The total pressure at the bottom of the
container is
\( ^{A} \cdot\left(\frac{H}{2}+\frac{L}{4}\right) d g \)
B. \( P_{0}+\left(\frac{3 H}{2}+\frac{L}{2}\right) d g \)
\( ^{\mathrm{c}} P_{0}+\left(H+\frac{L}{4}\right) d g \)
D \( P_{0}+\left(\frac{3 H}{2}+\frac{L}{4}\right) d g \)


An urn contains 4 red and 7 blue balls.
Find the probability of getting Blue balls


If \( m \) parallel lines in a plane are
intersected by a family of \( n \) parallel lines, the number of parallelograms than can be formed is
A \( \cdot \frac{1}{4} m n(m-1)(n-1) \)
в. \( \frac{1}{2} m n(m-1)(n-1) \)
c. \( \frac{1}{4} m^{2} n^{2} \)
D. None of these


What is the valency of the element with atomic number 35 and \( 15 ? \)


In a string the speed of wave is \( 10 \mathrm{m} / \mathrm{s} \)
and its frequency is 100 Hz. The value of
the phase difference at a distance 2.5
cm will be :
\( \mathbf{A} \cdot \pi / 2 \)
в. \( \pi / 8 \)
c. \( 3 \pi / 2 \)
D. \( 4 \pi \)


Riboflavin vitamin is:
\( A \cdot B_{1} \)
\( B \cdot B_{2} \)
\( c \cdot B_{12} \)
D. B \( _{6} \)


Evaluate
\( \lim _{x \rightarrow 0} \frac{\sqrt{2}-\sqrt{1+\cos x}}{\sin ^{2} x} \)


A current of 3 A is flowing in a linear conductor having a length of \( 40 \mathrm{cm} . \) The conductor is placed in a magnetic field
of strength 500 gauss and makes an
angle \( 30^{\circ} \) with the direction of the field.
It experiences a force of magnitude
\( \mathbf{A} \cdot 3 \times 10^{-4} N \)
B. \( 3 \times 10^{-2} N \)
c. \( 3 \times 10^{2} N \)
D. \( 3 \times 10^{4} N \)


If the corresponding sides of two triangles are proportional, then the two triangles are similar by which test
\( A \cdot \) SSS test
B. SAS test
C. AAA test
D. ASA test


Chromosome theory of \( X Y \) sex determination was proposed by.
A. Henking
B. Wilson and Stevens
c. Johannsen
D. Punnet


Atom with atomic radii and
ionisation potential tends to gain electrons
A. large, high
B. large, low
c. small, low
D. small, high


Dependent Population refers to -
A. Children and Old Persons
B. Employed Persons
C. Both (a) and (c)
D. Neither
(a) nor \( (b) \)


Assertion
Bohr had to postulate that the electrons in stationary orbits around the nucleus
do not radiate.
Reason
According to classical physics all moving electrons radiate.
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


Which vitamin deficiency in human blood increases blood clotting time?


Three resistors of each \( 1 \Omega \) are joined in the form of a triangle.The value of resistance between an the corners:
A \( \cdot \frac{2}{3} \Omega \)
B . \( \frac{3}{2} \Omega \)
\( c \cdot \frac{3}{4} \Omega \)
D. 3\Omega


The given figure shows development of
an embryo that undergoes two phases \( A \) and B. Select the correct option
regarding it
of division loose capacity to divide
A. A-Geometric phase
B - Arithmetic phase
B. A - Arithmetic phase,
B - Geometric phase
c. A - Arithmetic phase
B - Exponential phase
D. A - Exponential phase, B - stationary phase


Calculate geometric mean for the following values 1,3,5,7,10,12
A. 1.82386
в. 2.82386
\( c .3 .82386 \)
D. 4.82386


The chemical formula of 2 -chloro
pentane is:
A \( \cdot C_{5} H_{5} C l \)
B. \( C_{5} H_{11} C l \)
\( \mathbf{c} \cdot C_{4} H_{9} C l_{2} \)
D. \( C_{5} H_{9} C l \)


Assertion
Ethyne is more reactive than ethane.
Reason
Due to presence of triple bond, electron
density is very high so it is more
reactive
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


\( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R}, \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{3} \boldsymbol{x}+\boldsymbol{2} \)
\( \boldsymbol{g}: \boldsymbol{R} \rightarrow \boldsymbol{R}, \boldsymbol{g}(\boldsymbol{x})=\boldsymbol{6} \boldsymbol{x}+\mathbf{5} \)
for the given functions \( \left(g o f^{-1}\right)(10)= \)
A . 21
B . 29
\( c \cdot 7 \)
D.


What is the arrangement of root zones
starting from root tip?
A. Root cap, cell division, cell enlargement and cell maturation
B. Root cap, cell division, cell maturation and cell enlargement
C. Cell division, cell maturation, cell enlargement and root cap
D. Cell division, cell enlargement, cell maturation and root cap


State the Krichhoff's law of electric
network. In the figure shown \( \boldsymbol{P}= \) \( 2 \mathrm{ohms} Q=4 \mathrm{ohms}, R=4 \mathrm{ohms} \) and
\( S=2 \) ohms. Resistance between \( C \) and
\( D \) is 1 ohms. Find the current through
each resistance


Find the centre and radius of the circle
\( x^{2}+y^{2}+6 x+8 y-96=0 \)


Which of the following is a hormonereleasing IUD?
A. LNG-20
B. Multiload-375
c. Lippes loop
D. \( c u-7 \)


A ball is released from the top of a tower
of height \( h \) meters. It takes \( T \) second to
reach the ground. What is the position
of the ball in \( T / 3 \) second?
A. \( 2 h / 9 \) meter from the ground
B. \( 7 h / 9 \) meter from the ground
c. \( 8 h / 9 \) meter from the ground
D. \( 17 h / 18 \) meter from the ground


If one of the roots of \( a x^{2}+b x+c=0 \) is
\( \mathbf{7}+\sqrt{\mathbf{2}} \) then find the other root
A. \( -7+\sqrt{2} \)
B. \( 7-\sqrt{2} \)
c. \( -7-\sqrt{2} \)
D. Cannot be determined


\( \left|\begin{array}{cc}\mathbf{2} & \mathbf{3} \\ \mathbf{4} & \mathbf{4}\end{array}\right|+\left|\begin{array}{cc}\boldsymbol{x} & \mathbf{3} \\ \boldsymbol{y} & \mathbf{1}\end{array}\right|=\left|\begin{array}{cc}\mathbf{1 0} & \mathbf{6} \\ \mathbf{8} & \mathbf{5}\end{array}\right|, \) then \( (\mathbf{x}, \mathbf{y})= \)
A \( \cdot(4,8) \)
\( B \cdot(8,4) \)
\( c \cdot(1,2) \)
\( D \cdot(2,4) \)


Two moles of an ideal gas expended isothermally and reversibly from 1 litre to 10 litre at 300 K. The enthalpy change (in kJ) for the process is:
A . 11.4
B. -11.4
\( c \cdot 0 \)
D. 4.8


Express 3825 as a product of prime factors


\( * \) is a binary operation on \( Z \) such that:
\( \boldsymbol{a} * \boldsymbol{b}=\boldsymbol{a}+\boldsymbol{b}+\boldsymbol{a} \boldsymbol{b} \)
The solution of \( (3 * 4) * x=-1 \) is
A . 1
B. -
\( c \cdot 4 \)
D. 3


Evaluate the following:
\( \tan ^{-1}(\tan 2) \)


If \( f(x)=\cos (\log x), \) then \( f(x) f(y)- \)
\( \frac{1}{2}\left[f\left(\frac{x}{y}\right)+f(x y)\right] \) is equal to
\( A \)
B. \( \frac{1}{2} \)
\( c .-2 \)
\( D \)


Autoignition temperature is the highest temperature at which substance can burn.
A. True
B. False


\( A 5 \mu F \) capacitor is connected to a 200 \( \mathrm{V}, 100 \mathrm{Hz} \) ac source. The capacitive
reactance is:
\( \mathbf{A} \cdot 212 \Omega \)
B. \( 312 \Omega \)
c. \( 318 \Omega \)
D. \( 412 \Omega \)


A light string passes over a frictionless
pulley. To one of its ends a mass of \( 6 k g \) is attached to the other end a mass of
10 \( k g \) is attached. The tension of the thread is:
A . \( 24.5 N \)
B . \( 2.45 N \)
\( c .79 N \)
D. \( 73.5 N \)


From kinematics equations of motion
is
A \( \cdot S=u t-\frac{1}{2} a t^{2} \)
B . \( S=u t+\frac{1}{2} a t^{2} \)
c. Both (a) and (b)
D. None of these


Dihydrogen gas used in Habers process is produced by reacting methane from natural gas with high temperature steam. The first stage of two stage reaction involves the formation of \( C O \)
and \( H_{2} . \) In second stage, \( C O \) formed in
first stage is reacted with more steam in water gas shift reaction,
\( \boldsymbol{C O}(\boldsymbol{g})+\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g})+ \)
\( \boldsymbol{H}_{2}(\boldsymbol{g}) \)
If a reaction vessel at \( 400^{\circ} \mathrm{C} \) is charged
with an equimolar mixture of \( C O \) and
steam such that \( \boldsymbol{P}_{C O}=\boldsymbol{P}_{\boldsymbol{H}_{2}} \boldsymbol{O}= \)
4.0bar, what will be the partial pressure
of
\( \boldsymbol{H}_{2} \) at equilibrium? \( \boldsymbol{K}_{\boldsymbol{P}}=\mathbf{0 . 1} \) at \( \mathbf{4 0 0}^{\circ} \boldsymbol{C} \)


\( \operatorname{In} \operatorname{both} N i(C O)_{4} \) and \( \left[N i C l_{4}\right]^{-2}, N i \) is
\( s p^{3} \) hybridised.
A. True
B. False


The surface of cartilage is surrounded by irregular connective tissue, called as
A. Periostium
B. Perichondrium
c. Lacunae
D. osteoclast


A capacitor of \( 10 \mu F \) is connected to a
\( \mathbf{1 0} \boldsymbol{V} \) cell. The maximum charge on the
capacitor will be:
A. \( 1 \mu C \)
B. \( 10 \mu C \)
c. \( 100 \mu C \)
D. \( 1000 \mu C \)


There are three solids made up of aluminium, steel and wood, of the same shape and same volume. Which of them would have highest inertia?
A. Steel.
B. Aluminium
c. wool
D. None of these


The ground water level increases due to
(recharging/discharging) of
wells.


The \( p H \) of \( 10^{-7} M N a O H \) is:
A . 7.01
B. between 7 and 8
c. between 8 and 9
D. greater than 10


Match the Column I with Column II.
Column Column A nn II \( \mathrm{O} \mathrm{h}_{\mathrm{m}} \)
\( \mathrm{i}_{\mathrm{S}} \)
\( \mathrm{applin}_{\mathrm{d}} \) Whe the the
(A)
\( (p) \)
metals applicable
to The
(B) Ohm's law
is not
applicable
to
\( (q) \)
grr
reer greater
resistivity
(C) alloys have \( \quad \) (r) \( \quad \) diodes,
electrolytes,
semiconductors
\( A \cdot A-r, B-q, C-p \)
B. \( A-p, B-r, C-q \)
C. \( A-r, B-p, C-q \)
D. A-q, B-r, C-p


A parrot is sitting on the floor of a wire cage which is being carried by a boy,
starts flying. The boy will feel that the
box is now
A. heavier
B. lighter
C. shows no change in weight
D. lighter in the beginning and heavier later


Which of the following statements is
not true?
A. The ratio of the mean speed of the RMS speed is independent of the temperature
B. The square of the mean speed of the molecules is equal to the mean square speed at a certain temperature
C. Mean kinetic energy of the gas-molecules at any given temperature is independent of the mean speed
D. The difference between RMS speed and mean speed at any temperature for different diminishes as larger and yet larger molar masses are considered


What type of forces act between the ions during the formation of a crystal of ionic compound?


\( \int x \sec ^{2} x d x \)


Which of the following has/have zero average value in a plane electromagnetic wave?
A. Both magnetic and electric fields
B. Electric fields only
c. Magnetic field only
D. None of these


How much heat is required to raise the
temperature of 150 g of iron from \( 20^{\circ} C \) to \( 25^{\circ} \mathrm{C} \) ? (Specific heat of iron
\( \left.480 J k g^{-1} o C^{-1}\right) \)
A . 350
B. 345 J
c. 360 J
D. 330 J


Two charges \( +6 \mu C \) and \( -4 \mu C \) are
placed \( 15 c m \) a part as shown. At what
distances from \( A \) to its right, the
electrostatic potential is zero?
\( \mathbf{A} \cdot 4,9,60 \)
B. 9,15,45
\( \mathrm{C} \cdot 20,30,40 \)
D. \( 9,45, \) infinity


The maximum force of friction which
just allows one body to slide upon another body is called


Reindeers are made to pull the sledges in artic regions.The force involved in this activity is
A. Frictional force
B. Gravitational force
c. Magnetic force
D. Muscular force


Which one of the following is/are correct statement(s) for physisorption? This question has multiple correct options
A . It is a reversible process
B. It requires less heat of adsorption
c. It requires activation energy
D. It takes place at low temperature


In a circle whose radius is 10 inches, a
chord is 6 inches from the center. What
is the length of the chord?
A. 4 inches
B. 6 inches
c. 8 inches
D. 16 inches


The mean value of 6,9,12 is


\( S(s)+O_{2}(g) \rightarrow S O_{2}(g) \quad \Delta H^{\circ}= \)
\( -297 k J \)
\( 2 S O_{2}(g)+O_{2}(g) \rightarrow \)
\( 2 S O_{3}(g) \quad \Delta H^{\circ}=-198 k J \)
Given the above thermochemical
reactions, what is the heat of reaction
for the formation of \( S O_{3}(g) \) provided
below?
\( \boldsymbol{S}(\boldsymbol{s})+\boldsymbol{3} / 2 \boldsymbol{O}_{2}(\boldsymbol{g}) \rightarrow \boldsymbol{S} \boldsymbol{O}_{3}(\boldsymbol{g}) \)
A \( .-495 \mathrm{kJ} \)
B . -396 k
c. -198 k
D . +99
E . +198 k


A 0.2 molar solution of formic acid is
\( 3.2 \% \) ionised, its ionisation constant is:
A. \( 9.6 \times 10^{-3} \)
B. \( 2.1 \times 10^{-4} \)
c. \( 1.25 \times 10^{-6} \)
D. \( 2.1 \times 10^{-8} \)


The monomer when treated with Zieglar
Natta catalyst undergo polymerisation. The polymer obtained when monomeric unit used is:
\( C^{l} \)
\( C H_{2}=C^{\prime}-C H=C H_{2} \)
A. neoprene
B. stilbene
c. styrene
D. chloropicrin


Find the negative of cube root of
-2744000:


Early colonisers of bare and barren
areas helps in
succession


Show that all rectangles inscribed in a fixed circle square has maximum area.


