In the diagram \( O \) is the centre of the
circle with diameter \( 20 \mathrm{cm} \)
The circle is the locus of a point \( \boldsymbol{X} \) State
the distance of \( X \) from \( O \)
\( A \cdot 5 \mathrm{cm} \)
B. \( 8 \mathrm{cm} \)
\( c .10 \mathrm{cm} \)
D. \( 20 \mathrm{cm} \)


the frequency of the first line in Lyman
series in the hydrogen spectrum is \( V \) What is the frequency of the corresponding line in the spectrum of doubly ionized Lithium?


Which of the following are the substances that are present in the soil and required for the growth of crops?
A. Manures
B. Pesticides
c. Fertilisers
D. Nutrients


If the critical temperature of a gas is \( 100 \mathrm{K} \) then its Boyle temperature will be:
A . 33.3 \( k \)
B. \( 103 \mathrm{K} \)
c. 337 к
D. 500 K


An equilibrium constant of \( 10^{-4} \) for a
reaction means, the equilibrium is
A. largely towards backward direction
B. largely towards forward direction
c. equally poised
D. never established


Find the vector equation of the plane through the points (2,1,-1) and (-1,3,4) and perpendicular to the
plane \( \boldsymbol{x}-\mathbf{2} \boldsymbol{y}+\mathbf{4} \boldsymbol{z}=\mathbf{1 0} \)


Find \( \lim _{x \rightarrow 4^{-}} f(x), \) where \( f(x)= \)
\( \left\{\begin{array}{ll}x+7, & x<4 \\ 2 x+3, & x>4\end{array}\right. \)


..is the last phase of karyokinesis
A . Metaphase
B. Anaphase
c. Telophase
D. Late prophase


\( A B \) is a segment. The point \( P \) is on the perpendicular bisector of segment AB such that length of AP exceeds length of AB by \( 7 \mathrm{cm} . \) If the perimeter of \( \Delta A B P \) is \( 38 \mathrm{cm} . \) Find the sides of \( \Delta A B P \)
\( \mathbf{A} .5 \mathrm{cm}, 12 \mathrm{cm} \) and \( 19 \mathrm{cm} \)
B. \( 8 \mathrm{cm}, 15 \mathrm{cm} \) and \( 15 \mathrm{cm} \)
c. \( 2 \mathrm{cm}, 17 \mathrm{cm} \) and \( 11 \mathrm{cm} \)
D. \( 6 \mathrm{cm}, 14 \mathrm{cm} \) and \( 18 \mathrm{cm} \)


The value of the sum \( 1.2 .3+2.3 .4+ \)
\( \mathbf{3} . \mathbf{4 . 5}+\ldots \ldots . \) upto \( n \) terms \( = \)
A \( \cdot \frac{1}{6} n^{2}\left(2 n^{2}+1\right) \)
B - \( \frac{1}{6} n^{2}\left(n^{2}-1\right)(2 n-1)(2 n+3) \)
C \( \cdot \frac{1}{8}\left(n^{2}+1\right)\left(n^{2}+5\right) \)
D・去 \( (n)(n+1)(n+2)(n+3) \)


Find the greatest possible number of points of intersection between a
parabola and a circle.
A .2
B. 3
\( c \cdot 4 \)
D. 6
\( E \)


A ray of light incidents normally on first face of the prism and the emergent ray grazes the second surface. If \( A \) is the
angle of the prism and \( C \) is its critical
angle then the correct choice is:
A. \( A \)
в. \( A>C \)
c. \( A=C \)
D. \( A \geq C \)


A 10 V battery of negligible internal resistance is connected across a \( 200 \mathrm{V} \)
battery and a resistance of \( 38 \omega \) as
shown in the figure. Find the value of the current in circuit.


Bryophytes differ from thallophytes in having
A. Embryo
B. Rhizoids
c. Sterile jacket around sex organs
D. All of the above


Negation of the statement:
\( \sqrt{5} \) is an integer or 5 is irrational is?
A. \( \sqrt{5} \) is not an integer or 5 is not irrational
B. \( \sqrt{5} \) is not an integer and 5 is not irrational
c. \( \sqrt{5} \) is irrational or 5 is an integer
D. \( \sqrt{5} \) is an integer and 5 is irrational


The self inductance of a coil is \( 5 \mathrm{m} \) H. If
a current of 2 A is flowing in it then the magnetic flux produced in the coil will be
A . 0.01 Weber
B. 10 Weber
c. zero
D. 1 Weber


Corrosion is the process of rusting of any kind of metal or alloy due to the presence of moisture and air in it's
surrounding. As it comes in contact with air and water it reacts with it and a
layer is formed above it's surface. Type 1
for true and 0 for False.


assertion - The interference of two
identical waves moving in same direction produces standing waves. Reason - Various elements of standing waves do not remain in constant phase.
A. Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A ride in an amusement park called
scream machine swings the riders
around a complete vertical circle during
the course of the ride.
Identify where on the ride both PE and
KE are equal?
A. Point \( A \)
B. Point B
c. Point \( C \)
D. Point D
E . Point E


Twenty dots will cover one square inch.
If a floor measures 5 feet by 2.5 feet, how many dots does it take to cover the
floor?
A . 1,800
B. 15,000
c. 36,000
D. 45,000


Find \( x \)


Bond angle in \( H_{2} O\left(104.5^{\circ}\right) \) is higher
than the bond angle of \( H_{2} S\left(92.1^{\circ}\right) . \) The
difference is due to:
A. 0 is diatomic and \( S \) is tetra-atomic
B. difference in electronegativity of S and 0
c. difference in oxidation states of S and 0
D. difference in shapes of hybrid orbitals of S and


Excess of carbon dioxide in the
atmosphere leads to
A. Global warming
B. Ozone depletion
c. Acid rain
D. None of the above


In triangle \( A B C \), the medians intersect
at point \( G . \) Suppose \( \angle A B C=90^{\circ} \) and
\( \angle B A C+\angle B G C=180^{\circ} . \) Find the value
of \( \cos \angle A C B \)
A \( \cdot \frac{\sqrt{2}}{\sqrt{3}} \)
B. \( \frac{\sqrt{2}}{\sqrt{5}} \)
c. \( \frac{2}{\sqrt{5}} \)
D. None of these


\[
\begin{aligned}
\boldsymbol{f}(\boldsymbol{x})=& \boldsymbol{x}, \boldsymbol{i} \boldsymbol{f} \boldsymbol{x} \leq 1 \\
\boldsymbol{5}, & \boldsymbol{i} \boldsymbol{f} \boldsymbol{x} \geq 1
\end{aligned}
\]
Check whether \( f(x) \) is continuous at
\[
\boldsymbol{x}=\mathbf{0} ? \boldsymbol{x}=\mathbf{1} ? \boldsymbol{x}=\mathbf{2} ?
\]


Thread-like filaments which form the
body of the fungi are
A. Rhizoids
B. Paraphyses
c. Hyphae
D. Haptera


Solve \( \frac{6 x^{2}-5 x-3}{x^{2}-2 x+6} \leq 4 \)


pH of water is 7. When substance Y is
dissolved in water, the pH becomes 13 The substance Y is salt of:
A. strong acid and strong base
B. weak acid and weak base
c. strong acid and weak base
D. strong base and weak acid


\( K F \) combines with \( H F \) to from \( K H F_{2} \)
The compound contains the species:
A \( \cdot K^{+}, F^{-} \) and \( H^{+} \)
B. \( K^{+}, F^{-} \) and \( H F \)
\( \mathbf{c} \cdot K^{+} \) and \( \left[H F_{2}\right]^{-} \)
D. \( [K H F]^{+} \) and \( F_{2} \)


Choose the correct answer from the
alternatives given:
In E. Coli, the lac operon gets switched
on when
A. Lactose is present and it binds to the repressor
B. Repressor binds to operator
C. RNA polymerase binds- to the operator
D. Lactose is present and it binds to RNA polymerase


When no current is passed through a
conductor
A. the free electrons do not move
B. the average speed of a free electrons over a large speed of time is zero
C. the average velocity of a free electron over a large period of time is zero
D. the average of the velocities of all the free electrons at an instant is zero


Observe the given diagram and fill in
the blanks by choosing the correct
option.
\( \mathbf{A} \cdot \mathbf{x}-H_{2(g)} \) at 1 atm \( , y-10^{-2} M H^{+}, z^{-} \) Finely divided \( P t \)
B . \( x-H_{2(g)} \) at 1 bar, \( y-1.00 M H^{+}, z \) - Finely divided Pt
C. \( x-1.00 M H^{+}, y-H_{2(g)} \) at 1 bar, \( z \) - Finely divided \( N \) i
D. \( x-H_{2}(g) \) at 1 bar, \( y-1.00 M H^{+}, z \) - Pt granules


When one mole each of \( \mathrm{CO} \) and \( \boldsymbol{O}_{2} \) are
made to react at STP, the total number
of moles at an end of the reaction is:
A. 1.5 moles
B. 1 mole
c. 4 moles
D. 2 moles


Evaluate:
\( \frac{\sec x^{o}+\tan x^{o}}{\sec x^{o}-\tan x^{o}} \)


If the lengths of the sides of a right angled triangle \( A B C \) right angled at \( C \)
\( \operatorname{are} \operatorname{in} A . P ., \) find \( 5(\sin A+\sin B) \)


Why water cannot control fire caused by oil or petrol?
A. Water reacts with oil
B. Water is denser than oil
c. water is less denser than oil
D. Water mixes with oil


Autumn wood is distinguishable from spring wood in having
A. Narrow tracheary elements
B. Broader tracheary elements
c. Lighter colour
D. Cambium


Find the area of a regular hexagon each of whose sides measures \( 5 \mathrm{cm} .(\sqrt{3}= \)
1.732)
A \( \cdot 64.95 \mathrm{cm}^{2} \)
B . \( 69.95 \mathrm{cm}^{2} \)
c. \( 64.95 \mathrm{m}^{2} \)
D. None of these


A block of mass \( m \) slides down an
inclined right angled trough. If the
coefficient of kinetic friction between
the block and the trough is \( \mu_{k} \)
acceleration of the block down the plane
is:
\( \mathbf{A} \cdot g\left(\sin \theta-2 \mu_{k} \cos \theta\right) \)
B \( \cdot g\left(\sin \theta+2 \mu_{k} \cos \theta\right) \)
\( \mathbf{c} \cdot g\left(\sin \theta-\sqrt{2} \mu_{k} \cos \theta\right) \)
\( \mathbf{D} \cdot g\left(\sin \theta-\mu_{k} \cos \theta\right) \)


The vapour pressure of water at \( 293 \mathrm{k} \) is 2438 Pa and the vapour pressure of an aqueous solution is 2395.8 Pa. If
solution density is \( 1080 \mathrm{kg} / \mathrm{m}^{3} \) at \( 313 \mathrm{K} \)
Calculate the osmotic pressure at 313
K. The molecular weight of solute =60.
A .24 .54 Pa
B . \( 24.54 \times 10^{5} \) Pa
c. 0.955 Pa
D. None of these


Draw the logic symbol of AND gate.


A magnet is suspended in such a way that it oscillate it horizontal plane.
It make 20 oscillation per minute at a
place were dip angle is 30 and 15 oscillation per minute t a place were dip angle is \( 60 . \) the ratio of total magnetic field at the two place is
A . 15 oscillations/minute
в. \( 1.7 \sqrt{3} \)
c. 18 oscillations/minute
D. zero


Pure water conducts electricity.
A. True
B. False
c. Ambiguous
D. Data insufficient


Phosphorous reacts with chlorine gas to give a colourless liquid, which fumes in moist air to produce HCl and.
A. \( P O C l_{3} \)
в. \( H_{3} P O_{3} \)
\( \mathrm{c} . P H_{3} \)
D. \( H_{3} P O_{4} \)


Reproductive tap roots occur in
A. Dalbergia
B. Peepal
c. Acacia
D. Banyan


A small isolated conductor has a large
positive charge.

What is true of the electric field and the
electric potential inside this conductor?
A . Electric Field inside Conductor - Electric Potential inside Conductor, large and positive - large and positive
B. Electric Field inside Conductor - Electric Potential inside Conductor, zero - zero
C. Electric Field inside Conductor - Electric Potential inside Conductor, zero - large and positive
D. Electric Field inside Conductor - Electric Potential inside Conductor, large and positive - zero
E. Electric Field inside Conductor - Electric Potential inside Conductor, large and positive - large and negative


Let \( a, b, c \) and \( d \) be any four real
numbers. Then, \( a^{n}+b^{n}=c^{n}+d^{n} \) holds
for any natural number \( n \), if
(This question has some ambiguity, but appeared in WBJEE 2015 exam)
A \( . a+b=c+d \)
В . \( a-b=c-d \)
c. \( a+b=c+d, a^{2}+b^{2}=c^{2}+d^{2} \)
D . \( a-b=c-d, a^{2}-b^{2}=c^{2}-d^{2} \)


Assertion
Coordination is the process through which two or more organs interact and complement the functions of one
another
Reason
In our body the neural system and the endocrine system jointly coordinate all the activities of the organs
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


If the magnetizing field on a ferromagnetic material is increased, its
permeability.
A . Decreased
B. Increased
c. Is unaffected
D. May be increased or decreased


An object of \( 2 \mathrm{cm} \) height is placed at a
distance of \( 10 \mathrm{cm} \) from a concave mirror
of radius of curvature \( 30 \mathrm{cm} . \) Find the image distance, height and magnification.


Give any three differences between an
artery and a vein.


A given wire of residence \( 1 \Omega \) is stretched to double its length. What will
be its new resistance.


At \( 340 \mathrm{K} \) one atmospheric pressure
\( N_{2} O_{4} \) is \( 66 \% \) dissociated into \( N O_{2} \)
What volume of \( \log N_{2} O_{4} \) occupy under
these conditions?


