The numbers 1,2,3 and 4 are written separately on four slips of paper. The slips are then put in a box and mixed thoroughly. A person draws two slips from the box, one after the other without replacement. Describe the following events: \( A= \) The number on the first slip
is larger than the one on the second slip. \( B= \) The number on the second slip is greater than \( 2 \quad C= \) The sum of the numbers on the two slip is 6 or 7 \( D= \) The number on the second slips is twice that on the first slip. Which pair
(s) of events is (are) mutually exclusive


Smallest bacterium among these is
A. Dialister
B. Nitrosomonas
c. Bacillus
D. spirillium.


A cylindrical vessel \( 60 \mathrm{cm} \) in diameter is partially filled with water. A sphere, \( 54 \mathrm{cm} \) in diameter is gently dropped into the vessel. To what further height will water rise in the cylinder?
A \( .20 .02 \mathrm{cm} \)
B . \( 30.29 \mathrm{cm} \)
c. \( 29.16 \mathrm{cm} \)
D. \( 25 \mathrm{cm} \)


The number of books bought at a book
fair by 200 students from a school are given in the following table.
\[
x
\]
's and 4 6 \( \mathbf{1 0} \) \( \mathbf{2} \) 8
\( f \) 4 15
Calculate the standard deviation.


State any two differences between
chemical reactions and nuclear
reactions.


Which o the following statement is incorrect with respect to molecular orbital?
A. They are polycentric
B. They are designated as \( \sigma, \sigma^{*}, \pi, \pi^{*} \) etc
c. They have complex shapes
D. Each of these


Torque/moment of inertia equals to:
A . angular velocity
B. angular acceleration
c. angular momentum
D. force


When light travels from optically denser medium to optically rarer medium after refraction
A. \( m<i>m<r \)
в. \( m<i<m<r \)
\( \mathbf{c} \cdot m<i=m<r \)
\( \mathbf{D} \cdot m<i \geq m<r \)


Which of the following is Bryophyte?
A. Funaria
B. Volvox
c. Chlorella
D. spirullina


An industrial method of preparation of
methanol is:
A. catalytic reduction of carbon monoxide in presence of \( Z n o-C r_{2} O_{3} \)
B. by reacting methane with steam at \( 900^{\circ} \mathrm{C} \) with a nickel catalyst
C. by reducing formaldehyde with lithium aluminium hydride
D. by reacting formaldehyde with aqueous sodium hydroxide solution


The area of the region bounded by the curves \( \boldsymbol{y}=\boldsymbol{x}^{2} \) and \( \boldsymbol{x}=\boldsymbol{y}^{2} \) is
A \( \cdot \frac{1}{3} \)
в. \( \frac{1}{2} \)
\( c \cdot \frac{1}{4} \)
D. 3


If a car is moving at a velocity \( v \) in a circular road with coefficient of friction
\( \mu \) and banking angle \( \theta \). Find the radius of the road such that friction force
doesn't act on the car in the radial
direction.
A \( \cdot_{r}=\frac{v^{2}}{g \tan \theta} \)
в. \( \quad r=\frac{\sqrt{v}}{g \tan \theta} \)
\( ^{\mathrm{c}} \cdot_{r}=\sqrt{\frac{v^{2}}{g \tan \theta}} \)
D. \( r=\frac{v^{2}}{\sqrt{g}} \)


Every subset of an infinite set is
infinite.?


what is Transitive relation?


The value of the sum \( \sum_{n=1}^{10}\left(i^{n}+i^{n+1}\right) \) where \( i=\sqrt{-1}, \) equals
\( \mathbf{A} \cdot i \)
B. -
c. \( -i \)
D.


The de-Broglie wavelength associated
with a material particle is :
A. directly proportional to its energy
B. directly proportional to momentum
C. inversely proportional to its energy
D. inversely proportional to momentum


The value due regard to significant figure \( 4.0 \times 10^{-4}-2.5 \times 10^{-6} \)
A \( \cdot 4.0 \times 10^{-4} \)
B. \( 3.975 \times 10^{-4} \)
c. \( 3.9 \times 10^{-4} \)
D. none of the above


If speed is a scalar quantity, then
average speed
A. is a vector quantity
B. may be a scalar or a vector quantity
c. is also a scalar quantity
D. is neither a scalar nor a vector quantity


\( \tan \left(2 \tan ^{-1}\left(\frac{\sqrt{5}-1}{2}\right)\right)= \)
\( A \)
B. 3
\( c \cdot 2 \)
\( D \)


Immediately after the right string is
cut, what is the linear acceleration
of the free end of the rod?


\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}[\boldsymbol{f}(\boldsymbol{x}) \cdot \boldsymbol{g}(\boldsymbol{x})]=\boldsymbol{f}(\boldsymbol{x}) \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}} \boldsymbol{g}(\boldsymbol{x})+ \)
\( g(x) \frac{d}{d x} f(x) \) is known as \( _{--}---r u l e \)
A. Product
B. Sum
c. Multiplication
D. None of these


Synthetic rubbers are usually obtained by copolymerisation of:
A. styrene and 1,3 - butadiene
B. 1,4 - polyisoprene
c. urea and formaldehyde
D. alkane and 1,3 - butadiene


In neutral equilibrium,
A. center of gravity is neither raised nor lowered.
B. center of gravity is raised.
C. center of gravity is lowered
D. None


A ball is dropped on a hard floor and no energy is being lost to the floor. The ball bounces back to the same position,
from where it was thrown. Is the ball
executing SHM
A. Yes, only for short displacements
B. Yes, for all displacements
c. No, for any kind of displacements
D. None of the above


The equivalent resistance of the combination of resistors shown in the
figure between the points \( A \) and \( B \) is:
\( A \cdot 2 R \)
в. \( \frac{R}{4} \)
c. \( \frac{R}{2} \)
0.4


John notices that a standard piece of
paper is a rectangle, how many lines of symmetry does it have?
\( A \)
B. 2
\( c \cdot 3 \)
D. 4


\( \Delta A B C \) is an isosceles right triangle
with area \( P \).The radius of the circle that
passes through the point \( A, B \) and \( C \) is
\( A \cdot \sqrt{P} \)
B. \( \sqrt{\frac{P}{2}} \)
c. \( \frac{\sqrt{P}}{2} \)
D. \( \sqrt{2 P} \)


A beautiful girl with two normal eyes
wants to see full width of her face by a plane mirror. The eye to eye and ear to ear distances of her face at 4 inch and 6
inch respectively. The minimum
width of the required mirror is
A. 1 inch
B. 2 inch
c. 3 inch
D. 4 inch


Rusting of iron is a chemical change because:
A. it is temporary
B. it can be cleaned and the original substance recovered
c. it is a slow reaction
D. a new substance is formed


Animals of which phylum contains open circulatory system?
A. Arthropoda
B. Annelida
c. Hemichordata
D. Both (a) and (c)


The probability of an event can be
greater than:
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
\( D \)


The decay of mass during nuclear fission and fusion are:
A . \( 0.1 \% \) and \( 0.231 \% \)
B. 0.231\% and 0.1\%
c. \( 0.4 \% \) and \( 0.2 \% \)
D. 0.3\% and 0.3\%


The conc. of \( F e^{3+} \) ions in a sample of
water is found to be \( 50 \times 10^{-5} M \)
Calculate the \( p H \) (nearest integer) at
which \( 99 \% \) of \( F e^{3+} \) will be precipitated. \( \boldsymbol{K}_{s p_{F e(O H)_{3}}}=\mathbf{1 0}^{-\mathbf{3 6}} \)


Calculate the \( I-I \) distance in the
given compound \( \boldsymbol{H}_{2} \boldsymbol{C}=\boldsymbol{C} \boldsymbol{I}_{2}, \) if \( \boldsymbol{C}-\boldsymbol{I} \)
bond length is 2.10 A. Give answer in nearest integer value in \( \boldsymbol{A} \)


An example of a colloid which is an emulsion is :
A. Wipped cream
B. Mayonnaise
\( c \cdot \) Fog
D. Gelatin


If a disc starting from rest acquires an
angular velocity of 240 revolution/ min in \( 10 s, \) then its angular acceleration
will be
A . 1.52 rads\( ^{-1} \)
B. 3.11 rads \( ^{-1} \)
c. 2.51 rads \( ^{-1} \)
D. 1.13 rads\( ^{-1} \)


\( \mathbf{f} \boldsymbol{y}=\log \left(\frac{\sqrt{(\boldsymbol{x}+\mathbf{1})}-\mathbf{1}}{\sqrt{(\boldsymbol{x}+\mathbf{1})}+\mathbf{1}}\right)+ \)
\( \frac{\sqrt{\boldsymbol{x}}}{\sqrt{(\boldsymbol{x}+\mathbf{1})}} \) the by using substitution
\( x=\tan ^{2} \theta, y \) reduces to


Which of the following devices convert light energy into electrical energy?
A. An electric bulb
B. A photocell
c. A microphone
D. A dynamo


The centre of gravity of a rod (of length
L), whose linear mass density varies as
the square of the distance from one end
is at:
A \( \cdot \frac{3 L}{5} \)
В \( \cdot \frac{2 L}{5} \)
c. \( \frac{L}{3} \)
D. \( \frac{3 L}{4} \)


Find out which of the following sequences are arithmetic progressions. For those which are arithmetic
progressions, find out the common
difference. \( 3,3,3,3, \dots . \)


Soil profile means
A. Composition of the soil
B. Texture of the soil
C. Layers of the soil
D. None of the above


In which of the following cases the net
force is not zero?
A. A kite skillfully held stationary in the sky
B. A ball freely falling from a height
c. An airplane rising upwards at an angle of 45 degree with the horizontal with a constant speed
D. A cork floating on the surface of water


Match the following:
\begin{tabular}{ccc|c}
& LIST I & & LIST II \\
A & Family & 1 & Diptera \\
B & Order & 2 & Arthropoda \\
C & Class & 3 & Muscidae \\
D & Phylum & 4 & Insecta
\end{tabular}
\( A \cdot A-4, B-3, C-2, D- \)
B. \( A-3, B-2, C-1, D-4 \)
C. \( A-2, B-3, C-4, D-1 \)
D. \( A-3, B-1, C-4, D-2 \)


A wire along \( x- \) axis carries a current
\( 3.5 A . \) Find the force on a \( 1 \mathrm{m} \) section of the wire exerted by \( \vec{B}=(0.74 \hat{j}- \) \( \mathbf{0} . \mathbf{3 6} \hat{\boldsymbol{k}}) \boldsymbol{T} .(\text { in } \mathbf{N}): \)
A. \( 2.59 \hat{k}+1.263 \)
3
в. \( 1.26 \hat{k}-2.59 \hat{\jmath} \)
c. \( -2.59 \hat{k}-1.26 \hat{j} \)
D . \( -1.26 \hat{k}+2.59 \hat{j} \)


A car is moving on a circular track of radius \( R \). The road is banked at \( \theta . \mu \) is the coefficient of friction. Find the
maximum speed the car can have.
\( \mathbf{A} \cdot\left[\frac{R g(\sin \theta+\mu \cos \theta)}{\cos \theta+\mu \sin \theta}\right]^{1 / 2} \)
B. \( \left[\frac{R g(\cos \theta+\mu \sin \theta)}{\cos \theta-\mu \sin \theta}\right]^{1 / 2} \)
\( ^{\mathbf{C}} \cdot\left[\frac{R g(\sin \theta+\mu \cos \theta)}{\cos \theta-\mu \sin \theta}\right]^{1 / 2} \)
D. None


An abundance of .........was conspicuously absent from the Earth's atmosphere 4 billion years ago.
A. Hydrogen
B. Carbon monoxide
c. Nitrogen
D. oxygen


For an equilibrium \( \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{s}) \rightleftharpoons \boldsymbol{H}_{2} \boldsymbol{O}(\ell) \)
which of the following statement is
true?
A. The pressure changes do not affect the equilibrium
B. More of ice melts if pressure on the system is increased
c. More of liquid freezes if pressure on the system is increase
D. The pressure changes may increase or decrease the degree of advancement of the reaction depending upon the temperature of the system.


