In a Young's double slit experiment D equals the distance of screen and dis
the separation between the slit. The distance of the nearest point to the
central maximum where the intensity is
same as that due to a single slit, is equal to:-
A. \( \frac{D \lambda}{d} \)
в. \( \frac{D \lambda}{2 d} \)
c. \( \frac{D \lambda}{3 d} \)
D. \( \frac{2 D \lambda}{d} \)


The lightest and the most abundant element in the universe is:
A . zinc
B. hydrogen
c. sodium
D. mercury


The value of diastolic blood pressure is
A. \( 120 \mathrm{mm} \) Hg
B. 80 mm Hg
c. \( 120 / 80 \mathrm{mm} \) нg
D. 40 \( \mathrm{mm} \) Hg


The planet, is called
morning or evening star.
A. Jupiter
B. Venus
c. Saturn
D. Earth


Balanced reaction \( : 2 \mathrm{MnO}_{4}^{-}+\mathrm{I}^{-}+\mathrm{H}_{2} \mathrm{O} \)
\( \rightarrow 2 \mathrm{MnO}_{2}+2 \mathrm{OH}^{-}+\mathrm{IO}_{3}^{-1} \)
If true enter 1 else 0
\( A \)


\( 1300 J \) of heat energy is supplied to
raise the temperature of \( 0.5 k g \) of lead
from \( 20^{\circ} \mathrm{C} \) to \( 40^{\circ} \mathrm{C} \). Calculate the
specific heat capacity of lead
A \( \cdot 130 J k g^{-1} K^{-1} \)
B . \( 260 J k g^{-1} K^{-1} \)
c. \( 650 J k g^{-1} K^{-1} \)
D. None of the above


Why is it difficult to hold a school bag having a strap made of thin and strong string?


\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}\left[(\boldsymbol{x}+\boldsymbol{a})\left(\boldsymbol{x}^{2}+\boldsymbol{a}^{2}\right)\left(\boldsymbol{x}^{4}+\boldsymbol{a}^{4}\right)\right]=? \)
\( ^{\mathbf{A} \cdot \frac{7 x^{8}+a\left(8 x^{7}-a^{7}\right)}{(x-a)^{2}}} \)
B. \( \frac{7 x^{8}-a\left(8 x^{7}-a^{7}\right)}{(x-a)^{2}} \)
c. \( \frac{7 x^{8}-a\left(8 x^{7}+a^{7}\right)}{(x-a)^{2}} \)
D. \( x^{4}+a^{4} \)


\( \frac{3 x-1}{\left(1-x+x^{2}\right)(2+x)}= \)
A \( \cdot \frac{x}{x^{2}-x+1}-\frac{1}{x+2} \)
в. \( \frac{x}{x^{2}-x+1}+\frac{1}{x+2} \)
c. \( \frac{x}{x^{2}+x+1}+\frac{2}{x+2} \)
D. \( \frac{x}{-x+1}-\frac{2}{x+2} \)


Why do two balloons come closer when
we blow in the space between them?
A. Greater pressure inside the balloons than the reduced pressure in between them drives the balloons towards one another.
B. Blowing air in between increases the pressure in between the balloons pulls them closer.
C. The gravitational force pulls the two balloons closer.
D. None of the above.


Enzymes that catalyse interconversion of optical, geometrical or positional isomers are called as
A . Ligases
B. Lyases
c. Hydrolases
D. Isomerases


If we add 1 to the numerator and
subtract 1 from the denominator a
fraction becomes \( 1 . \) It also becomes \( \frac{1}{2} \)
if we only add 1 to the denominator what
is the numerator of the fraction?
\( A \cdot 2 \)
B. 4
\( c \cdot 5 \)
D.


The floor of a rectangular hall has a
perimeter 250 m. If the cost of painting
the four walls at the rate of 10 per \( m^{2} \) is
15000, find the height of the hall (in
meters).


Light of wavelength \( \lambda \), strikes a photoelectric surface and electrons are ejected with an energy E. If E is to be increased to exactly twice its original
value, the wavelength changes to \( \lambda^{\prime} \)
where
A \( \cdot x^{\prime} \) is less than \( \frac{\lambda}{2} \)
B. \( \lambda^{\prime} \) is greater than \( \frac{\lambda}{2} \)
c. \( \lambda^{\prime} \) is greater than \( \frac{\lambda}{2} \) but less than \( \lambda \)
\( \lambda^{\prime} \lambda^{\prime} \) is exactly equal to \( \frac{\lambda}{2} \)


Which of the following is/are true regarding the following linear equation:
\( \boldsymbol{y}=\mathbf{2} \boldsymbol{x}+\mathbf{3} \)
A \( \cdot \) It passes through (3,0) and \( m=\frac{1}{2} \)
B. It passes through (3,0) and \( m=-2 \)
c. It passes through (0,3) and \( m=2 \)
D. It passes through
(0,3) and \( m=\frac{1}{2} \)


Consider the following statements.
I) Bohr's theory can also be used to
explain the spectra of \( \boldsymbol{H} \boldsymbol{e}^{+} \) ion
II) Energy of an electron in the first Bohr orbit of hydrogen atom is \( -13.6 \mathrm{eV} \)
III) Bohr's theory is only applicable to
hydrogen atom and not to any other species
IV) The energy of an electron in a hydrogen atom is quantized
The correct statements are:
A. ।, ॥।, IV
B. ॥, ॥ा
c. ॥, IV
D. I, II, III, IV


Explain Third law of thermodynamics.


Substance which vaporize during burning gives
A. sound
B. flame
c. combustion
D. none of these


The area under the curve \( y=2 \sqrt{x} \)
bounded by the lines \( x=0 \) and \( x=1 \) is
\( A \cdot \frac{4}{3} \)
B. \( \frac{2}{3} \)
c. 1
D.


Force is a scalar quantity. Is statement
true or false
A . True
B. False


Which of the following statements is
not true regarding molecular orbital
theory?
A. The atomic orbitals of comparable energies combine to form molecular orbitals
B. An atomic orbital is monocentric while a molecular
orbital is polycentric.
C. Bonding molecular orbital has higher energy than antibonding molecular orbital
D. Molecular orbitals like atomic orbitals obey Aufbau principle for filling of electrons.


Find the particular solution of the differential equation \( \log \left(\frac{d y}{d x}\right)=3 x+ \)
4 \( y \), given that \( y=0 \) when \( x=0 \)


The atomic mass of a hypothetical element \( X \) is 33.42 amu. \( A \) 27.22 \( g \) sample of \( X \) combines with 84.10 g of another hypothetical element Y to form the compound XY. The atomic mass of Y is:
A. 68.50 amu
B. 69.84 amu
c. 103.3 amu
D. 111.3 amu


In which case van't Hoff factor is
maximum (assuming no hydrolysis)?
A . \( K C l, \) 50\% ionised
B. \( K_{2} S O_{4}, 40 \% \) ionised
c. \( F e C l_{3}, \) 30\% ionised
D. \( S n C l_{4}, \) 20\% ionised


The saponification number of fat or oil
is defined as the number of \( m g \) of

KOH required to saponify 1 g oil or fat. A sample of peanut oil weighing \( 1.5763 g \) is added to \( 25 m L \) of
\( 0.421 M \) KOH.After saponification is
complete, \( 8.46 m L \) of \( 0.2732 M H_{2} S O_{4} \)
is needed to neutralize excess of \( K O H \)
What is the saponification number of
peanut oil?


If the total electrical power consumed when they are both connected to this
emf source in parallel is \( \boldsymbol{X} \boldsymbol{P}_{1}+\boldsymbol{Y} \boldsymbol{P}_{2} \)
Find out the value of \( X+Y \) ?


Evaluate the following determinant:
\( \left|\begin{array}{lll}\boldsymbol{a} & \boldsymbol{h} & \boldsymbol{g} \\ \boldsymbol{h} & \boldsymbol{b} & \boldsymbol{f} \\ \boldsymbol{g} & \boldsymbol{f} & \boldsymbol{c}\end{array}\right| \)


The heat energy required to raise the
temperature of of a
substance through is
called its specific heat capacity.
A. water, \( 10^{\circ} \mathrm{C} \)
B. hot, \( 10^{\circ} \mathrm{C} \)
C . one gram, \( 1^{\circ} \mathrm{C} \)
D. none of the above


Energy transfer from one trophic level to another is
A . 10\%
B. 5\%
c. 15\%
D. 20\%


Which of the following quantities is zero about the center of mass of a body.
A. Mass
B. Moment of mass
c. Acceleration
D. Angular acceleration


A cell drives a current through a circuit
The emf of the cell is equal to the work done in moving unit charge This question has multiple correct options
A. from the positive to the negative plate of the cell
B. from the positive plate, back to the positive plate
c. from the negative plate, back to the negative plate
D. from any point in the circuit back to the same point


Which of the following is a wrong
statement?
A \( . D=1 / f \) where \( f \) is the focal length and \( D \) is called the
refractive power of a lens
B. Power is expressed in a diopter when \( f \) is in metres
C. Power is expressed in diopter and does not depend on the system of unit used to measure \( f \)
D. D is positive for convergent lens and negative for divergent lens


The co-efficient of y in the expansion of
\( \left(y^{2}+c / y\right)^{5} \) is?
\( \mathbf{A} \cdot 10 c^{3} \)
B . \( 20 c^{2} \)
\( c \cdot 10 c \)
D. 20c


The equation of a stationary wave is
\( \boldsymbol{Y}=\mathbf{1 0} \sin \frac{\boldsymbol{\pi} \boldsymbol{x}}{\boldsymbol{4}} \cos 20 \boldsymbol{\pi} \boldsymbol{t} . \) The distance
between two consecutive nodes in
meters is -
\( A \cdot 4 \)
B. 2
\( c \cdot 5 \)
D. 8


In a \( \triangle A B C, \) the angles \( A \) and \( B \) are two
different values of \( \theta \) satisfying
\( \sqrt{\mathbf{3}} \cos \theta+\sin \theta=k,|k|<2 . \) The
triangle:
A. is an acute angled
B. is aright angled
c. is an obtuse angled
D. has one angle \( =\frac{\pi}{3} \)


Substances, which are added to soaps
change their properties in order to make them more useful for a particular application, are called
A. fillers
B. absorbant
C. reagent
D. none


A nuclear transformation is denoted by
\( X(n, \alpha) \rightarrow_{3} L i^{7} . \) The nucleus of element \( X \)
is
\( A \cdot_{6} C^{12} \)
B \( \cdot_{5} B^{10} \)
\( \mathbf{c} \cdot_{5} B^{9} \)
\( \mathbf{D} \cdot_{4} B e^{1} \)


The angular resolution of a \( 10 \mathrm{cm} \) diameter telescope at a wavelength of
\( 5000 A^{0} \) is of the order of
\( \mathbf{A} \cdot 10^{4} r a d \)
B \( \cdot 10^{-6} \mathrm{rad} \)
\( \mathbf{c} \cdot 10^{6} r a d \)
D. \( 10^{2} r a d \)


What is the resultant resistance of the
given circuit ?
A . \( 20 \Omega \)
B. \( 8 \Omega \)
\( \mathbf{c} .7 .2 \Omega \)
D. \( 12 \Omega \)


Which of the following statements is
incorrect for ethyl alcohol?
A. It is neutral to litmus.
B. It gives yellow crystalline precipitate with \( I_{2}+ \) dil. NaOH
C. It gives a product of fruity odour on reaction with \( C H_{3} C O O H \)
D. It gives turbidity spontaneously on the addition of Lucas reagent.


At \( t=0, \) when the magnetic field is
switched on tehe conducting rod is moved to the left at constant speed
\( 5 c m / s \) by some external means. At \( t= \)
\( 2 s, \) net induced emf has magnitude
A . \( 0.12 V \)
B. \( 0.08 V \)
c. \( 0.04 V \)
D. \( 0.02 V \)


Match the columns:
\( \begin{array}{ll}\text { । } & \text { II } \\ \text { 1. Mass } & \text { a. } m / s^{2} \\ \text { 2. Weight } & \text { b. kilogram } \\ \text { 3. Gravitational acceleration } & \text { c. } N m^{2} k g^{-2} \\ \text {4. Gravitational constant } & \text { d. Newton }\end{array} \)
A. \( 1-a, 2-b, 3-c, 4-d \)
B. \( 1-b, 2-a, 3-d, 4-c \)
c. \( 1-b, 2-d, 3-c, 4-a \)
D. \( 1-b, 2-d, 3-a, 4-c \)


Assertion
Butene can be converted into butane
Reason
The addition reaction of hydrogen gas to an alkene will form and alkane
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


If the sum of the roots of the quadratic
equation \( a x^{2}+b x+c=0 \) is equal to
the sum of the square of their reciprocals, then \( \frac{a}{c}, \frac{b}{a} \) and \( \frac{c}{b} \) are in
A . GP
в. нР
c. АGР
D. AP


The value of Henry's constant \( \boldsymbol{K}_{\boldsymbol{H}} \) is :
A. greater for gases with higher solubility
B. greater for gases with lower solubility
c. constant for all gases
D. not related to the solubility of gases


If the denominator of a fraction has
factors other then 2 and 5 , the decimal
expression
A. repeats
B. is that of a whole number
c. has equal numerator and denominator
D. terminates


Select the incorrect statement about
Nylon - \( 2- \) nylon - 6
A. It is a copolymer
B. It is biodegradable.
C . It is an alternating polyamide.
D. It is made up of \( C H_{3}-C_{N H_{2}} H-C O O H \) and \( H_{2} N\left(C H_{2}\right)_{5} C O O H \)


An ultrasonic wave is sent from a ship towards the bottom of the sea. It is
found that the time interval between the
sending and receiving of wave is 1.6 s. What is the depth of the sea, if the
velocity of sound in sea water is \( 1400 \mathrm{m} \)
\( s^{-1} ? \)
A. \( 1120 \mathrm{m} \)
B. 60 \( m \)
\( c .1400 \mathrm{m} \)
D. 112 m


Quick Lime can be obtained by:
A. adding hydrochloric acid to calciumm
B. heating limestone in a lime kiln
c. putting calcium in hot water
D. none of these


Which of the following statement(s)
is/are true?
This question has multiple correct options
A. A hole is an electric charge carrier with a positive charge, equal in magnitude but opposite in polarity to the charge on the electron
B. A hole is the absence of an electron in a particular place in an atom
C. A hole is an electric charge carrier with a negative charge
D. none of these


Arrange the following types of polymer in order of decreasing force of
attraction.
Fibres Elastomer
Thermoplastic
(1)
(II)
c. ॥>1>॥|
D. \|\|\( >\|>1 \)


Write the important structural and
functional differences between DNA and
RNA.