Biochemical oxygen demand in a river
water
A. Remains unchanged when algal bloom occurs
B. Increases when sewage gets mixed up with river water
C. Has no relationship with concentration of oxygen in water
D. Gives a measure of Salmonella in water


A block of mass \( 5 k g \) is released from rest when compression in spring is \( 2 m \)
Block is not attached with the spring and natural length of the spring is \( 6 m \) Maximum height of block from ground
is: \( \left(\boldsymbol{g}=\mathbf{1 0} \boldsymbol{m} / \boldsymbol{s}^{2}\right) \)


State whether the given algebraic expressions are polynomials? Justify. \( x^{2}+7 x+9 \)


Convert the following ratio into the
percentage.
\( \mathbf{1 5}: \mathbf{2 5} \)


Sl unit of resistance is volt.
A. True
B. False


A steady current flows in a long wire. It is bent into a circular loop of one turn and the magnetic field at the centre of
the coil is \( B \). If the same wire is bent
into a circular loop of \( n \) turns, the magnetic field at the centre of the coil
is:
A \( \cdot \frac{B}{n} \)
в. \( n B \)
\( c \cdot n B^{2} \)
D . \( n^{2} B \)


If you have a finite arithmetic sequence, the first number is 2 and the common
difference is \( 4, \) what is the \( 5^{t h} \) number
in the sequence?
\( \mathbf{A} \cdot \mathbf{6} \)
B. 10
c. 14
D. 18


Explain the resemblance of hydrogen to the other members of its group.


The primary source of energy stored in fossil fuels is derived from
A . Sea
B. Earth
c. sun
D. Rivers


A ray falls on a prism ABC (AB = BC) and travels as shown in figure. The
minimum refractive index of the prism
material should be
4
B. \( \sqrt{2} \)
c. 1.5
D. \( \sqrt{3} \)


The d-electron configurations of \( \boldsymbol{C r}^{2+}, \boldsymbol{M n}^{2+}, \boldsymbol{F} \boldsymbol{e}^{2+} \) and \( \boldsymbol{C o}^{2+} \) are
\( d^{4}, d^{5}, d^{6} \) and \( d^{7} \) respectively. Which one
of the following will exhibit minimum paramagnetic behaviour? (Atomic numbers of \( \mathrm{Cr}=\mathbf{2 4}, \boldsymbol{M n}= \)
\( \mathbf{2 5}, \mathbf{F e}=\mathbf{2 6}, \mathbf{C o}=\mathbf{2 7}) \)
\( \mathbf{A} \cdot\left[M n\left(H_{2} O\right)_{6}\right]^{2+} \)
в. \( \left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2} \)
c. \( \left[\operatorname{Co}\left(H_{2} O\right)_{6}\right]^{2+} \)
D \( \cdot\left[C r\left(H_{2} O\right)_{6}\right]^{2} \)


Assertion
Oral Rehydration Therapy (ORT) has been strongly recommended for reducing infant mortality.
Reason
Gastrointestinal problems are very common among children especially in the developing countries
A. Both A and R are true but R is the correct explanation of A
B. Both A and R are true but R is not a correct explanation of A
c. A is true but R is false
D. A is false but R is true


Select the incorrect statements about
the plots of \( \ln \boldsymbol{K} \) vs \( \frac{\mathbf{1}}{\boldsymbol{T}} \)
This question has multiple correct options
A . Linear with slope equal to \( \frac{\Delta G^{o}}{R} \) and intercept \( \Delta H \)
B. Curve
c. Linear with slope \( -\frac{\Delta H^{o}}{R} \) and intercept \( \frac{\Delta S^{o}}{R} \)
D. Linear with slope \( -\frac{\Delta S^{o}}{R} \) and intercept \( \frac{\Delta H^{o}}{R} \)


\( \boldsymbol{p} \boldsymbol{K}_{\boldsymbol{b}} \) of \( \boldsymbol{N} \boldsymbol{H}_{3} \) is \( \boldsymbol{4} . \boldsymbol{7} 4 \) and \( \boldsymbol{p} \boldsymbol{K}_{\boldsymbol{b}} \) of \( \boldsymbol{A}^{-}, \boldsymbol{B}^{-} \)
and \( C^{-} \) are 4,5 and 6 respectively.
Aqueous solution of \( 0.01 M \) has \( p H \) in
the increasing order.
A \( . N H_{4} A<N H_{4} B<N H_{4} C \)
B. \( N H_{4} C<N H_{4} B<N H_{4} A \)
C . \( N H_{4} C<N H_{4} A<N H_{4} B \)
D. All have equal \( p H \)


Ozone hole is widest over
A. Equator
B. North pole
C. North temperate area
D. Antarctica


If for an \( A, P ., S_{8}=16 \) and \( S_{16}=8, \) find
the first negative term


In which of the following transition will the wavelength be minimum?
A \( . n=6 \) to \( n=4 \)
в. \( n=4 \) to \( n=2 \)
c. \( n=3 \) to \( n=1 \)
D. \( n=2 \) to \( n=1 \)


Carbon tetrachloride and benzene are:
A . immiscible in water
B. miscible in water
c. both \( A \) and \( B \)
D. none of these


Example of intrinsic colloid is:
B. sulphur sol
c. egg-albumin
D. \( F e(O H)_{3} \) sol


The error in the measurement of length
of a simple pendulum is \( 0.1 \% \) and error in the time period is \( 2 \% \). The possible maximum error in the quantity having dimensional formula \( L T^{-2} \) is
A . \( 1.1 \% \)
в. \( 2.2 \% \)
c. \( 4.1 \% \)
D. 6.1\%


The point on the curve \( x y^{2}=1 \) which is
nearest to the origin is
A. (1,1)
) 1
в. (1,-1)
c. \( \left(4, \frac{1}{2}\right) \)
D. \( \left(\frac{1}{2^{\frac{1}{3}}}, 2^{\frac{1}{6}}\right) \)


During photorespiration, when two \( O_{2} \)
molecules react with 2 moles of RUBP
then how many \( 3-P G A \) molecules are
formed from 2 molecules of \( 2- \)
phosphoglycolate
A . 2
B. 1
\( c .3 \)
D. 4


\( \begin{array}{ll}\text { List I } & \text { List II } \\ \text { a. Troposphere } & 1.11-50 \mathrm{Km} \\ \text { b. Stratosphere } & 2.85-500 \mathrm{Km} \\ \text { c. Mesosphere } & \text { 3. 0-11 Km } \\ \text { d. Thermosphere } & \text { 4. 50-85 Km } \\ \text { 5. Above 500 Km } & \text { 1) }\end{array} \)
The correct match is:
A. \( a-5, b-2, c-3, d-4 \)
B. \( a-1, b-2, c-3, d-4 \)
\( c \cdot a-3, b-1, c-4, d-2 \)
D. \( a-2, b-4, c-5, d-1 \)


The domain of \( \frac{1}{\log _{10}(1-x)}+ \)
\( \sqrt{(x+2)} \) is
A \( \cdot(-2 \leq x<-1) \cup(0<x<1) \)
B . \( (-2 \leq x<2) \)
c. \( (-2 \leq x<1) \)
D \cdot \( (-2 \leq x<0) \cup(0<x<1) \)


The frequencies of two sound sources are \( 256 \mathrm{Hz} \) and \( 260 \mathrm{Hz}, \) At \( \mathrm{t}=0, \) the intensity of sound is maximum. Then
the phase differance at the time \( t=1 / 16 \)
sec will be
A. zero
в. \( \pi \)
c. \( \pi / 2 \)
D. \( \pi / 4 \)


The molarity of \( M g^{2+} \) ions in a
saturated solution of \( M g_{3}\left(P O_{4}\right)_{2} \)
whose solubility product is \( 1.08 \times \)
\( \mathbf{1 0}^{-13} \boldsymbol{M}^{\mathbf{5}} \) is
A . \( 1.0 \times 10^{-3} M \)
В. \( 2.0 \times 10^{-3} M \)
c. \( 3.0 \times 10^{-3} M \)
D. \( 4.0 \times 10^{-3} M \)


If \( p^{t h}, 2 p^{t h}, 4 p^{t h} \) terms of an A.P. are in
G.P. then common ratio of G.P. is
\( A \)
B. 2
\( c \cdot 3 \)
D. 4


How many \( 6 \mathrm{mF}, 200 \mathrm{V} \) condensers are
needed to make a condenser of \( 18 \mathrm{mF} \)
\( 600 \vee ? \)
\( A \cdot 9 \)
B. 18
\( c \cdot 3 \)
D. 27


The ratio of the radii of the planets \( \boldsymbol{R}_{1} \)
and \( R_{2} \) is \( k . \) The ratio of the acceleration
due to gravity is \( r . \) The ratio of the escape velocities from them will be
\( \mathbf{A} \cdot k r \)
B. \( \sqrt{k r} \)
c. \( \sqrt{(k / r)} \)
D. \( \sqrt{(r / k)} \)


Fill in the blank spaces by choosing the correct word.
A prism is a piece of transparent material having three rectangular surfaces and \( \ldots \ldots . . . . \) triangular surfaces.
A. three
B. \( t w o \)
c. four
D. one


A neutral water molecule is placed in electic field \( \boldsymbol{E}=\mathbf{1 . 2 5} \times \mathbf{1 0}^{\mathbf{4}} \boldsymbol{N} / \boldsymbol{C} . \) The
work done to rotate it by \( 180^{\circ} \) is \( 2.5 \times \)
\( 10^{-25} J . \) Find aproximate separation of
center of charges.
A. \( 0.625 \times 10^{-9} \mathrm{m} \)
в. \( 0.65 \times 10^{-10} \mathrm{m} \)
C \( .0 .75 \times 10^{-10} \mathrm{m} \)
D. \( 0.625 \times 10^{-10} m \)


What are the advantages of using armature as the stator in a power
generator?


(a) Name the enzyme responsible for the transcription of tRNA and the amino
acid the initiator tRNA gets linked with.
(b) Explain the role of initiator tRNA in initiation of protein synthesis.


Simplify, using trigonometric tables
\( \tan 63^{\circ} 12^{\prime}-\cos 12^{\circ} 42^{\prime} \)


The nature of image formed on
the retina of human eye is:
A. virtual and erect
B. virtual and inverted
c. real and erect
D. real and inverted


In n-type semiconductors, the electron concentration is equal to:
A. density of donor atoms
B. density of acceptor atoms
C. density of both type of atoms
D. neither density of acceptor atoms nor density of donor atoms


The ratio in which the line joining
(2,-4,3) and (-4,5,-6) is divided by the plane \( 3 x+2 y+z-4=0 \) is
A .2: 1
B . 4: 3
\( c \cdot-1: 4 \)
D. 2: 3


50 g of copper is heated to increase its
temperature by \( 10^{\circ} \mathrm{C} \). If the same quantity of heat is given to 10 g of water, the rise in temperature is (specificheat of copper \( = \)
\( 420 J k g^{-1} K^{-1}, \) specificheat of water
\( \left.4200 J k g^{-1} K^{-1}\right) \)
\( \mathbf{A} \cdot 5^{\circ} C \)
B . \( 6^{\circ} \mathrm{C} \)
\( \mathrm{c} \cdot 7^{\circ} \mathrm{C} \)
D. \( 8^{\circ} \mathrm{C} \)


Define isomerism. Give the IUPAC name
of the isomer \( C_{4} H_{10} \) which has a branched chain


From a piece of cardboard, in the shape
of a trapezium \( A B C D, \) and \( A B \| C D \) and \( \angle \)
\( \mathrm{BCD}=90^{\circ}, \) quarter circle is removed
Given \( A B=B C=3.5 \mathrm{cm} \) and \( \mathrm{DE}=2 \mathrm{cm} \)
Calculate the area of the remaining
piece of the cardboard.(Take \( \pi \) to be \( \frac{22}{7} \)
A \( .9 .625 \mathrm{cm}^{3} \)
в. \( 6.125 . \) ст
\( \mathbf{c} \cdot 2.625 \mathrm{cm}^{2} \)
D. None of these


Which of the following haloalkanes is most reactive?
A. 1-chloropropane
B. 1-bromopropane
c. 2-chloropropane
D. 2-bromopropane


The binding energy of an electron in the
ground state of \( \boldsymbol{H} \boldsymbol{e} \) atom is \( \boldsymbol{E}_{\mathbf{0}}= \)
24.6e \( V \). The energy required to remove
both the electrons from the atom is
A . \( 24.6 e V \)
в. \( 79.0 e V \)
c. \( 54.4 e V \)
D. None of these


The distance versus time graph of a
particle moving is shown below.
What does the graph indicate?
A. The particle starts with certain velocity with retardation and finally comes to restt
B. The velocity of the particle is constant.
C. The acceleration of the particle is uniform throughout
D. The particle starts with a certain velocity and finally becomes uniform after certain time


Very short answer type.
What is the source for aldosterone?


Identify the correct sequence of stages
in the water cycle.
A. Evaporation, condensation, precipitation
B. Condensation, precipitation, evaporation
C. Evaporation, precipitation, condensation
D. Precipitation, evaporation, condensation


Element P has atomic number 19. To
which group does P belongs to?
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot 17 \)
\( D \cdot 16 \)


Alcea rosea (hollyhock) belongs to the family of
A. Cruciferae
B. Malvaceae
c. cucurbitaceae
D. Leguminosae


The minimum value of \( f(x)=x^{2}+ \)
\( \mathbf{2} \boldsymbol{x}+\mathbf{3}, \boldsymbol{x} \in \boldsymbol{R} \) is equal to
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
\( D \)


Reflection of a light wave at a fixed point results in a phase difference between incident and reflected wave of
This question has multiple correct options
A \( \cdot \frac{3 \pi}{2} \)
в. \( 2 \pi \)
\( c . \pi \)
D.


