q(x)) d x \)
c \( \cdot \int_{a}^{b}|p(x)-q(x)| d x \)
D \( \cdot \int_{a}^{b}|f(x)-g(x)| d x \)


Special relativity is a branch of physics that deals with the relationship between space and time. The Lorentz
term, is the factor by which time, length and relativistic mass change for an object while that object is moving, is given by the following formula: \( \gamma= \)
\( \sqrt{1-\frac{v^{2}}{c^{2}}} \)
where, v is the relative velocity of the object \( c \) is the speed of light in a vacuum Which of the following equations
correctly represents the relative velocity
A \( \cdot v=c \sqrt{\frac{1}{\gamma^{2}}-1} \)
B . \( v=c \sqrt{1-\gamma^{2}} \)
c. \( v=c\left(1-\frac{1}{\gamma^{2}}\right) \)
D. \( v=c \sqrt{1-\frac{1}{\gamma^{2}}} \)


Which of the following represents
increasing order of ionic conductance?
\( \mathbf{A} \cdot F^{-}<C l^{-}<B r<I^{-} \)
B \( \cdot I^{-}<B r^{-}<F^{-}<C l^{-} \)
\( \mathbf{c} \cdot F^{-}<C l^{-}<I^{-}<B r^{-} \)
D \( \cdot F^{-}<I^{-}<C l^{-}<B r^{-} \)


One ticket is selected randomly from the set of 100 tickets numbered as
\( \{00,01,02,03,04,05, \ldots, 98,99\} . E_{1} \) and
\( E_{2} \) denote the sum and product of the digits of the number of the selected ticket. The value of \( \boldsymbol{P}\left(\frac{\boldsymbol{E}_{1}=\boldsymbol{9}}{\boldsymbol{E}_{2}=\mathbf{0}}\right) \) is
A \( \cdot \frac{1}{19} \)
B. \( \frac{2}{19} \)
\( c \cdot \frac{3}{19} \)
D. \( \frac{1}{18} \)


If \( A \) and \( B \) are invertible matrices of the
same order, then prove that \( (A B)^{-1}=B^{-1} A^{-1} \)


If the matrix \( A B \) is a zero matrix, then
which one of the following is correct?
A. \( A \) must be equal to zero matrix or \( B \) must be equal to zero matrix
B. \( A \) must be equal to zero matrix and \( B \) must be equal to zero matrix
c. It is not necessary that either \( A \) is zero matrix or \( B \) is zero matrix
D. None of the above


The potential energy of a particle of
mass \( 0.5 \mathrm{kg} \) moving along \( \mathrm{x} \) -axis is
given by \( U=\left(x^{2}-4 x\right) \) joule where \( x \) is
in metres. The time period of oscillation of the particle is?


The substance having the highest specific latent heat of fusion is :
A . lead
B. wax
\( c . \) ice
D. gold


Write the equations involved in the preparation of nitric acid by Ostwald's process by maintaining the reaction conditions


When heat is given to gas in an isothermal change, the result will be
A. external work done
B. rise in temperature
c. increase in internal energy
D. external work done and also rise in temperature


Amount of light reflected depends upon
A. Nature of material of the object
B. Nature of the surface
c. Smoothness of the surface
D. All of these


Let \( a_{1}, a_{2}, \dots \) be positive real numbers in geometric progression. For each \( n \), let
\( A_{n}, G_{n}, H_{a} \) be respectively, the arithmetic mean, geometric mean and
harmonic mean of \( a_{1}, a_{2}, \dots, a_{n} . \) Find an
expression for the geometric mean of
\( G_{1}, G_{2}, \ldots, G_{n} \) in terms of
\( \boldsymbol{A}_{1}, \boldsymbol{A}_{2}, \ldots ., \boldsymbol{A}_{n}, \boldsymbol{H}_{1}, \boldsymbol{H}_{2}, \ldots . ., \boldsymbol{H}_{n} \)


If \( f(x)=\frac{a x+b}{c x+d} \) and \( (f o f) x=x, \) then
\( d=? \)
\( A \)
в. \( -a \)
\( c \cdot b \)
D. \( -b \)


A block rest on a horizontal table which
is executing SHM in the horizontal with
an amplitude \( a \) if the coefficient of friction is \( \mu, \) then the block just start to slip when the frequency of oscillation is
A \( \cdot \frac{1}{2 \pi} \sqrt{\frac{\mu g}{a}} \)
В \( \cdot 2 \pi \sqrt{\frac{a}{\mu g}} \)
\( ^{\mathrm{C}} \cdot \frac{1}{2 \pi} \sqrt{\frac{a}{\mu g}} \)
D. \( \sqrt{\frac{a}{\mu g}} \)


Find the volume of a sphere whose
radius is
(i) \( 7 \mathrm{cm} \)
(ii) \( 0.63 m \)


If \( \boldsymbol{A}=\left[\begin{array}{lll}\boldsymbol{a} & \boldsymbol{b} & \boldsymbol{c} \\ \boldsymbol{x} & \boldsymbol{y} & \boldsymbol{z} \\ \boldsymbol{p} & \boldsymbol{q} & \boldsymbol{r}\end{array}\right], \boldsymbol{B}= \)
\( \left[\begin{array}{ccc}\boldsymbol{q} & -\boldsymbol{b} & \boldsymbol{y} \\ -\boldsymbol{p} & \boldsymbol{a} & -\boldsymbol{x} \\ \boldsymbol{r} & \boldsymbol{-} \boldsymbol{c} & \boldsymbol{z}\end{array}\right] \) then
This question has multiple correct options
B . \( |A|=-\mid B \)
c. \( |A|=2|B| \)
D. \( A \) is invertible if and only if \( B \) is invertible


The intermediate form in the
preparation of phenol by sodium benzene sulphonate is:
A. sodium propoxide
B. sodium phenoxide
c. sodium ethoxide
D. None of these


The correct order of bond angles in
\( \boldsymbol{H}_{2} \boldsymbol{S}, \boldsymbol{N} \boldsymbol{H}_{3}, \boldsymbol{B} \boldsymbol{F}_{3} \) and \( \boldsymbol{S} \boldsymbol{i} \boldsymbol{H}_{4} \) is:
A. \( H_{2} S<S i H_{4}<N H_{3}<B F_{3} \)
B. \( N H_{3}<H_{2} S<S i H_{4}<B F_{3} \)
c. \( H_{2} S<N H_{3}<S i H_{4}<B F_{3} \)
D. \( H_{2} S<N H_{3}<B F_{3}<S i H_{4} \)


In a closed lab, experiment is conducted by heating of water. When water is heated, the vapour pressure increased slowly then rapidly increases. As the water reaches to its boiling point, i.e.
\( \mathbf{1 0 0}^{0} \boldsymbol{C}, \) the vapour pressure reaches 1 atm. Which of the following functions best describes the increase in vapour
pressure as water is heated to its boiling point?
A. Linear
B. Quadratic
c. Polynomial
D. Exponential


Infrasound can be heard by
\( A \cdot \operatorname{dog} \)
B. bat
c. rhinoceros
D. human beings


A refrigerator was sold at a gain of \( 12 \% \)
Had it been sold for Rs. 357 more, the gain would have been \( 15 \% \). Find the cost
price of the refrigerator.


Write a wave function describing the
wave
A. \( y=0.075 \cos (1.05 x-4 \pi t) \)
\( t \)
B. \( y=0.075 \cos (1.05 x-2 t) \)
c. \( y=0.075 \sin (1.05 x-4 \pi t) \)
D. None


Among the metal carbonyls
\( \left[\boldsymbol{M} \boldsymbol{n}(\boldsymbol{C O})_{\boldsymbol{6}}\right]^{+},\left[\boldsymbol{T} \boldsymbol{i}(\boldsymbol{C} \boldsymbol{O})_{\boldsymbol{6}}\right],\left[\boldsymbol{C r}(\boldsymbol{C O})_{\boldsymbol{6}}\right] \)
and \( \left[V(C O)_{6}\right]^{-} \) the \( C-O \) bond order
would be lowest in :
\( \mathbf{A} \cdot\left[M n(C O)_{6}\right]^{+} \)
в. \( \left[T i(C O)_{6}\right]^{2} \)
\( \mathbf{c} \cdot\left[C r(C O)_{6}\right] \)
D. \( \left[V(C O)_{6}\right]^{-} \)


Nitrogen liberated by the thermal decomposition of only:
A. \( \mathrm{NH}_{4} \mathrm{NO}_{2} \)
B. \( \mathrm{NaN}_{3} \)
\( \mathrm{c} \cdot\left(\mathrm{NH}_{4}\right)_{2} \mathrm{Cr}_{2} \mathrm{O}_{7} \)
D. all the three


Using intergration find the area of the region included between the parabola \( 4 y=3 x^{2} \) and the line \( 3 x=2 y+12=0 \)


Match the Column
The answers to these questions have to be appropriately doubled


Find \( a_{20} \) given that \( a_{3}=\frac{1}{2} \) and \( a_{5}=8 \)
(Given : The terms are in A.P.)


Explain \( s p^{2} \) hybridization.


By reducing the pressure in the container, the boiling point of liquids in the mixture can be reduced and the
mixture can be distilled at a lower
temperature. This technique is called:
A. vacuum distillation
B. steam distillation
c. fractional distillation
D. none of these


Which of the following parts of a neuron is covered by fatty sheath?
\( A \cdot A \times O n \)
B. Cyton
c. Dendrite
D. Node of Ranvier


\( \int \frac{e^{\cot ^{-1} x}}{1+x^{2}}\left(x^{2}-x+1\right) d x \)
\( ^{A} \cdot \frac{e^{\cot ^{-1} x}}{1+x^{2}} \)
B. \( x \cdot e^{\cot ^{-1} x} \)
\( \mathbf{c} \cdot e^{\cot ^{-1} x} \)
D. \( -e^{\cot ^{-1} x} \)


If each observation is multiplied by \( \frac{1}{3} \)
then the mean of the new data will de
A \( \cdot \frac{1}{3} \) times
B. 3 times
c. \( \frac{1}{\sqrt{3}} \) times
D. \( \frac{2}{3} \) times


Which of the following does not contain any coordinate bond?
\( \mathbf{A} \cdot H_{3} O^{+} \)
B. \( B F_{4}^{-} \)
c. \( H F_{2} \)
D. \( N H_{4}^{+} \)


A stone is dropped from the top of a tower. When it crosses a point \( 5 \mathrm{m} \) below the top, another stone is let fall from a point \( 25 \mathrm{m} \) below the top. Both
stones reach the bottom of the tower
simultaneously. Find the height of the tower. Take \( g=10 m / s^{2} \)


Prosimian includes
A . Lemur
B. Tarsier
c. New World Monkey
D. Both A and B


Phosphorylation of glucose is increased
by
A. Auxins
B. Insulin
c. Ethylene
D. Traumatic acid


Chief difference between RBCs of
human and frog is?
A. Enucleate RBCs in frog
B. Only human RBCs have haemoglobin
c. Human RBCs have more nuclei
D. Human RBCs are without nuclei


A steel ring of radius \( r \) and cross
sectional area \( A \) is fitted onto a wooden
disc of radius \( R(R>r) . \) If the Young's
modulus of steel is \( Y \), then the force
with which the steel ring is expanded is
A. \( A Y(R / r) \)
в. \( A Y(R-r) / r \)
c. \( (Y / A)[(R-r) / r] \)
D. \( Y r / A R \)