Assertion
\( P \) orbital is dumb-bell shaped.
Reason
Electron present in p orbital can have any one of the three values of the magnetic quantum number, i.e 0,+1 or
-1
Read the above assertion and reason
and choose the correct option regarding
¡t.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


There are 7 men and 8 women. In how
many ways a committee of 4 members
can be made such that a particular woman is always included


If \( y^{2}=a x^{2}+b x+c, \) where \( a, b, c \) are
constants, then \( y^{3} \frac{d^{2} y}{d x^{2}} \) is equal to.
A \( \cdot \frac{-1}{4} \)
в. \( \frac{-1}{6} \)
c. \( \frac{-3}{4} \)
D. \( \frac{-1}{8} \)


The slope of a line is double of the slope
of another line. If the tangent of the angle between them is \( \frac{1}{3} \) find the slopes of the lines.


Find the slope of the line passing
through the points \( A(-2,1) \) and
\( \boldsymbol{B}(\mathbf{0}, \boldsymbol{3}) \)


In the given figure, \( A B C \) is an equilatera
triangle whose side is \( 2 \sqrt{3} \mathrm{cm} . \) A circle
is drawn which passes through the
midpoints \( D, E \) and \( F \) of its sides. The area of the shaded region is:
\( A \)
B \( \cdot \frac{1}{4}(2 \pi-\sqrt{3}) c m^{2} \)
c. \( \frac{1}{4}(\pi-3 \sqrt{3}) c m^{2} \)
D.


A ball dropped from some height covers half of its total height during the last second of its free fall. Find
(a) time of flight
(b) height of its fall
(c) speed wit which it strikes the ground.


What do you call a parallelogram which has equal diagonals?
A. A trapezium
B. A rectangle
c. A rhombus
D. A kite


If \( |z+5| \leq 2 \) then the maximum value of \( |z+3| \) is ( where \( z \) is a complex number)
A. zero
B . 2
\( c \cdot 4 \)
D. 6


f \( \boldsymbol{A}=\{\mathbf{2}, \mathbf{3}, \mathbf{4}, \mathbf{5}, \mathbf{6}, \mathbf{7}\} \) and \( \boldsymbol{B}= \)
\( \{3,5,7,9,11,13\}, \) then find \( A-B \) and
\( \boldsymbol{B}-\boldsymbol{A} \)


is the heat supplied during change of state of matter.
A. Enthalpy
B. Latent heat
c. Endothermic
D. Exothermic


A substance with more specific heat can absorb a greater amount of heat for a given mass. State whether given statement is True/False
A. True
B. False


Most primitive living vascular plants
are
A. Sphagnum
B. cycads
c. Brown algae
D. Ferns


Which one of the following is employed as Antihistamine?
A. Omeprazole
B. Chloramphenicol
c. Diphenhydramine
D. Norethindrone


The three angles of a triangle are in the
ratio \( 1: 2: 1 . \) Find all the angles of the
triangle, classify the triangle in two different ways.


In the figure \( C \) is a right angle DE \( \wedge A B \)
\( A E=6, E B=7 \) and \( B C=5 . \) The area of the
quadrilateral EBCD is
A. 27.5
B . 25
c. 22.5
D. 20


A table-top measures \( 2 m 25 \mathrm{cm} \) by
1 \( m 50 \mathrm{cm} . \) What is the perimeter of the table-top?


In which year Paul Ehrlich got the Noble Prize for medicine?
A. 1980
B. 1908
\( c \cdot 1907 \)
D. 1478


If \( \boldsymbol{A}=\left[\begin{array}{lll}\mathbf{0} & \mathbf{0} & \mathbf{1} \\ \mathbf{0} & \mathbf{1} & \mathbf{0} \\ \mathbf{1} & \mathbf{0} & \mathbf{0}\end{array}\right], \) then
This question has multiple correct options
A. AdjA is zero matrix
B.
\[
A d j A=\left[\begin{array}{ccc}0 & 0 & -1 \\ 0 & -1 & 0 \\ -1 & 0 & 0\end{array}\right]
\]
\( \mathbf{c} \cdot A^{-1}=A \)
D. \( A^{2}=I \)


During which stage of the cell cycle is cell growth and replication of organelles most significant?
A. M phase
B. \( G_{1} \) phase
\( \mathrm{c} \cdot G_{2} \) phase
D. S phase


What are the characteristics of isobars?
A. They have different atomic numbers.
B. They have same electronic configuration.
C. They have same number of neutrons.
D. All of the above


The difference of slopes of lines
represent by \( y^{2}-2 x y \sec ^{2} \alpha+ \)
\( \left(3+\tan ^{2} \alpha\right)\left(\tan ^{2} \alpha-1\right) x^{2}=0 \) is
\( A \cdot 3 \)
B. 4
\( c \cdot 0 \)
D.


If \( P, V, T \) represents pressure, volume
and temperature of the gas, the correct representation of Boyle's law is :
A \( \cdot V \propto \frac{1}{P}(\mathrm{P} \text { is constant }) \)
В. \( P V=R T \)
\( ^{\mathrm{c}} \cdot_{V} \propto \frac{1}{P}(\text { at constant } \mathrm{T}) \)
D. \( P V=n R T \)


Integrate: \( \frac{\mathbf{3} \boldsymbol{x}-\mathbf{1}}{(\boldsymbol{x}+\mathbf{2})^{2}} \)


The length of a wire of cross-sectional
\( \operatorname{area} 1 \times 10^{-6} m^{2} \) is \( 10 \mathrm{m} . \) The young's
modulus of the material of the wire is
25 G.pa. When the wire is subjected to a tensile force of \( 100 N \), the
elongation produced in \( m m \) is:
A . 0.04
B. 0.4
\( c \cdot 4 \)
D. 40


Choose the correct answers from the
alternatives given The classification category below the level of family is:
A . class
B. genus
c. phylum
D. species


The study of radioactive substances is
called:
A. Nuclear chemistry
B. Analytical chemistry
c. Radio active chemistry
D. Geo chemistry


What relation about elements did
Dobereiner want to establish?


If \( \tan \theta=\frac{-4}{3} \) then \( \sin \theta \) is
A \( \cdot \frac{-4}{5} \) but not \( \frac{-4}{3} \)
B. \( \frac{-4}{5} \) or \( \frac{4}{5} \)
c. \( \frac{4}{3} \) but not \( \frac{-4}{5} \)
D. None of thses.


Let \( * \) be a binary operation on \( N \) given by \( a * b=\operatorname{LCM}(a, b) \) for all \( a, b \in N \)
Find \( 5 * 7 \)


Lichen is a pioneer vegetation of
A. Hydrosere
B. Psammosere
c. Lithosere
D. Halosere


Explain the term - 'Hydrocarbons'


Magnetic susceptibility \( \chi \) of a paramagnetic material changes with
absolute temperature \( T \) as
A \( \cdot \chi \propto T^{-1} \)
B. \( x= \) constant
c. \( \chi \propto e^{r} \)
D. \( \chi \propto T \)


Which part of the photosynthetic process does not require light and temperature?
A. Hill's reaction
B. Blackman's reaction
c. warburg's reaction
D. Emerson's reaction


A cord is wound around the
circumference of a bicycle wheel
(without tyre) of diameter 1 m. A mass
of \( 2 k g \) is tied to the end of the cord and
it is allowed to fall from rest. The weight
falls \( 2 m \) in \( 4 s \). The axle of the wheel is
horizontal and the wheel rotates with its
plane vertical. The angular acceleration produced is:
\( \left(\operatorname{take} g=10 m s^{-2}\right) \)
A \( \cdot 0.5 \) rads\( ^{-2} \)
B. 1 rads\( ^{-2} \)
c. 2 rads \( ^{-2} \)
D. 4 rads \( ^{-2} \)


Consider the following equation for a
cell
\( \boldsymbol{A}+\boldsymbol{B} \rightleftharpoons \boldsymbol{C}+\boldsymbol{D} \)
\( \boldsymbol{E}^{o}= \)
\( \boldsymbol{X} \boldsymbol{v o l t}, \quad \boldsymbol{K}_{e q}=\boldsymbol{K}_{1} \)
\( \mathbf{2 A}+\mathbf{2 B} \rightleftharpoons \mathbf{2 C}+\mathbf{2 D} ; \quad \boldsymbol{E}^{\boldsymbol{o}}= \)
\( \boldsymbol{y} \) volt, \( \quad \boldsymbol{K}_{e q}=\boldsymbol{k}_{2} \)
A. \( X=y, K_{1}=K_{2} \)
B . \( X=2 y, K_{1}^{2}=K_{2} \)
C . \( X=y, K_{1}^{2}=K_{2} \)
D. \( X^{2}=y, K_{1}^{2}=K_{2} \)


The ratio of the mass of \( C-12 \) atom to
that of an atom of element \( X \) (whose
atomicity is four) is \( 1: 9 . \) The molecular mass of element X is :
A \( \cdot 480 \mathrm{gmol}^{-1} \)
в. 432 gmol-\( ^{-1} \)
c. \( 36 g m o l^{-1} \)
D. \( 84 ~ g m o l^{-1} \)


A solenoid of inductance \( L \) carrying a certain current is linked with a total
magnetic flux \( \phi \). Now it is connected to a condenser with which it shares half of its initial energy. The total flux now linked with the solenoid is:
\( A \cdot \frac{\phi}{2} \)
в. \( \frac{\phi}{\sqrt{2}} \)
\( c \cdot \frac{\phi}{2 \sqrt{2}} \)
D.


A ring of mass \( m \) and radius r rolls on an inclined plane. A torque is produced in the ring due to
A. mgsin\theta and the radius of the ring
B. the perpendicular distance between the force and the point of contact and the force \( m g \) acting on it
c. the perpendicular distance between the force and the point of contact and the normal force acting on the object
D. the perpendicular distance between the force and the point of contact and the force \( m g \sin \theta \) acting on it


Write the structural formulae for the
compounds that yield the following products on reductive ozonolysis:
penta-3-one + glyoxal + propanal


The purpose of soft iron cylinder
between the pole pieces of the horse-
shoe magnet in a moving
coil galvanometer is
A. to increase the magnetic induction in the polar
\( \operatorname{gap} \)
B. to evenly distribute the magnetic lines of force
C. to provide a radial magnetic field
D. to reduce the magnetic flux leakage in the polar
\( \operatorname{gap} \)


Birds produce sound by using:
A. vocal chord
B. larynx
c. glottis
D. syrinx


A transformer with turns ratio \( \frac{N_{1}}{N_{2}}= \) \( \mathbf{5 0} \)
\( \frac{w}{1} \) is connected to a 120 volt \( A C \) supply
If primary and secondary circuit resistance are \( 1.5 k \Omega \) and \( 1 \Omega \)
respectively then find out power out put
A \( .5 .76 \mathrm{w} \)
B. \( 11.4 \mathrm{w} \)
c. \( 2.89 \mathrm{w} \)
D. \( 7.56 \mathrm{w} \)


If a conducting rod of length \( 4 l \) is
rotated about at point \( \boldsymbol{O} \) in a uniform
magnetic field \( B \) directed into the
paper and \( D E=l, E A=3 l \), then which
of the folowing is true?
\[
\begin{array}{rrrrrrrrrr}
\times & \times & \times & \times & \times & \times & \times & \times & \times & \times & \times \\
\times & \times & \times & \times & \times & \times & \times & \times & \times & \times & \times \\
\times & \times & \times & \times & \times & \times & \times & \times & \times & \times & \times \\
\times & \times & \times & \times & \times & \times & \times & \times & \times & \times & \times \\
\times & \times & \times & \times & \multicolumn{1}{c} {\omega_{M}} & \times & \times & \times & \times & \times \\
\multicolumn{1}{c} {\times} & \times & \times & \times E_{\times} & & \times & \times & \times & \times & \times \\
\times & \times & \times & \times & \times & \times & \times & \times & \times & \times & \times \\
\times & \times & \times & \times & \times & \times & \times & \times & \times & \times & \times \\
\times & \times & \times & \times & \times & \times & \times & \times & \times & \times & \times
\end{array}
\]
A.
\[
V_{A}-V_{E}=\frac{9}{2} B \omega l^{2}
\]
B.
\[
V_{E}-V_{A}=\frac{9}{2} B \omega l^{2}
\]
\( \mathbf{c} \)
\[
V_{D}-V_{E}=\frac{B \omega l^{2}}{2}
\]
D. \( V_{A}-V_{E}=4 B \omega l^{2} \)


A thin semicircular conducting ring of
radius \( \mathrm{R} \) is falling with its plane vertical
in a horizontal magnetic field B. At the
position MNQ, the speed of the ring is \( \mathbf{v} \) and the potential difference across the
ring is
A. zero
B \( \cdot \frac{1}{2} B v \pi R^{2} \) and \( \mathrm{M} \) is at higher potential
\( \mathrm{c} . \pi R B v \) and \( \mathrm{Q} \) is at higher potential
D. \( 2 R B v \) and \( Q \) is at higher potential


Assertion
Generally, covalent compounds are gases, liquids or soft solids at room temperature.
Reason
Between covalent compounds Vander
Waals forces of attractions exists
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 term of the progression
\( 250,240,230 \ldots \ldots \) is the first negative
term?


