Numerical Problems
Two stones \( A \) and \( B \) are dropped from the top of two different towers such that
they travel \( 44.1 \mathrm{m} \) and \( 63.7 \mathrm{m} \) in the last second of their motion respectively. Find the ratio of the heights of the two towers from where the stones were
dropped.
A . 25: 49
B. 45: 49
\( c \cdot 35: 49 \)
D. 125 : 49


The electron beam in a television
picture tube travels a distance lin evacuated space of the tube. If the speed of the electrons is \( v \) and the beam
current is i, then the number of
electrons in the beam at any instant will
be
A. \( \frac{i l}{e v} \)
в. \( \frac{i}{l e v} \)
c. \( \frac{v}{i l e} \)
D. \( \frac{e}{i l v} \)


\( A B \) is a chord of a circle with center 0
Diameter CD is perpendicular to AB intersecting it at E. Show that \( \triangle A B C \) is isosceles.


Khadins, Bundhis, Ahars and Kattas are
ancient structures that are examples
for
A. Grain storage
B. Wood storage
c. water harvesting
D. Soil conservation


Which has more heat capacity: a bucket
full of water or a mug full of water?


A n insurance company insured 2000 scoo terdrivers. 4000 car drivers and
6000 truck drivers, 7 he probeblitey of an accident involving a scooter. a and truck is \( \frac{1}{100}, \frac{3}{100} \) and \( \frac{3}{20} \) respectively. one
of the insured persons meets with an accident. what is the probability that he is a scooter driver?


a sodium lamp of power 10 W is emmiting phtons of wavelength 590 nm Assuming that \( 60 \% \) of the consumed energy is converted into light, Find the number of photons emitted per second by the lamp.


Which of the air pressures is
appropriate for the production of cathode rays in the discharge tube?
\( A \cdot 1 \mathrm{cm} \) нв
B. \( 1 \mathrm{mm} \) Нg
c. \( 0.001 \mathrm{cm} \) Hg
D. 0.001 \( \mathrm{mm} \) ну


The atomic number of magnesium is 12 The number of protons in the nucleus of magnesium atom is:
\( A \cdot 6 \)
B. 10
c. 12
D. 24


Give the IUPAC names of the following compounds:
Acetaldehyde


State whether given set is empty or
not?
Set of even prime numbers


A sphere ' \( A \) ' is placed at frictionless table. another sphere ' \( B \) ' is suspended
as shown in fig. both the spheres are identical in all respects.equal quantity of heat is supplied to both sphere all kind of heat loses are neglected the
final temperature of \( \boldsymbol{A} \) and \( \boldsymbol{B} \) are \( \boldsymbol{T}_{\boldsymbol{A}} \)
and \( T_{B} \) respectively then :
A \( \cdot T_{A}=T_{B} \)
В . \( T_{A}<T_{B} \)
\( c \cdot T_{A}>T_{B} \)
D. data is insufficient


What is the smallest distance between
the point (-2,-2) and a point on the circumference of the circle given by
\( (x-1)^{2}+(y-2)^{2}=4 ? \)
\( A \cdot 3 \)
B. 4
\( c .5 \)
D. 6
E. 7


There wires are situated at the same
distance. A current of \( 1 A, 2 A, 3 A \) flows
through these wires in the same
direction. What is ratio \( \boldsymbol{F}_{1} / \boldsymbol{F}_{2} \) where \( \boldsymbol{F}_{1} \)
is force on 1 and \( F_{2} \) on \( 2 ? \)
A . \( 7 / 8 \)
B.
c. \( 9 / 8 \)
D. none of the above


Which of the following parent oxy acid does not have its hypo acid?
A. \( H_{2} S O_{2} \)
в. \( H N O_{2} \)
\( \mathrm{c} . H_{3} P O_{3} \)
D. \( H C l O_{3} \)


Water of mass \( m_{2}=1 \mathrm{kg} \) is contained in a copper calorimeter of mass \( m_{1}=1 \mathrm{kg} \)
Their common temperature \( t=10^{0} C \)
Now a piece of ice of mass \( m_{3}=2 \mathrm{kg} \) and temperature is \( 11^{0} C \) dropped into the calorimeter. Neglecting any heat loss, the final temperature of system is. [specific heat of copper \( =0.1 \mathrm{Kcal} / \mathrm{kg}^{0} \boldsymbol{C} \)
specific heat of water \( =1 \mathrm{Kcal} / \mathrm{kg}^{0} \boldsymbol{C} \)
specific heat of ice \( =0.5 \mathrm{Kcal} / \mathrm{kg}^{0} \boldsymbol{C} \)
latent heat of fusion of ice \( =78.7 \)
Kcal/kg]
\( \mathbf{A} \cdot 0^{0} C \)
в. \( 4^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot-4^{0} C \)
D. \( -2^{0} C \)


How will you obtain OR, AND gates from
the NAND and NOR gates? Write symbol, Boolean formula and truth table.


Work function of a metal is the:
A. Energy required by an electron to get absorbed in the metal surface.
B. Minimum energy required by an electron to escape from the metal surface.
C. Energy required by an electron to be retained in the metal surface.
D. Maximum energy required by an electron to escape from the metal surface.


A potentiometer wire of length \( 1 \mathrm{m} \) has a resistnce of \( 10 \Omega \).It is connected to a 6 v
battery in series with a resistance of \( 5 \Omega \) Determine the emf of the primary cell which gives a balance point at \( 40 \mathrm{cm} \)


Which compound acts as an oxidizing as well as a reducing agent?
\( A \cdot S O_{2} \)
в. \( M n_{2} O_{7} \)
c. \( A l_{2} O_{3} \)
D. \( C r O_{3} \)


Find the amount of work done by friction and gravity till the chain leaves the table, if the hanging part is pulled gently and released
A \( \cdot \frac{5 m g \ell}{18} \)
в. \( \frac{18 m g \ell}{5} \)
c. \( \frac{m g \ell}{5} \)
D. \( \frac{m g \ell}{18} \)


The rate of change of surface area of a
sphere of radius \( r \) when the radius is
increasing at the rate of \( 2 \mathrm{cm} / \) sec is
proportional to
A \( \cdot \frac{1}{r^{2}} \)
B. \( \frac{1}{r} \)
\( c \cdot r^{2} \)
D.


An electric charge produces an electric intensity of \( 500 N / C \) at a point in air. If the air is replaced by a medium of dielectric constant \( 2.5, \) then the intensity of the electric field due to the
same charge at the same point will be:
A \( .100 N / C \)
в. \( 150 N / C \)
c. \( 200 N / C \)
D. \( 300 N / C \)


A car covers half the distance at a
speed of \( 50 \mathrm{km} / \mathrm{hr} \) and the other half at
\( 40 \mathrm{km} / \mathrm{hr} . \) Find the average speed of
the car.


If \( z \) is a unimodular complex number, then its multiplicative inverse is,
\( \mathbf{A} \cdot \bar{z} \bar{z} \)
B.
\( c \cdot-z \)
D. - \( \bar{z} \)


When we jump forward out of a boat standing in water it moves backwards.
A. True
B. False


When simplified the value of \( \left[\boldsymbol{i}^{57}-\right. \)
\( \left.\left(1 / i^{25}\right)\right] \) is?
\( \mathbf{A} \cdot \mathbf{0} \)
в. \( 2 i \)
c. \( -2 i \)
D. 2


Calculate the total number of optical isomers of the following compounds respectively:
Tartaric acid, lactic acid, fumaric acid
and cinnamic acid.
в. 3,2,0,1
\( \mathrm{c} .2,2,0,0 \)
D. 3,2,0,0


Among the following the number of
compounds that can react with \( P C l_{5} \) to
give \( P O C l_{3} \) is :
\( \boldsymbol{O}_{2}, \boldsymbol{C} \boldsymbol{O}_{2}, \boldsymbol{S} \boldsymbol{O}_{2}, \boldsymbol{H}_{2} \boldsymbol{O}, \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4}, \boldsymbol{P}_{4} \boldsymbol{O}_{10} \)
A
B. 3
\( c \cdot 4 \)
D. 5


topp
Q Type your question
are arranged in 100 rows, each row stretching horizontally along the body of
the fish containing 5000 electroplaques. The arrangement is suggestively shown below. Each
electroplaques has an emf of 0.15 V and
internal resistance of \( 0.25 \Omega . \) The water
surrounding the Eel completes a circuit between the head and its tail. If the
water surrounding it has a resistance of
\( 500 \Omega, \) the current an Eel can produce in
water is about :
\( A \cdot 1.5 \mathrm{A} \)
в. 3.0 А
\( c \cdot 15 \)
0.30


When will multiple objects of different nature, shape, size etc fall from the
same height at the same rate?
A. In the presence of vaccum
B. on the poles
c. on the equator
D. None of the above


The process of separating of cream from milk is called :
A. Emulsification
B. Demulsification
c. Emulsions
D. Electro-osmosis


n \( \triangle P Q R, \) seg \( P M \) is the median
Bisectors of \( \angle \boldsymbol{P} M Q \) and \( \angle \boldsymbol{P} M \boldsymbol{R} \)
intersect side \( P Q \) and side \( P R \) in
points \( X \) and \( Y \) respectively, then prove
that \( \boldsymbol{X} \boldsymbol{Y} \| \boldsymbol{Q} \boldsymbol{R} \)


The values of \( x \) at which \( f(x)=\sin x \) is stationary are given by
A. \( \mathrm{n} \pi, \forall n \in Z \)
в. \( (2 \mathrm{n}+1) \frac{\pi}{2}, \forall n \in Z \)
c. \( \frac{\mathrm{n} \pi}{4}, \forall n \in Z \)
D. \( \frac{\mathrm{n} \pi}{2}, \forall n \in Z \)


Which scientists are related with light
reaction and what is its site?
A. Arnon and Hill, grana
B. Ruben and Kamen, Stroma
C. Willstatter, Stoll, inner membrane of chloroplast
D. Calvin and Benson, outer membrane of choloplast


Assertion
In atomic form hydrogen consists one proton and one electron.
Reason
In elemental form hydrogen exists as a diatomic molecule and is called
dihydrogen.
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


What is the formula of Acrolein?
A. \( C H_{2}=C H-C H O \)
в. \( C H_{2}=C H-C N \)
c. \( C H_{2}=C N-C O O H \)
D. \( C H_{2}=C H-C O N H_{2} \)


\( p K_{a_{1}} \) of carbonic acid in blood at body
temperature \( \left(37^{\circ} C\right) \) is \( 6.1 . \) Hence, ratio
\( \left[\boldsymbol{H} \boldsymbol{C O}_{3}^{-}\right] /\left[\boldsymbol{H}_{2} \boldsymbol{C O}_{3}\right] \) is approximately:
A . 1.3:
B. 1: 1.3
\( c \cdot 20: \)
D. 1: 20


\( \boldsymbol{C H}_{3}-\underset{\boldsymbol{C} \boldsymbol{H}_{3}}{\boldsymbol{C} \boldsymbol{H}}-\stackrel{\boldsymbol{P} \boldsymbol{h}}{\boldsymbol{C} \boldsymbol{H}}-\boldsymbol{N} \boldsymbol{H}_{2} \)
The IUPAC name of the compound is :
A. 1-Amino-1-phenyl-2-methyl propane
B. 2-Methyl-1-phenyl propan-1-amine
c. 2-Methyl-1-amino-1-phenyl propane
D. 1-lsopropyl-1-phenyl methyl amine


State whether true or false.
The image formed by a plane mirror is always real
A. True
B. False


Which among the following devices work on the basis of photo-voltaic effect?

This question has multiple correct options
A. Photo-diode
B. Light Emitting Diode (LED)
c. solar Cell
D. None of these


The coefficient of \( x^{n} \) in the expansion of \( \frac{1}{(1-x)(1-2 x)(1-3 x)} \) is
A \( \cdot \frac{1}{2}\left(2^{n+2}-3^{n+3}+1\right) \)
B. \( \frac{1}{2}\left(3^{n+2}-2^{n+3}+1\right) \)
c. \( \frac{1}{2}\left(2^{n+3}-3^{n+2}+1\right) \)
D. none of these


Find the sum of -23 and 3


Consider the function \( f(x)=8 x^{2}- \)
\( 7 x+5 \) on the interval \( [-6,6] . \) The value
of \( c \) that satisifies the conclusion of the
mean value theorem is
A \( -\frac{7}{8} \)
B. -4
\( c \cdot \frac{7}{8} \)
D. 0


The element with the electronic
configuration \( 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 3 d^{10} 4 s^{1} \)
is:
A. \( C u \)
в. \( C a \)
\( c \cdot C r \)
D. \( C o \)


A compound (X) of molecular formula
\( C_{3} H_{8} O \) can be oxidized to a compound
of molecular \( C_{3} H_{6} O_{2}(Y) .(X) \) is most
likely to be
A. aldehyde
B. alcohol
c. ether
D. both B and C


Two open pipes of length \( L \) are vibrated
simultaneously. If length of one of the
pipes is reduced by \( y, \) then the number of beats heard per second will nearly be (if the velocity of sound is \( v \text { and } y<L) \)
A \( \cdot \frac{v y}{2 L} \)
B. \( \frac{2 L^{2}}{V y} \)
c. \( \frac{v y}{2 L^{2}} \)
D. \( \frac{v y}{L^{2}} \)


Ellingham diagram represents the change in:
A. G with temperature
B. \( H \) with temperature
c. \( G \) with pressure
D. \( G-T S \) with temperature


A train 110 metres long is running with a speed of \( 60 \mathrm{km} / \mathrm{hr} \). In what time it pass
a man who is running at 6 kmph in the direction opposite to that in which the train is going?
A . 5 sec
B. 6 sec
\( c \cdot 7 \sec \)
D. 10 sec


f \( \boldsymbol{y}=\boldsymbol{a} \cos (\sin 2 \boldsymbol{x})+\boldsymbol{b} \sin (\sin 2 \boldsymbol{x}) \)
then \( \boldsymbol{y}^{\prime \prime}+(2 \tan 2 \boldsymbol{x}) \boldsymbol{y}^{\prime}= \)
\( A \)
B \( \cdot 4\left(\cos ^{2} 2 x\right) y \)
c. \( -4\left(\cos ^{2} 2 x\right) y \)
\( D \cdot-\left(\cos ^{2} 2 x\right) y \)


Equation of the plane containing the \( \operatorname{lines} \overline{\boldsymbol{r}}=(\overline{\boldsymbol{i}}-\boldsymbol{2} \overline{\boldsymbol{j}}+\overline{\boldsymbol{k}})+\boldsymbol{t}(\overline{\boldsymbol{i}}+\mathbf{2} \overline{\boldsymbol{j}}-\overline{\boldsymbol{k}}) \)
\( \boldsymbol{\boldsymbol { r }}=(\overline{\boldsymbol{i}}+\mathbf{2} \overline{\boldsymbol{j}}-\overline{\boldsymbol{k}})+\boldsymbol{s}(\overline{\boldsymbol{i}}+\overline{\boldsymbol{j}}+\mathbf{3} \overline{\boldsymbol{k}}) \) is
A. \( \bar{r}(7 \bar{i}-4 \bar{j}-\bar{k})=14 \)
В. \( \bar{r}(\bar{i}+2 \bar{j}-\bar{k})=10 \)
c. \( \bar{r}(\bar{i}+\bar{j}+3 \bar{k})=20 \)
D. \( \bar{r}(\bar{i}-2 \bar{j}+\bar{k})=27 \)


A ray of light passes from medium 1 to
medium 2. Which are the quantities of the refracted ray will not differ from that
of the incident ray?
A. Speed
B. intensity
c. wavelength
D. frequency


\( f\left(a_{1}, a_{2}, a_{3} \dots, a_{n} \cdot \) are in G.P, then the \right.
determinant \( \Delta= \) \( \left|\begin{array}{ccc}\log a_{n} & \log a_{n+1} & \log a_{n+2} \\ \log a_{n+3} & \log a_{n+4} & \log a_{n+5} \\ \log a_{n+6} & \log a_{n+7} & \log a_{n+8}\end{array}\right| \) is equal
to
A . 0
B. 1
\( c \cdot 2 \)
D.