Left hand derivative and right hand derivative of a function \( f(x) \) at a point \( \boldsymbol{x}=\boldsymbol{a} \) are defined as
\( f^{\prime}\left(a^{-}\right)=\lim _{h \rightarrow 0^{+}} \frac{f(a)-f(a-h)}{h}= \)
\( \lim _{h \rightarrow 0^{-}} \frac{f(a)-f(a-h)}{h}= \)
\( \lim _{x \rightarrow a^{+}} \frac{f(a)-f(x)}{a-x} \) respectively
Let \( f \) be a twice differentiable function.
We also know that derivative of an even
function is odd function and derivative
of an odd function is even function
The statement
\( \lim _{h \rightarrow 0} \frac{f(-x)-f(-x-h)}{h}= \)
\( \lim _{h \rightarrow 0} \frac{f(x)-f(x-h)}{-h} \) implies that for all
\( \mathbf{x} \boldsymbol{\epsilon} \boldsymbol{R} \)
\( A . f \) is odd
B. \( f \) is even
c. \( f \) is neither odd nor ever
D. nothing can be concluded


The refractive indices of glass and
quartz w.r.t. air are \( 3 / 2 \) and \( 12 / 5 \) respectively. The refractive index of quartz w.r.t. glass is:
A. \( 8 / 5 \)
B. 5/8
\( c \cdot 5 / 18 \)
D. 18/5


A force acts on a \( 30 g m \) particle in such
a way that the position of the particle as a function of time is given by \( \boldsymbol{x}=\mathbf{3} \boldsymbol{t}- \)
\( 4 t^{2}+t^{3}, \) where \( x \) is in metres and \( t \) is in
seconds. The work done on the particle
during the first 4 second is
A. \( 3.84 J \)
в. \( 1.68 J \)
c. \( 5.28 J \)
D. \( 5.41 J \)


Assertion
\( Z n C O_{3}(s) \) is soluble in \( N H_{3}(a q) \) but
\( \operatorname{Zn} S(s) \) is not
Reason
Solubility product \( \left(K_{s p}\right) \) for \( Z n S \) is
much smaller than for \( Z n C O_{3} \) and a
saturated solution of \( Z n S \) does not
produce a large enough \( \left[Z n^{2+}\right] \) for the
complex ion to form
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


Why do stars twinkle?


Two objects of same mass \( m \) are
attached at end of a light rod of length \( l \)
and rotating about axis \( O O^{\prime} \) as shown
in the figure. The moment inertia of the
system about the axis \( O O^{\prime} \) is
A \( \frac{m l^{2}}{12} \)
B. \( \frac{5 m l^{2}}{18} \)
c. \( \frac{5 m l^{2}}{24} \)
D. \( \frac{5 m l^{2}}{36} \)


Assertion
Euglenoids change their shape.
Reason
They have no rigid cell wall.
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.


Solve the system of inequalities graphically:
\( 4 x+3 y \leq 60, y \geq 2 x, x \geq 3,(x, y \geq 0) \)


Which cell does not have perforated cell
wall?
A. Tracheids
B. Vessels
c. sieve tubes
D. None of the above


Prove the following identities:
\[
\begin{array}{l}
\frac{\boldsymbol{a}^{3}(\boldsymbol{b}+\boldsymbol{c})}{(\boldsymbol{a}-\boldsymbol{b})(\boldsymbol{a}-\boldsymbol{c})}+\frac{\boldsymbol{b}^{3}(\boldsymbol{c}+\boldsymbol{a})}{(\boldsymbol{b}-\boldsymbol{c})(\boldsymbol{b}-\boldsymbol{a})}+ \\
\frac{\boldsymbol{a}^{3}(\boldsymbol{a}+\boldsymbol{b})}{(\boldsymbol{c}-\boldsymbol{a})(\boldsymbol{c}-\boldsymbol{b})}=\boldsymbol{b} \boldsymbol{c}+\boldsymbol{c} \boldsymbol{a}+\boldsymbol{a} \boldsymbol{b}
\end{array}
\]


A temperature difference of \( 27^{\circ} \) on the
Kelvin scale is
A . 27
B. 300 K
c. \( -246 k \)
D. zero


An open capillary tube contains a drop
of water. When the tube is in its vertical
position, the drop forms a column with a length of \( 2.98 \mathrm{cm} \). The internal
diameter of the capillary tube is 1 mm.
The radii of curvature of the upper meniscus (in \( \mathrm{mm} \) )is \( \frac{x}{4} \). Consider the wetting to be complete. Surface tension of water \( =0.0075 N / m . \) Find the value
of \( x \)


In case of a planet revolving around the sun, the net torque is
A. zero
B. Maximum
c. Minimum
D. Depends on the shape of the orbit


toppr
Q Type your question_
\( (\mathbf{B}) \)
This question has multiple correct options
\( \mathbf{A} \)
B.
\( c \)
D. In E2 elimination, the acidic H atoms is removed. The
inductive effect (-I) of Br atom increases the acidity of H atoms to which Br atoms bonded.
Decreasing acidity of \( \mathrm{H} \) atom in (B) is as follows:
\( \mathrm{H} \) at \( \mathrm{C}-1>\mathrm{H} \) at \( \mathrm{C}-2>\mathrm{H} \) at \( \mathrm{C}-3 \)


Conversion of glucose to ethyl alcohol can be carried by:
A. lactose
B. invertase
c. zymase
D. diastase


An experiment to verify ohm's law, a conductor of resistance \( R \) is taken
During the experiment, temperature of the conductor increases with the flow of
current. Resistance of the conductor
will
A. Remains same
B. Decrease
c. Increase
D. First increases then decreases


The position of a particle moving along \( x-a x i s \) is given by \( x=10 t-2 t^{2} . \) Then
the time (t) at which it will momently come to rest is


f \( \alpha, \beta, \gamma \) are the roots of the equation
\( x^{3}+p x+q=0 \) then the value of the
determinant \( \left|\begin{array}{lll}\boldsymbol{\alpha} & \boldsymbol{\beta} & \gamma \\ \boldsymbol{\beta} & \gamma & \boldsymbol{\alpha} \\ \boldsymbol{\gamma} & \boldsymbol{\alpha} & \boldsymbol{\beta}\end{array}\right| \) is
\( \mathbf{A} \cdot \mathbf{q} \)
B.
c. \( p \)
D. \( p^{2}-2 q \)


Acromion process is characteristically found in the of
mammals.
A. pectoral girdle
B. sperm
c. pelvic girdle
D. skull


Water pollution is due to:
A. agricultural discharges
B. sewage and other wastes
C. industrial effluents
D. all of the above


Some elements show the property of
existing in two or more distinct physical form which shows different
physical properties but same chemical properties. These distinct forms of an element are called:
\( A \). isomers
B. allotropes
c. compounds
D. isobars


Concentration of pure solid and liquid is
not included in the expression of
equilibrium constant because:
This question has multiple correct options
A. Pure Solid and pure liquid concentrations are independent of their quantities.
B. Solid and liquids react slowly.
C. Solid and liquids at equilibrium do not interact with gaseous phase.
D. The molecules of solids and liquids cannot migrate to the gaseous phase.


On the basis of composition, which of the following is a type of matter?
A. Compound
B. Solid
c. Liquid
D. Both b and c


Distances covered by a freely falling body (starting from rest) during \( 1^{s t}, 2^{n d}, 3^{r d} \ldots . n^{t h} \) second of its motion
are proportional to :
A. even numbers
B. odd numbers
c. all integral numbers
D. square of integral numbers


The device which is used to measure
specific heat capacity of solid and liquids is


A body when acted upon by a force of
10 \( k g f \), gets displaced by \( 0.5 m \) normal to the force. Calculate the work done by
the force, when the displacement is in the direction of force.
A . \( 5 . J \)
в. \( 500 J \)
c. \( 0.5 J \)
D. \( 50 J \)


The order of the differential equation, of
which \( x y=c e^{x}+b e^{-x}+x^{2} \) is a
solution, is:
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot 3 \)
D. none of these


Which of the following properties of Zr and Hf can be explained due to lanthanide contraction?
A. Radius of Zr and Hf is same
B. Their EN is same
C. Their position in periodic table
D. All


Draw a labelled diagram of experiment explaining Ohm's Law.


toppr
Q Type your question
insulted from each other. The entire loop
lies in the plane (of the paper). A uniform magnetic filed \( \vec{B} \) point into the
plane of the paper. At \( t=0 \), the loop
starts rotating about the common
diameter as axis with a constant
angular velocity \( \omega \) in the magnetic field.
Which of the following option is/are
correct?
A. The rate of change of the flux is maximum when the plane of the loops is perpendicular to plane of the
paper
B. The net emf induced due to both the loops is proportional to cos \( \omega t \)
C. The emf induced in the loop is proportional to the sun of the areas of the two loops.
D. non of the above.


Escherichia coli is abundantly found in
A. water
B. Soil
c. мilk
D. Human intestine


For an electrolyte solution of \( \mathbf{0 . 0 5} \boldsymbol{M} \) the conductivity has been found to be
\( 0.0110 \mathrm{S} \mathrm{cm}^{-1} . \) The molar conductivity
is:
A. \( 0.055 \mathrm{Scm}^{2} \mathrm{mol}^{-1} \)
B. \( 550 \mathrm{Scm}^{2} \mathrm{mol}^{-1} \)
c. \( 0.22 \mathrm{Scm}^{2} \mathrm{mol}^{-1} \)
D. \( 220 \mathrm{Scm}^{2} \mathrm{mol}^{-1} \)


The metals which can produce amphoteric oxides are:
A. sodium and aluminium
B. zinc and potassium
c. calcium and sodium
D. aluminium and zinc


Solve the differential equation:
\( \left(x y^{2}-e^{1 / x^{3}}\right) d x-x^{2} y d y=0 \)
A \( \cdot 3 y^{2}=2 x^{2} e^{1 / x^{3}}+c x^{2} \)
B . \( 3 y^{2}=2 x^{2} e^{1 / x^{3}}-c x^{2} \)
c. \( 3 y^{2}=-2 x^{2} e^{1 / x^{3}}+c x^{2} \)
D. None of these.


Why both Freundlich and Langmuir adsorption isotherms hold good at high pressure and fail at low pressure?


