Q Type your question
through the side, along the diameter of
a cross section of the coil. From out
point of view, we are looking straight through the coil.
We can see from the diagram that from
out perspective, the coil carries a clockwise conventional current, and the straight wire carries a conventional
current to the right. From our perspective, what is the
direction of the force on the segment of straight wire in the coil, due to the magnetic field produced by the coil?
A. Away from us
B. Toward us
\( c \cdot u p \)
D. Down
E . Right


Substances do not show their acidic
properties without:
A. base
B. water
c. acid
D. all of the above


A car moves in a semicircular track of
radius 700 m. If it starts from one end
of the track and stops at the other end, the displacement of car is:
A . \( 2200 m \)
B. \( 700 m \)
c. \( 1400 m \)
D. \( 800 m \)


An insulated charged conducting sphere of radius \( 5 \mathrm{cm} \) has a potential of \( 10 \mathrm{V} \) at
the surface. What is the potential at
centre?
A . \( 10 V \)
в. zero
c. same as that at \( 5 \mathrm{cm} \) from the surface
D. same as that at \( 25 \mathrm{cm} \) from the surface


Find the limit :-
\( \lim _{x \rightarrow \infty}\left\{\frac{x^{2}+2 x+3}{2 x^{2}+x+5}\right\}^{\frac{3 x-2}{3 x+2}} \)


A sealed gas cylinder is left outside on a
hot, sunny day. What happens to the average speed of the gas molecules and to the pressure of the gas in the cylinder
as the temperature of the gas rises?
Average speed of \( \quad \) Pressure of gas gas molecules \( \quad \) in cylinder
Decreases

Decreases
Decreases

Increases
Increases

Decreases
Increases
\( A \cdot A \)
B. B
\( c \cdot c \)
D. D


Two persons \( P \) and \( Q \) of the same height are carrying a uniform beam of length \( 3 m . \) If \( Q \) is at one end, then the
distance of \( P \) from the other end such
that \( P, Q \) receive loads in the ratio 5: 3
is:
\( \mathbf{A} \cdot 0.5 m \)
B. \( 0.6 m \)
c. \( 0.75 m \)
D. \( 1 m \)


Among the following, the continuous function is ?
A. \( \tan x \)
B. \( \sec x \)
\( c \cdot \sin 1 / x \)
D. None of these


Which statements are correct about the
figure given below?
This question has multiple correct options
A. It is sucrose
B. Due to presence of hemi-acetal linkage, it is a non educing sugar
c. Left side unit is \( \alpha \) -D-Glucose and right side unit is \( \beta-D \) ructose
D. Due to absence of hemi-acetal linkage, it can't show mutarotation


The vapour pressure of a mixture of
diethyl aniline and water is \( 1.013 \times \) \( 10^{5} N m^{-2} \) at \( 99.4^{\circ} C . \) The vapour
pressure of water at this temperature is
\( 0.992 \times 10^{5} N m^{-2} . \) The grams of steam
are necessary to distill over 100 g of diethylaniline are (write answer as nearest integer after dividing by 60 ).


Find the mean deviation about median
for the following data.
\begin{tabular}{lllll}
\multirow{2}{*} {\( \boldsymbol{C I} \)} & \( \boldsymbol{8}- \) & \( \mathbf{1 3}- \) & \( \mathbf{1 8}- \) & \( \mathbf{2 3}- \) \\
& \( \mathbf{1 2} \) & \( \mathbf{1 7} \) & \( \mathbf{2 2} \) & \( \mathbf{2 7} \)
\end{tabular}
14
20


Central and hottest part of Earth is called:
A. inner core
B. outer core
c. crust
D. mantle


The chemical formulae of iron ore is:
A \( \cdot \) Fe \( S_{2} \)
в. \( F e_{3} O_{4} \)
\( \mathrm{c} \cdot F e_{2} O_{3} \)
D. All of these


A ball thrown by a boy from a roof-top
has
A. Curvilinear
B. oscillatory motion
c. Periodic motion
D. Linear motion


A container contains 0.25 kg of a liquid at its boiling temperature. If the latent heat of fusion for the liquid is 500 Joules/kg and the latent heat of
vaporization for the liquid is 1000 Joules/Kg. How much heat must be
added to the liquid to boil all of the liquid away?
A \( .125 \mathrm{J} \)
J.
в. \( 2000 J \)
c. \( 4000 J \)
D. \( 0.50 J \)
E . \( 250 J \)


Chances of inheritable and evolutionary changes are more in such species
which reproduce by
A. Parthenogenesis
B. Fission
c. Sexual reproduction
D. All of the above


A sample of chloroform before using as anaesthetic is tested by:
A. Fehling solution
B. \( A g N O_{3} \) solution
c. Boiling with \( K O H \)
D. Ammoniacal cuprous chloride


Van't-Hoff factor(i) for this reaction is:
A .2
B.
\( c \)
\( D \)


In Young's double slit experiment, the two slits act as coherent sources of
equal amplitude a and of wavelength \( \lambda \) In another experiment with the same set up, the two slits are source of equal
amplitude \( n \) and wavelength \( \lambda \), but are incoherent. The ratio of intensities of
light at the mid point of the screen in the first case to that in the second case
is
A .2: 1
B . 1: 2
\( c \cdot 3: 4 \)
\( D \cdot 4: 3 \)


Drones are specified for:-
A. Collection of food
B. Fertilization of eggs
C. Protection
D. Egg laying


State and explain Universal law of Gravitation. Give its vector form.


Antiparallel strands of a DNA molecule
means that
A. One strand turns anti-clockwise
B. The phosphate groups of two DNA strands, at their ends, share the same position.
c. The phosphate groups at the start of two DNA strands are in opposite position (pole).
D. One strand turns clockwise.


Electric discharges in the atmosphere is associated with natural phenomena
such as :
A. lightning
B. reflecting
c. refracting
D. none of the above


If \( I=\int \frac{x^{2}}{(x-a)(x-b)} d x, \) then
equals
A \( \cdot x+\frac{1}{a-b} \log \left|\frac{x-a}{x-b}\right|+C \)
в. \( \quad x+\frac{1}{a-b} \log \left|\frac{x-a}{x-b}\right|^{a^{2}+b^{2}}+C \)
c. \( x+\frac{1}{a-b}\left\{a^{2} \log |x-a|-b^{2} \log |x-b|\right\}+C \)
D. none of these


Explain normal or standard hydrogen electrode.


Statement 1: The scalar product of two
vector can be zero.
Statement 2:If two vector are
perpendicular to each other, their scalar product will be zero.
A \( \cdot \) a) Statement- -1 is false, statement- 2 is true
B. b) Statement-1 is true, Statement-2 is true, Statement
2 is a correct explanation for statement-
c. c) Statement- - is true, Statement-2 is true; Statement
2 is not a correct explanation for statement-
D. d) Statement-1 is true, Statement-2 is false


State true or false:
Five rational numbers between. \( \frac{-3}{2} \) and \( \frac{5}{3} \) are \( \frac{-8}{6}, \frac{-7}{6}, 0, \frac{1}{6}, \frac{2}{6} \)
A. True
B. False


Given below are few mixtures formed by mixing two components. Which of the following binary mixtures will have same composition in liquid and vapour phase?
(i) Ethanol \( + \) Chloroform
(ii) Nitric acid + Water
(iii) Benzene + Toluene
(iv) Ethyl chloride \( + \) Ethyl bromide
A. (i) and (iii)
B. (i) and (ii)
c. (i), (ii) and (iii)
D. (iii) and (iv)


Choose the odd members of pyrrophyta.
A. Gonyaulax
B. Noctiluca
c. Gymnodinium
D. Physarum


\( A \) is a point on \( x- \) axis with abscissa
-8 and \( B \) is point on \( y- \) axis with
coordinate \( 15 . \) Find distance \( A B \)


A galvanometer (coil resistance \( 99 \Omega) \)
is converted into a ammeter using a
shunt of \( 1 \Omega \) and connected as shown in
the figure ( \( i \) ). The ammeter reads \( 3 A \)
The same galvanometer is converted
into a voltmeter by connecting a
resistance of \( 101 \Omega \) in series. This
voltmeter is connected as shown in
figure ( \( i i \) ). Its reading is found to be \( 4 / 5 \)
of the full scale reading. Find the internal resistance \( r \) of the cell (in
ohms)


For any gas the pressure coefficient \( (\beta) \) is equal to the volume coefficient ( \( \alpha \) ).
This can be proved by:
A. Charle's law
B. Boyle's law
c. Grahm's law
D. Avogadro's number


Tell whether the following is certain to happen, possible can happen but not certain
Tomorrow will be a cloudy day.


Which of the following is the example of
direct proportion?
A. Number of mangoes in a bag and weight of the bag.
B. Speed goes up, travel times goes down
c. More the number of men lesser the time taken to complete it.
D. None of these.


The divalent metal whose oxide is
reduced to metal by electrolysis of its fused salt is
\( (A l / N a / M g / K) \)


The products of (A) on ozonolysis
followed by oxidation with \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) are :
\( A \)
B.
\( c \)
\( D \)


The noble gases are nonreactive
because:
A. they react with sodium
B. they have a full outer shell of electrons
C. they have a half outer shell of neutrons
D. they are too thin


Example of viviparous fish is
A . Labeo
B. Scoliodon
c. Hippocampus
D. Exocoetus


\( C-O \) bond lengths designated by
\( \boldsymbol{\alpha}, \boldsymbol{\beta}, \gamma \) and \( \boldsymbol{\delta} \) are in order.
A \( \cdot \alpha=\gamma<\beta=\delta \)
в. \( \alpha<\beta<\gamma=\delta \)
c. \( \alpha<\gamma=\delta<\beta \)
D. All are equal


Which plants bear petaloid bracts?
A. Bougainvillea
B. cassia fistula
c. Mimosa pudica
D. Ricinus


A sound wave travels with a speed of
\( 330 m s^{-1} \) in air. If the wavelength of the
wave is \( 110 c m, \) then frequency of the wave is


Assertion: Metal ions must be present in a solution used for electroplating a particular metal.

Reason: Electroplating occurs only on
anode.
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


In the spectrum of white light by a prism, the colour at the extreme end opposite to the base of prism is:
A . violet
B. yellow
\( c \cdot \) red
D. blue


Let \( \vec{a}=\hat{i}+\hat{j}+\hat{k}, \vec{b}=\hat{i}+3 \hat{j}+5 \hat{k} \) and
\( \vec{c}=7 \hat{i}+9 \hat{j}+11 \hat{k} . \) Then the area of the
parallelogram with diagonals \( \vec{a}+\vec{b} \) and \( \vec{b}+\vec{c} \) is
A \( .4 \sqrt{6} \)
в. \( \frac{1}{2} \sqrt{21} \)
c. \( \frac{\sqrt{6}}{2} \)
D. \( \sqrt{6} \)
E \( \cdot \frac{1}{\sqrt{6}} \)


The \( p H \) of water is:
\( A \cdot 9 \)
B. 3
\( c \cdot 7 \)
D. 4


In the given figure, \( A B C \) is a triangle,
side \( \mathrm{CB} \) is produced to \( \mathrm{E} \) and \( \angle \boldsymbol{A}: \angle \boldsymbol{B} \)
\( \angle C=2: 1: 3 . \) Find \( \angle D B E, \) if DB is
perpendicular to AB.
A \( \cdot 66^{\circ} \)
B . \( 46^{\circ} \)
\( c \cdot 60^{\circ} \)
D. none of the above


Rain is falling vertically with a speed of
\( 30 \mathrm{m} s^{-1} . \) A woman rides a bicycle with a
speed of \( 10 \mathrm{m} s^{-1} \) in the north to south
direction. What is the direction in which
she should hold her umbrella?


Find the area of the region bounded by
the curve \( y=x^{2} \) and the line \( y=4 \)


In the given figure, \( \angle B=65^{\circ} \) and
\( \angle C=45^{\circ} \) in \( \triangle A B C \) and \( D A E \| B C . \) If
\( \angle D A B=x^{o} \) and \( \angle E A C=y^{o} \) and
\( \angle E A C=y^{o}, \) find the values of \( x \) and \( y \)


Which of the following gas is used in fuel cell?
A. Carbon-dioxide
B. Hydrogen
c. sulphur dioxide
D. Chlorine


\( \ln \operatorname{an} A C \) circuit \( V \) and \( I \) are given \( V= \)
\( 100 \sin (100 t) V \) and \( I= \)
\( \mathbf{1 0 0} \sin (\mathbf{1 0 0} t+\boldsymbol{\pi} / \mathbf{3}) \boldsymbol{m m} . \) The power
dissipated in the circuit is:
A \( \cdot 10^{4} \) watt
B. 10 watt
c. 2.5 watt
D. 5 watt


Find the cube root of 0.000000027
A . 0.03
B. 0.3
c. 0.003
D. 0.0003


Most animals that live in deep oceanic
waters are
A. Primary consumers
B. Secondary consumers
c. Tertiary consumers
D. Detrivores


Find the values of the following determinants
\( \left|\begin{array}{cc}\mathbf{1}+\mathbf{3} i & \boldsymbol{i}-\mathbf{2} \\ -\boldsymbol{i}-\mathbf{2} & \mathbf{1}-\mathbf{3} \boldsymbol{i}\end{array}\right| \)
where \( i=\sqrt{-1} \)


Green house effect is caused by :
A \( . N O_{2} \)
в. \( C O \)
c. \( N O \)
D. \( C O_{2} \)


All power entering a house enters via
A. Electricity Meter
B. Various loads in house
C. Electricity board motor
D. Potential Barrier


A steady current of 10.0 Amps is passed through a nickel production cell of 15 minutes.