\( \boldsymbol{M} \boldsymbol{e}_{2} \boldsymbol{C H}-\boldsymbol{C H}-\boldsymbol{M e} \frac{\boldsymbol{A l}_{2} \boldsymbol{O}_{3}}{\boldsymbol{3} \boldsymbol{5} 0^{\circ}} \)
\( O H \)
\( (\boldsymbol{A}) \frac{(I) \boldsymbol{H} \boldsymbol{I}}{(I I) A g O H}(\boldsymbol{B}) \)
Product (B) of above reaction:
A \( \cdot M e_{2} C(O H) C H_{2} M e \)
в. \( M e_{2} C H-C H-M e \)
oH
c. \( M e-C H-C M e_{3} \)
oh
D. \( H O-C H_{2}-\left(C H_{2}\right) M e \)


Find the vector equation of a plane which is at a distance of 8 units from the origin and which is normal to the vector \( 2 \hat{i}+\widehat{j}+2 \widehat{k} \)


Sequence of amino acid in polypeptide chain is determined by
\( A \cdot r R N A \)
B. sn RNA
c. n RNA
D. m RNA


The current in the shown circuit is found to be \( 4 \sin \left(314 t-\frac{\pi}{4}\right) A . \) Find the value of inductance


Let \( * \) be a binary operation on the set \( I \)
of integers, defined by \( a * b=2 a+b- \)
3. Find the value of \( 3 * 4 \)


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


Using the Mathematical induction,
show that for any number \( n \geq 2 \)
\[
\begin{array}{c}
\frac{1}{1+2}+\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+ \\
\dots+\frac{1}{1+2+3+\ldots+n}=\frac{n-1}{n+1}
\end{array}
\]


At what rate percent compound interest, \( \boldsymbol{R} \boldsymbol{s} \boldsymbol{8 0 0} \) amounts to \( \boldsymbol{R} \boldsymbol{s} \boldsymbol{9 2 6 . 1 0} \)
in \( 1 \frac{1}{2} \) years, interest being compounded half yearly?


The coefficient of linear expansion of
brass is \( 2 \times 10^{-5} C^{-1} . \) Find its (i)
coefficient of superficial expansion, (ii) coefficient of cubical expansion. Let \( x \) and \( y \) be the answers write \( (y- \)
\( \boldsymbol{x}) \times \mathbf{1 0}^{\mathbf{5}} \)


The wave number of the \( H_{\alpha}- \) line in
Balmer series of hydrogen spectrum is:
A \( \cdot \frac{5 R}{36} \)
в. \( 3 R \)
c. \( \frac{21 R}{100} \)
D. \( \frac{3 R}{4} \)


In a throw of coin, find the probability of getting a head.


A thin convergent glass lens \( \mu=1.5 \) has a power of \( +5 D . \) When this lens is
immersed in a liquid of refractive index
\( \mu \) it acts as a diverging lens of focal length \( 100 \mathrm{cm} . \) The value of \( \mu \) must be :
\( A \cdot 5 / 3 \)
B. \( 4 / 3 \)
c. \( 5 / 4 \)
D. \( 6 / 5 \)


Dendrochronology is
the
A. Histological analysis of the annual rings signifying the age of tree.
B. Chemical analysis of the chlorophyll content in a plant.
C. Statistical analysis of the amount of food prepared by the plant, the amount is used, and the quantity stored.
D. Study of the light and the dark reactions of photosynthesis.


Which of the following is not an characteristics of metal?
A. Malleability
B. High conductivity
c. Ductile
D. None of these


Which of the following option hold true for the above heat engine?
\[
\begin{array}{ccc}
& \begin{array}{c}
\text { Work } \\
\text { Output }
\end{array} \\
\hline \begin{array}{c}
\text { Hot } \\
\text { Reservoir }
\end{array} & \text { Q } & \begin{array}{c}
\text { Hoat } \\
\text { Engine }
\end{array} & \begin{array}{c}
\text { Q }_{\text {Reservoir }} \\
\mathbf{T}
\end{array}
\end{array}
\]
A. Positive work
B. An adiabatic process
c. An isobaric process
D. An isochoric process
E. An isothermal process


A ball of mass \( m \) is projected from the
ground with an initial velocity \( u \) making
an angle of \( \theta \) with the horizontal. What
is the change in velocity between the point of projection and the highest point?
A . \( u \sin \theta \)
B . \( u^{2} \cos \theta \)
c. \( u \cos \theta \)
D. \( u^{2} \sin \theta \)


Bi-focal lens is required to correct:
A. cataract
B. astigmatism
c. myopia
D. presbyopia


Center of the hyperbola \( x^{2}+ \) \( 4 y^{2}+6 x y+8 x-2 y+7=0 \quad \) is
A \( .(1,1) \)
в. (0,2)
\( c \cdot(2,0) \)
D. None of these


A long solenoid has 200 turns per cm
and carries a current \( I \). The magnetic
field at its centre is \( 6.28 \times \)
\( 10^{-2} W b / m^{2} . \) Another long solenoid has
100 turns per cm and it carries a
current \( I / 3 . \) The value of the magnetic
field at its centre is
A \( \cdot 1.05 \times 10^{-2} \mathrm{Wb} / \mathrm{m}^{2} \)
B . \( 1.05 \times 10^{-5} \mathrm{Wb} / \mathrm{m}^{2} \)
c. \( 1.05 \times 10^{-3} \mathrm{Wb} / \mathrm{m}^{2} \)
D. \( 1.05 \times 10^{-4} \mathrm{Wb} / \mathrm{m}^{2} \)


Which of the following has only \( 1^{\circ} \) and
\( \mathbf{2}^{\circ} \boldsymbol{C} \) atom?
A. \( 2- \) Methylbutane
B. Butane
c. \( 2,2- \) Dimethylbutane
D. 2,2,3,3 - Tetramethylpentane


There is a regular polygon whose each
interior angle is \( 150^{\circ} \) State true or false.
A. True
B. False


Find acceleration of com of two masses
1kg and 2kg having acceleration \( \overrightarrow{a_{1}}=2 \hat{i}+3 \hat{j} \) and \( \overrightarrow{a_{2}}=\hat{i}-\widehat{j}+ \)
\( 2 \widehat{k} \) respectively.


Evaluate the following integral:
\( \int_{0}^{3} x^{2} d x \)


In preparation of sulphuric acid from sulphur dioxide in lead chamber process.What substance is used as a
catalyst?
A. Manganese dioxide
B. Vanadium pentoxide
c. Nitric oxide
D. Raney Nickel


Find the principle value of :
\( \tan ^{-1}\left(\frac{1}{\sqrt{3}}\right) \)


Mendeleev's periodic law states that the properties of elements are a periodic function of their:
A. reactivity of elements
B. atomic size
c. atomic mass
D. electronic configuration


Solve: \( \int \frac{1}{1+x^{4}} d x \)
A \( \cdot \frac{1}{4 \sqrt{2}} \log \left(\frac{x^{2}+\sqrt{2} x-1}{x^{2}-\sqrt{2} x+1}\right)+\frac{1}{4 \sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2} x}{1-x^{2}}\right)+C \)
B \( \cdot \frac{1}{\sqrt{2}} \log \left(\frac{x^{2}+\sqrt{2} x+1}{x^{2}-\sqrt{2} x+1}\right)-\frac{1}{2 \sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2} x}{1-x^{2}}\right)+C \)
C \( \frac{1}{2 \sqrt{2}} \tan ^{1} \frac{x^{2}-1}{\sqrt{2} x}+\frac{1}{4 \sqrt{2}} \log \left|\frac{x^{2}+1+\sqrt{2} x}{x^{2}+1-\sqrt{2} x}\right|+c \)
D. \( \frac{1}{2 \sqrt{2}} \log \left(\frac{x^{2}+\sqrt{2} x-1}{x^{2}-\sqrt{2} x+1}\right)-\frac{1}{\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2} x}{1-x^{2}}\right)+C \)


A satellite is launched into a circular
orbit of radius \( R \) around the earth. \( A \)
second satellite is launched into an
orbit of radius \( 1.01 R \). The time period of the second satellite is larger than that of the first one by approximately
A . \( 0.5 \% \)
в. \( 1.5 \% \)
\( c \cdot 1 \% \)
D. \( 3 \% \)


For \( \boldsymbol{x}>\boldsymbol{o}, \) if \( (\boldsymbol{2} \boldsymbol{x})^{2 \boldsymbol{y}}=\boldsymbol{4} \boldsymbol{e}^{2 \boldsymbol{x}-\boldsymbol{2} \boldsymbol{y}}, \) then
\( \left(1+\log _{e} 2 x\right)^{2} \frac{d y}{d x} \) is equal to
\( \mathbf{A} \cdot \log _{e} 2 x \)
в. \( \frac{x \log _{e} 2 x-\log _{e} 2}{x} \)
c. \( x \log _{e} 2 x \)
D. \( \frac{x \log _{e} 2 x+\log _{e} 2}{x} \)


Of the five isomers of hexanes, the
isomer which can give two
monochlorinated compounds is:
A. 2-methyl pentane
B. 2,2-dimethylbutane
c. 2,3 -dimethylbutane
D. n-hexane


The probability that a man will live 10 more years, is \( \frac{1}{4} \) and the probability that his wife will live 10 more years, is
\( \mathbf{1} \)
- Then, what is the probability that
\( \overline{\mathbf{3}} \)
neither will be alive in 10 years?
A \( \cdot \frac{1}{2} \)
в. \( \frac{3}{7} \)
\( c \cdot \frac{2}{3} \)
D.


Show that:
\( \sin ^{-1} x+\cos ^{-1} x=\frac{\pi}{2} \)


State True or False.
The CGS unit of pressure is 10 times greater than the MKS unit of pressure.
A. True
B. False


A particle of mass \( m \) is at rest in a train
moving with constant velocity with
respect to ground. Now the particle is
accelerated by a constant force \( \boldsymbol{F}_{\mathbf{0}} \) acting along the direction of motion of
train for time \( t_{0} . \) A girl in the train and a boy on the ground measure the work done by this force. Which of the
following are INCORRECT?