A sharp image of a distant object is obtained on a screen using a convex lens. In order
to determine the focal length of a lens, a student needs to measure the distance
between:
A. lens and the object
B. lens and the screen
c. object and the screen
D. lens and the screen and also object and the screen


The total volume of air accommodated
in the lungs at the end of forced inspiration is known as Total Capacity(TLC). TLC is equal to (where, TV= Tidal volume, IRV =
Inspiratory reserve volume, ERV Expiratory reserve volume, RV= Residual volume)
A . TLC = ERV+ IRV+TV
B. TLC= TV+RV+ERV
c. \( \mathrm{TLC}=\mathrm{ERV}+\mathrm{RV} \)
D. TLC = ERV+IRV+TV+RV


Match the following
Codes:
\[
P Q R S
\]
(A) 3412
\( \begin{array}{llll}\text { (B) } & 2 & 1 & 3 & 1\end{array} \)
\( (C) \quad 3142 \)
\( (D) \quad 4123 \)
(Species)
(Relation)


Assertion
Gauss theorem can be applied only for a
closed surface.
Reason
Electric flux can be obtained passing
from an open surface also.
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


With what type of source of light are cylindrical wave fronts associated?


Protonema state occurs in which of the
following Bryophytes?
A. Anthoceros
B. Rica
c. Funaria
D. Porella


Who is known as the father of organic chemistry?
A. Issac Newton
B. Galileo
c. Friedrich Wohler
D. Narendra Modi


Construct a triangle with sides \( 5 \mathrm{cm}, 6 \mathrm{cm} \) and \( 7 \mathrm{cm} \) and then another
triangle whose sides are \( \frac{7}{5} \) of the
corresponding sides of the first triangle.


Sulphur and oxygen are known to form two compounds. The sulphur content in one of these is \( 51 \% \) while in the other is
\( 41 \% \). Show that this data is in
agreement with the law of multiple proportions. Hint : Ratio of oxygen in oxides of sulphur is 2: 3


Hydrogen resembles IV-A elements in what respect?
A. All are metals.
B. All are non metals.
c. All are metalloid.
D. They have half-filled electronic configuration


on x-axis at \( (-a, 0) \) and \( (+a, 0) \)
respectively, as shown in Fig. They are
connected by a light string. A force F is applied at the origin along vertical direction. As a result, the masses move
towards each other without loosing
contact with ground. What is the
acceleration of each mass? Assuming
the instantaneous position of the masses as \( (-x, 0) \) and \( (x, 0) \)
respectively.
\( ^{\mathbf{A}} \cdot \frac{2 F}{m} \cdot \frac{\sqrt{a^{2}-x^{2}}}{x} \)
B. \( \frac{2 F}{m} \cdot \frac{x}{\sqrt{a^{2}-x^{2}}} \)
c. \( \frac{F}{2 m} \cdot \frac{x}{\sqrt{a^{2}-x^{2}}} \)
D. \( \frac{F}{m} \cdot \frac{x}{\sqrt{a^{2}-x^{2}}} \)


Which of the following is not a path function?
\( A \cdot \Delta Q \)
B. \( \Delta Q+\Delta \) W
\( c \cdot \Delta w \)
D. \( \Delta Q-\Delta w \)


If \( \bar{a} \) is collinear with \( \bar{b}=3 \bar{i}+6 \bar{j}+6 \bar{k} \)
and \( \bar{a} \cdot \bar{b}=27 . \) Then \( \bar{a} \) is equal to?
A \( .3(\bar{i}+\bar{j}+\bar{k}) \)
B . \( \bar{i}+3 \bar{j}+3 \bar{k} \)
c. \( \bar{i}+2 \bar{j}+2 \bar{k} \)
D. \( 2 \bar{i}+2 \bar{j}+2 \bar{k} \bar{k}+2+2+2+2+2 \bar{k}+2 \bar{i}+2 \bar{i} \bar{i} \)


According to the VB thoery the bonds formed in methane due to overlapping
are:
A. \( 1 \sigma s-s, 3 \sigma s-p \)
B. \( 1 \sigma s-p, 3 \sigma s-s \)
c. \( 2 \sigma s-s, 2 \sigma s-p \)
D. \( 4 \sigma s p^{3}-s \)


Draw a neat (labelled) diagram for the formation of image in a simple microscope.


If \( a>0, b>0, c>0 \) are respectively
the \( p^{t h}, q^{t h}, r^{t h} \) terms of a G.P., then the value of the deteminant \( \left|\begin{array}{lll}\log \boldsymbol{a} & \boldsymbol{p} & 1 \\ \log \boldsymbol{b} & \boldsymbol{q} & 1 \\ \log \boldsymbol{c} & \boldsymbol{r} & 1\end{array}\right| \) is
A . 1
B. 0
\( c \cdot-1 \)
D. None of these


State true or false:
The differential coefficient of \( \boldsymbol{f}(\log \boldsymbol{x}) \) w.r.t. \( \log x \) where \( f(x)=\log x \) is \( \frac{1}{\log x} \)
A. True
B. False


Two parallel sides of a trapezium are \( 60 \mathrm{cm} \) and \( 77 \mathrm{cm} \) and the other two sides
are \( 15 \mathrm{cm} \) and \( 26 \mathrm{cm} \). Find the area of the
trapezium.


The roots of the equation \( x^{\sqrt{x}}=(\sqrt{x})^{x} \)
are
A. 0 and 1
B. 0 and 4
c. 1 and 4
D. 0,1 and 4


A light bulb is rated at \( 100 W \) for a
\( 220 V \) supply. Find the peak voltage of
the source:
A. \( 111 V \)
в. \( 211 V \)
\( \mathbf{c} \cdot 311 V \)
D. \( 411 V \)


The equation \( \boldsymbol{y}= \) \( 5 \sin (3 x / 50) \cos (450 t) \) represents the
stationary wave setup in a vibrating sonometer wire, where \( x, y \) are in \( c m \) and \( t \) in second. The velocity of
one of the two progressive waves in that stationary wave is
A. \( 2.7 m s-1 \)
B. \( 27 m s^{-1} \)
c. \( 7.5 m s^{-1} \)
D. \( 75 \mathrm{ms}^{-1} \)


For a first order reaction \( t_{0.75} \) is
138.6 sec. Its specific rate constant is
\( \left(\operatorname{in} s^{-1}\right) \)
A \( \cdot 10^{-2} \)
- \( ^{-2} \)
B . \( 10^{-6} \)
\( \mathrm{c} \cdot 10^{-4} \)
D. \( 10^{-5} \)


\( \lim _{x \rightarrow 0^{-}} \frac{3 \sin \left(2 x^{2}\right)}{x^{2}}=A \)
then the value of \( \boldsymbol{A} \) is
A . 2
B. 4
\( c \cdot 6 \)
D. 8


Assertion
Warming a room by a heat blower is an example of forced convection.
Reason
Natural convection takes place due to gravity
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


Discuss the various forms of bacteria.


On a hot summer day cooling of the
plant occurs due to
A. Loss of water vapours from leaf
B. Transport of water in plant
c. Loss of liquid water
D. Loss of water from entire plant


The number of ways in which we can
select 5 letters of the word
INTERNATIONAL is equal to
A .200
в. 220
\( c \cdot 242 \)
D. 256


A force \( \overrightarrow{\boldsymbol{F}}=4 \hat{\boldsymbol{i}}-5 \hat{\boldsymbol{j}}+\boldsymbol{3} \hat{\boldsymbol{k}} \) is acting at a
point \( \vec{r}_{1}=\hat{i}-2 \hat{j}+3 \hat{k} . \) Find the torque acting about a point \( \vec{r}_{2}=3 \hat{i}-2 \hat{j}-3 \hat{k} \)


If \( \log _{10}\left(x^{3}+y^{3}\right) \)
\( \log _{10}\left(x^{2}+y^{2}-x y\right) \leq 2, \) then the
maximum value of \( x y, \) for all \( x \geq \)
\( \mathbf{0}, \boldsymbol{y} \geq \mathbf{0}, \) is
A . 2500
в. 3000
c. 1200
D. 3500


The kinetic energy of one mole of
hydrogen gas at \( 127^{\circ} \mathrm{C} \) in cal / mol is
A . 30
B. 600
c. 900
D. 1200


A body starts moving with an initial velocity of \( 5 m s^{-1} \) and an acceleration
of \( 1 m s^{-2} . \) The distance travelled by it in
the 5 th second is
\( \mathbf{A} \cdot 9.5 \mathrm{m} \)
B. \( 22.5 \mathrm{m} \)
c. \( 50 \mathrm{cm} \)
D. \( 10 \mathrm{cm} \)


A conducting disc of radius R is rotating with angular velocity \( \omega . \) Mass of electron is and charged e. If electrons are the
current carries in a conductor, the
potential difference between the center and the edge of the disc is:
\( ^{A} \cdot \frac{m \omega^{2} R^{2}}{e} \)
B. \( \frac{m \omega^{2} R^{2}}{4 e} \)
c. \( \frac{m \omega^{2} R^{2}}{3 e} \)
D. \( \frac{m \omega^{2} R^{2}}{2 e} \)


According to Joule's law, if the potential difference across a conductor of
resistivity \( \rho \) remains constant, then the
heat produced in the conductor is
proprotional to
\( A \cdot \frac{1}{\rho} \)
в. \( \frac{1}{\sqrt{\rho}} \)
\( \mathbf{c} \cdot \rho^{2} \)
D.


Resistivity of a given conductor depends upon
A. temperature
B. length of conductor
c. area of cross section
D. shape of the conductor


How does the energy gap of an intrinsic semiconductor vary, when doped with a trivalent impurity?


\( \boldsymbol{L}=\lim _{\boldsymbol{x} \rightarrow 2} \frac{\boldsymbol{x}^{4}-\boldsymbol{8} \boldsymbol{x}}{\sqrt{\boldsymbol{x}^{2}+\mathbf{2 1}-\mathbf{5}}} \)


Non - biodegradable substances are the one which
A. Do not degrade
B. Degrades efficiently
c. Degrades very slowly
D. Remains unharmed


The pulleys and strings shown in the fig are smooth and of negligible mass. For the system to remain in equilibrium,
the angle \( \theta \) should be:
\( A \cdot 0^{\circ} \)
B. \( 30^{\circ} \)
\( c \cdot 45^{\circ} \)
D. \( 60^{\circ} \)


An atom has \( x \) energy level, then total
number lines in its spectrum are?
A \( .1+2+3 \ldots .(x+1) \)
B. \( 1+2+3 \ldots\left(x^{2}\right) \)
c. \( 1+2+3 \ldots .(x-1) \)
D. \( (x+1)(x+2)(x+4) \)


Round dance of bee indicates
A. Courtship
B. Arrival of queen
c. Location of flowers
D. Location of predator


Heat capacity is
This question has multiple correct options
A. amount of heat energy taken per degree decrease in temperature
B. amount of heat energy supplied per degree rise in temperature
C. heat energy supplied per time taken
D. all of the above


In the arrangement shown in figure
when the switch \( S_{2} \) is open, the
galvanometer shows no deflection for
\( l=L / 2 . \) When the switch \( S_{2} \) is closed,
the galvanometer shows no deflection
for \( l=5 L / 12 . \) The internal resistance
\( (r) \) of \( 6 \mathrm{V} \) cell, and the emf \( E \) of the other
battery are respectively
\( A \cdot 3 \Omega, 8 V \)
B. \( 2 \Omega, 12 V \)
c. \( 2 \Omega, 24 V \)
D. \( 3 \Omega, 12 V \)


toppr
Q Type your question
structure is:
\( A \)
\( B \)
\( c \)
\( D \)


Write Kirchhoff's first rule. A battery of
\( \mathbf{1 0} \boldsymbol{V} \) and negligible internal resistance is connected to the diagonally opposite corners of a cubical network consisting
of 12 resistors each of resistance \( 2 \Omega \)
Determine the equivalent resistance of the network.


When a substance A reacts with water, it
produces a combustible gas \( \mathrm{B} \) and a solution of substance \( C \) in water. D reacts
with this solution of \( \mathrm{C} \) and produces the
same gas B on warming. D can also
produce gas \( \mathrm{B} \) on reaction with dilute
\( H_{2} S O_{4} . \) A imparts a deep golden yellow colour to smokeless flame. \( A, B, C \) and \( D \)
respectively are:
\( \mathbf{A} \cdot N a, H_{2}, N a O H, Z n \)
B . \( K, H_{2}, K O H, A l \)
\( \mathbf{c} \cdot_{C a}, H_{2}, C a(O H)_{2}, S n \)
D \( \cdot \operatorname{caC}_{2}, C_{2} H_{2}, C a(O H)_{2}, F e \)


The equation of a line is \( 3 x+2 y+1= \)
0. Find its slope and y-intercept.


For the following reaction, select the
statement that best describes the
change.
\( \boldsymbol{R} \boldsymbol{C H}_{2} \boldsymbol{O H}+ \)
\( \boldsymbol{P C C} \quad\left[\boldsymbol{C _ { 5 }} \boldsymbol{H}_{5} \boldsymbol{N} \boldsymbol{H}^{+} \boldsymbol{C l} \boldsymbol{C r} \boldsymbol{O}_{3}^{-}\right] \longrightarrow \)
A. The alcohol is oxidized to an acid, and the \( C r(V I) \) is reduced
B. The alcohol is oxidized to an aldehyde, and the \( C r(V I) \) is reduced
c. The alcohol is reduced to an aldehyde, and the \( \operatorname{Cr}(I I I) \) is oxidized
D. The alcohol is oxidized to a keton, and the \( C r(V I) \) is reduced


on the P-T phase diagram of carbon
dioxide:
(a) At what temperature and pressure can the solid, liquid and vapour phases
of \( C O_{2} \) co-exits in equilibrium?
(b) What is the effect of decrease of
pressure on the fusion and boiling point
of \( \boldsymbol{C} \boldsymbol{O}_{2} ? \)
(c) What are the critical temperature
and pressure for \( C O_{2} \) ? what is their
significance ?
(d) Is \( C O_{2} \) solid, liquid or gas at \( (a) \)
\( -70^{\circ} \mathrm{C} \) under 1 atm, \( (\mathrm{b})-60^{\circ} \mathrm{C} \) under 10
\( \operatorname{atm},(c) 15^{\circ} C \) under 56 atm \( ? \)


Which represents one mole?
This question has multiple correct options
\( \mathbf{A} \cdot 22.4 L H e \) at \( S T P \)
\( \mathbf{B} \cdot 16 g O_{2} \)
\( \mathbf{c} \cdot 158 g K M n O_{4} \)
D. \( 392 g \) FeSO\( _{4} \cdot\left(N H_{4}\right)_{2} S O_{4} \cdot 6 H_{2} O \)


Give the IUPAC name of the given
compounds:
\[
\begin{array}{c}
\mathrm{CH}_{3} \\
\mathrm{CH}_{3}-\mathrm{CH}_{2}-\mathrm{CH}-\mathrm{CH}-\mathrm{CH}_{2}-\mathrm{CH}_{2}-\mathrm{CH}_{3} \\
\\
\mathrm{CH}-\mathrm{CH}_{2}-\mathrm{CH}_{3} \\
\mathrm{CH}_{3}
\end{array}
\]


Name the process associated with the
following. Dry ice is kept at room temperature and at one atmospheric pressure.
A. Evaporation
B. Sublimation
c. condensation
D. Liquefaction


In the given figure, the straight line \( A B \)
and \( \mathrm{CD} \) are parallel to each other. If
angle \( \boldsymbol{p}=\mathbf{5 5}^{\circ}, \) and, \( \boldsymbol{q}=\mathbf{4 3}^{\boldsymbol{o}} \) then
answer the given questions. Find the
value \( x \)
\( \mathbf{A} \cdot 55^{\circ} \)
B. \( 82^{\circ} \)
\( \mathbf{c} \cdot 98^{\circ} \)
D. \( 108^{\circ} \)


The IUPAC name of the structure is:
A. 5 -Amino-3-bromo-5-methyl-6-nitroundec-3-en-2-ol
B. 9-Amino-3-bromo-7-methyl-4-nitroundec-2-en-2-ol
C. 10 -Amino-8-bromo-7-methyl-6-nitroundec-4-en-2-ol
D. 2-Amino-6-bromo-5-methyl-4-nitroundec-2-en-2-ol


(a) Explain Newton's first law of motion with an example.
(b) \( F=\frac{G m_{1} m_{2}}{d^{2}} \) is the mathematical
form of Newton's law of gravitation. Give the statement of Newton's law of
gravitation.