Which of the following is the correct expression for calculating the number of grams of nickel produced? Note:
9. faraday\( =96,500 \) Coulombs
The electroytic cell involves the following half-reaction:
\( N i_{(a q)}^{2+}+2 e^{-} \rightarrow N i_{(s)} \)
A \( \frac{(10.0)(15)(96,500)}{(59)(60)} g \)
в. \( \frac{(10.0)(15)(59)}{(60)(96,500)} \),
c. \( \frac{(10.0)(15)(60)(59)}{(96,500)(2)} g \)
D. \( \frac{(96,500)(59)}{(10)(15)(60)(2)} g \)


If 25 is the arithmetic mean between \( x \)
and \( 46, \) then find \( x \)
\( A \cdot 2 \)
B. 4
\( c \cdot 8 \)
\( D \cdot 16 \)


With reference to the Aichi Biodiversity Targets, consider the following statements.
1. It aims to bring pollution, including from excess nutrients to levels that are
not detrimental to ecosystem function and biodiversity.
2. It aims to control or eradicate
invasive alien species on priority basis. Which of the statement(s) given is/are
correct?
A. 1 only
B. 2 only
c. Both 1 and 2
D. Neither 1 nor 2


Which is correct in case of
heterogeneous catalyst?
This question has multiple correct options
A. The catalyst decreases the energy of active ion.
B. The surface of catalyst plays an important role.
C. The catalyst actually forms a compound with reactants.
D. There is no change in the energy of activation.


When a p-njunction is reverse biased, the current becomes almost constant at
\( 25 \mu A . \) When it is forward biased at
\( 200 m e V, \) a current of \( 75 \mu A \) is obtained Find the magnitude of diffusion current when the diode is
(a) unbiased
reverse-biased at \( 200 m V \) and
forward-biased at \( 200 m V \)


Explain by an example that a body may posses energy when it is not in motion.


\( \operatorname{Let} f(x)=\frac{1-\tan x}{4 x-\pi}, x \neq \frac{\pi}{4}, \) then
\( \lim _{x \rightarrow \frac{\pi}{4}} f(x)= \)
\( \mathbf{A} \cdot \mathbf{1} \)
в. \( \frac{1}{2} \)
\( c \cdot-\frac{1}{2} \)
D. -


Hardness of water is due to soluble
salts:
A. Bicarbonates
B. Sulphates
c. chlorides
D. All of these


\( b \)
0
0


State two differences between an
electromagnet and a permanent
magnet.


Radiation emitted from a radioactive
element, of half life period of 30 min, are measured by a Geigar-Mullar counter The count rate of the sample reduces to 5 disintegrations /sec. in 2hrs. then the initial count rate in disintegration/sec is :-
A. 805
в. 200
\( c .250 \)
D. 40


\( 0.1 M N a O H \) is titrated with \( 0.1 M \)
\( \boldsymbol{H} \boldsymbol{A} \) till the end point; \( \boldsymbol{K}_{\boldsymbol{a}} \) for \( \boldsymbol{H} \boldsymbol{A} \) is
\( 5.6 \times 10^{-6} \) and degree of hydrolysis is
less compared to \( 1 . \) Calculate pH of the resulting solution at the end point.


State and prove Basic proportionality (Thales) theorem.


The homogeneous reaction is carried out in a 2 -litre container at a particular
temperature by taking 1 mole each of A,
B, \( C \) and \( D \) respectively. If \( K_{C} \) for the
reaction is \( \frac{1}{4} \) then the equilibrium concentration of \( \mathrm{C} \) is :
\( \boldsymbol{A}(\boldsymbol{g})+\boldsymbol{B}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{C}(\boldsymbol{g})+\boldsymbol{D}(\boldsymbol{g}) \)
A \( \cdot \frac{1}{3} M \)
в. \( \frac{2}{3} \)
\( ^{c} \cdot \frac{4}{3}^{M} \)
D. \( \frac{1}{2} M \)


An \( \alpha- \) particle of energy \( 5 \mathrm{MeV} \) is
scattered through 180 by a fixed uranium nucleus. The distance of the
closest approach is of the order of
\( \mathbf{A} \cdot \mathbf{1} \)
В. \( 10^{-10} \mathrm{cm} \)
\( \mathbf{c} \cdot 10^{-12} \mathrm{cm} \)
D. \( 10^{-15} \mathrm{cm} \)


A ring of mass kept on a horizontal
rough A force \( F \) is applied tangentially
at its rim as shown. The coefficient of
frictionless between the ring and the
surface is \( \mu \) Then
A. Friction will act in the forward direction
B. Friction will act in the backward direction
c. Friction force will not act
D. Frictional force will be \( \mu g \)


With what velocity was it thrown? (in
\( \mathrm{m} / \mathrm{s}) \)
\( \mathbf{A} \cdot 25.98 \)
B. 26.98
c .27 .98
D. 26


From which of the following case, the
current in the loop will not be induced?
A. The loop is moved in the direction of the magnet.
B. The magnet is moved in the direction of the loop.
C. The loop and magnet are moved in the opposite direction with the same speed.
D. The loop and magnet are moved in one direction with the same speed.


The set of real values of \( x \) satisfying the equality \( \left[\frac{\mathbf{3}}{\boldsymbol{x}}\right]+\left[\frac{\mathbf{4}}{\boldsymbol{x}}\right]=\mathbf{5} \) (where [.]
denotes the greatest integer function) belongs to the interval \( \left(a, \frac{b}{c}\right] \) where \( \boldsymbol{b} \)
\( a, b, c \in N \) and \( - \) is in its lowest form. \( \boldsymbol{c} \)
Find the value of \( a+b+c+a b c \)
A . 25
B . 18
c. 20
D. 10


What will happen if the bile duct is choked?
A. Acidic chyme will not be neutralizedd
B. Little absorption of fat will occur
c. Little digestion of carbohydrates will occur in the intestine
D. Faeces will become dry


Write two properties of equipotential surfaces. Depict equipotential surfaces due to an isolated point charge. Why do the equipotential surfaces get closer as the distance between the equipotential surface and the source charge
decreases?


A positive number is 5 times another
number. If 21 added to both the
numbers, then one of the new numbers
becomes twice the other new number.
What are the numbers?


Give the IUPAC names of the given
compounds:


If \( \vec{a}=2 \hat{i}+6 n \hat{j}+m \hat{k} \) and \( \vec{b}=\hat{i}+ \)
\( 18 \hat{j}+3 \hat{k} \) are parallel to each other then
the values of \( \boldsymbol{m}, \boldsymbol{n} \) are:
A . 6,6
B. \( 6, \)
\( c \cdot-1,6 \)
D. - -1.- 6


Whenever current is changed in a coil an induced e.m.f. is produced in the same coil, This property of the coil is due to
A. mutual induction
B. self induction
c. eddy currents
D. hysteresis


Solve the equations \( \frac{\mathbf{1 0}}{\boldsymbol{x}+\boldsymbol{y}}+\frac{\mathbf{2}}{\boldsymbol{x}-\boldsymbol{y}}=4, \frac{\mathbf{1 5}}{\boldsymbol{x}+\boldsymbol{y}}-\frac{\mathbf{5}}{\boldsymbol{x}-\boldsymbol{y}}= \)
-2


'Water hyacinth' which is a free floating weed and infests India's waterways choking off plants, fish and animal growth is a native of
A. Australia
B. France
c. south America
D. North America


Petroleum is also known as Black gold?
A. True
B. False


A square loop of side length \( a \) having \( n \)
turns is kept in a horizontal plane. \( \mathbf{A} \) uniform magnetic field \( B \) exists in vertical direction as shown in figure. Now, the loop is rotated with constant angular speed \( \omega \) as shown below. Which of the following statement is correct?
\( \begin{array}{llllll}\mathbf{X} & \mathbf{X} & \mathbf{X} & \mathbf{X} & \mathbf{X} & \mathbf{X}\end{array} \)
\( \mathbf{x} \quad \mathbf{x} \quad \mathbf{x} \quad \mathbf{x} \quad \mathbf{x} \quad \mathbf{x} \quad \mathbf{x} \)
A. Same emf is induced in both cases (i) and (ii)
B. Maximum emf is induced in case (i)
c. Emf induced in case
(ii) is more than (i)
D. No emf induced in case (ii)


Assertion
More/s and Truffles are edible fungi
Reason
Ascocarps are edible
A. If both the assertion and the reason are true and the
reason
is a correct explanation of the assertion
B. If both the assertion and reason are true but the
reason is
not a correct explanation of the assertion
C. If the assertion is true but the reason is false
D. If both the assertion and reason are false


At what distance in front of a concave
mirror of focal length \( 10 \mathrm{cm}, \) an object
be placed so that its real image of size five times that of the object obtain?


Which factor is most responsible for the increase in boiling points of noble gases from He to \( X e ? \)
A . Decrease in \( I . E \)
B. Monoatomic nature
c. Decrease in polarisability
D. Increase in polarisability


A magnetic field of \( 100 \mathrm{G}\left(1 \mathrm{G}=10^{-4} \mathrm{T}\right) \) is required which is uniform in a region of linear dimension about \( 10 \mathrm{cm} \) and area
of cross-section about \( 10^{-3} m^{2} . \) The
maximum current-carrying capacity of a given coil of wire is 15 A and the
number of turns per unit length that can be wound round a core is at most
1000 turns \( m^{-1} . \) Suggest
some appropriate design particulars of a solenoid for the required purpose. Assume the core is not ferromagnetic.


Find the remainder when \( x^{4}+4 x^{3}- \)
\( 5 x^{2}-6 x+7 \) is divided by \( x+1 \)


A body of mass m moving with a velocity v is acted upon by a force. Write expression for change in
momentum when \( \boldsymbol{v} \rightarrow \boldsymbol{c} \)
\( \mathbf{A} \cdot m \Delta v \)
B . \( \Delta(m v) \)
c. \( v \Delta(m) \)
D. \( m v \)


Cyberviatic is associated with
A. Flow of energy
B. Cycle of energy
c. Energy released
D. Study of energy


The normal at any point \( \boldsymbol{P}(\boldsymbol{x}, \boldsymbol{y}) \) of \( \mathbf{a} \)
curve meets the \( x \) -axis at \( Q \) and \( N \) is
the foot of the ordinate at \( P \)

If \( N Q=\frac{x\left(1+y^{2}\right)}{1+x^{2}}, \) then equation of such curve, given that it passes through the point (3,1) is:
A. \( x^{2}-y^{2}=8 \)
B . \( x^{2}+2 y^{2}=11 \)
c. \( x^{2}-5 y^{2}=4 \)
D. \( x^{2}+3 y^{2}=7 \)


Name the element that first shows
some visible metallic properties at
room temperature
A. Fluroine
B. Chlorine
c. Bromine
D. lodine
E. Astatine


Match the statements in Column I with
statements in column II


The probability of happening of an event
\( A \) is 0.5 and that of \( B \) is \( 0.3 . \) If \( A \) and \( B \)
are mutually exclusive events, then the probability of neither A nor B is?
A . 0.4
B. 0.5
\( c .0 .2 \)
D. 0.9


Percentage of oxygen transported by haemoglobin is
A . 93
B. 95
c. 97
D. 99


Let
\( |X| \) denote the number of elements in a set \( X \).let \( S=\{1,2,3,4,5,6\} \) be a
sample space,where each elements is equally likely to occur.If \( A \) and \( B \) are
independent events associated with \( S \) then the number of ordered pairs \( (A, B) \) such that \( 1 \leq|B|<|A| \) equals.


The final product obtained in the reaction is:
\[
\mathrm{H}_{3}-\langle\bigcirc\rangle-\mathrm{O} \mathrm{CH}_{3}+\mathrm{HBr} \longrightarrow
\]
\( A \)
в.
\( c \)
\[
\mathrm{cH}_{3}(\bigcirc)-\mathrm{O} \sqrt{\bigcirc}-\mathrm{cH}_{3}
\]
D. none of these


The solution of \( B i C l_{3} \) in dil. \( H C l \) when
diluted with water, white precipitate is formed which is:
A. bismith oxychloride
B. bismith oxide
c. bismith hydroxide
D. none of the above


sides 2 a lies on a smooth horizontal
plane as shown in the figure. Three
point masses of mass m each strike the
block at \( A, B \) and \( C \) with speeds \( v \) as
shown. After the collision, the particles
come to rest. Then the angular velocity
acquired by the triangular block is (I is
the moment of inertia of the triangular
block about \( \mathrm{G} \), perpendicular to the
plane of the block)
\( A \)
clockwise
B. \( \frac{2 m v a}{l} \) clockwise
\( \frac{2 \sqrt{3} m v a}{l} \) clockwise
D. None of these


A body of mass \( m_{1} \) moving with an unknown velocity of \( v_{1} \hat{i}, \) undergoes a collinear collision with a body of mass \( m_{2} \) moving with a velocity \( v_{2} \hat{i} \). After
collision, \( m_{1} \) and \( m_{2} \) move with velocities of \( v_{3} \hat{i} \) and \( v_{4} \hat{i}, \) respectively. If
\( m_{2}=0.5 m_{1} \) and \( v_{3}=0.5 v_{1}, \) then \( v_{1} \) is :
A \( \cdot v_{4}-\frac{v_{2}}{4} \)
B. \( v_{4}-\frac{v_{2}}{2} \)
\( \mathbf{c} \cdot v_{4}-v_{2} \)
\( \mathbf{D} \cdot v_{4}+v_{2} \)


Superoxide ion has electrons in anti-bonding molecular
orbitals.


Find the unknown number: \( _{---}+\frac{3}{7}=\frac{3}{7} \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot \frac{3}{7} \)
D.