Divide \( 15 x^{3}-20 x^{2}+13 x-12 \) by
\( 3 x-6 \)


The hybridisation of \( C \) atoms in \( (C- \)
\( \boldsymbol{C}) \operatorname{single} \) -bond of \( \boldsymbol{H}-\boldsymbol{C} \equiv \boldsymbol{C}- \)
\( \boldsymbol{C H} \equiv \boldsymbol{C H}_{2} \) is
\( \mathbf{A} \cdot s p^{3}-s p^{3} \)
B \( \cdot s p^{2}-s p^{3} \)
c. \( s p-s p^{2} \)
D. \( s p^{3}-s p \)


Match List-I (species) with List-II
(Hybrid orbitals used by the central atom in their formation) and select the
correct answer:
List-I
\( s p^{3} \) \( N i(C N)_{5}^{3-} \)
(A) 's
(B) \( \mathrm{CuCl}_{5}^{3-} \)
(2) \( d s p^{2} \)
(c)
(3) \( s p^{3} d_{z^{2}} \) \( A u C l_{4}^{-} \) ( )
(D) \( \mathrm{ClO}_{4}^{-} \) ) \( d_{x^{2}-y^{2}} s p^{3} \)
\( ^{3} \) (4)
A \( \cdot(A)-1,(B)-3,(C)-2,(D)-4 \)
B. \( (A)-3,(B)-4,(C)-2,(D)-1 \)
c. \( (A)-4,(B)-2,(C)-1,(D)-3 \)
D. \( (A)-4,(B)-3,(C)-2,(D)-1 \)


In which of the following months, the Great Bear constellation can be seen
clearly in the northern part of the sky at night?
A. October
B. December
c. April
D. June


Watson and Crick were awarded Nobel
Prize for their finding of
A. RNA is single stranded
B. DNA is double stranded
c. DNA is genetic material
D. DNA guides mRNA synthesis


A strong acid will ionize
in water while a weak acid will only
ionize.
A . partially, partially
B. completely, completely
c. partially, completely
D. completely, partially


In the adjoining figure, the position time graph of a particle of mass \( 0.1 \mathrm{kg} \) is shown. The impulse at \( t=2 s \) is :
A . \( 0.02 \mathrm{kgm} / \mathrm{s} \)
B. \( 0.1 \mathrm{kgm} / \mathrm{s} \)
c. \( 0.2 k g m / s \)
D. \( 0.4 k g m / s \)


Which anion is stable towards water:
\( A \cdot O^{2} \)
в. \( O_{2}^{2} \)
\( c \cdot O_{2} \)
D. None of these


Electric current is passed through a straight conductor passing through the center of a piece of cardboard.Some iron fillings are sprinkled on the cardboard and tapped.The iron fillings
around the conductor
A. Settle as parallel lines
B. Settle as circles
c. settle at one point
D. Do not acquire any regular pattern


Consider the following metallurgical
processes:
1) Heating impure metal with \( \mathrm{CO} \) and distilling the resulting volatile carbonyl
(b.pt. \( \left.43^{\circ} \mathrm{C}\right) \) and finally decomposing at
\( 150^{\circ} \mathrm{C} \) to \( 230^{\circ} \mathrm{C} \) to get the pure metal.
2) Heating the sulphide ore in the air until a part is converted to oxide and
then further heating in the absence of
air to let the oxide react with
unchanged sulphide.
3) Electrolyzing the molten electrolyte
containing \( C a C l_{2} \) to obtain the metal.
The processes used for obtaining sodium, nickel and copper are,
respectively:
A. 1,2 and 3
B. 2, 3 and 1
c. 3,1 and 2
D. 2,1 and 3


A liquid will NOT wet the surface of a solid if its angle of contact is
A. Zero
B. Less than 90
c. More than 90
D. \( 90^{\circ} \)


How would you define reflection of light?


From the schematic electric field lines,
we can infer that
A. the left charge is higher in magnitude than the right
one
B. the left charge is lower in magnitude than the right one
c. the left charge is equal in magnitude to the right one
D. None of these


The displacement of a particle after
time \( t \) is given by \( \boldsymbol{x}=\left(\boldsymbol{k} / \boldsymbol{b}^{2}\right)\left(\mathbf{1}-\boldsymbol{e}^{-\boldsymbol{b} \boldsymbol{t}} \boldsymbol{t}\right. \)
where b is a constant. What is the
acceleration of the particle?
A \( \cdot k e^{-b} \)
B. \( -k e^{-b} \)
\( \mathbf{c} \cdot \frac{k}{b^{2}} e^{-b t} \)
D. \( \frac{-k}{b^{2}} e^{-b t} \)


Assertion
In each of the three planes determined by two of the lines \( O A, O B, O C \) ( \( O \) being the origin), a straight line is drawn through \( O \) perpendicular to the third line.
The three lines so determined are
coplanar.
Reason
\( (a \times b) \times c+(b \times c) \times a+(c \times a) \times \)
\( b=0, \) where \( O A=a, O B=b \) and
\( \boldsymbol{O} \boldsymbol{C}=\boldsymbol{c} \)
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


Convert the following into proper fraction: \( 4 \frac{3}{5} \)


Which of the following can fix atmospheric nitrogen directly?
A . Pea
B. Brassica
c. castor
D. Petunia


Q Type your question-
the figure. The coefficient of friction,
between the particle and the rough
track equals \( \mu . \) The particle is released,
from rest, from the point \( \boldsymbol{P} \) and it comes
to rest at a point \( R \). The energies, lost by
the ball, over the parts, \( P Q \) and \( Q R \), of
the track, are equal to each other, and
no energy is lost when particle changes
direction from \( P Q \) to \( Q R \) The values of
the coefficient of friction \( \mu \) and the
distance \( x(=Q R), \) are respectively
close to.
A. 0.2 and 6.5 m
B. 0.2 and 3.5 m
c. 0.29 and \( 3.5 m \)
D. 0.29 and 6.5


An air bubble in a glass with refractive
index 1.5 (near normal incidence) i.e.
\( 5 \mathrm{cm} \) deep when viewed from one
surface and \( 3 \mathrm{cm} \) deep when viewed
from the opposite face. The thickness(in
cm) of the is.
A . 16
B. 8
c. 10
D. 12.5


Three identical point masses, each of
mass \( 1 k g \) lie in the \( x \) -y plane at points \( (0,0),(0,0.2 m) \) and \( (0.2 m, 0) . \) The
gravitational force on the mass at the origin is
A \( \cdot 1.67 \times 10^{-9}(\hat{i}+\hat{j}) N \)
B. \( 3.34 \times 10^{-10}(\hat{i}+\hat{j}) N \)
c. \( 1.67 \times 10^{9}(\hat{i}-\hat{j}) N \)
D. \( 3.34 \times 10^{10}(\hat{i}-\hat{j}) N \)


If \( z_{1}, z_{2}, z_{3}, \) and \( z_{4} \) are the complex roots
of the equation \( z^{4}+3 z^{2}+1=0, \) then
the value of \( \prod_{i=1}^{4} 4+\left(z_{i}^{2}\right) \) is
\( \mathbf{A} \cdot \mathbf{9} \)
B. 12
c. 25
D. 27


A geostationary satellite is orbiting the earth at a height \( 6 \mathrm{R} \) above the surface of earth, where \( R \) is the radius of the
earth. The time period of another satellite at a height of \( 2.5 \mathrm{R} \) from the surface of earth in hour is
В. \( 1.5 \sqrt{2} h \)
c. \( 6 \sqrt{2} h \)
D. \( 12 \sqrt{2} h \)


A conducting sphere is negatively charged. Which of the following
statements is true?
A. The charge is uniformly distributed throughout the entire volume
B. The charge is located at the center of the sphere
c. The charge is located at the bottom of the sphere because of gravity
D. The charge is uniformly distributed on the surface of the sphere


\( \int \frac{1}{\left[\left(1-x^{2}\right)\left\{\left(2 \sin ^{-1} x\right)^{2}-9\right\}\right]^{1 / 2}} d x \)
A. \( \frac{1}{2} \log \left[2 \sin ^{-1} x+\sqrt{\left(2 \sin ^{-1} x\right)^{2}-9}\right] \)
B. \( \log \left[2 \sin ^{-1} x+\sqrt{\left(2 \sin ^{-1} x\right)^{2}-9}\right] \)
c. \( \frac{1}{2} \log \left[2 \sin ^{-1} x+\sqrt{\left(2 \sin ^{-1} x\right)^{2}+9}\right] \)
D. \( \frac{1}{2} \log \left[2 \sin ^{-1} x+\sqrt{\left(2 \cos ^{-1} x\right)^{2}-9}\right] \)


The \( 4^{t h} \) and \( 7^{t h} \) terms of a \( G P \) are \( \frac{1}{27} \) and \( \frac{1}{729} \) respectively. Find the sum of
\( m \) terms of the \( G P \)


The label of a herbarium sheet does not
carry information on
A. Local names
B. Height of the plant
c. Date of collection
D. Name of collector


The sum of the infinite series
\( 1+\frac{1+2}{2 !}+\frac{1+2+2^{2}}{3 !}+\frac{1+2+2^{2}+2^{3}}{4 !} \)
is \( e^{y}-e^{x} \) Find \( x+y^{2} \)


Assertion
If a ball in the shape of a sphere has a surface area of \( 221.76 \mathrm{cm}^{2}, \) then its diameter is \( 8.4 \mathrm{cm} \)
Reason
If the radius of the sphere be \( r, \) then surface area, \( S=4 \pi r^{2}, \) i.e. \( r=\frac{1}{2} \sqrt{\frac{s}{\pi}} \)
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


Equilibrium constants for the following reaction at \( 1200 \mathrm{K} \) are given
\( 2 H_{2} O(g) \leftrightharpoons 2 H_{2}(g)+O_{2}(g) ; K_{1}= \)
\( 6.4 \times 10^{-8} \)
\( 2 C O_{2}(g) \leftrightharpoons 2 C O(g)+O_{2}(g) ; K_{2}= \)
\( \mathbf{1 . 6} \times \mathbf{1 0}^{-\mathbf{6}} \)
The equilibrium constant for the reaction
\( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g}) \leftrightharpoons \boldsymbol{C} \boldsymbol{O}(\boldsymbol{g})+\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \)
at \( 1200 \mathrm{K} \) will be:
A. 0.05
в. 20
c. 0.2
D. 5.0


A combination of a ribose molecule, a
thymine and a sugar molecule will form
\( a \)
A. Ribosome
B. Nucleotide
c. Nucleic acid
D. ATP
E. ADP


f \( a_{1}, a_{2}, a_{3}, a_{4} \) are the terms in AP.
if \( a_{1}=5 ; d=9, a_{4} \) is equal to
A . 32
B. 27
c. 25
D. 22


\( \boldsymbol{C H}_{3}-\boldsymbol{M} \boldsymbol{g}-\boldsymbol{B r}+\boldsymbol{C O}_{2} \rightarrow \boldsymbol{X} \stackrel{\boldsymbol{H}_{3} \boldsymbol{O} \oplus}{\longrightarrow} \)
\( Y \) In this reaction Y is :
\( \mathbf{A} \cdot H C O O H \)
в. \( C H_{3} \) СООН
с. \( C_{2} H_{5} \)СООН
D. \( H C H O \)


Differentiate \( \frac{\tan ^{-1} x}{1+\tan ^{-1} x} \) w.r.t. \( \tan ^{-1} x . \)
A. \( \frac{1}{\left(1+\tan ^{-1} x\right)^{2}} \)
s. \( \frac{1}{\left(1-\tan ^{-1} x\right)^{4}} \)
c. \( \frac{1}{\left(1+\tan ^{-1} x\right)^{4}} \)
D. \( \frac{1}{\left(1-\tan ^{-1} x\right)^{2}} \)


If \( (x, y, z) \neq(0,0,0) \) and \( (\hat{i}+\hat{j}+ \)
\( \mathbf{3} \hat{\boldsymbol{k}}) \boldsymbol{x}+(\mathbf{3} \hat{\boldsymbol{i}}-\mathbf{3} \hat{\boldsymbol{j}}+\hat{\boldsymbol{k}}) \boldsymbol{y}+(-\mathbf{4} \hat{\mathbf{i}}+ \)
\( \mathbf{5} \hat{\boldsymbol{j}}) z=\boldsymbol{\lambda}(\boldsymbol{x} \hat{\boldsymbol{i}}+\boldsymbol{y} \hat{\boldsymbol{j}}+\boldsymbol{z} \hat{\boldsymbol{k}}), \) then the value
of \( \lambda \) will be
A \( .-2,0 \)
B. 0,-2
c. -1,0
D. 0,-1


Answer the question in at least 50
words.

Give the characteristic of magnetic
field lines.


Which of the given alternatives represent a point in Argand plane, equidistant from roots of the equation \( (z+1)^{4}=16 z^{4} ? \)
B \( \cdot\left(-\frac{1}{3}, 0\right) \)
\( ^{c} \cdot\left(\frac{1}{3}, 0\right) \)
D \( \cdot\left(0, \frac{2}{\sqrt{5}}\right) \)


\( \bar{a}, \bar{b} \) and \( \bar{c} \) are three vectors having magnitudes 1,1 and 2 respectively. If \( \bar{a} \times(\bar{a} \times \bar{c})+\bar{b}=0, \) then acute angle
between \( \overline{\boldsymbol{a}} \) \& \( \overline{\boldsymbol{c}} \) is
\( \mathbf{A} \cdot \pi / 6 \)
в. \( \pi / 4 \)
c. \( \pi / 3 \)
D. \( 5 \pi / 12 \)


Type your question
\( (e n=\text { ethane }-1,2-\text { diamine }) \)
\( \mathbf{A} \)
\( B \)
\( c \)
\( D \)


In Fig, the side \( Q R \) of \( \triangle P Q R \) is
produced to a point \( S \). If the bisector of
\( \angle P Q R \) and \( \angle P R S \) meet at point \( T, \) then prove that \( \angle Q T R=\frac{1}{2} \angle Q P R \)


A position-dependent force \( \boldsymbol{F}=\mathbf{4} \boldsymbol{x}^{\mathbf{3}}+ \)
\( 3 x^{2}+2 x-4 \) newton acts on a small
body of mass \( 2 k g \) and displaces it from \( x=0 \) to \( x=2 m . \) Calculate the work
done.
A . \( 20 J \)
в. \( 24 J \)
c. 16.5
D. \( 12 J \)


The greatest value of \( a b^{3} c \) is
\( A \cdot 3 \)
B. 9
c. 27
D. 81


How many lines of symmetry are there in a regular octagon?


There are three coplanar parallel lines. If any p points are taken on each limes, the maximum number of triangles with vertices at these points is


Which of the following oxoacid of phosphorous does not disproportionate?
A \( . H_{3} P O_{2} \)
в. \( H_{3} P O_{4} \)
c. \( H_{3} P O_{3} \)
D. All of these


\( I \) is the moment of inertia of a thin
square plate about an axis passing through opposite corners of plate. The moment of inertia of same plate about an axis perpendicular to the plane of plate and passing through its centre is :
A \( \cdot \frac{I}{2} \)
в. \( \frac{I}{\sqrt{2}} \)
\( c \cdot \sqrt{2} I \)
D. \( 2 I \)


The yellow colour of \( H N O_{3} \) is due to the
dissolution of


Arrange the following in increasing
order of their nucleophilicity in a polar
aprotic solvent.
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{O}^{-}, \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{S}^{-}, \boldsymbol{C H}_{3} \boldsymbol{C S}_{2} \)
A \( \cdot C H_{3} C S_{2}^{-}<C H_{3} C H_{2} O^{-}<C H_{3} C H_{2} S^{-} \)
в. \( C H_{3} C H_{2} O^{-}<C H_{3} C S_{2}^{-}<C H_{3} C H_{2} S^{-} \)
c. \( C H_{3} C H_{2} S^{-}<C H_{3} C S_{2}^{-}<C H_{3} C H_{2} O \)
D. None of these


Find the shortest distance between the
skew lines:
\( l_{1}: \frac{x-1}{2}=\frac{y+1}{1}=\frac{z-2}{4} \)
\( l_{2}: \frac{x+2}{4}=\frac{y-0}{-3}=\frac{z+1}{1} \)


A square frame ABCD is formed by four identical rods each of mass 'm' and
length 'T'. This frame is in \( X \) - Y plane such that side \( A B \) coincides with \( X- \)
axis and side \( A D \) along \( Y \) - axis. The moment of inertia of the frame about \( X \)
axis is
A \( \cdot \frac{5 m l^{2}}{3} \)
B. \( \frac{2 m l^{2}}{3} \)
c. \( \frac{4 m l^{2}}{3} \)
D. \( \frac{m l^{2}}{12} \)


(a) List three properties of ionic compounds.
(b) Show the formation of \( N a C l \) by transfer of electron
(c) How is it that ionic compounds in
the solid state do not conduct
electricity but they do so when in molten state?