\( \frac{-8}{11}+\frac{-4}{11}=\frac{p}{11} \)
then
\( \boldsymbol{p}=? \)


\( \int_{0}^{\pi / 2} \frac{\sin x d x}{(\sin x+\cos x)^{2}}= \)
A \( \cdot \sqrt{2} \log (\sqrt{2}+1) \)
B \( \cdot \frac{1}{\sqrt{2}} \log (\sqrt{2}+1) \)
\( \mathbf{c} \cdot 2 \log (\sqrt{2}+1) \)
D \( \frac{1}{2 \sqrt{2}} \log (\sqrt{2}+1) \)


What is the area enclosed by \( |x|+ \) \( |\boldsymbol{y}|=\mathbf{1} ? \)
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c .3 \)
D. 4


If \( 2 \bar{a}-4 \hat{i}-2 \widehat{j}+\widehat{k}=0 \) then find \( \bar{a} \)
\( \mathbf{A} \cdot 2 \bar{j}+\overline{\mathbf{k}} \)
B . \( 2 \hat{i}+\hat{j}-\frac{1}{2} \widehat{k} \)
c. \( 2 \bar{i}+\overline{\mathbf{j}} \)
D. \( 2 \overline{i-j} \)


All living organisms are made up of
A. Blood
B. Cells
c. water
D. All of the above


The value of the equilibrium constant
for the reaction
\( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{I}_{2}(\boldsymbol{g}) \rightleftharpoons 2 \boldsymbol{H} \boldsymbol{I}(\boldsymbol{g}) \)
at \( 720 \mathrm{K} \) is \( 48 . \) What is the value of the
equilibrium constant for the following
reaction?
\( \frac{1}{2} \boldsymbol{H}_{2}(\boldsymbol{g})+\frac{1}{2} \boldsymbol{I}_{2}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{H} \boldsymbol{I}(\boldsymbol{g}) \)


Secondary growth occur in which Pteridophyte?
A . Azolla
B. Salvinia
c. Isoetes
D. Selaginella


Which are the sources of phenol?
This question has multiple correct options
A. Cumene
B. Hydrolysis
C. Middle oil of coal tar distillation
D. Reaction of diazonium salt with \( H_{3} P O_{2} \)


Write primary and secondary valency of \( \boldsymbol{C o} \operatorname{in}\left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{n}_{\boldsymbol{3}}\right)_{\boldsymbol{6}}\right] \boldsymbol{C l}_{3} ? \)


If \( \hat{i}, \hat{j} \) and \( \widehat{k} \) are unit vectors along \( \mathbf{x}, \mathbf{y} \) and z axes respectively. the angle \( \theta \) between the vector \( \hat{\mathbf{i}}+\widehat{\mathbf{j}}+\widehat{\boldsymbol{k}} \) and vector
\( \widehat{\boldsymbol{i}} \)
A \( \cdot \theta=\cos ^{-1}\left(\frac{1}{\sqrt{3}}\right) \)
В \( \cdot \theta=\sin ^{-1}\left(\frac{1}{\sqrt{3}}\right) \)
C \( \cdot \theta=\cos ^{-1}\left(\frac{\sqrt{3}}{2}\right) \)
D. \( \theta=\sin ^{-1}\left(\frac{\sqrt{3}}{2}\right) \)


A bullet of mass \( \mathrm{X}, \) moving with a velocity \( V \), strikes a wooden block of mass \( Z \) and gets embedded. If the block
is free to move, its velocity after impact will be.
A \( \cdot \frac{X}{X+Z} \mathrm{v} \)
в. \( \frac{X+Z}{Z} \vee \)
c. \( \frac{x}{x-Z} V \)
D. \( \frac{X+Z}{X} V \)


What is the basis for classification?


The amount of heat required to raise the temperature of a body by \( 1^{0} \mathrm{C} \) is
called
A . latent heat
B. specific heat
c. thermal capacity
D. none of these


State whether given statement is True or False.

Centre of gravity of a freely suspended body always lies vertically below the point of suspension.
A. True
B. False


Evaluate the given integral: \( \int_{0}^{1} x^{4} d x \)


The water temperature should
preferably be less than \( _{--} \) degree
Celsius.
A . 10
B. 25
c. 15
D. 30


One half of slab of ice is covered with
black cloth and the other half with white
cloth. This is then placed in sunlight. After some time the pieces of cloth are removed. Then
A. ice has melted equally under both the pieces.
B. more ice has melted under white cloth
c. more ice has melted under black cloth.
D. it will depend on the medium in which ice is placed


Find the differential equation of \( \boldsymbol{y}= \)
\( \boldsymbol{a} e^{3 x}+\boldsymbol{b} e^{3 x} \)


A bag contains 6 red balls and 8 green balls. A ball is drawn at random. What
is the probability that the ball is green


If vector \( \vec{a}=4 \hat{i}+5 \hat{j}-3 \hat{k} \) and \( \vec{b}=5 \hat{i}+ \)
\( 3 \hat{j}+8 \hat{k} \) then value of \( \frac{\text { projection of vector b on a }}{\text { projection of vector a on b }} \) is :
A \( \cdot \frac{7}{5} \)
B. \( \frac{2}{7} \)
\( c \cdot \frac{5}{8} \)
D. None of these.


\( \triangle L M N \sim \triangle X Y Z . \ln \triangle L M N, L M= \)
\( 6 \mathrm{cm}, M N=6.8 \mathrm{cm}, L N=7.6 \mathrm{cm} \) and
\( \frac{L M}{X Y}=\frac{4}{5} ; \) Construct \( \triangle X Y Z \)


When a person suffers from a marked
fall in blood pressure, it is helpful to administer the hormone:
A. thyroxine
B. adrenaline
c. insulin
D. parathormone


Which mineral has been
named incorrectly?
A. Bauxite \( : A l_{2} O_{3} \cdot 2 H_{2} O \)
B. Corundum: \( A l_{2} O_{3} \)
C . Cryolite \( : 3 \mathrm{NaF} \cdot \mathrm{AlF}_{3} \)
D. Feldspar: \( B e_{3} A l_{2} S i_{5} O_{18} \)


For an electromagnetic radiation,
A. only momentum is quantised
B. only energy is quantised
C. both energy and momentum are quantised
D. neither of them is quantised


A bulb emits light of wavelength \( \lambda= \) \( 4500 A \). The bulb is rated as 150 watt
and \( 8 \% \) of the energy is emitted as light. How many photons are emitted by the bulb per second?


\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C O O A} \boldsymbol{g}+\boldsymbol{B r}_{2} \stackrel{\boldsymbol{C C l}_{4}}{\longrightarrow} \)
\( \boldsymbol{X} \stackrel{\boldsymbol{a q} \cdot \boldsymbol{K O H}}{\longrightarrow} \boldsymbol{Y} \stackrel{\boldsymbol{r e d} \boldsymbol{P}_{4} / \boldsymbol{B} \boldsymbol{r}_{2}}{\longrightarrow} \boldsymbol{Z} \)
\( Z \) is:
A \( \cdot C H_{3} C H_{2} C H_{2} B r \)
в. \( C H_{3} C H_{2} B r \)
c. \( C H_{3} B r \)
D. \( C H_{3} C H_{2} C H_{3} \)


A uniform meter scale can be balanced
at the \( 70.0 \mathrm{cm} \) mark when a mass
\( 0.05 k g \) is hung from the \( 94.0 c m \) mark.
Find the mass of the metre scale :
\( \mathbf{A} \cdot 6 k g \)
в. \( 0.06 \mathrm{kg} \)
c. \( 0.07 \mathrm{kg} \)
D. \( 60 \mathrm{kg} \)


The total number of neutrons in all
isotopes of hydrogen is equal to:
A. 6
B. 2
\( c \cdot 4 \)
D.


Methyl phenyl ether can be obtained by reacting:
A. Phenolate ions and methyl iodide
B. Bromobenzene with methoxide ions
c. Methanol and phenol
D. Bromobenzene and methyl iodide


A baseball of mass \( 200 \mathrm{g} \) is moving with velocity \( 30 \times 10^{2} \mathrm{cm} / \mathrm{s} \). If we can locate
the baseball with an error equal in
magnitude to the \( \lambda \) of the light used \( \mathbf{5 0 0 0} \boldsymbol{A} \), then the uncertainty in
momentum compared with the total momentum of base ball is:
A \( .1 .75 \times 10^{-29} \)
В. \( 1.34 \times 10^{-29} \)
c. \( 1.89 \times 10^{-29} \)
D. \( 2.03 \times 10^{-29} \)


Which of the following rotates the plane of plane polarised light?
A. Compound which is having enantiomeric excess
B. Diastereomers
c. Racemic mixture
D. None


Two particles of masses \( m_{1} \) and \( m_{2} \) in
projectile motion have velocities \( \bar{v}_{1} \) and
\( \overline{\boldsymbol{v}}_{2} \) respectively at time \( \boldsymbol{t}=\mathbf{0} . \) They
strike at time \( t_{0} \) and their velocities
become \( \overline{v^{\prime}}_{1} \) and \( \overline{v^{\prime}}_{2} \) at time \( 2 t_{0} \) while
still moving in air. The value of
\( \left|\left(\boldsymbol{m}_{1} \overline{\boldsymbol{v}^{\prime}}_{1}+\boldsymbol{m}_{2} \overline{\boldsymbol{v}^{\prime}}_{2}\right)-\left(\boldsymbol{m}_{1} \overline{\boldsymbol{v}}_{1}+\boldsymbol{m}_{2} \overline{\boldsymbol{v}}_{2}\right)\right| \) is
\( \mathbf{A} \cdot z \) ero
\( \mathbf{B} \cdot\left(m_{1}+m_{2}\right) g t_{0} \)
\( \mathbf{c} \cdot 2\left(m_{1}+m_{2}\right) g t_{0} \)
D \( \cdot \frac{1}{2}\left(m_{1}+m_{2}\right) g t_{0} \)


The ratio of the wavelength for \( 2 \rightarrow 1 \)
transition in \( L i^{+}, H e^{+} \) and \( H \) is :
A .1: 2: 3
B. 1: 4: 9
c. 4: 9: 36
D. 3: 2: 1


In a given figure,ABCD is a trapezium in
which the parallel sides \( A B \) and \( C D \) are
both perpendicular to BC.If \( \boldsymbol{A B}= \)
\( \mathbf{1 6}, \boldsymbol{A D}=\mathbf{1 7} \) and \( \boldsymbol{C D}=\mathbf{8}, \) then \( \mathbf{B C} \) is
A .15
B. 25
\( c .25 .5 \)
0.39


The activity of radioactive sample is
measured as 9750 counts per minute at \( t=0 \) and as 975 counts per minute
at \( t=5 \) minutes, the decay constant is
approximately
A . 0.922 per minute
B. 0.270 per minute
c. 0.461 per minute
D. 0.39 per minute


Show that \( f(x)=\frac{-x^{3}}{3}-x^{2}-x+7 \) is
always increasing in \( \mathrm{R} \).


Let the algebraic sum of the perpendicular distance from the points (2,0)(0,2) and (1,1) to a variable straigth line be zero, then the passes through a fixed point whose coordinates
are........ Find the condition on \( a \) and \( b \)
such that the portion of thelineax \( + \)
\( b y-1=0, \) intercepted between the
line axis.


\( \boldsymbol{C}_{4} \boldsymbol{H}_{10}(\boldsymbol{g})+\frac{13}{2} \boldsymbol{O}_{2}(\boldsymbol{g}) \longrightarrow \boldsymbol{4} \boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g})+ \)
\( \mathbf{5} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l}) ; \boldsymbol{\Delta} \boldsymbol{H}=-\mathbf{2} \mathbf{8} \mathbf{7} \mathbf{8} \boldsymbol{k} \boldsymbol{J} \)
\( \Delta H \) is the heat of combustion of
butane gas.If true enter 1 else 0
\( A \)


If the length of the side of the cube is doubled, then the ratio of the volume of
the new cube and the orignal cube is
A .1: 2
B . 2: 1
c. 4: 1
D. 8: 1


\( \lim _{x \rightarrow 0} \frac{\sqrt{2}-\sqrt{1+\cos x}}{\sin ^{2} x} \) equals
A \( \cdot \sqrt{2} \)
B. \( \frac{\sqrt{2}}{8} \)
c.
D. none of these


\( \int e^{x}\left(\sec ^{2} x+\tan x\right) d x \)


A liquid is flowing in a horizontal uniform capillary tube under a constant
pressure difference p. The value of pressure for which the rate of flow of the
liquid is doubled when the radius and length both are doubled, is
\( A \cdot \rho \)
в. \( \frac{3 \rho}{4} \)
c. \( \frac{\rho}{2} \)
D. \( \frac{\rho}{4} \)


0
0
\( \widehat{O} \)
\( \widehat{O}_{\operatorname{actg}}^{a k} \)
\( \widehat{O}^{a_{b}} \)


There is no resistance in the inductive
circuit. Kirchhoff's voltage law for the
circuit is
A \( \cdot V+L \frac{d i}{d t}=0 \)
B. \( v=L \frac{d i}{d t} \)
\( ^{\mathbf{C}} \cdot V-L^{2} \frac{d i}{d t}=0 \)
D. None of these


If \( \vec{a}=\hat{i}+2 \hat{j}-3 \hat{k}, \vec{b}=2 \hat{i}+\hat{j}-\hat{k} \) and
\( \vec{u} \) is a vector satisfying \( \overrightarrow{\boldsymbol{a}} \times \overrightarrow{\boldsymbol{u}}=\overrightarrow{\boldsymbol{a}} \times \overrightarrow{\boldsymbol{b}} \)
and \( \vec{a} \cdot \vec{u}=0, \) then \( 2|\vec{u}|^{2} \) is equal to
A. 5
B. 4
\( c \cdot 8 \)
D. None of these


Which of the following metal fall under platinum group?
A . Silver
B. Osmium
c. Rhodium
D. Both b and


Match the column
\( \begin{array}{lllll}\text { Sr.No } & \text { a } & \text { b } & \text { c } & \\ \text { (i) } & + & + & \text { (1) Commensalism } \\ \text { (ii) } & + & - & \text { (2) Competition } \\ \text { (iii) } & - & - & \text { (3) Parasitism } \\ \text { (iv) } & + & \text { 0 } & \text { (4) mutualism }\end{array} \)
\( A \)
\( (i) 1,(i i) 2,(i i i) 3,(i v) 4 \)
B. \( (i) 2,(i i) 3,(i i i) 1,(i v) \)
C . \( (i) 4,(i i) 3,(i i i) 2,(i v) 1 \)
\( D \)
\( (i) 3,(i i) 2,(i i i) 1,(i v) \)


In above shown figure, two speaker, \( \boldsymbol{S}_{1} \)
and \( S_{2} \) are kept at \( 3 \mathrm{m} \) apart. Speakers emit a sound wave of wavelength of \( \mathrm{m} \) Emitted waves are in phase with each other. Compare the amplitude of
resulting wave at point \( P \) and \( Q \) if \( A_{P} \)
and \( A_{Q} \) resulted amplitude at point \( P \) and \( Q \) respectively.
A. \( A_{P}<A_{Q} \)
в. \( A_{P}=A_{Q} \)
c. \( A_{P}>A_{Q} \)
D. \( A_{P}<0, A_{Q}>0 \)
E. \( A_{P} \) and \( A_{Q} \) vary with times, so no comparison can be made


If the temperature of a wire of length
\( 2 m \) area of cross-section \( 1 \mathrm{cm}^{2} \) is
increased from \( 0^{\circ} C \) to \( 80^{\circ} C \) and is not
allowed to increase in length, then force
required for it is \( \left\{\boldsymbol{Y}=\mathbf{1 0}^{\mathbf{1 0}} \boldsymbol{N} / \boldsymbol{m}^{2}, \boldsymbol{\alpha}=\right. \)
\( \left.10^{-6} /^{o} C\right\} \)
A . \( 80 N \)
в. \( 160 N \)
c. \( 400 N \)
D. \( 120 N \)


The Lenz's law gives:
A. direction of induced current
B. magnitude of induced emf
C . magnitude of induced current
D. magnitude and direction of induced current


Find force \( \boldsymbol{F} \) required to keep the system in equilibrium. The dimensions
of the system are \( \boldsymbol{d}=\mathbf{0 . 3 m} \) and \( \boldsymbol{a}= \)
\( 0.2 m . \) Assume the rods to be massless
A . \( 150 \mathrm{N} \)
B. -150 N
c. \( 100 \mathrm{N} \)
D. It cannot be in equilibrium