A rectangular \( A 4 \) size paper is kept on cartesian plane coinciding the points \( (3,0),(-1,0),(0,-2) . \) Find the
perimeter of the paper.
A. 10 Units
B. 16 Units
c. 9 units
D. 12 Units


Axis of a parabola is \( y=x \) and vertex
and focus are at a distance \( \sqrt{2} \) and \( 2 \sqrt{2} \) respectively from the origin. The equation of the parabola is
A \( \cdot(x-y)^{2}=8(x+y-2) \)
B . \( (x+y)^{2}=2(x+y-2) \)
c. \( (x-y)^{2}=4(x+y-2) \)
D. \( (x+y)^{2}=2(x-y+2) \)


The IUPAC name of \( P h C N \) is :
A. Phenyl cyanide
B. Benzonitrile
C. Benzene nitrile
D. All


n given figure, \( D \) is a point on the side \( B C \) of \( \triangle A B C \) such that \( \angle B A C= \)
\( \angle A D C \) prove that
\( \boldsymbol{C A}^{2}=\boldsymbol{C B} \times \boldsymbol{C D} \)


The area of a rhombus, one of whose
diagonals measures \( 8 \mathrm{cm} \) and the side
is \( 5 \mathrm{cm}, \) is
A \( .25 \mathrm{cm}^{2} \)
B. \( 24 \mathrm{cm}^{2} \)
c. \( 24.5 \mathrm{cm}^{2} \)
D. \( 26 \mathrm{cm}^{2} \)


Which of the following terms defines the prefix 'eco'?
A. Ecology
B. Environment
c. Adaptation
D. Exchange


Find equivalent capacitance between
points \( A \) and \( B: \)
Essume each conducting plate is having same dimensions and neglect the thickness of the plate, \( \frac{\varepsilon_{0} A}{d}=7 \mu F \) where A is area of plates
\( \mathbf{A} \cdot 7 \mu F \)
B. \( 11 \mu F \)
\( \mathbf{c} \cdot 12 \mu F \)
D. \( 15 \mu F \)


\( \boldsymbol{x}=\mathbf{1}+\boldsymbol{a}+\boldsymbol{a}^{2}+\ldots \infty, \boldsymbol{y}=\mathbf{1}+\boldsymbol{b}+ \)
\( \boldsymbol{b}^{2}+\ldots \infty \quad \) then \( \quad \mathbf{1}+\boldsymbol{a} \boldsymbol{b}+\boldsymbol{a}^{2} \boldsymbol{b}^{2}+ \)
\( \ldots \infty= \)


The greenhouse gas is:
A. \( C O_{2} \)
в. \( S O_{2} \)
c. \( N_{2} \)
D. \( H_{2} S_{S} \)


Two spheres of copper of diameters 10 \( \mathrm{cm} \) and \( 20 \mathrm{cm} \) will have thermal capacities in the ratio
A \( \cdot \frac{1}{8} \)
B. \( \frac{1}{2} \)
\( c \cdot \frac{1}{4} \)
D.


The main problem caused by the use of
pesticides is
A. Their residues persist in water and other components of the environment.
B. Mosquitoes have become resistant to DDT.
C. They kill silk worm.
D. They deform the gills of some fishes.


No two electric lines of intersect each
other. Why?


Bud is formed in
A . Maple
B. Bread mould
c. Yeast
D. Algae


Four pieces of iron are heated to different temperatures.The colours exhibited by them are respectively red, yellow, orange and white respectively. The one that is heated to the
highest temperature will exhibit the colour:
A. White
B. Yellow
c. Red
D. orange


Number of peroxide bonds in \( K_{3} C r O_{8} \)
is 4
If true enter 1 , else enter 0 .
\( A \)


Total work done on an isolated system is equal to
A. Change in its P.E.
B. Change in its K.E.
c. change in its total mechanical energy
D. Can't say


The order and degree of the differential equation \( \sqrt{\frac{\boldsymbol{d y}}{\boldsymbol{d} \boldsymbol{x}}}-4 \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}-\boldsymbol{7} \boldsymbol{x}=\boldsymbol{0} \) are


Angle between force and momentum
vectors in uniform circular motion is
A . \( 0^{\circ} \)
B. \( 30^{\circ} \)
\( c \cdot 45^{\circ} \)
D. \( 90^{\circ} \)


Which of the following statement about
quantum number is correct?
This question has multiple correct options
\( A . \) If the value of \( l=0, \) the electron distribution is
spherical
B. The shape of orbital is given by subsidiary quantum number
C. The Zeeman's effect is explained by magnetic quantum number
D. The spin quantum number gives the orientations of electron cloud


Solve the following Linear Programming Problems graphically:
Minimise \( Z=-3 x+4 y \)
subject to \( x+2 y \leq 8,3 x+2 y \leq \)
\( \mathbf{1 2}, \boldsymbol{x} \geq \mathbf{0}, \boldsymbol{y} \geq \mathbf{0} \)


\( \ln \Delta A B C, B C=A B \) and \( \angle B=80^{\circ} \)
Then \( \angle A \) is equal to
A . \( 80^{\circ} \)
В . \( 40^{\circ} \)
\( c .50^{\circ} \)
D. \( 100^{\circ} \)


The least number of times a fair coin is
to be tossed in order that the probability of getting atleast one head is at least \( \mathbf{0 . 9 9} \) is
A . 5
B. 6
\( c \cdot 7 \)
\( D \)


A non-zero vector \( \vec{a} \) is parallel to the
line of intersection of plane \( \boldsymbol{p}_{\mathbf{1}} \)
determined by \( \hat{i}+\hat{j} \) and \( \hat{i} \) and plane \( P_{2} \) determined by vectors \( \hat{\mathbf{i}}-\hat{\mathbf{j}} \) and \( \hat{\mathbf{i}}+\hat{\boldsymbol{k}} \)
then angle between a and vector \( \hat{\mathbf{i}}- \) \( 2 \hat{j}+2 \hat{k} \) is
This question has multiple correct options
A \( \cdot \frac{\pi}{4} \)
B. \( \frac{\pi}{2} \)
c. \( \frac{\pi}{3} \)
D. \( \frac{3 \pi}{4} \)


Which of the following substances is
amphoteric?
\( \mathbf{A} \cdot H_{3} O^{+} \)
в. \( H_{2} S O_{4} \)
c. \( H S O_{4}^{-} \)
D. \( S O_{4}^{2-} \)


Assertion
\( a, b, c \) are three unequal positive
numbers.
STATEMENT-1: The product of their sum and the sum of their reciprocals
exceeds 9
Reason
STATEMENT-2: AM of \( n \) positive
numbers exceeds their HM.
A. Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-
B. Statement-1 is True, Statement-2 is True; Statement-2 is Not a correct explanation for Statement-
c. Statement-1 is True, Statement-2 is False
D. Statement-1 is False, Statement-2 is True


Find the value of the following
expressions, when \( x=-1 \)
\( 2 x^{2}-x-2 \)


An atom of an element contains 13
electrons. Its nucleus has 14 neutrons.
Find out its atomic number and
approximate atomic mass. An isotope
has atomic mass 2 units higher. What will be the number of protons, neutrons and electrons in the isotope?


\( \left(3 x^{4}-x^{3}+4\right)^{5 / 2} \) differentiate w.r.t \( x \)


The coulombic force of attraction
between two charges increases with increase in the distance of separation between them.
A. True
B. False


Two locomotives approach each other on the parallel tracks. Each has speed of \( 95 k m / h \) with respect to the ground. If they are initially \( 8.5 k m \) apart, how long will it be before they reach each other? (in hours)
\( \mathbf{A} \cdot 0.045 \)
B. 0.065
c. 0.025
D. 0.078


If the differential equation of a body of mass \( m \) falling from rest subjected to the force of gravity and an air resistance proportional to the square of the velocity is given by \( m v \frac{d v}{d x}=k a^{2}- \) \( k v^{2}, \) then it can be proved that \( \frac{2 k x}{m}= \) \( \log \left(\frac{\boldsymbol{a}^{2}}{\boldsymbol{a}^{2}-\boldsymbol{v}^{2}}\right), \) where \( \boldsymbol{m} \boldsymbol{g}=\boldsymbol{k} \boldsymbol{a}^{2} \)
A. True
B. False


Two wires of the same material and
length have radii in the ratio of 2: 3
Compare their resistance.


Alkalimetals are paramagnetic but their salts are diamagnetic. Why?


The unit of measurement used for
expressing dimension (size) of cells is
A. Centimeter
B. Millimeter
c. Micrometer
D. Meter


In an RLC series circuit shown in figure,
the readings of voltmeters \( V_{1} \) and \( V_{2} \)
are \( 100 \mathrm{V} \) and \( 120 \mathrm{V}, \) respectively. The
same voltage is \( 130 \mathrm{V} \). For this situation, mark out the incorrect statement.
A. Voltage across resistor, inductor and capacitor are 50 \( \vee, 50 \sqrt{3} \mathrm{V} \) and \( 120+50 \sqrt{3} \mathrm{V}, \) respectively
B. Voltage across resistor. inductor and capacitor are 50 V, \( 50 \sqrt{3} \) V and \( 120-50 \sqrt{3} \) V, respectively
c. Power factor of the circuit is \( 5 / 13 \)
D. The circuit is capacitance in nature


The half life of a radioactive isotope is 3 hours.What is the value of its
disintegration constant?
A. 0.3 hour \( ^{-1} \)
B. 0.693 hour \( ^{-1} \)
c. 0.231 hour \( ^{-1} \)
D. \( 0.231 \min ^{-1} \)


The greatest possible number of points of intersection of 9 different straight lines and 9 different circles in a plane
is:
A . 117
B. 153
c. 270
D. none of these


A sphere is released on a smooth
inclined plane from the top. When it
moves down, its angular momentum is
A. conserved about every point
B. conserved about the point of contact only
C. conserved about the centre of the sphere only
D. conserved about any point on a line parallel to the inclined plane and passing through the centre of the ball


In above shown figure, a ball of mass 4 kg slides over frictionless surface and
strikes the post with velocity of \( 1 \mathrm{m} / \mathrm{s} \)
and rebounds toward the north at the
same speed. The change in the magnitude of the eastward component
of the momentum of the disk is:
A. \( -4 k g-m / s \)
в. \( -1 k g-m / s \)
c. \( 0 k g-m / s \)
D. \( 1 k g-m / s \)
E . \( 4 k g-m / s \)


If \( 200 \mathrm{ml} \) solution of \( 0.5 \mathrm{M} \) NaOH is
diluted to \( 800 \mathrm{ml} \) then find molarity of
resultant solution.
A. 0.250 М
в. 0.125 м
c. 0.225 м
D. \( 0.4 \mathrm{M} \)


If the \( (\boldsymbol{m}+\mathbf{1}) \) th \( ,(\boldsymbol{n}+\mathbf{1}) \) th and \( (\boldsymbol{r}+\mathbf{1}) \)
th terms of an A.P are in G.P and \( m, n, r \)
are in H.P, then the ratio of the first
term of the A.P to its common difference
in terms of \( n \) be \( n / k \).Find \( -k ? \)


In convection currents, heat is transferred upwards
A. horizontally
B. diagonally
c. vertically
D. none of these


Bohr's atomic model is based on the
following postulates that:
This question has multiple correct options
A. an atom consists of nucleus
B. an electron can rotate only in certain energy levels
C . an electron remains moving with continuous loss of energy
D. None of the above


When an organic compound containing phosphorous is fused with fusion mixture, it gives:
A. \( N a_{2} H P O_{4} \)
в. \( N a_{2} P O_{4} \)
c. \( \operatorname{NaH}_{2} P O_{4} \)
D. \( N a_{3} P O_{3} \)


Name the part of the neuron, where
information is acquired.
\( A \cdot A \times O n \)
B. Dendrites
c. Synapse
D. Schwann cells


The capacity and the energy stored in a charged parallel plate condenser with air between its plates are respectively \( C 0 \) and \( W 0 . \) If the air is replaced by glass (dielectric constant = 5) between
the plates, the capacity of the plates
and the energy stored in it will
respectively be:


In an ideal transformer, the voltage is stepped down from 11KV to 220V. If the primary current be 20 A the current in
the secondary should be
A. 5 k \( A \)
B. 1 kA
c. \( 0.5 \mathrm{kA} \)
D. 0.1 kA


A cylinder of radius \( R \) is to roll without
slipping between two planks as shown in the figure, Then
This question has multiple correct options
A. angular velocity of the cylinder is \( \frac{v}{R} \) counter clockwise
B. angular velocity of the cylinder is \( \frac{2 v}{R} \) clockwise
c. velocity of centre of mass of the cylinder is v towards left
D. velocity of centre of mass of the cylinder is \( 2 v \) towards right


During night time cool breeze blows from
A. land, sea
B. sea,land
c. mountain,land
D. land,mountain


Solve: \( \int_{0}^{1} \frac{1}{2 x^{2}+x+1} d x \)


Check wheather the equality of the equation in maintained or not, by putting the value of the given variable written next to the equation below. \( \boldsymbol{x}+\mathbf{4}=\mathbf{1 7} \) if \( \boldsymbol{x}=\mathbf{2} \)
A. True
B. False


A system is oscillating with undamped simple harmonic motion.Then the
This question has multiple correct options
A. average total energy per cycle of the motion is its maximum kinetic energy
B. average total energy per cycle of the motion is \( \frac{1}{\sqrt{2}} \)
times its maximum kinetic energy
C root mean square velocity is \( \frac{1}{\sqrt{2}} \) times its maximum
velocity
D. mean velocity is \( \frac{1}{2} \) of maximum velocity


In a nuclear reactor the number of \( U^{235} \)
nuclei undergoing fissions per second
is \( 4 \times 10^{20} . \) If the energy released per
fission is \( 250 M e V \), the total energy
released in 10 hours is
\( \left(1 e V=1.6 \times 10^{-19} J\right) \)
A \( .576 \times 10^{6} J \)
В. \( 576 \times 10^{12} J \)
c. \( 576 \times 10^{15} J \)
D. \( 576 \times 10^{18} J \)


Acid rain is caused due to increase
in concentration of (in atmosphere)
A. \( S O_{2} \) and \( N O_{2} \)
B. \( \operatorname{coand} C O_{2} \)
c. \( \operatorname{coand} S O_{3} \)
\( \mathrm{D} \cdot O_{3} \) and dust


\( f(x)=[x] \) is a greatest integer
function,then it is continuous at?
\( A \cdot R \)
B. z
\( c . \)
D. R-z


Enzyme present on cristae are related
with
A. Anaerobic respiration
B. Aerobic respiration
\( c \cdot c O_{2} \) formation
D. Reduction of pyruvic acid


A skylab of mass \( \mathrm{m} \) kg is first launched from the surface of the earth in a
circular orbit of radius \( 2 \mathrm{R} \) (from the
centre of the earth) and then it is
shifted from this circular orbit to
another circular orbit of radius 3 R. The
minimum energy required to place the
lab in the first orbit and to shift the lab
from first orbit to the second orbit are.
\( \mathbf{A} \cdot \frac{3}{4} m g R, \frac{m g R}{6} \)
В. \( \frac{3}{4} m g R, \frac{m g R}{12} \)
c. \( \mathrm{mgR}, \mathrm{mgR} \)
\( \mathbf{D} \cdot 2 m g R, \) mgR


What is wavefront? Describe Huygen's
theory of secondary wavelets.