For an exothermic reaction to be
sponteneous:
A. temperature must be high
B. temperature must be zero
c. temperature may have any magnitude
D. temperature and \( \Delta H<T \Delta S \).


Enzymes, which catalyze biochemica reactions are very complex. They help in the reaction of very specific substances This suggests that the enzyme and the reacting biochemicals are complementary to one another like a:
A. \( \operatorname{dog} \) in his kennel
B. horse and a rider
c. lock and key
D. leaf and a bud


\( 20 \mathrm{ml} \) of \( 1 \mathrm{M} \mathrm{BaCl}_{2} \) solution and \( 25 \mathrm{m} \)
of \( 0.1 \mathrm{M} \mathrm{Na}_{2} \mathrm{SO}_{4} \) are mixed to form
\( B a S O_{4} . \) The amount of \( B a S O_{4} \)
precipitated are:
A . 2.5 g
B. 2.5 moles
c. 2.5 millimoles
D. 0.05 millimoles


Name the compound of nitrogen occur in earth crust?


Find the area of the following circle, given that: (Take \( \pi=\frac{22}{7} \) )
Radius \( =14 \mathrm{mm} \)


The position vector of point \( F, \) is?
\( ^{\mathbf{A}} \cdot \frac{3|\bar{a}||\bar{c}|}{3|\bar{c}|+2|\bar{a}|}\left(\frac{\vec{a}}{|\bar{a}|}+\frac{\vec{c}}{|\bar{c}|}\right) \)
В \( \cdot \vec{a}+|\overrightarrow{\vec{c}}| \vec{c} \)
c. \( _{\vec{a}+} \frac{2|\vec{c}|}{|\vec{c}|} \vec{c} \)
D・ \( \quad \vec{a}-|\overrightarrow{\vec{c}}| \vec{c} \)


Concave and convex lenses, each have
the same focal length \( 20 \mathrm{cm} \) and they
are put in contact to form a
combination lens. This combination
lens is used to view an object of \( 5 \mathrm{cm} \)
length, kept at a distance \( 20 \mathrm{cm} \) from
the lens combination. As compared to
the object the image will be
A. Magnified and inverted.
B. Reduced and erect.
C. of the same size as the object and erect.
D. of the same size as the object but inverted.


Diameter of a sphere is \( 28 \mathrm{cm} \). Find its
surface area(in \( \left.c m^{2}\right) \)


A man, after a tour, finds that he had
spent every day as many rupees as the number of days he had been on tour How long did his tour last, if he had
spent in all \( R s .1,296 ? \)


Let \( f \) be differentiable for all \( \mathbf{x} . \) If \( \boldsymbol{f}(\mathbf{1})= \)
-2 and \( f^{\prime}(x) \geq 2 \) for all \( x \epsilon[1,6] \) then
A \( \cdot f(6)<8 \)
B. \( f(6) \geq 8 \)
\( \mathbf{c} \cdot f(6) \geq 5 \)
D. \( f(6) \leq 5 \)


Define the following with an example of Denatured protein.


The voltage gain of the following amplifier is
A . 10
B. 100
c. 1000
D. 9.9


Is the following number a perfect cube?
\( \mathbf{4 6 6 5 6} \)
Say yes or no.
A. Yes
B. No
c. Ambiguous
D. Data insufficient


What will be the distance between two
slits which, when illuminated by light of
wavelength \( 5000 A^{\circ}, \) produce fringes of
width \( 0.5 m m \) on a screen distant 1
meter from the slits?
\( \mathbf{A} \cdot 10^{-2} \) meter
B . \( 10^{-3} \) meter
\( \mathbf{c} \cdot 10^{-4} \) meter
D. \( 10^{-6} \) meter


What is another name for the wind
pipe?
A. Trachea
B. Larynx
c. oesophagus
D. Lungs


Which of the following statements is
true for wave motion?
A. Mechanical transverse wave can propagate through all medium.
B. Longitudinal waves can propagate through solids only.
C. Mechanical transverse waves can propagate through solids only.
D. Longitudinal waves can propagate through vacuum.


Draw the shape of water molecule.


Two elements \( A \) and \( B \) form
compounds having molecular formulae
\( A B_{2} \) and \( A B_{4} . \) When dissolved in 20.0 g
of benzene, 1.0 g of \( A B_{2} \) lowers the freezing point by \( 2.3^{\circ} \mathrm{C} \), whereas \( 1.0 \mathrm{g} \)
of \( A B_{4} \) lowers the freezing point by
\( 1.3^{\circ} \mathrm{C} . \) The molal depression constant for benzene in 1000 g is \( 5.1 . \) Calculate the atomic masses of \( A \) and \( B \)


The following shape has rotational
symmetry about the marked point of
order


According to Mendleev's periodic law which properties of the elements are the periodic function of their atomic
masses?
A. Physical properties
B. Chemical properties
c. Physical and chemical properties both
D. None of these


The energy absorbed in a body, when it
is strained within elastic limits is
known as
A . Resilience
B. Potential energy
c. Kinetic energy
D. Strain energy


Which of the following can occupy space and has mass?
A. Density
B. weight
c. Matter
D. A solid
E. volume


The correct thermodynamic conditions
for the spontaneous reaction at all
temperatures is:
\( \mathbf{A} \cdot \triangle H<0 \) and \( \Delta S=0 \)
B. \( \triangle H=0 \) and \( \triangle S<0 \)
c. \( \triangle H<0 \) and \( \Delta S>0 \)
D. \( \triangle H<0 \) and \( \triangle S<0 \)


A region in space has a total charge \( Q \)
distributed spherically such that the
volume charge density \( \rho(r) \) is given by
\( \boldsymbol{\rho}(\boldsymbol{r})=\boldsymbol{3} \boldsymbol{a} \boldsymbol{r}(\boldsymbol{2} \boldsymbol{R}) \)
for \( r \leq \frac{R}{2} \)
\( \boldsymbol{\rho}(\boldsymbol{r})=\boldsymbol{a}\left[\mathbf{1}-\left(\frac{r}{R}\right)^{2}\right] \quad \) for \( \frac{R}{2} \leq r \leq \)
\( \boldsymbol{R} \)
\( \rho(r)=0 \)
for \( r>R \)
Find the electric field at \( \rho\left(\frac{R}{2}<x<R\right) \)


If \( \boldsymbol{A}=(\mathbf{4}, \mathbf{1}, \mathbf{5}) \) and \( \boldsymbol{B}=(\mathbf{3}, \mathbf{4}, \mathbf{5}) \) The
direction ratios of \( \overline{A B} \) are


\( \Delta A B C \) is not right-angled and is inscribed in a fixed circle. If \( a, A, b, B \) be slightly varied keeping \( c, C \) fixed, then \( \frac{d a}{\cos A}+\frac{d b}{\cos B}=? \)
A \( .2 R \)
в. \( \pi \)
\( c \cdot 0 \)
D. none of these


When your car takes a sudden turn, you are thrown towards the outer side. Which law explains this process?
A. Newton's third law
B. Newton's second law
c. Newton's first law
D. Law of gravitation


Assertion
In short day plant, day length should be less than critical day length.
Reason
Long night should be continuous.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct, but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct.


The net resistance of the circuit at
resonance is
\( ^{A} \cdot \frac{\mathrm{L}}{\mathrm{CR}} \)
в. \( R \)
\( c \cdot \frac{\mathrm{CR}^{3}}{\mathrm{L}} \)
D \( \frac{\mathrm{L}^{2}}{\mathrm{C}^{2} \mathrm{R}^{3}} \)


Which one represents regulative
function of forests?
A. Production of wood
B. Conservation of soil and water
c. Production of essential oils
D. Storage and release of gases


The truth table given in figure
represents:
\begin{tabular}{|c|c|c|}
\hline \( \mathrm{A} \) & \( \mathrm{B} \) & \( \mathrm{Y} \) \\
\hline 0 & 0 & 0 \\
\hline 0 & 1 & 1 \\
\hline 1 & 0 & 1 \\
\hline 1 & 1 & 1 \\
\hline
\end{tabular}
A. AND-Gatt
B. NOR - Gate
c. NAND - Gate
DR - Gat


If \( ^{n} C_{r-1}=\left(k^{2}-8\right)\left(^{n+1} C_{r}\right), \) then \( k \)
belongs to This question has multiple correct options
A \( \cdot[-3,-2 \sqrt{2}] \)
(年 \( -[-3,-2 \sqrt{2},-\sqrt{2},-\sqrt{2}] \)
в. \( [-3,-2 \sqrt{2}) \)
c. \( 2 \sqrt{2} .3 \)
D. \( (2 \sqrt{2}, 3 \)


A metallic wire of young's modulus Y
and poisson's ratio \( \sigma \), length L and area of cross section A is stretched by a load of W kg. The increase in volume of the wire is:
\( \mathbf{A} \cdot \sigma\left(W^{2} L / 2 A Y^{2}\right) \)
В \( \cdot \sigma\left(W^{2} L / A Y^{2}\right) \)
c. \( \sigma\left(W^{2} L / 4 A Y^{2}\right) \)
D \( \cdot \sigma\left(2 W^{2} L / A Y^{2}\right) \)


\( (\boldsymbol{x}) \boldsymbol{C} \boldsymbol{H}_{3}-\underset{\prod_{0}^{M}-\boldsymbol{S}}{\|} \boldsymbol{O}-\boldsymbol{H} \)
\( (\boldsymbol{y}) \boldsymbol{C H}_{3}- \)
14 \( \begin{array}{ll}0 \\ \stackrel{1}{C}-O-H & (z) C H_{3}-O H\end{array} \)
Set the following in increasing order of
their \( p K_{a} \) values.
A. \( y<x<z \)
в. \( x<y<z \)
\( \mathbf{c} \cdot y<z<x \)
D. \( x<z<y \)


A current \( I \) passes through a wire of length \( l \), radius \( r \) and resistivity \( \rho \). The
rate of heat generated is
\( ^{\text {A }} \cdot \frac{I^{2} \rho}{r} \)
в. \( \frac{I^{2} \rho l}{\pi r} \)
c. \( \frac{I^{2} \rho}{\pi r^{2}} \)
D. none of these


is the flow of water
molecules from the region of higher water potential to the region of lower water potential through a semipermeable membrane.
A. Osmosis
B. Diffusion
c. Both A and B
D. None


Polyarch and exarch vascular bundles are the characteristic of
A . Dicot stem
B. Dicot root
c. Monocot stem
D. Monocot root


Let \( \overrightarrow{O A}=\vec{a}, \overrightarrow{O B}=10 \vec{a}+2 \vec{b} \) and
\( \overrightarrow{O C}=\vec{b}, \) where \( O, A \) and \( C \) are non
collinear points. Let \( p \) denote the area of
quadrilateral \( O A B C, \) and \( q \) denote the
area of the parallelogram with \( O A \) and \( O C \) as adjecent sides, then \( \frac{p}{q} \) is equal
to
A. 4
в. 6
\( ^{\mathrm{c}} \frac{1}{2} \frac{|\vec{a}-\vec{b}|}{\vec{a}} \)
D. None of these


State Raoult's law for the solution
containing volatile components. What is the similarity between Raoult's law
and Henry's law?


which of the following statements is true about effective nuclear charge?
This question has multiple correct options
A. \( Z_{\text {eff}} \) decreases from top to bottom
B. \( Z_{\text {eff}} \) increases from top to bottom
C. \( Z_{\text {eff}} \) increases as we move from left to right in periodic table
D. \( Z_{e f f}=Z \times \sigma \) (here \( \sigma \) is screening constant


Write the definition of figure of merit of
Galvanometer.


A Plane polarized light is incidents on an analyzer. The intensity then becomes three-fourth. The angle of the axis of the analyzer with the beam is
A \( \cdot 30^{\circ} \)
B \( .45^{\circ} \)
\( c \cdot 60^{\circ} \)
D. zero


A card is drawn at random from a well
shuffled pack of 52 cards. The probability that the cards drawn is
neither a red card nor a queen is
A \( \cdot \frac{6}{13} \)
в. \( \frac{5}{13} \)
c. \( \frac{4}{13} \)
D. \( \frac{2}{13} \)


A swimming pool is to be drained for cleaning. If L represents the number of liters of water in the pool t seconds after
the pool has been plugged off to drain and \( L=200(10-t)^{2} . \) What is the
average rate at which the water flows out during the first 5 seconds \( \left(\frac{\text {litres}}{\text {sec}}\right) \)
7


Solve the given inequalities graphically:
\( 2 x+y \geq 8, x+2 y \geq 10 \)


Rutherford scattering experiment is related to the size of the
A. Nucleons
B. Electron
c. Atom
D. Nucleus


Galileo's law of inertia is another name
for newton's (...) law of motion
A. First
B. second
c. Third
D. Any one of the above


Aphids with the help of
absorbs nutrients from the phloem of
the plants.