Which of the following compounds are
formed when \( B C l_{3} \) is treated with
water?
A. \( H_{3} B O_{3} \)
в. \( B_{2} H_{6} \)
\( \mathbf{c} \cdot B_{2} O_{3} \)
D. \( H B O_{2} \)


For motion of an object along the \( x \) -axis,
the velocity v depends on the
displacement \( x \) as \( v=3 x^{2}-2 x, \) then
what is the acceleration at \( x=2 m \)
A. \( 48 \mathrm{ms}^{-2} \)
B . \( 80 \mathrm{ms}^{-2} \)
c. \( 18 m s^{-2} \)
D. \( 10 m s^{-2} \)


7 boys and 8 girls have to sit in a row on
15 chairs numbered from 1 to 15 then?
A. Number of ways boys and girls sit alternately is \( 8 ! 7 ! \)
B. Number of ways boys and girls sit alternately is \( 2(8 ! 7 !) \)
C. The number of ways in which first and fifteenth chair are occupied by boys and between any two boys an even number of girls sit is \( ^{9} C_{4} 8 ! 7 ! \)
D. The number of ways in which first and last seat are occupied by boys and between any two boys an even number of girls sit is \( \left(2^{9} C_{4} 8 ! 7 !\right) \)


If \( \sin ^{-1} x+\sin ^{-1} y=\frac{\pi}{2}, \) then \( \frac{d y}{d x} \) is
equal to
A \( \cdot \frac{x}{y} \)
в. \( -\frac{x}{y} \)
c. \( \frac{y}{x} \)
D. \( -\frac{y}{x} \)


Barometer can be used to forecast the
weather by checking pressure fluctuations. Type 1 for true and 0 for
false


In \( \triangle A B C, A C^{2}=A B^{2}+B C^{2}, \) then
right angle is at


Conjugate base of a strong acid is:
A. a weak base
B. a strong base
c. neutral
D. a weak acid


If radius of a sphere is doubled, how
many times its volume will be affected
A. 2 times
B. 4 times
\( c .6 \) times
D. 8 times


Give the structural formula of the
following.
1-Propanal


Which one of the following would not be limiting factor in photosynthesis?
\( A \cdot O_{2} \)
в. \( C O_{2} \)
c. chlorophyll
D. Light


How do ultraviolet rays coming from sun affect the living organisms?


Solve the following systems of equations:
\( \frac{1}{2 x}+\frac{1}{3 y}=2 \)
\( \frac{1}{3 x}+\frac{1}{2 y}=\frac{13}{6} \)


speed of \( 340 \mathrm{m} \mathrm{s}^{-1} \). The wavelength of
the wave is :
\( \mathbf{A} \cdot 1.5 \times 10^{5} m \)
B. 0.77 \( m \)
\( \mathbf{c} .1 .4 \mathrm{m} \)
D. 1.1


If the glancing angle of incidence is \( 30^{\circ} \) what will be the angle of incidence?
A . \( 30^{\circ} \)
B. \( 60^{\circ} \)
\( \mathrm{c} \cdot 90^{\circ} \)
D. \( 150^{\circ} \)


541
negligible resistance and radius \( a \). It is
hinged at the center of the ring and
rotated about this point in clockwise
direction with a uniform angular
velocity \( \omega . \) There is a uniform magnetic
field of strength \( B \) pointing inward and
\( r \) is a stationary resistance. Then
This question has multiple correct options
A. current through \( r \) is zero
B. current through \( r \) is \( \left(2 B \omega a^{2}\right) / 5 r \)
c. direction of current in external resistance \( r \) is from
center to circumference
D. direction of current in external resistance \( r \) is from
circumference to center
E. answer required


A pump is used to pump a liquid of
density \( \rho^{\prime} \) continuously through a pipe
of cross section area \( A \). If liquid is
flowing with speed \( V \), then power of
pump is:
A \( \cdot \frac{1}{3} \rho A V^{2} \)
B. \( \frac{1}{2} \rho A V^{2} \)
с. \( 2 \rho A V^{2} \)
D \( \cdot \frac{1}{2} \rho A V^{3} \)


\( \operatorname{Let} f(x)=\left\{\begin{array}{cc}x^{2} & x<1 \\ x & 1<x<4, \text { then } \\ 4-x & x>4\end{array}\right. \)
This question has multiple correct options
A \( \cdot \lim _{x \rightarrow 1^{-}} f(x)=1 \)
B. \( \lim _{x \rightarrow 1^{+}} f(x)=1 \)
\( \mathbf{c} \cdot \lim _{x \rightarrow 4^{-}} f(x)=4 \)
D. \( \lim _{x \rightarrow+4^{+}} f(x)=4 \)


A fair coin and an unbiased die are
tossed. Let \( A \) be the event 'head appears
on the coin' and \( B \) be the event '3 on the
die'. Check whether \( A \) and \( B \) are
independent events or not.
A. True
B. False


Give two examples of water soluble
vitamins.


Diaphragms are used by
A. Male
B. Females
c. Both A and B
D. None of the above


Bleaching powder is not used:
A. as a disinfectent
B. as a reducing agent
C . for bleaching purpose
D. for manufacturing chloroform


In the Ostwald's process for the
manufacture of \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3}, \) the catalyst
used is:
A . \( F e \)
в. \( P t \)
\( c \cdot V_{2} O_{5} \)
D. \( M o \)


Solve the following pairs of equations, graphically:
\( 2 x-3 y=-6 \) and \( x-\frac{y}{2}=1 \)
\( \mathbf{A} \cdot(3,2) \)
в. (3,3)
c. (4,4)
D. (3,4)


Identify the metal \( M \)
A. Calcium
B. Sodium
\( c . \) zinc
D. Iron


\( \left|\begin{array}{ccc}x^{2}+x & x+1 & x+2 \\ x^{2}+3 x-1 & 3 x & 3 x-3 \\ x^{2}+2 x+3 & 2 x-1 & 2 x-1\end{array}\right|= \)
\( A x+B \) where \( A \) and \( B \) are
determinants of order \( 3 . \) Then \( A+2 B \) is
equal to


Which of the following does not produce
\( \mathrm{H}_{2} \) at the anode on electrolysing using
Pt electrode?
This question has multiple correct options
A . molten CaH \( _{2} \)
B. \( N a C l(a q) \)
\( c \cdot \operatorname{cus} 0_{4}(a q) \)
D. \( \operatorname{dil} \mathrm{H}_{2} \mathrm{SO}_{4} \)


In spectrum obtained with prism which color is deviated maximum?
A . Violet
B. Redd
c. Green
D. orange


Assertion
In adiabatic process work is
independent of path.
Reason
In adiabatic process work done is equal to negative of change in internal energy.
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


Let \( f(x) \) be a function satisfying
\( f^{\prime}(x)=f(x)=e^{x} \) with \( f(0)=1 \) and
\( g(x) \) be a function that satisfies \( f(x)+ \)
\( g(x)=x^{2} . \) Then, the value of the integral \( \int_{0}^{1} f(x) g(x) d x \) is
\( ^{A} \cdot_{e}+\frac{e^{2}}{2}-\frac{3}{2} \)
B. \( _{e}-\frac{e^{2}}{2}-\frac{3}{2} \)
c. \( _{e}+\frac{e^{2}}{2}+\frac{5}{2} \)
D. \( _{e}-\frac{e^{2}}{2}-\frac{5}{2} \)


\( L, C \) and \( R \) represents the physical quantities, inductance, capacitance and resistance respectively. The
combinations which have the
dimensions of frequency are:
A. \( 1 / R C \)
в. \( R C / L \)
c. \( 1 / \sqrt{L R C} \)
D. \( C / L \)


If \( (x+3,4-y)=(1,7), \) then \( (x- \)
\( \mathbf{3}, \mathbf{4}+\boldsymbol{y}) \) is equal to
A \( \cdot(-2,-3) \)
в. (-5,1)
c. (3,4)
(年. \( (3,4)) \)
D. None of these


The Venn diagram shows the sets
\( \boldsymbol{\xi}, \boldsymbol{P}, \boldsymbol{Q} \) and \( \boldsymbol{R} \). Which of the following is
not true?
\( \mathbf{A} \cdot P \cap Q \neq \phi \)
в. \( R \subset Q \)
\( \mathbf{c} \cdot(P \cap R) \subset Q \)
D. \( (P \cap Q)=R \)


Write the units digit of the cube of 833
\( A \cdot 3 \)
B. 7
\( c .1 \)
D.


There is a transition from \( n=1 \) to \( n=2 \)
and then \( n=2 \) to \( n=3, \) then:
A. \( \Delta E \) values as well as frequency are additive
B. wave length as well as frequency are additive
c. \( \Delta E \) values as well as wavelength are additive
D. all of the parameters, \( (\Delta E, \) frequency and wave length are additive


Evolution of man took place in
A. Central Africa
B. Central Asia
c. Australia
D. America


Evaluate: \( \int \sec x \tan x d x \)


What is \( \Delta_{r} G(k J / \text { mole }) \) for synthesis of ammonia at \( 298 \mathrm{K} \) at following sets of
partial pressure :
\( N_{2}(g)+3 H_{2}(g) \rightleftharpoons \)
\( \mathbf{2} N \boldsymbol{H}_{3}(\boldsymbol{g}) ; \boldsymbol{\Delta}_{r} \boldsymbol{G}^{\circ}=-\mathbf{3 3} \boldsymbol{k} \boldsymbol{J} / \boldsymbol{m o l} \)
\( [\text { Take } \boldsymbol{R}=\mathbf{8 . 3} \boldsymbol{J} / \boldsymbol{K} \text { mole, } \log \mathbf{2}= \)
\( \mathbf{0 . 3} ; \log \mathbf{3}=\mathbf{0 . 4 8} \)
Gas \( \quad: N_{2} \quad H_{2} \quad N H_{3} \)
Pressure (atm) : 1
3
A \( .+6.5 \)
B . -6.5
c. +60.5
D. - 60.5


The half-life period of an 1st order reaction is 60 minutes. What
percentage will be left over after 240
minutes?
\( \mathbf{A} \cdot 6.25 \% \)
B. \( 4.25 \% \)
c. \( 5 \% \)
D. \( 6 \% \)


A point source of light, \( \mathrm{S} \) is placed at a distance \( L \) in front of the centre of plane mirror of width d which is hanging vertically on a wall. A man walks in front of the mirror along a line parallel to the mirror, at a distance \( 2 L \) as shown
below. The distance over which the man
can see the image of the light source in the mirror is :
A . \( 3 d \)
B. \( \frac{d}{2} \)
\( c \cdot d \)
D. \( 2 d \)


The M.I of a thin rod of length \( l \) about
the perpendicular axis trough its center
is \( I_{0} . \) The M.I of the square structure
made by four such rods about a perpendicular axis to the the plane and through the center will be :-
A \( .4 I_{0} \)
в. \( \frac{8}{3} I_{0} \)
c. \( \frac{4}{3} I_{0} \)
D. \( 6 I_{0} \)


Identify the odd one out:
Barium, Radium, Calcium, Francium


What is myopia? How does it occur? How can it be corrected? Explain with
figure.


Define Electromagnetism
A. The study of attraction or repulsion between two magnets is called electromagnetism
B. The study of electric effects due to magnetic interaction is called electromagnetism
C. The study of magnetic effects produced due to electric current is called electromagnetism
D. The study of magnetic effects produced due to electric charge is called electromagnetism


toppr
Q Type your question
graph correctly shows the momentum
of the blue object in each case. The red
graphs are all different.
Which graph best represents the
possible momentum of the red object before, during, and after the collision?
\( A \)
\( B \)
\( c \)
\( D \)
E


If a cathode ray tube has a potentia
difference \( V \) volt between the cathode
and anode, then the speed \( v \) of cathode
rays is given by:
A \( \cdot v \propto V^{2} \)
В. \( v \propto \sqrt{V} \)
\( ^{\mathrm{c}} \cdot_{v} \propto \frac{1}{V} \)
D. \( v \propto V \)


\( \frac{\pi}{4} \)


Find the eccentricity of an ellipse, if its
latus rectum be equal to one half its
minor axis.


\( N a_{2} S O_{3} \cdot x H_{2} O \) has \( 50 \% H_{2} O \) by mass.
Hence, \( x \) is:
A .4
B . 45
\( c \cdot 6 \)
D.


How is a pinnately compound leaf
different from a palmately compound
leaf?


Hydrogen peroxide is obtained by the electrolysis of
A. water
B. sulpharic acid
c. hydrochoric acid
D. fused sodium


If the area of the region bounded by the curves, \( \boldsymbol{y}=\boldsymbol{x}^{2}, \boldsymbol{y}=\frac{\mathbf{1}}{\boldsymbol{x}} \) and the lines
\( \boldsymbol{y}=\mathbf{0} \) and \( \boldsymbol{x}=\boldsymbol{t}(\boldsymbol{t}>\mathbf{1}) \) is \( \mathbf{1} \) sq. unit
then \( t \) is equal to?
A \( \cdot \frac{4}{3} \)
В. \( e^{2 / 3} \)
\( c \cdot \frac{3}{2} \)
\( \mathbf{D} \cdot e^{3 / 2} \)


If \( (5+2 \sqrt{6})^{n}=m+f \), where \( n \) and \( m \)
are positive integers and \( 0 \leq f<1 \)
then
\( \frac{1}{1-f}-f \) is equal to
A \( \cdot \frac{1}{m} \)
в. \( m \)
c. \( _{m+\frac{1}{m}} \)
D. \( _{m-} \frac{1}{m} \)


In simple distillation of liquids, it involves simultaneously.
A. Vaporisation and condensation
B. Heating and sublimation
c. vaporisation and sublimation
D. Boiling and filtration


Two charges \( 4 \mu C \) and \( 36 \mu C \) are placed \( 60 \mathrm{cm} \) apart. At what distance from the
larger charge is the electric field
intensity is zero?


Describe with the help of a diagram an
instrument which can be used to detect
a charged body.


Name the macromolecules that are
chosen as drug targets.