Which one of the following is proteinaceous in chemical nature?
A. Thyroxine
B. Insulin
c. Progesterone
D. Oxytocin


Discuss the main purpose of
vulcanisation of rubber


Factors responsible for the rapid spread of bread mould on slices of bread are
(i) Large number of spores.
(ii) Availability of moisture and nutrients in bread.
(iii) Presence of tubular branched
hyphae.
(iv) Formation of round shaped
sporangia.
A. (i) and (iii)
B. (ii) and iv)
c. (i) and (ii)
D. (iii) and (iv)


State True or False.
\( \boldsymbol{n}^{n}>1 \times \mathbf{3} \times \mathbf{5} \times \mathbf{7} \times \ldots \ldots \times(\mathbf{2 n}-\mathbf{1}) \)
A. True
B. False


Biological importance of ozone layer is:
A. it stops ultraviolet rays
B. ozone layer reduces green house effect
C. ozone layer reflects radio waves
D. ozone layer controls \( O_{2} / H_{2} \) ratio in atmosphere


Enzyme catalysis is an example of:
A . autocatalysis
B. heterogeneous catalysis
c. homogeneous catalysis
D. induced catalysis


The practical unit of resistance is \( \Omega \) and \( 1 \Omega \) is equal to:
A \( \cdot 10^{18}_{e m u} \)
В. \( 10^{9} \)ети
\( \mathbf{c} \cdot 10^{15} e m u \)
D. none of these


The equivalent resistance between the points 1 and 7 the adjoining circuit (fig)
will be
\( A \cdot \frac{7}{1} \)
12
в. \( \frac{5}{6} r \)
\( c \)
D. none of these


Assertion
Group 2 metals have higher melting points when compared to the group 1
metals.
Reason
+2 charge on the cations in the metallic
lattice causes them to be more strongly
attracted to the sea of electrons and
making it difficult to pull them apart.
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


To hear a distinct echo, the minimum
distance of a reflecting surface should
be
A. \( 7 m \)
в. \( 17 m \)
\( c .27 m \)
D. \( 10 m \)


Reflex arcs are formed in the
\( A \). Brain
B. Spinal cord
c. Heart
D. Eye


Explain what is observed when:
(i) a beam of light is passed through a colloidal sol.
(ii) an electrolyte, \( N a C l \) is added to hydrated ferric oxide sol.
(iii) electric current is passed through a colloidal sol.


If \( a b c=1, \) then \( \frac{1}{1+a+b^{-1}}+ \)
\( \frac{1}{1+b+c^{-1}}+\frac{1}{1+c+a^{-1}} \) is equal to
\( A \)
B. 0
\( c \)
D. - 5


The shaded portion on a 24 hour clock given below tells the sleeping time of a sloth' (a bear). Find the time for which
the sloth is asleep. Find the time for which the sloth is awake. If it sleep at 6 h 15 min then when does the sloth
awake.


The reciprocal of resistance is conductance. The unit of resistance is
ohm. Therefore, the unit of conductance
is
A. ohm
B. henry
c. per ohm
D. moles/litre


Which of the following is(can be) continuous at each point of its
domain-
This question has multiple correct options
A \( . f(x) \)
в. \( g(x) \)
c. \( k(x) \)
D. all three \( f, g, k \)


The value of the expression \( \lim _{x \rightarrow 0} \frac{x \sin (\sin x)}{1-\cos x} \) is
\( A \)
B. 2
\( c \cdot 4 \)
D.


(i) With reference to their direction of
action, how does a centripetal force differ from a centrifugal force?
(ii) State the Principle of conservation of energy.
(iii) Name the form of energy which a body may possess even when it is not in motion.


Pick out among the following species
isoelectronic with \( C O_{2}: \) This question has multiple correct options
A. \( N_{3}^{-} \)
в. \( (C N O)^{-} \)
C \( \cdot(N C N)^{2} \)
D. \( N O_{2}^{-} \)


A body of mass \( 2 \mathrm{kg} \) makes an elastic collision with another body at rest and continues to move in the original direction at a speed equal to \( 1 / 3 \) of its original speed. The mass of the second body is
A. \( 2 k g \)
в. \( 3 k g \)
c. \( 1 k g \)
D. \( 4 k g \)


Which of the following reaction gives secondary amine?
A. Reduction of amide
B. Reduction of carbylamine
c. Reduction of nitro compound
D. Hoffmann reduction


The IUPAC name for the coordination
compound \( \boldsymbol{B} \boldsymbol{a}\left[\boldsymbol{B} \boldsymbol{r} \boldsymbol{F}_{4}\right]_{2} \) is:
A. barium tetrafluorobromate (V)
B. barium tetrafluorobromate (III)
c. barium bis(tetrafluorobromate) (III)
D. none of these


An aeroplane is flying vertically upwards with a uniform speed of
\( 500 m / s \) When it is at a height of 1000 \( m \) above the ground a shot is fired at it with the speed of \( 700 m / s \) from a point directly below it.The minimum uniform acceleration of the aeroplane now so that it may escape from being hit? \( \left[\boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{2}\right] \)
A \( \cdot 10 m / s^{2} \)
в. \( 8 m / s^{2} \)
\( \mathbf{c} \cdot 12 m / s^{2} \)
D. None of these


What will be change in value of gravitational acceleration with increase in \( r \) from the center of the earth?
A. Decreases continuously
B. Increases continuously
C. Initially increases then decreases
D. Initially decreases then increases


Hydrogen bonding plays a central role in
the following phenomena:
This question has multiple correct options
\( \mathbf{A} \cdot \) Ice floats in water
B. Higher Lewis basicity of primary amines than tertiary amines in aqueous solutions.
C. Formic acid is more acidic than acetic acid.
D. Dimerisation of acetic acid in benzene.


What is the nomenclature of
\( \left[\boldsymbol{C o C l}_{2}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4}\right]^{+} ? \)


Mark the correct alternative of the
following.
The least and greatest values of \( f(x)= \) \( x^{3}-6 x^{2}+9 x \) in \( [0,6], \) are?
A .3,4
в. 0,6
c. 0,3
D. 3,6


In the figure, find \( x \)


The major product of the reaction is :
\( A \)
\( B \)
\( c \)
\( D \)


The figure shows in apart of an electric
circuit, then the current I is
A . \( 1 A \)
B. \( 3 A \)
\( c .2 A \)
D. \( 4 A \)


If the sum of the squares of the distance of a point from the three
coordinate axes be \( 36, \) then its distance
from the origin is
A. 6 units
B. \( 3 \sqrt{2} \) units
c. \( 2 \sqrt{3} \) units
D. none of these


Mrs. Priya earns 24000 per month. She spends \( \frac{7}{12} \) on household items and \( \frac{1}{8} \) on rest of the things. The amount she saves is
A. Rs. 8000
B. Rs. 7000
c. Rs. 6000
D. Rs. 5000


A book is purchased for Rs.75 and sold for Rs.100.Find the gain percent.


Choose the correct answer
A. Every scalar matrix is an identity matrix
B. Every identity matrix is a scalar matrix
C. Every diagonal matrix is an identity matrix
D. A square matrix whose each element is 1 is an identity matrix


Which one is the weakest type of bonding in solids?
A. Ionic
B. Covalent
c. Metallic
D. vander wall's


To which of the following mixtures Dalton's law is not applicable?
This question has multiple correct options
A \( \cdot C O_{2} \) and \( \operatorname{co~at~room~temperature~} \)
B. Ammonia and hydrogen chloride at room temperature
\( \mathrm{c} \cdot N H_{3} \) and steam at room temperature
D. He and \( H_{2} \)


The formula to find SD is
This question has multiple correct options
\( \mathbf{A} \cdot \sqrt{\frac{\sum(x-\bar{x})^{2}}{n}} \)
B. \( \sqrt{\frac{\sum x^{2}}{n}-\left(\frac{\sum x}{n}\right)} \)
\( \mathbf{C} \cdot \sqrt{\frac{\sum x^{2}}{n}-\left(\frac{\sum x}{n}\right)^{2}} \)
\( ^{\mathrm{D}} \cdot \frac{\sum x}{n}-\left(\frac{\sum x}{2}\right)^{2} \)


If \( A \) and \( B \) are invertible matrices of
order
3. \( |\boldsymbol{A}|=\mathbf{2} \) and \( \left|(\boldsymbol{A B})^{-1}\right|=-\frac{\mathbf{1}}{\mathbf{6}} \)
Find \( |\boldsymbol{B}| \)


\( \boldsymbol{C H}_{3}-\boldsymbol{C} \equiv \boldsymbol{C}-\boldsymbol{C H}_{3} \frac{(i) \boldsymbol{x}}{(i i) Z n / \boldsymbol{H}_{2} \boldsymbol{O}} \)
\( \boldsymbol{C H}_{3}-\underset{\boldsymbol{O}}{\boldsymbol{V}}-\underset{\boldsymbol{O}}{\boldsymbol{V}}-\boldsymbol{C H}_{\boldsymbol{3}} \)
In the above reaction \( x \) is:
A \( . H N O_{3} \)
B. \( O_{2} \)
\( c \cdot O_{3} \)
D. \( K M n O_{4} \)


Find the ratio in which the \( y- \) axis
divides the line segment joining the points (5,-6) and \( (-1,-4) . \) Also find the point of intersection.


At high temperatures,nitrogen directly combines with:
This question has multiple correct options
\( A \cdot Z n \)
в. Мв
\( c \cdot A \)
D. Fe


Show that the straight line \( 3 x+2 y- \)
\( 12=0 \) and \( 6 x+4 y+8=0 \) are
parallel.


Write the unit vector in the direction of \( \overrightarrow{\boldsymbol{A}}=\mathbf{5} \overrightarrow{\boldsymbol{i}}+\overrightarrow{\boldsymbol{j}}-\boldsymbol{2} \overrightarrow{\boldsymbol{k}} \)


Which of the following statements is
true?
A. Wings of birds and insects are homologous organs
B. Human hands and bird's wings are analogous organs
C. Human hands and bat's wings are analogous organs
D. Flipper of penguin and dolphin are analogous organs


Solve: \( \left(\frac{1}{1-2 i}+\frac{3}{1+i}\right)\left(\frac{3+4 i}{2-4 i}\right) \)


Rocket works on the principle of conservation of:
A. Mass
B. Energy
c. Momentum
D. Velocity


metres
\( \mathbf{A} \cdot 10^{-1} \)
B . \( 10^{-2} \)
\( \mathbf{C} \cdot 10^{1} \)
D. \( 10^{2} \)


Evaluate \( \int \frac{1}{\sqrt{3} \sin x+\cos x} d x \)


A plane polarized light passed through successive polarizers which are rotated
by \( 30^{\circ} \) with respect to each other in the
clockwise direction. Neglecting absorption by the polarizers and given that the first polarizer's axis is parallel to the plane of polarization of the incident light, the intensity of light at the exit of the fifth polarizer is closest
to.
A. Same as that of the incident light
B. 17.5\% of the incident light
c. \( 30 \% \) of the incident light
D. zero


The angular momentum of the earth revolving round the sun, is proportional
to \( r^{n}, \) where \( r \) is the distance between
the centres of earth and the sun. The
value of \( n \) is :
A . 1
B. -2
c. -1
D. \( \frac{1}{2} \)


toppr
Q Type your question
4
\( (a) \)
3
\( (b) \)
2
\( (c) \)
\( (d) \)


If \( \mathbf{3} \boldsymbol{A}=\left[\begin{array}{ccc}\mathbf{1} & \mathbf{2} & \mathbf{2} \\ \mathbf{2} & \mathbf{1} & -\mathbf{2} \\ \boldsymbol{x} & \mathbf{2} & \boldsymbol{y}\end{array}\right], \) and \( \boldsymbol{A} \boldsymbol{A}^{\prime}=\boldsymbol{I} \)
then \( -\boldsymbol{x}-\boldsymbol{y}=\ldots \)


The line \( A D \) is divided in the ratio of
\( A B: B C: C D=1: 3: 4 . \) If \( A B= \)
\( 0.8 \mathrm{cm}, \) calculate the length of \( A D \)
A . \( 3.5 \mathrm{cm} \)
B. \( 6.4 \mathrm{cm} \)
c. \( 5.89 \mathrm{cm} \)
D. \( 6.5 \mathrm{cm} \)


Illustrate the following terms:
(a) Copolymerization
(b) Vulcanization


ff \( (9)=0, f^{\prime}(9)=4, \) then
\( \lim _{x \rightarrow 9} \frac{\sqrt{f(x)}-3}{\sqrt{x}-3}= \)
\( A \cdot 9 \)
B. 4
\( c . \) 36
D. None of these


Clinging roots occur in
A. Trapa
B. Orchid
c. Screwpine
D. Podostemon


Find the derivative with respect to \( x \) of
the function
\( \left(\log _{\cos x} \sin x\right)\left(\log _{\sin x} \cos x\right)^{-1}+ \)
\( \sin ^{-1} \frac{2 x}{1+x^{2}} \) at \( x=\frac{\pi}{4} \)
A \( \cdot g\left(\frac{4}{\pi^{2}+16}-\frac{1}{\log 2}\right) \)
B. \( -8\left(\frac{4}{(\pi+4)^{2}}-\frac{1}{\log 2}\right) \)
\( ^{\mathbf{c}} \cdot_{8}\left(\frac{4}{\pi^{2}+16}+\frac{1}{\log 2}\right) \)
D \( \cdot g\left(\frac{4}{(\pi+4)^{2}}-\frac{1}{\log 2}\right) \)


Explain the cause of algal bloom in a
water body. How does it affect an
ecosystem.