In Young's experiment with white light, the central fringe is white. If now a transparent film is introduced in the
upper beam coming from the top slit, then the white fringe:
A. moves downward
B. moves upward
c. remains at the same place
D. totally disappears


A uniform circular sheet has a radius r.
A square sheet of diagonal length equal to the radius of the plate is removed from one end of it. The distance of the
centre of mass of the reminder plate
from the centre of the original sheet is
A \( \cdot \frac{r}{2(2 \pi-1)} \)
в. \( \frac{r}{(\pi-2)} \)
c. \( \frac{2 r}{(\pi-3)} \)
D. \( \frac{r}{2(\pi-1)} \)


Caprolactam is the monomeric unit of :
A. Nylon 6,6
B. Nylon 2-Nylon 6
c. Nylon 6
D. None of these


At a certain locations, the strength of the electric field is \( 30.0 \mathrm{N} / \mathrm{C} \). A charge of \( 3.00 \mathrm{C} \) is placed at this location. How much force does this charge experience due to the electric field?
A. 90.0 N
B. 10.0
c. \( 0.100 \mathrm{N} \)
D. 270 N/C
E. \( 3.33 \mathrm{N} / \mathrm{C} \)


Find out the EMF of the following cells at \( 25^{0} \mathrm{C} \)
\( p t, B r_{2(l)}\left|B r^{-}(0.010 M)\right|\left|H^{+}(0.030 M)\right| H_{2}(1 a \)
\( \$ \$ 1 \) binom \( \left\{E\{\{0\}\}_{-}\left\{B r_{-}\{2\} / 2 B r^{\wedge}\{-\}\right\}=+1.08\right. \)
\( \left.V, R=8.314 J K^{\wedge}\left\{-\left.1 m o\right|^{\wedge}\{-1\}\right\},\right\} \)
\( \left\{F=96,\left.500 C m o\right|^{\wedge}\{-1\}\right\} \$ \)
A. \( 0.872 v \)
\( v \)
B . -0.872v
c. -1.052v
D. 1.288v


In a hockey match, both teams \( A \) and \( B \)
scored same number of goals up to the end of the game, so to decide the winner, the referee asked both the captains to throw a die alternately and decided that the team, whose captain gets a six first, will be declared the winner. If the captain of team \( A \) was
asked to start, find their respective probabilities of winning the match and state whether the decision of the referee
was fair or not.


Which one of the following is wrongly matched?
A \( \cdot\left[C u\left(N H_{3}\right)_{4}\right]^{2+} \) - Square planar
B . \( \left[N i(C O)_{4}\right] \) - Neutral ligand
c. \( \left[F e(C N)_{6}^{3-}\right]-s p^{3} d^{2} \)
D. \( \operatorname{Co}(e n)_{3}^{3+} \) - Follows EAN rule


Pacemaker of amphibians is located
A. Near inter-auricular septum
B. Inside right atrium
c. Inside right ventricle
D. In sinus venosus


Do the following subtraction with the help of numberline:
\( 8-2 \)


Rational numbers on the number line
represented by \( \boldsymbol{A}, \boldsymbol{E} \) and \( \boldsymbol{H} \)
\( \operatorname{are} \boldsymbol{A}=\frac{\mathbf{1}}{\mathbf{1 0}}, \boldsymbol{E}=\frac{\mathbf{5}}{\mathbf{1 0}}, \boldsymbol{H}=\frac{\mathbf{8}}{\mathbf{1 0}} . \) Are the
values correct?
A. Yes
B. No
c. cannot be determined
D. None


In translatory motion, The axis of frame
of object remains always parallel to the corresponding axis of ?
A. Mover's frame of reference
B. observer's frame of reference
c. Rotator's frame of reference
D. None of the above


Which modifications are necessary to
determine resistance of solutions by usual method of conductance
measurement?

This question has multiple correct options
A. A.c. should be used
B. A conductivity cell is used
c. Galvanometer is replaced by headphone or magic eye arrangement
D. None of the above


The catalyst used in preparation of oxygen from hydrogen peroxide is:
A. manganese dioxide
B. magnesium oxide
c. manganese oxide
D. manganese sulphate


Which is rich in energy?
A. NAD
B. Mitochondria
c. FAD
D. ATP


A wire is suspended vertically from one of its ends is stretched by attaching a weight of \( 200 \mathrm{N} \) to the lower end. The wire stretches the wire by \( 1 \mathrm{mm} \). The elastic energy stored in the wire is:


On doubling the distance between two masses the gravitational force between them will
A. Remain unchanged
B. Become one-fourth
c. Become half
D. Become double


If \( \left|\frac{z_{1}}{z_{2}}\right|=1 \) and \( \arg \left(z_{1} z_{2}\right)=0, \) then
A \( . z_{1}=z_{2} \)
В \( \cdot\left|z_{2}\right|^{2}=z_{1} z_{2} \)
\( \mathbf{c} \cdot z_{1} z_{2}=1 \)
D. \( z_{1}=-z_{2} \)


State True or False and write the correct
statement.
1. In the cartesian plane the horizontal line is called Y-axis.
2. In the cartesian plane the vertical line is called Y-axis.
3. The point which lies both the axes is called origin.
4. The point (2,-3) lies in the third quadrant.
5. (-5,-8) lies in the fourth quadrant.
6. The point \( (-x,-y) \) lies in the first quadrant where \( \boldsymbol{x}<\mathbf{0}, \boldsymbol{y}, \mathbf{0} \)


The path difference between two monochromatic light waves of wavelength \( 4000 A \) is \( 2 \times 10^{-7} m . \) The
phase difference between them is
A . \( \pi \)
B. \( 2 \pi \)
c. \( \frac{3 \pi}{2} \)
D.


Write the basicity order of the following.
\( \begin{array}{ll}\text { сн }_{3}-c \overbrace{C}^{\mathscr{Y}}^{\mathrm{NH}} & \mathrm{cH}_{3}-\mathrm{cH}_{2}-\mathrm{NH}_{2} \quad\left(\mathrm{cH}_{3}\right)_{2} \mathrm{NH} \\ & \mathrm{NH}_{3}\end{array} \)
(I)
\( A \cdot(\|)>(1)>(\| 1)>(1 V) \)
B. (I) > (III) > (II) > (IV)
\( c \cdot(\| I)>(I)>(\|)>(I V) \)
D. (I) > (II) > (III) > (IV)


000
000
000
000
00


A man throws a packet from a tower directly aiming at his friend who is standing at a certain distance from the base which is same as a height of the tower. If packet is thrown with a speed of \( 4 m / s \) and it hits the ground midway between the tower base \( \& \) his friend.
Find the height of the tower. (Take \( g= \) \( 9.8 m / s^{2} \)
A. 3.8
в. 4.4
\( c .3 .2 \)
D. 2.2


toppr
Q Type your question
option represents the correct arrangement of lipids in lipid bilayer?
\( A \)
B.
\( c \)
D.


\( \mathbf{A} \)
\( 13 \mathrm{N} \) weight and a \( 12 \mathrm{N} \) weight are connected by a mass less string over a mass less friction less pulley, The \( 13 \mathrm{N} \) weight has a downward acceleration with magnitude equal to that of a freely falling body time
\( A \)
B. 1 /12
\( c \cdot 1 / 13 \)
D. 1/25


What type of lens from the following would you have in your magnifying lens to read a page in small print?
A. A convex lens of focal length \( 80 \mathrm{cm} \)
B. A concave lens of focal length 80 cm
c. A concave lens of focal length \( 4 \mathrm{cm} \)
D. A convex lens of focal length of \( 4 \mathrm{cm} \)


What is the partial pressure (atm) of HI in the equilibrium mixture?
A . 6.385
в. 12.77
c. 40.768
D. 646.58


A conducting square loop of side \( L \) and
resistance \( R \) moves in its plane with a
uniform velocity \( v \) perpendicular to one
of its sides. A magnetic induction \( B \) constant in time and space, pointing perpendicular and into the plane of the loop exists everywhere, then the current induced in the loop is
88888888888
A. \( B L v / R \) clockwise
B. \( B L v / R \) anticlockwise
c. \( 2 B L v / R \) anticlockwise
D.


A thin rod of length \( l \) in the shape of a semicircle is pivoted at one of its ends such that it is free to oscillate in its own
plane. The frequency \( \boldsymbol{f} \) of small oscillations of the semicircular rod is :
A \( \cdot \frac{1}{2 \pi} \sqrt{\frac{g \pi}{2 l}} \)
в. \( \frac{1}{2 \pi} \sqrt{\frac{g \sqrt{\pi^{2}+4}}{2 l}} \)
c. \( \frac{1}{2 \pi} \sqrt{\frac{g \sqrt{\pi+2}}{l}} \)
D. \( \frac{1}{2 \pi} \sqrt{\frac{g \sqrt{\pi^{2}+1}}{2 \pi l}} \)


Fossil fuels are formed by decomposition of biomass buried under the earth over millions of years ago.
Name any two fossil fuels.


The work done in carrying a charge \( q \) once round a circle of radius a with a
charge \( Q \) at its centre is:
A \( \cdot \frac{q Q}{4 \pi \varepsilon_{0} a} \)
в. \( \frac{q Q}{4 \pi \varepsilon_{0} a^{2}} \)
c. \( \frac{q}{4 \pi \varepsilon_{0} a} \)
D. zero


Define the following terms as related to proteins.
(i) Peptide linkage
(ii) Primary structure
(iii) Denaturation


What conclusion would you draw from
the following graphs for an ideal gas?
This question has multiple correct options
A. As the temperature is reduced, the volume as well as pressure increase
B. As the temperature is reduced, the volume becomes zero and the pressure reaches infinity
C. As the temperature is reduced, the pressure decrease
D. A point is reached where, theoretically, the volume become zerc


Similarity between DNA and RNA is that
both have
A. Similar sugars
B. Similar mode of replication
c. similar pyrimidines
D. Polymers of nucleotides


Specimens found underground which are 1000 years old or more are
A. Cadavers
B. Fossils
c. Bones
D. None of the above


Which of the following is not a nonmetal?
A. Hydrogen
B. Silicon
C. Mercury
D. Chlorine


The value of \( \lim _{n \rightarrow \infty} \frac{(n !) \frac{1}{n}}{n} \) is?
\( \mathbf{A} \cdot \mathbf{1} \)
в. \( \frac{1}{e^{2}} \)
c. \( \frac{1}{2 e} \)
D.


Assertion
Yield strength is the stress required to produce a small specific amount of deformation.
Reason
The offset yield strength can be
determined by the stress corresponding
to the intersection of the stress-strain
curve and a line parallel to the elastic line offset by a strain of 0.2 or \( 0.1 \% \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


For which of the following dependences
of drift velocity \( v_{d} \) on electric field \( \mathrm{E} \), is
Ohm's law obeyed?
A \( \cdot v_{d} \propto E \)
в. \( v_{d} \propto E^{2} \)
c. \( v_{d} \propto \sqrt{E} \)
D. \( v_{d} \propto \frac{1}{E} \)


Which of the following does not represent a standing wave
A \( . y=A \sin \omega x \cos \omega t \)
B. \( y=A \sin \omega x \sin \omega t \)
c. \( y=A \cos \omega x \cos \omega t \)
D. none


The greatest value of the function \( f(x)=x e^{-x} \) in \( [0, \infty), \) is
A .
B.
\( c \cdot-c \)
D.


Draw a triangle \( P Q R \) in which \( P Q= \)
\( \mathbf{7} \boldsymbol{c m}, \boldsymbol{Q} \boldsymbol{R}=\mathbf{3} \boldsymbol{c m}, \boldsymbol{R} \boldsymbol{P}=\mathbf{4} \boldsymbol{c m} . \) Is the
construction of triangle possible?


A motor cyclist takes a U-turn in 4 seconds. His angular velocity will be
\( \boldsymbol{r} \boldsymbol{a} \boldsymbol{d} \boldsymbol{s}^{-1} \)
A . 0.7855
B. 0.7955
c. 0.8955
D. 0.9955


Solve \( : \int \sec ^{-1} \sqrt{x} d x \)


The value of \( X^{2} \) describes the
magnitude of the difference between
A. two normal distributions
B. expected and observed frequency
c. both (A) and (B)
D. two samples


The relation connecting the energy and distance \( r \) between dipole and induced dipole is :
\( \mathbf{A} \cdot U \propto r \)
B. \( U \propto r^{2} \)
c. \( U \propto r^{-6} \)
D. \( U \propto r^{6} \)


Which member of solar system also known as minor planets?
A. comet
B. Asteroids
c. Meteors
D. stars


Electric flux per unit solid angle is defined as
A. Electric force
B. Electric field intensity
c. Electric potential
D. Electric power


Assertion
In elastic collision, kinetic energy is
conserved.
Reason
Energy is always conserved.
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.


Nitric acid undergoes self dissociation.
A. True
B. False


Prove the following identity :
\( (1+\tan \alpha \tan \beta)^{2}+(\tan \alpha- \)
\( \tan \beta)^{2}=\sec ^{2} \alpha \sec ^{2} \beta \)


A solid sphere and a solid hemisphere have the same total surface area. Find
the ratio of their volumes.


In section \( A, 45 \) students out of 50
passed. In section \( B, 5 \) out of 60 failed. Which section had the better results?


The stability of benzene diazonium salts is because of:
A . inductive effect
B. resonance
c. hyperconjugation
D. mesomeric effect


\( 84 P_{0}^{210} \) originally at rest emits \( \alpha \) particles of KE 'K' Find the KE of recoiling nucleus:
A \( \cdot \frac{4}{214} K \)
в. \( \frac{4}{206} K \)
c. \( \frac{K}{206} \)
D. \( \frac{K}{214} K \)


The movement of sol particles under an applied electric field is called:
A. electro deposition
B. electrodialysis
c. electro-osmosis
D. electrophoresis


The mass of a full bottle of cooking oil is
\( 1.30 k g \)
When exactly half of the oil has been used, the mass of the bottle plus the
remaining oil is 0.90 kg.