Consider a p-njunction as a capacitor, formed with \( p \) and \( n \) material acting as thin metal electrodes and depletion layer width acting as separation between them. Based on this,
assume that an n-p-n transistor is working as a amplifier in CE
configuration. If \( C_{1} \) and \( C_{2} \) be base-
emitter and collector-emitter
junction capacitances, then
A \( \cdot C_{1}>C_{2} \)
B. \( C_{1}<C_{2} \)
\( \mathbf{c} \cdot C_{1}=C_{2} \)
\( \mathbf{D} \cdot C_{1}=C_{2}=0 \)


If different values of variable \( x \) are
\( 9.8,5.4,3.7,1.7,1.8,2.6,2.8,8.6,10.5 a r \)
find the mean.
A . 5.8
B. 7.8
\( \mathrm{c} .9 .8 \)
D. None of these


The initial speed with which water flows out from the orifice in \( \mathrm{ms}^{-1} \) is \( \mathrm{g} \)
\( \left.=10 \mathrm{ms}^{-2}\right) \)
A . 10
B. 5
\( c \cdot 5 \cdot \sqrt{2} \)
D. \( 10 . \sqrt{2} \)


The multiple bonds that nitrogen forms
with itself are:
\( \mathbf{A} \cdot d \pi-d \pi \) bonds
В. \( d \pi-p \pi \) bonds
C. \( p \pi-p \pi \) bonds
D. none of the above


Sketch for \( \boldsymbol{y}=\cos ^{-1}\left(\frac{1-x^{2}}{1+x^{2}}\right) \)


If \( E_{1}, E_{2} \) and \( E_{3} \) are the respective kinetic energies of an electron, an alpha particle and a proton each having the same de Brogli wavelength then
A. \( E_{1}>E_{3}>E_{2} \)
B . \( E_{2}>E_{3}>E_{1} \)
c. \( E_{1}>E_{2}>E_{3} \)
D. \( E_{1}=E_{2}=E_{3} \)


Quiescent centre is found on
A. Root tip
B. Shoot tip
C. Floral tip
D. Leaf tip


In onion root tip during mitotic metaphase, the number of kinetochores
is
\( A \cdot 4 \)
B. 64
\( c \cdot 32 \)
D. 16


The energy of thermal neutrons is nearly
A \( .0 .25 \mathrm{eV} \)
B. \( 0.025 \mathrm{eV} \)
c. \( 200 \mathrm{MeV} \)
D. 0.025 Joule


State whether true or false:
When light falls on a prism the result can be magnification.
A. True
B. False


Match the following with reference to
Taenia solium.
List-I List-II
(A) Mehlis
(I) Tegument formation glands
(B) Vitelline
(II) Osmoregulation and gland excretion
\( (C) \)
(III) Lubricate passage of Mesenchymal capsules into uterus cel
(D) Flame
(IV) Secretion of embryophore cells
(V) Capsule formation around zygote
\( A \cdot A-(111), B-(V), C-(11), D-(1 V) \)
B. \( A-(V), B-(1), C-(11), D-(I V) \)
C \( \cdot A-(\mid V), B-(|I|), C-(1), D-(\mid I) \)
D. \( A-(111), B-(V), C-(1), D-(11) \)


\( H_{2} S \) a toxic gas with rotten egg like smell is used for the qualitative
analysis. If the solubility of \( H_{2} S \) in
water at STP is \( 0.195 m \), calculate
Henry's law constant.


Find the mode of the following
distribution
\begin{tabular}{llllll}
Daily & \( 31- \) & \( 37- \) & \( 43- \) & \( 49- \) & 55 \\
Wages & 36 & 42 & 48 & 54 & 6 \\
No. of workers & 6 & 12 & 20 & 15 & 9 \\
\hline
\end{tabular}
\( \mathbf{A} \cdot 48.5 \)
B. 47.5
c. 46.2
D. 48.3


Read the following information and answer the three items that follow:
Let \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2}+\boldsymbol{2} \boldsymbol{x}-\boldsymbol{5} \) and \( \boldsymbol{g}(\boldsymbol{x})= \)
\( 5 x+30 \)
What are the roots of the equation
\( \boldsymbol{g}[\boldsymbol{f}(\boldsymbol{x})]=\mathbf{0} ? \)
A . 1,-1
B. -1,-1
\( c .1,1 \)
D. 0,1


Solve by factorization \( \sqrt{\mathbf{3}} \boldsymbol{x}^{2}+\mathbf{1 1} \boldsymbol{x}+ \)
\( \mathbf{6} \sqrt{\mathbf{3}}=\mathbf{0} \)


Gurpreet bought a cycle for Rs. \( \mathbf{7 5 0 . 0 0} \)
The transport charges were Rs. 10. If he
sold the cycle for Rs. 798 , find his gain or loss.


\( \boldsymbol{A}=\left[\begin{array}{ccc}\mathbf{1} & \mathbf{2} & \mathbf{3} \\ \mathbf{1} & \mathbf{2} & \mathbf{3} \\ \mathbf{- 1} & \mathbf{- 2} & \mathbf{- 3}\end{array}\right], \) then A is a
nilpotent matrix of index
\( A \)
B. 3
\( c \cdot 4 \)
D. 5


By which smallest number must the
following numbers be divided so that the quotient is a perfect cube?
\( \mathbf{3 5 7 2 1} \)


If Leah is 6 years older than Sue and
John is 5 years older than Leah and the total of their ages is \( 41 . \) Then how old is
Sue?
A . 8
B. 10
c. 14
D. 19
E . 21


Evaluate the following integral
\( \int \frac{1}{x(3+\log x)} d x \)


Compound X has the molecular formula
\( \boldsymbol{C}_{3} \boldsymbol{H}_{\boldsymbol{6}} \boldsymbol{O}_{3} \)
Heating X under reflux with acidified
\( K_{2} C r_{2} O_{7} \) forms \( H O_{2} C C O C O_{2} H \)
Reacting \( X \) with \( N a B H_{4} \) forms
\( \boldsymbol{H} \boldsymbol{O} \boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{C} \boldsymbol{H}(\boldsymbol{O} \boldsymbol{H}) \boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{O} \boldsymbol{H} \)
What is a possible structural formula
for \( X ? \)
1. \( \boldsymbol{H} \boldsymbol{O} \boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{C} \boldsymbol{O}_{2} \boldsymbol{H} \)
2. \( \boldsymbol{H} \boldsymbol{O} \boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{C H}(\boldsymbol{O} \boldsymbol{H}) \boldsymbol{C H O} \)
3. \( \boldsymbol{H} \boldsymbol{O} \boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{C O C H}_{2} \boldsymbol{O H} \)
A. 1,2 and 3 are correct
B. 1 and 2 only are correct
c. 2 and 3 only are correct
D. 1 only is correct


Draw a labeled ray diagram of a refracting telescope. Define its magnifying power and write the
expression for it. Write two important limitation of a refracting telescope over a reflecting type telescope


A cell of emf \( \boldsymbol{E} \) Volt with no internal
resistance is connected to a wire whose
cross section changes. The wire has
three sections of equal length. The
middle section has a radius \( a \), whereas
the radius of the outer two sections is
2a. The ratio of the potential difference
across section \( A B \) to the potential
difference across section \( C A \) is :
\( A \)
B. 4
\( c \cdot \frac{1}{2} \)
D.


For n moles of gas Vander waal's equation is \( \left(\boldsymbol{P}-\frac{\boldsymbol{a}}{\boldsymbol{V}^{2}}\right)(\boldsymbol{V}-\boldsymbol{b})=\boldsymbol{n} \boldsymbol{R} \boldsymbol{T} \)
Find the dimensions of a and b, where \( \mathrm{P} \)
is gas pressure, \( V= \) volume of gas \( T= \) temperature of gas


The system that forms maximum boiling azeotrope is :
A. acetone-chloroform
B. ethanol- acetone
C. n-hexane- n- heptane
D. carbon disulphide - acetone


If a conducting rod \( A B \) placed in a uniform magnetic field pointing in positive z-direction (as shown in figure), moves parallel to y-axis, then
end \( A \) of the rod will be
A. Neutral
B. Positively charged
c. Negatively charged
D. None of these


In a class \( 25 \% \) of the total students are
absent. If 45 students are presents, then what is the total strength of the class.


Number of bonding electrons and anti-
bonding electrons in \( 2 p \) MO of \( N_{2} \)
molecule are respectively:
A .6,2
в. 4,0
c. 6,0
D. 4,2


Write chemical equation to represent the most probable outcome in the following reaction and choose the
correct option.
\[
\boldsymbol{C d C O}_{3} \stackrel{\boldsymbol{\Delta}}{\rightarrow}
\]
A \( \cdot \mathrm{CdCO}_{3} \stackrel{\Delta}{\longrightarrow} \mathrm{Cd} \mathrm{O}+\mathrm{CO}_{2} \)
в. \( 2 \mathrm{CdCO}_{3} \) 오 \( 2 \mathrm{CdO}+2 \mathrm{CO}+\mathrm{O}_{2} \)
c. No reaction
D. None of these


Consider the following steps \( C u S \stackrel{\text {roastin air}}{\rightarrow} \)
\( (A) \)
\( \stackrel{\text {roast without ai}}{\rightarrow} \)
Which of the one is not the
correct statement?
A. It is self-reduction
B. It involves disproportionation \( C u_{2} S \rightarrow C u+C u S \)
\( c \cdot(A) \) is a mixture of \( C u_{2} \) Oand \( C u \) and
(B) is a mixture of
\( C u \) and \( S O_{2} \)
D. All are incorrect statement


One of the reaction that takes place in
producing steel from iron ore is the reduction of iron(ll) oxide by carbon
monoxide to give iron metal and \( C O_{2} \)
\( \boldsymbol{F e O}(\boldsymbol{s})+\boldsymbol{C O}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{F} \boldsymbol{e}(\boldsymbol{s})+\boldsymbol{C O}_{2}(\boldsymbol{g}) \)
\( \boldsymbol{K}_{\boldsymbol{P}}=\mathbf{0 . 2 6 5} \) at \( \boldsymbol{m} \) at \( \mathbf{1 0 5 0} \boldsymbol{K} . \) What are
the equilibrium partial pressures of \( \mathrm{CO} \)
and \( C O_{2} \) respectively at \( 1050 \mathrm{K} \) if the
initial partial pressures are: \( \boldsymbol{p}_{c o}= \)
1.4 atm and \( p_{c o_{2}}=0.80 \) atm?
A \( \left.\cdot\left[P_{C O}\right]=1.739 \text { at } m \text { and } P_{C O_{2}}\right]=0.461 \) at
B . \( \left[P_{C O}\right]=17.39 a t m \) and \( P_{C O_{2}}=0.461 a t m \)
C \( \left.\cdot\left[P_{C O}\right]=1.79 \text { at } m \text { and } P_{C O_{2}}\right]=0.46 \) at \( m \)
D . \( \left.\left[P_{C O}\right]=2.739 \text { at } m \text { and } P_{C O_{2}}\right]=1.461 \) at


What is van't Hoff factor of aqueous
phosphate solution? (assume \( 100 \% \) ionise).


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


Find the radius of nucleus of an atom
having atomic mass number equal to
125. \( \left(\text { Take } \boldsymbol{R}_{0}=\mathbf{1 . 3} \times \mathbf{1 0}^{-\mathbf{1 5}} \boldsymbol{m}\right) \)


Match the column.


The sugar and purine rings are connected at which carbons?
A . 1,3
в. 1,6
\( \mathrm{c} .1,9 \)
D. 5,9


A Ge specimen is doped with \( A l \). The
concentration of acceptor atoms is \( \sim \) \( 10^{21} \) atoms \( / m^{3} . \) Given that the intrinsic
concentration of electron-hole pairs is \( \sim 10^{19} / m^{3}, \) the concentration of
electrons in the specimen is
\( \mathbf{A} \cdot 10^{17} / m^{3} \)
B . \( 10^{15} / m^{3} \)
c. \( 10^{4} / m^{3} \)
D. \( 10^{2} / m^{3} \)


Which of the following statement is incorrect?
A. Average temperature decreases progressively form plains to the mountain tops
B. Average temperature decreases progressively form the equator towards the poles
c. Temperature affects the kinetic of enzymes and through it the basal metabolism of organism
D. None of these


Two particle \( P \) and \( Q \) are executing
simple harmonic motion with equal amplitude and frequency. At a distance of half the amplitude one of them is moving away from the mean position while the other is observed at a
distance half the amplitude to be
moving towards mean position as
shown in figure. The phase difference between them is:
\( A \cdot \frac{\pi}{2} \)
в. \( \frac{\pi}{3} \)
c. \( \frac{4 \pi}{3} \)
D. \( \frac{\pi}{6} \)


Water turns anhydrous copper sulphate solution in the carbon-hydrogen detection experiment:
A. brown
B. red
c. blue
D. green


A coin is tossed three times, where
(i) \( E: \) head on third toss, \( F: \) heads on
first two tosses
(ii) \( E: \) at least two heads, \( F: \) at most
two heads
(iii) \( E: \) at most two tails, \( F: \) at least
one tail.


Write the IUPAC Name of the following
structure
\[
\begin{array}{rl}
\mathbf{C H}_{3}-\underset{\mathbf{U}}{\mathbf{O}} \mathbf{H}-\mathbf{C} \mathbf{H}-\mathbf{C} \mathbf{H}-\mathbf{C} \mathbf{H}_{3} \\
\mathbf{O} \mathbf{H} & \mathbf{O} \mathbf{H}
\end{array}
\]


In a beaker containing colloidal solution of sodium thiosulphate and a drop of con. sulphuric acid, light observed from side of beaker is:
A. Blue
B. Red
c. Green
D. Yellow


Which of the following statements are
not true?
This question has multiple correct options
A. All charges at rest tend to move higher electric potential to lower electric potential
B. All charges at rest tend to move lower electric potential to higher electric potential
C. Positive charges at rest tend to move form lower electric potential to higher electric potential and negative charges at rest tend to move from higher electric potential to lower electric potential
D. Positive charges at rest tend to move from higher potential to lower potential and negative charges at rest tend to move from lower electric potential to higher potential


In YDSE, let \( A \) and \( B \) be two slits. Films
of thicknesses \( t_{A} \) and \( t_{B} \) and refractive
indices \( \mu_{A} \) and \( \mu_{B} \) are placed in front of
\( A \) and \( B, \) respectively. If \( \mu_{A} t_{A}=\mu_{B} t_{B} \)
then the central maxima will :
A. Not shift
B. Shift toward \( A \)
c. shift toward \( B \)
D. (b) if \( t_{B}>t_{A} \) and (c) if \( t_{B}<t_{A} \)


How are dots arranged in cells of Braille
system?
A. Arranged in cells of two vertical rows of three dots each
B. Arranged in cells of three vertical rows of three dots each
c. Arranged in cells of two vertical rows of two dots each
D. Arranged in four vertical rows of two dots each


At \( 283 \mathrm{K} \) a saturated solution of solid \( \mathrm{X} \)
can be prepared by dissolving 21.0 g of it in 100 g of water. The maximum amount of \( X \) which can be dissolved in 100 g of water at \( 313 \mathrm{K} \) is \( 62.0 \mathrm{g} \). An attempt is made to dissolve 50.0 g of \( X \) in 100 g of water at \( 313 \mathrm{K} \)
. All the 50.0 g of \( X \) will dissolve at 313 K.
2. At \( 313 \mathrm{K} 29.0 \mathrm{g} \) of \( \mathrm{X} \) will remain undissolved.
3. Solubility of X decreases with an
increase in temperature.
4. On cooling the solution of \( X \) from 313 \( \mathrm{K} \) to \( 283 \mathrm{K} \) more than \( 21.0 \mathrm{g} \) of \( \mathrm{X} \) will crystallize out.