A negatively charged particle called Negatron was discovered. In the Millikan's oil-drop experiment, the charges of the oil-drops in five experiments are reported as \( 3.2 \times \)
\( 10^{-19} \) coulomb; \( 4.8 \times 10^{-19} \) coulomb
\( 6.4 \times 10^{-19} \) coulomb


1 g of ice at \( 0^{\circ} \mathrm{C} \) is supplied with \( 500 \mathrm{J} \) of heat energy. Explain the temperature change of material


Draw a circle of radius \( 5 \mathrm{cm} . \) From a
point \( 8 \mathrm{cm} \) away from the centre,
construct two tangents to the circle.
Measure them.
(Write the steps of construction).


Assertion
The value of the determinant
\( \begin{array}{|ccc|}\tan ^{-1} x & \cot ^{-1} x & \pi / 2 \\ \sin ^{-1}(4 / 5) & \sin ^{-1}(3 / 5) & \sin ^{-1} 1 \\ \cos ^{-1}(3 / 5) & \cos ^{-1}(4 / 5) & 1\end{array} \)
equal to zero for all values of \( x \)
Reason
\( 2 \cos ^{-1} x=\cos ^{-1}\left(2 x^{2}-1\right) \) if \( -1 \leq \)
\( x \leq 1 \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


\( 100 \mathrm{ml} \) of \( 0.1 \mathrm{M} C \mathrm{H}_{3} \mathrm{COOH} \) is mixed
with \( 50 \mathrm{ml} \) of \( 0.1 \mathrm{M} \) NaOH solution and
pH of the resulting solution is 5. The change in pH if \( 100 \mathrm{ml} \) of \( 0.05 \mathrm{M} \) NaOH
is added in the above solution is:
A . 1.30
B. 4.74
\( c \cdot 5 \)
D. 3.8


The maximum speed of a body vibrating
under S.H.M. with time period of \( \pi / 4 \) s
amplitude \( 7 \mathrm{cm} \) is
\( A \cdot 488 \mathrm{cm} / \mathrm{s} \)
B. \( 56 \mathrm{cm} / \mathrm{s} \)
c. \( 38.5 \mathrm{cm} / \mathrm{s} \)
D. \( 5.5 \mathrm{cm} / \mathrm{s} \)


If \( (2.3)^{x}=(0.23)^{y}=1000 \) then find the value of \( \frac{1}{x}-\frac{1}{y} \)


The advantages of being short and stocky is that you're less likely to get knocked over. This is because
A. The short and stocky person has a lower center of gravity
B. The short and stocky person has a larger center of gravity
c. They have less height and less weight
D. None of the above


In "Rivet popper hypothesis "Paul Ebrlich, the rivets on the wings
represents in
ecosystem
A. key species
B. Exotic species
c. Extinct species
D. Invasive species


What is parallax? Explain.


According to Le Chatelier principle, an
increase in the temperature of the following reaction will:
\( N_{2}+O_{2} \rightleftharpoons 2 N O-43200 \) cal


If the angle \( x \) and \( y \) are equal, then find
the value of \( x \) and \( y \)
\( \mathbf{A} \cdot x=y=55^{\circ} \)
\( \mathbf{B} \cdot x=y=45^{\circ} \)
\( \mathbf{C} \cdot x=y=60^{\circ} \)
D \( . x=y=90^{\circ} \)


In the first two groups of periodic table, the group number represents the :
A. valency
B. atomic weight
c. atomic number
D. oxidising nature


The current drawn by a \( 220 V \) DC series
motor of armature resistance 0.50 and
back emf \( 200 \mathrm{V} \) is
A \( .40 A \)
в. \( 400 A \)
\( \mathbf{c} \cdot 450 A \)
D. \( 500 A \)


Using differentials, find the sum of digits approximate value of the following up to 3 places of decimal. \( (82)^{\frac{1}{4}} \)


The speed of sound in a perfectly rigid
rod is
A. infinite
в. Zero
\( \mathrm{c} .332 \mathrm{m} / \mathrm{s} \)
D. \( 3 \times 10^{8} \mathrm{m} / \mathrm{s} \)


A \( 1.5 m \) wide by \( 2.5 m \) long water bed
weighs \( 1025 N \). Find the pressure that
the water bed exerts on the floor.

Assume that the entire lower surface of
the bed makes contact with the floor.
A. \( 273.3 P a \)
в. \( 373.5 P a \)
\( \mathbf{c} .173 .3 P a \)
D. \( 473.3 P a \)


The region between \( \boldsymbol{x}=\mathbf{0} \) and \( \boldsymbol{x}=\boldsymbol{L} \) is
filled with uniform, steady magnetic field \( B_{0} \hat{k} . \) A particle of mass \( m, \) positive charge \( q \) and velocity \( v_{0} \hat{i} \) travels along
x-axis and enters the region of magnetic field. Neglect gravity throughout the question. The field now
extends up to \( x=2.1 L \) If the time
spent by the particle in the magnetic field is \( T=\frac{\pi m}{X \times q B_{0}} . \) Find \( X ? \)


For describing law of multiple proportions, which among the following pair can be used?
A . NO and \( N O_{2} \)
B. \( C H_{4} \) and \( C O_{2} \)
c. \( Z n O_{2} \) and \( Z n C l_{2} \)
D. \( N H_{3} \) and \( N H_{4} C l \)
E. \( H_{2} O \) and нс


If \( \boldsymbol{A}+\boldsymbol{B}=\frac{\boldsymbol{\pi}}{\boldsymbol{4}} \) then value of \( (\boldsymbol{1}+ \)
\( \tan A)(1+\tan B)= \)
\( A \cdot 4 \)
B.
\( c \cdot 2 \)
D. none of these


If \( \frac{1+4 p}{4}, \frac{1-p}{2}, \frac{1-2 p}{2} \) are
probabilities of three mutually exclusive events, then
A \( \cdot \frac{1}{3} \leq p \leq \frac{1}{2} \)
в. \( \frac{1}{3} \leq p \leq \frac{2}{3} \)
c. \( \frac{1}{6} \leq p \leq \frac{1}{2} \)
D. None of these


Name the type of motion in which a girl is skipping a rope at a particular spot
A. Rotatory motion
B. Periodic motion
c. simple harmonic motion
D. none


Assertion: The standard potential of
hydrogen half-cell is zero at all conditions of temperature and
pressure. Reason: Standard conditions require 298 K temperature and 1 atm pressure.
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
E. Both Assertion and Reason are false


Man A is sitting in a car moving with a speed of \( 54 \mathrm{km} / \mathrm{hr} \) observes a man \( \mathrm{B} \) in
front of the car crossing perpendicularly a road of width \( 15 \mathrm{m} \) in three seconds. Then the velocity of man
\( \mathrm{B}(\text { in } \mathrm{m} / \mathrm{s}) \) will be
A \( .5 \sqrt{10} \) towards the car at some angle
B. \( 5 \sqrt{10} \) away from the car at some angle
c. 5 perpendicular to the road
D. 15 along the road


How many minimum NAND GATEs are
required for obtaining an output of \( A . B+C . D ? \)


All first order reactions are
unimolecular.
A. True
B. False


\( M g^{2+} O^{2-} \) is formed since :
A. IE of \( M g \) is low
B. EA of \( O \) is low
c. IE of \( M g \) is high
D. IE of \( O \) is low


The magnetic field \( B=2 t^{2}+4 t^{2} \)
(where \( t= \) time ) is applied perpendicular to the plane of a circular wire of radius \( r \) and resistance \( R \). If all
the units are in SI the electric charge that flows through the circular wire during \( t=0 s \) to \( t=2 s \) is
A \( \cdot \frac{6 \pi r^{2}}{R} \)
в. \( \frac{24 \pi r^{2}}{R} \)
c. \( \frac{32 \pi r^{2}}{R} \)
D. \( \frac{48 \pi r^{2}}{R} \)


If a cell with 5 chromosome pairs undergoes mitosis, then what be the total number of chromosomes in its
anaphase stage?
A . 5
B. 10
c. 15
D. 20


Plant organs can detect a change in their orientation with respect of gravity
A. Within a few seconds
B. Atleast a minimum of thirty minutes
c. Atleast they have to be kept for a day
D. Atleast they have to be kept for a week


A long spring is fixed at one end. \( A \)
person holding the other end compresses the spring with a jerk. The compression travels along the length of the spring. Which kind of wave is
travelled along the length of the spring?
A. Electromagnetic waves
B. Transverse waves
c. Longitudinal waves
D. Both (A) and (C)


The coordinates of the foot of the
perpendicular drawn from of the origin to a plane are \( (12,-4,3) . \) Find the equation of the plane.


\( H_{2} O_{2} \) decomposes below its boiling point if it is distilled at ordinary
pressure.
A. True
B. False


In the given figure, the area of the
shaded portion APB is?
A \( -\frac{1}{4} \pi r^{2} \)
B. \( \frac{1}{4}(\pi-2) r^{2} \)
c. \( \frac{1}{4}(\pi-1) r^{2} \)
D. None of these


Match the reactions in list I with the
number of electrons that participate in list II.


Determine the set of values of \( k \) for
which the given quadratic equation has
real roots:
\( \mathbf{2} \boldsymbol{x}^{2}+\boldsymbol{k} \boldsymbol{x}-\boldsymbol{4}=\mathbf{0} \)


The foci of an ellipse are \( \boldsymbol{S}(-1,-1), \boldsymbol{S}^{\prime}(0,-2) \) and its \( \mathbf{e}=\frac{1}{2} \)
then the equation of the directrix corresponding to the focus \( S \) is :
A. \( x-y+3=0 \)
в. \( x-y+7=0 \)
c. \( x-y+5=0 \)
D. \( x-y+4=0 \)


Weight of 40 eggs were recorded as given below
weight
in
grams
90- 95- 100\( \begin{array}{ll}85- & 5 \\ 90 & 5\end{array} \) 104 \( \operatorname{gram} \)
90
94
Number
of eggs
12
14
Find the modal weight.


Accumulation of non-biodegradable pesticides in the food chain in increasing amount at each higher trophic level is known as
A. Eutrophication
B. Pollution
c. Biomagnification
D. Accumulation


How many different words can be
fanned by jumbling the letters of the word MISSISSIPPI in which no two 's' are
adjacent
A \( \cdot 7 \cdot^{6} C_{2} \cdot^{8} C_{4} \)
B . \( 6 \cdot 7 \cdot^{8} C_{4} \)
\( \mathbf{c} \cdot 6 \cdot 8 \cdot^{7} C_{4} \)
D. \( 8 \cdot^{6} C_{4} \cdot^{7} C_{4} \)


Which of the following is not a purpose
of transpiration?
A. Supplies water for photosynthesis
B. Helps in translocation of sugar from source to sink
C. Maintain shape and structure of the plant
D. Transport minerals from the soil to all parts of the plant


For a reaction \( \boldsymbol{A}_{(g)} \rightarrow \boldsymbol{B}_{(g)}+\boldsymbol{C}_{(g)}, \) the
rate constant for the reaction is \( 3 x \)
\( 10^{-3} M^{-} \) min \( ^{-1} . \) At what concentration
of \( A \) will at the rate of reaction be \( 2 x \)
\( 10^{-3} \mathrm{M} \mathrm{min} \)
A. 1 м
в. 0.52 М
c. 0.82 М
D. \( \frac{2}{3} \) N


Which of the following are greenhouse gases?
A. Carbon dioxide
B. Water vapour
c. Both A and B
D. None of these


Which one among the following is
correct?
A. Gametes are invariably haploid
B. Spores are invariable haploid
C. Gametes are generally haploid
D. Both spores and gametes are invariably haploid


Three identical. spheres of mass in each are placed at the corners of an equilateral triangle of side 2 in. Taking one of the corner as the origin, the
position vector of the centre of mass is
\( \mathbf{A} \cdot \sqrt{3}(\hat{i}-\hat{j}) \)
B. \( \frac{i}{\sqrt{3}}+\hat{j} \)
\( c \cdot \frac{i+3}{3} \)
D. \( \hat{i}+\frac{j}{\sqrt{3}} \)


Which of the following is a chemical effect of electric current?
A. Formation of gas bubbles on the electrodes
B. Change of color of solution
c. Deposition of metals on the electrodes
D. All of the above


The pH of an aqueous solution of sodium acetate is more than 7
A . True
B. False


\( \boldsymbol{E} \boldsymbol{t} \boldsymbol{N} \boldsymbol{H}_{2}+ \)
\( M e M g I \frac{\text {Heated} \text { in high temp.}}{\text {in the presence of pyridine}} \)
\( \operatorname{Gas}(\boldsymbol{A}) \)

The volume of \( \operatorname{gas}(A) \) obtained at \( \mathrm{S.T.P} \)
when \( 0.45 g m \) of \( E t N H_{2} \) reacts with
MeMgI is:
\( \mathbf{A} \cdot 224 m l \)
в. \( 22.4 m l \)
c. \( 448 m l \)
D. \( 44.8 \mathrm{ml} \)


Quality that is not suitable for a fuel is
A. high calorific value with ignition temperature that is well above the normal room temperature
B. low rate of evaporation at room temperature
C. carbon particles are expelled with smoke
D. low content of non-combustibles


Two equal forces to \( P \) and \( 2 P \) act on a
particle.If the first be doubled and the second be increased by \( 20 \mathrm{N} \), the direction of the resultant is
unaltered.Find the value of \( P \)


Rate of heating in forced convection
experiment can be increased by This question has multiple correct options
A. increasing the speed of flow of liquid accross the heated section.
B. increasing the surface area of contact of water with heated section.
c. decreasing the thermal conductivity of fluid flowing.
D. increasing the thermal conductivity of heated container


Figure represents a negatively charged gold leaf electroscope. The distribution of charges on the different parts will be
as:
A. \( A, D \) and \( E \) will have positive charges. \( B \) and \( C \) will have no charge
B. A, D and E will have negative charges. B and C will have no charge
C. \( A, D \) and \( E \) will have negative charges. B and \( C \) will have positive charges.
D. A, D and E will have positive charges. B and C will have negative charges


The given graph depicts the free energy
change before, during and after a
biochemical reaction. The effect of a
catalytic enzyme can be described by
A. Energy decreases at point
B. Energy increases at point
C. Energy decreases at point
D. Energy increases at point 2
E. Energy decreases at point


Compound 'P' of the following reaction sequence can be :
\( \langle 0\rangle-c \equiv c-\sqrt{0} \)
B.
\( \langle O\rangle-\mathrm{cH}_{2}-\mathrm{c} \equiv \mathrm{CH} \)
\( c \)
\( \langle O\rangle-c \equiv c H \)
\( D \)
\( \langle O\rangle-c=c H_{2} \)


Which one of the following precedes reformation of the nuclear envelope during M phase of the cell cycle?
A. Formation of the contractile ring and formation of the phragmoplast
B. Formation of the contractile ring and transcription from chromosomes
c. Decondensation of chromosomes and reassembly of the nuclear lamina
D. Transcription from chromosomes and ressembly of the nuclear lamina


At what voltage is the electric power from generating station transmitted?
A \( .200 k V \)
В. \( 11 k V \)
\( \mathbf{c} \cdot 220 V \)
D. \( 220 k V \)


Carotid labyrinth in frog is present on
\( A \). Brain
B. Pulmocutaneous trunks
c. carotid artery
D. Index finger of frog


A 0.5 kg ball is thrown up with an initial speed \( 14 \mathrm{m} / \mathrm{s} \) and reaches a maximum
height of \( 8.0 \mathrm{m} . \) How much energy is dissipated by air drag acting on the ball during the ascent?
A. 19.6 Joule
B. 4.9 Joule
c. 10 Joule
D. 9.8 Joule


Arrange according to ascending order of
BOD.
(a) Highly polluted pond water
(b) Unpolluted pond water
(c) Distilled water
A. b-c-a
B. c-b-a
c. \( c-a-b \)
D. a-c-b


Of all the closed right circular
cylindrical cans of volume \( 128 \pi c m^{3} \)
find the dimensions of the can which
has minimum surface area.