What is the mass of the empty bottle?
A. \( 0.40 \mathrm{kg} \)
B. \( 0.50 \mathrm{kg} \)
c. \( 0.65 \mathrm{kg} \)
D. \( 0.80 \mathrm{kg} \)


The value of \( ^{\prime} g^{\prime} \) will be \( 1 \% \) of its value at the surface of the earth at a height of
\( \left(R_{e}=6400 k m\right) \)
\( A \cdot 6400 \mathrm{km} \)
B. 57600 km
c. \( 12560 \mathrm{km} \)
D. 64000 km


In the hydrogen atom, the kinetic energy
of the electron is \( 3.4 e V . \) The distance of
that electron from the nucleus:
A . \( 2.116 \AA \)
в. \( 0.529 \AA \)
c. \( 1.587 \hat{h} \)
D. \( 21.16 \AA \)


In the extraction of aluminium the
electrolyte is:
A. fused cryolite with felspar
B. fused cryolite with fluorspar
c. pure alumina in molten cryolite with fluorospar
D. pure alumina with bauxite and molten cryolite


The largest number of molecules is in:
A. \( 36 g \) of water
B. 28 g of carbon monoxide
c. \( 46 \mathrm{g} \) of ethly alcohol
D. \( 54 \mathrm{g} \) of nitrogen pentoxide


The number of moles of \( \boldsymbol{C} \boldsymbol{O}_{2} \) produced
when 3 moles of \( H C l \) react with excess
of \( \boldsymbol{C a} \boldsymbol{C O}_{3}, \) is:
\( \mathbf{A} \cdot \mathbf{1} \)
в. 1.5
\( c \cdot 2 \)
D. 2.5


In an atom bomb, the energy is released because of the:
A. chain reaction of neutrons and \( _{92} U^{23} \)
B. chain reaction of neutrons and \( _{\text {g2 }} U^{23} \)
C. chain reaction of neutrons and \( _{\text {y } 2} U^{236} \)
D. chain reaction of neutrons and \( _{92} U^{24} \)


A tunnel is dug along a diameter of the Earth. The force on a particle of mass \( \boldsymbol{m} \)
placed in the tunnel at a distance \( x \)
from the centre is:
A \( \cdot \frac{G M_{e} m}{R^{3}} x \)
в. \( \frac{G M_{e} m}{R^{2}} x \)
c. \( \frac{G M_{e} m}{R^{3} x} \)
D. \( \frac{G M_{e} m R^{3}}{x} \)


The electron density between \( 1 s \) and \( 2 s \)
is:
A . high
B. low
c. zero
D. abnormal


Evaluate \( \int \frac{d x}{\sqrt{x}(1+\sqrt{x})} \)
A \( \cdot \log (1+x)+c \)
B. \( 2 \log (x)+c \)
c. \( 6 \log (1+\sqrt{x^{2}})+c \)
D. \( 2 \log (1+\sqrt{x})+c \)


Atomic wt. of \( P \) is 31 and \( S b \) is 120 . What
will be the atomic wt. of As, as per Dobernier triad rule?
A . 151
B. 75.5
c. 89.5
D. Unpredictable


Let \( f \) and \( g \) be differential functions
satisfying \( \boldsymbol{g}^{\prime}(\boldsymbol{a})=\mathbf{2}, \boldsymbol{g}(\boldsymbol{a}) \boldsymbol{b} \) and \( \boldsymbol{f} \boldsymbol{o} \boldsymbol{g}=\boldsymbol{I} \)
(identify function) then \( \boldsymbol{f}^{\prime}(\boldsymbol{b})= \)
A \( \cdot 1 / 2 \)
B . 2
\( c \cdot 2 / 3 \)
D. None of these


A thin bar magnet of length \( 2 L \) is bent at the mid-point so that the angle
between them is \( 60^{\circ} . \) The new length of
the magnet is
A \( \cdot \sqrt{2} L \)
B. \( \sqrt{3} L \)
\( c \cdot 2 L \)
D. \( L \)


\( N_{2}(g)+3 H_{2}(g) \rightleftharpoons 2 N H_{3}(g)+22 \)
kcal. The activation energy for the
forward reaction 50 kcal. What is the
activation energy for the backward reaction?
A . 72 kcal
B. 28 kcal
c. -72 kcal
D. -28 kcal


Assertion
Chlorofluorocarbons are responsible for
ozone depletion.
Reason
Ozone level decreases by as much as
\( 67 \% \) every year.
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.


NaOH is:
A. a strong acid
B. a strong base
c. a weak acid
D. a weak base


The olefin which on ozonolysis gives
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H O} \) and \( \boldsymbol{C H}_{3} \boldsymbol{C H O} \) is :
A. 1 -butene
B. 2-butene
c. 1-pentene
D. Pent-2-ene


On interchanging the resistances, the balance point of a meter bridge shifts to
the left by \( 10 \mathrm{cm} . \) The resistance of their series combination is \( 1 k \Omega \). How much
was the resistance on the left slot
before interchanging the resistances?
A . \( 550 \Omega \)
в. \( 910 \Omega \)
\( \mathbf{c} .990 \Omega \)
D. \( 505 \Omega \)


Assertion
Light waves have different refractive indices in different media.
Reason
Variations in the velocities of light in different media cause the refractive
indices to be different.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A brass tray is in the shape of a parallelogram was polished at a total \( \operatorname{cost} \) pf \( R s 2250 \) at the rate of

Rs 2 per \( 10 \mathrm{cm}^{2} \). If the altitude of the
parallelogram is \( 45 \mathrm{cm}, \) find the length of its base.


If \( \boldsymbol{P}(\boldsymbol{E})=\mathbf{0 . 8 7}, \) find \( \boldsymbol{P}(\overline{\boldsymbol{E}}) \)


Which of the following statements
İs incorrect?
A. Physical adsorption is multilayer, non-directional, non-specific and decreases with temperature
B. Chemical adsorption is unilayer, directional, specific and increases with temperature initially
C. Rate of fruit fermentation increases with time
D. Langmuir adsorption isotherm is not valid for chemisorption


The stress at which extension of the
material takes place more quickly as compared to the increase in load is called
A. Elastic point of the material
B. Plastic point of the material
c. Breaking point of the material
D. Yield point of the material


Mercury does not wet glass, wood or iron
because:
A. cohesive force is less than adhesive force
B. cohesive force is greater than adhesive froce
C . angle of contact is less than \( 90^{\circ} \)
D. cohesive force is equal to adhesive force


An electric spark is struck between two
electrodes placed near each other, inside a closed tank full of petrol. What'll happen?
A. Spontaneous combustion of petrol
B. Explosion
c. Slow combustion of petrol
D. Nothing will happen


Two numbers are selected at random
(without replacement) from the first six positive integers. Let X denote the larger of the two numbers obtained. Find \( E(X) \)
A \( \cdot \frac{14}{3} \)
B. \( \frac{13}{3} \)
\( c \cdot \frac{12}{3} \)
D. \( \frac{11}{3} \)


2-acetoxy benzoic acid is used as an:
A . antimalarial
B. antidepressant
C. antiseptic
D. antipyretic


Identify the pairs of metals and their ores from the folllowing


A fair die is rolled. Find the probability
of getting the number 5
A \( \cdot \frac{1}{6} \)
в. \( \frac{5}{6} \)
\( c \cdot \frac{2}{6} \)
D. \( \frac{3}{6} \)


The electric field strength produced at a point some distance away from a source charge does NOT depend on:
A. The magnitude of the source charge
B. The sign of the source charge
c. The distance from the source charge
D. The nature of the medium surrounding the source charge
E. None of the above


Select the non-elastic gel out of the
following.
A. Starch
B. Agar-agar
c. silicic acid
D. Gelatin


State the law of conservation of mass.


A uniform chain is just at rest over a
rough horizontal table with its \( \frac{I}{\eta} \) th part
of length hanging vertically. Find the
of co-efficient of static friction between
the chain and the table.


The number of nodes in \( 3 p \) orbital are :


The process of crossing over between homologous chromosomes that takes place during meiosis is advantageous
because it
A. Makes for healthy offspring
B. Provides a source of genetic variation
c. Creates a random mix of chromosomes
D. Allows gametes to have half the number of chromosomes
E. Increases the number of gametes


Consider the following statements A and B and identify the correct statements.
Statement \( A: p-n ; p-p ; n-n \) forces
between nucleons are not equal and charge dependent statement B : In nuclear reactor the
fission reaction will be in accelerating state if the value of
neutron reproduction factor is \( k>1 \)
A. Both A and B are correct
B. Both A and B are wrong
c. A is wrong B is correct
D. A is correct B is wrong


A progressive wave of wavelength \( 5 \mathrm{cm} \) moves along \( +\mathrm{X} \) axis. What is the phase difference between two points on the wave separated by a distance of \( 3 \mathrm{cm} \) at
any instant
A . \( 3 \pi / 5 \)
в. \( 6 \pi / 5 \)
c. \( 2 \pi / 5 \)
D. \( 7 \pi / 5 \)


Extraction of aluminium from
aluminium oxide \( \left(A l_{2} O_{3}\right) \) is best done
by:
A. Electrolytic reduction of \( A l_{2} O_{3} \)
B. Reduction of \( A l_{2} O_{3} \) with carbon
c. Reduction of \( A l_{2} O_{3} \) with sodium
D. Reduction of \( A l_{2} O_{3} \) with \( c o \)


Pressurize cabins are used in
A. Ships
B. Mountaineering
C. Aircrafts
D. Sphygmomanometer


The lines \( 3 x+4 y=9 \) and \( 6 x+8 y+ \)
\( \mathbf{1 5}=\mathbf{0} \) are tangents to the same circle.
The radius of the circle is :-
A \( \cdot \frac{3}{10} \)
в. \( \frac{33}{20} \)
\( c \cdot \frac{33}{10} \)
D. \( \frac{33}{5} \)


Which of the following are
correct properties of diamond, and
account for them in terms of structure
and bonding.
This question has multiple correct options
A. Diamond is very hard, high melting solid.
B. It is an electrical insulator.
C. Diamond has a covalent network structure in which
each \( C \) -atom uses \( s p^{3} \) -hybrid orbitals to forms a tetrahydral array of \( \sigma \) -bonds.
D. The interlocking, three-dimensional network of strong bonds makes diamond the hardest known substance
with highest m.p for an element.


The discomfort caused by indigestion
due to over-eating can be cured by taking:
A. vinegar
B. lemonjuice
c. baking soda
D. caustic soda


Use differentials to a approximate the values of ; (i) \( \sqrt{\mathbf{3 6 . 6}} \) and (ii) \( \sqrt[3]{\mathbf{2 6}} \)
A . (i) 6.02
(ii) \( \frac{80}{9} \)
B. (i) 6.03
(ii) \( \frac{80}{18} \)
c. \( (\text { i) } 6.25 \)
(ii) \( \frac{80}{27} \)
D. (i) 6.05
(ii) \( \frac{80}{27} \)


Match the following:
\( \boldsymbol{A} \)
\( \boldsymbol{B} \)
(1) Ursa Major
(a) Early part of summer night
(2) Orion
(b) Late part of winter evenings
(3) Cassiopeia
(c) Early part of winter night


"Electrons can jump from one orbit to
other orbit. They cannot flow from one
orbit to another" Justify.


A man standing on a trolley pushes another identical trolley (both trolleys are at rest on a rough surface), so that
they are set in motion and stop after some time. If the ratio of mass of first
trolley with man to mass of second trolley is \( 3, \) then find the ratio of the stopping distances of the second trolley to that of the first trolley. (Assume coefficient of friction to be the same for
both the trolleys)


Three forces of magnitudes 1,2 and 3 dynes meet in a point and act along diagonals of three adjacent faces of a cube. The resultant force is?
A. 114 dynes
B. 6 dynes
c. 5 dynes
D. None of the above


It is found that a body on an inclined plane just starts sliding down if inclination is \( \sin ^{-1}(3 / 5), \) then the angle of repose (friction) is
This question has multiple correct options
A \( \cdot \sin ^{-1} 3 / 5 \)
B \( \cdot \sin ^{-1} 3 / 4 \)
c. \( \tan ^{-1} 3 / 5 \)
\( \mathbf{D} \cdot \tan ^{-1} 3 / 4 \)


On the earth surface, 'g' is a vector and its direction is oriented towards the
centre of the
\( A \cdot \) body
B. sun
c. earth
D. none of these


A gas undergoes a process in which its pressure \( P \) and volume \( V \) are related as
\( \boldsymbol{V} \boldsymbol{P}^{n}= \) constant. The bulk modulus for
the gas in this process is:
A . np
B. \( p^{1 / n} \)
c. \( \frac{p}{n} \)
D. \( p^{n} \)


Write the product of this reaction?
\[
\mathrm{C}_{6} \mathrm{H}_{5}-\mathrm{CH}-\mathrm{CH}_{3} \frac{\mathrm{OH}}{\mathrm{CCl}_{4}}>
\]


An equilateral triangle has been constructed with an uniform wire whose
resistance per unit length is 4 ohm
\( c m^{-1} . \) If the length of each side of the
triangle is \( 10 c, \) the resistance across any side will be
A. 80 ohm
B. 40 ohm
c. \( \frac{80}{3} \) onm
D. \( \frac{40}{3} \) ohm


\( \mathbf{A} \)
1 kg stationary bomb is exploded in three parts having mass ratio 1: 1: 3
Parts having same mass move in perpendicular directions with velocity \( 30 m / s, \) then the velocity of bigger part will be:
\( \mathbf{A} \cdot 10 \sqrt{2} \mathrm{m} / \mathrm{s} \)
В. \( \frac{10}{\sqrt{2}} m / s \)
c. \( 15 \sqrt{2} \mathrm{m} / \mathrm{s} \)
D. \( \frac{15}{\sqrt{2}} m / s \)


The coordinates of the fixed point of the
chord cut off by \( 2 x-5 y+18=0 \) by
the circle \( x^{2}+y^{2}-6 x+2 y-54=0 \)
are
A \( .(1,4) \)
в. (2,4)
c. (4,1)
()
D. (1,1)


Which of the following conclusion is related to Lamarck?
A. Survival of the fittest
B. Inheritance of acquired character
c. Struggle for existence
D. origin of species by natural selection


What do you mean by producers?


The temperature at which \( \mathbf{H}_{2} \) has same
rms speed (at 1 atm) as that of \( \mathrm{O}_{2} \) at
NTP is:
A. 37 k
B. 17 K
c. \( 512 \mathrm{k} \)
D. 27 K


The amplitude of vibration of oscillating particle goes on decreasing because it is opposed by...
A. resistive force of the medium
B. resistive force by source oscillator
c. resistive force by observer
D. resistive force produced itself


Assertion \( (A): O_{3} \) is used to
study tailing effect. Reason (R): Mercurous oxide is formed
as a result of oxidation of mercury
using ozone. The correct answer is:
A. Both Assertion and Reason are correct and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are correct and Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true


A particle is moving along an elliptical
path with a constant speed. As it moves
from \( A \) to \( B, \) magnitude of its
acceleration
A. continuously increases
B. continuously decreases
c. Remains constant
D. first increases and then decreases


The carbonyl carbon is:
A. electrophilic
B. nucleophilic
C . amphoteric
D. lewis base


Increased incidences of lung, skin, and
bladder cancers are associated with
occupational exposure to PAHs
A. True
B. False


A ball is thrown vertically upwards. It returns \( 6 s \) later. Calculate: \( (i) \) the greatest height reached by the ball, and
\( (i i) \) the initial velocity of the ball. (Take \( \boldsymbol{g}=\mathbf{1 0 m} \boldsymbol{s}^{-2} \mathbf{)} \)
A \( \cdot\left(\text { i) } 40 m, \text { (ii) } 30 m s^{-1}\right. \)
B. (i) \( 45 \mathrm{m}, \) (ii) \( 30 \mathrm{m} s^{-1} \)
\( \mathbf{c} \cdot(\mathbf{i}) 45 m,\left(\text { i) } 60 m s^{-1}\right. \)
D. (i) \( 45 m \), (ii) \( 20 m s^{-1} \)


Soaps cannot be used in hard water
because they:
A. contain sodium
B. form precipitates
c. create environmental problems
D. create ozone depletion


A semicircular wire.has a length L and mass M.A particle of mass m is placed at the center of the circle. Find the
gravitational attraction on the particle
due to the wire.