Which of the following statement are
correct?
A \( . \) and 2
B. 1 and 4
\( c \cdot 2 \) and 3
D. 1,3 and 4


Maize, Sugarcane and some other tropical plants have high efficiency of
\( C O_{2} \) fixation because they operate
A. Calvin cycle
B. Hatch-Slack cycle
c. TcA cycle
D. PP pathway


Define quality factor of resonance in
series LCR circuit.


Find that point on y axis which as
equidistant from point (6,5) and (-4,3)


Difference between homopolymer and co-polymer.


A ball has the dimensions \( 10 m \times \)
\( 12 m \times 14 m . A \) fly starting at one corner
ends up of a diametrically opposite corner. What is the magnitude of its displacement.
A . \( 17 \mathrm{m} \)
B. 26 m
c. \( 36 \mathrm{m} \)
D. 21


An infinite number of electric charges each equal to 2 nano coulombs in
magnitude are placed along \( x \) -axis at \( x=1 \mathrm{cm}, x=3, \quad x=9 \mathrm{cm}, x=27 \mathrm{cm} \)
and so on. In these setup if the consecutive charges have oppsoite \( \operatorname{sign}, \) then the electric potential at \( x=0 \) will be?


Based on the first law of
thermodynamics, which one of the following is correct?
A. For an isochoric process, \( \mathrm{E}=-\mathrm{C} \)
B. For an adiabatic process, E = -Q
c. For an isothermal process, \( \mathrm{E}=-\mathrm{Q} \)
D. For an cyclic process, \( \mathrm{W}=-\mathrm{Q} \)


The correct statement is (are):
Consider the reaction sequence below
This question has multiple correct options
A. The major product \( Y \) is 1 -methylcyclohexane
B. \( x \) is a racemic mixture
C. \( x \) is a single pure enantiomer
D. Y is 2-methylcyclohexane


Do the planets twinkle like stars? (Yes)
No)


If phase Difference between \( \mathrm{E} \) and 1 is \( \frac{\pi}{4} \) and \( f=50 \mathrm{Hz} \) then calculate time
difference.


Find the degree of the given algebraic
expression
\( 2 y^{2} z+9 y z-7 z-11 x^{2} y^{2} \)
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D.


The elements with atomic numbers 9
17,35,53 and 85 belong to noble gases columnz
A. True
B. False


A line segment DE is drawn parallel to base BC of \( \Delta A B C \) which cuts AB at
point \( \mathrm{D} \) and \( \mathrm{AC} \) at point \( \mathrm{E} \). If \( \mathrm{AB}=5 \mathrm{BD} \) and \( \mathrm{EC}=3.2 \mathrm{cm} . \) Find the length of AE.
A . \( 12.8 \mathrm{cm} \)
в. \( 1.28 \mathrm{cm} \)
c. \( 2.8 \mathrm{cm} \)
D. 12.6 \( \mathrm{cm} \)


When disc B is brought in contact with
disc \( A, \) they acquire a common angular velocity in time t. The average frictional torque on one disc by the other during this period is:
A \( \cdot \frac{2 I \omega}{3 t} \)
B. \( \frac{9 \text { I }}{\text { ? }} \)
c. \( \frac{9 \mathrm{Ic}}{4 \mathrm{t}} \)
\( D \cdot \frac{31}{2 t} \)


For the synthesis of benzoic acid, the only correct combination is:
A. (1) (iv) (Q)
B. (III) (iv) (R)
c. (IV) (ii) (P)
D. (II) (i) (S)


\( x^{2}+6 x+9=0 \)
\( x=? \)


\( 19.5 g \) of \( C H_{2} F C O O H \) is dissolved in \( \mathbf{5 0 0} g \) of water. The depression in the freezing point of water observed is
\( 1.00^{0} C . \) Calculate the van't Hoff factor
and dissociation constant of
fluoroacetic acid.


Define relative premittivity. Write its
unit.


The correct statements among the
following is:
A. fly ash is generated by steel industry
B. green chemistry is concerned about minimum pollution
C . green fuel is that obtained from plastic wastes
D. All of the above


Evaluate \( \int_{1}^{2} \frac{-1}{x^{2}} d x \)


If the bandgap between valence band
and conduction band in a material is
0 \( e V \), then the material is
A. Semiconductor
B. Good conductor
c. superconductor
D. Insulator


The frequency of oscillation of current in
the inductor is
\( \frac{1}{3 \sqrt{L C}} \)
3. \( \frac{1}{6 \pi \sqrt{L C}} \)
c. \( \frac{1}{\sqrt{L C}} \)
D. \( \frac{1}{2 \pi \sqrt{L C}} \)


In which of the following bond angle is maximum?
A \( . N H_{3} \)
B. \( N H_{4}^{+} \)
c. \( P C l_{3} \)
D. \( S C l_{2} \)


A number \( x \) is selected at random from
the numbers 1,4,9,16 and another
number \( y \) is selected at random from
the number \( 1,2,3,4 . \) Find the
probability that the value of \( x y \) is more
than 16


How many students watched TV for less
than 4 hours?
\( A, 34 \)
В. 32
\( c, 24 \)
\( D, 30 \)


In the figure shown, the springs are
connected to the rod at one end and at
the midpoint. The rod is hinged at its
lower end. Rotational SHM of the rod
(Mass \( \boldsymbol{m} \), length \( \boldsymbol{L} \) ) will occur only if
\( \mathbf{A} \cdot k>m g / 3 L \)
В. \( k>2 m g / 3 L \)
c. \( k>2 m g / 5 L \)
D. \( k>0 \)


Given a balanced chemical equation for
each of the following:
Catalytic oxidation of Ammonia.


Solve: \( 3 \tan ^{-1} x+\cot ^{-1} x=\pi \)


Polarization may be called the distortion of the shape of an anion by an
adjacently placed cation. Which of the following statements is/are incorrect? This question has multiple correct options
A. Minimum polarization is brought about by a cation of low radius
B. A large cation is likely to bring about a large degree of polarization.
c. Maximum polarization is brought about by a cation of high charge.
D. A small anion is likely to undergo a large degree of polarization.


Solve \( 9 x-4 y=8 \& 13 x+7 y=10 \)
A. \( x=7, y=3 \)
в. \( x=9, y=3 \)
c. \( x=1, y=3 \)
D. \( x=4, y=7 \)


Let \( f(x)=\left(a-x^{n}\right)^{\frac{1}{n}}, a>0 \) and \( n \) is positive integer, then prove that \( \boldsymbol{f}[\boldsymbol{f}(\boldsymbol{x})]=\boldsymbol{x} \)


\( \Delta G^{o} \) at \( 25^{\circ} C \) for the reaction
\( \frac{1}{2} N_{2}(g)+\frac{3}{2} H_{2} \rightleftharpoons N H_{3}(g) \) is
\( -16.5 k J \) mol \( ^{-1} . \) Hence
thermodynamic equilibrium constant is:
A . 1.08
B. \( 7.80 \times 10^{2} \)
C \( .4 .57 \times 10^{6} \)
D. \( 7.98 \times 10^{34} \)


\( \lim _{x \rightarrow 0} \frac{x^{4}\left(\cot ^{4} x-\cot ^{2} x+1\right)}{\left(\tan ^{4} x-\tan ^{2} x+1\right)} \) is equal to
A . 1
B.
\( c \cdot 2 \)
D. None of these


Statement- - I: The addition of ammonia
derivatives on carbonyl compound is carried in weakly acidic medium. Statement- II : In weakly acidic medium attacking nuclephile is also protonated.
A. Both the statements are true and statement-ll is the correct explanation of statement-I.
B. Both statements are true but statement-ll is not the correct explanation of statement-I.
c. statement-l is true but statement-ll is false
D. Statement-I is false but statement-II is true.


The hybridization and geometry of
Br \( F_{3} \) molecules are:
A \( \cdot s p^{3} d \) and \( T \) -shaped
B \( \cdot s p^{3} d^{2} \) and tetragonal
\( \mathrm{c} \cdot s p^{3} d \) and bent
D. none of these


Evaluate \( : l t_{x \rightarrow 0} x \operatorname{cosec} x \)


A bar Magnet of Magnetic Moment 3.0 amp.m \( ^{2} \) is placed in a uniform Magnetic
induction field \( 2 \times 10^{-5} \) T. If each pole of
the magnet experience a force of \( 6 \times 10^{-4} \)
N, the length of the magnet is
\( A \cdot 05 \mathrm{m} \)
B. \( 0.3 \mathrm{m} \)
c. \( 0.2 \mathrm{m} \)
D. \( 0.1 \mathrm{m} \)


State the difference between the
structural gene in a transcription unit
of prokaryotes and eukaryotes.


Assertion
Let \( f \) be a real valued function satisfying \( \boldsymbol{f}\left(\frac{\boldsymbol{x}}{\boldsymbol{y}}\right)=\boldsymbol{f}(\boldsymbol{x})-\boldsymbol{f}(\boldsymbol{y}) \) and
\( \lim _{x \rightarrow 0} \frac{f(1+x)}{x}=3 . \) Then the area
bounded by the curve \( y=f(x), \) the \( y- \)
axis and the line \( y=3 \) is \( 3 e . \) sq.unit.
Reason

The function \( f(x) \) is concave down.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Find the area of a sector with an arc
length of \( 20 c m \) and a radius of \( 6 \mathrm{cm} \)
\( \mathbf{A} \cdot 20 \mathrm{cm}^{2} \)
B. \( 40 \mathrm{cm}^{2} \)
\( c \cdot 60 c m^{2} \)
D. \( 80 \mathrm{cm}^{2} \)


Moment about the point \( \vec{i}+2 \vec{j}-\vec{k} \) of a force represented by \( \vec{i}+2 \vec{j}+\vec{k} \) acting through the point \( 2 i+3 j+k \) is
\( \mathbf{A} \cdot 3 \vec{i}+\vec{j}-\vec{k} \)
B. \( 3 \vec{i}-\vec{j}+\vec{k} \)
c. \( -3 \vec{i}+\vec{j}+\vec{k} \)
D. \( 3 \vec{i}+\vec{j}+\vec{k} \)


A curve \( y=f(x) \) which passes through
(4, 0) satisfies the differential equation \( x d y+2 y d x=x(x-3) d x . \) The area
bounded by \( \boldsymbol{y}=\boldsymbol{f}(\boldsymbol{x}) \) and line \( \boldsymbol{y}=\boldsymbol{x} \) (in
square unit) is
A . 32
B. \( \frac{64}{3} \)
c. \( \frac{128}{3} \)
D. 64


Correct order of rate of \( E A S \)
(electrophilic aromatic substitution) is:
А \( . c>b>a>d \)
В . \( c>d>a>b \)
\( c \cdot a>b>c>d \)


is the key to increase the number of cells in a living being.
A. Metabolism
B. Growth
c. Cell division
D. Reproduction


Evaluate the following question:
\( \lim _{x \rightarrow 0} x^{2}-3 \)


Lattice energy depends on:
A. only radius of cation
B. only radius of anion
C. cation to anion radius ratio
D. sum of the radii of cation and anion


A family has five girls and no son. Probability of son as the 6th child will
be
A. 50\%
B. 75\%
c. Full
D. No chance


Out of 100 bicycles, 10 bicycles have puncture. What is the probability of not having any punctured bicycle in a
sample of 5 bicycles?
A \( \cdot \frac{1}{2^{9}} \)
B. \( \left(\frac{9}{10}\right)^{5} \)
c. \( \frac{1}{10^{5}} \)
D. \( \frac{1}{2^{5}} \)


Among \( K, M g, A u \) and \( C u, \) the one which is extracted by heating its ore in air is:
A. \( K \)
в. \( M g \)
c. \( A u \)
D. \( C u \)


Solve for differntial equation:
\( \left(x^{3}-x\right) \frac{d y}{d x}-\left(3 x^{2}-1\right) y=x^{5}- \)
\( 2 x^{3}+x \)
A \( \cdot y \frac{1}{x\left(x^{2}+1\right)}=\log x+c \)
в. \( y \cdot \frac{1}{x\left(x^{2}-1\right)}=-\log x+c \)
c. \( y \frac{1}{x\left(x^{2}-1\right)}=\log x+c \)
D. None of these.


If \( a=2 \hat{i}-\hat{j}-m \hat{k} \) and \( b=\frac{4}{7} \hat{i}-\frac{2}{7} \hat{j}+ \)
\( 2 \hat{k} \) are collinear, then the value of \( m \) is
equal to
A . -7
в. - -
\( c \cdot 2 \)
D.
E. -2


Which of the following has negative charge and is present in atom as pairs with opposite spin?
A. Proton
B. Neutron
c. Electron
D. Isotope
E. Ion


Ester linkages occur in
A. Nucleic acids
B. Nucleus
c. Carbohydrates
D. Proteins


If statements \( p, q, r \) have truth values \( T \)
\( F, T \) respectively then which of the following statement is true
A \( \cdot(p \rightarrow q) \wedge r \)
в. \( (p \rightarrow q) \vee \sim r \)
C \( .(p \wedge q) \vee(q \wedge r) \)
D. \( (p \rightarrow q) \rightarrow r \)


Compute the age specific death rate for the following data:
Number of
deaths \( \begin{array}{ll}\text { Age } & \text { Population (in } \\ \text { Group } & \text { thousands) } \\ \text { (years) } & \text { thousands) }\end{array} \)
5 Below
5 360
\( _{5}-30 \) na
\begin{tabular}{l|l}
Above & \\
30 & 10
\end{tabular} 280


The energy required to transfer an electron from second Bohr's orbit to
third Bohr's orbit in a hydrogen-
like atom with nuclear charge \( Z_{e} \) is
\( 68 . e V . \) The value of \( Z \) will be.
\( A \cdot 3 \)
B. 4
\( c .5 \)
D. 6


Find the equation of tangent at (3,4) for the circle \( x^{2}+y^{2}=25 \)
A. \( 3 x+4 y=25 \)
в. \( 3 x-4 y=25 \)
c. \( 3 x+4 y+25=0 \)
D. \( 4 x-3 y=25 \)


Mass number is silghtly less than the actual atomic mass. Give reasons.


Assertion
Nitroalkanes and alkyl nitrites exhibit functional isomerism.
Reason
Compounds having same molecular formula but different functional group
are called functional isomers.
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


Heating of rubber with sulphur is called
A. Vulcanisation
B. Galvanisation
c. sulphonation
D. Bessemerisation


State Bohr's Model.