Calculate the masses of cane sugar and
water required to prepare 250 g of \( 25 \% \) cane sugar solution.


Either a fuse or a circuit-breaker can be
used to protect electrical cables from
large currents that could cause
overheating.
When a fuse is used, where should it be
connected, and when a circuit-breaker
is used, where should it be connected?
A. Position of fuse \( -X \), Position of circuit-breaker \( -X \)
B. Position of fuse - \( X \), Position of circuit-breaker - \( Y \)
c. Position of fuse \( -Y \), Position of circuit-breaker \( -X \)
D. Position of fuse - \( Y \), Position of circuit-breaker - \( Y \)


Which of the following is correct
statement:
A. Equipotential lines are always perpendicular to the electric field
B. Work done for moving a charge along the conducting surface (closed and containing charge) very close to it may be negative or positive
C. Electric field may cross each other
D. None of the above


A car is fitted with a convex side-view
mirror of focal length \( 20 \mathrm{cm} . \) A second
car \( 2.8 \mathrm{m} \) behind the first car is
overtaking the first car at a relative speed of \( 15 \mathrm{m} / \mathrm{s} \). The speed of the image of the second car as seen in the mirror
of the first one is :
A \( \cdot \frac{1}{10} \mathrm{m} / \mathrm{s} \)
в. \( \frac{1}{15} \mathrm{m} / \mathrm{s} \)
c. \( 10 \mathrm{m} / \mathrm{s} \)
D. \( 15 \mathrm{m} / \mathrm{s} \)


Two sides of a parallelogram in the ratio
\( \mathbf{5}: \mathbf{3} \) if its perimeter is \( \mathbf{6 4 c m}, \) find this
lengths of its sides.


When sunlight passes through the window of the classroom, the path of the light is visible. What is this effect called? Give reason


Which of the following is a weak acid?
A. Acetic acid
B. Formic acid
c. Carbonic acid
D. All of the above


Express the complex number given in the form \( a+i b \)
\( \boldsymbol{i}^{-\mathbf{3 9}} \)


In the reaction \( \mathrm{CH}_{3} \mathrm{OH} \rightarrow \mathrm{HCOOH} \), the
number of electrons that must be
addad to the right is :
A .4
B. 3
\( c \cdot 2 \)
D.


The equation of the plane that passes through the points (1,0,2),(-1,1,2),(5,0,3) is
A. \( x+2 y-4 z+7=0 \)
B. \( x+2 y-3 z+7=0 \)
c. \( x-2 y+4 z+7=0 \)
D. \( 2 y-4 z-7+x=0 \)


Write the Lewis dot structure of \( C O \)
molecule.


Henry's law constant for solubility of
methane in benzene is \( 4.27 \times 10^{-5} \)
\( m m^{-1} H g m o l d m^{-3} \) at constant
temperature. Calculate solubility of
methane at 760 mm \( H g \) pressure at
same temperature


Alternating current of peak value \( \left(\frac{2}{\pi}\right) \) ampere flows through the primary coil of the transformer. The coefficient of
mutual inductance between primary and secondary coil is 1 henry. The peak
e.m.f. induced in secondary coil is (Frequency of a.c. \( =50 \mathrm{Hz}) \)
\( A \cdot 100 v \)
B. 200 V
c. 300
D. 400


Find square of the following expression \( \frac{3 a}{2 b}-\frac{2 b}{3 a} \)
A \( \cdot \frac{9 a^{2}}{4 b^{2}}-2+\frac{b^{2}}{a^{2}} \)
в. \( \frac{9 a^{2}}{4 b^{2}}+2+\frac{4 b^{2}}{9 a^{2}}^{2} \)
c. \( \frac{a^{2}}{4 b^{2}}-2+\frac{4 b^{2}}{9 a^{2}} \)
D. \( \frac{9 a^{2}}{4 b^{2}}-2+\frac{4 b^{2}}{9 a^{2}} \)


The example given in the problem
represents collision.
A. elastic
B. partially inelastic
c. perfectly inelastic
D. none


Venter is the part of
A. Sporogonium
B. Sporangium
c. Antheridium
D. Archegonium


The correct order of electron affinity of \( B, C, N, O \) is :
A. \( O>C>N>B \)
в. \( B>N>C>O \)
c. \( O>C>B>N \)
D. \( O>B>C>N \)


An inductance \( L, \) a capacitance \( C \) and
a resistance \( \boldsymbol{R} \) may be connected to an
\( A C \) source of angular frequency \( \omega, \) in
three different combinations of \( \boldsymbol{R} \boldsymbol{C}, \boldsymbol{R} \boldsymbol{L} \)
and \( L C \) in series. Assume that \( \omega L= \) \( \frac{1}{\omega C} . \) The power drawn by the three
combinations are \( \boldsymbol{P}_{1}, \boldsymbol{P}_{2}, \boldsymbol{P}_{3} \)
respectively. Then,
\( \mathbf{A} \cdot P_{1}>P_{2}>P_{3} \)
B \( \cdot P_{1}=P_{2}<P_{3} \)
\( \mathbf{C} \cdot P_{1}=P_{2}>P_{3} \)
D \( \cdot P_{1}=P_{2}=P_{3} \)


Two streams of electrons are moving parallel to each other in the same direction. They
A. attract each other
B. repel each other
c. cancel the electric field of each other
D. cancel the magnetic field of each other


If \( \boldsymbol{x}+\boldsymbol{y}=\mathbf{2 5} \) and \( \frac{\mathbf{1 0 0}}{\boldsymbol{x}+\boldsymbol{y}}+\frac{\mathbf{3 0}}{\boldsymbol{x}-\boldsymbol{y}}=\mathbf{6} \)
then the value of \( x-y \) is
A . 18
B . 20
c. 15
D. 10


How much work does the atmospheric
pressure do in compressing the spring?


The distance covered by a particle in \( t \)
second is given by \( \boldsymbol{x}=\mathbf{3}+\mathbf{8} \boldsymbol{t}-\mathbf{4} \boldsymbol{t}^{2} \)
After \( 1 s \) its velocity will be
A. 0 unit \( / \) s
B. 3unit/
c. \( 4 u n i t / s \)
D. \( 7 u n i t / s \)


Calculate the accelerating potential that must be imparted to a proton beam to wavelength of \( 0.005 \mathrm{nm} \)


Why are hormones released into venous
blood and not to arteial blood?


The chemical name of vitamin D is:
A. Retinol
B. Ferridoxin
c. calciferol
D. Ergosterol


The area of a trapezium is \( 405 \mathrm{cm}^{2} \). its
parallel sides are in the ratio 4: 5 and
the distance between them is \( 18 \mathrm{cm} \)
Find the length of each of the parallel sides.


A wire of length \( L \) and 3 identical cells of negligible internal resistances are connected in series. Due to the current, the temperature of the wire is raised at \( \triangle T \) in time \( t . N \) number of similar cells
is now connected in series with a wire of
the same material and cross-section
but of length \( 2 L \). The temperature of the
wire is raised by the same amount \( \triangle \boldsymbol{T} \) in the same time \( t \). The value of \( \boldsymbol{N} \) is:
\( A \)
B. 6
\( c \cdot 8 \)
\( D \)


A boy pulls a \( 5 k g \) block along a \( 20 m \) long horizontal surface at a constant
velocity by applying a horizontal force \( \boldsymbol{F} \)
If the coefficient of kinetic friction is 0.2
how much work does the boy do on
the block? \( \left(g=10 m s^{-2}\right) \)
\( \mathbf{A} \cdot 100 J \)
B. \( 300 J \)
c. \( 200 J \)
D. \( 400 J \)


The radius and height of a cylinder are equal. If the radius of the sphere is equal to the height of the cylinder, then the ratio of the rates of increase of the
volume of the sphere and the volume of the cylinder is
A .4: 3
в. 3: 4
\( \mathbf{c} \cdot 4: 3 \pi \)
\( \mathbf{D} \cdot 3: 4 \pi \)


If \( 0<\alpha<\pi / 2 \) then the value of
\( \int_{0}^{\alpha} \frac{\boldsymbol{d} \boldsymbol{x}}{1-\cos \boldsymbol{x} \cos \boldsymbol{\alpha}} \) is
\( A \cdot \pi / \alpha \)
B . \( \pi / 2 \sin \alpha \)
c. \( \pi / 2 \cos \alpha \)
D. \( \pi / 2 \alpha \)


Find the cosine of the angle between the vectors \( \overrightarrow{\boldsymbol{A}}=(\mathbf{3} \hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}+\mathbf{2} \hat{\boldsymbol{k}}) \boldsymbol{a n d} \hat{\boldsymbol{B}}= \)
\( (2 \hat{i}-2 \hat{j}+4 \hat{k}) \)
A \( \cdot \frac{3}{\sqrt{21}} \)
B. \( \frac{\sqrt{12}}{\sqrt{21}} \)
c. \( \frac{9}{\sqrt{21}} \)
D. \( \frac{3}{\sqrt{12}} \)


Reaction by which Benzaldehyde cannot
be prepared?
\( \mathbf{A} \)
co in \( \mathrm{CS}_{2} \) followed by \( \mathrm{H}_{3} \mathrm{O} \)
B.
in presence of \( \mathrm{Pd}-\mathrm{BaSO}_{4} \)
\( c \)
in presence of anhydrous
\[
\mathrm{AlCl}_{3}
\]
D.
and conc. HCl


An organic compound 'A', \( C_{8} H_{6} \) on
reacting with dil \( H_{2} S O_{4} \) and \( H g S O_{4} \) gives a compound'B' which can also be obtained from reaction of benzene with
acid chloride in the presence of anh.
\( A l C l_{3} . \) Compound 'B' when reacted with
iodine and aq. NaOH yields 'C' and a yellow compound 'D'. Identify A to D with proper justification.


Suppose a girl throws a die. If she gets a
5 or \( 6, \) she tosses a coin 3 times and
notes the number of heads. If she gets
1,2,3 or 4 she tosses a coin once and notes whether a head or tail is obtained.
If she obtained exactly one head, what
is the probability that she threw 1,2,3
or 4 with the die?
\( \mathbf{A} \cdot \frac{1}{9} \)
в. \( \frac{5}{16} \)
c. \( \frac{2}{13} \)
D. \( \frac{8}{11} \)


Two points \( P \) and \( Q \) are maintained at
the potential of \( 10 ~ V \) and \( -4 V \)
respectively. The work done in moving
100 electrons from \( P \) to \( Q \) is:
A. \( -19 \times 10^{-7} J \)
\( J \)
В. \( 9.60 \times 10^{-17} J \)
c. \( -2.24 \times 10^{-16} J \)
D. 2.24 \( \times 10^{-16} \mathrm{J} \)


The rate constant for the forward
reaction \( \boldsymbol{A}(\boldsymbol{g}) \rightleftharpoons \mathbf{2} \boldsymbol{B}(\boldsymbol{g}) \) is \( 1.5 \times \)
\( 10^{-3} s^{-1} \) at 100 K. If \( 10^{-5} \) moles of \( A \) and
100 moles of \( \mathrm{B} \) are present in a 10 litre vessel at equilibrium, then rate
constant for the backward reaction at
this temperature is:
A. \( 1.50 \times 10^{4} L \) mol \( ^{-1} s^{-1} \)
B . \( 1.5 \times 10^{11} L \) mol \( ^{-1} s^{-1} \)
c. \( 1.5 \times 10^{10} L m o l^{-1} s^{-1} \)
D. \( 1.5 \times 10^{-11} L \) mol \( ^{-1} s^{-1} \)


A graph of \( \frac{x}{m} \) vs temperature at constant pressure is called adsorption isotherm.
A . True
B. False


A charged spherical drop of mercury is in equilibrium in a plane horizontal air capacitor and the intensity of the
electric field is \( 6 \times 10^{4} V m^{-1} . \) If the
charge on the drop is \( 8 \times 10^{-18} C, \) the
radius of the drop is :
\( \left[\rho_{a i r}=1.29 k g / m^{3} ; \rho_{H g}=13.6 \times 10^{3}\right. \)
A \( \cdot 0.95 \times 10^{-8} m \)
n
в. \( 2.7 \times 10^{-10} \mathrm{m} \)
c. \( 2.7 \times 10^{-8} \mathrm{m} \)
D. \( 0.95 \times 10^{-6} \mathrm{m} \)


Ratio of area of hole to beaker is 0.1
Height of liquid in beaker is \( 3 m, \) and
hole is at the height of \( 52.5 \mathrm{cm} \) from the
bottom of beaker, find the square of the velocity of liquid coming out from the hole:
\( \mathbf{A} \cdot 50(m / s)^{2} \)
B. \( 50.5(m / s)^{2} \)
c. \( 51(m / s)^{2} \)
D. \( 42(m / s)^{2} \)


When \( M n O_{2} \) is fused with \( \mathrm{KOH} \) and \( O_{2} \)
what is the product formed and its
colour?
A. Mno - colourless
B . \( K M n O_{4} \) - purple
C. \( K_{2} M n O_{4} \) - dark green
D. \( M n O_{3} \) - black


Water is falling from 160m height. Assuming that half the K.E. of falling water gets converted into heat, the rise
in temperature of water is approximately
\( \mathbf{A} \cdot 0.1^{0} C \)
B. \( 0.2^{0} C \)
\( \mathbf{c} \cdot 0.3^{0} C \)
D. \( 0.4^{\circ} \mathrm{C} \)


Amongst the following, the strongest base in aqueous medium is
A \( \cdot C H_{3} N H_{2} \)
в. \( N C C H_{2} N H_{2} \)
c. \( \left(C H_{3}\right)_{2} N H \)
D. \( C_{6} H_{5} N H C H_{3} \)


Three bars having length \( l, 2 l \) and \( 3 l \) and area of cross-section \( A, 2 A \) and \( 3 A \) are
joined rigidly and to end. Compound rod is subjected to a stretching force \( \boldsymbol{F} \). The increase in length of rod is (Young's modulles of material is \( Y \) and bars are
massless)
A \( \cdot \frac{13 F l}{2 A Y} \)
в. \( \frac{3 F l}{A Y} \)
c. \( \frac{9 F l}{A Y} \)
D. \( \frac{13 \mathrm{Fl}}{\mathrm{AY}} \)


Evaluate: \( \left(4 x^{2}-\frac{1}{5} x+7\right)- \)
\( \left(-2 x^{2}-\frac{1}{2} x+\frac{1}{3}\right) \)


Cropland ecosystem is a natural
ecosystem
A. True
B. False


Two open pipes of length \( 25 \mathrm{cm} \) and 25.5 cm produced 10 beat/second. The velocity of sound will be:
A. \( 255 \mathrm{m} / \mathrm{s} \)
B. 250 m/s
c. \( 350 \mathrm{m} / \mathrm{s} \)
D. None of these


In protochordates, the epidermis is
A. Absent
B. Multilayered
c. A few layered
D. single layered


Name two types of terrestrial habitats
with low temperatures.