The function \( f(x) \) defined on the real numbers has the property that \( \boldsymbol{f}(\boldsymbol{f}(\boldsymbol{x})) \cdot(1+\boldsymbol{f}(\boldsymbol{x}))=-\boldsymbol{f}(\boldsymbol{x}) \) for all \( \boldsymbol{x} \) in
the domain of \( f \). If the number 3 is in
the domain and range of \( f, \) compute the
value of \( \boldsymbol{f}(\mathbf{3}) \)
A. \( -\frac{3}{4} \)
в. \( -\frac{3}{2} \)
\( c \cdot \frac{2}{3} \)
D. \( -\frac{2}{3} \)


The diagram shows equipotential lines from an unknown charge configuration.
Determine the direction of the field at \( A \)
\( A \cdot U p \)
B. Down
c. Left
D. Right


According to theory of significant figures the value of \( \sqrt{\mathbf{3 . 0}} \) is:
A. 1.732
в. 1.7
c. 1.73
D. 1.8


Which of the following numbers are perfect cubes? In case of perfect cube find the number with cube is the given number.
\( \mathbf{2 1 9 5 2} \)


10 different pens and two different books are distributed randomly to 3 students giving 4 things to each. The probability that books go to different students is
A \( \cdot \frac{5}{11} \)
в. \( \frac{6}{11} \)
\( c \cdot \frac{7}{11} \)
D. \( \frac{8}{11} \)


The properties of light can best be explained by assuming that light is composed of:
I earticles
II : Waves
III : Atoms
A. I only
B. II only
c. I and II
D. II and III


ff \( \boldsymbol{y}=\boldsymbol{x}+\frac{1}{\boldsymbol{x}+\frac{1}{\boldsymbol{x}+\frac{1}{\boldsymbol{x}+\cdots}}} \) then \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}= \)
A \( \cdot \frac{d y}{d x}=\frac{x}{2 x-y} \)
в. \( \frac{d y}{d x}=\frac{y}{2 y-x} \)
c. \( \frac{d y}{d x}=\frac{2 y}{2 x-y} \)
D. None of these


\( \left|\begin{array}{ccc}\boldsymbol{a} & \boldsymbol{b} & \boldsymbol{a}+\boldsymbol{b} \\ \boldsymbol{b} & \boldsymbol{c} & \boldsymbol{b}+\boldsymbol{c} \\ \boldsymbol{a}+\boldsymbol{b} & \boldsymbol{b}+\boldsymbol{c} & \boldsymbol{0}\end{array}\right|=\mathbf{0}, \) then \( \boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c} \)
\( \operatorname{are} \) in
A. A.P
B. G.P.
\( c . \) н.
D. None of these


The potentiometer wire AB is made of
two equal parts \( A N \) and \( N B \) of cross
sectional radius \( 2 r \) and \( r \)
respectively.The material of both parts is same. A cell is connected between \( \mathbf{A} \)
and B. The potential gradient in the part
AN is \( 1 V / m . \) Potential difference
between two points \( C \) and \( D \) (shown in figure) separated by \( 20 \mathrm{cm} \) is found to
be \( 0.5 V . \) The separation between \( C \) and \( \mathrm{N} \) is \( \frac{t}{3} \mathrm{cm} . \) Then \( t \) is


Assume that life has existed on the
surface of the moon, without changing its present acceleration due to gravity
i.e., one sixth that on the surface of the
moon. If 5 kg weight of sugar is purchased on the Earth and the Moon,
how many cups of tea can be made out
of it on the Earth and the Moon
respectively? Note, From 100 g of sugar 10 cups of tea can be mode on the earth. \( \left(g=10 \mathrm{m} \mathrm{s}^{-2}\right) \)


Solve the following problem graphically:
Minimise and Maximise
\( \boldsymbol{z}=\mathbf{3} \boldsymbol{x}+\mathbf{9} \boldsymbol{y} \)
Subject to the constraints:
\( \boldsymbol{x}+\mathbf{3} \boldsymbol{y} \leq \mathbf{6 0} \)
\( \boldsymbol{x}+\boldsymbol{y} \geq \mathbf{1 0} \)
\( \boldsymbol{x} \leq \boldsymbol{y} \)
\( \boldsymbol{x} \geq \mathbf{0}, \boldsymbol{y} \geq \mathbf{0} \)


Consider the following statements and arrange in the order of true/false as given in the codes.
\( S_{1}: \) The rate of the reaction \( A \rightarrow B \) having the rate \( \operatorname{law}-\frac{\boldsymbol{d}[\boldsymbol{A}]}{\boldsymbol{d} \boldsymbol{t}}=\boldsymbol{k}[\boldsymbol{A}][\boldsymbol{B}] \)
when plotted against time will exhibit a
maximum at some time.
\( S_{2}: \) A catalyst in a chemical reaction
increases the forward \( \mathrm{E}_{a} \) and decreases
the backward \( \boldsymbol{E}_{\boldsymbol{a}} \)
\( S_{3}: \) A catalyst in a chemical reaction
decreases both forward and backward
\( \boldsymbol{E}_{\boldsymbol{a}} \)
\( S_{4}: \) For a first-order reaction, the time
required to reduce successively the concentration of reactant by a constant fraction is always same.
A. गाग
B. FFFF
c. FTFT
\( D \)


Draw a triangle \( A B C \) in which \( A B=5 \mathrm{cm} \)
\( \mathrm{BC}=7 \mathrm{cm}, \) and \( \angle B=75^{\circ} \)


RNAI prevents translation of copies of
RNA that appear viral in nature.
Which of the following describes an
instance in which it would be beneficial
to insert a copy of a gene that would
trigger RNAi?
A. To improve immune response by producing more white blood cells
B. To reduce overgrowth of blood vessels in certain types of glaucoma
C. To develop a more vivid flower color by increasing pigment production.
D. To transform bacteria so they will produce specific proteins.


The value of the determinant
\( \left|\begin{array}{ccc}5 & 5 & 14 \\ ^{5} C_{1} & ^{5} C_{4} & 1 \\ ^{5} C_{2} & ^{5} C_{5} & 1\end{array}\right| \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B. -576
c. 80
D. none of these


For the system shown in the figure, the cylinder on the left at L has a mass of
\( 600 \mathrm{kg} \) and a cross sectional area of
\( 800 c m^{2}, \) the piston on the right, at \( S \)
has cross sectional area \( 25 c m^{2} \) and
negligible weight. If the appartus is
filled with oil. \( \left(\rho=0.75 g m / c m^{3}\right) \) Find
the force \( F \) requird to hold the system in equilibrium.
A . 50 N
В. 33 n
D. 22.5


Explain blood circulation in human
heart.


The \( (I E)_{1} \) and the \( (I E)_{2} \) in \( \mathrm{kJ} \mathrm{mol}^{-1} \) of
a few elements designated by Roman
numerals are shown below
\( \begin{array}{lll}\text { Element } & (I E)_{1} & (I E)_{2} \\ A & 2372 & 5251 \\ B & 520 & 7300 \\ C & 900 & 1760 \\ D & 1680 & 3380\end{array} \) Based on above information, Which
represents a noble gas?
\( \mathbf{A} \cdot A \)
B. \( B \)
\( c \cdot C \)
D. \( D \)


What type of deviation is shown by a mixture of ethanol and acetone? What
type of azeotrope is formed by mixing
ethanol and acetone?


The following relations are defined on the set of real numbers check them for
Reflexivity,Symmetry, Transitivity. \( 1+a b>0 \)


If \( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{c}\boldsymbol{a}^{2} \cos ^{2} \boldsymbol{x}+\boldsymbol{b}^{2} \sin ^{2} \boldsymbol{x}, \boldsymbol{x} \leq \mathbf{0} \\ \boldsymbol{e}^{\boldsymbol{a} \boldsymbol{x}+\boldsymbol{b}}, \boldsymbol{x}>\mathbf{0}\end{array}\right. \)
\( f(x) \) is continuous at \( x=0 \) then
\( \mathbf{A} \cdot 2 \log |a|=b \)
B. \( 2 \log |b|=e \)
c. \( \log a=2 \log \mid b \)
\( \mathbf{D} \cdot a=b \)


If \( g(x)=1+\sqrt{x} \) and \( f(g(x))=3+ \)
\( 2 \sqrt{x}+x, \) then \( f(x)= \)
A \( \cdot 1+2 x^{2} \)
B \( \cdot 2+x^{2} \)
c. \( 1+x \)
D. \( 2+x \)


The value of \( x \) is \( 3 x+4=13 \)
A . 3
B. 4
c. 5
D. None of these


A body is moving with a velocity 1 ms \( ^{-1} \)
a force \( F \) is needed to stop it within a
distance \( x \). If the speed of the body is
\( 3 m s^{-1}, \) the force needed to stop it with
in the same distance \( (x) \) will be:
A \( .9 F \)
в. \( 6 F \)
\( c .3 F \)
D. \( 1.5 F \)


The electric potential \( V \) at any point \( P(x, y, z) \) in space is given by \( V= \)
\( 4 x^{2} V . \) The electric field at the point
\( (1 m, 2 m) \) is:
A . \( -8 i \)
B. \( 8 \hat{i} \)
\( \mathrm{c} \cdot-16 \hat{i} \)
D. \( 16 \hat{i} \)


Prove that \( 7-4 \sqrt{2} \) is irrational


The number of bonding pairs electron
\( (X) \) and lone pairs electron \( (Y) \) around
the central atom in the \( I_{3}^{-} \) ion are \( X+ \)
\( Y: \)
A .22
B. 23
\( c .32 \)
D. 43


Among the following bonds formed by the chlorine atom, the strongest bond is formed with which of the following elements?
A. lodine
B. Hydrogen
c. carbon
D. Chlorine


When the dice are thrown, the event
\( E=4, \) then this event is called
A. compound event
B. simple event
c. impossible event
D. complementary event


\( \int_{0}^{1} \frac{\log (1+x)}{1+x^{2}} d x= \)
\( A \cdot \pi \log 2 \)
в. \( \frac{\pi}{8} \log 2 \)
c. \( \frac{\pi}{4} \log 2 \)
D. \( -\pi \log 2 \)


For which of the following reaction
\( \Delta \boldsymbol{H} \neq \Delta \boldsymbol{U}: \)
\( \mathbf{A} \cdot H_{2}(g)+C l_{2}(g) \rightarrow 2 H C I(g) \)
B. \( N_{2}(g)+3 H_{2}(g) \rightarrow 2 N H_{3}(g) \)
\( \mathbf{c} \cdot N H_{4} H S(s) \rightarrow N H_{3}(g)-H_{2} S(g) \)
D \( \cdot \operatorname{CaCO}_{3}(s) \rightarrow \operatorname{CaO}(s)+C O_{2}(g) \)


Find the common ratio and the general
term of the following geometric
sequences. \( \frac{2}{5}, \frac{6}{25}, \frac{18}{125}, \dots \)


The points which are not collinear are:
A. (0,1),(8,3) and (6,7)
B. (4,3),(5,1) and (1,9)
C. (2,5),(-1,2) and (4,7)
D. (-3,2)(1,-2) and (9,-10)


If \( a, b, c \) and \( d \) are points on a number line such that \( a<b<c<d, b \) is twice
as far from \( c \) as from \( a \), and \( c \) is twice as
far from \( b \) as from \( d \), then what is the
value of \( \frac{c-a}{d-b} ? \)
A \( \cdot \frac{1}{3} \)
B. \( \frac{2}{3} \)
\( c \cdot \frac{1}{2} \)
\( D \)


Q Type your question.
1. \( \boldsymbol{y}=\boldsymbol{e}^{\boldsymbol{x}}+\mathbf{1} \quad: \boldsymbol{y}^{\prime \prime}-\boldsymbol{y}=\mathbf{0} \)
2. \( \boldsymbol{y}=\boldsymbol{x}^{2}+\boldsymbol{2} \boldsymbol{x}+\boldsymbol{C} \quad \quad: \boldsymbol{y}^{\prime}-\boldsymbol{2} \boldsymbol{x}- \)
\( \mathbf{2}=\mathbf{0} \)
3. \( \boldsymbol{y}=\cos \boldsymbol{x}+\boldsymbol{C} \quad: \quad \boldsymbol{y}^{\prime}+ \)
\( \sin x=0 \)
4. \( y=\sqrt{1+x^{2}} \)
\( : \boldsymbol{y}^{\prime}= \)
\( \frac{x y}{1+x^{2}} \)
\( \mathbf{5} . \boldsymbol{y}=\boldsymbol{A} \boldsymbol{x} \quad \quad: \quad \boldsymbol{x} \boldsymbol{y}= \)
\( \boldsymbol{y}(\boldsymbol{x} \neq \mathbf{0}) \)
6. \( \boldsymbol{y}=\boldsymbol{x} \sin \boldsymbol{x} \)
\( : \boldsymbol{x} \boldsymbol{y}=\boldsymbol{y}+ \)
\( \boldsymbol{x} \sqrt{\boldsymbol{x}^{2} \boldsymbol{y}^{2}}(\boldsymbol{x} \neq \boldsymbol{0} \boldsymbol{a} \boldsymbol{n} \boldsymbol{d} \boldsymbol{x}>\boldsymbol{y} \operatorname{or} \boldsymbol{x}<\boldsymbol{y}) \)
7. \( \boldsymbol{x} \boldsymbol{y}=\log \boldsymbol{y}+\boldsymbol{C} \quad \quad: \boldsymbol{y}^{\prime}= \)
\( \frac{y^{2}}{1-x y}(x y \neq 1) \)
8. \( y-\cos y=x \)
\( (y \sin y+ \)
\( \cos \boldsymbol{y}+\boldsymbol{x}) \boldsymbol{y}^{\prime}=\boldsymbol{y} \)
9. \( x+y=\tan ^{-1} y \)
\( : \quad y^{2} y^{\prime}+ \)
\( \boldsymbol{y}^{2}+\mathbf{1}=\mathbf{0} \)
10. \( \boldsymbol{y}=\sqrt{\boldsymbol{a}^{2}-\boldsymbol{x}^{2}} \boldsymbol{x} \epsilon(-\boldsymbol{a}, \boldsymbol{a}): \boldsymbol{x}+ \)
\( \boldsymbol{y} \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\mathbf{0}(\boldsymbol{y} \neq \mathbf{0}) \)