This question has multiple correct options
A. Both will measure the same work
B. Boy will measure higher value than the girl
C. Girl will measure higher value than the boy
D. Data is insufficient for the measurement of work done by the force \( F_{0} \)


Ozone is tested by:
A \( . A g \)
в. \( H g \)
\( c \cdot Z n \)
D. \( A u \)


The correct representation of the given
alphabets is
A. A- muscle; B- tendon; C-ligament; D- ulna
B. A-ligament; B- - muscle; C- radius; D- tendon
C. A-ligament; B- muscle; C- tendon; D- radius
D. A- tendon; B- muscle; C- ligament; D- radius
E. A- tendon; B- muscle; C-ligament; D- ulna


Which of the following is/are energy
efficient products?
This question has multiple correct options
A. Tube lights
B. Bulbs
c. LEDs
D. CFLS


\( \ln \) a series \( L-C-R \) circuit, current in
the circuit is \( 11 A \) when the applied voltage is \( 220 V . \) Voltage across the
capacitor is \( 200 V . \) If value of resistor
\( 20 \Omega, \) then the voltage across the unknown inductor is
A. zero
в. \( 200 \mathrm{V} \)
\( c .20 V \)
D. None of these


Hydrochloric acid react with metals to
form their :
A. hydroxide
B. chloride
c. carbonates
D. none of these


Determine \( n \) if \( ^{2 n} C_{3}:^{n} C_{3}=11: 1 \)


If the frequency of the AC source connected across a series LCR circuit is
continuously in which the following is observed. Assume all other parameters
are kept the same.
A. rms current continously increases.
B. rms current remains constant
c. rms current first increases, reaches a maximum and then decrease
D. rms current first decreases, reached a minimum and then increases


If \( \boldsymbol{X}=\{1,2,3,4,5,6,7,8,9,10\} \) is the
universal set and \( \boldsymbol{A}=\{1,2,3,4\}, B= \)
\( \{2,4,6,8\}, C=\{3,4,5,6\} \) verify the
following.
(a) \( \boldsymbol{A} \cup(\boldsymbol{B} \cup \boldsymbol{C})=(\boldsymbol{A} \cup \boldsymbol{B}) \cup \boldsymbol{C} \)
\( (b) A \cap(B \cup C)=(A \cap B) \cup(A \cap C) \)
(c) \( \left(\boldsymbol{A}^{\prime}\right)^{\prime}=\boldsymbol{A} \)
A. Only a is true
B. Only b and c are true
c. only a and b are true
D. All three a, b and c are true.


n the circuit shown in figure, the \( A C \)
source gives a voltage \( V= \)
\( 20 \cos (2000 t) . \) Neglecting source
resistance, the voltmeter and ammeter
readings will be
A. \( 0 V .2 .0 \)
В. \( 0 V, 1.4 A \)
\( c .5 .6 V, 1.4 \)
) \( .8 V, 2.0 A \)


The dipole moment of \( C O_{2} \) is zero, which implies that:
A. carbon and oxygen have equal electronegativities.
B. carbon has no polar bond.
\( \mathrm{c} \cdot \mathrm{CO}_{2} \) is a linear molecule
D. carbon has bond moments of zero value


Which of the following statements is correct, if the intermolecular force of
attraction between the particles in liquid \( A, B, C \) is in the order \( A<B<C ? \) This question has multiple correct options
A. All the three evaporate at the same rate
B. B evaporates faster than A
c. B evaporates more readily than \( c \)
D. A evaporates more readily than


The water is used as a coolant in motor
car engines because it has a very specific latent heat of fusion.
A . Low
B. Highh
c. Normal
D. Can't say


A lossless coaxial cable has a
capacitance of \( 7 \times 10^{-11} \mathrm{F} \) and an
inductance of \( 0.39 \mu H . \) Calculate
characteristic impedance of the cable.
A . 65
B. 75
\( c \cdot 66 \)
D. 77


A charged body is brought near a positively charged gold leaf electroscopes. The divergence of its leaves increases.What is the kind of
charge on the body?
A. Positive
B. Negative
c. Neutral
D. Data insufficient


Among identical spheres \( A \) and \( B \)
having charges \( -15 C \) and \( -16 C: \)
A. \( -15 C \) is at higher potential
B. \( -16 C \) is at higher potential
c. both are at equal potential
D. no such comparison can be made


Two numbers are in the ratio \( 9: 2 . \) If
thhe smaller number is 320 ,find the
larger number.


The H atom of water carries a slightly
charge and the 0 atom
carries a slightly charge.
A. positive, negative
B. positive, positive
c. negative, negative
D. negative, positive


Solve for \( x: \frac{1}{3}=\frac{\sqrt{x}}{2} \)
A \( \cdot \frac{7}{9} \)
в. \( \frac{5}{9} \)
\( c \cdot \frac{4}{9} \)
D. \( \frac{2}{9} \)


The distance of the point \( 3 \hat{i}+5 \hat{k} \) from the line parallel to the vector \( 6 \hat{i}+\hat{j}- \) \( 2 \hat{k} \) and passing through the point \( 8 \hat{i}+ \) \( \mathbf{3} \hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} \) is
A . 1
B . 2
\( c .3 \)
D.


Determine the percentage composition
of \( K \) in \( K M n O_{4} \)
A . \( 31 \% \)
в. \( 43.58 \% \)
c. \( 25 \% \)
D. \( 55 \% \)


The dimensions of latent heat are -
A \( \cdot M^{0} L^{2} T^{-2} \)
В. \( M^{0} L^{1} T^{-2} \)
c. \( M^{2} L^{0} T^{-2} \)
D. \( M^{0} L^{-2} T^{-2} \)


According to Dalton, what are the
smallest particles of matter?
A. Molecules
B. Ions
c. Atoms
D. None of the above


The distance between the origin and the tangent to the curve \( y=e^{2 x}+x^{2} \) drawn
at the point \( x=0 \) is
A \( \cdot \frac{1}{\sqrt{5}} \)
в. \( \frac{2}{\sqrt{5}} \)
c. \( \frac{-1}{\sqrt{5}} \)
D. \( \frac{2}{\sqrt{3}} \)


Raju bought a bat and a ball for one-
third the money he had saved. The cost of the bat was three-fourths of the
amount he spent. What fraction of his saving did he spend on it? What fraction did he spend on the ball?


Maximum number of \( \boldsymbol{H}- \) bonds that
can be formed by a water molecule is:
A .2
B. 3
\( c \cdot 4 \)
D. 6


The work done by all the forces on a system equals the change in
A. total energy.
B. kinetic energy.
c. potential energy.
D. none of these


For transport of food in plants it requires
A. ATP and phloem
B. ADP and phloem
c. ATP and xylem
D. ADP and xylem


Rate constant (K) of a first order
reaction is \( 5.5 \times 10^{-14} s e c^{-1} . \) Find the
half life of reaction.


\( C_{4} \) pathway of \( C O_{2} \) fixation was discovered by
A. Blackman
B. Hatch and Slack
c. Emerson and Arnold
D. Arnon


In a Young's double slit experiment, the fringe pattern is observed on a screen placed at a distance \( D \). The slits are
separated by \( d \) and are illuminated by light of wavelength \( \lambda \). The distance from the central point, where the intensity falls to half the maximum is
A \( \frac{\lambda D}{3 d} \)
в. \( \frac{\lambda D}{2 d} \)
c. \( \frac{\lambda D}{d} \)
D. \( \frac{\lambda D}{4 d} \)


A charge \( Q \) is distributed uniformly in a sphere (solid). Then the electric field at any point r where \( r<R \) (R is radius of the sphere) varies as
A \( \cdot r^{1 / 2} \)
B \( \cdot r^{-1} \)
\( c \)
D. \( r^{-2} \)


What is the number of possible structural isomers for bromopentane?
A.
B. 3
\( c \cdot 6 \)
\( D \)


In cyclic photophosphorylation, which one of the following is formed?
A. ATP
B. NADP and ATP
\( \mathrm{c} \cdot \mathrm{NADH}_{2} \) and \( O_{2} \)
D. NADPH \( _{2} \), ATP and \( O_{2} \)


Distance between the points (12,4,7) and (10,5,3) is
A \( \cdot \sqrt{21} \)
B. \( \sqrt{5} \)
c. \( \sqrt{17} \)
D. none of these


Find the derivative of \( f(x)=\tan x \) at
\( \boldsymbol{x}=\mathbf{0} \)


What is \( \frac{\cot 54^{\circ}}{\tan 36^{\circ}}+\frac{\tan 20^{\circ}}{\cot 70^{\circ}} \) equal to?
\( A \cdot 0 \)
B. 1
\( c \cdot 2 \)
D.


When a hydrogen atom emits a photon in going from \( n=5 \) to \( n=1 \), its recoil
speed is almost
\( \mathbf{A} \cdot 10^{-4} m / s \)
B . \( 2 \times 10^{-2} \mathrm{m} / \mathrm{s} \)
c. \( 4 m / s \)
D. \( 8 \times 10^{-2} \mathrm{m} / \mathrm{s} \)


An iron ball and a wooden ball of the
same radius are released from a height \( \mathrm{H} \) in vacuum. The times taken by both of
them of reach the ground are
A. Roughly equal
B. Unequal
c. Exactly equal
D. In the inverse ratio of their diameters


How can you improve the quality factor of a parallel resonance circuit. Obtain the resonant frequency and quality factor of a series L-C-R
circuit with \( L=4 \mathrm{H}, \mathrm{C}=64 \mu F \) and \( \mathrm{R}= \)
\( 20 \Omega \)


The larva of cyclostomates is known as
A. Lamprey
B. Amphioxus
c. Ascridian
D. Ammocoete


Satpal organized a 'health camp' for the poor farmers living in a nearby village.
After check-up, he was shocked to see
that most of the farmers suffered from
cancer due to regular exposure to pesticides and many were diabetic. They distributed free medicines to
them. Dr. Satpal immediately reported
the matter to the National Human
Rights Commission (NHRC). On the
suggestions of NHRC, the government decided to provide medical care,
financial assistance, setting up of super-speciality hospitals for treatment and prevention of the deadly disease in the affected villages all over India.
(i) Write the values shown by
(a) Dr.
Satpal
(b) NHRC?
(ii) What type of analgesics are chiefly used for the relief of pains of terminal
cancer?
(iii) Give an example of artificial
sweetener that could have been
recommended to diabetic patients.


Electron microscope is based on which scientific principle?
A. Light amplification by stimulated emission of radiation
B. Wave nature of electrons
c. Digital logic
D. Reflection of ultrasonic waves


If a particle of charge \( q \) is moving with velocity v along the z-axis and the magnetic field B is acting along \( \mathbf{x} \) - axis, use the expression \( \vec{F}=q(\vec{v} \times \vec{B}) \) to
find the direction of the force \( F \) acting on it.