Which of the following coenzyme is a derivative of pantothenic acid (Vitamin
B complex)?
A. NAD
B. NADP
c. FAD
D. coA


The cells are joined in parallel to get the
maximum current when
A. External resistance is very large as compared to the total internal resistance
B. Internal resistance is very large as compared to the external resistance
C. Internal resistance and external resistance are equal
D. Emf of each cell is very large


A body of mass m moving at a constant velocity v hits another body of the same mass moving with a velocity v/2 but in the opposite direction and sticks to it. The common velocity after collision is
\( A \)
B. v/
c. \( 2 v \)
D. v/2


Two beams, \( A \) and \( B \), of plane polarized light with mutually perpendicular planes of polarization are seen through a polaroid. From the position when the beam A has maximum intensity (and beam B has zero intensity), a rotation of
Polaroid through \( 30^{\circ} \) makes the two
beams appear equally bright. If the initial intensities of the two beams are
\( \boldsymbol{I}_{A} \) and \( \boldsymbol{I}_{B} \) respectively, then \( \boldsymbol{I}_{\boldsymbol{A}} / \boldsymbol{I}_{\boldsymbol{B}} \)
equals:
A . \( I \)
B. \( I / 3 \)
\( c \cdot 3 \)
D. \( 3 / 2 \)


The gases \( (\mathrm{B}),(\mathrm{C}) \) and \( (\mathrm{D}), \) respectively
are:
A. \( H C \equiv C H, C O_{2} \) and \( H_{2} \)
B. \( H C \equiv C H, H_{2} \) and \( C O_{2} \)
c. \( C H_{3}-C \equiv C-C H_{3}, C O_{2} \) and \( H_{2} \)
D. \( C H_{3}-C \equiv C-H, H_{2} \) and \( C O_{2} \)


In the diagram of T.S. of stele of a dicot
root, the different parts have been indicated by alphabets; choose the answer in which these alphabets correctly match with the parts
they indicate.
A. A- Endodermis, B-Conjunctive tissue, C- Metaxylem,
D- Protoxylem, E- Phloem, F- Pith
B. A- Endodermis, B- Pith, C- Protoxylem, D- Metaxylem,
E- Protoxylem, F- conjunctive tissue
C. A-Pericycle, B-Conjunctive tissue, C- Metaxylem, DProtoxylem, E- Phloem
D. A- Endodermis, B- conjunctive tissue, C- Protoxylem,
D- Metaxylem, E- Phloem, F- Pith


Atomic number of an element is 16 .
What is the nature of the element?
A . Alkali metal
B. Transition metal
c. Non metal
D. Halogen


Choose the fraction which is equivalent
to \( \frac{15}{20} \)
A \( \cdot \frac{12}{15} \)
B. \( \frac{51}{12} \)
\( c \cdot \frac{4}{3} \)
D. \( \frac{12}{16} \)


Which of the following compounds has a zero dipole moment?
A. 1,1 - Dichloroethylene
B. cis-1,2-Dichloroethylene
c. trans- 1,2 - Dichloroethylene
D. None of the above


Which of the following statement is not true about covalent compounds?
A. They may exhibit space isomerism
B. They have low melting and boiling points
c. They show ionic reactions
D. They show molecular reactions


Which of the following are correct in
respect of the system of equations \( \boldsymbol{x}+ \)
\( \boldsymbol{y}+\boldsymbol{z}=\mathbf{8}, \boldsymbol{x}-\boldsymbol{y}+\mathbf{2} \boldsymbol{z}=\boldsymbol{6} \) and \( \boldsymbol{3} \boldsymbol{x}- \)
\( \boldsymbol{y}+\mathbf{5} \boldsymbol{z}=\boldsymbol{k} ? \)
1. They have no solution, if \( k=15 \)
2. They have infinitely many solutions, if
\( k=20 \)
3. They have unique solution, if \( k=25 \)
Select the correct answer using the code given below
\( A \cdot 1 \) and 2 only
B. 2 and 3 only
C. 1 and 3 only
D. 1,2 and 3


Two rail tracks are \( 1 m \) apart and insulated from each other and
insulated from ground. A milli-voltmeter is connected across the rail-tracks.
When a train travelling at \( 180 \mathrm{km} / \mathrm{h} \)
passes through what will be the reading in milli-voltmeter? Given : horizontal
component of earth's field \( \sqrt{3} \times 10^{-4} T \)
and dip at the place \( 60^{\circ} \)
A. \( 1.5 \mathrm{mV} \)
B. \( 15 \mathrm{mV} \)
c. \( \frac{15}{\sqrt{3}} m V \)
D. \( \frac{1.5}{\sqrt{3}} m V \)


Solubility of \( N a C l \) in \( D_{2} O, \) compared
with its solubility in \( H_{2} O \) is:
A . less
B. equal
c. more
D. cannot be predicted


If \( 27 \times 3=243 \) and \( 5 \times 4=80 \)
Then the value of \( 3 \times 7 \) is
A . 84
B. 147
\( c \cdot 63 \)
D. 23


The A.M. of \( 1,3,5, \dots,(2 n-1) \) is-
\( \mathbf{A} \cdot n+1 \)
B. \( n+2 \)
\( c \cdot n^{2} \)
D.


Assertion: A current carrying wire
should be charged.
Reason: The current in a wire is due to
flow of free electrons in a definite
direction.
A. Both (A) and (R) are true and
(R) is the correct explanation of A
B. Both (A) and (R) are true but (R) is not the correct explanation of A
c. (A) is true but (R) is false
D. (A) is false but (R) is true


Write the structures of two chair
conformations of 1-tert-butyl-2methylcyclohexane. Which
conformation is more stable? Explain
your answer.


Glisson's capsule is associated with
A. Liver
B. Pancreas
c. Lungs
D. Kidney
E. Adernal glands


What is the distinction between a
relation and function and when do you call a relation reflexive, symmetric and transitive?


\( A: A \) mixture of raw rubber and sulphur on heating at \( 373 K-415 K \)
gives vulcanised rubber
\( \mathrm{R}: \mathrm{ZnO} \) decreases the rate of
vulcanisation of rubber.
A. both A and R are correct and R is the correct explanation of the A
B. both A and R are correct but R is not the correct explanation of the \( A \)
C. A is correct but R is incorrect
D. A is incorrect but R is correct


\( ^{87} \) Rb undergoes \( \beta \) -decay \( \left(t_{1 / 2}=4.7 \times\right. \) \( \left.10^{10} \text { year }\right) \) to form \( ^{87} \) Sr. An analysis of
the rock sample shows relative number of \( ^{87} \mathrm{Sr} \) and \( ^{87} \) Rb atoms \( 0.052: 1 . \) If all
the \( ^{87} \mathrm{Sr} \) is formed from \( \beta \) -decay of \( ^{87} \mathrm{Rb} \)
The age of the rock is :
A . \( \left[2.21 \times 10^{9} \text { year }\right] \)
B . \( \left[3.43 \times 10^{9} \text { year }\right] \)
C . \( \left[4.13 \times 10^{9} \text { year }\right] \)
D. none of these


From the table, find the median class
for the following data.
\begin{tabular}{|c|c|c|c|}
\hline\( x \) & \( f \) & Class Boundaries & c.f \\
\hline \( 8-10 \) & 2 & \( 7.5-10.5 \) & 2 \\
\( 11-13 \) & 4 & \( 10.5-13.5 \) & 6 \\
\( 14-16 \) & 6 & \( 13.5-16.5 \) & 12 \\
\( 17-19 \) & 4 & \( 16.5-19.5 \) & 16 \\
\( 20-22 \) & 3 & \( 19.5-22.5 \) & 19 \\
\( 23-25 \) & 1 & \( 22.5-25.5 \) & 20 \\
\hline & 20 & & \\
\hline
\end{tabular}
A . \( 13.5-16.5 \)
B . \( 12.5-13.5 \)
c. \( 10.5-14.5 \)
D. \( 12.5-10.5 \)


The electric potential due to a small electric dipole at a large distance \( r \)
from the centre of the dipole is
proportional to :
\( A \)
B. 1 /
c. \( 1 / r^{2} \)
D. \( 1 / r^{3} \)


In which crystal system, the length of each stage (edge length) is same?
A \( . \) BaSO \( _{4} \)
в. Нg S
\( c \cdot \operatorname{cas} O_{4} \)
D. \( Z n O \)


From the following equations, pick out
the possible nuclear fusion reaction
This question has multiple correct options
\( \mathbf{A} \cdot_{6} C^{13}+_{1} H^{1} \rightarrow_{6} C^{14}+4.3 M e V \)
\( \mathbf{B} \cdot_{6} C^{12}+_{1} H^{1} \rightarrow_{7} C^{13}+2 M e V \)
\( \mathbf{C} \cdot_{7} C^{14}+_{1} H^{1} \rightarrow_{8} O^{15}+7.3 M e V \)
\( \mathbf{D} \cdot_{92} U^{235}+_{0} n^{1} \rightarrow_{54} X e^{104}+_{38} X r^{94}+_{0} n^{1}+_{0} n^{1}+y+ \)
\( 200 M e V \)


Which of the following statements
regarding hydrogen peroxide is/are incorrect?
This question has multiple correct options
A. The two hydroxy groups in hydrogen peroxide lie in the same plane
B. Aqueous solution of \( H_{2} O_{2} \) turns blue litmus red
C. When \( H_{2} O_{2} \) behaves as a reducing agent, the \( O-O \)
bond in its molecules is not broken down
D. Aqueous solution of \( H_{2} O_{2} \) is stored in plastic bottles and some urea, phosphoric acid or glycerol is added to that solution


A, \( \mathrm{B}, \mathrm{C} \) are three elements with atomic numbers, Z-1, Z, and Z+1 respectively. B is an inert gas.
Identify the group to which \( A \) and \( C \) belong.
A. Alkali metal, Alkaline earth metal
B. Halogen, Alkali metal
c. Inert gas, Alkali metal
D. Halogens, Inert gas


How does the amount of work needed to
move this charge compare for these
three cases?
A. Most work required in
B. Most work required in II
C. Most work required in III
D. I and II required the same amount of work but less than III
E. All three would require the same amount of work


The function \( \boldsymbol{f}(\boldsymbol{x})=\int_{0}^{x} \boldsymbol{e}^{-\boldsymbol{x}^{2} / 2}\left(\boldsymbol{x}^{2}-\right. \)
\( 3 x+2) d x \) is maximum at \( x= \)
\( A \)
B. 2
\( c \cdot 3 \)
D. 4


\( \boldsymbol{p}: \) He is hard working.
\( \boldsymbol{q}: \) He will win
The symbolic form of "He is hard working then he will win", is
A \( . p \vee q \)
в. \( p \wedge q \)
\( \mathbf{c} \cdot p \Rightarrow q \)
D. \( q \Rightarrow p \)


The angle made by orbital angular momentum of electron with the
direction of the orbital magnetic
moment is?
A \( \cdot 120^{\circ} \)
B. \( 60^{\circ} \)
\( c \cdot 180^{\circ} \)
D. \( 90^{\circ} \)


Detergents are better than soaps
because:
A. they wash clothes better
B. they absorb the hardness of water
C. they are less affected by hard water
D. they are less soapy


Find the volume of the recycled material
used in making the solid as shown in
figure. It is given that diameter of
cylinder is \( 20 \mathrm{cm} \) and diameter of each of two equal conical cavity is \( 10 \mathrm{cm} \)
What values are reflected by using recycled material?


Among the following statements which is/are incorrect?
A. In the preparation of compounds of \( X e \), Bartlett had \( \operatorname{taken} O_{2} P t F_{6} \) as a base compound because both \( O_{2} \)
and \( X e \) have almost same ionisation enthalpy
B. Nitrogen does not show allotropy
C. A brown ring is formed in the ring test for \( N O_{3}^{-} \) ion. It is due to the formation of \( \left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{5}(\mathrm{NO})\right]^{2+} \)
D. On heating white phosphorous with concentrated \( N a O H \) solution in an inert atmosphere of \( C O_{2}, P H_{3} \)
gas is formed


A cylinder contains \( 10 \mathrm{kg} \) of \( \operatorname{gas} \) at \( \mathrm{a} \) pressure of \( 10^{7} \mathrm{N} \boldsymbol{m}^{-2} . \) The quantity of
gas taken out of the cylinder, if final pressure is \( 2.5 \times 10^{6} \mathrm{N} m^{-2} \) is?
A. \( 9.5 \mathrm{kg} \)
B. \( 7.5 \mathrm{kg} \)
c. \( 14.2 \mathrm{kg} \)
D. zero


\( \boldsymbol{x}=\mathbf{0}, \boldsymbol{y}=\mathbf{0}, \boldsymbol{z}=+\mathbf{0 . 5 0 0 m} \)


Which of the following species formed by homolytic bond fission?
A. carbocation
B. carbanion
c. free radical
D. none of these


Which non-metal has semi-conductor
property?
A. Boron
B. Carbon
c. silicon
D. Magnesium


A black precipitate is formed when lead
acetate solution is added to acidified
sodium extract of an organic compound containing sulphur
A. True
B. False


If the latusrectum of an ellipse is equal to half of minor axis, find its
eccentricity.