Two parallel plates have equal and opposite charge. When the space between them is evacuated. the electric
field between the plates \( 2 \times 10^{5} V / m \)
When the space is filed with dielectric
the electric field becomes \( 10^{5} V / m \) The
dielectric constant of he dielectric
material is
A . 2
B. 4
c. 5
D. 9


e.m.f. is measured in
A. Joules
B. \( \frac{\text { Joules }}{\text { coulomb }} \)
c. Joule-coulombs
D. coulomb


A car is moving at a constant speed of \( 40 k m / h \) along a straight road which heads towards a large vertical wall and
makes sharp \( 90^{\circ} \) turn by side of the wall. A fly flying at a constant speed of
\( 100 k m / h, \) starts from the wall towards
the car at an instant when the car is
\( 20 k m \) away, flies until it reaches the glass pane of the car and returns to the wall at the same speed. It continues to fly between the car and the wall till the
car makes the \( 90^{\circ} \) turn. How many trips has it made between the car and the
wall?
A . 50
B. Infinite
\( c \cdot 66 \)
D. 150


tor measuring acceleration) can be
made in the form of a tube filled with a
liquid and bent as shown. During
motion, the level of the liquid in the left
\( \operatorname{arm} \) will be at height \( h_{1} \) and in the right
\( \operatorname{arm} \) at a height \( h_{2} . \) Determine the
acceleration a of a carriage in which the accelerometer is installed, assuming
that the diameter of the tube is much
smaller than \( h_{1} \) and \( h_{2} \)
A \( \cdot \frac{g\left(h_{1}-h_{2}\right)}{h_{1}+h_{2}} \)
B. \( \frac{g\left(h_{1}+h_{2}\right)}{h_{1}-h_{2}} \)
c. \( \frac{g\left(h_{2}-h_{1}\right)}{h_{1}+h_{2}} \)
D. \( \frac{g\left(h_{2}\right)}{h_{2}-h_{1}} \)


The +3 ion of which one of the following has half-filled \( 4 f \) subshell?
A . \( L a \)
в. \( L u \)
\( c . G d \)
D. \( A c \)


Two elements A and B on burning in air give corresponding oxides. oxides of both \( A \) and \( B \) are soluble in water. The
aqueous solution of oxide of \( A \) is
alkaline and reacts with aqueous
solution of oxides of \( \mathrm{B} \) to give another compound. A and B are
A. A and B both are metal
B. A and B are non-metal
C . A is metal and B is non metal
D. A is non metal and B is metal


\( A B C \) is a right-angle triangle, right angled at A. A circle is inscribed in it. The lengths of the two sides containing the right angle are \( 6 \mathrm{cm} \) and \( 8 \mathrm{cm} \) then radius of the circle is :
\( A \cdot 3 \mathrm{cm} \)
B. \( 2 \mathrm{cm} \)
\( c \cdot 4 \mathrm{cm} \)
D. \( 8 \mathrm{cm} \)


Write the name of electromagnetic wave produced by vacuum tube
magnetron.


The energy of a photon having wavelength 700 nm is:
A . 1.77 ev
B. 2.47 ev
c. 700 ev
D. 3.57 ev


A tree breaks due to storm and the
broken part bends so that the top of the
tree touches the ground by making \( 30^{\circ} \)
angle with the ground. The distance between the foot of the tree and the top
of the tree on the ground is 6 m. Find the height of the tree before falling down.


Prove that: \( 1 . P(1,1)+2 . P(2,2)+ \)
\( 3 . P(3,3)+\ldots+n . P(n, n)= \)
\( P(n+1, n+1)-1 \)


A nerve cell transmits it's impulse to
another through
its
A. Dendrite
B. Cyton
c. Axons
D. Myeline sheeth


Which one is a mineral of zinc?
A. Galena
B. Calamine
c. Cerussite
D. cinnabar


If there are two possible positive integer
values for \( \boldsymbol{x} \) satisfying \( \boldsymbol{y}=\boldsymbol{x}(1+\boldsymbol{x}) \)
What is a possible value for \( y ? \)
A . -30
B. - 1
c. 0
D. 15
E .20


In Ostwald's process for the manufacture of nitric acid, the first step involves the oxidation of ammonia
gas by oxygen gas to give nitric oxide gas and steam. What is the maximum
weight of nitric oxide that can be obtained starting only with 10.00 g. of ammonia and 20.00 g of oxygen?


A force \( \overrightarrow{\boldsymbol{F}}=(3 \boldsymbol{t} \hat{\boldsymbol{i}}+\boldsymbol{5} \hat{\boldsymbol{j}}) \) N acts on a
particle whose position vector varies as \( \vec{S}=\left(2 t^{2} \hat{i}+5 \hat{j}\right) \mathrm{m}, \) where \( t \) is time in
seconds. The work done by this force
from \( t=0 \) to \( t=2 s \) is:
A . 23 J
B. 32 J
c. zero
D. can't be obtained


An isolated system is one which neither shows an exchange of \( _{--}- \) -nor with surroundings.
A. heat, mass
B. heat, temperature
c. temperature, mass
D. None of these


Differentiate w.r.t \( \boldsymbol{x} \)
\( e^{\operatorname{cosec}^{2} x} \)


A prism \( (\mu=1.5) \) has the refracting
angle of \( 60^{\circ} . \) The deviation of a monochromatic ray incident normally on its one surface will be \( \left(\sin 48^{\circ} 36^{\prime}=\right. \) \( \mathbf{0 . 7 5}) \)
\( \mathbf{A} \cdot 36^{\circ} 72 \)
B . \( 20^{\circ} 30^{\prime} \)
\( c \cdot 18^{\circ} \)
D. \( 22^{\circ} 1^{\prime} \)


The characteristic of a good unit is
A. It should be universally accepted
B. It should be invariable and not perishable
C. It should be easily available \& easy to reproduce
D. All of these


Assertion : Every periodic motion is not simple harmonic motion.
Reason: The motion governed by the
force law
\( \boldsymbol{F}=-\boldsymbol{k} \boldsymbol{x} \) is simple harmonic.
A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true and reason is not the correct explanation of assertion.
c. If assertion is true but reason is false.
D. If both assertion and reason are false


Which of the following statements is
correct for \( \boldsymbol{C} \boldsymbol{s} \boldsymbol{B} \boldsymbol{r}_{3} \)
A. It is covalent compound
B. It contains \( C s^{3+} \) and \( B r^{-} \)
c. ।t contains \( C s^{+} \) and \( B r_{3}^{-} \)
D. It contains \( C s^{+}, B r^{-} \) and lattice \( B r_{2} \) molecule


Give any two differences between
lyophilic and lyophobic colloids.


Glomeruli are confined to
A. Cortex
B. Medulla
c. Pelvis
D. Pyramid


Select correct statements:
A. Catenation is maximum in carbon.
B. Carbon has pronounced ability to form \( p \pi-p \pi \) multiple bonds to itself and to other elements like \( O \) and \( N \)
C. Both (a) and (b) are correct.
D. None of the above is correct.


Kinetic energy per unit length for a particle in a standing wave is zero at:
A. nodes
B. antinodes
c. mid-way between a node and an antinode
D. None of the above


The rate of the reaction:
\( \boldsymbol{C H}_{3} \boldsymbol{C O O C}_{2} \boldsymbol{H}_{5}+\boldsymbol{N a O H} \rightarrow \)
\( \boldsymbol{C H}_{3} \boldsymbol{C O O N a}+\boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{O H} \)
is given by the equation,
rate\( =\boldsymbol{k}\left[\boldsymbol{C H}_{3} \boldsymbol{C O O C}_{2} \boldsymbol{H}_{5}\right][\boldsymbol{N a O H}] \)
If concentration is expressed in \( m o l / L \)
the units of \( k \) are:
A \( \cdot m o l^{-2} L^{2} s^{-1} \)
B . \( \operatorname{molL}^{2} s^{-1} \)
c. \( L m o l^{-1} s^{-1} \)
D. \( s^{-1} \)


In figure
A. Retardation is uniform
B. Velocity is decreasing with time
C. Beyond \( M \), the body has negative velocity
D. All the above are incorrect


A hollow cylinder has mass \( M \) outside
radius \( R_{2} \) and inside radius \( R_{1} \).Its
moments of inertia about an axis
parallel to its symmetry axis and tangent to the outer surface in equal to:
\( ^{\mathrm{A}} \cdot \frac{M}{2}\left(R_{2}^{2}+R_{1}^{2}\right) \)
B. \( \frac{M}{2}\left(R_{2}^{2}-R_{1}^{2}\right) \)
c. \( \frac{M}{4}\left(R_{2}+R_{1}\right)^{2} \)
D. \( \frac{M}{2}\left(3 R_{2}^{2}+R_{1}^{2}\right) \)


Expand: \( \left|\begin{array}{ccc}1 & -7 & 3 \\ 5 & -6 & 0 \\ 1 & 2 & -3\end{array}\right| \)


How many electrons are there is the
outermost shell of silicon atom?


If \( x \) is \( 90 \% \) of \( y, \) what per cent of \( x \)
is \( \boldsymbol{y} ? \)
A . 90
в. 190
c. 101.1
D. 111.1


The mean marks scored by 40 students
were found to be \( 60 . \) Later it was
observed that a score of 48 was misread
as \( 84 . \) Then the correct mean is
\( \mathbf{A} \cdot 58 \)
B. 58.2
c. 59.1
D. 59


The decomposition of \( K C l O_{3} \) on
heating is an example of:


\( \int \frac{6 x+7}{(x-5)(x-4)} d x \)


The function \( f(x)=\frac{\lambda \sin x+2 \cos x}{\sin x+\cos x} \) is
increasing, if
\( A \cdot \lambda<1 \)
B \( . \lambda>1 \)
c. \( \lambda<2 \)
D \( . \lambda>2 \)


Write the parts of human digestive
system?


Why is alpha ( \( \alpha \) ) hydrogen of carbony compounds acidic in nature?


The end product of glycolysis is
A. Pyruvic acid
B. Glucose
c. Ethyl alcohol
D. \( C O_{2} \)


A thin biconvex lens of refractive index
\( 3 / 2 \) is placed on a horizontal plane mirror as shown. The space between the
lens and the mirror is then filled with
water of refractive index \( 4 / 3 . \) It is found that when a point object is placed \( 15 \mathrm{cm} \) above the lens on its principal axis, the object coincides with its own images. On representing with another liquid, the object and the image again coincide at a distance \( 25 \mathrm{cm} \) from the lens.

Calculate \( x, \) if the refractive index of the liquid is \( \frac{10+x}{10} \)


Potential difference between centre and
the surface of sphere of \( R \) and having uniform volume charge density. p with it will be :
A \( \cdot \frac{p R^{2}}{6 \epsilon_{0}} \)
в. \( \frac{p R^{2}}{4 \epsilon_{0}} \)
\( c \cdot 0 \)
D. \( \frac{p R^{2}}{2 \epsilon_{0}} \)


Which of the following pairs is incorrect?
A. Gneiss - Metamorphic
B. Rock salt- - Sedimentary
c. Dolerite - - gneous
D. Dolomite - -Igneous


Few figures are expressed in scientific notation. mark the incorrect one.
A \( \cdot 234000=2.34 \times 10^{5} \)
В. \( 8008=8 \times 10^{3} \)
c. \( 0.0048=4.8 \times 10^{-3} \)
D. \( 500.0=5.00 \times 10^{2} \)


In the electrolytic refining of a metal \( M \) what would you take as the anode, the cathode, and the electrolyte?


Find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \) if \( \boldsymbol{y}=\boldsymbol{x}^{2}-\boldsymbol{2}^{\sin \boldsymbol{x}} \)


Construct a \( \triangle A B C, \) when \( A B= \)
\( 6.2 \mathrm{cm}, A C=5.2 \mathrm{cm} \) and \( \angle B=45^{\circ} \)


The dimension of universal gas
constant R are
A \( \cdot M^{2} L^{2} T^{-2} \)
B. \( M L^{2} T^{-2} \theta^{-1} \)
\( \mathbf{c} \cdot M^{2} L^{2} T^{-2} \theta^{-2} \)
D. \( M L T^{-2} \theta^{-2} \)


topp
\( Q \) Type your question
as 'positive' when the wires repel each ther and 'negative' when the wires attract each other, the graph showing
the dependence of 'F', on the product
\( I_{1} I_{2}, \) would be
\( c \)
\( D \)


Solve the equations \( 2 x-3 y=9 \)
\( 4 x+6 y=18 \)


Verify: \( (\boldsymbol{a}+\boldsymbol{b})^{3}=\boldsymbol{a}^{3}+\boldsymbol{3} \boldsymbol{a}^{2} \boldsymbol{b}+\boldsymbol{3} \boldsymbol{a} \boldsymbol{b}^{2}+ \)
\( b^{3} \)


Experimental value of magnetic
momentum of \( M n^{2+} \) complex is 5.96
B.M. This indicates:
A. Axial and orbital motion of electron in same direction
B. Axial and orbital motion of electron in opposite direction
C. Electron does not exhibit orbital motion, it only exhibits axial motion
D. Electron does not exhibit axial motion, it only exhibits orbital motion


Rough surfaces have centres on
account of free valencies.
A. more
B. less
c. average
D. may be more may be less


The temperature of \( 3 \mathrm{kg} \) of nitrogen is raised from \( 10^{\circ} \mathrm{C} \) to \( 100^{\circ} \mathrm{C} \). Compute the
heat added, the work done, and the change in internal energy if this is done at constant volume
A . \( 199800 \mathrm{J} \)
B. 19000 J
c. 199000 J
D. 190000 J


At \( 25^{\circ} C \), the standard emf of a cell
having reaction involving two electrons change is found to be \( 0.295 V \). The
equilibrium constant of the reaction is
\( \mathbf{A} \cdot 29.5 \times 10^{-2} \)
B. 10
\( c \cdot 1 \times 10^{10} \)
0
D . \( 29.5 \times 10^{10} \)


Describe in words the atomic
composition denoted by chemical
formula \( C_{12} H_{22} O_{11} \)


An incident ray strikes a plane mirror at
an angle of \( 20^{\circ} \) with respect to
horizontal surface as shown. What is
the change in the angle of reflection, if
the incident ray moves towards normal
by \( 1^{\circ} ? \)


Vant Hoff factor (i) for dimerisation of benzoic acid insome solvent
assuming \( 30 \% \) degree of association
A . 0.85
B. 0.95
\( c .0 .90 \)
D.