The position of a particle along \( x \) -axis at
time \( t \) is given by \( x=1+t-t^{2} \). the
distance travelled by the particle on first 2 second is
A. \( 1 \mathrm{m} \)
B. 2 \( m \)
c. \( 2.5 \mathrm{m} \)
D. 3 \( m \)


Oxygen is highly soluble in water.
A. True
B. False


Draw Venn diagrams to illustrate \( (\boldsymbol{A} \cup \)
\( \boldsymbol{B}) \backslash(\boldsymbol{A} \cup \boldsymbol{C}) \)


Two coherent sources \( S_{1} \) and \( S_{2} \)
vibrating in phase emit light of wavelength \( \lambda \). The separation between them is \( 2 \lambda \) as shown in figure. The first bright fringe is formed at \( P \) due to
interference on a screen placed at a
distance \( D \) from \( S_{1}(D>>\lambda), \) then \( O P \)
is:
A \( \cdot \sqrt{2} D \)
в. \( 1.5 D \)
c. \( \sqrt{3} D \)
D. \( D \)


One mole of hydrogen, assumed to be ideal, is adiabatically expanded from
its initial state \( \left(P_{1}, V_{1}, T_{1}\right) \) to the final
state \( \left(P_{2}, V_{2}, T_{2}\right) . \) The decreases in the internal energy of the gas during this process will be given by
A. \( C_{v}\left(T_{1}-T_{2}\right) \)
в. \( C_{p}\left(T_{1}-T_{2}\right) \)
c. \( \frac{C_{P}+C_{V}}{2}\left(T_{1}-T_{2}\right) \)
D. \( \left(C_{p}-C_{v}\right)\left(T_{1}-T_{2}\right) \)


The density and eq. wt. of a metal are \( 10.5 g c m^{-3} \) and \( 100, \) respectively. The
time required for a current of 3 amp to deposit a 0.005 mm thick layer of the
same metal on an area of \( 80 \mathrm{cm}^{2} \) is
closest to:
\( \mathbf{A} \cdot 120 s \)
B. 135 s
c. \( 67.5 s \)
D. 270 \( s \)


In Boron atom, screening is due to:
A. Electrons of K shell only
B. All the electrons of \( K \) and \( L \) shell
C. Two electrons of 1 s and 2 s each
D. Only by electrons of L shell


\( \operatorname{Given} \boldsymbol{A}=\left[\begin{array}{lll}\mathbf{1} & \mathbf{1} & \mathbf{1} \\ \mathbf{2} & \mathbf{4} & \mathbf{1} \\ \mathbf{2} & \mathbf{3} & \mathbf{1}\end{array}\right], \boldsymbol{B}=\left[\begin{array}{ll}\mathbf{2} & \mathbf{3} \\ \mathbf{3} & \mathbf{4}\end{array}\right] \)
Find \( P \) such that \( B P A=\left[\begin{array}{lll}1 & 0 & 1 \\ 0 & 1 & 0\end{array}\right] \)


\( \left(\boldsymbol{C H}_{3}\right)_{2} \boldsymbol{C H}-\boldsymbol{C}- \)
\( \boldsymbol{C H}\left(\boldsymbol{C H}_{3}\right)_{2} \frac{\left(\boldsymbol{C H}_{3}\right)_{2} \boldsymbol{C H} \boldsymbol{M} \boldsymbol{g} \boldsymbol{B r}}{\boldsymbol{H}_{3} \boldsymbol{O}^{+}}[\boldsymbol{N}]+[\boldsymbol{O}] \)
\( \overbrace{H_{2} O}^{\left(C H_{3}\right)_{2} C H-L i}[\mathrm{M}] \)
Then [M] is:
\( \mathbf{A} \cdot[\mathrm{M}] \) is \( C H_{3}-C H=C H_{2} \) while \( [\mathrm{N}] \) and \( [\mathrm{O}] \) are
\( \left[\left(C H_{3}\right)_{2} C H\right]_{3} \) СОН апа \( C H_{3}-C H=C H_{2} \)
B . \( [M] \) is \( \left(C H_{3}\right)_{2} C H-C H-C H\left(C H_{3}\right)_{2} \) while \( [N] \) and
\( [O] \operatorname{are}\left(C H_{3}\right)_{2} C H O H \) and \( C H_{3}-C H=C H_{2} \)
c. \( [M] \) is \( \left(C H_{3}\right)_{2} C H-_{\text {। }}^{C H}-C H\left(C H_{3}\right)_{2} \) while \( [N] \) and
\( [O] \operatorname{are}\left(\left(C H_{3}\right)_{2} C H\right)_{3} C-O H \) and \( C H_{3}-C H=C H_{2} \)
D - \( [M] \) is \( \left[\left(C H_{3}\right)_{2} C H\right]_{3} C-O H \) while \( [N] \) and \( [O] \) are
\( -S H \)
\( \left(C H_{3}\right)_{2} C H-C H-C H\left(C H_{3}\right)_{2} \) and \( C H_{3} \)
\( _{O H} \)
\( C H_{2} \)


Gases: ammonia, chlorine, hydrogen
chloride and sulphur dioxide
Select the gas that matches the description given.
Statement : The gas turns moist red litmus paper blue.
A. Chlorine
B. Ammonia
c. Sulphur dioxide
D. Hydrogen chloride


A spherical balloon is being inflated so that its volume increase uniformly at
the rate of \( 40 \mathrm{cm}^{3} / \) minute. The rate of
increase in its surface area when the
radius is \( 8 \mathrm{cm} \) is
\( \mathbf{A} \cdot 10 \mathrm{cm}^{2} / \mathrm{minute} \)
B . \( 20 \mathrm{cm}^{2} / \) minute
\( \mathbf{c} \cdot 40 \mathrm{cm}^{2} / \mathrm{minute} \)
D. none of these


A uniform metal disc of radius R is
taken and out of it a disc of diametere \( \mathrm{R} \)
is out off from the end. The centre of
mass of the remaining part will be
\( ^{A} \cdot \frac{R}{4} \) from the centre
B. \( \frac{R}{3} \) from the centre
\( ^{\mathrm{C}} \cdot \frac{R}{5} \) from the centre
D. \( \frac{R}{6} \) from the centre


Find the values of the following:
\( (1+i \sqrt{3})^{3} \)


A material produces a magnetic field which helps the applied magnetic field, then it is
This question has multiple correct options
A. diamagnetic
B. paramagnetic
c. electro magnetic
D. ferro magnetic


What is the shape of the wavefront in each of the following cases:
(a) Light diverging from a point source.
(b) Light emerging out of a convex lens when a point source is placed at its focus.(c) The portion of the wavefront of light from a distant star intercepted by
the Earth.


Mark the correct one regarding
typhlosole.
A. Internal median fold of ventral intestinal wall
B. Extends from \( 20^{t h}-35^{t h} \) segments
C. Increases the surface area for absorption
D. Decreases the surface area for absorption


IF \( \theta \) is in the first quadrant and \( \cos \theta= \)
3. then value of
\( \overline{\mathbf{5}} \)
\( 5 \tan \theta-4 \operatorname{cosec} \theta \sec \theta-4 \cot \theta \) is
A \( \cdot \frac{-14}{3} \)
в. \( \frac{5}{16} \)
\( c \cdot \frac{5}{-34} \)
D. \( \frac{-5}{16} \)


The sum of all the solutions of the
equation \( \cos \theta \cos \left(\frac{\pi}{3}+\theta\right) \cos \left(\frac{\pi}{3}-\theta\right)= \)
\( \frac{1}{4}, \theta \epsilon[0,6 \pi] \)
A. \( 15 \pi \)
в. \( 30 \pi \)
c. \( \frac{100 \pi}{3} \)
D. None of these


Liquid \( N H_{3} \) ionises to a slight extent
At a certain temperature, its ionization
constant \( \boldsymbol{K}_{\boldsymbol{S I C}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)}=\mathbf{1 0}^{-\mathbf{3 0}} . \) The
number of \( N H_{4}^{+} \) ions present per \( 100 \mathrm{cm}^{3} \) of pure liquid is:
\( \mathbf{A} \cdot 10^{-15} \)
B . \( 6.022 \times 10^{8} \)
c. \( 6.022 \times 10^{7} \)
D. \( 6.022 \times 10^{6} \)


Most common causative agent for acute diarrhoea is
A. Virus
B. Protozoa
c. Bacteria
D. Algae


Differentiate sec \( x \) by first principle.


Constant volume thermometer works on
A. Archemedis principle
B. Boyles law
c. charles law
D. Pascal law


Suspension of slaked lime in water is
known as:
A . lime water
B. quick lime
c. milk of lime
D. aqueous solution of slaked lime.


Multiplication of a negative integer for even number of times gives a
number.
A. negative
B.
C. positive
D. none of these


Assertion
It is desirable to slow down fast moving neutrons to sustain controlled chain
reactions.
Reason
Slow moving neutrons efficiently
collides with \( U^{235} \)
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


Two point dipoles \( p \hat{k} \) and \( \frac{p}{2} \hat{k} \) are located at (0,0,0) and \( (1 \mathrm{m}, 0,2 \mathrm{m}) \). Find
the field at the point (1,0,0)
\( ^{A} \cdot \frac{9 p}{32 \pi \varepsilon_{0}} \hat{k} \)
в. \( \frac{-7 p}{32 \pi \varepsilon_{0}} \)
c. \( \frac{7 p}{32 \pi \varepsilon_{0}} \)
D. none of these


Escape velocity when a body of mass \( m \) is thrown vertically from the surface of the earth is \( v, \) what will be the escape
velocity of another body of mass \( 4 m \) if thrown vertically
\( A \)
B . \( 2 v \)
c. \( 4 v \)
D. None of these


Arrange the following orbitals in the order in which they are filled with
electrons.
\( 6 s, 5 d, 6 p, 7 s, 5 f \)
A. \( 6 s<5 d<6 p<7 s<5 f \)
B. \( 6 s<6 d<5 d<5 f<7 s \)
c. \( 6 d<5 f<6 s<6 p<7 s \)
D. \( 6 s<7 s<5 d<5 f<6 p \)


Order of increasing acidic strength
\( (\|) \)
A \( . I>I I>I I I \)
B. \( I I>I I I>I \)
c. \( I>I I I>I I \)
D. \( I I I>I I>I \)


If \( \frac{a+3 l}{2+i b}=1-1, \) show that \( (5 a- \) \( \mathbf{7 b})=\mathbf{0} \)


State true or false:
The statement \( 0>1 \rightarrow \sin x=2 \)
A. True
B. False


Q Type your question
performing SHM with an amplitude of
1 \( m \). When the cannon reaches \( x= \)
\( \frac{\sqrt{3}}{2} m \) from the equilibrium
moving along +x direction, a bullet of \( \frac{1}{2} k g \) is suddenly fired from it with \( a \)
velocity of \( 20 m / s \) relative to the ground. What will be the new amplitude of the
cannon?
\( ^{A} \cdot \frac{\sqrt{3}}{2} \)
B. \( \frac{\sqrt{5}}{2} \)
c. \( \frac{\sqrt{7}}{2} \)
D. \( \frac{\sqrt{11}}{2} \)


Area of \( \Delta A B C(\text { in sq units }) \) is?
A .24
B. \( 8 \sqrt{6} \)
\( c \cdot 4 \sqrt{6} \)
D. None of these


Name the tissue found in the husk of
coconut. List its two characteristics


Each edge of a cube is increased by \( 50 \% \). The per cent of increase in the
surface area of the cube is
A. 50
B. 125
c. 750
D. 300


Which of the following graphs is correct
regarding the effects of adrenaline secreted into the blood?
\( A \)
B.
\( c \cdot C \)
\( D \cdot C \)


In alcoholic fermentation, \( \mathrm{CO}_{2} \) is evolved
during
A. Decarboxylation of pyruvic acid
B. Formation of acetaldehyde
c. Oxidation of acetaldehyde
D. Both A and B


Prove \( \left(\frac{1+\tan ^{2} A}{1+\cot ^{2} A}\right)=\left(\frac{1-\tan A}{1-\cot A}\right)^{2} \)


The length of a minute hand of a clock is \( 4 \mathrm{cm} . \) Find the displacement and average velocity of the tip of the minute hand when it moves during a time interval from 3: 15 pm to 3: 30 pm?