If \( \boldsymbol{a}=\boldsymbol{i}+\boldsymbol{j}+\boldsymbol{k}, \boldsymbol{b}=\boldsymbol{i}+\boldsymbol{3} \boldsymbol{j}+\mathbf{5} \boldsymbol{k} \) and
\( c=7 i+9 j+11 k, \) then the area
of Parallelogram having diagonals \( a+b \) and \( b+c \) is.
A. \( 4 \sqrt{6} \) sq. units
B . \( \frac{1}{2} \sqrt{21} \) sq. units
c. \( \frac{\sqrt{6}}{2} \) sq.units
D. \( \sqrt{6} \) sq. units


Find the expression equivalent to \( \frac{1}{2} y^{2}(6 x+2 y+12 x-2 y) \)
A \( \cdot 9 x y^{2} \)
\( \begin{array}{ll}2 & 2 \\ 2 & 2\end{array} \)
в. \( 18 x y \)
c. \( 3 x y^{2}+12 x \)
D. \( 9 x y^{2}-2 y^{3} \)
E \( .3 x y^{2}+12 x-y^{3}-2 y \)


Prove by mathematical induction,
\( \mathbf{1}^{2}+\mathbf{2}^{2}+\mathbf{3}^{2}+\ldots+\boldsymbol{n}^{2}= \)
\( \frac{\boldsymbol{n}(\boldsymbol{n}+\mathbf{1})(\boldsymbol{2} \boldsymbol{n}+\mathbf{1})}{\boldsymbol{6}} \)


Compute the tension in the wire.


The number of people living per is known as density of population.
A. square metre
B. square kilometre
c. square hectare
D. square feet


Antacids are
A. acidic
B. basic
c. salt
D. ionic


A block is suspended by an ideal spring of force constant k. If the block is pulled
down by applying a constant force \( F \) and if maximum displacement of the block from its initial position of rest is \( \delta, \) then
A \( \cdot \frac{F}{k}<\delta>\frac{2 F}{k} \)
B . \( \delta \frac{2 F}{k} \)
c. work done by force F is equal to \( F \delta \)
D. Increase in energy stored in the spring is \( \frac{1}{2} k \delta^{2} \)


The equation of the tangent to the curve \( y=x+\frac{4}{x^{2}}, \) that is parallel to the \( x- \)
axis, is
\( \mathbf{A} \cdot \mathbf{y}=1 \)
В. \( \mathrm{y}=2 \)
\( \mathbf{c} \cdot \mathbf{y}=3 \)
D. \( \mathrm{y}=0 \)


An electron is projected into a magnetic
field along the lines of force. Then
A. there will be no effect on its motion
B. the electron will travel along a circle and its speed remains unchanged
C. the electron will follow the path of a parabola and its speed will increase
D. the velocity will increase in magnitude but its direction will remain unchanged.


Suppose a pure Si crystal has \( 5 \times 10^{28} \)
atoms \( m^{-3} . \) it is doped by 1 ppm
concentration of pentavalent As. Calculate the number of electrons and
holes. Given that \( n_{1}=1.5 \times 10^{16} m^{-3} \)


According to Lewis concept, acid is:
A. proton donor
B. electron pair donor
C . electron pair acceptor
D. proton acceptor


Identify the first component of an ordered pair \( (\mathbf{0},-\mathbf{1}) \)
\( \mathbf{A} \cdot \mathbf{0} \)
B. -
\( c \cdot 2 \)
\( D \)


The coercivity of a small magnet where the ferromagnet gets demagnetized is
\( 3 \times 10^{3} A m^{-1} . \) The current required to
be passed in a solenoid of length \( 10 \mathrm{cm} \)
and number of turns \( 100, \) so that the magnet gets demagnetized when inside the solenoid, is:
\( A \cdot 3 A \)
в. \( 6 A \)
\( c .30 m A \)
D. \( 60 \mathrm{mA} \)


In Hatch and Slack pathway the
A. Chloroplasts are of same type
B. Occurs in Kranz anatomy, where mesophyll cells have small chloroplasts whereas bundle sheath cells have agranal chloroplasts
C. Occurs in Kranz anatomy, where mesophyll cells have small chloroplasts whereas bundle sheath cells have larger chloroplasts
D. Kranz anatomy, where mesophyll cells are diffused


For preparing a buffer solution of \( \boldsymbol{p} \boldsymbol{H}= \)
7.0, which buffer system you will choose:
A \( \cdot H_{3} P O_{4}, H_{2} P O_{4}^{-} \)
B . \( H_{2} P O_{4}^{-}, H P O_{4}^{2} \)
\( \mathbf{c} \cdot H P O_{4}^{2-}, P O_{4}^{3} \)
D. \( H_{3} P O_{4}, P O_{4}^{3-} \)


The distance between electron and
proton in the H-atom is about 5.3
\( \times 10^{-11} \) metre. What is the magnitude
of electric force between these two
particles? \( \left(\frac{1}{4 \pi \varepsilon_{0}}=9 \times 10^{9} \frac{N m^{2}}{C^{2}}\right) \)


4 normal distinguishable dice are rolled once. The number of possible outcomes in which at least one dice shows up 2?
A . 216
B. 648
c. 625
D. 67


Evaluate:
\( \lim _{x \rightarrow a} \frac{\sqrt{x}-\sqrt{a}}{x-a} \)


If \( y=\left(\sin ^{-1} x\right)^{2}, \) then prove that \( (1- \)
\( \left.x^{2}\right) \frac{d^{2} y}{d x^{2}}-x \frac{d y}{d x}=2 \)


What is the current of \( I_{2} ? \)


Gibberellin stimulates flowering in
A. The plants growing in Japanese farms
B. The short day plants
c. The long day plants
D. Day neutral plants


Which one is found in free state?
A . \( I \)
B. \( S \)
c. \( U r \)
D. \( A g \)


Select the option having correct
matching for different parts of male reproductive system of cockroach.
A . A-Phallic gland, B-Seminal vesicle, C-Vas deferens, DEjaculatory duct
B. A-Phallic gland, B-Seminal vesicle, C-Ejaculatory duct D-vas deferens
c. A-seminal vesicle, B-Phallic gland, C-Vas deferens, DEjaculatory duct
D. A-Phallic gland, B-Vas deferens, C-Seminal vesicle, DEjaculatory duct


Organic compounds are nonconductors of electricity State True or false.
A. True
B. False


A motion which repeats itself after a fixed interval of time is called
motion
A. periodic
B. linear
c. oscillatory
D. curvilinear


Solve \( \left|\begin{array}{ccc}\mathbf{1} & \mathbf{1} & \mathbf{1} \\ \boldsymbol{a} & \boldsymbol{b} & \boldsymbol{c} \\ \boldsymbol{a}^{\mathbf{3}} & \boldsymbol{b}^{\mathbf{3}} & \boldsymbol{c}^{\mathbf{3}}\end{array}\right|= \)
\( (\boldsymbol{a}-\boldsymbol{b})(\boldsymbol{b}-\boldsymbol{c})(\boldsymbol{c}-\boldsymbol{a})(\boldsymbol{a}+\boldsymbol{b}+\boldsymbol{c}) \)


Balance the following equation by ion electron method.
\( M n O_{4}^{-}+H^{+}+H_{2} O_{2} \rightarrow M n^{2+}+ \)
\( \boldsymbol{H}_{2} \boldsymbol{O}+\boldsymbol{O}_{2} \)


Name the physical quantity of which the unit is coulomb:
A. capacitance
B. charge
c. current
D. inductance


is present around the
magnet.


A thief is running away on a straight road with a speed of \( 9 m s^{-1} . \) A police man chases him on a jeep moving at a speed of \( 10 \mathrm{ms}^{-1} \) If the instantaneous
separation of the jeep from the motorcycle is \( 100 \mathrm{m}, \) how long will it take. for the police man to catch the thief?
A . 1 s
B. \( 19 s \)
\( c \cdot 90 s \)
D. 100 s


The percentage of s- character of the hybrid orbitals in ethane, ethene and ethyne are respectively:
A. 50,75,100
В. 10,20,40
\( \mathbf{c} \cdot 25,33,50 \)
D. 25,50,75


Why was corpuscular theory of light discarded?


Which of the following statements is
wrong for gases?
A. Gases do not have a definite shape and volume
B. Volume of the gas is equal to volume of container confining the gas
C. Confined gas exerts uniform pressure on the walls of its container in all directions
D. Mass of gas cannot be determined by weighing a container in which it is enclosed


Three coins are tossed describe
(i) Two events which are mutually exclusive
(ii) Three events which are mutually exclusive and exhaustive
(iii) Two events which are not mutually
exclusive
(iv) Two events which are mutually exclusive but not exhaustive
(v) Three events which are mutually exclusive but not exhaustive


An organic compound with molecular
formula \( C_{2} H_{4} O_{2} \) produces brisk effervescence on addition of sodium
carbonate/bicarbonate.
(a) Identify the organic compound
(b) Name the gas evolved.
(c) How will you test the gas evolved?
(d) Write the chemical equation for the
above reaction.
(e) List two important uses of the above
compound


The rate of change of momentum represents
A. pressure
B. force
c. work
D. kinetic energy


A ray is reflected in turn by three plane mirrors mutually at right angles to each other. The angle between the incident and the reflected rays is.
\( \mathbf{A} \cdot 180^{\circ} \)
B . 0
\( c \cdot 90 \)
D. 45


The S.D.is not less than the mean
deviation. If this is true enter 1 , else
enter 0


A vector having magnitude 30 unit
makes equal angles with each of \( \boldsymbol{x}, \boldsymbol{y} \)
and \( z \) axes. The component along each
of \( x, y \) and \( z \) -axis are
A \( \cdot 10 \sqrt{3} \)
is
в. \( 20 \sqrt{3} \)
c. \( 30 \sqrt{3} \)
is
D. \( 18 \sqrt{3} \)


A particle starts moving from rest with uniform acceleration. It travels a
distance \( X \) in the first three seconds
and a distance \( Y \) in next three seconds,
then :
A. \( Y=x \)
B. \( Y=3 x \)
\( c \cdot Y=2 x \)
D. \( Y=4 x \)


Magnetic moment of \( x^{n+} \) is \( \sqrt{24} \) B.M.
Hence No. of unpaired electron and
value of ' \( n \) ' respectively. (Atomic number \( =26) \)
\( A \cdot 4,3 \)
B. 3, 5
\( c \cdot 4,2 \)
\( D \cdot 4, \)


The correct sequence of occurrence of
the given stages of mitosis is
A. II, IV, VI, I, V, III
B. \( \|, \) ।V, \( \vee \), ।, VI, II
c. ॥, \( v, \) ।V, VI, ।, ॥ा
D. III, VI, V, I, IV, II
E . \( \| \) II, IV, \( \vee \), VI, I, ।


Release of adrenaline results in the
supply of
A. Nitrogen and glucose
B. Carbon and oxygen
c. oxygen and glucose
D. Carbon and nitrogen


Find the simple interest of 25000 at the
rate of \( 6 \% \) for 3 years.


The \( _{--}-_{-}-_{-}- \) drawn at any point on the magnetic lines of force gives direction of magnetic field at that point.
A. tangent
B. perpendicular
c. chord
D. None


Which of the following was the transitio
nal stage (connective link) between apes and hu mans?
A. Homo habiliss
B. Homo erectus
c. Australopithecus ramidus
D. Australopithecus africanus


The bar graph as shown in above fig. represents the circulation of
newspapers in 10 languages.
study the bar graph and answer the
following question:

What percent is the number of news
papers published in Hindi of the tota
number of newspapers?


A particle when thrown. moves such that it passes from same height at 2
and \( 10 s, \) the height is:
\( \mathbf{A} \cdot g \)
в. \( 2 g \)
c. \( 5 g \)
D. \( 10 g \)


A unit vector which is coplanar to vector \( i+2 j+k \) and \( i+2 j+k \) and
perpendicular to \( i+j+k, \) is
A \( \frac{i-j}{\sqrt{2}} \)
\( ^{\mathrm{B}} \pm\left(\frac{j-k}{\sqrt{2}}\right) \)
c. \( \frac{k-i}{\sqrt{2}} \)
D. \( \frac{i+j+k}{\sqrt{3}} \)


Deuterium is the most common isotope
of hydrogen. How many neutrons does it have?
\( A \cdot 4 \)
B. 3
\( c \cdot 2 \)
\( D \)
E.


The following data shows the number of visitors to a zoological park every hour. Calculate the average number of visitors to the park during the whole
day.
Time \( \begin{array}{ll}10- & 11-12 \\ 11 & \text { noon } \quad 12-1 \\ \text { a.m } & \text { p.m }\end{array} \)
Number of 30 40
34
visitors


Mention the difference between
amylose and amylopectin.


The value of \( \int_{0}^{\pi / 2} \frac{\sin 2 t}{\sin ^{4} t+\cos ^{4} t} d t \)
\( A \)
в.
c.
D. \( \frac{\pi}{2} \)


What is the action of ligases?


Karthik performed the following
experiment by taking a few solutions and phenolphthalein indicator.
Identify \( p, q, r \) in his experiment :
\( \mathbf{A} \cdot \mathbf{p} \rightarrow \operatorname{Acid}, \mathbf{q} \rightarrow \operatorname{Acid}, \mathbf{r} \rightarrow \mathbf{B} \) ase
B. \( p \rightarrow \) Base \( q \rightarrow \) Acid, \( r \rightarrow \) Base
c. \( p \rightarrow \) Base, \( q \rightarrow \) Base, \( r \rightarrow \) Acid
D. \( p \rightarrow \) Base, \( q \rightarrow A c i d, r \rightarrow \) Acid


In a situation, a board is moving with a
velocity \( v \) with respect to earth, while a
man A and man B are running with a
velocity \( 2 v \) with respect to earth and
both men are running from the opposite
ends of the board at the same time, as
shown. Length of the board is \( L \). If they
meet after time \( \boldsymbol{T}, \) then
This question has multiple correct options
A. value of \( \mathrm{T} \) is \( \mathrm{L} / 4 \mathrm{v} \)
B. value of \( T \) is \( L / 2 v \)
C. Displacement of man B with respect to board in time \( T \) is \( 3 L / 4 \)
D. Displacement of man A with respect to board in time \( T \) is L/4


Assertion
When the radius of a copper wire is doubled, its specific resistance is increased.
Reason
Specific resistance is independent of cross-section of material used.
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


Radioactive material'A' has decay
constant \( ^{\prime} 8 \lambda^{\prime} \) and material 'B' has decay
constant \( ^{\prime} \lambda^{\prime} . \) Initially they have same
number of nuclei. After what time, the
ratio of number of nuclei of material 'B'
to that of 'A' will be \( \frac{1}{e} ? \)
A \( \cdot \frac{1}{\lambda} \)
в. \( \frac{1}{7 \lambda} \)
c. \( \frac{1}{8 \lambda} \)
D. \( \frac{1}{9 \lambda} \)


Which of the following is a statement?
A. Open the door.
B. Do your home work.
c. Hurrah! We have won the match.
D. Two plus two is five


Measure of one angle of linear pair is given. Find the measure of another
angle:
\( 111^{\circ} \)


A proton in motion makes head on collision with an unknown particle at rest. If the collision is perfectly elastic and proton rebounds back with \( \frac{4}{9} \) of its initial kinetic energy after collision, the mass of unknown particle is
A. Equal to mass of proton
B. Twice the mass of proton
c. 3 times the mass of proton
D. 5 times the mass of proton


In which condition do the leaves of a
green plant respire?
\( \begin{array}{lll} & \text { bright light } & \text { darkness } \\ \mathrm{A} & \text { right } & \text { right } \\ \mathrm{B} & \text { right } & \text { wrong } \\ \mathrm{C} & \text { wrong } & \text { right } \\ \mathrm{D} & \text { wrong } & \text { right }\end{array} \)


What potential difference is needed between the hands for a lethal shock
current?
\( A \cdot 100 V \)
B. 10 \( v \)
c. \( 120 v \)
D. 150 V


The splitting of white light into several colours on passing through a glass prism is due to
\( A \). refraction
B. reflection
c. dispersion
D. none of these


An electron revolving round the nucleus in an orbit whose angular momentum equal to \( \frac{\mathbf{0 . 5 h}}{\boldsymbol{\pi}} \) can lose energy?