The ions \( N^{3-}, O^{2-}, F^{-}, N a^{+}, M g^{2+} \) are isoelectronic. Their ionic radii shows:
A. an increase from \( N^{3-} \) to \( F^{-} \) and then decrease from \( N a^{+} \) to \( M g^{2+} \)
B. a decrease from \( N^{3-} \) to \( F^{-} \) and then increase from \( N a^{+} \) to \( M g^{2+} \)
C . a significant increase from \( N^{3-} \) to \( M g^{2+} \)
D. a significant decrease from \( N^{3-} \) to \( M g^{2+} \)


\( C^{14} \) is:
A. a natural non-radioactive isotope
B. an artificial non-radioactive isotope
C . an artificial radioactive isotope
D. a natural radioactive isotope


A copper wire of cross-section A is under a tension \( \mathrm{T} \). Find the decrease in
the cross-section area. Young's
modulus is \( Y \) and Poisson's ratio is \( \sigma \)
\( ^{\text {A }} \cdot \frac{\sigma T}{2 A Y} \)
в. \( \frac{\sigma T}{A Y} \)
c. \( \frac{2 \sigma T}{A Y} \)
D. \( \frac{4 \sigma T}{A Y} \)


Thomson experimented with
A. protrons
B. cathode rays
c. alpha particles
D. gold foil


A body of mass \( 10 \mathrm{kg} \) is on a rough inclined plane having an inclination of
\( 30^{\circ} \) with the horizontal. If coefficient of
friction between the surfaces of contact
of the body and the plane is \( 0.5 . \) Find the least force required to pull the body up
the plane.
\( \mathbf{A} \cdot 80.5 N \)
B. \( 91.4 N \)
c. \( 85.4 N \)
D. \( 78.4 N \)


Let the absolute maxima/minima value
of \( \boldsymbol{f}(\boldsymbol{x})=\mathbf{3} \boldsymbol{x}^{4}-\boldsymbol{8} \boldsymbol{x}^{3}+\mathbf{1} \boldsymbol{2} \boldsymbol{x}^{2}-\boldsymbol{4} \boldsymbol{8} \boldsymbol{x}+ \)
\( \mathbf{2 5} ; \boldsymbol{x} \in[\mathbf{0}, \mathbf{3}] \) be max, min. Find
\( 2(\max )+\min ? \)


Sexual reproduction is absent in
A. Phycomycetes
B. Deuteromycetes
c. zygomycetes
D. Basidiomycetes


Which of the following is a free living nitrogen fixing bacteria?
A. Pseudomonas putida
B. Bacillus polymyxa
c. Rhizobium
D. xanthomonas


A dielectric with a dielectric constant of
\( k \) is inserted between the plates of the
capacitor of capacitance \( C \) having
a potential difference of \( \Delta V \) between
the two plates. Calculate the energy
stored in the capacitor?
A \( \cdot \frac{1}{2}(C / k)(\Delta V)^{2} \)
B \( \cdot \frac{1}{2}(k / C)(\Delta V)^{2} \)
\( ^{\mathrm{c}} \cdot \frac{1}{2} k C(\Delta V)^{2} \)
D. \( \frac{1}{2} k C \Delta V \)
E \( \cdot \frac{1}{2}(C / k) \Delta V \)


A luminous object is placed at a distance of \( 30 \mathrm{cm} \) from the convex lens
of focal length \( 20 \mathrm{cm} . \) The distance from
the lens a convex mirror of radius of
curvature \( 10 \mathrm{cm} \) should be placed on the
other side of the lens such that the real
images formed on the source itself is
\( \mathbf{A} \cdot 12 c m \)
B. \( 30 \mathrm{cm} \)
\( \mathbf{c} .50 \mathrm{cm} \)
D. \( 60 \mathrm{cm} \)


A constant voltage is applied between the two ends of a uniform metallic wire.
Some heat is developed in it. The heat developed is double if:
A. both the length and radius of wire are halved
B. both length and radius of wire are doubled
c. the radius of wire is doubled
D. the length of the wire is doubled


\( \lim _{x \rightarrow 3} \frac{\sqrt{x+13}+\sqrt{x+6}}{\sqrt{x+1}+2}= \)
\( A \)
B. 7
\( c \cdot 1 / 4 \)
D. 7/4


Solve the following equations. \( \cos ^{6} x-\sin ^{6} x=\frac{13}{8} \cos ^{2} 2 x \)


Increase 180 by \( 25 \% \)


A dipole of dipole moment 'p' is placed in non-uniform electric field along \( x \) axis. Electric field is increasing at the
rate of \( 1 ~ V m^{-1} . \) The force on dipole is:
\( \mathbf{A} \cdot \mathbf{0} \)
в. \( 2 p \)
c. \( p / 2 \)
D.


The atomic size refers to:
A. diameter of an atom.
B. radius of an atom.
C. size of two atoms in a molecule.
D. none of the above.


Define Aufbau Principle


The concept of atom comes from:
A. Dalton's atomic theory
B. Law of conservation of mass
C. Law of mass theory
D. Law of chemical combination


A magnetic field of \( 2 \times 10^{-2} T \) acts at
right angles to a coil of area \( 100 \mathrm{cm}^{2} \)
with 50 turns. The average emf induced in the coil is \( 0.1 V . \) When it is removed
from the field in \( t \) second, the value of \( t \)
is
A . \( 10 s \)
B. \( 0.1 s \)
c. \( 0.01 s \)
D. \( 1 s \)


Explain:
(i) Why do transition elements show
variable oxidation state?
(ii) Give two differences between
Lanthanide and Actinide.


Column I shows some vector equations. Match Column I with the value of angle between \( \vec{A} \) and \( \vec{B} \) given in Column II
Column I Column I


Which one does not affect apical dominance?
\( A \cdot \) IAA
B. IBA
c. Gibberillins
D. Indole Acetaldehyde


Let \( \boldsymbol{x}>-\mathbf{1}, \) then statement \( \boldsymbol{p}(\boldsymbol{n}):(\mathbf{1}+ \)
\( \boldsymbol{x}^{n}>1+\boldsymbol{n} \boldsymbol{x}, \) where \( \boldsymbol{n} \in \boldsymbol{N} \) is true for
A. For all \( n \epsilon N \)
B. For all \( n>1 \)
c. For all \( n>1 \), provided \( x \neq 0 \)
D. For all \( n>2 \)


Obtain an expression for e.m.f. induced in a coil rotating with uniform angular velocity in a uniform magnetic field. Show graphically the variation of e.m.f.
with time \( (t) \)

Resistance of a potentiometer wire is \( 0.1 \Omega / c m . \) A cell of e.m.f. \( 1.5 V \) is balanced at \( 300 \mathrm{cm} \) on this
potentiometer wire. Calculate the current and balancing length for
another cell of e.m.f. \( 1.4 \mathrm{V} \) on the same
potentiometer wire


Which of the following elements give light green colour in flame test?
\( \mathbf{A} \cdot K \)
в. \( R b \)
\( c . C a \)
D. \( B a \)


Which term of the AP \( 121,117,113, \ldots \ldots \) is the
first negative


A superconductor has \( T_{c}(0)=100 K \)
When a magnetic field of 7.5 T is
applied, its \( T_{c} \) decreases to 75 K. For this
material one can definitely say that
when
A \( \cdot B=5 T, T_{c}(B)=80 K \)
В. \( B=5 T, 75 K<T_{c}(B)<100 K \)
C . \( B=10 T, 75 K<T_{c}(B)<100 K \)
D. \( B=10 T, T_{c}=70 K \)


If a line through one vertex of a triangle
divides the opposite sides in the ratio of other two sides, then the line bisects
the angle at the vertex.
A. True
B. False


Artificial sweetener which is 600 times
sweeter than sucrose is:
A. aspartame
B. alitame
c. sucralose
D. saccharin


Ina parallelogram \( A B C D \) the bisector
of \( \angle A \) also bisects \( B C \) at \( X . \) prove that
\( A D=2 A B \)


If horizontal and vertical component of
earth's magnetic field are equal to a certain place, the angle of dip is:
\( A \cdot 90^{\circ} \)
B . \( 45^{\circ} \)
\( c \cdot 60 \)
\( D \cdot 0^{\circ} \)


State the position of cerium \( (z=58) \) and uranium \( (z=92) \) in periodic table?


Washing soaps produce scum with hard
water and not much foam because hard
water contains:
A. chalk and sulphur
B. many dissolved inorganic salts
c. many suspended particles
D. organic matter


Consider a thin spherical shell of radius R with its center at the origin, carrying uniform positive surface charge density. The variation of the magnitude
of the electric field and the electric
potential \( V(r) \) with the distance \( r \) from the center, is best represented by which
\( \operatorname{graph} \)
\( A \cdot A \)
B. B
\( c . c \)
\( D \)


Fill in the blanks with appropriate
words.
The process of purifying blood by means of an artificial kidney is called..........


Tritium is the isotope of hydrogen with 1
neutron
A . True
B. False


In a laminar flow, the velocity of the liquid in contact with the walls of the
tube is :
A. zero
B. Maximum
c. In between zero and maximum
D. Equal to critical velocity


If \( \boldsymbol{x}=\log _{5} \boldsymbol{3}+\log _{7} \mathbf{5}+\log _{9} \boldsymbol{7} \) then
A \( \cdot x \geq \frac{3}{2} \)
в. \( x \geq \frac{1}{\sqrt[3]{2}} \)
c. \( x \geq \frac{3}{\sqrt[3]{2}} \)
D. none of these


Lower alcohols are more soluble in
water than higher alcohols.
A. True
B. False


n the given figure if \( A B \| D E, \angle B A C= \)
\( 35^{\circ} \) and \( \angle C D E=53^{\circ}, \) find \( \angle D C E \)


Smoke contains
charged particles in
air.
1. positively; silica
2. negatively; silica
3. positively; carbon
4. negatively; carbon
Choose the correct option.