Length of the chord joining the points
\( P(\alpha) \) and \( Q(\beta) \) on the circle \( x^{2}+y^{2}= \)
\( a^{2} \) is
A \( \cdot \cos \left(\frac{\alpha-\beta}{2}\right) \)
в. \( 2 a \sin \left(\frac{\alpha-\beta}{2}\right) \)
c. \( 2 a \tan \left(\frac{\alpha-\beta}{2}\right) \)
D. \( 2 a \csc \left(\frac{\alpha-\beta}{2}\right) \)


The co-ordinates of a particle restricted to move in a plane is given by \( \boldsymbol{X}=\boldsymbol{6} \cos \pi \boldsymbol{t} \)
\( \boldsymbol{y}=1-4 \cos 2 \pi t \)
The magnitude of acceleration of particle at \( t=1.5 s \) is (where \( x \) and \( y \)
are in meter and \( t \) is in seconds)
A. Zero
В. \( 6 \pi^{2} m / s^{2} \)
c. \( 16 \pi^{2} \mathrm{m} / \mathrm{s}^{2} \)
D. \( 8 \pi^{2} m / s^{2} \)


If \( \sin x-\cos y=\sin \frac{\pi}{7} \) and \( \cos x+ \)
\( \sin y=\cos \frac{\pi}{7} \) then find the value of
\( \sin (x-y) \)


Curie temperature is the temperature
above which
A. a ferromagnetic material becomes paramagnetic
B. a paramagnetic material becomes diamagnetic
C . a ferromagnetic material becomes diamagnetic
D. a paramagnetic material becomes ferromagnetic.


Between two numbers whose sum is \( \frac{13}{6} \) an even number of A.M.s is inserted,
the sum of these means exceeds their
number by unity. Find the number of
means.


In the formula \( X=3 Y Z^{2}, X \) and \( Z \) have
dimensions of capacitance and magnetic induction respectively. The dimensions of Y in MKSQ system are
A. -2 in mass, -2 in length, 4 in time and 5 in charge.
B. - 3 in mass, - 2 in length, 4 in time and 4 in charge.
c. -4 in mass, -5 in length, 4 in time and 4 in charge.
D. -3 in mass, -2 in length, 8 in time and 7 in charge.


\( A \) and \( B \) are two steel wires and the
radius of \( A \) is twice that of \( B \), if they are stretched by the same load, then the stress on B is
A. Four times that of A.
B. Two times that of A
c. Three times that of \( A \)
D. Same as that A.


Show how you would connect 3 resistors
each of resistance 6 ohm, so that the
combination has a resistance of (i) 9
ohm
(ii) 4 ohm


Factorise and then divide the given
algebraic expressions.
1. \( \left(12 r^{2}+8 r^{2}-4 r^{2}\right) b y\left(-4 r^{2}\right) \)
2. \( \left(\frac{4}{9} x^{2}-49 z^{2}\right) b y(2 x+21 z) \)
\( 3 \cdot\left(5 a^{2} b^{2}+15 a^{2} b^{2}-20 a^{4} b\right) b y 25 a b^{2} \)
4. \( \left(49 a^{2}-56 a\right) b y(21 a-24) \)


Find out which one is not related to
leaves?
A. Photosynthesis
B. Respiration
c. Transpiration
D. Transportation


Let \( \mathbf{x}=\mathbf{3}^{\mathbf{n}} . \) The index 'n' is given a
positive integral value at random. The
probability that the value of 'x' will have
3 in the units place is
A . \( 1 / 4 \)
B. \( 1 / 2 \)
c. \( 1 / 3 \)
D. \( 1 / 5 \)


Complete the following table


if \( f^{\prime}(x)<0 \forall x \in R \) and \( g(x)=f\left(x^{2}-\right. \)
2) \( +\boldsymbol{f}\left(\boldsymbol{6}-\boldsymbol{x}^{2}\right) \) then
\( A \cdot g(x) \) is an increasing in \( [2, \infty) \)
B. \( g(x) \) is an increasing in [-2,0]
c. \( g(x) \) has a local minima \( a t x=-2 \)
D. \( g(x) \) has a local maxima at \( x=2 \)


\( \boldsymbol{H}_{2} \boldsymbol{O}_{(l)} \rightleftharpoons \boldsymbol{H}_{2} \boldsymbol{O}_{(g)} \)
What type of change is represented by
the equation above?
A. This is a physical change because the equation is balanced
B. This is chemical change because the equation is balanced
c. This a physical change because the same compound is represented as both the reactant and product.
D. This a chemical change because the same compound is represented as both the reactant and product


What is meant by the Semicarbazone? Give an example of reaction(with mechanism) showing its formation.


Figure shows the position time graph of
a particle moving on the \( x \) -axis.
A. The particle is continuously going in positive \( x \) direction
B. Area under x - t curve shows the displacement of particle
C. The velocity increases up to a time \( t_{0} \), and then becomes constant
D. The particle moves at a constant velocity up to a time
\( t_{0}, \) and then stops


The place value of 7 in 17.5 is
A. tens
B. units
c. one-tenth
D. one-hundredths


Three solid cubes of sides \( 1 \mathrm{cm}, 6 \mathrm{cm} \) and \( 8 \mathrm{cm} \) respectively are melted to form a new cube. Find the surface area
of the cube so formed.
A. 520 sq. \( \mathrm{cm} \)
B. 486 sq. \( \mathrm{cm} \)
c. 289 sq. \( \mathrm{cm} \)
D. 300 sq. \( \mathrm{cm} \)


If the extremities of a diagonal of a square are (1,-2,3) and (2,-3,5) then the length of its side is:
A \( \cdot \sqrt{6} \)
B. \( \sqrt{3} \)
c. \( \sqrt{5} \)
D. \( \sqrt{7} \)


toppr
Q туре your question
currents is \( \frac{7}{4}, \) then what is the ratio of
their drift velocities?
(1)
(2)
(3)


Which part shows the presence of
Iymph node?
\( A \)
B. G
\( c . \)
D All of the above


Based on VSEPR theory predict the
geometry and shape of :
a) \( C l F_{3} \)
b) \( \boldsymbol{N} \boldsymbol{H}_{4}^{+} \)
Draw the figure also.


Which one of the following is not a synthetic auxin?
\( A \cdot 2,4-D \)
B. IBA
\( c \cdot \) IPA
D. IAA


A uniform bar of mass \( m \) is supported
by a pivot at its top about which the bar
can swing like a pendulum. If a force \( \boldsymbol{F} \) is applied perpendicular to the lower end of the bar as shown in figure, what is the value of \( F \) in order to hold the bar
in equilibrium at an angle \( (\theta) \) from the vertical
\( \mathbf{A} \cdot 2 m g \sin \theta \)
в. \( m g \sin \theta \)
\( c . m g \cos \theta \)
\( D \)


Assertion: A capacitor blocks direct current in the steady state.

Reason : The capacitive reactance of the capacitor is inversely proportional to frequency f of the source of emf
A. If both Assertion and Reason are true and the Reason is the correct explanation of the Assertion.
B. If both Assertion and Reason are true but the Reason is not the correct explanation of the Assertion.
c. If Assertion is true statement but Reason is false
D. If both Assertion and Reason are false statements


Two blocks \( A \) and \( B \), each of mass \( m \), are
connected by a massless spring of natural length L and spring constant k. The blocks are initially resting on a smooth horizontal floor with the spring
at its natural length as shown in Fig. A
third identical block \( C \), also of mass \( m \)
moves on the floor with a speed \( \mathbf{v} \) along the line joining \( A \) and \( B \) and collides with \( A, \) then
This question has multiple correct options
A. The KE of the AB system at maximum compression of the spring is zero.
B. The KE of the AB system at maximum compression of the spring is \( (1 / 4) m v^{2} \)
c. The maximum compression of the spring is \( v \sqrt{\frac{m}{k}} \)
D. The maximum compression of the spring is \( v \sqrt{\frac{m}{2 k}} \)


A sample of a radioactive element has a mass of \( 10 g \) at an instant \( t=0 . \) The
approximate mass of this element in
the sample after two mean lives is
A. \( 1.35 g \)
в. \( 2.50 g \)
c. \( 3.70 g \)
D. \( 6.30 g \)


The electric field at a distance \( \frac{3 R}{2} \) from
the centre of a charged conducting spherical shell of radius \( \mathrm{R} \) is \( \mathrm{E} \). The electric field at a distance \( \frac{\boldsymbol{R}}{\mathbf{2}} \) from the centre of the sphere is :
A. zero
B. E
c. \( \frac{E}{2} \)
D. \( \frac{E}{3} \)


Which of the following oxide has the maximum basicity?
A. \( \operatorname{Pr}_{2} \) O \( _{3} \)
в. \( L a_{2} O_{3} \)
\( \mathrm{c} \cdot \mathrm{Sm}_{2} \mathrm{O}_{3} \)
D. \( G d_{2} O_{3} \)


Let \( \boldsymbol{A}=\{\mathbf{1}, \mathbf{3}, \mathbf{3}, \mathbf{1}\} \) and \( \boldsymbol{B}=\{\mathbf{1}, \boldsymbol{4}\} \)
then:
\( \mathbf{A} \cdot A \neq B \)
в. \( A=B \)
\( c \cdot A \subset B \)
D. \( B \subset A \)


\( s p^{2} \) hybrid orbitals have equal \( s \) and \( p \)
characters.

State whether the statement is True or
False


The solubility of \( A g I \) in \( N a I \) solution is less than that in pure water because:
A. \( A g I \) forms complex with \( N a I \)
B. of common ion effect
c. solubility product of \( A g I \) is less
D. the temperature of the solution decreases


How many d-orbitals are involved in hybridization of \( C r O_{4}^{2-} ? \)
\( A \cdot 3 \)
B. 2
\( c \cdot 4 \)
D.


Assertion
Chlorine gas turns moist potassium bromide paper red.
Reason
Chlorine gas acts as an oxidising agent.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


A square of side \( a \) lies above the \( x \) -axis
and has one vertex at the origin. The side passing through it makes an angle \( \left(0<\alpha<\frac{\pi}{4}\right) \) with the positive direction of \( x \) -axis. The equation of its diagonal not through the origin
A \( \cdot y(\cos \alpha-\sin \alpha)-x(\sin \alpha-\cos \alpha)=a \)
B \cdot \( y(\cos \alpha+\sin \alpha)+x(\sin \alpha-\cos \alpha)=a \)
c. \( y(\cos \alpha+\sin \alpha)+x(\sin \alpha+\cos \alpha)=a \)
D・ \( y(\cos \alpha+\sin \alpha)+x(\cos \alpha-\sin \alpha)=a \)


Ammonia is used in detection of \( C u^{2+} \)
ion because:
A. aqueous solution of \( N H_{3} \) reacts with \( C u^{2+} \) ion to form deep blue coloured complex
B. \( N H_{3} \) reacts with \( C u^{2+} \) ion to give blue precipitate of \( C u O \)
C . aqueous solution of \( N H_{3} \) reacts with \( C u^{2+} \) ion to form white coloured complex.
D. \( N H_{3} \) reacts with \( C u^{2+} \) ion to give green precipitate.


Fill in the blanks:
Hydrogen reacts with metal oxides to form .............. and


: The area bounded by \( x=2 \cos \theta, y= \)
\( 3 \sin \theta \) is \( 36 \pi \) sq. units.
II: The area bounded by \( x=2 \cos \theta, y= \)
\( 2 \sin \theta \) is \( 4 \pi \) sq.units.
Which of the above statement is
correct?
A. Onlyı
B. Only II
c. Both I and II
D. Neither I nor II.


If \( A=\left[\begin{array}{ccc}1 & 2 & 3 \\ 2 & 3 & 4 \\ 0 & 5 & 6\end{array}\right], \) then \( 2 A= \)
A. \( \left[\begin{array}{lll}2 & 4 & 6 \\ 2 & 3 & 4 \\ 0 & 5 & 6\end{array}\right] \)
в. \( \left[\begin{array}{lll}1 & 2 & 3 \\ 4 & 6 & 8 \\ 0 & 5 & 6\end{array}\right] \)
с. \( \left[\begin{array}{lll}1 & 2 & 3 \\ 2 & 3 & 4 \\ 0 & 10 & 12\end{array}\right] \)
D. \( \left[\begin{array}{lll}2 & 4 & 6 \\ 4 & 6 & 8 \\ 0 & 10 & 12\end{array}\right] \)


Assertion
Force experienced by moving charge
will be maximum if direction of velocity of charge is parallel to applied magnetic field.
Reason
Force on moving charge is independent of direction of applied magnetic field.
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


Bull frog of India is
A. Rana tigrina
B. R. sylvatica
c. R. ecutesbeiana
D. R. esculenta


In the given figure, \( A B=D C \) and
\( B D=C A . \) Prove that \( \Delta A B C \cong D C B \)


Assertion
A proton and an alpha particle having the same kinetic energy are moving in circular paths in a uniform magnetic field. The radii of their circular paths will be equal
Reason Any two charged particles having equal kinetic energies and entering a region of uniform magnetic field \( \vec{B} \) in a direction perpendicular to \( \vec{B}, \) will describe circular trajectories of equal radii.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The gas which helps to keep swimming pool clean is:
A. chlorine
B. oxygen
c. argon
D. helium


Displacement time equation of a
particle SHM is \( \boldsymbol{x}= \) \( \mathbf{1 0} \sin \left(\frac{\boldsymbol{\pi}}{\mathbf{3}} \boldsymbol{t}+\frac{\boldsymbol{\pi}}{\mathbf{6}}\right) \boldsymbol{c m} . \) The distance
covered by particle in \( 3 s \) is
A . \( 5 \mathrm{cm} \)
B. \( 20 \mathrm{cm} \)
c. \( 10 \mathrm{cm} \)
D. \( 15 \mathrm{cm} \)


Fill in the blank:
The plane, in which the Earth revolves around the Sun, is called
plane of Sun.
A . equatorial
B. tangential
c. normal
D. orbital


In a first order reaction, \( 1010 \% \) is
complete Calculate:The half life of the
reaction:


Human male sex hormone or androgen
present in urine of males is
A. Testosterone
B. Andostenedione
c. Dehydroepiandrosterone
D. Androsterone


Find the principal argument of the complex number \( \sin \frac{6 \pi}{5}+i(1+ \)
\( \left.\cos \frac{6 \pi}{5}\right) \)


In the figure, \( A C=9, B C=3 \) and \( D \) is
3 times as far from \( A \) as from \( B \). What
is \( B D ? \)
A. 6
B. 9
c. 12
D. 15
E. 18


¡) ff force\( = \)mass\( \times \)acceleration
then momentum \( = \)
ii) If liquid hydrogen is for rocket, then is for MRI


State three factors which determine the quantity of heat absorbed by a body.