The radius of a metal sphere at room
temperature \( \boldsymbol{T} \) is \( \boldsymbol{R} \) and the coefficient
of linear expansion is \( \alpha . \) The sphere
heated a little by a temperature \( \triangle T . \) So
that its new temperature is \( \boldsymbol{T}+\triangle \boldsymbol{T} \)
The increase in the volume of the sphere is approximate:
\( \mathbf{A} \cdot 4 \pi R^{3} \alpha \triangle T \)
В \( \cdot 2 \pi R^{3} \alpha \triangle T \)
\( \mathbf{c} \cdot \pi R^{3} \alpha \Delta T \)
D. \( 4 \pi R^{3} \alpha \Delta T / 3 \)


Calculate the equilibrium constant for
the reaction, at \( 25^{\circ} C \)
\( \boldsymbol{C u}(\boldsymbol{s})+\boldsymbol{2} \boldsymbol{A} \boldsymbol{g}^{+}(\boldsymbol{a q}) \rightarrow \boldsymbol{C u}^{2+}(\boldsymbol{a q})+ \)
\( \mathbf{2} \boldsymbol{A} \boldsymbol{g}(\boldsymbol{s}) \)
\( \boldsymbol{E}_{c e l l}^{o}=\mathbf{0 . 4 7} \boldsymbol{V}, \boldsymbol{R}=\mathbf{8 . 1 3 4} \boldsymbol{J} \boldsymbol{K}^{-1} \boldsymbol{F}= \)
\( 96500 C \) is
A \( \cdot 1.8 \times 10^{15} \)
B. \( 8.5 \times 10^{15} \)
c. \( 1.8 \times 10^{10} \)
D. \( 85 \times 10^{15} \)


A beam of metal supported at the two edges is loaded at the centre. The depression at the centre is proportional
to
\( \mathbf{A} \cdot Y^{2} \)
в. \( Y \)
c. \( 1 / Y \)
D. \( 1 / Y^{2} \)


A large tank is filled with two liquids of specific gravities \( 2 \sigma \) and \( \sigma . \) Two holes
are made on the wall of the tank as
shown. Find the ratio of the distances
from \( O \) of the points on the ground
where the jets from holes \( A \& B \) strike.


Which of the following functions of \( \boldsymbol{A} \)
and \( B \) may be performed if \( A \) and \( B \) possess different dimensions?
A \( \cdot \frac{A}{B} \)
B. \( A+B \)
c. \( A-B \)
D. None


Total number of equivalence relations defined in the \( \operatorname{set} S=\{a, b, c\} \) is
A . 5
в. 3
\( c \cdot 2^{3} \)
D. \( 3^{3} \)


The marks of a student in 6 tests are
41,45,54,57,43 and \( x \). If the mean marks of these tests is \( 48, \) then
standard deviation of these tests is?
A \( \cdot \frac{10}{\sqrt{3}} \)
B. \( \frac{10}{\sqrt{2}} \)
c. \( \frac{10}{3} \)
D. \( \frac{20}{3} \)


A body of mass \( 3 k g \) moving with a constant acceleration covers a distance
of \( 10 m \) in the \( 3^{r d} \) second and \( I b m \) in
the \( 4^{t h} \) second respectively. The initial
velocity of the body is:
A \( \cdot 10 m s^{-1} \)
B. \( 8 m s^{-1} \)
\( \mathbf{c} \cdot 5 m s^{-1} \)
D. \( -5 \mathrm{ms}^{-1} \)


Electron transfer from \( F e\left(H_{2} O\right)_{6}^{2+} \) to \( F e\left(H_{2} O\right)_{6}^{3+} \) is likely to occur via:
A. \( d-d \) transition
B. inner sphere electron transfer
c. \( S_{N} 1 \) mechanism
D. outer sphere electron transfer


Complete the following, so as to make a
true statement:

The measures of each angle of a convex
quadrilateral is \( \mathbf{1 8 0}^{\circ} \)


Rs. 2,000 is invested at annual rate of interest of \( 10 \% . \) What is the amount
after two years if compounding is done
monthly?
\( \mathbf{A} \cdot 2,420 \)
в. 2,431
c. 2,436.80
D. 2,440.58


If \( \bar{E} \) and \( \bar{F} \) are the complementary events of events \( E \) and \( F, \) respectively,
and if \( \mathbf{0}<\boldsymbol{P}(\boldsymbol{F})<\mathbf{1}, \) then
A \( \cdot P(E / F)+P(\bar{E} / F)=1 / 2 \)
B . \( P(E / F)+P(E / \bar{F})=1 \)
c. \( P(\bar{E} / F)+P(E / \bar{F})=1 \)
D. \( P(E / \bar{F})+P(\bar{E} / \bar{F})=1 \)


Find the modulus, argument and the principal argument of the complex numbers.
\( z=\frac{\sqrt{5+12 i}+\sqrt{5-12 i}}{\sqrt{5+12 i}-\sqrt{5-12 i}} \)


Define transcription.


A mass \( M \) is split into two parts \( m \) and \( (M-m), \) which are then separated by
a certain distance. What ratio \( (\boldsymbol{m} / \boldsymbol{M}) \)
maximizes the gravitational force
between the parts.


For which functional derivative of
carboxylic acids,acidic hydrolysis is
avoided?
A. Acid chlorides
B. Acid amides
c. Acid anhydrides
D. Esters


Find three consecutive odd numbers
whose sum is 147


A sample of \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) solution labelled as 28 volume has density of \( 26.5 g / L \) Mark the correct option(s)
representing concentration of same solution in other units.
This question has multiple correct options
\( \mathbf{A} \cdot M_{H_{2}} o_{2}=2.5 \)
В \( \cdot \% \frac{w}{v}=17 \)
C. Mole fraction of \( H_{2} O_{2}=0.2 \)
D \( \cdot m_{H_{A}} o_{2}=13.88 \)


Which of the following substance is responsible for the formation of setae in earthworm?
A. Trachein
B. Chitin
c. cellulose
D. Proteins


The products formed when a pinch of sugar is strongly heated for fifteen minutes in a test tube are:
A. carbon and water vapour
B. carbon, hydrogen and oxygen
c. carbon dioxide and water vapour
D. carbon dioxide and hydrogen


Draw a Venn-diagram to show the
relationship between two overlapping sets \( A \) and \( B \). Now shade the region
representing \( \boldsymbol{A} \cup \boldsymbol{B} \)


Which of the following is not correct for
heterogeneous catalysis?
A. The catalyst decreases the energy of activation
B. The surface of catalyst plays an important role
C. The catalyst actually forms a compound with reactants
D. There is no change in the energy of activation


Sonar system is found only in
A. Bats
B. Whales
c. Both A and B
D. None of the above


In which of the following species the bonds are non directional?
A \( \cdot N C l_{3} \)
B. \( R b C l \)
c. \( B e C l_{2} \)
D. \( B C l_{3} \)


An \( L-C-R \) series circuit with \( L= \)
\( 0.120 H, R=240 \Omega, \) and \( C=7.30 \mu F \)
carries an rms current of \( 0.450 A \) with a
frequency of \( 400 H z . \) The average rate at
which electrical energy is converted to thermal energy in the resistor is given as \( \frac{x}{10} W . \) Find \( x \)


Find the nine rational numbers
between 0 and 1
A. \( 0.1,0.2,0.3, \ldots, 0.9 \)
в. \( 1.1,0.2,10.3, \ldots, 0.9 \)
c. \( 0.1,0.2,0.3, \ldots, 20.9 \)
D. \( 0.1,0.2,10.3, \ldots, 0.9 \)


Platelets have no nucleus and genetic material.
A . True
B. False


A person having a myopic eye uses a concave lens of focal length \( 50 \mathrm{cm} \)
What is its nature?


Statement - I : The molecularity of the
reaction \( \boldsymbol{H}_{2}+\boldsymbol{B} \boldsymbol{r}_{2} \rightarrow 2 \mathrm{HBr} \) is 2
Statement - II: The order of this reaction
is \( 3 / 2 \)
A. Both statements are true Statement- - I is correct explanation of Statement- -
B. Both statements are true but statement- -II is not correct explanation of Statement- -
c. Statement-lis true but Statement- -II is false
D. Statement- - lis false but Statement - / l is true


A wire of uniform cross section is hanging vertically and due to its own weight its length changes. There is a point 'C' on the wire such that change in length AC is equal to the change in length BC. Points \( A, B \) and \( C \) are shown in the figure. Find \( \frac{\boldsymbol{A C}}{\boldsymbol{B C}} \)
A \( \cdot \sqrt{2}-1 \)
B. \( \frac{\sqrt{2}-1}{\sqrt{2}+1} \)
c. \( \frac{\sqrt{2}+1}{\sqrt{2}-1} \)
D. None of these


A body of mass \( \mathrm{M} \) is kept on a rough horizontal surface (friction coefficient =
\( \mu \) ). A person is trying to pull the body by applying a horizontal force but the body is not moving. The force by the surface on A is F where
A. \( F=M g \)
в. \( F=\mu M g \)
c. \( M g \leq F \leq M g \sqrt{1+\mu^{2}} \)
D. \( M g \geq F \geq M g \sqrt{1-\mu^{2}} \)


Name the unit in which work function of
a metal is generally expressed. How is it related to the S.I. unit joule?
\( \mathbf{A} \cdot e V, 1 e V=1.6 \times 10^{9} J \)
B . \( e V, 1 e V=1.6 \times 10^{-9} J \)
c. \( e V, 1 e V=1.6 \times 10^{-19} J \)
D. \( e V, 1 e V=1.6 \times 10^{19} J \)


An object is placed at a distance \( 2 f \)
from the pole of a convex mirror of focal length \( f \). The linear magnification is:
A \( \cdot \frac{1}{3} \)
B. \( \frac{2}{3} \)
\( c \cdot \frac{3}{4} \)
D.


Evaluate the following as the limit of
sum :
\( \int_{0}^{2}(x+4) d x \)
A .4
B. 6
c. 8
D. 10


Which property of hydrogen is shown by the following reactions?
\( \boldsymbol{F} \boldsymbol{e}_{3} \boldsymbol{O}_{4}+\boldsymbol{4} \boldsymbol{H}_{2} \rightarrow \boldsymbol{3} \boldsymbol{F} \boldsymbol{e}+\boldsymbol{H}_{2} \boldsymbol{O} \)
\( \boldsymbol{C O}+\boldsymbol{H}_{2} \frac{\boldsymbol{C r}_{2} \boldsymbol{O}_{3}}{\boldsymbol{Z n O}_{3}} \boldsymbol{C H}_{3} \boldsymbol{O H} \)
A. Reducing character
B. Oxidizing character
c. combustibility
D. High reactivity


Standing chlorine water turn yellow.
A. True
B. False


A particle is projected at \( 60^{00} \) to the horizontal with a kinetic energy K. The kinetic energy at the highest point is-
\( A \cdot K \)
B. zero
\( c \cdot k / 4 \)
D. K /2


The magnetic moment order is correctly
given in:
\( \mathbf{A} \cdot F e^{2+}<F e^{3+}<M n^{4+}<C r^{3+} \)
B \( \cdot C r^{3+}=M n^{4+}<F e^{2+}<F e^{3+} \)
\( \mathbf{c} \cdot C r^{3+}=M n^{4+}<F e^{3+}<F e^{2+} \)
D \( \cdot F e^{2+}<C r^{3+}<F e^{3+}<M n^{4+} \)


Find the angle which is \( 56^{\circ} \) more than
its complement
A . 73
B. 83
c. 45
D. 68


Renu is standing in a dining line \( 6.38 \times 10^{4} k m \) from the centre of the
earth. The mass of the earth is \( 6 \times \)
\( 10^{24} k g \)
i) Find the acceleration due to gravity
ii) Will the value change after she
finishes her lunch?