Find the mean deviation about the
mean for the data
\( \boldsymbol{X}_{i} \quad 10 \quad \) 30 \( \quad \) 50 \( \quad \) 70
16 28 \( f_{i} \quad 4 \quad 24 \)


When \( K M n O_{4} \) acts as an oxidising
agent and forms \( M n^{+2}, \) the number of
electrons transferred per molecule of
\( K M n O_{4} \) is :


\( \mathrm{K} \) for the reaction \( 2 \boldsymbol{A}+\boldsymbol{B} \rightleftharpoons 2 \boldsymbol{C} \) is
\( 1.5 \times 10^{12} . \) This indicates that in
equilibrium the concentration of would be maximum.
\( A \cdot A \)
B. B
\( c \cdot c \)
D. none


Agonist can help transfer of message to
receptors If this is true enter 1 , if false enter 0 .


\( G d(64) \) has unpaired
electrons with sum of spin
\( \mathbf{A} \cdot 7,3.5 \)
в. 8,3
\( c .6,3 \)
D. 8,4
E . 9,3.5


Casseterite ore consists of magnetic impurity named as:
A. chromite
B. wolframite
c. magnetite
D. Limonite


Derive an expression:
\[
\frac{\mu}{v}-\frac{1}{u}=\frac{\mu-1}{R}
\]
for refraction of light at spherical
surface.


A small ball (menu) falling under
gravity in a viscous medium
experiences a drag force proportional to the instantaneous speed u such that
\( F_{d r a g}= \) Ku. Then the terminal speed of the ball within the viscous medium is:
A \( \cdot \frac{K}{m g} \)
в. \( \frac{m g}{K} \)
c. \( \sqrt{\frac{m g}{K}} \)
D. \( \left(\frac{m g}{K}\right)^{2} \)


Write balanced chemical equations for the following reactions:
(i) Ozone and lead sulphide.
(ii) Chlorine is passed through hot concentrated NaOH solution.
(iii) Sulphuric acid is treated with phosphorous.


The probability of happening of an event is \( 45 \% . \) The probability of an event is :
A . 45
B. 4.
\( c \cdot 0.45 \)
D. 0.045


\( N_{2}(g)+3 H_{2}(g) \stackrel{F e+M o}{\rightleftharpoons} 2 N H_{3}(g) \)
Haber's process. Mo is used as:
A. a catalyst
B. a catalytic promoter
c. an oxidising agent
D. a catalytic poison


The transformation ratio of a
transformer is \( 10: 1 . \) The current in the
primary circuit if the secondary current required is 100 A assuming the transformer be ideal, is
\( A \cdot 500 A \)
B. 200 A
\( c \cdot 1000 A \)
D. 2000 A


Decomposition of hydrogen peroxide is retarded in the presence of
This question has multiple correct options
A. alcohol
B. glycerine
c. manganese dioxide
D. molybdenumm


\( f \cos ^{2} 2 x-\cos ^{2} 6 x=\sin m x \sin 8 x \)
Find \( \boldsymbol{m} \)


Solve the following differential eqauton
\( \boldsymbol{y}^{2} \boldsymbol{d} \boldsymbol{y}-\boldsymbol{x}^{2} \boldsymbol{d} \boldsymbol{x}=\mathbf{0} \)


To demonstrate the phenomenon of interference we require two soruces which emit radiation of
A. nearly the same frequency
B. the same frequency
c. different wavelength
D. the same frequency and having a definite phase relationship.


Write IUPAC names of the products
obtained by the ozonolysis of the pent-2-
ene?
A. Ethanal and propanal
B. Only Ethanal
c. only propanal
D. Ethanol and propanone


Give balanced equations for the following reactions:
Dilute nitric acid and Copper carbonate


Define octate rule \( \& \) its significance \( \& \)
limitation.


The diagram shows a sphere of radius
\( \boldsymbol{R} \) that carries a charge \( \boldsymbol{Q} \) uniformly
distributed throughout its volume. \( A \)
Gaussian sphere of radius \( a \) is
imagined that is concentric to the
charged sphere.
If \( a<R, \) what is the charge enclosed in
the Gaussian surface?
\( ^{\mathbf{A}} \cdot Q_{e n c}=Q \frac{a^{4}}{R^{4}} \)
\( ^{\mathbf{B}} \cdot Q_{e n c}=Q \frac{a}{R} \)
\( ^{\mathbf{C}} Q_{e n c}=Q \frac{a^{2}}{R^{2}} \)
\( ^{\mathrm{D}} Q_{e n c}=Q \frac{a^{3}}{R^{3}} \)
\( ^{\mathrm{E}} \cdot Q_{e n c}=Q \frac{a^{5}}{R^{5}} \)


The compounds whose molecules are
shown below would have:
A. different melting points
B. equal but opposite optical rotation
C. the same melting poin
D. more than one of the above


The working of a microwave oven
involves
A. Absorption of microwaves by matter
B. Reception of microwaves by optical fibre
C. Microwave amplification by stimulated emission of radiation
D. Transmission of microwaves through a metal


A cylinder of mass \( 1 \mathrm{kg} \) is given heat of \( 20000 \mathrm{J} \) at atmospheric pressure. If
initially temperature of cylinder is \( 20^{\circ} \mathrm{C} \) find change in internal energy of the cylinder. (Given that Specific heat capacity of cylinder \( =400 \mathrm{J} \mathrm{kg}^{-10} \mathrm{C}^{-1}, \) Coefficient
of volume expansion \( =\mathbf{9} \times \mathbf{1 0}^{-\mathbf{5} \mathbf{0}} \mathbf{C}^{-\mathbf{1}} \)
Atmospheric pressure \( =10^{5} N / m^{2} \)
and Density of cylinder \( =9000 \mathrm{kg} / \mathrm{m}^{3} \) )
A. 39999.95 J.
в. 29999.95
c. 19999.95 s
D. 59999.95 J.


The coordinates of a point on the line
\( \boldsymbol{x}+\boldsymbol{y}+\mathbf{3}=\mathbf{0} \) whose distance from
\( x+2 y+2=0 \) is \( \sqrt{5} \) is equal to
в. (-9,6)
c. (-9,-6)
(年 (-9,-6),(-6)
D. none of these


In a transverse section of a dicot root
A. The protoxylem vessels are present towards the periphery and metaxylem vessels are present towards the centre.
B. The protoxylem vessels are present towards the centre and the metaxylem vessels are present towards the periphery.
C. Both protoxylem and metaxylem vessels are present towards the centre.
D. Both protoxylem and metaxylem vessels are present towards the periphery


Which is not a ketone body?
A. Succinic acid
B. Acetone
c. Acetoacetic acid
D. p-hydroxybutyric acid


On the pole of the Earth a body is
imparted velocity \( v_{0} \) directed vertically
up. Knowing the radius of the Earth and
the free-fall acceleration on its surface,
the height to which the body will ascend is given as \( h=\frac{R v_{0}^{2}}{x g R-v_{0}^{2}} . \) The air drag
is to be neglected. Find \( x \)


56 cells are produced in meiosis in
which
A. First division is reductional
B. First division is equational
c. second division is reductional.
D. None of the above


The diameter of a sphere is \( 3.34 m \)
Calculate its volume with due regard to significant figures.


\( ^{35} C l \) and \( ^{37} C l \) are the two isotopes of
chlorine, in the ratio 3: 1 respectively. If
the isotope ratio is reversed the average atomic mass of chlorine will be:
\( \mathbf{A} \cdot 35.0 u \)
B. \( 35.5 u \)
c. \( 36.0 u \)
D. 36.5 \( u \)


An oscillator is producing FM waves of frequency \( 2 \mathrm{kHz} \) with avariation of
10kHz. The modulating index=?
A . 0.20
B. 5.0
c. 0.67
D. 1.5


When a block of mass ' \( m^{\prime} \) is released
from point \( ^{\prime} \boldsymbol{A}^{\prime} \) on the surface of a smooth bowl, the normaal reaction on it
\( B \) would be equal to
\( \mathbf{A} \cdot m g \)
B. \( 2 m g \)
c. \( 3 m g \)
D. Zero


If a solution of mercuric cyanide containing 3 g per litre has an osmotic pressure \( 3.092 \times 10^{4} N m^{-2} \) at \( 298 \mathrm{K} \)
the degree of dissociation of mercuric
cyanide is (Atomic mass of \( \boldsymbol{H} \boldsymbol{g}= \)
\( \left.200.6 g m o l^{-1}\right)(\text {write only integer part }) \)


f \( a=3, b=-3, \) find the value of
\( (a-2)^{2}+(b-2)^{2} \)


20 tuning forks are so arranged in series that each fork gives 4 bets per second with the previous one.The frequency of the 20 th fork is three times that of the first. What is the frequency of the first tuning fork?
\( A \cdot 60 \) Н
B. 57 Н
c. 40 нz
D. 38 нz


Study the graph which shows results of
three different experiments \( P, Q \) and \( R \)
In a few sentences, summarize what the
results of these experiments tell you
about the factors which limit
photosynthesis under different
environmental conditions?
A. In comparison with curve \( R \), curve P was limited by low temperature and low \( C O_{2} \) concentration, curve \( Q \) was limited by low \( C O_{2} \) concentration
B. In comparison with curve R, curve P was limited by high temperature and low \( C O_{2} \) concentration, curve \( Q \)
was limited by high \( C O_{2} \) concentration
C. In comparison with curve \( R \), curve P was limited by low temperature and high \( C O_{2} \) concentration, curve \( Q \) was
limited by high \( C O_{2} \) concentration.
D. None of the above


Implict function \( x^{3}+y^{3}=3 a x y \)


Divide the first polynomial by the second polynomial in each of the following. Also, write the quotient and remainder:
\( \boldsymbol{y}^{4}+\boldsymbol{y}^{2}, \boldsymbol{y}^{2}-\boldsymbol{2} \)


In a homogeneous reaction \( \boldsymbol{A} \longrightarrow \boldsymbol{B}+ \)
\( C+D \) the initial pressure was \( P_{0} \) and
after time \( t \) it was \( P . \) Expression for rate
constant \( k \) in terms of \( P_{0}, P \) and \( t \) will
be:
A \( \quad k=\frac{2.303}{t} \log \frac{2 P_{0}}{3 P_{0}-P} \)
В. \( _{k=} \frac{2.303}{t} \log \frac{2 P_{0}}{P_{0}-P} \)
c. \( _{k=} \frac{2.303}{t} \log \frac{3 P_{0}-P}{2 P_{0}} \)
D. \( _{k}=\frac{2.303}{t} \log \frac{2 P_{0}}{3 P_{0}-2 P} \)


Calcium phosphate is the principal form of calcium found in bovine milk.
A. True
B. False


Find the left and right hand limits of \( f(x)=\left\{\begin{array}{ll}\frac{3 x^{2}+2}{3 x-2} & x<1 \\ \frac{4 x^{2}-3}{4 x+3} & x>1\end{array} \text { at } x=1\right. \)
\( A \)
(a) 5 and \( \frac{1}{7} \)
B. \( (b)-\frac{1}{2} \) and -1
C \( \cdot(c)-\frac{7}{2} \) and 2
D \cdot (d) \( -\frac{9}{2} \) and 3


Draw the following angles using ruler and compasses. Also label them.
\( \mathbf{1 8 0}^{\circ} \)


In which stage of cell division, division of matrix of chromosome occurs?
A. Late prophase
B. Early metaphase
c. Late metaphase
D. Anaphase


In the figure, \( A B=C D \) and \( \angle A= \)
\( \mathbf{9 0}^{\circ}=\angle D . \) Then
A. \( \Delta A B C \cong \Delta D B C \) by SAS postulate
B. \( \Delta A B C \cong \Delta D C B \) by RHS postulate
c. \( \Delta A B C \cong \Delta D B C \) by AAS postulate
D. \( \Delta A B C \cong \Delta D C B \) by SSS postulate


The trend in the hydrides from Bi to \( N \)
is :
A. Bond length increases
B. Bond length decreases
c. Acidic nature increases
D. Bond energy decreases


\( P C l_{5} \) dissociates according to the
reaction \( \boldsymbol{P} \boldsymbol{C l}_{5}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{P} \boldsymbol{C l}_{3}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g}) \)
At \( 523 \mathrm{K}, K_{p}=1.78 a t m . \) Find the density of the equilibrium mixture at a total pressure of 1 atm :
A. \( 0.271 \mathrm{g} / \mathrm{L} \)
B. 2.71 \( \$ / L \)
c. 27.1 \( g / L \)
D. None of these


In which of the following there is no differentiation heart wood and sap
wood?
A. Neem
B. Ashok
c. Mango
D. Palm


In Young's double slit experiment, the
ratio of maximum to minimum
intensities of the fringe system is 4: 1 The amplitudes of the coherent sources are in the ratio:
A . 4: 1
B. 3: 1
c. 2: 1
D. 1: 1


Fill in the blank:
In order to increase the capacity of a parallel plate condenser, one should
introduce a sheet of between
the plates (assume that the space is completely filled).
A. Mica
B. Tin
c. copper
D. Stainless Steel


(Use a graph paper for this question.)
The daily pocket expenses of 200 students in a school are given below:
\[
\begin{array}{llll}
\text { Pocket } & \mathbf{0}- & \mathbf{5}- & \mathbf{1 0} \\
\text { expenses } & \mathbf{5} & \mathbf{1 0} & \mathbf{1 5}
\end{array}
\]
(in Rs)
Number of students
28
(frequency)
Draw a histogram representing the above distribution and estimate the
mode from the graph.