State whether true or false.
The quantity of matter in a body is called its mass.
A. True
B. False


Consider a hypothetical hydrogen like
atom. The wavelength in \( A^{\circ} \) for the
spectral lines for transition from \( \boldsymbol{n}=\boldsymbol{p} \)
to \( n=1 \) are given by:
\( \lambda=\frac{1500 p^{2}}{p^{2}-1}, \) where \( p>1 \)
Find the ionization potential of this element?
A. 16.56 ev
B. 8.28 ev
c. 4.14 ev
D. 22.4 ev


\( A, B \) and \( C \) are three charged bodies. If \( A \)
and B repel each other and A attracts C, what is the nature of the force between
B and C?


In Sarracenia, the insect traping structure
is modified
A . Leaf
B. Leaf base
c. stipule
D. Axillary shoot


f \( f(x)=\sin (\log x), \) then show that
\( f(x y)+f\left(\frac{x}{y}\right)-2 f(x) \cos (\log y)= \)
\( \mathbf{n} \)


Calculate formal charge of atoms \( \boldsymbol{H} \boldsymbol{C l} \boldsymbol{O}_{4}, \boldsymbol{C O}_{3}^{2} \)


If \( \tan ^{4} \theta+\cot ^{4} \theta=A, \) then
A \( . A>2 \)
в. \( A \geq 2 \)
c. \( A>4 \)
D. \( A \geq 4 \)


When a sound wave is reflected from a
rigid wall, the phase difference between the reflected and incident wave
A. 0
в. \( \pi \)
c. \( \pi / 2 \)
D. \( \pi / 4 \)


Assertion
f some ferromagnetic substance is filled inside a soleniod, its coeffecient of
self-induction \( L \) will increase.
Reason
By increasing the current in a coil its coefficient of self induction \( L \) can be
increased.
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


\( \operatorname{ls}\left(K_{2} S O_{4} \cdot C r_{2}(S O)_{4}\right)_{3} \cdot 24 H_{2} O \)
correct formula of chrome alum?
If yes enter 1 , else enter 0


Which of the following can't increase
the voltage produced by the generator?
A. Using a powerful electromagnet to make the magnetic field stronger in place of a permanent magnet.
B. By winding the coil round a soft iron core to increase the strength of magnetic field.
C. By using a coil with more turns.
D. Changing the material of the coil.


In the network shown, resistance
between terminals a and b is X. Then
This question has multiple correct options
A. \( X-8=4 \)
B. \( X-8=0 \)
\( \mathbf{c} \cdot X+8=16 \)
D. \( X+8=20 \)


Give reason oxygen is a gas but sulphur is a solid?


\( A B C D \) is a rectangle \( A C \) is diagonal
Find the angles of \( \triangle A C D . \) Give reasons


If \( 100 \mathrm{J} \) of heat is needed to completely
change the substance from a solid to a
liquid state, what is the heat of fusion
for the substance?
A \( \cdot 1,000 \mathrm{J} / \mathrm{kg} \)
B. \( 100 \mathrm{J} / \mathrm{kg} \)
\( c \cdot 50 J / k g \)
D. 20 J/kg
E. 5 J/kg


How watt is related to the fundamental
units?
A \( \cdot \mathrm{kg} \mathrm{m}^{2} s^{-3} \)
B. \( \mathrm{kg} \mathrm{m}^{2} s^{-2} \)
\( \mathrm{c} \cdot \mathrm{Nm} s^{-1} \)
D. Nm


In an equilateral triangle of side \( 3 \sqrt{3} \) find the length of the altitude.


If \( y=\log (\log x)+2 \sin x, \) find \( \frac{d y}{d x} \)


is the crystalline allotrope of carbon
A. coal
B. Coke
c. Diamond
D. Graphite


What is the angle of incidence when the incident ray is normal to the interface or boundary separating two media?
A \( \cdot 0^{\circ} \)
B. \( 90^{\circ} \)
\( c \cdot 180^{\circ} \)
D. \( 45^{\circ} \)


Prove that the following are irrational \( \sqrt{3}+\sqrt{5} \)


D-Ribose forms a five-membered ring.
A. True
B. False


Mass of the earth has been determined
through
A \( \cdot \) use of Kepler's \( \frac{T^{2}}{R^{3}} \) constancy law
B. sampling the density of earth's crust and using earth's radius.
C. Cavendish's determination of G and using earth's radius and \( g \) at its surface.
D. use of periods of satellites at different heights above earth's surface.


is a method of writing
numbers as the product of their factors or divisors.
A. Polynomial
B. Factorisation
c. Division algorithm
D. Quadratic equation


A regular polygon with 4 sides has area:
\( \mathbf{A} \cdot \) length \( \times \) breadth
B. (side) \( ^{2} \)
C. \( \frac{\sqrt{3}}{4}(\text { side })^{2} \)
D \( \cdot \frac{1}{2}(\text { sum of two parallel sides }) \)


In earthworm, haemoglobin is present
in


The transport of nutrients is brought
about by part labelled as
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
0.5
\( E \cdot 6 \)


The mean of \( x_{1}, x_{2} \dots x_{50} \) is \( M, \) if every
\( \boldsymbol{x}_{i},=1,2 \ldots 50 \) is replaced by \( \boldsymbol{x}_{i} / \mathbf{5 0} \) then
the mean is
A.
в. \( _{M+\frac{1}{50}} \)
c. \( \frac{50}{M} \)
D. \( \frac{M}{50} \)


Trimethylamine oxide and trimethyl phosphine oxide can be represented as
\( \left(\boldsymbol{C H}_{3}\right)_{3}^{+} \boldsymbol{N}-\boldsymbol{O}^{-} \quad\left(\boldsymbol{C H}_{3}\right)_{3} \dot{\boldsymbol{P}}-\boldsymbol{O}^{-} \)
(1)
(11)
Select the correct structure
\( \mathbf{A} \cdot\left(C H_{3}\right)_{3} N=O \)
B \( \cdot\left(C H_{3}\right)_{3} P=O \)
c. Both (A) and (B)
D. None of these


The reaction, \( A \stackrel{k}{\longrightarrow} \) Product, is zero order while the reaction, \( \boldsymbol{B} \stackrel{\boldsymbol{k}}{\longrightarrow} \)
Product, is first order reaction. For what
initial concentration of \( A \) are the half
lives of the two reactions equal?
\( \mathbf{A} \cdot(\ln 4) M \)
в. 2 М
c. \( (2 \log 2) M \)
D. \( (\ln 2) M \)


While dusting a carpet, we give a
sudden jerk or beat with a stick
because:
A. Inertia of rest keeps the dust in its position and the dust is removed by movement of carpet away.
B. Inertia of motion removes dust.
C. No inertia involved in process.
D. None of the above


In a circle of radius \( 13 \mathrm{cm}, P Q \) and \( R S \)
are two parallel chords of length \( 24 \mathrm{cm} \) and IOcm respectively. The chords are on the opposite sides of the centre. The distance between the chords
is?
A. \( 7 \mathrm{cm} \)
B. \( 17 \mathrm{cm} \)
\( c \cdot 26 c m \)
D. \( 12 \mathrm{cm} \)


If \( A \) is non-singular and \( (A-2 I)(A- \) \( 4 I)=0 \) then \( \frac{1}{6} \mathbf{A}+\frac{4}{3} \mathbf{A}^{-1}= \)
\( A \cdot I \)
B.
c. \( 2 I \)
D. \( 6 I \)


Which of the following is not a part of
nephron?
A . PCT
в. DCT
c. Loop of Henlen
D. collecting duct


Maxwell's equation describe the fundamental laws of
A. electricity
B. magnetism
c. mechanics
\( D . \) both \( (A) \) and \( (B) \)


A charge of \( 10 \mu C \) is placed at the origin of \( (x-y) \) coordinate system. The potential difference between two points \( (0, a) \) and
\( (a, 0) \) in volts is
\( \mathbf{A} \cdot 9 \times 10^{4} / a \)
B . \( 9 \times 10^{4} / a \sqrt{2} \)
c. \( 9 \times 10^{4} 2 a \)
D.


Calculate the momentum of a particle which has a de Broglie wavelength of
\( 2.5 \times 10^{-10} m \)
\( \left(h=6.6 \times 10^{-34} k g m^{2} s^{-1}\right) \)


The most stable form of phosphorus is:
A. white \( P \)
B. red \( P \)
c. black \( P \)
D. scarlet \( P \)


The total number of solutions of
\( \cos x=\sqrt{1-\sin 2 x} \) in \( [0,2 \pi] \) is equal
to
A . 2
B. 3
c. 5
D. None of these


Find the sum of the following A.P
\( 2,7,12, \dots . . \) to 10 terms


Flora and fauna in lake or pond is
A . Lentic biota
B. Lotic biota
c. Abiotic biota
D. Field layer


An uncharged capacitor of capacitance \( 4 \mu F, \) a battery of emf 12 volt and a resistor of \( 2.5 ~ M \Omega \) are connected
in series. The time after which \( v_{c} \) ?
\( 3 v_{R}=0.693 \)
A. 6.93 sec
B. \( 13.86 \mathrm{sec} \)
c. \( 20.52 \mathrm{sec} \)
D. none of these


Sclerenchyma cells have thickening of
A. Cellulose
B. Lignin
c. silica
D. Cellulose, silica


Internal forces are always balanced
State whether true or false.
A. True
B. False


Match the isomers given in column
with their names given in column II and
mark the appropriate choice.
(A) - (iii)
\( A \)
, (B) \( -(i),(C)-(i v),(D)- \) (ii)
B. (A) - (iv), (B) - (iii), (C) - (ii), (D) - (i)
\( c \)
(A) \( -(i),(B)-(i i),(C)-(i i i),(D)-(i v) \)
\( D \)
(A) - (ii)
(B) \( - \) (iii) \( (C)-(i v) \) (D) \( (i \)


Conversation of a] sulphur b] iron pyrites to sulphur dioxide in the first
step of the Contact process is
\( \boldsymbol{S}+\boldsymbol{O}_{2} \rightarrow \boldsymbol{S} \boldsymbol{O}_{2} \)
\( \boldsymbol{F} \boldsymbol{e} \boldsymbol{S}_{2}+\boldsymbol{x} \boldsymbol{F} \boldsymbol{e}^{3+}+\boldsymbol{8} \boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \mathbf{1 5} \boldsymbol{F} \boldsymbol{e}^{2+}+ \)
\( \boldsymbol{y} \boldsymbol{S} \boldsymbol{O}_{4}^{2-}+\mathbf{1 6} \boldsymbol{H}^{+} \)
find then value of \( x \) and \( y: \)
A . \( x=15, y=1 \)
в. \( x=14, y=2 \)
c. \( x=7, y=2 \)
D. \( x=14, y=1 \)


If \( \boldsymbol{y}=\log [\log (\log \boldsymbol{x})], \) then value of \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \)
is.
A \( \cdot \frac{1}{x \log x} \)
в. \( \frac{1}{x \log x \log (\log x)} \)
c. \( \frac{1}{x \log (\log x)} \)
D.


For a metal \& a non-metal with
particular emphasis on valency:
A. Both have covalency
B. Both have electrovalency
C. Non-metal exhibit covalency but metals do not
D. Both B and C


Q Type your question
rate of formation of \( Y \) against time \( t \) will
be
\( A \)
B.
\( c \)
\( D \)


Major product of following reaction:
\( \boldsymbol{C H}_{3} \)
\( \boldsymbol{C H}_{3} \dot{\boldsymbol{C}}-\boldsymbol{C H}-\boldsymbol{C H}_{3} \frac{\boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{O}^{-}}{\mid} \)
\( \boldsymbol{C H}_{3} \quad \boldsymbol{C l} \)
\( ^{\text {A. }} C H_{3}-\stackrel{C H_{3}}{C}-C_{\mid}^{\perp}-C_{3}-C H_{3} \)
B. \( \quad C H_{3}-\stackrel{C H_{3}}{_{I}}-C H=C H_{2} \)
C.
\[
C H_{3}-C=C_{1}^{H_{3}}
\]
\( _{C H_{3}}-C H_{3} \)


The number and type of bonds between two carbon atoms in calcium carbide
are :
A. one sigma, one pi
B. one sigma, two pi
c. two sigma, one pi
D. two sigma, two pi


Two balls of equal mass are projected upwards simultaneously, one from the ground with initial velocity \( 50 m s^{-1} \)
and the other from a 40 m tower with
initial velocity of \( 30 m s^{-1} \). The
maximum height attained by their centre of mass will be:
\( A .80 m \)
B. \( 60 m \)
c. \( 100 m \)
D. \( 120 m \)


Show that \( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}\left(\tan \boldsymbol{h}^{-1} \boldsymbol{x}\right)=\frac{\mathbf{1}}{\mathbf{1 - x}^{\mathbf{2}}} \)


If true enter 1 , if false enter 0 .
The formula of heavy water is \( \boldsymbol{H}_{3} \boldsymbol{O}^{+} \)
A .


The motion of a planet around sun in an
elliptical orbit is shown in the following
figure. Sun is situated on one focus. The
shaded areas are equal. If the planet
takes time \( t_{1} \) and \( t_{2} \) in moving from \( A \) to
B and from \( C \) to D respectively then
\( \mathbf{A} \cdot t_{1}>t_{2} \)
B . \( t_{1}<t_{2} \)
c. \( t_{1}=t_{2} \)
D. information incomplete


Which of the following is called a Wilkinson's catalyst?
\( \mathbf{A} \cdot\left[\left(P h_{3} P\right)_{3} R h C l\right] \)
в. \( \operatorname{TiCl}_{4}+\left(C_{2} \mathrm{H}_{5}\right)_{3} \) Аl
\( \mathbf{c} \cdot\left(C_{2} H_{5}\right)_{4} P b \)
D \( \cdot\left[P t C l_{2}\left(N H_{3}\right)_{2}\right] \)


Assertion
NAND or NOR gates are called digital
building blocks.
Reason
The repeated use of NAND (or NOR) gates can produce all the basis or complicated gates.
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


When a body moves in a circular path,
no work is done by the force since:
A. force and displacement are perpendicular to each other.
B. the force is always away from the centre.
C. there is no displacement.
D. there is no net force.