What number must be multiplied to \( 6912, \) so that the product becomes a perfect cube?
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. 6
E . 10


The idea of multiple images formed by plane mirrors is used in:
A . a periscope
B. a kaleidoscope
c. a telescope
D. all the above


The value of entropy of solar system is :
A. increasing
B. decreasing
c. constant
D. zero


Solve the differential equation \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}= \)
\( \frac{\boldsymbol{x} \boldsymbol{y}+\boldsymbol{y}}{\boldsymbol{x} \boldsymbol{y}+\boldsymbol{x}} \)


What does the electronic configuration
\( 1 s^{2}, 2 s^{2}, 2 p^{5}, 3 s^{1} \) indicate?
A. Ground state of fluorine
B. Excited state of fluorine
c. Excited state of neon
D. Excited state of the \( O_{2}^{-} \) ion


A wooden stick of length \( 3 l \) is rotated
about an end with constant angular velocity \( \omega \) in a uniform magnetic field \( B \) perpendicular to the plane of motion. If the upper one-third of its length is coated with copper, the potential difference across the whole length of the stick is
\( A \)
\[
\frac{9 B \omega l^{2}}{2}
\]
в.
\[
\frac{4 B \omega l^{2}}{2}
\]
c.
\[
\frac{5 B \omega l^{2}}{2}
\]
D.
\[
\frac{B \omega l^{2}}{2}
\]


Planck constant has the dimension of :
\( \mathbf{A} \cdot M^{-1} L^{2} T^{-1} \)
B. \( M L^{-2} T^{-1} \)
\( \mathbf{c} \cdot M L^{2} T^{-1} \)
D. \( C M L^{3} T^{-1} \)


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


Find \( a_{30} \) given that the first few terms of
a geometric sequence are given by \( -2,1,-\frac{1}{2}, \frac{1}{4} \dots \)
A \( \cdot \frac{1}{2^{27}} \)
в. \( \frac{1}{2^{2}} \)
c. \( \frac{1}{2^{28}} \)
D. \( \frac{1}{2^{29}} \)


The number of elements that shows
ductility among the following:
copper, silver, phosphorus, platinum, zinc, iodine, aluminium, carbon, lead


Sea water is found to conatin
\( \mathbf{5 . 8 5 \%} \) Nacl and \( \mathbf{9 . 5 0 \%} \boldsymbol{M g C l}_{2} \) by
weight of solution. Calculate its normal
boiling point assuming \( 80 \% \) ionisation for \( N a C l \) and \( 50 \% \) ionisation of
\( M g C l_{2} \)
\( \left[\boldsymbol{K}_{\boldsymbol{b}}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)=\mathbf{0 . 5 1} \boldsymbol{k g} \boldsymbol{m o l}^{-1} \boldsymbol{K}\right] \)
A. \( T_{b}=51.15^{\circ} \mathrm{C} \)
в. \( T_{b}=78.6^{\circ} \mathrm{C} \)
c. \( T_{b}=102.3^{\circ} \mathrm{C} \)
D. \( T_{b}=157.2^{\circ} \mathrm{C} \)


In the figure above, points \( A, D, B, \) and \( G \)
are collinear. If \( \angle C A D \) measures \( 76^{\circ} \)
\( \angle B C D \) measures \( 47^{\circ}, \) and \( \angle C B G \)
measures \( 140^{\circ}, \) find the degree
measure of \( \angle \boldsymbol{A} \boldsymbol{C} \boldsymbol{D} \)
A \( \cdot 12^{\circ} \)
B . \( 14^{\circ} \)
\( c \cdot 17 \)
\( \mathbf{D} \cdot 36 \)
\( E \cdot 43 \)


Assertion
When a ray of light travels from ice to water the refracted ray at the point of incidence bends towards the normal
Reason
The ray goes from rarer to denser
medium.
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


Alternative current generator is basically based upon:
A. Amperes law
B. Lenz's law
c. Faradays law
D. coulombs law


When the concentration of a reactant in reaction \( A \rightarrow B \) is increased by 8
times but rate increases only 2 times,
the order of the reaction would be \( 1 / n \)
value of \( n \) is \( ? \)


The area of a rectangular field is given
as 300 square metres. It is also given that the breadth of the field is 3 metres
more than its length. Can this
information be expressed mathematically as a Quadratic
Equation. If yes, what would be the resulting Quadratic Equation?


A particle having a charge of \( 10 \mu C \) and
mass \( 1 \mu g \) moves in a horizontal circle of radius \( 10 \mathrm{cm} \) under the influence of a
magnetic field of 0.1 T. When the particle
is at a point \( P, \) a uniform electric field is
switched on so that the particle starts
moving along the tangent with uniform
velocity. The electric field is
A. \( 0.1 \mathrm{V} / \mathrm{m} \)
B. 1.0 \( \mathrm{V} / \mathrm{m} \)
c. \( 10.0 \mathrm{V} / \mathrm{m} \)
D. \( 100 \mathrm{V} / \mathrm{m} \)


In Fig., \( A B C \) is the cross section of a
right-angled prism and \( A C D E \) is the
cross section of a glass slab. The value of \( \theta \) so that light incident normally on
the face \( A B \) does not cross the face \( A C \)
s (given \( \left.\sin ^{-1}(3 / 5)=37^{\circ}\right) \)
A \( \cdot \theta \leq 37 \)
В \( \cdot \theta<37 \)
\( c \cdot \theta \leq 53 \)
\( \theta<53 \)
3


What is Secondary structure of protein?


Which of the following is not the allotropic form of sulphur?
A. Roll sulphur
B. Monoclinic sulphur
c. Plastic sulphur
D. Rhombic sulphur


A rectangular solid has a square base, with each side of the base measuring 4 meters. If the volume of the solid is 112
cubic meters, what is the surface area
of the solid?
A \( .144 \mathrm{m}^{2} \)
B . \( 250 m^{2} \)
c. \( 172 m^{2} \)
D . \( 228 \mathrm{m}^{2} \)


Select the correct statement(s) about
the compound \( N O\left[B F_{4}\right] \)
This question has multiple correct options
A. It has \( 5 \sigma \) and \( 2 \pi \) bonds.
B. Nitrogen-oxygen bond length is higher than nitric oxide (NO).
C. It is a diamagnetic species.
D. \( B-F \) bond length in this compound is lower than in
\( B F_{3} \)


Angiosperms and gymnosperms resemble in having
A. Vessels in wood
B. Mode of fertilization
c. siphonogamy
D. Nature of endosperm


The turn ratio of a transformer is \( 2: 3 . \) If
the current through primary is \( 3 A \), then current through load resistance is
\( A \cdot 1 A \)
B. 4.5 A
\( c \cdot 2 A \)
D. 1.5 A


Nitrous oxide supports combustion more vigorously than air. Explain.


The parameter which does not change during polarisation of light is?
A. Intensity of light wave
B. Frequency of light wave
c. wavelength of light wave
D. Phase


The molecular orbital configuration of
\( C N^{+} \) is :
\( \mathbf{A} \cdot K K \sigma(2 s)^{2}, \sigma^{*}(2 s)^{2}, \pi\left(2 p_{x}\right)^{2}, \pi\left(2 p_{y}\right)^{2} \)
B . \( K K \sigma(2 s)^{2}, \sigma^{*}(2 s)^{2}, \sigma\left(2 p_{z}\right)^{2}, \pi\left(2 p_{x}\right)^{1}, \pi\left(2 p_{y}\right)^{1} \)
C \( \cdot K K \sigma(2 s)^{2}, \sigma^{*}(2 s)^{2}, \sigma\left(2 p_{z}\right)^{2}, \pi\left(2 p_{x}\right)^{2}, \pi\left(2 p_{y}\right)^{1} \)
D. \( K K \sigma(2 s)^{2} \sigma^{*}(2 s)^{2}, \sigma\left(2 p_{z}\right)^{2} \pi\left(2 p_{x}\right)^{2}, \pi\left(2 p_{y}\right)^{2} \)


The perimeter of the following shaded
portion of the figure is
\( A \cdot 40 \mathrm{m} \)
В. 40.07 m
\( c . \) 35.72m
D. 35


The number of integral values of \( \boldsymbol{m}, \) for
which the \( x \) -coordinate of the point of intersection of the lines \( 3 x+4 y=9 \)
and \( y=m x+1 \) is also an integer is
A .2
B.
\( c \cdot 4 \)
D.


N-Ethylphthalimide \( \longrightarrow \) Ethylamine Reagent for the conversion of this
reaction is:
A \( . H_{2} O \)
в. \( N a B H_{4} \)
c. \( N H_{2}-N H_{2} \)
D. \( C a H_{2} \)


The ratio of the pressure exerted by the oxygen gas to the pressure exerted by the hydrogen gas is:
A . 6: 1
B. 5: 1
c. 4: 1
D. 1: 1
E . 1: 5


Assertion
The acid hydrolysis of ester takes place
more rapidly in \( D_{2} O \) than \( H_{2} O \)
Reason
\( D_{3} O^{+} \) is stronger acid than \( H_{3} O^{+} \)
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


Write the name of the major organic product formed in the reaction of 1 pentene with hydrogen iodide.
A. 1-iodopentane
B. 2-iodopentane
c. 3-iodopentane
D. None of these


A potential difference of \( 600 \mathrm{V} \) is
applied across the plates of a parallel plate capacitor placed in a magnetic field. The separation between the plates is \( 3 \mathrm{mm} . \) An electron projected vertically upward, parallel to the plates, with a velocity of \( 2 \times 10^{6} m s^{-1} \) moves
undeflected between the plates. Find the magnitude and direction of the magnetic field in the region between the capacitor plates. Find the magnitude and direction of the magnetic field in the region between the capacitor plates. Given the Charge of the electron \( =-1.6 \times 10^{-19} C \)


is a separation process for temperature sensitive materials like
natural aromatic compounds.
A. Vacuum distillation
B. Steam distillation
c. Fractional distillation
D. None of the above


The length of two adjacent sides of a parallelogram are \( 17 \mathrm{cm} \) and \( 12 \mathrm{cm} \). one
of its diagonals is \( 25 \mathrm{cm} \) long. Find the area of the parallelogram.


The extremities of a diagonal of a
parallelogram are the points (1,-2) and \( (-4,3) . \) If third vertex is (-1,0) Then the co-ordinates of fourth vertex
are :
A. (2,1)
(i)
B. (-2,-1)
c. (-2,1)
D. none of these


If \( \mathrm{E} \) and \( \mathrm{B} \) denote electronic and
magnetic field respectively, which of the following is dimensionless?
A \( \cdot \sqrt{\mu_{0} \varepsilon_{0}} \frac{E}{B} \)
в. \( \quad \mu_{0} \varepsilon_{0} \frac{E}{B} \)
\( ^{\mathbf{c}} \cdot_{\mu_{0} \varepsilon_{0}}\left(\frac{B}{E}\right)^{2} \)
D. \( \frac{E}{\varepsilon_{0}} \frac{\mu_{0}}{B} \)


Show that
\( (\sec \theta-\tan \theta)^{2}=\frac{1-\sin \theta}{1+\sin \theta} \)


If the equation \( \sin ^{-1}\left(x^{2}+x+1\right)+ \)
\( \cos ^{-1}(a x+1)=\frac{\pi}{2} \) has exactly two
distinct solutions then value of \( a \)
could not be

This question has multiple correct options
\( A \cdot-1 \)
B.
\( c \)
\( D \)


Convert \( \frac{14}{25} \) into percentage
A . \( 55 \% \)
B. \( 56 \% \)
c. \( 57 \% \)
D. \( 58 \% \)


The force with which the earth attracts
a body is called its mass. True or false.
A. True
B. False


(i) Name the method used for the refining of zirconium.
(ii) What is the role of \( C O \) in the
extraction of Iron?
(iii) Reduction of metal oxide to metal
becomes easier if the metal obtained is
in the liquid state. Why?


If the velocity of a body changes in a non-uniform rate, then the body moves
with:
A. uniform acceleration
B. non-uniform acceleration
c. either uniform or non-uniform acceleration
D. neither uniform nor non-uniform acceleration


The theory of natural selection was
given by
A . Lamarck
B. Alfred Wallace
c. charles Darwin
D. oparin and Haldane


Find the amplitude response \( \left|\frac{V_{2}}{V_{1}}\right| \) for
the circuit shown in figure. Determine
the half-power frequency.
A \( \cdot \frac{1}{R C} \)
B. \( \frac{\sqrt{2}}{R C} \)
\( c \cdot \frac{\sqrt{3}}{B C} \)
D. \( \frac{2}{R C} \)


Choose the correct order of the steps
involved in protein synthesis and
modification that takes place in several different locations throughout the cell.
I. Ribosome
II. Nucleus
III. Golgi apparatus
IV. Endoplasmic reticulum
A . ।, ॥, III and IV
B. ॥,।, IV and III
c. ॥ा, ॥, Iv and ।
D. ॥, I, III and IV
E . IV, III, II and I


\( \int e^{x}\left[\log (\cosh x)-\operatorname{sech}^{2} x\right] d x= \)
A \( \cdot e^{x}(\log \cosh x-\tanh x)+c \)
B. \( e^{x} \log \cosh x+c \)
c. \( -e^{x} \tanh x+c \)
D. \( e^{x}(\log \cosh x+\tanh x)+c \)


\( f \frac{1-\cos x}{\cos x(1+\cos x)}=\frac{\sin \alpha}{\cos x}-\frac{2}{1+\cos x} \)
then \( \boldsymbol{\alpha}= \)
A. \( \frac{\pi}{8} \)
B.
\( c \cdot \frac{\pi}{2} \)
\( D \)


Prove the following by using the principle of mathematical induction for all \( \boldsymbol{n} \in \boldsymbol{N} \)
\( \mathbf{1}+\mathbf{3}+\mathbf{3}^{2}+----+\mathbf{3}^{n-1}= \)
\( \frac{\left(3^{N}-1\right)}{2} \)


What happens when:
(i) \( S O_{2} \) gas is passed through an
aqueous solution \( \boldsymbol{F e}^{+3} \) salt?
(ii) \( X e F_{4} \) reacts with \( S b F_{5} ? \)


The statement, which prompted Neil
Bartlett to prepare the first noble gas
compound was:
A. \( X e-F \) bond has high bond energy
B. \( F_{2} \) has exceptionally low bond energy
C. \( P t F_{6} \) is a strong oxidant
D. \( O_{2} \) molecule and Xe atom have very similar ionization energies


State true or false
\( (-5)-4=-9 \)
A. True
B. False


Ear drum is
A. Tensor tymphani
B. Scala tympani
C. Tympanic membrane
D. Scala vestibuli


The metal with which hydrogen reacts to form metal hydride is:
A. \( H g \)
в. \( C a \)
\( c . A g \)
D. \( H \)


A stone is allowed to fall from the top of
a tower \( 100 \mathrm{m} \) high and at the same
time another stone is projected vertically upwards from the ground with a velocity of \( 25 m / s . \) Calculate when and where the two stones will meet


Find the area of trapezium \( \boldsymbol{A B C D} \)
where \( A B \) is parallel to \( D C . A B= \)
\( \mathbf{7} \mathbf{7} \boldsymbol{c m}, \boldsymbol{B} \boldsymbol{C}=\mathbf{2} \boldsymbol{8} \boldsymbol{c m}, \boldsymbol{C} \boldsymbol{D}= \)
\( 60 c m, D A=26 c m \)


A bag contain 4 white, 7 black and 5 red
balls. A ball is drawn Find the
probability that the ball drawn is red.