One hundred identical coins, each with
probability \( p \) of showing heads are
tossed once. If \( 0<p<1 \) and the
probability of heads showing on 50 coins is equal to that of heads showing on 51 coins, the value of \( p \) is
A \( \cdot 1 / 2 \)
B. \( 51 / 101 \)
c. \( 49 / 101 \)
D. 3 / 101


You are told that 1331 is a perfect cube
Can you guess without factorisation what is its cube root? Similarly, guess the cube root of 4913,12167,32768


At a given place on the earth's surface, the horizontal component of earth's
magnetic field is \( 3 \times 10^{-6} T \) and
resultant magnetic field is \( 6 \times 10^{-6} T \)
Angle of dip at this place is :
A . \( 30^{\circ} \)
B . \( 40^{\circ} \)
\( c \cdot 50^{\circ} \)
D. \( 60^{\circ} \)


I wo lathtical roas one and two each on
mass M and length L are performing
general plane motion on the horizontal
plane as shown in the figure if \( V \) is
velocity of center of mass of both the
rods and \( \omega \) is the angular speed about
the certical axis then angular momentum of rod 1 in the frame of
reference of center of mass of rod 2 at
the given instant will be
\( ^{\mathbf{A}} \cdot\left(M v \frac{3 L}{2}+\frac{M L^{2}}{12} \omega\right)(-k) \)
B \( \cdot\left(M v \frac{3 L}{2}\right)(-k) \)
\( ^{\mathbf{C}} \cdot\left(\frac{M L^{2}}{12} \omega\right)(-K) \)
D \( \cdot\left(M v \frac{3 L}{4}\right)(-k) \)


is a mixture of loamy and yellow soils.
A. Red soil
B. Black soil
c. Alluvial soil
D. None of the above


Which selection is a polar molecular substance with a weak dipole-dipole interaction?
A. \( B a C l_{2} \)
в. \( C H_{3} C l \)
c. \( B I_{3} \)
D. \( H_{2} O \)


When acetone and chloroform are
mixed together, which of the following
observations is correct?
\( (\mathbf{A}) \)
A. A-A and B-B interactions are stronger than A-B interactions
B. A-A and B-B interactions are weaker than A-B
interactions
C. A-A and B-B interactions are equal
D. The liquid form separate layers and are immiscible


Write (i) \( -1-i \) (ii) \( 1-i \) in polar form.


In a polygon, no three diagonals are concurrent. If the total number of points of intersection of diagonals interior to
the polygon is 70 then the number of diagonals of the polygon is


Find the zero of the polynomial given below:
\( \boldsymbol{p}(\boldsymbol{x})=\boldsymbol{9} \boldsymbol{x}-\boldsymbol{3} \)
A \( \cdot \frac{6}{7} \)
B. \( \frac{1}{2} \)
c. \( \frac{1}{3} \)
D. \( \frac{7}{3} \)


Which of the following motions is different from the rest?
A. a ball thrown horizontally in air
B. a bomb released from a flying aeroplane
c. a javelin thrown by an athlete
D. a bird flying in the air


The phenomenon of dispersion proves
that:
A. white light is made up of seven constituent colours
B. Iight moves in a straight line
C. light passes through a transparent medium
D. light does not pass through an opaque medium and absence of light causes shadow


Find out the following in the electric
circuit given in Figure.

Difference in reading of ammeter \( \boldsymbol{A}_{\mathbf{1}} \)
and \( A_{2}(\text { if any }) \)


Match the List-I with List-II and select
the correct answer using the codes
given below the lists.
List

List II
A. Coagulation \( \quad \) 1. Scattering
B. Lyophilization 2. Washing of precipitates
C. Peptization
3. Purification of colloids
D. Tyndall effect \( \quad \) 4. Electrolyte
A. A- \( 4 ; \) B-3; C-2; D-1
B. A-2; B-1; C-3; D-4
c. \( A-3 ; B-1 ; C-2 ; D-4 \)
D. A-4; B-3; C-1; D-2


An \( \alpha \) -particle of charge \( 2 e \) is projected with high speed towards two protons (each of charge \( e \) ) kept at a distance
\( 4 m \) apart, along a perpendicular passing through the mid-point of the line joining the protons. Initially, \( \alpha \) particle starts very far away from the protons. The change In potential energy of the system, when the \( \alpha \) -particle undergoes the greatest repulsion, in terms of \( \frac{\mathbf{e}^{2}}{\pi \epsilon_{0}} \) will be:
A \( \cdot \frac{1}{\sqrt{3}} \)
B. \( \sqrt{2} \)
c. \( \frac{1}{\sqrt{6}} \)
D. \( \sqrt{3} \)


\( 10 \mathrm{mL} \) of a gaseous hydrocarbon is exploded with 100 mL of oxygen. The residual gas on cooling is found to
measure \( 95 \mathrm{mL} \) of which \( 20 \mathrm{mL} \) is
absorbed by caustic soda and the remainder by alkaline pyrogallol. The
formula of the hydrocarbon is :
A \( . C H_{4} \)
в. \( C_{2} H_{6} \)
\( \mathbf{c} \cdot C_{2} H_{4} \)
D. \( C_{2} H_{2} \)


In the given figure, diameter of
lens equals
\( A \cdot F O \)
B. 2FO
\( c \cdot 3 F O \)
D. \( 4 \mathrm{FO} \)


\( P H_{3} \) and \( N H_{3} \) on separate reaction with bleaching powder produce respectively
A. P and \( N_{2} \)
B. \( P C l_{3} \) and \( N C l_{3} \)
c. \( P C l_{3} \) and \( N_{2} \)
D. \( P C l_{5} \) and \( N C l_{3} \)


Write the IUPAC name of following
compound


Write \( \frac{\mathbf{3}}{\mathbf{2 0}} \) as percentage.


An aquatic quadrifoliate pteridophyte is
A. Isoetes
B. Marsilea
c. Equisetum
D. ophioglossum


Write the reaction for the conversion of
1-hexanol \( \rightarrow 1 \) - heptanamine


A conducting rod of length \( 2 \mathrm{m} \) is placed on a horizontal table in north-south
direction. It carries a current of 5 A from
south to north. Find the direction and
magnitude of the magnetic force acting on the rod. Given that the Earth's
magnetic field at the place is \( 0.6 \times \) \( 10^{-4} T \) and angle of dip is \( \frac{\pi}{6} \)


\( \operatorname{Let} f(x)=\left\{\begin{array}{l}\frac{\sin [x]}{[x]} ;[x] \neq 0 \\ 0 ;[x]=0\end{array}, \) then \right.
\( \lim _{x \rightarrow 0} f(x)= \)
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( \sin 1 \)
\( c \cdot 2 \)
D. does not exist


State whether the given statement is True or False:
\( 3+\sqrt{2} \) is an irrational number.
A . True
B. False


Q Type your question
work up gives:
\( A \)
\( B \)
\( c \)
\( D \)


If we keep pop corn in a pressure cooker
on a flame, heat is transferred from
flame to corn by :
A. Conduction
B. Radiation
c. convection
D. None


dentify the operation performed by the
circuit given below:
A . NOT
B. AND
\( c . \) ов
D. NAND


An object is placed at a distance of
\( 15 \mathrm{cm} \) from a convex lens of focal length
10cm. On the other side of the lens, a
convex mirror is placed at its focus
such that the image formed by the
combination coincides with the object
itself. The focal length of the convex
mirror is :
\( \mathbf{A} \cdot 20 \mathrm{cm} \)
B. \( 10 \mathrm{cm} \)
\( c .15 \mathrm{cm} \)
D. \( 30 \mathrm{cm} \)


When we pay for our electricity bill, we are paying for the:
A. charge used.
B. current used
c. power used.
D. energy used


If the area of the \( \triangle A B C \) is 68 sq.units
and the vertices are \( \boldsymbol{A}(\boldsymbol{6}, \boldsymbol{7}), \boldsymbol{B}(-\boldsymbol{4}, \boldsymbol{1}) \)
and \( C(a,-9) \) taken in order, then find
the value of \( a \).


The element with electronic
configuration 2,8,6 is:
A. metallic with valency 2
B. non-metallic with valency - 2
c. non-metallic with valency 2
D. none of these


When in thermal contact, the quantity of heat lost by the hotter body is the amount of heat gained by the colder body.
A. Equal to
B. Greater than
c. Less than
D. cannot say


Find the maximum value of \( 2 x^{3}- \)
\( 24 x+107 \) in the interval \( [1,3] . \) Find the
maximum value of the same function in
[-3,-1]


Which of these is o, p-directing and deactivating group?
A. \( -F \)
в. \( -C l \)
\( \mathrm{c} .-B r \)
D. All of these


The gravitational field is a conservative
field. The work done in this field by
moving an object from one point to
another
A. depends on the end-points only.
B. depends on the path along which the object is moved.
C. depends on the end-points as well as the path between the points.
D. is not zero when the object is brought back to its initial position.


The area of an isosceles triangle, each of whose equal sides is \( 13 \mathrm{cm} \) and
whose base is \( 24 c m \) is
\( \mathbf{A} \cdot 60 \mathrm{cm}^{2} \)
B. \( 55 \mathrm{cm}^{2} \)
c. \( 50 \mathrm{cm}^{2} \)
D. \( 40 \mathrm{cm}^{2} \)


If \( a_{1}, a_{2}, a_{3}, \dots \) are in AP then \( a_{p}, a_{q}, a_{r} \)
\( \operatorname{are} \operatorname{in} A P \) if \( p, q, r \) are in
\( A \cdot A P \)
в. GP
c. нр
D. none of these


The hormones that have 'anti
inflammatory' effect are the:
A. Thyroxin
B. Insulin
c. Glucocorticoids
D. Auxins


An aqueous solution of a salt \( M X_{2} \) at
certain temperature has a van't Hoff
factor of \( 2 . \) The degree of dissociation for this solution of the salt is:
A . 0.50
B. 0.33
c. 0.67
D. 0.80


The equilibrium constant for the reaction:
\( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{B} \boldsymbol{r}_{2}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{2} \boldsymbol{H} \boldsymbol{B} \boldsymbol{r}(\boldsymbol{g}) \)
is 67.8 at \( 300 K . \) The equilibrium
constant for the dissociation of \( \boldsymbol{H} \boldsymbol{B} \boldsymbol{r} \) is:
A . 0.0147
B. 67.8
c. 33.90
D. 8.349


The element eka-silicon in Mendeleev's
period table is known as in
the modern periodic table.


Increase in area per unit of the original
area, per degree celcius rise in
temperature is called
A. Coefficient of superficial expansion
B. Coefficient of volumetric expansion
c. coefficient of cubical expansion
D. All


A coil with 100 turns has an inductance
of \( 0.05 H \) and \( 0.02 A \) current is passed
through it. Flux linked with the coil is
A \( \cdot 10^{-2} W b \)
В \( \cdot 10^{-3} W b \)
\( \mathbf{c} \cdot 10^{-4} W b \)
D. \( 10^{-5} W b \)


f \( x+y=1, \) then \( \sum_{r=0}^{n} r^{n} C_{r} x^{r} . y^{n-r}= \)
\( \mathbf{A} \cdot \mathbf{1} \)
B.
c. \( n x \)
D. \( n y \)


A ball is dropped from the roof of a tower of height h. The total distance covered it in the last seconds of its motion is
equal to the distance covered by it in first three seconds. The value of h in
meters is \( \left(\boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{2}\right) \)
A . 125
B. 200
\( c \cdot 100 \)
\( D \cdot 80 \)


Most appropriate word for protozoans is
A . Cellular
B. Unicellular.
c. Acellular
D. Multicellular.


Q Type your question
substance is best represented by figure
\( A \)
B.
\( c \)
\( D \)


The H-zone in the skeletal muscle fibre
is due to
A. The absence of myofibrils in the central portion of \( A- \) band.
B. The central gap between myosin filaments in the \( A- \) band.
C. The central gap between actin filaments extending through myosin filament in the A-band.
D. Extension of mysoin filaments in the central portion of the A-band.


Butylated hydroxyanisole (BHA) is an example for:
A. antioxidant in food
B. antibiotic
c. antifertility drug
D. antiseptic


In the arrangement shown below, a
block of \( 2800 \mathrm{kg} \) is in equilibrium on
applying a force of 45 N. Find the density of the liquid?


Correct percentage of \( \mathrm{CO}_{2} \) present in the
atmosphere is
A . 0.03\%
B. 0.3\%.
c. \( 1 \% \)
D. 1.1\%


\( \frac{\sqrt{6}}{\frac{\sqrt{6}}{5}} \)


The distribution of genetic material occurs from generation to generation and permits great genetic diversity by frequent re-organisation of genetic complement. This occurs during
A. Mitosis
B. Meiosiss
c. organogenesis
D. Metamorphosis


Dipoles are found in:
A. Water
B. Hydrogen bromide
C. Iron
D. Argon
E. Sodium chloride


When the object is at distances \( u_{1} \) and
\( u_{2} \) the images formed by the same lens
are real and virtual respectively and of the same size. Then focal length of the
lens is:
A \( \cdot \frac{1}{2} \sqrt{\mu_{1} \mu_{2}} \)
в. \( \frac{\mu_{1}+\mu_{2}}{2} \)
c. \( \sqrt{\mu_{1} \mu_{2}} \)
D. \( \sqrt{\left(\mu_{1}+\mu_{2}\right)} \)


One of the most widely used drug in
medicine, iodex is?
A. Ethyl salicylate
B. Methyl salicylate
c. o-hydroxy benzoic acid
D. Acetyl salicylic acid


The mode of asexual reproduction in
bacteria is
This question has multiple correct options
A. Formation of gametes
B. Endospore formation
c. conjugation
D. Zoospores formation


Seven digits from the numbers 1,2,3,4 5,6,7,8,9 are written down nonrepeatedly in a random order to form a seven digit number. The probability that this seven digit number is divisible by 9
is
\( A \cdot \frac{2}{9} \)
B. \( \frac{7}{36} \)
\( c \cdot \frac{1}{9} \)
\( D \cdot \frac{7}{12} \)


Convert the given fractional numbers to
percentage. \( \frac{2}{7} \)


The marks in science of 80 students of
class \( X \) are given below. Find the mode of the marks obtained by the students in science
c... \( \begin{array}{llll}0- & 10- & 20- & 30- \\ 10 & 20 & 30 & 40\end{array} \)
Freq. 1 3
A. 17.36
B. 36.56
c. 53.17
D. 75.12


The standard electrode potential of Zinc
is \( 0.76, \) V. The potential of \( 0.1 \mathrm{M} \) zinc electrode is:
\( \mathbf{A} \cdot 0.8196 \mathbf{V} \)
B. 0.7895 V
c. \( 0.9484 \mathrm{V} \)
D. \( 0.7508 \mathrm{V} \)


Let \( A, B, C \) be the subsets of the
universal set \( X \) Let \( A^{\prime} B^{\prime} C^{\prime} \) denote their
complements in X Then which of below
corresponds to the shaded portion in
the given figure
\( \mathbf{A} \cdot A^{\prime} \cap B \cap C \)
B \( \cdot A \cap B^{\prime} \cap C \)
c. \( A \cap B \cap C^{\prime} \)
\( \mathbf{D} \cdot A^{\prime} \cap B^{\prime} \cap C \)


object and screen are fixed \( 90 \mathrm{cm} \) apart. The lens is displaced. two sharp images
are obtained when lens is at \( L_{1} \) and \( L_{2} \)
respectively such that \( I_{1}=4 I_{2} \). Find
the focal length of the lens?
\( \mathbf{A} \cdot 18 \mathrm{cm} \)
B. \( 15 \mathrm{cm} \)
c. \( 16 \mathrm{cm} \)
D. 20 cm


Prove that \( \sqrt{3}+\sqrt{5} \) is an irrational
number.