Let \( \alpha \) and \( \beta \) be any two positive values
of \( x \) for which \( 2 \cos x,|\cos x|, \) and \( 1- \)
\( 3 \cos ^{2} x \) are in G.P. The minimum value
of \( |\boldsymbol{\alpha}-\boldsymbol{\beta}| \) is
A \( \cdot \frac{\pi}{3} \)
в.
c. \( \frac{\pi}{2} \)
D. None of these


Three elements \( A, B, C \) belong to IIA, IVA VIA group respectively of the periodic table. Identify the elements that form covalent bonds and that form
electrovalent bond?


A proton moving with velocity \( V \) is acted upon by electric field \( \boldsymbol{E} \) and
magnetic field \( B \). The proton will move undeflected if


Define atomic size. Give its unit of
measurement. In the modern periodic table what trend is observed in the
atomic radius in a group and a period and why is it so?


Buna-N is used in making oil seals and
tank linings, etc. because:
A. it is resistant to the action of lubricating oil and organic solvents
B. it is more elastic than natural rubber
\( \mathrm{C} \). it can be stretched twice its length
D. it does not melt at high temperatures


Two unit vector when added give a unit
vector. Then choose the correct
statement.
A. Magnitude of their difference is \( \sqrt{3} \)
B. Magnitude of their difference is 1
c. Angle between the vectors is \( 90^{\circ} \)
D. Angle between the sum and the difference of the two vectors is \( 90^{\circ} \)


Explain with examples types of asexual reproduction in unicellular organism.


The frequency of light in air is \( 5 \times \) \( 10^{14} H z . \) What will be the frequency of
light, when it enters in the water?
A \( .2 .5 \times 10^{14} \mathrm{Hz} \)
В. \( 5 \times 10^{14} \mathrm{Hz} \)
\( \mathbf{c} \cdot 10^{15} H z \)
D. 2.5 \( \times 10^{12} \mathrm{Hz} \)


Write any two places where methanogens can be found.


Equation of a straight line passing through the origin and making with \( x- \) axis an angle twice the size of the angle
made by the line \( y=0.2 x \) with the \( x- \)
axis, is :
A. \( y=4.0 x \)
В. \( y=\frac{5}{12} x \)
c. \( 6 y-5 y=0 \)
D. none of these


Circule of unit radius is in a rectangle of length and \( 10 \pi \mathrm{m} \) width \( 2 \pi \) metres.
The area of the remaining portion
except the circle is:
A \( \cdot\left(\frac{39}{2} \pi\right) m^{2} \)
В \( \cdot\left(\frac{77}{4} \pi\right) m^{2} \)
\( \mathbf{c} \cdot\left(\frac{35}{2} \pi\right) m^{2} \)
D. \( (19 \pi) m^{2} \)


Statement I: Water has a higher boiling point than expected. Statement II: Each molecule forms a
hydrogen bond with an adjacent molecule.
A. Both Statement I and Statement II are correct and Statement I I is the correct explanation of Statement
B. Both Statement I and Statement II are correct, but Statement II is not the correct explanation of Statement I.
c. statement lis correct, but Statement II is incorrect.
D. Statement I is incorrect, but Statement II is correct


10 g of NaCl is dissolved in 250 g water. The correct way to express concentration of NaCl in solution are :
This question has multiple correct options
A. mass fraction \( =0.04 \)
B. mole fraction \( =0.0122 \)
c. molality \( =0.684 \)
D. molarity =0.684


Assertion
Atomic size decreases across period
but increases down a group of the
periodic table.
Reason
Moving from left to right across a period, electrons are added one at a
time to the outer energy shell. Electrons within a shell cannot shield each other
from the attraction to protons, while
moving down a group in the periodic
table, the number of electrons and filled
electron shells increases.
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


Ramesh paid Rs. 345.60 as Sales Tax on a purchase of Rs. \( 3,840 . \) Find the rate of
Sales Tax.
A . 7\%
B. 9\%
c. \( 11 \% \)
D. 13\%


The chemical reaction in which heat is
absorbed is known as
reaction.
A. exothermic
B. endothermic
c. reversible
D. spontaneous


Qoppr
5
s.
\( " \)
".


If \( Q_{1}=5 \mu C, Q_{2}=3 \mu C \) and \( Q_{3}= \)
\( -2 \mu C, \) then the net charge in the
system is :
A. \( -6 \mu C \)
в. \( 6 \mu C \)
\( c \cdot 8 \mu C \)
D. \( -2 \mu C \)


The echinoderms, hemichordates and
chordates had which of the following larva as common ancestral form?
A. Tornaria
B. Trochophore
c. Dipleurula
D. Bipinnaria


Which of the following is correct for the
given figure?
A. Angle of incidence is equal to angle of reflection
B. Angle of incidence is greater than the angle of reflection
C. Normal is perpendicular to incident ray
D. Normal is perpendicular to reflected ray


Assertion
Pentane and 3-methylpentane are chain isomers.
Reason
Pentane is a straight-chain alkane while 3 -methyl pentane is a branched-
chain alkane
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect and Reason is correct


Extend the definition of the following by continuity. \( f(x)=\frac{1-\cos 7(x-\pi)}{5(x-\pi)^{2}} \) at the point
\( \boldsymbol{x}=\boldsymbol{\pi} \)


Which of the four couples claiming the baby with \( 0+ \) blood type are possible the biological presents of it?
A. AB-and At
B. At and O-
c. \( 0+ \) and \( A B+ \)
D. B- and O-


In a saturated solution of electrolytes,
the ionic products of their
concentration are constant at a
particular temperature. This constant for an electrolyte is known as:
A. lonic product
B. Ionisation constant
c. Dissociation constant
D. Solubility product


From the above figures which one
corresponds to a typical semiconductor


The oxidation number of underlined
element in \( \left[\boldsymbol{F e}(\boldsymbol{N O})\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{5}\right] \boldsymbol{S} \boldsymbol{O}_{4} \)
compound is :
\( A \cdot+1 \)
B. +3
\( c .+5 \)
D. None of these


\( \sqrt[3]{27000}= \)
A . 300
в. 3000
\( c .30 \)
D. 900


The value of
\( \sin ^{-1}\left(\cot \left(\sin ^{-1} \sqrt{\frac{2-\sqrt{3}}{4}}+\cos ^{-1} \frac{\sqrt{2}}{2}\right)\right. \)
is
A . 0
B. \( \frac{\pi}{2} \)
\( c \cdot \frac{\pi}{3} \)
D. none of these


Show that all the diagonal elements of a skew-symmetric matrix are zero.


Difference of 23 and 17.081 is
A . 0.5919
B. 59.19
c. 591.9
D. 5.919


A heavy nucleus \( X \) of mass number 240
and binding energy per nucleon \( 7.6 M e \) is split into two fragment \( Y \) and \( Z \) of
mass numbers 110 and \( 130 . \) The
binding energy per nucleon in \( Y \) and \( Z \) is \( 8.5 M e V \) per nucleon. Calculate the
energy \( Q \) released per fission in \( M e V \)


A bilaterally symmetrical animal can be
divided into mirror images by
A. Any cut from its anterior to its posterior end
B. Any cut from its dorsal to its ventral surface
c. only a cut through the midline of its body from its anterior to its posterior end
D. Only a cut through the midline of its body from its dorsal to its ventral surface


The escape velocity of a body thrown vertically upwards from the surface of
earth is
\( 11.2 \mathrm{Km} / \mathrm{s} . \) If it is thrown in a
direction making an angle of \( 30^{0} \) from the vertical, the new escape velocity will
be
\( \mathbf{A} \cdot 5.6 \mathrm{Km} / \mathrm{s} \)
B. \( 11.2 \mathrm{Km} / \mathrm{s} \)
c. \( 11.2 \times \sqrt{2} \mathrm{km} / \mathrm{s} \)
D. \( _{11.2} \times \frac{\sqrt{3}}{2} \mathrm{km} / \mathrm{s} \)


State True or False.
Real gases show deviation from ideal behaviour at high temperature and low
pressure.
A. True
B. False


In uncorrected myopia, the image is formed
A. In front of the lens
B. At the back of the lens
c. In front of the retina
D. Behind the retina


Two particles \( A \) and \( B \) are moving in a
horizontal place anticlockwise on two different concentric circles with
different constant angular velocities \( 2 \omega \)
and \( \omega \) respectively. Find the relative
velocity (in \( m s \) ) of \( B \) w.r.t \( A \) after time
\( \boldsymbol{t}=\boldsymbol{\pi} / \omega . \) They both start at the position
as shown in figure (Take \( \omega= \)
3 radsec, \( r=2 m \)


A thin lens of refractive index 1.5 has a
focal length of \( 15 \mathrm{cm} \) in air. When the
lens is placed in a medium of refractive
index \( 4 / 3, \) its focal length will becomes
\( \mathrm{cm} \)


No medium is required for transfer of heat by the process of


10 students of class \( X \) took part in a Mathematics quiz. If the number of girls
is 4 more than the number of boys, find the number of boys and girls who took part in the quiz by graphical method.
A .2,7
в. 6,9
\( \mathrm{c} .3,12 \)
D. None of these


Chemiosmotic hypothesis given by Peter Mitchell proposes the mechanism of
A. Synthesis of ATP.
B. synthesis of FADH
c. synthesis of NADH.
D. Synthesis of NADPH.


The following data were obtained during the first order thermal composition of
\( S O_{2} C l_{2} \) at a constant volume.
\[
\boldsymbol{S} \boldsymbol{O}_{2} \boldsymbol{C l}_{2(\boldsymbol{g})} \rightarrow \boldsymbol{S} \boldsymbol{O}_{2(\boldsymbol{g})}+\boldsymbol{C l}_{2(\boldsymbol{g})}
\]
Total pres Experiment \( \quad \) Time \( / \) s \( ^{-1} \) (atm)
\[
0.5
\]
What is the rate of reaction when total
pressure is 0.65 atm?
A .0 .35 atm \( s^{-1} \)
В. \( 2.235 \times 10^{-3} \) atm \( s^{-1} \)
c. \( 7.8 \times 10^{-4} \) atm \( s^{-1} \)
D. \( 1.55 \times 10^{-4} \) atm \( s^{-1} \)


Fuse is always connected to the wire.
A. live
B. neutral
c. earth
D. green


Which of the following plots may
represent the reactance of a series \( L C \)
combination?
\( 4 \cdot(a) \)
\( B .(b) \)
\( c \cdot(c) \)
\( D \cdot(d) \)


If \( f(x) \) is continuous at \( x=c \) and \( g(x) \)
is continuous at \( x=f(c) \) then which of
the following is/are continuous at \( x=c \)
\( ? \)
A \( \cdot(f(x)-g(x)) * f(x) \)
в. \( f(g(x)) \)
c. \( f(f(x)) \)
D. None


Let \( A \) be the sum of the first 20 terms
and \( B \) be the sum of the first 40 terms
of the series \( 1^{2}+2.2^{2}+3^{2}+2.4^{2}+ \)
\( 5^{2}+2.6^{2}+\ldots . . \) If \( B-2 A=100 \lambda, \) then
\( \lambda \) is equal to
\( \mathbf{A} \cdot 464 \)
в. 496
c. 232
D. 248


Which of the following perform reproduction in plants?
A . Roots
B. Stem
c. Flower
D. All of the above


On heating \( K C l O_{3} \) at a certain temperature, it is observed that one
mole of \( K C l O_{3} \) yields one mole of \( O_{2} \)
What is the mole fraction of \( K C l O_{4} \) in the final solid mixture containing only
\( K C l \) and \( K C l O_{4}, \) the latter being
formed by the parallel reaction?
A . 0.50
B. 0.25
c. 0.75
D. 0.67


The reason for green-house effect is
A. Higher \( C O_{2} \) concentration causing global warming
B. Absorption of infra-red rays by gases and dust particles
\( \mathbf{C} . \) Both \( A \) and \( \mathbf{B} \)
D. Rarefaction of \( C O_{2} \)


increases by \( 2 \% \)


Write the two processes that take place
in the formation of a \( \boldsymbol{p}-\boldsymbol{n} \) junction.
Explain with the help of a diagram, the formation of depletion region and barrier potential in a \( \boldsymbol{p}-\boldsymbol{n} \) junction.


Two persons \( A \) and \( B \) are throwing an
unbiased six faced die alternatively, with the condition that the person who
throws 3 first wins the game. If \( A \) starts the game, the probabilities of \( A \) and \( B \) to win the same are respectively
A \( \cdot \frac{6}{11}, \frac{5}{11} \)
в. \( \frac{5}{11}, \frac{6}{11} \)
c. \( \frac{8}{11}, \frac{3}{11} \)
D. \( \frac{3}{11}, \frac{8}{11} \)


Express each of the following exponential expressions as a rational number. \( \left(\frac{2}{3}\right)^{(-1)}+\left(\frac{3}{2}\right)^{(-2)} \)


A boy is standing at the center of a boat
which is free to move on water. The
distance of the boy from the shore is
100m. If mass of the boy and boat are
\( 40 K g \) and \( 60 K g \) respectively and boy
moves with a velocity \( 1 m / \)sec towards
the shore, what is the distance of the
boy from the shore at the end of 5 th second?


If \( \phi(x)=\phi^{\prime}(x) \) and \( \phi(1)=2 \) then \( \phi(3) \)
is equal to
\( A \cdot \phi^{2} \)
B . \( 2 \phi^{2} \)
\( c \cdot 3 \phi^{2} \)
D. \( 2 \phi^{3} \)


Determine bond order of \( N_{2}, N_{2}+, N_{2} \)
and arrange in decreasing order of bond strength.Predict their magnetic character.