Choose the correct statements from the
following
This question has multiple correct options
A. The gravitational forces between two particles are an action and reaction pair
B. Gravitational constant \( (G) \) is scalar but acceleration due to gravity \( (g) \) is a vector
C. The values of \( G \) and \( g \) are to be determined
experimentally
D. \( G \) and \( g \) are constant everywhere


How is tetany cousted?


Which one of the following statements
is not true regarding \( (+) \) lactose?
A. On hydrolysis, (+) lactose give equal amount of \( D(+) \) glucose and \( D(+) \) galactose
B. \( (+) \) Lactose is a \( \beta- \) glucoside formed by union of a molecule of \( D(+) \) glucose and a molecule of \( D(+) \) galactose
\( \mathrm{C} \cdot(+) \) Lactose is a reducing sugar and does not exhibit mutarotation
D. (+) Lactose, \( C_{12} H_{22} O_{11} \) contains 8-OH goups


Find the components along the coordinate axes of the position vector of each of the following point:
\( S(4,-3) \)


a. What are Isotopes?
b. Write any three applications of
Avogadros law?


One insulin molecule contains:
A. Three peptide chains, two persulphide linkages.
B. Two peptide chains, two persulphide linkages.
C. Two peptide chains, three persulphide bonds.
D. Three peptide chains, three persulphide bonds.


Assertion
Transition metals are efficient
catalysts.
Reason Transition metals usually contain incomplete d-orbitals and provide larger
surface area for adsorption.
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


If \( 9 g m H_{2} O \) is electrolysed completely with the current of \( 50 \% \) efficiency then :
A. 96500 charge is required
B. \( 2 \times 96500 C \) charge is required
c. \( 5.6 L \) of \( O_{2} \) at STP will be formed
D. \( 11.2 L \) of \( O_{2} \) at STP will be formed


Good conductor of heat is
A. Hydrogen
B. Oxygen
C. Nitrogen
D. None


A ball of mass \( 3 k g \), moving with a speed
of \( 10 m s^{-2} \) strikes a wall at an angle of
\( 60^{\circ} \) (as shown). The ball rebounds at the
same speed. Find the impulse imparted to the ball by the wall


The extremities of a diagonal of a rectangular parallelopiped whose faces are parallel to the reference planes are (-2,4,6) and \( (3,16,6) . \) The length of the base diagonal is
A . 13
B. \( \sqrt{13} \)
c. \( 2 \sqrt{13} \)
D. 169


The \( _{--}-_{-}- \) colloidal dispersions are called emulsions.
A. liquid-liquid
B. solid-solid
c. gas-gas
D. A and C


Example of Dobereiner's triad is
A. \( L i, \) Al \( , C a \)
в. \( L i, N a, K \)
c. \( L i, K, N a \)
D. \( K, A l, C a \)


Express as kilometre (km) using decimals:
\( 15 k m 35 m \)


Which of the following is not an iron
ore?
A. Malachite
B. Haematite
c. siderite
D. limonite


A conducting wire in the form of circular loop of radius \( \sqrt{\frac{2}{\pi}} \mathrm{m} \) is places normal to a uniform magnetic field of induction 2T. If the magnetic induction is uniformly reduced to T in 2s, the induced e.m.f in the loop is
A. 4 volt
B. 2volt
c. 1 volt
D. 0.4volt


The amount of heat energy required to raise the temperature of 1 g of Helium at \( \mathrm{NTP}, \) from \( \boldsymbol{T}_{1} \boldsymbol{K} \) to \( \boldsymbol{T}_{2} \boldsymbol{K} \) is
A \( \cdot \frac{3}{8} N_{a} k_{B}\left(T_{2}-T_{1}\right) \)
B \( \cdot \frac{3}{2} N_{a} k_{B}\left(T_{2}-T_{1}\right) \)
c. \( \frac{3}{4} N_{a} k_{B}\left(T_{2}-T_{1}\right) \)
D. \( \frac{3}{4} N_{a} k_{B}\left(\frac{T_{2}}{T_{1}}\right) \)


A body describing SHM has a maximum
acceleration of \( 8 \pi \mathrm{m} / \mathrm{s}^{2} \) and a
maximum speed of \( 1.6 \mathrm{m} / \mathrm{s} \). Find the period \( T \) and the amplitude \( A \)


A spring wrapped on a wheel of MOI 0.2
\( \mathrm{kg} \mathrm{m}^{2} \) and radius \( 10 \mathrm{cm} \) over a light
pulley to support a block of mass \( 2 \mathrm{kg} \) as shown in fig. Find the acceleration of the block.
A \( \cdot 0.89 \mathrm{ms}^{-2} \)
B. \( 1.12 \mathrm{ms}^{-2} \)
\( c \cdot 0.69 \mathrm{ms}^{-2} \)
D. none


Carbon cannot be used to reduce :
A. \( Z n O \)
в. \( \operatorname{Sn} O_{2} \)
\( \mathrm{c} \cdot F e_{2} O_{3} \)
D. \( A l_{2} O_{3} \)


A block of mass \( 3 m \) and base \( ^{\prime} a^{\prime}, \) height
\( b^{\prime}, \) is resting on the smooth horizontal
surface. A man of mass \( m \) goes from \( \mathrm{P} \) to \( Q \) on the wedge. Find the
displacement of the centre of mass of \( (\text { man }+\text { block }) \) system.


If \( \tan \alpha=\frac{1}{7}, \tan \beta=\frac{1}{\sqrt{10}}, \) prove that
\( \alpha+2 \beta=\frac{\pi}{a}, \) where \( 0<\alpha<\frac{\pi}{2} \) and
\( \mathbf{0}<\boldsymbol{\beta}<\frac{\boldsymbol{\pi}}{\mathbf{2}} \)
Find \( a \)


Calculate the de Broglie wavelength for a beam of electron whose energy is 100
\( \mathrm{eV}: \)
\( A \cdot 1 A \)
B. 1.23 A
c. \( 2.46 \mathrm{A} \)
D. None of these


If \( \boldsymbol{A}=\{1,2,3\}, B=\{1,4,6,9\} \) and \( R \)
is a relation from \( A \) to \( B \) defined by \( x \) is
greater than \( y \). The range of \( R \) is
\( \mathbf{A} \cdot\{1,4,6,9\} \)
в. \{4,6,9\}
\( c \cdot\{1\} \)
D. none of these


If \( \sin x=\sin y \) and \( \cos x=\cos y, \) then
\( x \) is
A \( .2 n \pi+y \)
в. \( 2 n \pi-y \)
c. \( n \pi+y \)
D. \( n \pi-y \)


Heart of fishes is
A. Two chambered
B. Venous heart
c. Both of the above
D. None of the above


In an orbit of radius \( 0.4 A^{0} \) an electron
revolves with a frequency of \( 6.25 \times 10^{15} \)
Hz. The magnetic induction field at its
centre is (in Tesla):
A . \( 4 \pi \)
в. \( 2 \pi \)
\( c \cdot 4 \)
\( D \cdot 2 \)


Mark the correct alternative of the
following.

If six men can do a piece of work in 6
days, then 3 men can do same work in?
A. 10 days
B. 12 days
c. 15 days
D. 18 days


In figure, \( \angle B A C=90^{\circ} \) and \( A D \perp B C \)
Then
\( \mathbf{A} \cdot B D \cdot C D=B C^{2} \)
B. \( A B . A C=B C^{2} \)
c. \( B D . C D=A D^{2} \)
D. \( A B . A C=A D^{2} \)


Half-life of a radioactive substance A is
two times the half-life of another
radioactive substance
B. Initially, the
number of \( A \) and \( B \) are \( N_{A} \) and \( N_{B} \)
respectively. After three half-lives of \( A \) number of nuclei of both are equal
Then, the ratio \( N_{A} / N_{B} \) is
A . \( 1 / 4 \)
в. \( 1 / 8 \)
c. \( 1 / 3 \)
D. \( 1 / 6 \)


The domain of definition of the function
\( \boldsymbol{y}(\boldsymbol{x}) \) given by \( \mathbf{2}^{\boldsymbol{x}}+\mathbf{2}^{\boldsymbol{y}}=\mathbf{2} \) is


Which one of the following has the highest bond order?
\( A \cdot O_{2} \)
B. \( C H^{+} \)
c. \( \mathrm{c} \)
D. \( C N \)


Two cells, having the same emf are connected in series through an external
resistance \( R \) Cells have internal
resistance \( r_{1} \) and \( r_{2}\left(r_{1}>r_{2}\right) \)
respectively. When the circuit is closed, the potential difference across the first
cell is zero, The value of \( \boldsymbol{R} \) is
\( \mathbf{A} \cdot r_{1}+r_{2} \)
В. \( r_{1}-r_{2} \)
c. \( \frac{r_{1}+r_{2}}{2} \)
D. \( \frac{r_{1}-r_{2}}{2} \)


If a straight line falling on two straight
lines makes the interior angles on the
same side of it taken together less than two right angles, then the two straight lines, if produced indefinitely, meet on that side on which the sum of angles is
less than two right angles?


Find the point on the curve \( y^{2}=2 x \)
which is at a minimum distance from
the point (1,4)


Along the sea-coast which of the
following is least likely to be found?
A. Brown algae
B. Red algae
c. Mosses
D. All of the above


Find the magnitude of the magnetic induction B of a magnetic field generated by a system of thin conductors (along which a current \( i \) is flowing) at a point \( A(0, R, 0), \) that is the
centre of a circular conductor of radius
\( R \). The circular part is in yz plane.


A block of wood is kept on table top. The mass of wooden block is \( 5 \mathrm{kg} \) and its dimensions are \( 40 \mathrm{cm} \times 20 \mathrm{cm} \times 10 \mathrm{cm} \)
Find the pressure exerted by the wooden block on the table top, if it is made to lie on the table top with its sides of
dimensions
(a) \( 20 c m \times 10 c m \) and
\( 40 \mathrm{cm} \times 20 \mathrm{cm} \)
B . (a) \( P=2450 \mathrm{Nm}^{-2} \) (b) \( P=612.5 \mathrm{Nm}^{-2} \)
c. (a) \( P=2460 N m^{-2} \) (b) \( P=618.5 N m^{-2} \)


The conversion of acid chlorides into
aldehydes by reduction is termed
A. Clemenson's reduction
B. Wolf-Kishner reaction
c. Rosenmund reduction
D. McMurry reaction


The degree of the differential equation \( \boldsymbol{y}(\boldsymbol{x})=\mathbf{1}+\frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}+\frac{\mathbf{1}}{\mathbf{1 . 2}}\left(\frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}\right)^{2}+ \)
\( \frac{1}{1.2 .3}\left(\frac{d y}{d x}\right)^{3}+\dots . . \frac{1}{1.2 .3 \dots \dots . n}\left(\frac{d y}{d x}\right)^{n} \)
is.
\( A \cdot 2 \)
B. 3
\( c \cdot 1 \)
\( D \)


A spherical raindrop evaporates at a rate proportional to its surface area. If originally its radius be \( 3 m m \) and
1 hour later it reduces to 2 mm, find an
expression for the radius of the rain
drop at any time \( t \)


Which of the following will form an ideal
solution?
A \( \cdot C_{2} H_{5} O H \) and water
B. \( H N O_{3} \) and water
c. \( C H C l_{3} \) and \( C H_{3} C O C H_{3} \)
D. \( C_{6} H_{6} \) and \( C_{6} H_{5} C H_{3} \)