According to IARC and EPA, which of the following PAHs are probable human carcinogens?
A. Benzoapyrene
B. Benzaanthracene
c. Anthracene
D. both A and B


A resistance of \( 20 \Omega \) is connected to a
source of alternating current rated \( 110 V, 50 H z \) Find the \( r m s \) current


Select the correct statement from the
following.
A. Equilibrium constant changes with addition of a catalyst
B. Catalyst increases the rate of forward reaction only.
C. The ratio of mixture at equilibrium does not change by catalyst
D. catalysts are active only in solution.


Find the area bounded by the curve \( y= \) \( \sin x, 0 \leq x \leq \pi \) and line \( y=\frac{1}{\sqrt{2}} \)


A current \( I_{1} \) carrying wire \( A B \) is placed
near another long wire CD carrying
current \( I_{2} \). If wire \( A B \) is free to moves, it
will have:
A. rotational motion only
B. translational motion only
c. rotational as well as translational motion
D. neither rotational nor translational motion


If a matrix has equal number of
columns and rows then it is said to be a
A. row matrix
B. identical matrix
c. square matrix
D. rectangular matrix


When a certain force is applied on a
string it extends by \( 0.01 \mathrm{cm} . \) When the same force is applied on another string of same material, twice the length and double the diameter, then the extension
in second string is
\( A \cdot 0.005 \mathrm{cm} \)
B. 0.02 cm
c. \( 0.08 \mathrm{cm} \)
D. \( 0.04 \mathrm{cm} \)


The endocrine gland present on the kidney is
A. Pituitary gland
B. Thyroid gland
c. Adrenal gland
D. Pancreatic glands


Give the electronic configurations of the following:
a. \( H^{-} \) b. \( \mathrm{He}^{+} \) c.F \( ^{-} \) d. \( \mathrm{N}^{2+} \)
t


Four charges are placed at the
circumference of dial clock as shown in
figure. If the clock has only hour hand,
then the resultant force on a positive
charge \( q_{0} \) placed at the centre, points in
the direction which show the time as:
\( \mathbf{A} \cdot 1: 30 \)
B. 7: 30
\( c \cdot 4: 30 \)
D. 10: 30


Which of the following statements is/are true?
(a) One ATP molecule yields \( 30-32 \) kJ of
energy.
(b) Pentose phosphate pathway was discovered by Dickens.
(c) When tripalmitin is used as a substance, the R.Q is 0.9
(d) Energy released by one molecule of glucose on complete oxidation corresponds to about \( 1292 \mathrm{kJ} \)
\( A \). a and b only
B. c and donly
c. a and donly
D. a, c and donly
E. conly


Assertion
Equilibrium constant for the reverse
reaction is the inverse of the
equilibrium constant for the reaction in
the forward direction.
Reason
Equilibrium constant depends upon the way in which the reaction is written.
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


At what temperature will the linear kinetic energy of a gas molecule be
equal to that of an electron accelerated through a potential difference of \( 10 \mathrm{V} ? \)
\( A \cdot \) 273 \( k \)
В . \( 19 \times 10^{3} K \)
c. \( 38.65 \times 10^{3} \)
D. \( 11.3 \times 10^{3} K \)


A person sitting in a chair in a satellite
feels weightless because
A. the earth does not attract the object in a satellite.
B. the normal force by the chair on the parson balance the earht's attraction.
C. the normal force is zero.
D. the person is satellite is not accelerated.


Cloud chamber technique is
experimentally used for.
A. Measurement of specific charge
B. Measurement of electronic charge
C. Measurement of electronic mass
D. Studying the interaction of charges in cloud


\( \operatorname{Let} \boldsymbol{A}=\left[\begin{array}{ll}\boldsymbol{a} & \boldsymbol{b} \\ \boldsymbol{c} & \boldsymbol{d}\end{array}\right] \) and \( \boldsymbol{f}(\boldsymbol{\lambda})=\operatorname{det}(\boldsymbol{A}- \)
\( \boldsymbol{\lambda} \boldsymbol{I}), \) then
This question has multiple correct options
A \( \cdot f(\lambda)=\lambda^{2}-(a+d) \lambda+a d-b c \)
в. \( f(A)=O \)
c. \( A^{2}=O \) implies \( A^{r}=O \forall r \geq 2 \)
D. none of these


An ideal fluid flown through a pipe of circular cross-section made of two
sections with diameters 25 an and 3.75
\( \mathrm{cm} . \) The ratio of the velocities in the two
pipes is
A .9: 4
B. 3:2
c. \( \sqrt{3}: \sqrt{2} \)
D. \( \sqrt{2}: \sqrt{3} \)


Find the equation of the line passing
through the point (2,3) and perpendicular to the straight line \( 4 x- \)
\( \mathbf{3} \boldsymbol{y}=\mathbf{1 0} \)
A. \( 3 x+4 y=18 \)
в. \( 3 x-4 y=18 \)
c. \( 3 x+4 y=-18 \)
D. \( 4 x-3 y=-18 \)


A force is given by \( \boldsymbol{F}=\boldsymbol{a} \boldsymbol{t}+\boldsymbol{b} \boldsymbol{t}^{2}, \) where \( \boldsymbol{t} \)
is time, the dimensions of \( a \) and \( b \) are
respectively:
\( \mathbf{A} \cdot\left[M L T^{-4}\right] \) and \( \left[M L T^{-1}\right] \)
B - \( \left[M L T^{-1}\right] \) and \( \left[M L T^{0}\right] \)
\( \mathbf{c} \cdot\left[M L T^{-3}\right] \) and \( \left[M L T^{-4}\right] \)
D \cdot \( \left[M L T^{-3}\right] \) and \( \left[M L T^{0}\right] \)


Isomers of propanoic acid are:
\( \mathbf{A} \cdot H C O O C_{2} H_{5} \) and \( C H_{3} C O O C H_{3} \)
B. \( H-C O O C_{2} H_{5} \) and \( C_{3} H_{7} C O O H \)
\( \mathbf{c} \cdot C H_{3} C O O C H_{3} \) and \( C_{3} H_{7} O H \)
D. \( C_{3} H_{7} O H \) and \( C H_{3} C O C H_{3} \)


The maximum current which can flow
through a fuse without melting it is called its
A. potential
B. power
c. rating
D. capacity


Heart pumps only impure blood in case of
A. Sharks
B. Whale
c. Lizard
D. Frog


What are Darwin's finches?


Which of the following on reaction with chloroform will give chloretone?
A. \( H N O_{3} \)
в. \( \left(C H_{3}\right)_{2} C=O \)
c. chloral
D \( \cdot\left(C H_{3}\right)_{2} C H C H O \)


Few organisms can breathe without air Justify


Write the uses of dihydrogen gas:


f \( A(1,2,1), B(2,6,2) \) and \( C(\lambda, 14,4) \)
are collinear, then value of \( \lambda \) is


Ascending limb of Henle's loop is to water whereas, the descending limb
is \( \ldots \ldots . . . . . . . \) to it.


In insulators, the valence bands are
completely and the large band gap prevents the promotion of electrons to empty space whereas in semiconductor
band gap is low.
A . false
B. true
c. band gap is high
D. none of these


Which of the following is not an example of perfectly inelastic collision?
A. A bullet fired into a block, if bullet gets embedded into block
B. Capture of an electron by an atom
c. A man jumping onto a moving boat
D. A ball bearing striking another ball bearing


Which of the following compound is ionic?
A. \( N a C l \)
в. \( C C l_{4} \)
c. \( C H_{4} \)
D. All the above


Car \( X \) of mass 200 kg moving at \( 5 \mathrm{m} / \mathrm{s} \) collides with car Y of mass \( 300 \mathrm{kg} \) moving in the same direction at \( 3 \mathrm{m} / \mathrm{s} \) After the collision they move off together. What is their common velocity just after the collision?
A. \( 4.2 \mathrm{m} / \mathrm{s} \)
B. \( 5.6 \mathrm{m} / \mathrm{s} \)
\( c \cdot 3.8 m / s \)
D. \( 7.8 \mathrm{m} / \mathrm{s} \)


\( Y(x, t)=\frac{0.05}{\left[(4 x+2 t)^{2}+5\right]} \) represents a
moving wave pulse, where \( x \) and \( y \) are
in meters and \( t \) is in seconds. Then
which statement(s) are correct:
This question has multiple correct options
A. pluse is moving in \( -x \) direction
B. wave speed is \( 0.5 \mathrm{m} / \mathrm{s} \)
c. max. particle displacement is \( 1 \mathrm{cm} \)
D. it is a symmetric pulse


Liana is a
A. Herb
B. Shrub
c. Tree
D. vine


An atom with an electron configuration of \( 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{4} \) will probably exhibit an oxidation state of:
\( A \cdot+2 \)
в. -2
\( c \cdot+3 \)
D. -
\( E \cdot+5 \)


A vertical wall of height \( a \) running from south to north has the height. A policeman of height \( b>a \) is standing
in front of the wall at a distance \( c \) from
it on the eastern side. What should be
the maximum distance of a crawling theif from the wall so that the thief can hide from the view of the policeman if the thief is on the other side of the wall
in the west of the policeman?
A \( \cdot \frac{a c}{b-a} \)
в. \( \frac{b c}{b-a} \)
c. \( \frac{a+b}{b-a} \cdot c \)
D. \( \frac{a c}{a+b} \)


Chlorine reacts with water to give a mixture of hydrochloric acid and hypochlorous acid.
A. True
B. False


The mean of \( \frac{1}{3}, \frac{3}{4}, \frac{5}{6}, \frac{1}{2} \) and \( \frac{7}{12}, \) is
A \( \cdot \frac{2}{5} \)
B. \( \frac{3}{5} \)
\( c \cdot \frac{1}{5} \)
D. None of these


Which of the following cannot undergo
\( E_{2} \) reaction?
\( \mathbf{A} \)
\( B \)
\( c \)
D. None of these


Bile pigments are formed in
A . Liver
B. Spleen
c. Every cell
D. Both A and B


Electrons revolves around the nucleus.
State True or False.
A. True
B. False


In a tangent galvanometer a current of
\( 0.1 A \) produces a deflection of \( 30^{\circ} . \) The
current required to produced a
deflection of \( 60^{\circ} \) is
A . \( 0.2 A \)
в. \( 0.3 A \)
\( c .0 .4 A \)
D. \( 0.5 A \)


A charged spherical conductor of radius
a and charge \( q, \) is surrounded by
another charged concentric sphere of
radius \( b(b>a) . \) The potential difference
between conductors is \( V . \) When, the spherical conductor of radius b is
discharged completely, then the potential difference between conductor will be:
A. \( V \)
B. \( \frac{v_{a}}{b} \)
c. \( \frac{q_{1}}{4 \pi \varepsilon_{0} a}-\frac{q_{2}}{4 \pi \varepsilon_{0} b} \)
D. None of the above


Which of the following compound does not react with concentrated alkali to
give corresponding alcohol and salt of carboxylic acid?
A. Trimethyl acetaldehyde
B. Benzaldehyde
c. Dimethyl acetaldehyde
D. Formaldehyde


A current of \( 5 \mathrm{A} \) is passing through a
metallic wire of length \( 5 \mathrm{m} \) and crosssectional area of \( 10^{-5} m^{2} . \) If the density
of the electrons in the wire is \( 6.25 x \)
\( 10^{26} m^{3}, \) find the time taken by the
electrons to travel from one end of the
wire to the other.


Non-metals don't show malleability
because of:
A. lesser extent of bonding than metalss
B. low density
c. smaller atomic size
D. none


Three solid spheres of gold whose radii
\( \operatorname{are} 1 \mathrm{cm}, 6 \mathrm{cm} \) and \( 8 \mathrm{cm}, \) respectively
are melted into a single solid sphere. Find the radius of the sphere.


Find solution of following inequality, also show it graphically:
\[
\boldsymbol{x}+\mathbf{3} \leq \mathbf{5}, \boldsymbol{x} \in \boldsymbol{Z}
\]
\( A \)
\begin{tabular}{rrrrrrrrrr}
\hline-3 & -2 & -1 & 0 & 1 & 2 & 3 & 4 & 5 & 6
\end{tabular}
B.
\begin{tabular}{rrrrrr}
\hline & & & & & & \\
\hline-2 & -1 & 0 & 1 & 2 & 3
\end{tabular}
\( c \)
\( \underbrace{\longleftarrow}_{-2}-1 \quad_{0} \quad_{1} \quad_{2} \quad_{1} \)
\( D \)
\begin{tabular}{rrrrrr}
\hline & 1 & 1 & & & 1 \\
-2 & -1 & 0 & 1 & 2 & 3
\end{tabular}


At \( 80^{\circ} C, \) distilled water has hydronium
\( \operatorname{ion}\left(H_{3} O^{+}\right) \) concentration equal to \( 1 \times \)
\( 10^{-6} \) mol \( / l . \) The value of \( K_{w} \) at this
temperature would be:
A \( \cdot 1 \times 10^{-6} \)
В. \( 1 \times 10^{-12} \)
c. \( 1 \times 10^{-9} \)
D. \( 1 \times 10^{-14} \)


Find the value of \( \sin ^{2} 30^{\circ}+\cos ^{2} 60^{\circ} \)


The value of the integral \( \int_{-1}^{1}\left\{\frac{x^{2013}}{e^{|x|}\left(x^{2}+\cos x\right)}+\frac{1}{e^{|x|}}\right\} d x \) is
equal to
A. 0
B. \( 1-e^{-1} \)
\( c \cdot 2 e^{-1} \)
D. \( 2\left(1-e^{-1}\right) \)


Prove that "In a trapezium, the line
joining the mid points of non-parallel
sides is (i) parallel to the parallel sides
and (ii) Half of the sum of the paralle
sides"


Find \( \boldsymbol{f}(-1) \) if \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{3}-\mathbf{1 0} \boldsymbol{x}+\mathbf{1 5} \)
A . 15
B. -6
\( c \cdot 24 \)
D. 4


Which of the following is 'lizard bird'?
A. Archaeopteryx
B. Struthio
c. Aptenodytes
D. Hesperornis


Which term of the sequence \( 8-6 i, 7- \)
\( \mathbf{4} i, \mathbf{6}-\mathbf{2} i, \ldots \) is purely real \( ? \)
A . 10
B. 12
\( c .9 \)
D.