Find the velocity of the boy as seen by
bird.
A \( .-12 \hat{j} \)
в. \( 12 \hat{j} \)
\( c \cdot 12 \hat{k} \)
D. \( 10 \hat{i}-12 \hat{j} \)


The following sets are equal. \( \boldsymbol{A}=\{\boldsymbol{x}: \boldsymbol{x} \in \boldsymbol{N} ; \mathbf{1}<\boldsymbol{x}<\mathbf{4}\} \) and
\( B=\left\{x: x \text { is a solution of } x^{2}+5 x+\right. \)
\( \mathbf{6}=\mathbf{0}\} \)
A . True
B. False


Give the name and symbol for each of the atoms which have the ground state electronic configuration in their outer shells:
\( (a) 2 s^{2}(b) 3 s^{2} 3 p^{5}(c) 3 s^{2} 3 p^{6} 4 s^{2}(d) 3 s^{2} 3 p^{6} \)


Pearl is a
A. colloid
B. mixture
C . suspension
D. none


A simple harmonic motion has an
amplitude \( A \) and time period \( T . \) The
time required by it to travel \( x=A \) to
\( \boldsymbol{x}=\frac{\boldsymbol{A}}{2} \) is:
A. \( T / 6 \)
в. \( T / 4 \)
c. \( T / 3 \)
D. \( T / 2 \)


what happens when the air between the rubber sucker and plane surface escape out by pressing it firmly?
A. stick to the surface
B. does not stick
c. stick loosely
D. none of the surface


0.197g of a substance, when heated with strong nitric acid and silver nitrate, gave \( 0.3525 g \) of silver iodide. Percentage of iodine is:
A . 95\%
B. 96.70\%
c. 95.50\%
D. 98.05\%


For transmission of e.m.wave of audible
frequency, these waves are
superimposed with waves of:
A . frequency less than \( 20 \mathrm{H} \)
B. frequency less than \( 10 \mathrm{KHz} \)
c. frequency in the audible range
D. radio-frequency


If the angular distance between the
stars turns out to be approximately 1100
arcseconds, or 0.30 degrees. The moon
appears to shift 0.3 degrees when we
observe it from two vantage points 2360
\( \mathrm{km} \) apart, then find the distance of the
moon from the surface of the
earth.Given angular diameter of moon
is 0.5 degrees.
A. \( 450642 \mathrm{km} \)
B. 450392 km
\( c .325684 \mathrm{km} \)
D. \( 480264 \mathrm{km} \)


The domain of the function \( \boldsymbol{f}= \)
\( \left((x, y): x, y \in R, 3^{x}+3^{y}=3\right) \) is
\( A \cdot(0,1] \)
B. [0, 1]
\( c \cdot(-\infty, 0] \)
\( D \cdot(-\infty, 1) \)


\( \int \frac{\sin 2 x}{1+\cos ^{4} x} d x \) is equal to
\( \mathbf{A} \cdot \cos ^{-1}\left(\cos ^{2} x\right)+c \)
B. \( \sin ^{-1}\left(\cos ^{2} x\right)+c \)
C \( \cdot \cot ^{-1}\left(\cos ^{2} x\right)+c \)
D. None of these


Find the dimensions of \( \frac{1}{\sqrt{L C}}(L= \) Inductance, \( C=\text { Capacitance }) \)
\( \mathbf{A} \cdot T^{-1} \)
B. \( T^{-2} \)
\( c . T \)
D. \( L \)


In the geiger-marsden experiment what
percentage of the \( \alpha \) particles were
deflected by an angle more than \( 1^{\circ} \)
\( \mathbf{A} \cdot<0.15 \% \)
в. \( <15 \% \)
\( \mathbf{c} .>99.85 \% \)
D. \( 100 \% \)


Terylene is a:
A. polymide
B. polyester
c. polyether
D. longchain hydrocarbon


\( M C Q: \sin \left(\sin ^{-1} \frac{5 \pi}{6}\right)+ \)
\( \cos ^{-1}\left(\cos \frac{5 \pi}{3}\right)+\tan ^{-1}\left(\tan \frac{7 \pi}{3}\right) \)
\( A \cdot \frac{5 \pi}{6} \)
в. \( \frac{\pi}{3} \)
c. \( \frac{7 \pi}{6} \)
\( D \cdot \frac{29 \pi \pi \pi}{6} \)


A small mass \( m \) is moved slowly from the surface of the earth to a height \( h \) above the surface. The work done (by an external agent) in doing this is
This question has multiple correct options
A. \( m g h, \) for all values of \( h \)
B. \( m g h, \) for \( h<<R \)
c. \( \frac{1}{2} \) mgR, for \( h=R \)
D. \( -\frac{1}{2} \) mgR, for \( h= \)


The percentage of s-character of the hybrid orbital of \( C \) involved in the bond
formation of \( >\boldsymbol{C}=\boldsymbol{C}< \) is?
A . \( 25 \% \)
B. \( 50 \% \)
\( c .33 .33 \% \)
D. \( 100 \% \)


Express the following in the form of \( a+ \)
\( \boldsymbol{b} \boldsymbol{i} \)
(i) \( (-i)(2 i)\left(-\frac{1}{8} i\right)^{3} \)


What effect did you ignore in your calculation
A. effect of gravity
B. effect of magnetic force
c. effect of electric force
D. \( K E \) of the particle


If \( \boldsymbol{r}=-\frac{\mathbf{3}}{\mathbf{2}} \frac{\boldsymbol{\Delta}[\boldsymbol{A}]}{\boldsymbol{\Delta} \boldsymbol{t}}=-\mathbf{5} \frac{\boldsymbol{\Delta}[\boldsymbol{B}]}{\boldsymbol{\Delta} \boldsymbol{t}}=+\frac{\boldsymbol{7}}{\boldsymbol{3}} \frac{[\boldsymbol{\Delta} \boldsymbol{C}]}{\Delta \boldsymbol{t}} \)
which of the following is the corresponding stoichiometric equation?
\( ^{\mathbf{A}} \cdot \frac{2}{3} A+\frac{1}{5} B \rightarrow \frac{3}{7} C \)
в. \( \frac{2}{3} A+\frac{5}{2} B \rightarrow \frac{7}{3} C \)
c. \( \frac{3}{2} A+\frac{5}{2} B \rightarrow \frac{7}{3} C \)
D \( \cdot \frac{7}{3} C+\frac{5}{2} B \rightarrow \frac{3}{2} A \)


Which of the following is a mixture?
A. water
B. Oxygen
c. Carbon dioxide
D. Air


Let \( f(x) \) satisfy the requirements of Lagrange's mean value theorem in [0,1] \( \boldsymbol{f}(\mathbf{0})=\mathbf{0} \) and \( \boldsymbol{f}^{\prime}(\boldsymbol{x}) \leq \mathbf{1}-\boldsymbol{x}, \forall \boldsymbol{x} \boldsymbol{\epsilon}(\mathbf{0}, \mathbf{1}) \)
then
A. \( f(x) \geq x \)
в. \( |f(x)| \geq 1 \)
C \( . f(x) \leq x(1-x) \)
D. \( f(x) \leq \frac{1}{4} \)


How do leaves of plants help in
excretion?
A. Plants store waste materials in the vacuoles of mesophyll cells and epidermal cells.
B. When old leaves fall, the waste materials are excreted along with the leaves.
C. Both A and B.
D. Plants release the waste material by transpiration.


Caffeine has a molecular weight of 194 If it contains \( 28.9 \% \) by mass of nitrogen, the number of atoms of nitrogen in one molecule of caffeine is:
\( A \cdot 4 \)
B. 6
\( c \cdot 2 \)
D.


The values of a for which
\( (8,-7, a),(5,2,4) \) and (6,-1,2) are
collinear, is given by?
A .2
B. -2
c. -1
D.


State the uses of dimensional analysis
using dimensions, show that 1 joule \( = \) \( \mathbf{1 0}^{\mathbf{7}} \) erg
OR
Explain different types of errors in
measurement.

An object was weighed by a physical balance and following readings were obtained
\( 5.04 g, 5.06 g, 4.17 g, 5 g m, 4.93 g m \)
Find
1.) Mean absolute error
2.) percentage error


Two persons \( A \) and \( B \) are throwing an unbiased six faced die alternatively, with the condition
that the person who throws 3 first wins
the game. If A starts the game, the
probabilities of \( A \) and \( B \) to win the same are
respectively
A \( \cdot \frac{6}{11}, \frac{5}{11} \)
B . \( \frac{5}{11}, \frac{6}{11} \)
c. \( \frac{8}{11}, \frac{3}{11} \)
D. \( \frac{3}{11}, \frac{8}{11} \)


In dyplcal wnealsuone nelwork trie
resistance in cyclic order are \( \boldsymbol{A}= \)
\( \mathbf{1 0} \mathbf{\Omega}, \boldsymbol{B}=\mathbf{5} \mathbf{\Omega}, \boldsymbol{C}=\mathbf{4} \mathbf{\Omega} \) and \( \boldsymbol{D}=\mathbf{4} \mathbf{\Omega} \)
for the bridge to be balanced :-
(a) \( 10 \Omega \) should be connected in parallel
with \( \mathbf{A} \)
(b) \( 10 \Omega \) should be connected in series
with \( \mathbf{A} \)
(c) \( 5 \Omega \) should be connected in series
with B
(d) \( 5 \Omega \) should be connected in parallel
with B
\( A \cdot a, b \)
B. b, c
\( c \cdot a, c \)
D. al


Which isotope of hydrogen is used to make self-luminous paint?
A. Tritium
B. Protium
c. Deuterium
D. None of the above


Solve the following equations.
\( 4 x-3=2 x+1 \)


Calculate the pressure if a force of \( 2 N \)
is applied on an area of \( 2 m m^{2}: \)
\( \mathbf{A} \cdot 10^{3} P a \)
B . \( 10^{4} P a \)
\( \mathbf{c} \cdot 10^{5} P a \)
D. \( 10^{6} P a \)


Sugar and amino acids are
A. Primary metabolites
B. Secondary metabolites
c. Feed stock
D. Inoculum


Which of the following statement is
correct?
A. Metallic elements gain electrons and become anions.
B. Metallic elements gain electrons and become negatively charged ions.
C. Metallic elements lose electrons and become cations.
D. All of the above.


Monomer of PTFE is:
A. Ethylene
B. Propylene
c. Butadiene
D. Tetrafluoro ethylene


Assertion
Thermodynamics process in nature are irreversible.
Reason
Dissipative effects cannot be eliminated
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A rail road car of mass \( \mathrm{M} \) is at rest on
friction less rails when a man of mass
of mass \( \mathrm{m} \) starts moving on the car towards the engine. If the car recoils with a speed v backward on the rails, with what velocity is the man
approaching the engine?


The magnetic field due to a current
carrying loop of radius \( 12 \mathrm{cm} \) at its
centre is \( 0.5 \times 10^{-4} \) T. Find the
magnetic field due to the loop at an axial point \( 5 \mathrm{cm} \) away from the centre.


cosmic rays are:
This question has multiple correct options
A. protons
B. \( \alpha \) -particles
C. nuclei of higher element
D. none of the above


If \( x^{x}+x^{y}+y^{x}=a^{b}, \) then find \( \frac{d y}{d x} \)


In the secondary coil of a step up transformer, the number of turns of the copper wire are :
A. More and the wire is thick
B. More and the wire is thin
c. Less and the wire is thick
D. Less and the wire is thin


The temperature of a gas contained in a closed vessel is increased by \( 2 \mathrm{K} \) when
the pressure is increased by \( 2 \% \). The initial temperature of the gas is :
A. \( 200 k \)
в. 100k
c. \( 200^{\circ} \mathrm{C} \)
D. \( 100^{\circ} \mathrm{C} \)


The redox reaction \( Z n(s)+ \)
\( \boldsymbol{P b C l}_{2}(\boldsymbol{a q}) \longrightarrow \boldsymbol{P b}(\boldsymbol{s})+\boldsymbol{Z n C l}_{2}(\boldsymbol{a q}) \)
can be represented as following half equations \( : Z n(s) \longrightarrow Z n^{2+}(a q)+ \)
\( 2 e^{-}(\text {oxidation }) \) and \( P b^{2+}(a q)+ \)
\( 2 e^{-} \longrightarrow P b(s)(\text { reduction }) \)
If true enter 1 , else enter 0 .
\( A \)


Which of the following is away to use water economically?
A. construction of bawris
B. Rain water harvesting
c. Drip irrigation
D. Infiltration


If two vertices of an equilateral triangle \( \operatorname{are}(3,0) \) and \( (6,0), \) find the third
vertex.


A solid sphere of mass \( m \) is lying at rest on a rough horizontal surface. The coefficient of friction between the
ground and sphere is \( \mu . \) The maximum
value of \( F, \) so that the sphere will not slip, is equal to
\( A \)
в.
\( c \)
\( D \)


Define critical angle and polarising angle what is the relation between the two angles?


Evolution of heart from one to two, three
and four chambered proves:
A. Biogenic law of Haeckel.
B. Neo darwinism.
c. Lamarkism
D. hardy weinberg's law.


Write a short note on starch:


If \( A \) and \( B \) are two events such that \( P(A \cup B) \geq \frac{3}{4} \) and \( \frac{1}{8} \leq P(A \cap B) \leq \frac{3}{8} \)
then
This question has multiple correct options
\( ^{\mathbf{A}} \cdot P(A)+P(B) \leq \frac{11}{8} \)
в. \( P(A) . P(B) \leq \frac{3}{8} \)
c. \( P(A)+P(B) \geq \frac{7}{8} \)
D. none of these


Write the following in the expanded
form:
\( (2 x-y+z)^{2} \)


Statement: The rate of instantaneous
reactions can be determined
experimentally.
State whether the given statement is
true or false.
A. True
B. False


If \( f(x)=\log _{e}\{\log (x)\}, \) then \( f^{\prime}(x) \) at
\( \boldsymbol{x}=\boldsymbol{e} \) is :
\( A \)
B. \( -c \)
\( c \cdot e^{2} \)
D. \( e^{-1} \)


If the area of parallelogram, whose diagonals are represented by \( (3 \hat{i}+\hat{j}+\hat{k}) \) and \( (\hat{i}-\hat{j}-\hat{k}), \) is in the
form of \( x \sqrt{2} \) square unit, the value of \( x \)
is :
A . 4
B. 2
\( c \cdot 3 \)
D. 6


The solubility product of a sparingly soluble salt \( A X_{2} \) is \( 3.2 \times 10^{11} \). Its
solubility (moles/litre) is:
A \( .3 .1 \times 10^{-4} \)
B. \( 2 \times 10^{3} \)
c. \( 4 \times 10^{-4} \)
D. \( 5.6 \times 10^{-6} \)