The de-broglie wavelength of an electron
and the wavelength of a photon are
same. The ratio between the energy of
the photon and the momentum of the electron is
\( A \cdot h \)
B.
\( c \cdot 1 / h \)
D. 1/c


The resonance point in \( \boldsymbol{X}_{L}-\boldsymbol{f} \) and
\( X_{c}-f \) curve is
\( r \)


Cardiac muscle fibres are
A. Involuntary
B. Non-fatigue
c. Striated like
D. All of the above


Given \( : A B=12 \mathrm{cm}, A C=13 \mathrm{cm}, \mathrm{ED}=\mathrm{FG}= \)
\( 5 \mathrm{cm}, \mathrm{EF}=10 \mathrm{cm} \) and \( \mathrm{GD}=4 \mathrm{cm} \)
Find the area and the perimeter of the
adjoining figure
\( A \cdot 88 \) sq. \( \mathrm{cm} \) and \( 50 \mathrm{cm} \)
B. 88 sq. \( m \) and 50 cm
\( c .88 \) sq. \( \mathrm{cm} \) and \( 50 \mathrm{m} \)
D. 8.8 sq. \( \mathrm{cm} \) and \( 50 \mathrm{cm} \)


A crop of wheat uses up to \( 20 \mathrm{kg} \) of nitrogen per hectare of soil. What is the mass of the fertilizer calcium nitrate
required to replace the nitrogen in a 10 hectare field?
\( (\boldsymbol{C a}=\mathbf{4 0}, \boldsymbol{N}=\mathbf{1}, \boldsymbol{O}=\mathbf{1 6}) \)
A. \( 1171.4 \mathrm{kg} \)
B. \( 1182 \mathrm{kg} \)
c. \( 1181 \mathrm{kg} \)
D. 2171 kg


Calculate the value of the following expression in celsius scale.
\( \frac{\left(298 K \times 50^{o} C\right)}{\left(275 K+3^{o} C\right)} \)
\( \mathbf{A} \cdot 300^{\circ} C \)
B . \( 250^{\circ} \mathrm{C} \)
c. \( 200^{\circ} \mathrm{C} \)
D. \( 350^{\circ} \mathrm{C} \)


A certain form of energy does not cause any pollution and is easily converted into electricity. It is not obtained directly or indirectly from the Sun. It is technically very difficult and expensive to obtain this form of energy
and it is not available everywhere. What is this form of energy called?
A. Wind energy
B. Nuclear energy
c. Geothermal energy
D. Tidal energy


List four methods of contraception used by humans. How does their use have a
direct effect on the health and
prosperity of a family?


The organic compound obtained from
coal is/are:
A. benzene and phenol
B. naphthelene
c. anthracene
D. all of the above


The common ratio of the G.P.
\( \boldsymbol{a}^{m-\boldsymbol{n}}, \boldsymbol{a}^{\boldsymbol{m}}, \boldsymbol{a}^{\boldsymbol{m}+\boldsymbol{n}} \) is
\( \mathbf{A} \cdot a^{m} \)
B. \( a^{-m} \)
\( \mathbf{c} \cdot a^{n} \)
\( D \cdot a^{-n} \)


Which of the following graphs depicts the variation of \( \mathrm{KE} \) of a ball, bouncing on
a horizontal floor with height? (neglect
air resistances)
\( A \)
B.
\( c \)
D. None of these


Classify \( C=\{\ldots,-3,-2,-1,0\} \) as
'finite' or 'infinite'.
A . Infinite
B. Finite
c. Data insufficient
D. None of these


A uniform chain of mass \( M \) and Length
\( \boldsymbol{L} \) is held vertically in such a way that its lower end just touches the horizontal floor. The chain is released from rest in
this position. Any portion that strikes the floor comes to rest. Assuming that the chain does not form a heap on the floor, calculate the force exerted by it on
the floor, when a length \( x \) has reached
the floor.


Write the equation for the preparation ethyne from Calcium carbide.


Sketch the graph for \( \boldsymbol{y}= \) \( \log _{\frac{1}{4}}\left(x-\frac{1}{4}\right)+ \)
\( \frac{1}{2} \log _{4}\left(16 x^{2}-8 x+1\right) \)


The pair that contains two \( \boldsymbol{P}-\boldsymbol{H} \)
bonds in each of the oxoacids is:
A. \( H_{3} P O_{2} \) and \( H_{4} P_{2} O_{5} \)
B. \( H_{4} P_{2} O_{5} \) and \( H_{4} P_{2} O_{6} \)
\( \mathrm{c} \cdot H_{3} P O_{3} \) and \( H_{3} P O_{2} \)
D. \( H_{4} P_{2} O_{5} \) and \( H_{3} P O_{3} \)


If the sum of \( m \) terms of an arithmetical
progression is equal to the sum of
either the next \( n \) terms or the next \( p \) terms, then \( \left(\frac{n+m}{n-m}\right)\left(\frac{p-m}{p+m}\right) \) is
A \( \cdot \frac{n}{p} \)
в. \( \frac{p}{n} \)
c. \( n p \)
D. \( \frac{p}{m} \)


Alcohols react with active metals e.g. Na, K etc. to give corresponding alkoxides. Write down the decreasing order of reactivity of sodium metal towards primary, secondary and tertiary alcohols.


Eutrophication means
A. excessive richness of nutrients in a water body or lake due to run off
B. decrease in growth of algae
C. increase in fertility of soil
D. all the above


Assertion
The laws of chemical combination
ultimately led to the idea of 'atoms' being the "smallest unit of" matter
Reason

The laws of chemical combination
played a significant role in the
development of Dalton's atomic theory
of matter
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


Assertion
It takes more fuel for a spacecraft to
travel from the earth to the Moon than
for the return trip.
Reason
The point of zero gravitational field
intensity due to the earth and the Moon
is Iying nearer to the Moon, i.e., in the
diagram shown, for \( r<r_{0} . E_{g} \) is
towards the earth's centre and for \( r> \)
\( r_{0}, E_{g} \) is towards the Moon's centre, and
\( \operatorname{at} r=r_{0}, E_{g} \) is zero.
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 and Reason is correct


Arrange the steps marked
(i) to (v) in
CORRECT order while constructing a line parallel to a given line, through a point not on the line using ruler and
compasses only. Step 1. Take a line 'I' and a point 'A' outside 'I'.
Step 2. Take any point B on I and join B to A.
(i) Now with \( A \) as centre and the same
radius as in previous step, draw an arc EF cutting \( A B \) at \( G \)
(ii) With the same opening as in previous step and with \( \mathrm{G} \) as centre, draw an arc cutting the arc EF at H.
(iii) With \( \mathrm{B} \) as centre and a convenient
radius, draw an arc cutting I at \( \mathrm{C} \) and BA at D.
(iv) Now, join AH to draw a line 'm'.
\( \mathbf{A} \cdot(\mathbf{i}) \rightarrow(\mathbf{i} \mathbf{i}) \rightarrow(\mathbf{i} \mathbf{v}) \rightarrow \) (iii)
B. (iii) \( \rightarrow(\mathrm{i}) \rightarrow(\mathrm{ii}) \rightarrow(\mathrm{iv}) \)
c. (iii) \( \rightarrow(\text { ii) } \rightarrow(i) \rightarrow \) (iv)
D. (i) \( \rightarrow \) (ii) \( \rightarrow \) (iii) \( \rightarrow \) (iv)


When 10 grams of methane is completely burnt in oxygen, the heat
evolved is \( 560 \mathrm{kJ} \). What is the heat of
combustion(in kJ. \( m o l^{-1} \) ) of methane?


If \( \mathbf{A} \) is skew-symmetric matrix and \( \mathbf{n} \) is
even positive integer, then \( \mathbf{A}^{\mathbf{n}} \) is
A. a symmetric matrix
B. skew-symmetric matrix
c. diagonal matrix
D. triangular matrix


Fruit lomentum is characteristic
feature of the sub family
A. Papilionatae
B. Caesalpinoideae
c. Mimosoideae
D. Leguminosae


Two small identical metal balls \( A \) and
\( B \) of radius ' \( r^{\prime} \) are placed apart. The
distance between centre of balls is 'a \( _{0} \).
The net potential of ball \( A \) is \( V_{1} \) and that
of \( B \) is \( V_{2} . \) Let \( q_{1} \) and \( q_{2} \) are the charges
on balls \( A \) and \( B \) respectively. Then the
charges on \( A \) and \( B \) are \( \left(\operatorname{given} r<<a_{0}\right) \)
A \( \cdot q_{1}=4 \pi \varepsilon_{0} \frac{a_{0} r\left(V_{1} a_{0}-V_{2} r\right)}{a_{0}^{2}-r^{2}} \)
B. \( \quad q_{1}=4 \pi \varepsilon_{0} \frac{a_{0} r\left(V_{1} a_{0}+V_{2} r\right)}{a_{0}^{2}+r^{2}} \)
\( ^{\mathbf{C}} \cdot_{q_{2}}=4 \pi \varepsilon_{0} \frac{a_{0} r\left(V_{1} a_{0}+V_{2} r\right)}{a_{0}^{2}+r^{2}} \)
D. \( _{q_{2}}=4 \pi \varepsilon_{0} \frac{a_{0} r\left(V_{1} a_{0}-V_{2} r\right)}{a_{0}^{2}-r^{2}} \)


Heres a collision event as shown in the
figure. In which system would the
momentum be conserved?
A. System of ball \( A \)
B. System of ball \( B \)
c. System of ball \( A+ \) ball \( B \)
D. In all of the above systems


If first ionisation energy of hydrogen is
\( \boldsymbol{E}, \) then the ionisation energy of \( \boldsymbol{H} \boldsymbol{e}^{+} \) would be:
A. \( E \)
в. \( 2 E \)
\( c .0 .5 E \)
D. \( 4 E \)


Equal masses of \( N_{2} \) and \( O_{2} \) gases are
filled in vessel A and B. The volume of
vessel B is double of A. The ratio of
pressure in vessel \( A \) and \( B \) will be
A . 16: 7
B. 16:14
c. 32: 7
D. 32:28


Stomata having pores bounded by a single ring shaped guard cell are found in the
A. Leaf of ferns
B. Pinnule of Cycas.
c. capsule of Funaria
D. All of the above


Blood analysis of a patient reveals an unusually high quantity of carboxyhaemoglobin content. Which of the following conclusions is most likely
to be correct?
A. Carbon dioxide
B. Carbon monoxide
c. Carbon disulphide
D. chloroform


Accuracy defines nearness of a measured value to the standard or true
value. If true enter 1 else enter 0


The total mass of a box measured by
grocer's balance is 2.300 kg. Two gold
pieces of masses \( 20.15 g \) and \( 20.17 g \)
are added to the box. What is:(a) the
total mass of the box?(b) the difference
in the masses of the pieces to correct significant figures?


Phenol is less acidic than:
A. \( o \) -nitrophenol
B. \( p \) -methoxy phenol
c. 2 -methylpropano
D. 2, 2-dimethyl pentanol


If helium and methane are allowed to
diffuse out of the container under the
similar conditions of temperature and
pressure, then the ration of rate of diffusion of helium to methane is:
A . 2.
B. 1.0
\( c \cdot 0.5 \)
D. 4.0


The net work done by the tension in the
figure when the bigger block of mass \( M \) touches the ground is:
\( \mathbf{A} \cdot+M g d \)
в. \( -(M+m) g d \)
\( \mathrm{c} .-m g d \)
D. zer


Select the incorrect statement.
A. Microelements involve \( \mathrm{N}, \mathrm{P}, \mathrm{Mn}, \mathrm{Cu}, \mathrm{Mo} \)
B. The concentration of microelements is \( 10 \mathrm{m} \) mole/kg
C. If the concentration is more than \( 10 \mathrm{m} \) mole/kg, they become toxic
D. The deficiency of microelements causes symptoms of disease


Determine the order and degree of the
following differential equation. State also whether it is linear or non-linear.
\( \left(y^{\prime \prime}\right)^{2}+\left(y^{\prime}\right)^{3}+\sin y=0 \)


Find the population of a city after 2
years which is at present 12 lakh, if the rate of increase is \( 4 \% \).p.a.