Tuatara, an organism with pentadacty limb, is an amniote. It also possesses the nictitating membrane and spines on the body. To which class does this organism belong?
A. Mammalia
B. Reptilia
c. Aves
D. Amphibia


Which of the following is the Metallic element in group-15?
A . As
B. sb
\( c \cdot B i \)
\( D \)


Multiply: \( (x-2)\left(x^{2}+3 x+7\right) \)
A \( \cdot x^{3}+2 x^{2}+6 x-14 \)
B. \( x^{3}+x^{2}+6 x-14 \)
c. \( x^{3}+x^{2}+x-14 \)
D. \( x^{3}+2 x^{2}+3 x-14 \)


can be used to verify Ohm's law :-
\( A \)
B.
\( c \)
\( D \)


The earth pull all objects towards
A. It's periphery
B. It's centre
C. Both centre and periphery
D. Earth never pulls any objects.lt is the inbuilt attractive force in a body which attracts it downwards


Two equal drops of water are falling through air with a steady velocity of \( 10 \mathrm{cm} / \mathrm{s} \). If the drops recombine to form a single drop then the terminal velocity is:
A \( \cdot 2^{\frac{2}{5}} \times 5 \) cm / \( s \)
B . \( 2^{\frac{2}{5}} \times 10 \mathrm{cm} / \mathrm{s} \)
c. \( 2^{\frac{2}{5}} \times 15 \mathrm{cm} / \mathrm{s} \)
D. \( 2^{\frac{2}{5}} \times 4 \) cm \( / s \)


Assertion
Diamond and graphite are allotropes of carbon
Reason
Some elements can have several
different structural forms while in the
same physical state. These differing forms are called allotropes.
A. If both Assertion and Reason are correct and Reason is the correct explanation of Assertion
B. If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion
c. If Assertion is correct but Reason is incorrect
D. If Assertion is incorrect but Reason is correct


Oxidation number of cobalt in
\( K\left[C o(C O)_{4}\right] \) is:
\( A \cdot+1 \)
\( B \cdot+3 \)
\( c \cdot-1 \)
\( D \cdot-3 \)


If the focal length of a lens is \( 50 \mathrm{cm} \), its power would be
A. 50 dioptres
B. 2 dioptres
c. 20 dioptres
D. 0.5 dioptres


A chord of radius \( 12 \mathrm{cm} \) subtends an
angle of \( 120^{\circ} \) at the centre. Find the
area of corresponding segment of the circle. \( (22 / 7=3.14 \text { and } \operatorname{root} 3=1.73) \)


Choose the correct options(s) from the
following.
This question has multiple correct options
A. Teflon is prepared by heating tetrafluoroethene in presence of a persulphate catalyst at high pressure
B. Natural rubber is polyisoprene containing trans alkene units
C. Nylon-6 has amide linkages
D. Cellulose has only \( \alpha-D-g l u \) cose units that are joined by glycosidic linkages.


Are \( R_{1}, R_{2}, R_{3}, R_{4} \) and \( R_{5} \) nearly in
phase
A . yes
B. na
\( c . \) maintain a constant phase
D. insufficient data to reply


The top of the atmosphere is at about \( 400 k V \) with respect to the surface of
the earth, corresponding to an electric field that decreases with altitude. Near
the surface of the earth, the field is
about \( 100 V m^{-1} . \) Why then do we not \( \operatorname{get} \) an electric shock as we step out of
our house into the open? (Assume the house to be a steel cage so there is no field inside


Why \( S c^{3+} \) salts are colorless whereas
\( C r^{3+} \) salt are coloured?


prove \( \rightarrow \frac{1+\cos \Theta+\sin \Theta}{1+\cos \Theta-\sin \Theta}=\frac{\operatorname{coz} \Theta}{1-\sin \Theta} \)


Given that \( x= \) displacement at time \( t \) and p,q,r are constants. Which of the following represents the motion with constant non zero acceleration?
A \( . x=p t-1+q t^{2} \)
B. x=qt
c. \( x=p t+q t^{2} \)
D. \( x=p t+q t^{2}+r t^{3} \)


\( O H \)
\( C H_{3}-C H_{2}-C H-C H_{2}-C H_{2}- \)
\( \underset{l}{C} \boldsymbol{H}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{3} \)
\( \boldsymbol{C H}_{3} \)
The IUPAC name of the compound is:
A. 6 -methyl-3-hexanol
B. 6-Methy|-3-octanol
c. 1-methy|-4-hexanol
D. 4-methyl-1-octanol


Match the statements given List 1 with the intervals/union of intervals given in
List 2


If the pressure in a reaction vessel for the following reaction is increased by decreasing the volume, what will happen to the concentrations of \( C O \) and
\( \boldsymbol{C O}_{2} ? \)
\( \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g})+\boldsymbol{C O}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{H}_{2}(\boldsymbol{g})+ \)
\( \boldsymbol{C O}_{2}(\boldsymbol{g})+\boldsymbol{H} \boldsymbol{e a t} \)
A \( \cdot \) both the \( [C O] \) and \( \left[C O_{2}\right] \) will decrease
B. neither the [CO] nor the [CO \( _{2} \) ] will change
c. the \( [C O] \) will decrease and the \( \left[C O_{2}\right] \) will increase
D. both the [CO] and [CO \( _{2} \) ) will increase


A metallic oxide which on heating gives a metal and oxygen is:
\( A \cdot S O_{2} \)
в. \( H g O \)
c. \( N a_{2} O \)
D. \( F e_{2} O_{3} . x H_{2} O \)


If \( \mathbf{A B}=\mathbf{0}, \) then
\( \mathbf{A} \cdot \mathbf{A}=0 \)
\( \mathbf{B} \cdot \mathbf{B}=0 \)
C. \( A \) and \( B \) need not be zero matrices
D. \( A \) and \( B \) are zero matrices


Match the column-I with Column-II
and select the correct answer:
Column -II Column - I
Curie
\[
\text { A. } 10^{6} \text { dis } s e c^{-1}
\]
(I) urle
(II) I) Rutherford
\[
\text { В. } 3.7 \times 10^{10} \text { dis sec}^{-1}
\]
(III) Becquerel C. 1 dis \( s e c^{-1} \) C. 1 \( s s e c \)
A. I-B II-A III-C
B. I-B II-C III-A
c. I-A II-B III-C
D. I-C II-B III-A


Water bodies like sea, rivers etc., which
are deep appear blue. Why?


Simplify the following expression.
\( f\left(a^{2 / 3}\right)^{3} \div a^{3 / 2} \times a^{-3} \) If \( a=\frac{1}{4} . \) Find
\( \boldsymbol{x}^{-1} \)


A weight is suspended from a long metal wire. If the wire suddenly breaks, its temperature.:-
A . rises
B. falls
c. remains unchanged
D. attains a velue \( 0 K \)


Two bodies \( A \) and \( B \) at temperatures
\( 327^{\circ} \mathrm{C} \) and \( 277^{\circ} \mathrm{C} \) are kept in vacuum
chamber at \( 27^{\circ} \mathrm{C} \). Then ratio of their
rates of loss of heat in a given time interval is nearly.
\( A \cdot 2: \)
B. 1: 2
\( c \cdot 1: 4 \)
D. 4: 1


If \( D_{p}=\left|\begin{array}{ccc}\boldsymbol{p} & \mathbf{1 5} & \mathbf{8} \\ \boldsymbol{p}^{2} & \mathbf{2 5} & \mathbf{9} \\ \boldsymbol{p}^{\mathbf{3}} & \mathbf{4 5} & \mathbf{1 0}\end{array}\right|, \) then \( \operatorname{det}\left(\boldsymbol{D}_{1}+\right. \)
\( D_{2} \) ) is equal to
\( \mathbf{A} \cdot \mathbf{0} \)
B . 25
\( c .625 \)
D. None of these


What is the action of carbon on the
following metal oxide.
\( F e_{2} O_{3} \) in blast furnace


If \( \boldsymbol{I}_{n}=\int_{\boldsymbol{\pi} / 4}^{\pi / 2}(\boldsymbol{T} \boldsymbol{a} \boldsymbol{n} \boldsymbol{\theta})^{-\boldsymbol{n}} \cdot \boldsymbol{d} \boldsymbol{\theta} \) for \( (\boldsymbol{n}>1) \)
then \( \boldsymbol{I}_{\boldsymbol{n}}+\boldsymbol{I}_{\boldsymbol{n}+\mathbf{2}}=? \)
A. \( \frac{1}{\mathrm{n}+1} \)
B. \( \frac{-1}{\mathrm{n}+1} \)
c. \( \frac{1}{\mathrm{n}-1} \)
D. \( \frac{-1}{\mathrm{n}-1} \)


Solutions which are decomposed due to
the current passed through them are called


Solve the inequalities and represent the solution graphically on number line.
\( 5 x+1>-24,5 x-1<24 \)


The differential equation of the simple harmonic motion given by \( \boldsymbol{x}= \)
\( \boldsymbol{A} \cos (\boldsymbol{n} \boldsymbol{t}+\boldsymbol{\alpha}) \) is
\( ^{A} \cdot \frac{d^{2} x}{d t^{2}}-n^{2} x=0 \)
B. \( \frac{d^{2} x}{d t^{2}}+n^{2} x=0 \)
c. \( \frac{d x}{d t}-\frac{d^{2} x}{d t^{2}}=0 \)
D. \( \frac{d^{2} x}{d t^{2}}-\frac{d x}{d t}+n x=0 \)


Freshly prepared pure dilute solution of
sodium in liquid ammonia:
This question has multiple correct options
A. shows copper-bronze colour
B. occupy larger volume than that from the sum of the volumes of \( N a \) and \( N H_{3}(1) \)
C . reduced the \( G e H_{4} \) to \( G e H_{2}^{-} \)
D. produced sodium amide and hydrogen gas with rusty iron wire.


The value of \( \cos (A+B) \) if \( \sin A=\frac{3}{5} \)
and \( \cos B=\frac{8}{17} \)


Find \( ^{\prime} \lambda^{\prime} \) when the projection of \( \vec{a}= \) \( \lambda \hat{i}+\hat{j}+4 \hat{k} \) on \( \vec{b}=2 \hat{i}+6 \hat{j}+3 \hat{k} \) is 4
units.


An object placed on a ground is in stable equilibrium. If the objects is given a slight push, then initially the position of centre of gravity:
A. moves nearer to ground
B. rises higher above the ground
c. remains as such
D. may remain at same leve


A proton moves at a speed \( \boldsymbol{v}=\mathbf{2} \times \)
\( 10^{6} m / s \) in a region of constant
magnetic field of magnitude \( \boldsymbol{B}= \)
\( 0.05 T . \) The direction of the proton when
it enters this field is \( \theta=30^{\circ} \) to the field.
When you look along the direction of the magnetic field, the path is a circle projected on a plane perpendicular to the magnetic field. How far will the
protons move along the direction of \( \boldsymbol{B} \)
when 2 projected circles have been completed?


If the same force is applied on two
bodies of different masses for the same
time, then the change produced in the momentum of the two bodies is also
same
A. True
B. False


If \( \frac{\boldsymbol{a}}{\boldsymbol{b}}=\frac{\boldsymbol{c}}{\boldsymbol{d}}=\frac{\boldsymbol{e}}{\boldsymbol{f}} \) and
\( \frac{2 a^{4} b^{2}+3 a^{2} c^{2}-5 e^{4} f}{2 b^{6}+3 b^{2} d^{2}-5 f^{5}}=\left(\frac{a}{b}\right)^{n} \) then
the value if \( n \) is
\( A \)
B. 2
\( c \cdot 3 \)
\( D \)


Statement 1: A solution of NaCl will
conduct electricity.
Statement 2: NaCl will not form ions in
Solution.
A. Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation of Statement 1
B. Both the Statement 1 and Statement 2 are correct 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 Statement 1 and Statement 2 are not correct.


Choose the reactions which are not
feasible
I. Iron \( + \) Zinc sulphate \( \rightarrow \) Iron sulphate \( + \) zinc
II. Magnesium + Silver nitrate \( \rightarrow \) Magnesium nitrate + Silver
III. Copper + dil. sulphuric acid \( \rightarrow \)
Copper sulphate \( +\boldsymbol{H}_{2} \)
IV. Zinc \( + \) Ferrous sulphate \( \rightarrow \) Iron \( + \) Zinc sulphate
A. I, Il and III
B. III and IV only
c. I and III only
D. All of these


A body rolling down a hill has:
A. K.E. only
B. P.E. only
C. neither K.E. nor P.E.
D. both K.E. and P.E


Which of the following thermodynamic relation is correct?
A. \( d G=V d p-S d T \)
в. \( d E=p d V+T d S \)
c. \( d H=-V d p+T d S \)
D. \( d G=V d p+S d T \)


Find the sequence if, \( \boldsymbol{T}_{\boldsymbol{n}}=\mathbf{5} \boldsymbol{n}+\mathbf{1} \)


Which gas cannot collected over water?
A. \( O_{2} \)
в. \( P H_{3} \)
c. \( N_{2} \)
D. \( S O_{2} \)


If \( \bar{z} \) lies in the third quadrant then \( z \) lies
in the
A. First quadrant
B. Second quadrant
c. Third quadrant
D. Fourth quadrant


Assertion
Darwin's finches show a variety of beaks suited for eating large seeds, flying insects and cactus seeds.
Reason
Ancestral seed-eating stock of Darwin's finches radiated out from South
American mainland to different
geographical areas of the Galapagos Islands, where they found competitor for new habitats.
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


In the circuit shown in figure charge stored in the capacitor of capacity
5 muf is
\( A \cdot 60 \mu C \)
В. \( 20 \mu C \)
\( c .30 \mu C \)
\( D \)


Modulus of nonzero complex number z
satisfying \( \bar{z}+z=0 \) and \( |z|^{2}-4 z i= \)
\( z^{2} \) is


\( \int \frac{(x-1)^{2}}{x^{4}+x^{2}+1}= \)


A beam of some kind of practical of velocity \( 2 \times 10^{7} m / s \) is scattered by a
gold \( (z=79) \) foil. Find specific charge of
this particle charge/mass if the distance of closest approach is \( \mathbf{7} . \mathbf{9 1 0}^{-\mathbf{1 4}} \mathbf{m} \)


A manufacturer has 600 litres of a
12\% solution of acid. How many litres of a \( 30 \% \) acid solution must be added to it
so that acid content in the resulting mixture will be more than \( 15 \% \) but less
than \( 18 \% ? \)


What is the legal age for the marriage
of?