The area of the region described by
\( A=(x, y): x^{2}+y^{2} \leq 1 \) and \( y^{2} \leq 1-x \)
is:
A \( \cdot \frac{\pi}{2}+\frac{4}{3} \)
В \( \cdot \frac{\pi}{2}-\frac{4}{3} \)
c. \( \frac{\pi}{2}-\frac{2}{3} \)
D. \( \frac{\pi}{2}+\frac{2}{3} \)


A lot of controversy has been generated over the use of 'BVO' in soft drinks on
the ground that it is carcinogenic (cancer-causing). What is 'BVO'?
A. Brominated vegetable oil
B. Basic vitamin overdose
c. B-complex vitamin overdoes
D. Bakery vanilla odour


Match the items given in Column I with
those in Column II and select the correct
option given below:
Column I
\( a \)
Tricuspid \( \quad 1 \quad \) Between left atrium valve
\( b \)
Bicuspid
valve 2 Between right ventricle and pulmonary artery
Semilunar
valve Between right
\( \mathrm{C} \)
3 atrium an
ventricle een right
m and right
icle
\( \mathbf{A} \cdot A-1, B-2, C-3 \)
B \( . A-3, B-1, C-2 \)
c. \( A-2, B-1, C-3 \)
D. \( A-1, B-3, C-2 \)


The number and type of bonds between
two carbon atoms in calcium carbide
are:
A. one \( \sigma \), one \( \pi \)
B. One \( \sigma \), two \( \pi \)
c. Two \( \sigma \), one \( \pi \)
D. None of these


Arrange the following in their
decreasing order of acidity.
\( \mathbf{1} \)
II.
III.
\( \mathbf{I V} . \mathrm{NH}_{3} \)
A. \( I I I>I V>I>I I \)
В . \( I>I I>I I I>I V \)
\( \mathbf{c} \cdot I V>I I I>I I>I \)
D. \( I I>I I I>I>I V \)


The distance between two points sources of light is \( 24 \mathrm{cm} \). Where should a converging lens with a focal length of \( f=9 \mathrm{cm} \) be placed between them to obtain the images of both sources at the same point?


If \( a=b, \) then \( a x= \)
\( \mathbf{A} \cdot a+x \)
B. \( b x \)
c. \( b-x \)
D. \( b \div x \)


The process of mRNA synthesis on a DNA is known as
A. Translation
B. Transcription
c. Transduction
D. Transformation


If \( \boldsymbol{\alpha}=\mathbf{3}, \boldsymbol{\beta}=\mathbf{5} \) and \( \gamma=\mathbf{8}, \) then the
value of \( \boldsymbol{\alpha}^{3}+\boldsymbol{\beta}^{3}+\boldsymbol{\gamma}^{3} \) is
A. -240
в. 240
c. -360
D.


Annual growth rings are formed due to activity
A. Extrastellar cambium
B. Intrastellar cambium
c. Interstellar cambium
D. Both (b) and (c)


Which of the following is a necessary
condition for a process to be reversible?
A. The substance undergoing a reversible change must at all instances be in thermodynamic equilibrium with its surroundings.
B. All the processes taking place in the cycle of operation must be infinitely slow.
C. There should not be any loss of energy due to conduction, convection or radiation during the cycle of operation.
D. All of the above.


If \( (\mathbf{1}+\boldsymbol{x})^{\mathbf{1 0}}=\boldsymbol{a}_{\mathbf{0}}+\boldsymbol{a}_{\mathbf{1}} \boldsymbol{x}+\boldsymbol{a}_{\mathbf{2}} \boldsymbol{x}^{\mathbf{2}}+ \)
\( \ldots \ldots a_{10} x^{10}, \) then value of
\( \left(a_{0}-a_{2}+a_{4}-a_{6}+a_{8}-a_{10}\right)^{2}+ \)
\( \left(a_{1}-a_{3}+a_{5}-a_{7}+a_{9}\right)^{2} \) is
\( \mathbf{A} \cdot 2^{10} \)
B . 2
\( c \cdot 2^{20} \)
D. None of these


The differential equation of all
parabola's with axis parallel to axis of \( y \)
-axis is:
A \( \cdot y_{2}=2 y_{1}+x \)
B \( \cdot y_{3}=2 y_{1} \)
c. \( y_{2}^{3}=y_{1} \)
D . \( y_{3}=0 \)


Which of the following statements is
not correct for sigma-and pi- bonds
formed between two carbon atoms?
A. Sigma-bond is stronger than a pi-bond.
B. Bond energies of sigma- and pi-bonds are of the order of \( 264 \mathrm{KJ} / \mathrm{mol} \) and \( 347 \mathrm{KJ} / \mathrm{mol} \), respectively.
C. Free rotation of atoms about a sigma bond is allowed but not in case of a pi-bond.
D. Sigma-bond determines the direction between carbon atoms but a pi-bond has no primary effect in this regard.


Three tuning fork of frequency \( 400 \mathrm{Hz} \)
\( 401 \mathrm{Hz} \) and \( 402 \mathrm{Hz} \) are sounded
simultaneously.the number of beats heard per second are :
\( A \cdot 1 \)
B. 2
\( c \cdot 3 \)
D. none of these


Which one of the following has the lowest melting point?
A. \( N \)
в. \( P \)
c. \( A s \)
D. \( S b \)


Perpendicular distance from the origin to the line joining the points \( (a \cos \theta, a \sin \theta),(a \cos \phi, a \sin \phi) \) is
\( A \cdot 2 a \cos (\theta-\phi) \)
в. \( \quad \operatorname{acos}\left(\frac{\theta-\phi}{2}\right) \)
\( ^{\mathbf{c}} \cdot 4 \mathrm{a} \cos \left(\frac{\theta-\phi}{2}\right) \)
D. \( \operatorname{acos}\left(\frac{\theta+\phi}{2}\right) \)


n given figure, \( A B C \) is a right triangle
right-angled at B. AD and CE are the two
medians drawn from A and C
respectively. IF \( \boldsymbol{A C}=\mathbf{5} c \boldsymbol{m} \) and \( \boldsymbol{A} \boldsymbol{D}= \)
\( \frac{3 \sqrt{5}}{2} c m, \) find the length of \( C E \)


If \( \sin A=\frac{5}{13} \) then evaluate \( \cos A \) and
\( \tan A \)


Which of the following is the correct pathway for propagation of cardiac impulse?
A. SA node \( \rightarrow \) AV node \( \rightarrow \) Bundle of His \( \rightarrow \) Purkinje fibers
B. AV node \( \rightarrow \) Bundle of His \( \rightarrow \) SA node \( \rightarrow \) Purkinje fibers
c. sa node \( \rightarrow \) Purkinje fibers \( \rightarrow \) AV node \( \rightarrow \) Bundle of His
D. Purkinje fibers \( \rightarrow \) AV node \( \rightarrow \) SA node \( \rightarrow \) Bundle of Hiss


Observe the given flowchart carefully
and mark the appropriate option
correctly representing I, II and III.
bite
\( \begin{array}{lll}\text { A. Sweet } & \text { Calamine } & \text { Formic acid }\end{array} \)
B. Bitter Formic acid Baking soda
C. Bitter Baking soda Calamine
D. Sweet Formic acid Baking soda


If \( \sin ^{-1} x+\sin ^{-1} y+\sin ^{-1} z=\frac{3 \pi}{2} \)
then the value of \( x^{9}+y^{9}+z^{9}-\frac{1}{x^{9} y^{9} z^{9}} \)
is equal to
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D.


In a sample of hydrogen like atoms all of which are in ground state, a photon beam containing photons of various energies is passed.In absorption spectrum, five dark lies are observed.
The number of bright lines in the emission spectrum will be (Assume that all transitions take place)
A. 5
B. 10
c. 15
D. none of these


At constant pressure, density of a gas is:
A. directly proportional to absolute temperature
B. inversely proportional to absolute temperature
C. independent of temperature
D. directly proportional to square root of absolute temperature


The thermodynamic efficiency of a cell is given by:
A \( \cdot \frac{\Delta H}{\Delta G} \)
B. \( \frac{n F E_{c l l}}{\Delta G} \)
\( \mathrm{c} \cdot-\frac{n F E_{c l}}{\Delta H} \)
D. zero


Find the value of \( \mathbf{x}, \mathbf{y}, \mathbf{z}\left[\begin{array}{cc}\boldsymbol{x}+\mathbf{2} & \mathbf{6} \\ \mathbf{3} & \mathbf{5} z\end{array}\right]= \)
\( \left[\begin{array}{cc}\mathbf{3} & \boldsymbol{y}^{2}+\mathbf{4} \\ \mathbf{3} & \mathbf{2 0}\end{array}\right] \)


The megasporangium of the angiosperms on maturation gives rise
to
A. cotyledons
B. Seed
c. Fruit
D. Endosperm


The applications of Schrodinger wave
equation are:
A. It is the basis of wave mechanics
B. It helps in studying the structure of atom
c. It shows all the wave like properties of matter
D. All of the above


Which one of the following is incorrect?
A. The bond order of \( H_{2}, N_{2} \) and \( O_{2} \) follows the order:
\( N_{2}>O_{2}>H_{2} \)
B. In \( C s C I \) lattice, each \( C s \) is surrounded by \( 8 C l^{-} \) ions
C. The ionic nature of \( K C l, M g C l_{2} \) and \( A l C l_{3} \) follows the
order: \( K C l>M g C l_{2}>A l C l_{3} \)
D. The central atoms in \( P F_{3}, C l F_{3} \) and \( X e F_{2} \) have \( s p^{3} d \) hybridisation


To which of the following atoms hydrogen be bonded to in order for hydrogen bonding to be exhibited?
A. Bromine
B. lodine
C. Fluorine
D. Chlorine


Anita takes a loan of \( \boldsymbol{R} \boldsymbol{s} . \mathbf{5}, \boldsymbol{0} \boldsymbol{0} \boldsymbol{0} \) for
donating books to the poor, at \( 15 \% \) per year as rate of interest. Find the interest
she has to pay at end of three years. What value depicted from this?


A triple bond is made of :
A. one \( \sigma \) - and two \( \pi \) - bonds
B. two \( \sigma \) - and one \( \pi \) - bonds
c. three \( \sigma \) - and three \( \pi \) - bonds
D. one \( \sigma \) - and four \( \pi \) - bonds


Antiderivative of \( \frac{\sin ^{2} x}{1+\sin ^{2} x} \) with
respect to x is?
A \( \cdot x-\frac{\sqrt{2}}{2} \arctan (\sqrt{2} \tan x)+c \)
B. \( x-\frac{1}{\sqrt{2}} \arctan \left(\frac{\tan x}{\sqrt{2}}\right)+c \)
c. \( x-\sqrt{2} a r c \tan (\sqrt{2} \tan x)+c \)
D. \( x-\sqrt{2} \arctan \left(\frac{\tan x}{\sqrt{2}}\right)+c \)


Draw the structure of the following compound:
4-Chloropentan-2-one


\( x \frac{d y}{d x} \frac{y^{2}}{x}+y=0 \)


State one advantage of using a.c. over
d.c.