Starch is insoluble in water yet it is accumulated in large quantities in
potato because
A. It is synthesized in potato tuber itself
B. It is translocated from the leaves to the potato tuber in the form of sugar and stored there as starch.
c. Soil micro-organsim deposit starch in tuber.
D. It is useful consumption


toppr ow
Q Type your question
Choose the correct body plan from \( A \) to \( G \)
and fill in the table.
Column I Column II
Name of the animal \( \quad \) Body Plan
(i) Silverfish
(ii) Planaria
(iii) Jellyfish
(iv) Lizard
(v) Ascaris
Ectoderm
I Fndodern
\( \therefore \therefore \). mesoderm
cavity


Assertion
Statement-I: In the extraction of Ag the
\( \operatorname{complex} N a\left[A g(C N)_{2}\right] \) is reacted with
Zn.
Reason
Statement- - II : Zn is transition metal
according to electronic theory.

Read the above assertion and reason
and choose the correct option regarding
¡t.
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 mixture containing equal quantity of germinating maize and groundnut seeds are taken. The RQ of this mixture
would be
A. one
B. Less than one
c. More than one
D. Infinity


Agar-agar is obtained from
A. Chlorella
B. Spirogyra
c. Ulothrix
D. Gelidium


List out the major air pollutants.


The formula for the compound tris ethane \( -1,2-\text { diamine }) \) cobalt \( (\| I) \)
sulphate is :
\( ^{\mathbf{A}} \cdot\left[\operatorname{Co}(e n)_{3}\right] S O_{4} \)
в. \( \left[\operatorname{Co}(S O)_{4}(e n)_{3}\right] \)
\( ^{\mathbf{c}} \cdot\left[\operatorname{Co}(e n)_{3}\right]\left(S O_{4}\right)_{2} \)
D. \( \left[\operatorname{Co}(e n)_{3}\right]_{2}\left(S O_{4}\right)_{3} \)


Fig. \( 29.17(a) \) shows two coherent
sources \( S_{1} \) and \( S_{2} \) which emit light of
wavelength \( \lambda \) in phase. The phase
separation between the sources is \( 3 \lambda . \) A
circular wire of radius \( \boldsymbol{R}>>\boldsymbol{I} \) is
placed symmetrically to \( S_{1} \) and \( S_{2} \) as
illustrated. Find the angular positions \( \theta \)
on the wire for which constructive
interference occurs.


If the difference between pressure
inside and outside of a soap bubble is
\( 6 m m \) of water
and its radius is 8 mm. What is the
surface tension in dynes per \( c m \)
A .117 .6
в. 256
\( c .378 \)
D. 450


Some substances are commonly used
for removing acidic gases. Which of the following is commonly used in the chemical industry for the removal of hydrogen sulphide from coal gas?
A. Milk of magnesia
B. Slaked lime
c. Quick lime
D. Sodium hydride


Huygen's concept of secondary wave
A. allows us to find the focal length of a thick lens
B. is a geometrical method to find a wavefront
\( \mathrm{C} \). is used to determine the velocity of light
D. is used to explain polarization


The energies of activation for \( \boldsymbol{A}_{\mathbf{2}}+ \)
\( B_{2} \rightleftharpoons 2 A B \) are \( 180 k J \) mol \( ^{-1} \) forward
and \( 200 k J \) mol \( ^{-1} \) reverse reactions
respectively. The presence of catalyst lowers the activation energies of both
(forward and reverse) reactions \( \left(\boldsymbol{A}_{2}+\right. \)
\( B_{2} \rightleftharpoons 2 A B \) by \( 100 k J \) mol \( ^{-1} . \) The
magnitude of enthalpy change of the
reaction in the presence of catalyst will be \( \left(\text { in } \mathbf{k} \text { J } \boldsymbol{m} \boldsymbol{o} \boldsymbol{l}^{-1}\right) \)
A. 300
B. 120
c. 20
D. -20


How many of the following can be oxidising agent?
\( \boldsymbol{H}_{2} \boldsymbol{S}, \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4}, \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{3}, \boldsymbol{H}_{2} \boldsymbol{S}_{2} \boldsymbol{O}_{3} \)


The neurons in the brain are myelinated by
A. Schwann cells
B. Astrocytes
c. oligodendrocytes
D. Microglia


define the peak voltage of the source:


The water drops fall at regular intervals from a tap 5 m above the ground. The third drop is leaving the tap at the
instant the first drop touches the ground. How far above the ground is the second drop at the instant?
\( \mathbf{A} \cdot 1.25 m \)
B. \( 2.50 m \)
\( c .3 .75 m \)
D. \( 4.00 m \)


If the coefficient of range is 0.18 and the largest value is 7.44 ,then the smallest value is?
A . 3.23
в. 4.15
c. 5.17
D. 5.14


One mole of oxygen is allowed to expand
isothermally and reversibly from \( 5 m^{3} \)
to \( 10 m^{3} \) at 300 K. Calculate the work
done in expansion of the gas.


A volume of \( 100 \mathrm{L} \) of hard water requires \( 5.6 \mathrm{g} \) of lime for removing temporary hardness. The temporary hardness in ppm of CaCO3CaC03 is:
A . 56
B. 100
\( c \cdot 200 \)
D. 112


Assertion: The atomic bomb uses the
principle of nulcear fission. Reason: Nuclear fusion reaction
requires high temperatures.
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
E. Both Assertion and Reason are false


\( P \) and \( Q \) are two objects with masses
5kg and 30kg respectively. Then
A. \( P \) has more inertia than \( Q \)
B. \( Q \) has more inertia than \( P \)
c. \( P \) and \( Q \) have the same inertia
D. Neither \( P \) nor \( Q \) has any inertia


Which of the following is not an oscillatory motion?
A. The tuning fork
B. The stretched string
c. The motion of the swing
D. None of the above


A sugar syrup of weight \( 214.2 \mathrm{g} \)
contains 34.2 g of sugar \( \left(C_{12} H_{22} O_{11}\right) \) Calculate. the molal concentration
(Write your answer as \( 18 X \), where, \( X= \) molality)


Explain the mechanism behind Motion
of a Rocket.


Figure shows the orbit of a planet \( \mathrm{P} \)
round the sun \( S . A B \) and \( C D \) are the
minor and major axes of the ellipse. If \( t_{1} \)
is the time taken by the planet to travel
along \( A C B \) and \( t_{2} \) the time along \( B D A \)
then:
A \( \cdot t_{1}=t_{2} \)
B \( \cdot t_{1}>t_{2} \)
\( \mathbf{c} \cdot t_{1}<t_{2} \)
D. nothing can be concluded


Prove that \( 1^{2}+2^{2}+3^{2}+\ldots .+n^{2}>\frac{n^{2}}{3} \)
for all \( n \in N \) using principle of
mathematical induction


Fizziness appears on opening a bottle of
cold drink.


Which one of the following pentafluoride cannot be formed?
A. \( P F_{5} \)
B. \( A s F_{5} \)
c. \( S b F_{5} \)
D. B iF


The bond between atoms of two
elements of atomic number 37 and 53
is:
A. covalent
B. ionic
c. co-ordinate
D. metalic


A paramagnetic liquid is taken in a Utube and arranged so that one of its limbs is kept between pole pieces of the magnet. The liquid level in the limb is
A. goes down
B. rises up
c. remains same
D. first goes down and then rise


If the pressure of an ideal gas contained in a closed vessel is increased by \( 0.4 \% \)
the increases in temperature is \( 1^{\circ} \mathrm{C} \) The initial temperature of the gas is:
\( \mathbf{A} \cdot 26^{\circ} C \)
B . \( 250^{\circ} \mathrm{C} \)
c. \( 250 K \)
D. \( 2500^{\circ} \mathrm{C} \)


Which of the following is not a characteristic feature of Fabaceae
A. Descendingly. imbricate, ten stamens, diadelphous,
ovary superior
B. Sepals five, gamoseepalous, imbricate aestivation,
placentation marginal
c. Monocarpellary, ovary superior, style long, slightly bent
at the apex
D. zygomorphic flowers, diadelphous stamens, many
ovules
E. Corolla five petals, polypetalous, anterior one large and
outermost


The length, breadth and height of a cuboid are in the ratio \( 5: 4: 2 . \) If the
total surface area is \( 1216 \mathrm{cm}^{2} \), find the
dimensions of the solid.
A . \( (21 \times 11 \times 8) \mathrm{cm} \)
B. \( (20 \times 16 \times 8) \mathrm{cm} \)
c. \( (27 \times 17 \times 8) \mathrm{cm} \)
D. \( (25 \times 19 \times 8) \mathrm{cm} \)


Prove the following by using the principle of mathematical induction for all \( \boldsymbol{n} \in \boldsymbol{N}: \mathbf{1} . \mathbf{2 . 3}+\mathbf{2 . 3 . 4}+\ldots \ldots+ \)
\( \boldsymbol{n}(\boldsymbol{n}+\mathbf{1})(\boldsymbol{n}+\mathbf{2})= \)
\( \frac{\boldsymbol{n}(\boldsymbol{n}+\mathbf{1})(\boldsymbol{n}+\mathbf{2})(\boldsymbol{n}+\mathbf{3})}{\mathbf{4}} \)


Duct of Bellini is found in
A. Pancreas
B. Salivary gland
c. Medulla of mammalian kidney
D. Liver


The solubility \( A g C l \) is maximum in:
A. acidic buffer solution
B. basic buffer solution
c. In pure water
D. equal in all solutions


Calculate the volume of the hemisphere.
A. \( 1095.23 \mathrm{cm}^{3} \)
B . \( 2095.23 \mathrm{cm}^{3} \)
c. \( 3095.23 \mathrm{cm}^{3} \)
D. \( 4095.23 \mathrm{cm}^{3} \)


Factorise \( : 6 x y^{2}+4 x^{2} y \)
A. \( 2 x y(3 x+y) \)
B. \( x y(3 x+2 y) \)
c. \( 2 x y(2 x+3 y) \)
D. none of these


Solve: for \( x \)
\( \frac{3-2 x}{2 x+5}=-\frac{3}{11} \)


Draw the histogram to represent the following data, hence find the mode.
Daily
\[
\begin{array}{llll}
\text { sales of } & 0- & 1000- & 2000- \\
\text { a store } & 1000 & 2000 & 3000 \\
\text { in (Rs.) } & & &
\end{array}
\]
Number
of days
12
in a month
\( \mathbf{A} \cdot \) Rs. 1500
B. Rs. 1600
c. Rs. 1700
D. Rs. 1800


A particle of mass \( m \) strikes elastically
with a disc of radius \( R, \) with a velocity \( \vec{v} \)
as shown in the figure. If the mass of the
disc is equal to that of the particle and
the surface of the contact is smooth,
then the velocity of the disc just after the collision is:
A \( \cdot \frac{2 v}{3} \)
B. \( \frac{v}{2} \)
c. \( \frac{\sqrt{3} v}{2} \)
D.