2, 4-D stands for
A. 2,4 -Dichlorophenoxy Acetic Acid
B. 2, 4-Dichloro Butyric Acid
C. \( 2, \) 4-Dichloronaphthoxy Acetic Acid
D. 2, 4-Dichloronaphthalene Acetic Acid


If \( x \) is the geometric mean of \( (x+2) \)
and \( (x-1), \) then find the value of \( x \)


The clarification of discrete energy
levels in atoms was first given
experimentally by :
A. Thomsons experiment
B. Millikans oil drop experiment
c. Frank - Hertz experiment
D. Leonard experiment


The D. \( E \) of the family of parabolas having their focus at the origin and axis along the \( x \) -axis is
A \( \cdot y_{1}\left[y y_{1}-2 x\right]=y \)
B . \( y_{1}\left(y_{1}\right)^{2}=2 x y_{1}+y \)
\( \mathbf{c} \cdot y y_{1}^{2}+2 x y_{1}=y \)
D. \( y y_{1}+2 x=y \)


Assertion
Melting and boiling points of \( D_{2} O \) are
higher than those of ordinary \( \boldsymbol{H}_{2} \boldsymbol{O} \)
Reason
\( D_{2} O \) has lesser degree of association
and lower molecular mass than \( \boldsymbol{H}_{2} \boldsymbol{O} \)
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


Fill in the blanks to make the
statements true,
In right triangle, the hypotenuse is the side


The relation between the acceleration
and time for an object is given below. Calculate the velocity with which the object is moving at \( \boldsymbol{t}=\mathbf{1}(\mathbf{A t} \boldsymbol{t}=\mathbf{0}, \boldsymbol{v}= \)
\( \mathbf{0} \)
\( \boldsymbol{a}=\boldsymbol{3} \boldsymbol{t}-\boldsymbol{4} \boldsymbol{t}^{2} \)


The following belongs to d-block but it is not transition element
A. Mn
B. Fe
\( c \cdot z n \)
D. cr


Soluation of D.E. \( \frac{d y}{d x}=\frac{3 x+4 y+3}{12 x+16 y-4} \)
is
A \( \cdot y=4 x+\ln |3 x+4 y|+C \)
B . \( 4 y=x+\ell n|3 x+4 y|+C \)
c. \( y=\ell n|3 x+4 y|+C \)
D・ \( x+y=\ell n|3 x+4 y|+C \)


Name the type of following triangle.
\( \Delta X Y Z \) with \( m \angle Y=90^{\circ} \) and \( X Y=Y Z \)


Which of the following provides nutrients and makes the soil fertile?
A . Gravel
B. Humus
c. clay
D. Loam


Which of the following is least basic?
\( \mathbf{A} \cdot L a(O H)_{3} \)
\( \mathbf{B} \cdot L u(O H)_{3} \)
\( \mathbf{c} \cdot \operatorname{Ce}(O H)_{3} \)
D. \( N d(O H)_{3} \)


Give an example of the following:
A compound containing both ionic and covalent bonds.


What are 'flocs', formed during
secondary of sewage?


If \( \boldsymbol{y}=\sec ^{-1}\left(\frac{\boldsymbol{x}+\mathbf{1}}{\boldsymbol{x}-\mathbf{1}}\right)+\sin ^{-1}\left(\frac{\boldsymbol{x}-\mathbf{1}}{\boldsymbol{x}+\mathbf{1}}\right) \)
then \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}= \)


If the tip of sugarcane plant is removed from the field, even then it keeps on growing in length. It is due to the presence of
A. Cambium
B. Apical meristem
c. Lateral meristem
D. Intercalary meristem


You are driving along the street at the speed limit \( (35 m p h) \) and 50 meters before reaching a traffic light you notice it becoming yellow. You accelerate to make the traffic light within the 3 seconds it takes for it to turn red. What
is your speed as you cross the intersection? Assume that the
acceleration is constant and that there
is no air resistance.
A. \( 30 m p h \)
в. \( 40 \mathrm{mph} \)
c. \( 50 m p h \)
D. \( 60 m p h \)


\( \mathrm{Zn}(s)\left|\mathrm{ZnCl}_{2}(\mathrm{aq})\right| \mathrm{Cl}^{-}(\mathrm{aq})\left|\mathrm{Cl}_{2}(g)\right| \mathrm{C}(s) \)
According to the above cell diagram the electrochemical cell described, the
reaction at anode is :
A \( \cdot z n \rightarrow z n^{2+}+2 e^{-} \)
B. \( z n^{2+}+2 e^{-} \rightarrow \) Zn
c. \( \mathrm{cl}_{2}+2 \mathrm{e}^{-} \rightarrow 2 \mathrm{Cl}^{-} \)
D . 2CI- \( \rightarrow \mathrm{Cl}_{2}+2 \mathrm{e}^{-} \)
E. \( z n+C l_{2} \rightarrow Z n C l_{2} \)


The weight(in \( \mathrm{kg} \) ) of 13 students in a class are
42.5,47.5,48.6,50.5,49,46.2,49.8,45.8
Find the range and coefficient of range.


Out of the following, how many features
belong to monocot root?
1. Radial vascular bundles
2. Closed vascular bundles
3. Endodermis absent
4. Pith developed
5. Polyarch condition
A. one
B. Two
c. Three
D. Four


A machine is run such that electrical
current is input and as a result rotation is achieved in the rotor. If current is
turned off and rotation is forced in the
machine
A. current is produced
B. Rotor motion faces resisting force
c. Machine acts as a generator
D. All of the above


Which of these is the final electron
acceptor in the electron transport
chain?
A. \( F A D H_{2} \).
B. \( N A D H \)
c. cytochrome c.
D. water
E. Oxygen


Study the following statements about
ozone:
(a) It is essential for the breathing of living organisms.
(b) It is used to disinfect water.
(c) It absorbs ultraviolet rays.
(d) Its proportion of air is about \( 3 \% \) Which of these statements are correct?
\( A \cdot(a),(b) \) and \( (c) \)
B. (b) and (c)
c. (a) and (d)
D. All four


The molar solubility of \( \mathrm{PbCl}_{2} \) in \( 0.20 \mathrm{M} \)
\( \mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2} \) solution is:
\( \left(\boldsymbol{K}_{\boldsymbol{s} p} \text { for } \boldsymbol{P b C l}_{2}=\mathbf{1 . 6} \times \mathbf{1 0}^{-\mathbf{5}}\right) \)
A . \( 1.7 \times 10^{-4} M \)
В. \( 9.2 \times 10^{-3} M \)
c. \( 1.7 \times 10^{-5} M \)
D. \( 4.6 \times 10^{-3} M \)
E . \( 8.5 \times 10^{-5} M \)


In a one dimensional collision between
two identical particles \( A \) and \( B, B \) is stationary and \( A \) has momentum \( p \)
before impact. During impact, \( B \) gives impulse \( J \) to \( A \) This question has multiple correct options
A. The total momentum of the \( A+B \) system is \( p \) before and after the impact, and \( (p-J) \) during the impact
B. During the impact \( A \) gives impulse of magnitude \( J \) to \( B \)
c. the coefficient of restitution is \( \frac{2 J}{p}-1 \)
D. The coefficient of the restitution is \( \frac{J}{p}+1 \)


A gaseous carbon compound is soluble in dilute HCI. The solution on treating
with \( N a N O_{2} \) gives off nitrogen leaving
behind a solution which smells of wood
spirit. The carbon compound is :
A. \( H C H O \)
в. \( C O \)
c. \( C_{2} H_{5} N H_{2} \)
D. \( C H_{3} N H_{2} \)


Most effective coagulant for a colloidal solution of arsenic sulphide in water is:
A. \( 0.1 M \) sodium phosphate
B. \( 0.1 M \) zinc sulphate
c. \( 0.1 M \) zinc nitrate
D. \( 0.1 M \) aluminium chloride


Define reaction quotient


Find the equation of the ellipse whose
foci are (0,±5) and length of the minor
axis is 20


A diamond weighs \( 3.71 g \). It is put into a
box weighing \( 1.4 k g . \) Find the total
weight of the box and diamond to the correct number of significant figures.


Amplitudes of two light waves of the
same frequency are in the ratio 4: 3
What will be the ratio of maximum and
minimum intensities if the two wave
interfere?


The line making an angle \( \left(-120^{\circ}\right) \) with
\( x \) -axis is situated in the :
A. First quandrant
B. Second quandrant
c. Third quandrant
D. Fourth quandrant


\( \frac{E}{L} \)


Define the photoelectric effect. Write the laws of the photoelectric effect.


The number of times a standard
quantity is present in a given physical quantity, is called its units
A. True
B. False
c. Ambiguous
D. Data insufficient


The wavelength of the pulse when it reaches the other end of the rope is
A. \( \sqrt{3} \lambda_{0} \)
B. \( \sqrt{\frac{3}{2}} \lambda_{0} \)
\( c \cdot \lambda_{0} \)
D. \( \frac{\lambda_{0}}{2} \)


When an alpha particle is emitted from a radioactive source.
A. Its atomic number increases by 4
B. Its atomic number decreases by 2
c. Its atomic number increases by 2
D. It atomic number decreases by 4


If the median of the following frequency distribution is \( 28.5 . \) find the missing frequencies.
30
\( \mathrm{c} \)
\[
\begin{array}{lll}
0- & 10- & 30 \\
10 & 20 &
\end{array}
\]
Freq.
२० 15
A \( \cdot f_{1}=7, f_{2}=8 \)
B . \( f_{1}=8, f_{2}=7 \)
c. \( f_{1}=6, f_{2}=9 \)
D. \( f_{1}=9, f_{2}=6 \)


Two thin lenses have combined power of 10 \( D \). When separated by \( 20 \mathrm{cm} \) their
equivalent power is 6.25 D.Their
individual powers in \( D \) are
A . 3.5 and 6.5
B. 5 and 5
c. 7.5 and 2.5
D. 9.0 and 1


Two identical metal plates are given
positive charge \( Q_{1} \) and \( Q_{2}\left(<Q_{1}\right) \)
respectively. If they are now brought close together to form a parallel plate
capacitor with capacitance \( C, \) the
potential difference between them is
\( \mathbf{A} \cdot\left(Q_{1}+Q_{2}\right) / 2 C \)
B \( \cdot\left(Q_{1}+Q_{2}\right) / C \)
c. \( \left(Q_{1}-Q_{2}\right) / C \)
D \( \cdot\left(Q_{1}-Q_{2}\right) /(2 C) \)


Assertion
Nuclide \( _{13}^{30} A l \) is less stable than \( _{20}^{40} C a \)
Reason

Nuclide having odd number of protons and neutrons are generally unstable.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


The increasing order of paramagnetism of the following compound is:
(।) \( M n S O_{4} .4 H_{2} O \)
(II) \( F e S O_{4} .7 H_{2} O \)
(III) \( N i S O_{4} .6 H_{2} O \)
\( (\mathrm{IV}) \mathrm{C} u S O_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O} \)
\( A \cdot|<||<|||<\mid V \)
B. IV<III<II<I
c. \( \||<| V<\|<1 \)


An organic compound whose functional group is carboxyl is :
A. Ethyne
B. Ethanol
c. Acetic acid
D. Ethene
E. Methane


A straight rod of length \( L \) extends frfom
\( \boldsymbol{x}=\boldsymbol{a} \) to \( \boldsymbol{x}=\boldsymbol{L}+\boldsymbol{a} . \) Find the
gravitational force it exerts on a point mass \( m \) at \( x=0 \) is(if the linear density
of \( \left.\operatorname{rod} \mu=A+B x^{2}\right) \)
\( ^{\mathbf{A}} \cdot G m\left[\frac{A}{a}+B L\right] \)
\( ^{\mathrm{B}} \mathrm{Gm}\left[A\left(\frac{1}{a}-\frac{1}{a+L}\right)+B L\right] \)
\( ^{\mathrm{c}} \cdot_{G m}\left[B L+\frac{A}{a+L}\right] \)
D. \( _{G m}\left[B L-\frac{A}{a}\right] \)


Number of genotypes found in \( \boldsymbol{F}_{2} \)
progeny of a dihybrid cross is
\( A \cdot 9 \)
B. 6
\( c \cdot 3 \)
D.


Consider the two gaseous equilibria involving \( S O_{2} \) and the corresponding equilibrium constants at \( 298 \mathrm{K} \)
\( \boldsymbol{S O}_{2}(\boldsymbol{g})+\frac{1}{2} \boldsymbol{O}_{2}(\boldsymbol{g}) \Leftrightarrow \boldsymbol{S} \boldsymbol{O}_{3}(\boldsymbol{g}) ; \boldsymbol{K}_{1} \)
\( 2 S O_{3}(g) \Leftrightarrow 2 S O_{2}(g)+O_{2}(g) ; K_{2} \)
The values of the equilibrium constants are related by:
A \( \cdot K_{1}=K_{2} \)
в. \( K_{2}=K_{1}^{2} \)
c. \( _{K_{2}=\frac{1}{K_{1}^{2}}} \)
D. \( _{K_{2}}=\frac{1}{K_{1}} \)


Where did the grinding of food in
Grasshopper?


How is benzyl alcohol obtained from
phenyl magnesium bromide?


The total number of rational terms in
the expansion of \( (\mathbf{7 3}+\mathbf{1 1 9})^{\mathbf{6 5 6 1}} \)
A . 73
в. 729
\( c .728 \)
D. 730
E. 732


The ash can cause
problems.
A. digestive
B. reproductory
c. respiratory
D. nervous


Why is the offspring formed by asexual reproduction referred to as clone?


The increasing order of solubility is :
A. \( C a C O_{3}, K H C O_{3}, N a H C O_{3} \)
в. \( \operatorname{NaHCO}_{3, K H C O_{3}, C a C O_{3}} \)
c. \( K H C O_{3}, N a H C O_{3}, C a C O_{3} \)
D. \( C a C O_{3}, N a H C O_{3}, K H C O_{3} \)


In a zener-regulated power supply a
zener diode with \( V_{z}=6 \) volt is used for
regulation. The load current is to be \( 4 m A \) and the unregulated input is 10
volt. What should be the value of series
resistor \( \boldsymbol{R}_{s} \) if the current through diode
is five times the load current?


How many NAND gates are needed to perform the logic function X.Y?
A . 1
B. 2
\( c \cdot 3 \)
\( D \)


If \( A \) is a \( 3 \times 3 \) matrix such that \( |A|= \)
\( 4 \operatorname{th} a n\left|(a d j A)^{-1}\right|= \)
A . 16
B. 64
c. \( \frac{1}{16} \)
D. None


If \( \boldsymbol{f}(\boldsymbol{x}+\boldsymbol{y}, \boldsymbol{x}-\boldsymbol{y})=\boldsymbol{x} \boldsymbol{y}, \) then the
arithmetic mean of \( \boldsymbol{f}(\boldsymbol{x}, \boldsymbol{y}) \) and \( \boldsymbol{f}(\boldsymbol{y}, \boldsymbol{x}) \)
is


Pair of enantiomers are:
A. \( I, I I \) and \( I I I, I V \)
в. \( I, I I \)
с. \( I I I, I V \)
D. \( I V, V \)


\( A M \) is a median of a triangle \( A B C . \) Is \( A B+B C+C A>2 A M ? \) (Consider
the sides of triangles \( \triangle A B M \) and
\( \triangle \boldsymbol{A} \boldsymbol{M} \boldsymbol{C} \)


A man is \( 180 \mathrm{cm} \) tall and his eyes are
10cm below the top of his head. In order
to see his entire height right from toe to head, he uses a plane mirror kept at a distance of \( 1 \mathrm{m} \) from him. The minimum
length of the plane mirror required is :
A . \( 180 \mathrm{cm} \)
B. \( 90 \mathrm{cm} \)
\( \mathbf{c} .85 \mathrm{cm} \)
D. \( 170 \mathrm{cm} \)


Phosphine is obtained by the reaction when
This question has multiple correct options
A. white phosphorous is heated with \( N a O H \)
B. \( C a_{3} P_{2} \) reacts with water
c. red phosphorus is heated with \( N a O H \)
D. phosphorus is heated in current of hydrogen


A frame made of metallic wire
enclosing a surface area \( A \) is covered with a soap film. If the area of the frame of metallic wire is reduced by \( 50 \% \), the energy of the soap film will be changed by
A. \( 100 \% \)
B. \( 75 \% \)
\( c .50 \% \)
D. \( 25 \% \)


(a) Account for the following:
(i) Acidic character increase from \( \boldsymbol{H} \boldsymbol{F} \)
to \( H I \)
(ii) There is large difference between melting and boiling points of oxygen and sulphur.
(iii) Nitrogen does not from pentahalide.
(b) Draw the structures of the following:
(i) \( C l F_{3} \)
\( (\text { ii }) X e F_{4} \)


Growth hormones connected with
bolting are
A. Cytokinins
B. Auxins
c. coumarins
D. Gibberellins


"BeO has hexagonal ZnS structure." Answer whether the above statement is
true or false.
If true enter 1 , else enter 0 .