A capacitor of capacitance \( C \) is charged to a potential difference \( V \) from a cell and then disconnected from it. A charge
\( +\mathrm{Q} \) is now given to its positive plate. The potential difference across the capacitor is now:
A.
в. \( v+\frac{Q}{C} \)
c. \( v+\frac{Q}{2 C} \)
D. \( V-\frac{Q}{C} \), if \( Q<C V \)


If a positively charged particle is
moving as shown in the figure, then it
will get deflected due to magnetic field towards:
A . \( +x \) direction
B. +y direction
c. - x direction
D. tz direction


The electric potential at a distance of \( 3 m \) on the axis of a short dipole of dipole moment \( 4 \times 10^{-12} \) coulomb-
metre is
A \( \cdot 1.33 \times 10^{-3} V \)
\( V \)
B. \( 4 m V \)
c. \( 12 m V \)
D. \( 27 \mathrm{mV} \)


Assertion
Isoelectric point is \( p H \) at which
colloidal can move towards either of
electrode.
Reason
At isoelectric point, colloidal solution
become electrically neutral.
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 incorrect but Reason is correct
D. Both Assertion and Reason are correct


Momentum is a \( _{-}-_{-}-_{-}-_{-} \) quantity Fill in the blank.
A. scalar
B. vector
c. tensor
D. none


The common ratio is used in
progression.
A . arithmetic
B. geometric
c. harmonic
D. series


The time taken-for \( 90 \% \) Of a first-order
reaction to complete is approximately
a. 1.1 times that of half life
b. 2.2 times that of half life
c. 3.3 times that of half life
d. 4.4 times that of half life


ЭТАТЕМЕNT-1 \( : \lim _{x \rightarrow \alpha} \frac{\sin (f(x))}{x-\alpha}, \) where
\( f(x)=a x^{2}+b x+c, \) is finite and non-
zero, then \( \lim _{x \rightarrow \alpha} \frac{\frac{e^{\frac{1}{f(x)}}-1}{\frac{1}{f(x)}} \text { does not }}{e^{\frac{1}{f(x)}+1}} \)
exist. STATEMENT-2 : \( \lim _{x \rightarrow \alpha} \frac{f(x)}{x-\alpha} \) can take
finite value only when it takes \( \frac{0}{0} \) form.
A. STATEMENT-1 is True, STATEMENT-2 is True STATEMENT-2 is a correct explanation for STATEMEN
B. STATEMENT-1 is True, STATEMENT-2 is True STATEMENT-2 is NOT a correct explanation fo STATEMENT-1
C. STATEMENT-1 is True, STATEMENT-2 is False
D. STATEMENT-1 is False, STATEMENT-2 is True


Ethanedioic acid has the formula
\( H O_{2} C C O_{2} H . \) What is the formula of
aluminium ethanedioate?
A \( . A l C_{2} O_{4} \)
в. \( A l\left(C_{2} O_{4}\right)_{3} \)
\( \mathbf{c} \cdot A l_{2} C_{2} O_{4} \)
D. \( A l_{2}\left(C_{2} O_{4}\right)_{3} \)


In which of the following points pulmonary artery is different from pulmonary vein?
A. Its lumen is broad.
B. Its wall is thick
c. It has valves.
D. It does not possess endothelium


Products of fermentation are
A. Alcohol and lipoprotein
B. Ether and nucleic acid
C. Protein and nucleic acid
D. Alcohol and lactic acid


The degree of dissociation of an electrolyte is \( \alpha \) and its van't Hoff factor
is \( i \). The number of ions obtained by complete dissociation of 1 molecule of the electrolyte is:
A. \( \frac{i+\alpha-1}{\alpha} \)
B. \( i-\alpha-1 \)
c. \( \frac{i-1}{\alpha} \)
D. \( \frac{i+\alpha+1}{1-\alpha} \)


\( \int x \sqrt{\frac{a^{2}-x^{2}}{a^{2}+x^{2}}} d x= \)
A \( \cdot \frac{1}{2} a^{2} \cos ^{-1}\left(\frac{x^{2}}{a^{2}}\right)+\frac{1}{2} \sqrt{a^{4}+x^{4}}+c \)
B \( \cdot \frac{1}{2} \sin ^{-1}\left(\frac{x^{2}}{a^{2}}\right)+\frac{1}{2} \sqrt{a^{4}+x^{4}}+c \)
c. \( \frac{1}{2} a^{2} \sin ^{-1}\left(\frac{x^{2}}{a^{2}}\right)+\frac{1}{2} \sqrt{a^{4}-x^{4}}+c \)
D. \( \frac{1}{2} \cos ^{-1}\left(\frac{x^{2}}{a^{2}}\right)+\frac{1}{2} \sqrt{a^{4}+x^{4}}+c \)


Write a note on the following:
(i) Genetic Code
(ii) Sex - determination in human.


Choose the correct answer among the alternatives given :
Haloalkanes contain halogen atom(s)
attached to the \( s p^{3} \) hybridised carbon
atom of an alkyl group. Identify haloalkane from the following compounds.
(i) 2-Bromopentane
(ii) Vinyl chloride
(iii) 2-Chloroacetophenone
(iv) Trichloromethane
A. Only (ii)
B. (ii) and (iv) only
c. (i) and (iv) only
D. (i), (ii) and (iii) only


A closed vessel contains a mixture of two
gases Neon \& Argon the total mass of mixture is 28 gm.The partial pressure due to Argon and neon are 4 atm and 12atm respectively.The mass of individual gases in vessel is \( \left(M_{\text {neon}}=\right. \)
\( \left.20, M_{\text {argon}}=40, R=8.3 \mathrm{J} / \mathrm{mol}-\mathrm{k}\right) \)
A. \( 4 \mathrm{gm}, 24 \mathrm{gm} \)
B . \( 1 \mathrm{gm}, 27 \mathrm{gm} \)
\( \mathrm{c} \cdot 6 \mathrm{gm}, 22 \mathrm{gm} \)
D. \( 2 g \mathrm{m}, 26 \mathrm{gm} \)


Which of the following is the decreasing order of their dipole moments?
A. \( N H_{3}>B F_{3}>N F_{3} \)
B. \( N H_{3}>N F_{3}>B F_{3} \)
c. \( B F_{3}>N H_{3}>N F_{3} \)
D. \( B F_{3}>N F_{3}>N H_{3} \)


At \( t=0, \) fringe width is \( \beta_{1}, \) and \( a t t= \)
\( 2 s, \) fringe width of figure is \( \beta_{2} . \) Then
\( A \cdot \beta_{1}>\beta_{2} \)
в. \( \beta_{2}>\beta_{1} \)
c. \( \beta_{1}=\beta_{2} \)
D. data is insufficient


The function \( f(x)=x^{2}+2 x-5 \) is
strictly increasing in the interval
B \( \cdot(-\infty,-1] \)
\( c \cdot[-1, \infty) \)
D. \( (-1, \infty) \)


How many elements were known at the
time of Mendeleevs classification of
elements?


Eka-silicon was the name given by Mendeleev to the element similar to
in properties.
A. Boron
B. Germanium
c. Aluminium
D. Silicon


An electric heater converts electrical
energy into:
A. chemical energy
B. heat energy
c. muscular energy
D. none of the above


What is the volume in cubic
centimetres of a 0.6 L bottle of
shampoo?
A \( .6000 \mathrm{cm}^{3} \)
B. \( 60 \mathrm{cm}^{3} \)
\( c \cdot 400 c m^{3} \)
D. \( 600 \mathrm{cm}^{3} \)


The atomic weight of an atom is because of
A. electrons and protons
B. electrons and neutrons
c. neutrons and protons
D. electrons, neutrons and protons


Two wires of same material \& length
are stored by the same force. Their masses are in the ratio 3: 2 . Find ratio of
their elongation


A particle moves along the curve \( y= \)
\( (2 / 3) x^{3}+1 . \) Find the points on the
curve at which the y-coordinate is changing twice as fast as the \( x \) coordinate.


The pH of blood stream is maintained
by a proper balance of \( \boldsymbol{H}_{2} \boldsymbol{C O}_{3} \) and
\( N a H C O_{3} \) concentration. What volume
of \( 5 M N a H C O_{3} \) solution should be
mixed with a \( 10 \mathrm{mL} \) sample of blood
which is \( 2 M \) in \( H_{2} C O_{3} \) in order to
maintain its pH?
\( \mathbf{A} \cdot 40 \mathrm{mL} \)
B . \( 38 \mathrm{mL} \)
c. \( 50 \mathrm{mL} \)
D. \( 78 \mathrm{mL} \)


Penicillin is effective against gram-
positive as well as gram-negative bacteria.
A. True
B. False


The relation between time \( t \) and
displacement \( x \) is \( t=\alpha x^{2}+\beta x, \) where
\( \alpha \) and \( \beta \) are constant, find the relation
between velocity and acceleration


Statement : If equal masses of sodium
metal and chlorine gas are allowed to
react, some sodium will be leftover after all the chlorine is used up.
Statement 2: The reaction required
twice as many atoms of chlorine as
Sodium.
A. Both Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation of Statement 1
B. Both Statement 1 and Statement 2 are correct and Statement 2 is not the correct explanation of Statement 1.
c. Statement 1 is correct but Statement 2 is not correct.
D. Statement 1 is not correct but Statement 2 is correct.
E. Both the Statement 1 and Statement 2 are not correct.


One end of a uniform rod having mass \( \mathrm{m} \) and length \( l \) is hinged. The rod is
placed on a smooth horizontal surface and rotates on it about the hinged end
at a uniform angular velocity \( \omega . \) The
force exerted by the hinge on the rod has a horizontal component equal to:
\( \mathbf{A} \cdot m \omega^{2} l \)
B. Zero
\( \mathrm{c} \cdot \mathrm{mg} \)
D \( \cdot \frac{1}{2} m \omega^{2} \)


Assertion
Current flows in a conductor only when there is an external electric field within
the conductor.
Reason
The drift velocity of the electron is
directly proportional to the electric field
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Chemisorption is unilayer and more
stronger.
A. True
B. False


An oil drop falls through air with a terminal velocity of \( 5 \times 10^{-4} m / s . \) The
terminal velocity of a drop with half of the initial radius will be ? Neglect density of air as compared to that of oil.
(Viscosity of air \( =\frac{18 \times 10^{-5}}{5} N-s / m^{2} \)
\( g=10 m / s^{2}, \) density of oil \( =900 \mathrm{kg} / \mathrm{m}^{3} \) )
A \( \cdot 3.25 \times 10^{-4} m / s \)
в. \( 2.10 \times 10^{-4} \mathrm{m} / \mathrm{s} \)
c. \( 1.5 \times 10^{-4} m / s \)
D. \( 1.25 \times 10^{-4} \mathrm{m} / \mathrm{s} \)


\( \int \frac{\sqrt{x^{2}+1}\left[\log \left(x^{2}+1\right)-2 \log x\right]}{x^{4}} \) is
equal to
A.
\[
\frac{1}{3}\left(1+\frac{1}{x^{2}}\right)^{\frac{3}{2}}\left[\log \left(1+\frac{1}{x^{2}}\right)+\frac{2}{3}\right]+C
\]
в. \( \quad-\frac{1}{3}\left(1+\frac{1}{x^{2}}\right)^{\frac{3}{2}}\left[\log \left(1+\frac{1}{x^{2}}\right)-\frac{2}{3}\right]+C \)
c. \( \quad \frac{1}{3}\left(1+\frac{1}{x^{2}}\right)^{\frac{1}{2}}\left[\log \left(1+\frac{1}{x^{2}}\right)+\frac{2}{3}\right]+C \)
D. None of these