A uniform ring of radius \( R \) and made up of a wire ofcross-sectional radius r is
rotated about its axis witha frcquency If density of the wire is p and Young's modulus is \( Y \). Find the fractional change in radiusof the ring.


Which of the following acidity order is
correct?
A. 1-Alkyne > Alkene > Alkane
B. Alkene > Alkane >1-Alkyne
C. Alkane > Alkene >1-Alkyne
D. None of these


Construct a \( 2 \times 2 \) matrix, \( A=\left[a_{i j}\right] \)
whose elements are given by:
(i) \( a_{i j}=\frac{(i+j)^{2}}{2} \)
(ii) \( a_{i j}=\frac{i}{j} \)
(iii) \( a_{i j}=\frac{(i+2 j)^{2}}{2} \)


\( C C l_{4} \) is the:
A. monohalogen derivative of alkane.
B. dihalohalogen derivative of alkane.
C. trihalogen derivative of alkane.
D. polyhalogen derivative of alkane.


An stoichiometric mixture of hydrogen
gas and the air at \( 25^{\circ} \mathrm{C} \) and a total
pressure of 1 atm, is exploded in a
closed rigid vessel. If the process occurs under adiabatic condition then using
the given data answer the questions
that follow:
Given:(i) \( C_{p}=8.3 \mathrm{cal} \) deg \( ^{-1} \) mol \( ^{-1} \)
\( (\mathrm{ii}) C_{p}=11.3 \mathrm{cal} \mathrm{deg}^{-1} \mathrm{mol}^{-1} \)
\( \Delta \boldsymbol{H}_{f}\left[\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g})\right]=-\mathbf{5 7 . 8} \boldsymbol{k} \boldsymbol{c} \boldsymbol{a l} \boldsymbol{l} \)
[Take air as 80 per \( N_{2}, 20 \) per \( O_{2} \) by volume \( ] \)
The value of \( C_{p} \) of \( N_{2} \& H_{2} O \) will be:
(in cal deg. \( ^{-1} \)mol\( ^{-1} \) )
A. 8.3,8.3
B. 8.3, 11.3
c. 11.3,11.3
D. 11.3,8.3


Evaluate:
\( \cos ^{-1}\left(\frac{2 x}{1+x^{2}}\right) \)


The initial and final temperatures are
recorded as \( (40.6 \pm 0.3)^{0} C \) and
\( (50.7 \pm 0.2)^{0} C . \) The rise in temperature
is:
A \( \cdot 10.1^{0} C \)
B \( \cdot(10.1 \pm 0.3)^{0} C \)
c. \( (10.1 \pm 0.5)^{0} C \)
D. \( (10.1 \pm 0.1)^{0} C \)


Find \( \arg (1+\sqrt{2}+i) \)
A \( . \pi / 16 . \)
в. \( \pi / 8 \)
c. \( \pi / 12 \)
D. \( \pi / 10 \)


If the statement is true enter 1 , else
enter 0
Repulsion between bond pair-bond pair electron is lesser than in between lone
pair-lone pair


Examine whether \( \boldsymbol{A}=\{\boldsymbol{x}: \boldsymbol{x} \) is a
positive integer divisible by \( 3\} \) is a subset of \( B=\{x: x \text { is a multiple of } 5 \)
\( \boldsymbol{x} \in \boldsymbol{N}\} \)


What will be the magnitude and polarity of induced emf across the rod, if it is
rotating about an axis at a distance \( \frac{\boldsymbol{L}}{\boldsymbol{4}} \) from one of its ends?


Raw materials for most of the synthetic fabrics are obtained from:
A. water
B. air
c. petroleum
D. sky


On connecting a shunt of \( 12 \Omega, \) the deflection of galvanometer reduces from 50 to 20 divisions. Calculate
resistance of galvanometer.


If 10 g of ice at \( 0^{\circ} C \) mixes with 10 g of
water at \( 10^{\circ} \mathrm{C} \), then the final
temperature \( t \) is given by
A \( \cdot(10 \times 80)+10(t-0)=10(10-t) \)
в. \( 10 \times 80=10(10-t)+10(t-0) \)
c. \( t=5^{\circ} \mathrm{C} \)
D . \( t=0^{\circ} \mathrm{C} \)


In a rocket of mass \( 1000 k g \) fuel is consumed at a rate of \( 40 k g / s . \) The velocity of the gases ejected from the rocket is \( 5000 m / s \). the thrust on the rocket is
A. \( 2 \times 10^{4} \) N
B . \( 2 \times 10^{6} \mathrm{N} \)
c. \( 4 \times 10^{2} \) N
D \( .4 \times 10^{6} \mathrm{N} \)


The impurity atoms, with which pure silicon should be doped to make a ptype semiconductor, are those of This question has multiple correct options
A. phosphorous
B. boron
C. antimony
D. aluminium


The half-life of tritium is 12.5 years
What mass of tritium of initial mass 64
mg will remain undecayed after 50
years?
A. \( 32 \mathrm{mg} \)
B. \( 8 \mathrm{mg} \)
c. \( 16 \mathrm{mg} \)
D. \( 4 \mathrm{mg} \)


Assertion
Be is readily attacked by acids.
Reason
Be shows diagonal relationship to Na.
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


Which among the following transitions will give Lyman series in Hydrogen emission atomic spectra?
\( A \cdot K \) to \( L \)
B. L to M, N etc
c. к to L, M, N etc
D. L, M, N etc to K


Consider a vector \( \boldsymbol{F}=\mathbf{4} \hat{\mathbf{i}}-\mathbf{3} \hat{\mathbf{j}} \). Another
vector which is perpendicular to \( \overrightarrow{\boldsymbol{F}} \) is:
A . \( 4 \hat{i}+3 \hat{j} \)
B. \( 6 \hat{i} \)
\( c .7 k \)
D. \( 3 \hat{i}-4 \hat{j} \)


At \( x=\frac{3}{2}, \) the value is real for
This question has multiple correct options
\( \mathbf{A} \cdot \tan ^{-1} x \)
B. \( \cos ^{-1} 2 x \)
\( \mathbf{c} \cdot \operatorname{cosec}^{-1} x \)
D. none of these


The lens shown in the figure is made of
two different materials. A point object is
placed on the axis the number of
images formed by the lens is
A. one
B. Two
c. Five
D. Three


Which of the following is an example of mineral acid?
A. Sulphuric acid
B. Acetic acid
c. Tartaric acid
D. All of above


Divide: \( \boldsymbol{x}^{\boldsymbol{6}}-\boldsymbol{1} \) by \( \boldsymbol{x}^{\boldsymbol{3}}-\boldsymbol{2} \boldsymbol{x}^{2}+\boldsymbol{2} \boldsymbol{x}-\boldsymbol{1} \)


An object may have
This question has multiple correct options
A. Varying speed without having varying velocity.
B. Varying velocity without having varying speed.
C. non-zero acceleration without having varying velocity.
D. Non-zero acceleration without having varying speed.


In an a.c. generator the speed at which the coil rotates is doubled. How would
this affect the frequency of output
voltage?
A. frequency is doubled
B. frequency is halvedd
c. frequency remains same
D. cant say


\( \lim _{x \rightarrow 5} \frac{x^{2}-25}{x-5}= \)
A . 10
B. 1
\( c \cdot \frac{2}{3} \)
D.


Find the distance between the points \( R(-3,0), S\left(0, \frac{5}{2}\right) \)


The treatment of \( \boldsymbol{C H}_{3} \boldsymbol{M} \boldsymbol{g} \boldsymbol{X} \) with
\( \boldsymbol{C H}_{3} \boldsymbol{C} \equiv \boldsymbol{C}-\boldsymbol{H} \) produces:
A. \( C H_{3} M g X=C-C H_{3} \)
в. \( C H_{3} C H=C H C H_{3} \)
c. \( C H_{4} \)
D. \( \left(C H_{3}\right)_{2} C=C H_{2} \)


When a \( 15 V \) dc source was applied across a choke coild then a current of 5
Amp flows in it. If the same coil is
connected to a \( 15 V, 50 \) rad/s ac source
a current of \( 3 A m p \) flows in the circuit
and its resonance frequency if a \( 2500 \mu f \) capacitor is connected in series with the coil.


Identify which of the following is the smallest discrete value of any quantity in physics?
\( A \cdot \) atom
B. molecule.
c. proton
D. electron
E . quantum


Function of loop of Henle is
A. Conservation of water
B. Formation of urine
C. Filtration of blood
D. Passage of urine


If \( A=\{2,3,5\} \) and \( B=\{5,7\}, \) find the set with highest number of elements:
\( \mathbf{A} \cdot A \times B \)
в. \( B \times A \)
c. \( A \times A \)
D. \( B \times B \)


For any \( + \) ve integer \( n, n^{3}+2 n \) is
always divisible by
A . 3
B. 7
\( c .5 \)
D. 6


In a final examination in Statistics the
mean marks of a group of 150 students
were 78 and the \( S . D \) was \( 8.0 . \ln \)

Economics, however, the mean marks
were 73 and the S.S was \( 7.6 . \) The
variability in the two subjects
respectively is
A. \( 10.3 \%, 10.4 \% \)
\( \% \)
B. \( 95 \%, 7.9 \% \)
c. \( 11.2 \%, 10.1 \% \)
D. none of these


Verify the points (0,7,-10)(1,6,-6) and (4,9,-6) are the vertices of an isosceles triangle.


A travelling acoustic wave of frequency \( 500 \mathrm{Hz} \) is moving along the positive \( x \)
direction with a velocity of \( 300 m s^{-1} \)
The phase difference between two
points \( x_{1} \) and \( x_{2} \) is \( 60^{\circ} . \) Then the minimum separation between the two pints is
\( \mathbf{A} \cdot 1 \mathrm{mm} \)
B. \( 1 \mathrm{cm} \)
c. \( 10 \mathrm{cm} \)
D. \( 1 \mathrm{m} \)


Derive an expression for the velocity of a particle performing linear SHM using differential equation. Hence, find the expression for the maximum velocity.


A convex lens produces a double size real image when an object is placed at a distance of \( 18 \mathrm{cm} \) from it. Where should the object be placed to produce a triple size real image?
A .44
B . -16
c. 22
D. 33


The molecule having three fold axis of symmetry is:
A \( . N H_{3} \)
B. \( C_{2} H_{4} \)
\( c \cdot C O_{2} \)
D. \( S O_{2} \)


Under the action of a force \( \boldsymbol{F}=\boldsymbol{C x} \), the
position of a body changes from 0 to \( x \) The work done is :
\( ^{\mathbf{A}} \cdot \frac{1}{2} C x^{2} \)
в. \( C x^{2} \)
\( c \cdot C x \)
D. \( \frac{1}{2} C x \)


If \( x_{1}, x_{2}, \dots, x_{n} \) are an observation such that \( \sum_{i=1}^{n} x_{i}^{2}=400 \) and \( \sum_{i=1}^{n} x_{i}=80 \),then the least value of \( n \) is
A . 18
B. 12
\( c \cdot 15 \)
D. 16


From the following which is the false
statement for the long form of the periodic table?
A. it reflects the sequence of filling the electrons in the order of sub-energy level s, p, d and f
B. it helps to predict the stable valency states of the elements
c. it reflects trends in physical and chemical properties of the elements
D. it helps to predict the relative ionic nature of the bond between any two elements


A beam of light consists of a bundle of light rays.
A . True
B. False


A heavy uniform bar is being carried by two men on their shoulders. The weight
of the bar is \( w \). If one man lets it fall
from the end carried by him, what will be the weight experienced by the other person at the instant when the
other man releases the bar?
A. \( w / 4 \)
в. \( w / 2 \)
\( c . w \)
D. None of these


A red litmus paper when dipped in an aqueous solution of potassium acetate turned blue. Arrange the following steps
in proper sequence to explain the above observation.
(a) Identification of spectator ions.
(b) Identification of free ions which
caused the colour change of the litmus
paper.
(c) Identification of positive and
negative radicals.
(d) Writing the net reaction taking
place
(e) Writing ionic equation for the reaction of positive and negative radicals with water.
\( A \cdot c \) e a d \( b \)
B. \( c \) a e d b
\( c \cdot e a d c b \)
D. e ca d b


The oxidant which cannot act as a
reducing agent is :
\( A \cdot S O_{2} \)
в. \( N O_{2} \)
\( c \cdot C O_{2} \)
D. \( C l O_{2} \)


Silk, honey and lac are
A. Secretory substance of insects.
B. Secretory substance of plants
C. Artificial chemicals.
D. All of the above.


In which of the following fields cathode rays show minimum deflection?
A. Electric field
B. Magnetic field
c. Plasma field
D. Gravitational field


A metal disc rotates freely, between the
poles of a magnet in the direction
indicated. Brushes \( P \) and \( Q \) make
contact with the edge of the disc and the metal axle. What current, if any,
flows through R?
A. a current from P to Q
B. a current from Q to P
c. no current, because the emf in the disc is opposed by the back emf
D. no current, because the emf induced in one side of the disc is opposed by the emf induced in the other side
E. no current, because no radial emf is induced in the
disc


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


In a division sum the divisor is 12
times the quotient and 5 times the
remainder. If the remainder is 48 then
what is the dividend?
A . 2404
в. 4808
c. 3648
D. 4848


A chemical that prevents blood clotting is most useful in the treatment of
A. Leukemia
B. Anaemia
c. coronary thrombosis
D. Haemophilia


RUBP is present in
A. Grana thylakoid
B. Stroma
C. Inner chloroplast membrane
D. Outer chloroplast membrane


An anticodon region is present in
nucleic acid
A. DNA
B. mRNA
c. rRNA
D. snRNA
E. tRNA


All the reactants listed in List-I react
with aqueous solution of hot sodium hydroxide. Match the result of the respective reactions with the appropriate options listed in List-II.


Sum of digits of the smallest number by which 1440 should be multiplied so that it becomes a perfect cube is
A . 4
B. 6
\( c \cdot 7 \)
D.