At \( 527^{0} \mathrm{C} \), the reaction
\( N H_{3}(g) \rightleftharpoons \frac{1}{2} N_{2}(g)+\frac{3}{2} H_{2}(g) \) has \( K_{c}= \)
4
What is the \( K_{c} \) for the reaction?
\( N_{2}(g)+3 H_{2}(g) \rightleftharpoons 2 N H_{3}(g) \)
\( A \cdot \frac{1}{4} \)
B. 16
\( c \cdot 4 \)
D. \( \frac{1}{16} \)


Playing with a lens one morning, Rita discovers that if she holds the lens 0.120
\( \mathrm{m} \) away from a wall opposite to a window, she can see a sharp but
upside-down picture of the outside
world on the wall. That evening, she covers a lighted lamp with a piece of card on which she has pierced a small hole, \( 0.005 \mathrm{m} \) in diameter. By placing
the lens between the illuminated card
and the wall, she manages to produce a sharp image of diameter \( 0.020 \mathrm{m} \) on the wall. What is the distance between the
card and the wall?
A. \( 0.450 \mathrm{m} \)
B. 0.750 \( \mathrm{m} \)
c. \( 0.600 \mathrm{m} \)
D. \( 0.300 \mathrm{m} \)


Economically important edible part of Ipomoea batatas is?
A. Rhizome
B. Stem tuber
c. Underground fruit
D. Underground root tuber


There are two radioactive substances \( A \)
and
B. Decay constant of B is two times that of A. Initially, both have equal number of nuclei. After 'n' half-lives of A,
rates of disintegration of both are equal
The value of \( ^{\prime} \boldsymbol{n}^{\prime} \) is
A . 1
B . 2
\( c \cdot 4 \)
D. all of these


What is the correct relationship between the following compound?
\[
\begin{array}{l}
\boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\underset{C H_{3}}{\boldsymbol{C}} \boldsymbol{H}-\boldsymbol{C} \boldsymbol{H}_{2}-\boldsymbol{C} \boldsymbol{H}_{3} \\
\boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\underset{C H_{3}}{\boldsymbol{C}} \boldsymbol{H}_{2}
\end{array}
\]


Find the minimum value of \( \frac{x^{2}+2 x+4}{(x+2)} \)
is ?
A .2
B.
\( c .3 \)
D. doesn't exist


Ionic compounds have
A. Low melting and high boiling points.
B. High melting and low boiling points.
C. Low melting and low boiling points
D. High melting and high boiling points.


BD is one of the diagonals of a quadrilateral ABCD.AM and CN are the perpendiculars from \( A \) and \( C \) respectively, on BD. Show that \( \boldsymbol{a r}(\boldsymbol{q u a d} . \boldsymbol{A B C D})=\frac{1}{2} \boldsymbol{B D} \cdot(\boldsymbol{A M}+ \)
\( \boldsymbol{C} \boldsymbol{N}) \)


Moment of force is
A . \( F a \)
в. \( F s \)
\( c \cdot \frac{d f}{d t} \)
D. None of these


Match List - I with List - II for the compositions of substances and select
the correct answer using the code given below the list:
List - -
List - II

Substances
Composition
(A) Plaster of paris
\( \boldsymbol{C a} \boldsymbol{S O}_{4} \cdot \boldsymbol{2} \boldsymbol{H}_{2} \boldsymbol{O} \)
(B) Epsomite \( \operatorname{Cas} O_{4} \cdot \frac{1}{2} H_{2} O \)
(C) Kieserite
\( M a S O_{4} \cdot 7 H_{2} O \)
(D) Gypsum
\( M g S O_{4} \cdot H_{2} O \)
\( (v) C a S O_{4} \)
B. (A) - (ii), (B) - (iii), (C) - (iv), (D) - (i)
D. (A) - (iv), (B) - (iii), (C) - (ii), (D) - (i)


The electric field between the plates of
two oppositely charged plane sheets of
charge density' \( \sigma^{\prime} \) is :
A \( \cdot+\frac{\sigma}{2 \epsilon_{0}} \)
в. \( -\frac{\sigma}{2 \epsilon_{0}} \)
c. \( \frac{\sigma}{\epsilon_{0}} \)
D. zero


The dimensions of \( \epsilon_{0} \) (permittivity in
free space) is
\( \mathbf{A} \cdot M L^{2} T^{4} A^{2} \)
B. \( M L^{-3} T^{2} A^{2} \)
\( \mathbf{c} \cdot M^{-1} L^{3} T^{4} A^{2} \)
D. \( M L^{3} T^{2} A^{2} \)
E \( \cdot M^{-1} L^{-3} T^{4} A^{2} \)


Define a simple event.


\( \pi \) bonds are formed by the
overlap of orbitals.


The spacecraft of mass \( M \) moves with velocity \( V \) in free space at first, then it explodes breaking into two pieces. If after explosion a piece of mass \( \boldsymbol{m} \) comes to rest, the other piece of
spacecraft will have a velocity:
A. \( \frac{M V}{(M-m)} \)
в. \( \frac{M V}{(M+m)} \)
c. \( \frac{m V}{(M m)} \)
D. \( \frac{m V}{(M+m)} \)


A block of mass \( 4 k g \) is kept over a rough horizontal surface. The coefficient of friction between the block
and the surface is 0.1. At \( t=0,(3 \hat{i}) \frac{m}{s} \)
velocity is imparted to the block and simultaneously \( (-2 \hat{i}) N \) force starts acting on it. Its displacment in first \( 5 s \) is
A. \( 8 i \)
в. \( -8 \hat{i} \)
\( c \cdot 3 i \)
D. \( -3 \hat{i} \)


Three particles, each of mass \( 1 g m \) and carrying a charge \( q, \) are suspended from a common point by insulated massless string, each \( 100 \mathrm{cm} \) long. If
the particles are in equilibrium and are located at the corner of an equilateral
triangle of side length 3 cm. Calculate
the charge \( q \) on each particle. (Take \( g= \)
\( \left.10 m / s^{2}\right) \)


An employer sends a letter to his employee but he does not receive the
reply (It is certain that employee would have replied if he did receive the letter).
It is known that one out of \( n \) letters does
not reach its destination. Find the
probability that employee does not receive the letter.
A \( \cdot \frac{1}{n-1} \)
B. \( \frac{n}{2 n-1} \)
c. \( \frac{n-1}{2 n-1} \)
D. \( \frac{n-2}{n-1} \)


Anthropogenic ecosystems
A. show high degree of nutrient cycling
B. show low productivity
C . show great biodiversity
D. Do not posses self regulatory mechanism


Mobility of free electrons in a conductor
¡s:
A. directly proportional to electron density
B. directly proportional to relaxation time
C. inversely proportional to electron density
D. inversely proportional to relaxation time


\( f\left(x+\frac{1}{x}\right)^{2}=3 \) then find the value of
\( \boldsymbol{x}^{\boldsymbol{6}} \)


The solution of the differential equation
\( \boldsymbol{x}^{2} \boldsymbol{d} \boldsymbol{y}+\boldsymbol{y}(\boldsymbol{x}+\boldsymbol{y}) \boldsymbol{d} \boldsymbol{x}=\mathbf{0} \) is:
A \( \cdot x^{2} y=c^{2}(2 x+y) \)
B . \( x y^{2}=c^{2}(2 x+y) \)
C. \( x^{2} y=c^{2}(x+2 y) \)
D. \( x y^{2}=c^{2}(x+2 y) \)


Evaluate the following integrals:
\( \int \frac{\cos x}{\sqrt{4+\sin ^{2} x}} d x \)


Biological unit controlling heredity is
A. Genome
B. Chromosome
c. Genotype
D. Gene


\( \int_{1}^{2} \frac{\mathbf{d x}}{\sqrt{1+\mathbf{x}^{2}}}= \)
\( ^{\mathbf{A}} \cdot \log _{\mathbf{e}}\left(\frac{2+\sqrt{5}}{\sqrt{2}+1}\right) \)
в. \( \log _{e}\left(\frac{\sqrt{2}+1}{2+\sqrt{5}}\right) \)
\( ^{\mathrm{c}} \cdot \log _{\mathrm{e}}\left(\frac{2-\sqrt{5}}{\sqrt{2}-1}\right) \)
D.


The position-time graph below
represents the motion of a
hummingbird as it moves horizontally
through the air.

Which of the following tables best lists
on the graph at the positions and times where the hummingbird's speed is the
greatest and the magnitude of its
acceleration is the greatest?
A. Greatest speed 1 , Greatest Acceleration 3
B. Greatest speed 3 , Greatest Acceleration 2
C. Greatest speed 2 , Greatest Acceleration 2
D. Greatest speed 3, Greatest Acceleration 3
E. Greatest speed 5 , Greatest Acceleration 4


Consider the matrix \( \boldsymbol{A}=\left(\begin{array}{ll}\mathbf{3} & -\mathbf{2} \\ \mathbf{4} & -\mathbf{1}\end{array}\right) \)
Then all possible values of \( \lambda \) such that
the determinant of \( B=A-\lambda I \) is 0
where \( \boldsymbol{I}=\left(\begin{array}{ll}\mathbf{1} & \mathbf{0} \\ \mathbf{0} & \mathbf{1}\end{array}\right) \) and \( i=\sqrt{-\mathbf{1}} \)
\( \mathbf{A} \cdot 1 \pm 2 i \)
B . \( 2 \pm 3 i \)
c. \( 3 \pm 4 i \)
\( \mathbf{D} \cdot 5 \pm 6 i \)


Sclereids are present in
A. fruit walls of nuts
B. grit of guava and pear
C. seed coats of legumes
D. all of these


The line segment joining any two points on a circle is called a or an
A. arc of the chord
B. radius of the circle
c. chord of the circle
D. tangent of the circle


If \( \alpha \) is the angle subtended at \( P\left(x_{1}, y_{1}\right) \)
by the circle \( S=x^{2}+y^{2}+2 g x+ \)
\( 2 f y+c=0, \) then
This question has multiple correct options
A \( \cdot \cot \alpha=\frac{\sqrt{S_{1}}}{\sqrt{g^{2}+f^{2}-c}} \)
B. \( \cot \alpha / 2=\frac{\sqrt{S_{1}}}{\sqrt{g^{2}+f^{2}-c}} \)
\( ^{\mathrm{c}} \tan \alpha=\frac{2 \sqrt{g^{2}+f^{2}-c}}{\sqrt{S_{1}^{1}}} \)
D. \( \quad \alpha=2 \tan ^{-1}\left(\frac{\sqrt{g^{2}+f^{2}-c}}{\sqrt{S_{1}}}\right) \)


If \( f(x)=x^{2}, g(x)=x^{2}-5 x+6, \) then
\( \boldsymbol{g}(\mathbf{2})+\boldsymbol{g}(\mathbf{3})+\boldsymbol{g}(\mathbf{0})-\boldsymbol{f}(\mathbf{0})-\boldsymbol{f}(\mathbf{1})- \)
\( \boldsymbol{f}(-2) \)
A . 2
B.
\( c \cdot \frac{5}{6} \)
\( D \)


The mth term of A.P is n and its nth term
is m. its pth term is
\( A \cdot m+n+p \)
B. \( m+n-p \)
\( c \cdot m-n+p \)
D. None


If \( \boldsymbol{A}=\left|\begin{array}{ll}\mathbf{1 0} & \mathbf{2} \\ \mathbf{3 0} & \mathbf{6}\end{array}\right| \)
then \( |\boldsymbol{A}|= \)
\( A \cdot O \)
B. 10
\( c \cdot 12 \)
D. 60


In one - dimensional head on
collision, the relative velocity of approach before collision is equal to:
A. relative velocity of separation after collision
B. \( e \) times relative velocity of separation after collision
c. \( 1 / e \) times relative velocity of separation after collision
D. sum of the velocities after collision


The number of lines of symmetry in a trapezium is
A . Infinite
B. 2
\( c .3 \)
D. None


II the ngurt, and
\( \operatorname{masses} m_{1} \) and \( m_{2}\left(m_{1}>m_{2}\right) . m_{1} \) has
a downward acceleration \( a \). The pulley \( P \)
has a radius \( r, \) and some mass. The
string does not slip on the pulley. Then which of the following statement(s) is/are true?
This question has multiple correct options
A. The two sections of the string have unequal tensions.
B. The two blocks have accelerations of equal magnitude.
C . The angular acceleration of P is \( \frac{a}{r} \)
D. \( a<\left(\frac{m_{1}-m_{2}}{m_{1}+m_{2}}\right) g \)


What is the significance of meiosis? How does meiosis differ from mitosis?