The angles of elevation of the top of a rock from the top and foot of a \( 100 \mathrm{m} \)
high tower are respectively \( 30^{\circ} \) and \( 45^{\circ} \) Find the height of the rock.


A circular coil of radius \( R \) carries an
electric current. The magnetic field due to the coil at a point on the axis of the coil located at a distance \( r \) from the
centre of the coil, such that \( r>>R \)
varies as
A. \( 1 / r \)
B . \( 1 / r^{3 / 2} \)
c. \( 1 / r^{2} \)
D. \( 1 / r^{3} \)


State True or False :
Evaporation takes place at all temperatures
A. True
B. False


Nitric oxide is formed by the reaction of
A. \( C+N_{2} O \)
в. \( C u+H N O_{3} \)
c. \( C u+N_{2} O \)
D. \( C u+N O_{2} \)


A horizontal telegraph wire \( 0.5 k m \) long
running east and west in a part of a circuit whose resistance is \( 2.5 \Omega \). The
wire falls to \( g=10.0 m / s^{2} \) and \( B= \)
\( 2 \times 10^{-5} w e b e r / m^{2}, \) then the current
induced in the circuit is
A. 0.7 amp
B. 0.04 amp
c. 0.02 amp
D. \( 0.01 a m p \)


If \( f(1)=3 \) and \( f^{\prime}(1)=-\frac{1}{3} \) then the
derivative of \( \left(x^{11}+f(x)\right)^{-2} \) at \( x=1 \) is
A. \( -\frac{1}{2} \)
B. - -
c. 1
D. \( f^{\prime}(1) \)


Read the following fours statements toD) about chylomicrons?
A. Chylomicrons are produced in the lumen of small intestine
B. Chylomicron contains triglycerides, cholesterol and phospholipids
C. Chylomicron is protein free small vesicles
D. Chylomicron released from the lacteal\% into epithelial cells
How many of the above statements are
correct?
A. Four
B. One
c. Two
D. Three


Find the sum of the order and degree of
the differential equation \( \boldsymbol{y}= \)
\( \boldsymbol{x}\left(\frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}\right)^{3}+\frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}} \)


The boiling point of a solution of 5 g sulphur in 100 g \( C S_{2} \) is \( 0.5^{\circ} C \) above
pure solvent. If the \( K_{b} \) of \( C S_{2} \) is 2.56
\( \mathrm{K} / \mathrm{m}, \) then find the atomicity of the sulphur in the solvent.


The only radioactive element among the lanthanoids is
A. Gadolinium
B. Holmium
c. Promethium
D. Neodymium


Two bodies of masses \( m \) and \( 4 m \) are
placed at a distance \( r . \) The
gravitational potential at a point on the line joining them where the gravitational field is zero is :
A . zero
B. \( -\frac{4 \mathrm{Gm}}{\mathrm{r}} \)
\( c \cdot-\frac{6 G m}{r} \)
D. \( -\frac{9 \mathrm{Gm}}{\mathrm{r}} \)


In a circle of radius \( 25 \mathrm{cm} \) two parallel chords of the length \( 14 \mathrm{cm} \) and \( 48 \mathrm{cm} \) respectively, are drawn on the same
side of the centre. The distance between
them is
A . \( 14 \mathrm{cm} \)
B. \( 24 \mathrm{cm} \)
\( c \cdot 17 \mathrm{cm} \)
D. \( 31 \mathrm{cm} \)


The quotient when
\( \left(2 x^{4}-3 x^{3}-x^{2}+4 x-2\right) \) divided by
is:


Which of the following is not an example of a biogas source of energy?
A. woodd
B. Gobar
c. Nuclear Energy
D. coal


Collision frequency of a gas at 1 atm pressure is \( Z \). Its value at 0.5 at \( m \) will
be:
A \( .0 .25 Z \)
в. \( 2 Z \)
c. \( 0.50 Z \)
D. \( z \)


To which part of the electromagnetic
spectrum does a wave of frequency \( 3 x \)
\( 10^{13} H z \) belong?


If a positive charge is shifted from a low potential region to a high potential region, the electric potential energy:
A. Increases
B. Decreases
c. Remains unchanged
D. May increase or decrease


The radii of two cylinder are in the ratio
3: 2 and their heights are in the ratio
\( 4: 5 . \) Calculate the ratio of their curved
surface areas.


Marsh gas mainly contains
\( A \cdot S O_{2} \)
B. \( \mathrm{cO}_{2} \)
\( \mathrm{c} \cdot \mathrm{cH}_{4} \)
\( D \cdot H_{2} O \)


An element belonging to 3d series of
modern periodic table has spin magnetic moment =5.92 B.M.in +3 oxidation state. Determine the atomic
number of element.


Which particles are responsible for current in conductors?


Two liquids \( A \) and \( B \) form a non ideal
solution which obey the equation:
\( \boldsymbol{P}_{\boldsymbol{T}}+\boldsymbol{P}_{\boldsymbol{A}}^{\boldsymbol{o}}+\boldsymbol{3}\left(\boldsymbol{P}_{\boldsymbol{B}}^{\boldsymbol{o}}-\boldsymbol{P}_{\boldsymbol{A}}^{\boldsymbol{o}}\right) \boldsymbol{X}_{\boldsymbol{B}}+\boldsymbol{2}\left(\boldsymbol{P}_{\boldsymbol{A}}^{\boldsymbol{o}}-\right. \)
\( \left.P_{B}^{o}\right) X_{B}^{2} \)
When an equimolar mixture of \( A \) and \( B \) is distilled, find the composition (by mole) when this mixture will have a
single boiling point.
\( \left(P_{B}^{o}>P_{A}^{o}\right) \) where \( P_{A}^{o} \) and \( P_{B}^{o} \) are vapour
pressure of pure \( A \) and \( B \) respectively
and \( X_{B}= \) is the mole fraction of \( B \) in
the liquid phase.
A. 3:
B. 2:3
c. 1: 2
D. 1: 3


At puberty women start producing
A. Sperms
B. Urine
c. Young ones
D. ova


Let \( (x+y, 1) \) and \( (3, x-y) \) be equal
ordered pairs then find the value of \( x, y \)


An infinitely long straight conductor is
bent into shape as shown in figure. It
carries a current I A. and the radius of
circular loop is r metre. Then the
magnetic induction at the centre of the
circular loop is:
\( A \)
B. \( \frac{\mu_{0}}{\pi r_{0}} \)
c. \( \frac{\mu_{0} i}{2 \pi r}(\pi+1) \)
D \( \cdot \frac{\mu_{0} i}{2 \pi r}(\pi-1) \)


The number of isomers possible for
square planar complex \( \boldsymbol{K}_{2}\left[\boldsymbol{P} d \boldsymbol{C l} \boldsymbol{B} \boldsymbol{r}_{2} \boldsymbol{S} \boldsymbol{C} \boldsymbol{N}\right] \) is:
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D.


Carius method for the estimation of
halogens measures the amount of halogens by:
A. titration
B. fractional distilation
c. precipitate formation
D. none


Let \( n \) be a positive integer. If the
coefficients of \( 2^{n d}, 3^{r d} \) and \( 4^{t h} \) terms in
the expansion of \( (1+x)^{n} \) are in A.P.
then the value of \( n \) is:
\( \mathbf{A} \cdot \mathbf{8} \)
B. 27
c. 12
D.


Define refraction and state the laws of
refraction.


reported by two students \( X \) and \( Y \) for
an experiment on the study of
temperature-time graph. The experiment is likely to have been
performed correctly by
\begin{tabular}{lll}
Time (in min) & Student \( \boldsymbol{X} \) & Student \( \boldsymbol{Y} \) \\
0 & \( 61^{\circ} \mathrm{C} \) & \( 61^{\circ} \mathrm{C} \) \\
2 & \( 60.5^{\circ} \mathrm{C} \) & \( 59.0^{\circ} \mathrm{C} \) \\
4 & \( 60.0^{\circ} \mathrm{C} \) & \( 58.0^{\circ} \mathrm{C} \) \\
\hline 6 & \( 59.0^{\circ} \mathrm{C} \) & \( 57.5^{\circ} \mathrm{C} \) \\
\hline 10 & \( 58.0^{\circ} \mathrm{C} \) & \( 57.0^{\circ} \mathrm{C} \) \\
\hline 12 & \( 56.5^{\circ} \mathrm{C} \) & \( 56.5^{\circ} \mathrm{C} \) \\
\hline
\end{tabular}
\( A \cdot X \)
B. \( Y \)
c. both \( X \) and \( Y \)
D. neithe


Integrate the following:
\( \int_{0}^{\pi / 2} \sin ^{3} x \cos x d x \)


To initiate a reaction, minimum energy
which is required to break bonds is called
bond energy activation energy breaking energy ionization energy
A.
B. 2
\( c \cdot 3 \)
\( D \)


A body weighs 8 g when placed in one pan and 18 g when placed on the other pan of a false balance. If the beam
horizontal when both the pans are
empty, then the true weight of the body is :
\( A \cdot 15 g \)
B. 138
\( c \cdot 10 g \)
D. 12


The \( S . I . \) unit of heat capacity is
A. \( J-k g^{-1} \)
B . \( J K^{-1} \)
c. \( J-k g^{-1} K^{-1} \)
D. \( c a l^{o} C^{-} \)


Covalency of carbon in the \( C \) O molecule
is three because:
A. an unexcited carbon atom has two unpaired electrons
B. the carbon atom can be an acceptor of an electron pair
c. the carbon atom has four valence electrons
D. maximum covalency of carbon is three


The electronic charge 'e' is the possible charge.
A. maximum
B. minimum
c. avarage
D. total


The solution set for \( (x+3)+4> \)
\( -2 x+5 \) is
\( ^{A} \cdot\left(-\frac{2}{3}, \infty\right) \)
B. \( (2, \infty) \)
\( c \cdot(\infty,-2) \)
D. (-2,2)


Find the mean, mode and median of
marks obtained by 20 students in an examination. The marks are given below.
\( \begin{array}{lllll}\text { Marks } & 0- & 10- & 20- & 3 \\ 10 & 20 & 30 & 4\end{array} \)
No. of 1 1 4 tident


When HCl gas is passed through a
saturated solution of common salt,
pure NaCl is precipitated because
A. HCl is highly ionised in solution
B. HCl is highly soluble in water
C. The solubility product of NaCl is lowered by HC
D. The ionic product of \( \left[N a^{+}\right]\left[C l^{-}\right] \) exceeds the solubility product of NaCl


What type of waves are generated by SONAR device fixed to a fishing ship?
A. water waves
B. radiowaves
c. sound waves
D. infrared waves


What is the concentration of nitrate
ions if equal volumes of \( 0.1 M A g N O_{3} \)
and \( 0.1 M \) NaCl are mixed together?
\( \mathbf{A} \cdot 0.1 \mathrm{M} \)
B. 0.2 М
c. 0.05 M
D. 0.25 м


Method used to separate Petrol from crude oil is:
A. Distillation
B. chromatography
c. substallisation
D. fractional distillation


A metal 'M' on oxidation gives metal oxides MO that contains \( 80 \% \) oxygen.
Calculate the atomic weight of metal.


Statement 1: Transition metal
compounds generally exhibit bright colors. Statement 2: The electrons in the
partially filled d orbitals are easily
promoted to excited states.
A. Both Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation of Statement 1
B. Both Statement 1 and Statement 2 are correct and Statement 2 is not the correct explanation of Statement 1.
c. statement 1 is correct but statement 2 is not correct
D. Statement 1 is not correct but Statement 2 is correct
E. Both the Statement1 and Statement 2 are not correct


Evaluate \( \int_{0}^{\pi / 2} \sin x d x \)


What is not required in the formation of biogas in a biogas plant?
A. water
B. Oxygen
c. cow-dung
D. Anaerobic bacteria


Which of the following is not correct
regarding basic strength?
\( \mathbf{A} \)
B.
\( c \)
D.


Identify the variable from the equation, \( (t-7)>5 ? \)


Rice, Cereals, monocots and plants represent
A. Different taxa at different level.
B. Same taxa of different category
c. Different category of same taxa
D. Same category for different taxa


Which of the following inorganic compound is famous as raising agent?
A. Ammonium bicarbonate
B. Ammonium carbonate
c. Ammonium chloride
D. Ammonium dichloride


The blood sugar level is regulated by
A. Pancreas
B. Thyroid
c. Anterior pituitary
D. Posterior pituitary
E. Hypothalamus


Evaluate
\( \frac{\sin ^{2} 63+\sin ^{2} 27}{\cos ^{2} 27+\cos ^{2} 63} \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot-1 \)
D.


Let \( \boldsymbol{f}:(1,2) \rightarrow \mathbb{R} \) satisfies the
inequality \( \frac{\cos (2 x-4)-33}{2}<f(x)<\frac{x^{2}|4 x-8|}{x-2} \mid \forall x \in \)
\( (1,2) . \) then find \( \lim _{x \rightarrow 2^{-}} f(x) \)


An infinite parallel plane sheet of a metal is charged to charge density \( \sigma \) coulomb per square metre in a medium of dielectric constant \( K . \) Intensity of electric field near the metallic surface
will be :
\( ^{\mathrm{A}} \cdot_{E}=\frac{\sigma}{\varepsilon_{0} K} \)
в. \( _{E}=\frac{\sigma}{2 \varepsilon_{0}} \)
\( ^{\mathrm{c}}=_{E}=\frac{\sigma}{2 \varepsilon_{\varepsilon} K} \)
D. \( _{E}=\frac{K \sigma}{2 \varepsilon_{0}} \)