Find the area of the region bounded by
the curve \( y^{2}=x \) and the lines \( x= \)
\( 1, x=4 \) and the \( x \) -axis
\( A \cdot \frac{8}{3} \)
в. \( \frac{14}{3} \)
\( c \cdot \frac{7}{3} \)
D. \( \frac{1}{3} \)


A mass of \( 10 \mathrm{kg} \) is at a point \( \mathrm{A} \) on a table. It is moved to a point B. If the line joining A and B is horizontal, what is the work done on the object by the gravitational force? Explain your
answer


The half life of \( ^{58} \) Co is 72 days. Its
average life is:
A. 102.9 days
B. 103.9 days
c. 104.9 days
D. 105.9 days


If \( |\overline{\boldsymbol{a}}|=\mathbf{1},|\overline{\boldsymbol{b}}|=\mathbf{2},|\overline{\boldsymbol{a}}-\overline{\boldsymbol{b}}|^{2}+|\overline{\boldsymbol{a}}+\mathbf{2} \overline{\mathbf{b}}|^{2}= \)
\( \mathbf{2 0}, \) then \( (\overline{\boldsymbol{a}}, \overline{\boldsymbol{b}})= \)
A \( \cdot \frac{\pi}{3} \)
в.
c.
D. \( \frac{2 \pi}{3} \)


Assertion
A ladder is more likely to slip when a person is near the top than when he is
near the bottom.
Reason
The friction between the ladder and the
floor decreases as he climbs up.
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


In damped oscillation mass is 1 kg and
spring constant \( =100 N / m, \) damping
coefficeint \( =0.5 \mathrm{kg} s^{-1} . \) If the mass
displaced by \( 10 \mathrm{cm} \) from its mean position then what will be the value of
its mechanical energy after 4 seconds?
A . \( 0.67 J \)
в. 0.067 Л
c. \( 6.7 J \)
D. \( 0.5 J \)


In a quadrilateral ABCD if \( \sin \left(\frac{A+B}{2}\right) \cos \left(\frac{A-B}{2}\right)+ \)
\( \sin \left(\frac{C+D}{2}\right) \cos \left(\frac{C-D}{2}\right)=2 \) then
\( \sum \cos \frac{A}{2} \cos \frac{B}{2} \) is equal to
\( \mathbf{A} \cdot \mathbf{0} \)
B. 6
\( c .3 \)
D.


A pulse of sound is produced at the
bottom of a boat. The sound travels
through the water and is
reflected from the sea-bed. The sound
reaches the boat again after 1.3 s. The
sea-bed is \( 1000 m \) below the boat
Using this information, what is the speed of sound in the water?
A. \( 769 \mathrm{m} / \mathrm{s} \)
в. \( 1300 \mathrm{m} / \mathrm{s} \)
c. \( 1538 \mathrm{m} / \mathrm{s} \)
D. \( 2600 \mathrm{m} / \mathrm{s} \)


Suggest reasons for and against the
inclusion of hydrogen in the main groups of the periodic table.


An iron rod is placed parallel to the magnetic field of intensity \( 2000 \mathrm{A} / \mathrm{m} \) The magnetic flux through the rod is \( 6 \times 10^{-4} W b \) and its cross-sectional
area is \( 3 \mathrm{cm}^{2} \). The magnetic permeability of the rod in \( \frac{W b}{A-m} \) is:
A \( \cdot 10^{-1} \)
B. \( 10^{-2} \)
\( \mathbf{c} \cdot 10^{-3} \)
D. \( 10^{-4} \)


Fossils are dated now by
A. Stratigraphic position
B. Amount of calcium residue
C. Association with other animals
D. Radioactive carbon (C-14) contents


A solution made by dissolving 0.32 g of a new compound in 25 g of water has freezing point \( -2.201^{\circ} \mathrm{C} . \) Calculate the molecular mass of the new compound.
A . 218.4
в. \( 118 . \)
c. 318.4
D. 10.81


The primary winding of a transformer
has 500 turns whereas its secondary has 5000 turns. The primary is connected to an ac supply of \( 20 \vee, 50 \mathrm{Hz} \) What will be the output of the secondary?
A \( .200 \vee, 50 \) Н \( z \)
в. \( 100 \vee, 50 \) Н \( z \)
c. \( 200 \vee, 500 \) Н \( z \)
D. 250 V, 50 нz


For watt-less power in an \( A C \) circuit the
phase angle between the current and
voltage is
A \( \cdot 0^{\circ} \)
B. \( 90^{\circ} \)
\( c \cdot 45^{\circ} \)
D. Not possibl


Same force acts on two bodies of
different masses \( 2 k g \) and \( 4 k g \) initially at rest. The ratio of times required to acquire same final velocity is:-
A .2: 1
B. 1: 2
\( c \cdot 1: 1 \)
D. 4: 16


In which case mean free path is not
affected?
A \( \cdot H_{2} \) gas at \( 100^{\circ} \mathrm{C} \) and 1 atm is transferred into a vessel at \( 50^{\circ} \mathrm{C} \) and 0.5 atm
B. \( O_{2} \) gas at \( 200 K \) and \( 2 a t m \) is transferred into a vessel at \( 400 K \) and 1 atm
c. \( O_{2} \) gas is replaced by \( H_{2} \) gas keeping other variables constant
D. Medium is made more viscous


un treatment wırn cola water, an
element (A) reacts readily liberating a
colorless, odourless gas \( (\mathrm{B}) \) and \( \mathrm{a} \) solution (C). Lithium is reacted with (B)
yielding a solid product (D) which effervescence with water to give a
strongly basic solution (E). When \( C O_{2} \)
gas is bubbled through the solution \( (\mathrm{C}) \) a white ppt (F) is formed but this
redissolved forming solution (G) when
more \( C O_{2} \) is passed. The precipitate \( (F) \)
effervesced when moistened with conc.
\( H C l \) and give deep red coloration to the
Bunsen burner flame. (F) on heating
with an excess of carbon at \( 2000^{\circ} C \)
give (H).

Solid (H) on hydrolysis gives a gas, which on passing through ammonical
\( A g N O_{3} \) solution, yields:
A. white ppt
B. red ppt
C. no ppt
D. brown ppt


Assertion
The enlarged \( Q \) and \( R \) waves indicate myocardial infraction.
Reason
Any deviation in the normal recording of ECG indicates possible abnormality or disease.
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


Corrosive sublimate \( \left(H g C l_{2}\right) \) can be
used to distinguish between:
A. formaldehyde and propanone
B. formic acid and acetic acid
c. acetaldehyde and butanone
D. all of the above


Show that the differential equation \( (x-y) \frac{d y}{d x}=x+2 y \) is homogeneous


A vector \( \vec{A} \) of length 10 units makes an angle of \( 60^{\circ} \) with a vector \( \vec{B} \) of length 6
units. Find the magnitude of the vector difference \( \vec{A}-\vec{B} \& \) the angle it makes with vector \( \vec{A} \).
A \( \cdot 2 \sqrt{19}, \tan ^{-1}\left(\frac{3 \sqrt{3}}{7}\right) \)
в. \( \sqrt{19}, \tan ^{-1}\left(\frac{3 \sqrt{3}}{7}\right) \)
c. \( 2 \sqrt{19}, \tan ^{-1}\left(\frac{\sqrt{3}}{7}\right) \)
D. \( \sqrt{19}, \tan ^{-1}\left(\frac{\sqrt{3}}{7}\right) \)


A car weighing 1 ton is moving twice as fast as another car weighing 2 ton. The kinetic energy of the one-ton car is
A. less than that of the two-ton car is
B. some as that of the two-ton car is
c. more than that of the two-ton car is
D. impossible to compare with that of the two-ton car unless the height of each


One mole of \( H_{2} O \) and one mole of \( C O \)
were heated in a \( 10 L \) closed vessel at
\( 1260 K . \) At equilibrium, \( 40 \% \) of water
was found to react in the equation,
\( \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g})+\boldsymbol{C O}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{H}_{2}(\boldsymbol{g})+ \)
\( \boldsymbol{C O}_{2}(\boldsymbol{g}) \)
Calculate the equilibrium constant of the reaction.


There are two A.P.'s each of \( n \) terms
\( \boldsymbol{a}, \boldsymbol{a}+\boldsymbol{d}, \boldsymbol{a}+\boldsymbol{2} \boldsymbol{d}, \ldots \boldsymbol{L}, \boldsymbol{p}, \boldsymbol{p}+\boldsymbol{q}, \boldsymbol{p}+ \)
\( 2 q, \ldots . . L^{\prime} . \) These A.P.'s satisfy the
following conditions: \( \frac{\boldsymbol{L}}{\boldsymbol{p}}=\frac{\boldsymbol{L}^{\prime}}{\boldsymbol{a}}= \)
\( 4, \frac{S_{n}}{S_{n^{\prime}}}=2 ; \) find out \( 2\left(\frac{L}{L^{\prime}}\right) \)


The halogen (Group 17 elements):
A. have an electron configuration of a noble gas less seven electrons
B. are highly electro positive
C. show variable oxidation state of -1,+1,+3,+5 and +7 in their various compounds
D. forms a volatile, covalent hydrides \( H X \) in which the halogen \( (X) \) shows an oxidation state of +1


For the construction of a thermometer
one of the essential requirements is a thermometric substance which
A. remains liauid over the entire range of temperatures to be measured
B. has a property that varies linearly with temperature
c. has a property that varies with temperature
D. obey Boyle's law


A \( 0.0020 M \) aqueous solution of an
ionic compound \( \boldsymbol{C} \boldsymbol{o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{5}\left(\boldsymbol{N} \boldsymbol{O}_{2}\right) \boldsymbol{C l} \)
freezes at \( -0.00732^{\circ} \mathrm{C} . \) Number of
moles of ions which 1 mole of ionic
compound produces on being dissolved in water will be:
\( \left[k_{f}=1.86^{\circ} C / m\right] \)
A . 1
B. 2
\( c .3 \)
D. 4


A \( 300 \mathrm{mm} \) long tube containing \( 60 \mathrm{cc} \) of
sugar solution produces a rotation of \( 9^{\circ} \) when placed in a polarimeter. If the
specific rotation is \( 60^{\circ} . \) Calculate the
quantity of sugar contained in the solution.


Height of a liquid column in a manometer decrease:
A. with decreasing density of liquid
B. with increasing density of liquid
c. with no change in density of liquid
D. as independent of liquid used


What is the action of :
(a) Sodium on arsenic
Magnesium on bismuth


If the extension of the spring is \( x_{0} \) at time \( t, \) then the displacement of the second block at this instant is :
\( ^{\mathrm{A}} \cdot \frac{F t^{2}}{2 m}-x_{0} \)
\( ^{\text {В }} \cdot \frac{1}{2}\left(\frac{F t^{2}}{2 m}+x_{0}\right) \)
c. \( \frac{1}{2}\left(\frac{2 F t^{2}}{m}-x_{0}\right) \)
\( \frac{1}{2}\left(\frac{F t^{2}}{2 m}-x_{0}\right) \)


Which is the correct formula for
calculating the power lost due to eddy currents per unit mass for a thin sheet
or wire?? Where \( P \) is the power lost per
unit mass \( (W / k g), B_{p} \) is the peak
magnetic field \( (T), d \) is the thickness of the sheet or diameter of the wire \( (\boldsymbol{m}), \boldsymbol{f} \)
is the frequency \( (H z), k \) is a constant equal to 1 for a thin sheet and 2 for a
thin wire
\( ^{\mathrm{A}} \cdot_{P}=\frac{\pi^{2} B_{p}^{2} d^{2} f^{2}}{6 k \rho D} \)
в. \( \quad P=\frac{\pi^{2} B_{p}^{2} d^{2} f}{k \rho D} \)
\( ^{\mathrm{C}} P=\frac{\pi^{2} B_{p}^{2} d^{2} f^{2}}{6 k \rho D^{3}} \)
D. \( P=\frac{\pi^{2} B_{p}^{2} d^{2} f}{6 k \rho D^{2}} \)


In the following reaction \( \boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{O} \boldsymbol{C}_{2} \boldsymbol{H}_{5}+\boldsymbol{4} \boldsymbol{H} \stackrel{\boldsymbol{R e d} \boldsymbol{P}+\boldsymbol{H I}}{\longrightarrow} \boldsymbol{2} \boldsymbol{X}+ \)
\( \boldsymbol{H}_{2} \boldsymbol{O}, \boldsymbol{X} \) is:
A. ethane
B. ethylene
c. butane
D. propane


Select the correct statements for
Ellingham diagram.

This question has multiple correct options
A. Any metal will reduce the oxide of other metals which lie above it in the Ellingham diagram
B. According to the Ellingham diagram, Al will not reduce MgO at temperature below \( 1350^{\circ} \mathrm{C} \)
C. According to the Ellingham diagram, Al will reduce
MgO at temperature below \( 1350^{\circ} \mathrm{C} \)
D. Any metal will not reduce the oxide of other metals which lie above it in the Ellingham diagram


The mean and the variance of a
binomial distribution are 4 and 2
respectively. Then the probability of 2
successes is
A \( \cdot \frac{128}{256} \)
в. \( \frac{219}{256} \)
c. \( \frac{37}{256} \)
D. \( \frac{28}{256} \)


\( A B \) and \( C D \) are two parallel chords of a circle such that \( A B=10 \mathrm{cm} \) and
\( C D=24 \mathrm{cm} . \) If the chords are on the
opposite sides of the centre and the distance between them is \( 17 \mathrm{cm} \), the radius of the circle is
A . \( 14 \mathrm{cm} \)
B. \( 10 \mathrm{cm} \)
c. \( 13 \mathrm{cm} \)
D. \( 15 \mathrm{cm} \)


Find the mean deviation about the
mean as well as the coefficient of Mean
Deviation about mean of the following \( \operatorname{set} \) data: 4,7,14,11,9
A . 2.8 and 0.311
B. 2.1 and 0.211
c. 24.8 and 0.411
D. 21.3 and0.566


A Young's double slit experiment is conducted with slit separation \( 10 \mathrm{mm} \) where the screen is \( 2 \mathrm{m} \) away from the
slits. If wavelength of light used is \( 6000 \AA, \) then fringe width in 'mm' is
A . 0.12
B. 0.24
c. 0.36
D. 0.48


If \( \tan (A-B)=1, \sec (A+B)=\frac{2}{\sqrt{3}} \)
then the smallest +ve value of B is?
A \( \cdot \frac{25 \pi}{24} \)
в. \( \frac{19 \pi}{24} \)
c. \( \frac{13 \pi}{24} \)
D. \( \frac{11 \pi}{24} \)