Find a unit vector perpendicular to the plane \( A B C, \) where the coordinates of
\( A, B \) and \( C \) is
\( \boldsymbol{A}(\mathbf{3},-\mathbf{1}, \mathbf{2}), \boldsymbol{B}(\mathbf{1},-\mathbf{1},-\mathbf{3}) \) and
\( \boldsymbol{C}(\mathbf{4},-\mathbf{3}, \mathbf{1}) \)


\( S O_{2} \) can act as both oxidant and
reductant.
A. True
B. False


Write any two differences between regular and irregular (diffused) reflection


Find the degree measure of the angle
subtended at the centre of a circle
of radius \( 100 \mathrm{cm} \) by an arc of length 22
\( \mathrm{cm} .\left(\boldsymbol{U s e} \boldsymbol{\pi}=\frac{\mathbf{2 2}}{\mathbf{7}}\right) \)


The average kinetic energy of hydrogen molecule at NTP will be
A. \( 0.4 \times 10^{-20} \) Joule /molecule
B . \( 1.56 \times 10^{-20} \) Joule / molecule
c. zero
D. \( 5.6 \times 10^{-20} \) Joule /molecule


Explain cardiac cycle with the help of diagrams.


The molar heat of vaporization of
toluene is \( \Delta H_{v} . \) If its vapour pressure at \( 315 \mathrm{K} \) is 60 torr \( \& \) that at \( 355 \mathrm{K} \) is 300
torr then \( \Delta H_{v}=?(\log 2=0.3) \)
A . 37.4 kJ/mole
B. 3.74 kJ/mole
c. 37.4 J/mol
D. 3.74 J/mole


Sprain is due to outstretching/pulling
of
A. Muscles
B. Tendons
c. Ligaments
D. Nerves


\( \begin{array}{ll}\text { List I } & \text { List II } \\ \text { 1) d.c's of } x-\text { axis } & \text { a) }(1,1,1) \\ \text { 2) d.c's of } y-\text { axis } & \text { b) } \\ \text { 3) d.c's of } z-\text { axis } & \left(\frac{1}{\sqrt{3}} \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}\right) \\ \begin{array}{l}\text { 4) d.c's of a line makes equal } \\ \text { angles with axes }\end{array} & \text { c) }(1,0,0) \\ \begin{array}{l}\text { d) }(0,1,0) \\ \text { e) }(0,0,1)\end{array}\end{array} \) The correct order for 1,2,3,4 is
\( \mathbf{A} \cdot c, d, e, b \)
B. \( a, b, c, e \)
\( \mathbf{C} \cdot c, d, a, b \)
D. \( b, c, a, e \)


How is ethanoic acid prepared from dry
ice?


Four particle each having a charge \( \boldsymbol{q} \)
are placed on the four vertices of a
regular pentagon. The distance of each
corner from the centre is \( a \). Find the
electric field at the centre of the
Pentagon.
A \( \cdot \frac{q}{4 \pi \epsilon_{0} a^{2}} \) Along OE
B. \( \frac{q}{3 \pi \epsilon_{0} a^{2}} \) Along OE
c. \( Z \) ero
D. \( \frac{q}{2} \) Along EO


Four one litre flasks are separately filled
with gases \( O_{2}, F_{2}, C H_{4} \) and \( C O_{2} \) under same conditions.

The ratio of the number of molecules in
these gases are:
\( \mathbf{A} \cdot 2: 2: 4: 3 \)
B. 1: 1: 1: 1
\( \mathbf{c} \cdot 1: 2: 3: 4 \)
D. 2: 2: 3: 4


A sum of Rs. 18750 is left by will by a father to be divided between two sons,
12 and 14 years of age, so that when they attain maturity at \( 18, \) the amount received by each of them at 5 per cent simple interest will be the
same. Find the sum allotted at present
to each son?
A. Rs. 9500 , Rs. 9250
B. Rs. 8000, Rs. 1750
c. Rs. \( 9000, \) Rs. 9750
D. Rs. 10000, Rs. 8750


\( \int \frac{\left(x^{2}+1\right)}{(x+1)^{2}} d x \)


Two wires made of same material have
Iengths in the ratio 1: 2 and their volumes in the same ratio. The ratio of
their resistances is:
A . 4: 1
B . 2: 1
c. 1: 2
D. 1: 4


A steady flow of water passes along a
horizontal tube from a wide section \( \boldsymbol{X} \)
to the narrower section \( Y \), see figure.
Manometers are placed at \( P \) and \( Q \) at
the sections. Which of the statements
\( A, B, C, D \) is most correct?
A. water velocity at \( X \) is greater than \( Y \)
B. the manometer at \( P \) shows lower pressure than at \( Q \)
C. kinetic energy per \( m^{3} \) of water at \( X= \) kinetic energy per \( m^{3} \) at \( Y \)
D. the manometer at \( P \) shows greater pressure than at \( Y \)


\( 2 C u I \rightarrow C u+C u I_{2}, \) the reaction is :
A. redox
B. neutralisation
c. displacement
D. none of the above


How would reversing the battery affect
the magnitude of current in R1 in the
circuit above?
A. It would increase but not double
B. It would double
c. It would decrease
D. It would not be affected


Decreasing order concentration of
minerals inside cell is
A \( \cdot \mathrm{ca}^{+2}-\mathrm{K}^{+}-\mathrm{Na}^{+} \)
B. \( k^{+}-C a^{+2}-N a^{+} \)
c. \( \kappa^{+}-N a^{+}-C a^{+} \)
D. \( \mathrm{Na}^{+}-\mathrm{K}^{+}-\mathrm{Ca}^{+2} \)


Which of the following reproduce by producing spores?
A. Jasmines
B. Roses
c. Ferns
D. Pomegranate


Rakesh went to a stationary shop to
purchase a total of 38 pens, erasers and sharpeners. He purchased at least 11
items of each. He purchased more
sharpeners than erasers and more
erasers than pens. If each pen cost Rs. 2
each eraser cost Rs. 3 and each
sharpener cost Rs. \( 4 . \) find the minimum
expenditure be could have incurred on the items (in Rs.)
A . 116
B . 118
c. 117
D. 119


sources of light of wavelength \( \lambda \) are placed on the dotted line in front of a large screen. The source emit waves in
phase with each other. The distance
between \( S_{1} \) and \( S_{2} \) is \( ^{\prime} d^{\prime} \) while their
distance from the screen is much
larger. Then,
(a) If \( d=7 \lambda / 2, O \) will be minima
(b) If \( d=4.3 \lambda \), there will be total of 8
minima on y-axis
(c) If \( d=7 \lambda, O \) will be maxima.
(d) If \( d=\lambda \), there will be only one
maxima on the screen.
Which is the set of correct statement:
A. \( a, b \) and \( c \)
B. \( b, c \) and \( d \)
c. \( a, b, c \) and \( d \)
D. \( a, c \) and \( d \)


\( \left[\begin{array}{cc}2 & 1 \\ 1 & 0 \\ -3 & 4\end{array}\right]+\left[\begin{array}{cc}-1 & -8 \\ 1 & -2 \\ 9 & 22\end{array}\right] \)


From the sum of -38 and \( 40 . \) subtract
\( \mathbf{1 2 0} \)


If \( f(a)=\log \left(\frac{2+a}{2-a}\right), 0<a<2 \) then
\( \frac{1}{2} f\left(\frac{8 a}{4+a^{2}}\right)= \)
A. \( f(a) \)
B. \( 2 f(a) \)
c. \( \frac{1}{2} f(a) \)
D. \( -f(a) \)


The product of two consecutive integers is \( 156 . \) Find the integers.
A. 10 and 13
B. 12 and 13
c. 12 and 11
D. 1 and 13


Which of the following statement(s) is incorrect ?
A . lonisation energy \( \propto \frac{1}{\text { Screening effect }} \)
B. The first ionisation energies of Be and Mg are more than ionisation energies of B and Al respectively
c. Atomic and ionic radii of Niobium and Tantalum are almost same
D. Metallic and covalent radii of potassium are 2.03 , and 2.3 \( \dot{A} \) respectively


The molecule/ion in which bond angle is
les than \( 109^{\circ} ? \)
\( \mathbf{A} \cdot N F_{4}^{+} \)
B. \( C C l_{4} \)
c. \( C L O_{4} \)
D. None of these


The value of mutual inductance can be
increased by
A. decreasing N
B. increasing
c. winding the coil on wooden frame
D. winding the coil on china clay


An electron and a photon each have a
wave length 1 nm. Find the energy pf the photon.


00
0
00
0


Write the measure of supplementary angle of the given angles:
\( \mathbf{6 0}^{\circ} \)


State one point of similarity and one point of difference between an A.C. generator ans a D.C. motor.


Porous wood contains
A. Fibres
B. Sieve tubes
c. Tracheids
D. vesselss


The maximum work that can be
obtained from the cell
\( \boldsymbol{A l}\left|\boldsymbol{A l}^{3+}(\mathbf{0 . 1} \boldsymbol{M}) \| \boldsymbol{F} \boldsymbol{e}^{\boldsymbol{2}+}(\boldsymbol{0 . 2} \boldsymbol{M})\right| \boldsymbol{F e} \) is:
\( \left[\text { Given }: \boldsymbol{E}_{A l^{3+} / A l}^{o}=-\mathbf{1 . 6 6} \mathbf{V} \) and \right.
\( \left.\boldsymbol{E}_{\boldsymbol{F} e^{2+} / \boldsymbol{F} e}^{\boldsymbol{o}}=-\mathbf{0 . 4 4} \boldsymbol{V}\right] \)
A. \( 605.8 \mathrm{kJ} \)
B. 505.8 kJ
c. 705.8 kJ
D. 905.8 kJ


The solution of the equation \( 1.5 y- \) \( \mathbf{7}=\mathbf{0 . 5 y} \) is
\( A \cdot 7 \)
в. -7
\( c .3 .5 \)
D. - 3.5


Cross-like configurations when non-
sister chromatids of a bivalent come in
contact during first meiotic division are
A. Chiasmata
B. Chromomeres
c. Centromere
D. Bivalents


The \( n \) th term of an A.P is \( 6 n+2 \). Find
the common difference.


\( f\left|\begin{array}{ccc}\mathbf{6} i & -\mathbf{3} i & \mathbf{1} \\ \mathbf{4} & \mathbf{3} i & -\mathbf{1} \\ \mathbf{2 0} & \mathbf{3} & \boldsymbol{i}\end{array}\right|=\boldsymbol{x}+\boldsymbol{i} \boldsymbol{y}, \) then
A \( . x=3, y=1 \)
B. \( x=1, y=3 \)
c. \( x=0, y=3 \)
D. \( x=0, y=0 \)


In the reaction
\( \boldsymbol{R O H}+\boldsymbol{P B r}_{3} \rightarrow \boldsymbol{R B r} \)
The number of moles of alcohol that
may be converted into alkyl bromide by
one mole of \( \boldsymbol{P} \boldsymbol{B r}_{3} \) is:
A . 1 mole
B. 2 mole
c. 3 mole
D. none of the above


Mineral activator of enzyme aconitase
is
A. Mn
в. Мв
c. \( \mathrm{Fe} \)
D. cu


Similarity between \( N b \) and \( T a \) is
because they:
A. are transition metals
B. belong to same group of periodic table
c. have the same mineral source
D. have almost same ionic and covalent radii


As the temperature increases, rate of
reaction increases because:
A. number of collisions between the molecules of
reactants increases
B. concentration of the reactants increases
C . activation energy is decreased
D. none of the above


During discharging of a charged glass rod via earthing, the connecting material can be
A. another glass rod
B. a conducting wire
\( c . \) fur
D. an ebonite rod


Let \( O B=\hat{i}+2 \hat{j}+2 \hat{k} \) and \( O A=4 \hat{i}+ \)
\( 2 \hat{j}+2 \hat{k} . \) The distance of the point \( B \) from the straight line passing through \( A \) and parallel to the vector \( 2 \hat{i}+3 \hat{j}+ \) \( 6 \hat{k} \) is
A \( \cdot \frac{7 \sqrt{5}}{9} \)
в. \( \frac{5 \sqrt{7}}{9} \)
c. \( \frac{3 \sqrt{5}}{7} \)
D. \( \frac{9 \sqrt{5}}{7} \)
E \( \cdot \frac{9 \sqrt{7}}{5} \)


Arrange the elements
\( F, N a, F e, C l, N e \) in increasing order
of ionization energy.
A. \( N a<F e<C l<F<N e \)
в. \( N e>F>C l>F e>N a \)
c. \( F e>C l>F>N e>N a \)


The U-tube of a manometer has:
A. one side open
B. both sides open
c. both sides closed
D. none of these


Sometimes blurred and less sharply
defined images are formed. This defect
is called
A. Chromatic aberration
B. Spherical aberration
c. Blurred lens
D. None of the above


The wavelength of visible light is :
A. 200nm- 370 nm
B. 780nm - 890nm
c. \( 380 \mathrm{nm}-760 \mathrm{nm} \)
D. 900nm - 2000nm


Identify the mirror
A. convex
B. Concave
c. Biconcave
D. Biconvex


The time period of an earth satellite in
circular orbits is independent of
A. both the mass and radius of the orbit
B. radius of its orbit
c. the mass of the satellite
D. neither the mass of the satellite nor the radius of its orbit


If \( n=\frac{\pi}{4 \alpha}, \) then
\( \tan \alpha \cdot \tan 2 \alpha \cdot \tan 3 \alpha \dots \tan (2 n-1) \alpha \) is
equal to
A . 1
B. - 1
\( c \cdot \infty \)
D. None of these


Speeds of two identical cars are u and
4u at a sufficient instant. What is the
ratio of the respective distance at which
the two cars are stopped from that instant?


Figure shows a bar magnet and a long
straight wire \( \mathrm{W} \), carrying current into
the
plane of paper.Point \( P \) is the point of intersection of axis of magnet and the
line
of shortest distance between magnet
and the wire. If \( P \) is the midpoint of the
magnet, then which of the following
statements is correct?
A. magnet experiences a torque in clockwise direction
B. magnet experiences a torque in anticlockwise direction
C. magnet experiences a force, normal to the line of shortest distance
D. magnet experiences a force along the line of shortest distance


Aliphatic ethers are purified by shaking with a solution of ferrous salt to remove
which are formed on
prolonged standing in contact with
water
A. aromatic ethers
B. aliphatic alcohols
c. peroxides
D. aldehydes


During a thunderstorm, rainwater contains nitric acid. Explain with
reaction.