Which of the following methods is not
used to coat metallic elements to
prevent corrosion?
A. Electroplating
B. Metal cladding
c. Metal spraying
D. None of the above


I: The sulfur in \( S O_{2}, \) is \( s p^{2} \) hybridized.
\( \|: S O_{2} \) has linear electron pair
geometry.


Block B rests on block A. Block A rests
on a horizontal surface \( C \) which is
frictionless. There is friction between \( \mathbf{A} \)
and B. If B is pulled to the right, then:
A. B moves forward and A to the left
B. B only moves to the left
c. B does not move
D. A and B move to right however their acceleration can be different.


Subtract the following algebraic expressions.
\( 4 x \) from \( 8 x \)
A .4
B. \( 4 x \)
\( c .-4 \)
D. \( -4 x \)


The refractive index of glass is 1.520 for
red light and 1.525 for blue light. Let \( D_{1} \)
and \( D_{2} \) be angles of minimum deviation for red and blue
lights respectively in a prism of this glass. Then
A. \( D_{1}<D_{2} \)
В. \( D_{1}>D_{2} \)
\( \mathbf{c} \cdot D_{1}=D_{2} \)
D. \( D_{1} \) can be less than or greater than \( D_{2} \) depending upon the angle of prism


f \( a, b, c \) are positive real numbers, prove
that
\( \frac{b^{2}+c^{2}}{b+c}+\frac{c^{2}+a^{2}}{c+a}+\frac{a^{2}+b^{2}}{a+b} \geq a+ \)
\( \boldsymbol{b}+\boldsymbol{c} \)


Name a non-metal that has lustre.


Find the odd one out:
A . Fe
B. 0
\( \mathrm{c} \cdot \mathrm{CH}_{4} \)
D.


Which of the following types of tissue form the thin surface for the gas
exchange in the lungs?
A. Epithelial
B. Connective
c. Nervous
D. Muscle


Identify a 'Chemical twin' among the followings.
\( \mathbf{A} \cdot Z r-T a \)
B. \( N b-T c \)
c. \( H f-R e \)
D. \( N b-T a \)


The oxidation state of chromium in
\( \left[\boldsymbol{C r}\left(\boldsymbol{P} \boldsymbol{P h}_{3}\right)_{3}(\boldsymbol{C O})_{3}\right] \) is :
\( A \cdot+3 \)
B. +8
c. 0
D. +5


Read the bar graph shown in given fig. and answer the following questions
Of which state were the minimum
number of tickets sold?
Bar graph of the tickets of different state lotteries sold by an agent on a day.


\( \mathbf{f} \boldsymbol{y}=\sin \left\{\tan ^{-1} \sqrt{\left(\frac{1-x}{1+x}\right)}\right\} \) prove that
\( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\frac{\boldsymbol{- x}}{\sqrt{\mathbf{1 - x}^{2}}} \)


Assertion
A super-saturated solution of glucose in boiling water crystallizes as it cools.
Reason
The solubility increases as the temperature decreases.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Find the dimensional formulae of the
following quantities:
1. the universal constant of gravitational
\( G \)
2. the surface tension \( S \)
3. the thermal conductivity \( k \) and
4. the coefficient of viscosity \( \eta \)


The coordinate of a point where parallel rays are focussed by the thin convex lens is [where focal length of convex lens is \( 10 \mathrm{cm} \) and it is placed along \( \mathrm{y} \) axis].


When a number is increased by \( 120, \) it becomes \( 130 \% \) of itself. What is the
number?
A . 400
в. 520
c. 460
D. 580


What is called the rate of doing work in an electric circuit?
A. Power
B. Energy
c. current
D. voltage


Find the area bounded by line \( y=3 x+ \)
2, x-axis and ordinates \( x=-1 \) and
\( \boldsymbol{x}=\mathbf{1} \)


toppr \( t \)
Q Type your question
magnetic force acting on each wire?
\( A \)
B.
\( c \)
D.
E. There is no net force acting on either wire


Which of the following is the function of MCB in household circuit?
This question has multiple correct options
A. This switches automatically turn off when current exceeds safe limit
B. This switches automatically turn on when current exceeds safe limit
c. saves the electrical appliances from getting damaged due to excess current
D. Saves from shortcircuiting


Which of the following is blue in colour?
A . Aqueous \( C u S O_{4} \)
в. \( F e S O_{4} \)
\( c \cdot Z n S O_{4} \)
D. \( A l_{2}\left(S O_{4}\right) \)


In uniform linear motion, the speed and
velocity are
A. Constant
B. Variable
c. zero
D. All


A line joining places of zero dip is called
A . aclinic
B. isoclinic
c. isodynamic
D. isogonal


State True or False.
Hydrogen atom can produce single spectral line due to a presence of one
electron.
A. True
B. False


Which of the following sol is not prepared using Bredig's arc method?
A. silver sol
B. Copper sol
c. Gold sol
D. Platinum sol


Let \( [x] \) denote the greatest integer part of a real number x. If
\( \boldsymbol{M}=\sum_{n=1}^{40}\left[\frac{\boldsymbol{n}^{2}}{\mathbf{2}}\right] \)
then m equals
A . 5700
B. 5720
\( c .5740 \)
D. 11060


Estimate the mean free path and
collision frequency of a nitrogen molecule in a cylinder containing nitrogen at 2.0 atm and temperature 17
\( ^{o} C . \) take the radius of a nitrogen
molecule to be roughly 1.0 A. Compare the collision time with the time the
molecule moves freely between two successive collisions (Molecular mass
of \( \mathrm{N}_{2}=28.0 \mathrm{u} \)


What is the value of \( a \) in terms \( b, \) if \( \frac{a}{b}+ \) \( \frac{a+2}{3 b}=\frac{1}{4} ? \)
A. \( \frac{b+4}{2} \)
в. \( \frac{b-4}{2} \)
c. \( \frac{3 b-2}{4} \)
D. \( \frac{3 b+8}{16} \)
E \( \cdot \frac{3 b-8}{16} \)


Determine the osmotic pressure of a solution prepared by dissolving 2.5
\( \times 10^{-2} \) of \( K_{2} S O_{4} \) in \( 2 L \) of water at
\( 25^{\circ} \mathrm{C}, \) assuming that it is completely dissociated
\( \left(R=0.0821 \mathrm{L} \operatorname{atm} K^{-1} m o l e^{-1}, \) Molar \right.
\( \operatorname{mass} K_{2} S O_{4}=174 \mathrm{g} \operatorname{mol} e^{-1} \)


The number of permutations of the letters of the word "ENGINEERING" is
A \( \cdot \frac{11 !}{3 ! ! ! !} \)
в. \( \frac{11 !}{(3 ! 2 !)^{2}} \)
c. \( \frac{11 !}{(3 !)^{2} \cdot 2 !} \)
D. \( \frac{11 !}{3 !(2 !)^{2}} \)


(a) (i)'Two independent monochromatic sources of light cannot produce a sustained interference pattern'. Give
reason
(ii) Light wave each of amplitude "a" and frequency " \( \omega " \), emanating from two coherent light sources superpose at a point. If the displacements due to these
waves is given by \( y_{1}=a c o s \omega t \) and
\( \boldsymbol{y}_{2}=\boldsymbol{a} \cos (\boldsymbol{\omega} \boldsymbol{t}+\boldsymbol{\phi}) \) where \( \boldsymbol{\phi} \) is the phase
difference between the two, obtain the
expression for the resultant intensity at
the point.
(b) In Young's double slit experiment, using monochromatic light of wavelength \( \lambda \), the intensity of light at a point on the screen where path
difference is \( \lambda \), is Kunits. Find out the
intensity of light at a point where path difference is \( \lambda / 3 \)


Identify the property in the following
statements:
\( \mathbf{2}+(\mathbf{3}+\mathbf{4})=(\mathbf{2}+\mathbf{3})+\mathbf{4} \)


Which of the following is a thermoplastic?
A. Polyvinyl
B. Bakelite
c. Terylene
D. Neoprene


One mole of an ideal gas at \( 300 \mathrm{K} \) is
heated at constant volume \( \left(V_{1}\right) \) until its temperature is doubled, then it is
expanded isothermally till it reaches the original the pressure. Finally, the gas is cooled at the constant pressure till system reached to the half of original volume \( \left(\frac{V_{1}}{2}\right) . \) Determine the total work done \( (\boldsymbol{w}) \) in calories. [Use \( \boldsymbol{\operatorname { l n }} \mathbf{2}=\mathbf{0 . 7 0 , 0} \boldsymbol{R}=\mathbf{2} \mathbf{c a l} \mathbf{K}^{-\mathbf{1}} \boldsymbol{m o l}^{-1} \mathbf{j} \)


A magnet is taken towards a conducting ring in such a way that a constant current of \( 10 m A \) is induced in
it. The total resistance of the ring is
\( 0.5 \Omega . \ln 5 s, \) the magnetic flux through
the ring changes by
\( \mathbf{A} \cdot 0.25 m W b \)
B. \( 25 m \) Wb
\( \mathbf{c} .50 m W b \)
D. \( 15 \mathrm{m} \mathrm{Wb} \)


Uniform electric field \( 10 N / c \) exist in a space direction of electric field is
positive x-axis. Find force on following charges placed in this field.
(i) \( +2 \mu C \)
(ii) \( -2 \mu C \)


Assume that the decomposition of
\( H N O_{3} \) can be represented by the
following equation: \( 4 \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{\boldsymbol{3}}(\boldsymbol{g}) \rightleftharpoons \)
\( 4 N O_{2}(g)+2 H_{2} O(g)+O_{2}(g) \)
The reaction approaches equilibrium at \( 400 \mathrm{K} \) temperature and \( 30 \mathrm{atm} \) pressure. At equilibrium, the partial
pressure of \( H N O_{3} \) is 2 atm.
The value of \( \boldsymbol{K}_{c}\left((\boldsymbol{m o l} / \boldsymbol{L})^{3}\right) \) at \( 400 \mathrm{K} \) is:
(Use \( : \boldsymbol{R}=.08 a t \boldsymbol{m}-\boldsymbol{L} / \boldsymbol{m} \boldsymbol{o l} \boldsymbol{e}-\boldsymbol{K}) \)


On an open ground, a motorist follows a track that turns to his left by an angle of
\( 60^{\circ} \) after every \( 500 m . \) Starting from a given turn, specify the displacement of the motorist at the third, sixth and
eighth turn. Compare the magnitude of the displacement with the total path
length covered by the motorist in each
case.


Calculate the torque \( N \) twisting a stee tube of length \( l=3.0 m \) through an
angle \( \varphi=2.0^{\circ} \) about its axis, if the
inside and outside diameters of the
tube are equal to \( d_{1}=30 m m \) and
\( \boldsymbol{d}_{2}=\mathbf{5 0} \boldsymbol{m} \boldsymbol{m} \)


Rutherford's alpha Scattering
experiment showed that:
A. the atoms were smashed up by alpha particles
B. the atoms consisted or protons in a matrix of electrons
C. the nucleus was quite large and was positively charged
D. the nucleus was very small and positively charged


An element has dull appearance, low density and low melting point are :
A. metalloid
B. non-metal
c. metal
D. minerals