An \( L-C-R \) series circuit has a
maximum current of \( 5 A . \) If \( L=0.5 H \)
and \( C=8 \mu F, \) then the angular
frequency of \( \boldsymbol{A} \boldsymbol{C} \) voltage is :
A. 500 rad/s
B. 5000 rad/s
c. 400 rad/s
D. \( 250 \mathrm{rad} / \mathrm{s} \)


Derive an expression for impedence and
current in the series \( L C R \) circuit using phasor diagram


Find out the acceleration of the ball
between \( t=0 \) and \( t=4 \) as shown above
velocity-time graph.
A . zero
B . \( 1 \mathrm{m} / \mathrm{s}^{2} \)
c. \( 2 m / s^{2} \)
D. \( 4 m / s^{2} \)
ह. \( 8 m / s^{2} \)


Mark the incorrect statement.
A. electric current produces magnetism.
B. magnets can produce electric current.
C. magnets can't produce electric current.
D. a and b


Evaluate the following integral as limit
of sums:
\( \int_{0}^{5}(x+1) d x \)


Charge \( Q \) is given a displacement \( \vec{r}= \) \( \boldsymbol{a} \hat{\boldsymbol{i}}+\boldsymbol{b} \hat{\boldsymbol{j}} \) in an electric field \( \overrightarrow{\boldsymbol{E}}=\boldsymbol{E}_{1} \hat{\boldsymbol{i}}+ \)
\( E_{2} \widehat{j} . \) The work done is :
A \( \cdot Q\left(E_{1} a+E_{2} b\right) \)
)
в. \( Q \sqrt{\left(E_{1} a\right)^{2}+\left(E_{2} b\right)^{2}} \)
c. \( Q\left(E_{1}+E_{2}\right) \sqrt{a^{2}+b^{2}} \)
D. \( Q \sqrt{\left(E_{1}^{2}+E_{2}^{2}\right)} \sqrt{a^{2}+b^{2}} \)


A die has six faces numbered from 1 to
6. It is rolled and number on the top face is noted. When this is treated as
random trial.
(a) What are the possible outcomes?
(b) Are they equally likely? Why?
(c) Find the probability of a composite number turning up on the top face.


Solve:
\( \lim _{x \rightarrow 2} \frac{x^{2}-4}{\sqrt{3 x-2}-\sqrt{x+2}} \)


Why does bread mould grow profusely on a moist slice of bread rather than on
a dry slice of bread?


A manometer is used to measure the
pressure of a gas trapped in a cylinder
At which labelled point on the diagram
is the pressure greatest?
4.4
в. \( B \)
\( c . c \)
D. \( D \)


In any G.P. the first term is 2 and last
term is 512 and common ratio is \( 2, \) then
\( 5^{t h} \) term from end is -
A . 16
B. 32
\( c \cdot 64 \)
D. None of these


A hydrocarbon has the molar mass 86 The number of chain isomers possible for the compound is :
A . five
B. six
c. four
D. ten


A uniform rod of length \( l=1 m \) is kept
as shown in the figure. \( \boldsymbol{H} \) is a horizontal
smooth surface and \( W \) is a vertical
smooth well. The rod is release from this
position. What is the angular angular acceleration of the rod just after the released?
A. \( \frac{6 g \cos \theta}{l} \)
B. \( \frac{3 g \cos \theta}{l} \)
\( c .6 g \cos \theta \)
D. \( \frac{2 g \cos \theta}{l} \)


Find the coordinates of points on the \( x \) axis which are at a distance of 17 units
from the point (11,-8)


What will be ratio of speed in first two
seconds to the speed in next 4 s?
A. \( \sqrt{2}: 1 \)
B. 3:
\( c \cdot 2: \)
\( D \cdot 1: 2 \)


Metals have
A. Zero resistivity
B. High resistivity
C . Low resistivity
D. Infinite resistivity


For an ideal solution with \( \boldsymbol{p}_{\boldsymbol{A}}^{\boldsymbol{o}}>\boldsymbol{p}_{\boldsymbol{B}}^{\boldsymbol{o}} \)
which of the following is true?
A \( \cdot\left(x_{A}\right)_{\text {liquid}}=\left(x_{A}\right)_{\text {vapour}} \)
В . \( \left(x_{A}\right)_{\text {liquid }}>\left(x_{A}\right)_{\text {vapour }} \)
C \( \cdot\left(x_{A}\right)_{\text {liquid}}<\left(x_{A}\right)_{\text {vapour}} \)
D \cdot \( \left(x_{A}\right)_{\text {liquid }} \) and \( \left(x_{A}\right)_{\text {vapour }} \) cannot be correlated with each other


Two planets have masses \( M_{1} \) and \( M_{2} \)
and radii \( \boldsymbol{R}_{1} \) and \( \boldsymbol{R}_{2} \) respectively. Then
the time periods of near surface satellite of the two planets will be equal if
A. \( M_{1} R_{2}^{2}=M_{2} R_{1}^{2} \)
B. \( M_{1} R_{2}^{3}=M_{2} R_{1}^{3} \)
\( \mathbf{c} \cdot M_{1}^{2} R_{2}=M_{2}^{2} R_{1} \)
D. \( M_{1} R_{1}^{3}=M_{2} R_{2}^{3} \)


Which of the following is the most primitive type of mitosis?
A. Amitosis
B. Cryptomitosis
c. Endomitosis
D. zygotic mitosis


Tidal Volume and Expiratory Reserve Volume of an athlete is \( 500 \mathrm{mL} \) and 1000
\( \mathrm{mL}, \) respectively. What will be his Expiratory Capacity if the Residual Volume is \( 1200 \mathrm{mL} \) ?
A. \( 1500 \mathrm{mL} \)
B. \( 1700 \mathrm{mL} \)
c. \( 2200 \mathrm{mL} \)
D. \( 2700 \mathrm{mL} \)


Potentiometer wire of length \( 1 \mathrm{m} \) is connected in series with \( 490 \Omega \)
resistance and \( 2 \mathrm{V} \) battery. If \( 0.2 \mathrm{mV} / \mathrm{cm} \) is the potential gradient, then resistance of the potentiometer wire is?
A . \( 4.9 \Omega \)
B. \( 7.9 \Omega \)
\( c .5 .9 \Omega \)
D. \( 6.9 \Omega \)


Antidote for carbon monoxide is :
A. Carborundum
B. Carbogen
c. carbonic acid
D. Pure oxygen


Divide
\( \frac{x^{3}+x+1}{x^{2}-1} \)


Smoke is inhaled by the
A. Digestive system
B. Respiratory system.
C. Nervous system.
D. Excretory system.


If \( \boldsymbol{p}=\boldsymbol{q} \) then \( \boldsymbol{p} \boldsymbol{x}= \)
\( \mathbf{A} \cdot \mathbf{q} \)
B. \( q x \)
\( \mathbf{c} \cdot q+x \)
D.


The diagonals of a parallelogram
\( P Q R S \) are along the lines \( x+3 y=4 \)
and \( 6 x-2 y=7 . \) Then \( P Q R S \) must be
\( a \)
A. rectangle
B. square
c. cyclic quadrilateral
D. rhombus


Which of the following sublimes without heating even at the room
temperature?
A. Camphor
B. Ammonium chloride
c. Dry lce
D. None of the above


In a sample survey of 640 people, it was found that 400 people have a secondary school certificate. If a person is selected at random, what is the probability that the person does not have such
certificate?
\( \mathbf{A} \cdot 0.375 \)
B. 0.625
c. 0.725
D. 0.875


How much greater is one micro coulomb compared to an electronic
charge?
A \( \cdot 10^{13} \) times
B. \( 10^{10} \) times
\( \mathbf{c} \cdot 10^{11} \) times
D. \( 10^{6} \) times


Select the correct IUPAC name for
\( N a_{2}\left[F e(C N)_{5} N O\right] \) complex.
This question has multiple correct options
A. Sodiumpentacyanidonitrosoniumferrate(II)
B. Sodiumpentacyanidonitrosyliumferrate(II)
c. sodiumpentacyanidonitrosyl ferrate(II)
D. sodiumpentacyanidonitrosyliron(II)


\( \int\left(\frac{e^{5 \log x}-e^{4 \log x}}{e^{3 \log x}-e^{2 \log x}}\right) d x= \)
A . \( x+c \)
B. \( 3 x^{2}+c \)
c. \( \frac{x^{3}}{3}+c \)
D. \( \frac{x^{3}}{2}+c \)


A container is filled with a radioactive
substance for which the half-life is 2
days. A week later, when the container is opened, it contains \( 5 g \) of the
substance. Approximately how may grams of the substances were initially
placed in the container?
A . 40
B. 60
c. 80
D. 100


Blood clot takes place mainly due to
A. Fibrin and corpuscles
B. Heparin and corpuscles
C. Plasma and corpuscles
D. Plasma and RBC


During an adiabatic process,the cube of the pressureis found to be inversely proportional to the fourth power of the volume. Then, the ratio of specific heats is :-
\( A \)
B. 1.33
c. 1.67
D. 1.4


The table shows some information
about elements in Group VII of the
Periodic Table.
yellow-
green \( \begin{array}{ll}\text { Name } & \begin{array}{l}\text { State at room } \\ \text { temperature }\end{array} \\ \text { Chlorine } & \text { Gas } \\ \text { Bromine } & \text { liquid } \\ \text { iodine } & \text { ? } \\ \text { Astaine } & \text { solid }\end{array} \) brown
? black
Which information about iodine
completes the table?
A. State - liquid, colour - black
B. State - liquid, colour - green
c. state - solid, colour - grey
D. State - solid, colour - yellow


A proton is travelling along the \( x \) direction with velocity \( 5 \times 10^{6} m s^{-1} \)
The magnitude of force experienced by
the proton in a magnetic field \( B= \) \( (0.2 \hat{i}+0.4 \hat{k}) \) tesla is
A. \( 3.2 \times 10^{-13} N \)
N
В. \( 5.3 \times 10^{-13} N \)
c. \( 3.2 \times 10^{13} N \)
D. \( 6.3 \times 10^{-13} \) 3
E \( .3 .5 \times 10^{-12} N \)


Calculate rms speed in \( c m / \)sec of oxygen molecules having K.E of \( 2 k c a l / m o l \)


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


An equilibrium mixture, \( N_{2}(g)+ \) \( O_{2}(g) \rightleftharpoons 2 N O(g) \) in a vessel of
capacity 100 litre contain
1 mol \( N_{2}, 2 \) mol \( O_{2} \) and 3 mol \( N O \)
Calculate the number of moles of \( O_{2} \) to
be added so that at new equilibrium the
conc. of \( N O \) is found to be 0.04 mol \( / \)lit
A . \( (101 / 18) \)
в. \( (101 / 9) \)
c. \( (202 / 9) \)
D. None of these


Choose the correct answers from the
alternatives given In mammals, mastication of the food is
done by
A. molars
B. premolars
c. incisors
D. canines


The yellow colour of urine is due to the
presence of
A . Bile
B. Lymph
c. cholesterol
D. Urochrome


In a pollen grain, if \( T=40 \%, C=10 \%, \) then
\( G=? \)
A . \( 40 \% \)
B . 10\%
c. 91\%
D. 20\%


The number of permutations of the letters of the word AGAIN taken three at
a time is
A .48
B. 24
\( c . \) 36
D. 33


The most poisonous form of
phosphorous is:
A. white
B. red
c. black
D. violet


If \( \boldsymbol{A}=\left[\begin{array}{ccc}-1 & 1 & -1 \\ 3 & -3 & 3 \\ 5 & 5 & 5\end{array}\right] \) and \( B= \)
\( \left[\begin{array}{ccc}0 & 4 & 3 \\ 1 & -3 & -3 \\ -1 & 4 & 4\end{array}\right], \) then find \( A^{2}-B^{2} \)


Plants are autotrophic. Can you think of
some plants that are partially heterotrophic?


A bullet of mass \( A \) and velocity \( B \) is
fired into a block of wood of mass \( C . \) If
loss of any mass and friction be neglected, the velocity of the system must be
A \( \cdot \frac{A B}{A+C} \)
в. \( \frac{A+C}{B+C} \)
c. \( \frac{A C}{B+C} \)
D. \( \frac{A+B}{A C} \)


When \( S O_{2} \) is passed through cupric chloride solution:
A. blue precipitate is obtained
B. solution becomes colourless,no ppt is obtained.
c. solution becomes colourless and white ppt is obtained.
D. no change


Find \( 8 t h \) and 12 th terms of the G.P.
\( 81,-27,9, \dots \dots \dots \)


Which of the following is true for electrical energy?
\( \mathbf{A} \cdot E=P \times t \)
в. \( \quad E=\frac{P}{t} \)
c. \( _{E}=\frac{V^{2}}{R t} \)
D. None of these


A student determined to test the law of
gravity for himself walks off a
skyscraper \( 320 m \) high with a stopwatch in hand and starts his free
fall (zero initial velocity). 5 seconds later, superman arrives at the scene
and dives off the roof to save the
student. what must be superman's initial velocity in order that he catches the student just before reaching the ground? [assume that superman's acceleration is that of a free-falling body, \( \left.g=10 m / s^{2}\right] \)
B . \( 25.8 \mathrm{ms}^{-1} \)
c. \( 4.785 \mathrm{ms}^{-1} \)
D. Cannot be determined


Find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}, \) when \( \boldsymbol{y}=\boldsymbol{3} \tan \boldsymbol{x}+ \)
\( \boldsymbol{5} \log _{\boldsymbol{a}} \boldsymbol{x}+\sqrt{\boldsymbol{x}}-\boldsymbol{3} \boldsymbol{e}^{\boldsymbol{x}}+\frac{\boldsymbol{1}}{\boldsymbol{x}} \)


Find the values of \( x, \) if \( \left|\begin{array}{ll}\mathbf{2} & \mathbf{3} \\ \mathbf{4} & \mathbf{5}\end{array}\right|=\left|\begin{array}{ll}\boldsymbol{x} & \mathbf{3} \\ \mathbf{2} \boldsymbol{x} & \mathbf{5}\end{array}\right| \)


An element has average atomic mass \( 20.426 u \) it has 2 isotopes with masses
\( \mathbf{2 2 . 1 8 2 4} \) and \( \mathbf{1 9 . 9 5 7 4 .} \) Calculate the
abundance of its isotopes \( X-22 \) and
\( X-20 \)


Find the area of a regular hexagon of
side
a) \( 8 \mathrm{cm} \)
b) \( 6 \mathrm{cm} \)


How many oxides are soluble in a
moderately concentrated aqueous
solution of NaOH.
\( \begin{array}{llll}s O_{3} & c l_{2} O_{7} & N_{2} O_{5} & \text { co } \\ (1) & \text { (2) } & \text { (3) } & \text { (4) } \\ K_{2} O & C r_{2} O_{3} & \text { Bao } & G e O_{2} \\ \text { (5) } & \text { (6) } & \text { (7) } & \text { (8) }\end{array} \)


A opaque card is held over the lower half
of a converging lens as shown in figure. Which picture is best shows the image
that appears on the screen
\( A \cdot A \)
B. B
\( c \cdot c \)
\( D \)


Select that pair(s) in which bond angle of first molecule is less than second
one.
This question has multiple correct options
A \( \cdot B r O_{3}^{-}, C l O_{3} \)
B. \( A s I_{3}, S b I_{3} \)
\( \mathrm{c} \cdot \operatorname{SbBr}_{3}, \mathrm{SbI}_{3} \)
D. \( N F_{3}, N H_{3} \)


Environment is warmed up by
A. water vapour
B. Methane
\( c \cdot C O_{2} \)
D. All of the above