The equation of the bisector of the angle
between the lines \( 3 x-4 y+7=0 \) and
\( 12 x+5 y-2=0 \)
A. \( 11 x+3 y-9=0 \)
B. \( 3 x-11 y+9=0 \)
c. \( 11 x-3 y-9=0 \)
D. \( 11 x-3 y+9=0 \)


Different communities appearing and replacing one another are called
A. Climax communities
B. Seral communities
c. Serial communities
D. successive communities


The normality of \( 10 \% \) ( weight / volume) acetic acid is:
\( A \cdot 1 N \)
B. 10 N
c. \( 1.67 \mathrm{N} \)
D. 0.83


One end of a lagged cylindrical metal rod of length \( 31.4 \mathrm{cm} \) and radius \( 2 \mathrm{cm} \)
is kept in contact with ice at \( 0^{\circ} \mathrm{c} \) and
the other end in water at \( 100^{\circ} \mathrm{C} \). Find
the rate of melting of ice per minute. \( \boldsymbol{L}=\mathbf{8 0} \boldsymbol{c a l} / \boldsymbol{g}, \boldsymbol{k}=\mathbf{1 0}^{\mathbf{5}} \) S.I. units \( (\mathbf{7 . 5} \boldsymbol{g}) \)


Density of oxygen gas at 1 atm pressure is \( 0.01429 g / c c \) at a given temperature.
The \( r m s \) velocity of oxygen is:
A. \( 4.612 \times 10^{4} \mathrm{cm} / \mathrm{s} \)
B. \( 1.45 \times 10^{4} \mathrm{cm} / \mathrm{s} \)
c. \( 4.612 \times 10^{3} \mathrm{cm} / \mathrm{s} \)
D. \( 1.35 \times 10^{4} \mathrm{cm} / \mathrm{s} \)


The property of metals producing a ringing sound when struck is called:
A. sonority
B. permeability
c. ductility
D. malleability


Select the appropriate statement from
the below:
A. The magnitude of maximum acceleration is \( A \omega \)
B. The magnitude of maximum acceleration is \( A \omega^{2} \)
c. The magnitude of minimum acceleration is \( A \omega \)
D. The magnitude of minimum acceleration is \( A \omega / 2 \)


The internal energy of a gas:
\( A . \) is the sum total of kinetic and potential energies.
B. is the total transitional kinetic energies
C . is the total kinetic energy of randomly moving molecules.
D. is the total kinetic energy of gas molecules


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


\( (A B)^{-1}= \)
\( A \cdot B A \)
B \( \cdot A^{-1} B^{-1} \)
c. \( B^{-1} A^{-1} \)
D. All of these


\( 2 . \overline{8768} \) expressed as a rational number is
A \( \cdot_{2} \frac{878}{999} \)
в. \( 2_{10}^{9} \)
c. \( 2 \frac{292}{333} \)
D. \( _{2} \frac{4394}{4995} \)


\( 100 \mathrm{kg} \) hard water contains \( 5 \mathrm{g} M g S O_{4} \) The hardness of water is:


A structure steel rod has a radius of
\( 10 m m \) and a length of \( 1.0 m . A 100 k N \)
force stretches it along its length.
(b) elongation. and Calculate ( \( a \) ) stress.
(c) strain on the rod. Young's modulus, of stricture steel is \( 2.0 \times 10^{11} N m^{-2} \)


If a point \( \boldsymbol{P} \) from where line drawn cuts
coordinates axes at \( A \) and \( B \) (with \( A \) on
\( x-\text { axis and } B \text { on } y-\text { axis }) \) satisfies \( \alpha \frac{x^{2}}{P B^{2}}+\beta \frac{y^{2}}{P A^{2}}=1, \) then \( \alpha+\beta \) is
\( A \cdot 1 \)
B. 2
\( c .3 \)
D. 4


A dip needle lies initially in the magnetic meridian when it shows an angle of dip \( \theta \) at a place. The dip circle
is rotated through an angle \( x \) in the
horizontal plane and then it shows an angle of \( \operatorname{dip} \theta \) '. Then \( \frac{\tan \theta^{\prime}}{\tan \theta} \) is
A \( \cdot \frac{1}{\cos x} \)
B. \( \frac{1}{\sin x} \)
c. \( \frac{1}{\tan x} \)
D. \( \cos x \)


Simplify \( (\boldsymbol{x}+\boldsymbol{y})(\boldsymbol{x}-\boldsymbol{y})+(\boldsymbol{2} \boldsymbol{x}- \)
\( \boldsymbol{y})(\boldsymbol{3} \boldsymbol{x}+\boldsymbol{y}) \)
A \( \cdot 7 x^{2}-2 y^{2}-x y \)
В. \( x^{2}-y^{2}+x y \)
c. \( 7 x^{2}-2 y^{2}+x y \)
D. \( x^{2}-2 y^{2}+x y \)


Social forestry is
A. Management and protection of forest
B. Afforestation of barren and deforested lands
C. Done with the purpose of helping environmental social and rural development
D. All of the above


A straight rod of length L has one of its
ends at the origin and the other at \( x= \)
L. If the mass per unit length of the rod
is given by Ax where \( A \) is constant, where is its mass centre?
A. \( L / 3 \)
B. \( L / 2 \)
c. \( 2 L / 3 \)
D. \( 3 L / 4 \)


Which of the following instruments can be needed to measure the volume of a
liquid? This question has multiple correct options
A. Measuring cylinder
B. Vernier callipers
c. Pipette
D. Measuring flask


Ratio of impedance to capacitive
reactance has
A . no units
B. ohm
c. ampere
D. tesla


Poisonous gas present in the exhaust
fume of
the automobile is: [EAMCET-97-E]
A. \( C_{2} H_{6} \)
в. \( C O_{2} \)
\( c \cdot c o \)
D. \( C H_{4} \)


The value of \( ^{n} C_{1} \) is


Formula of
diamminediaquadichloroplatinum (IV)
bromide is \( \left[\boldsymbol{P t}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{2}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{2} \boldsymbol{C l}_{2}\right] \boldsymbol{B} \boldsymbol{r}_{2} \)
If true enter 1 , else enter 0 .


The radius of a circle is increasing at
the rate of \( 0.7 \mathrm{cm} / \mathrm{s} \). What is the rate of
increases of its circumference?


\( P \) and \( Q \) are the mid points on the sides
\( C A \) and \( C B \) respectively of triangle
\( A B C \) right angled at \( C . \) Prove that
\( 4\left(A Q^{2}+B P^{2}\right)=5 A B^{2} \)


Find ampere force acting on the frame


The sum of the numbers 436.32,227.2 and 0.301 in appropriate significant figures is then
A . 663.821
B. 664
c. 663.8
D. 663.82


Four waves are expressed as
(i) \( y_{1}=a_{1} \sin \omega t \)
(ii) \( y_{2}=a_{2} \sin 2 \omega t \)
(iii) \( \boldsymbol{y}_{3}=\boldsymbol{a}_{3} \cos \boldsymbol{\omega} \boldsymbol{t} \)
(iv) \( \boldsymbol{y}_{4}=\boldsymbol{a}_{4} \sin (\boldsymbol{\omega} \boldsymbol{t}+\boldsymbol{\phi}) \)
The interference is possible between
A \( \cdot \) (i) and (iii)
B. (i) and (ii)
c. (ii) and (iv)
D. Not possible at all


The third term from the end in the
expansion of \( \left(\frac{3 x}{5}-\frac{5}{2 x}\right)^{8} \) is
A \( \cdot \frac{35451}{15 x^{4}} \)
в. \( \frac{45455}{16 x^{4}} \)
c. \( \frac{39372}{15 x^{4}} \)
D. \( \frac{39375}{16 x^{4}} \)


State true or false:
The determinant of a skew-symmetric matrix is a perfect square if it's
elements are integers.
A. True
B. False


Find \( \boldsymbol{m}, \) if \( \boldsymbol{v}=\mathbf{3}, \boldsymbol{g}=\mathbf{1 0}, \boldsymbol{h}=\mathbf{5} \) and \( \boldsymbol{E}= \)
\( \mathbf{1 0 9} \)
A .
B . 2
\( c .3 \)
D.


The correct IUPAC name of the
compound is:
A. 3,3 -dimethyl-3-cyclopentyl propanal
B. 3-Cyclopentyl-3-methyl butanal
C. \( 1-(1 \) -methyl-1-formyl to ethylcyclopropane
D. 3,3 -diethyl-3-cyclobutyl butanal


How many of the following properties are shown by liquid state? Rigidity, Definite volume. No free surface, Define shape
A . 1
B . 2
\( c .3 \)
\( D \)


In the relation \( \frac{d y}{d x}=2 \omega \sin \left(\omega t+\phi_{0}\right) \) the
dimensional formula for \( \omega t+\phi_{0} \) is
A . MLT
в. мLт
c. мL \( ^{0} \neg^{0} \)
D. M^ \( ^{0} \) L \( ^{0} \) Т \( ^{0} \)


Which of the following pairs is wrong?
A. Uricotelic- -Birds
B. Ureotelic- -Insects
c. Ammonotelic - Tadpole
D. Ureotelic - Elephant


Find the ranges of the following
functions:
\( f(x)=1-x-x^{2} \)
\( f(x)=\frac{3 x+7}{x-8} \)
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2}+\boldsymbol{2} \boldsymbol{x}+\boldsymbol{8} \)
\( f(x)=\frac{4 x-7}{x-3} \)


An equiconvex lens, \( f_{1}=10 c m, \) is
placed \( 40 \mathrm{cm} \) in front of a concave
mirror, \( f_{2}=7.50 \mathrm{cm}, \) as shown in fig. An
object \( 2 \mathrm{cm} \) high is placed \( 20 \mathrm{cm} \) to the left of the lens. If overall magnification
is X/1000. Then find out the value of X?


Which of the following reactions is taking place resulting in discolouration of marble of the buildings like Taj Mahal?
A \( \cdot C a C O_{3}+H_{2} S O_{4} \rightarrow C a S O_{4}+H_{2} O+C O_{2} \)
в. \( C a C O_{3}+H C l \longrightarrow C a C l_{2}+H_{2} O+C O_{2} \)
\( \mathrm{c} \cdot \mathrm{CaCO}_{3}+\mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{Ca}(O \mathrm{H})_{2}+\mathrm{CO}_{2} \)
D. \( \operatorname{CaCO}_{3} \rightarrow \) СаО \( + \) СО \( _{2} \)


Assertion : Element number 12 and
element number 20 undergo similar
chemical reactions
Reason : Element number 12 and
element number 20 have similar
valence electron configuration
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
E. Both assertion and reason are incorrect


Find the equation of following planes:


In the following circuit, the battery \( \boldsymbol{E}_{\mathbf{1}} \)
has an emf of \( 12 V \) and zero internal
resistance while the battery \( E \) has emf
of 2 volt. If the galvanometer \( G \) reads
zero, then the value of the resistance \( \boldsymbol{X} \)
in ohm is
A . 10
в. 100
c. 500
D. 200


Among the following outer electronic configurations of atoms, the highest oxidation state is achieved by which one of them?
A \( \cdot(n-1) d^{8} n s^{2} \)
B . \( (n-1) d^{8} n s^{1} \)
c. \( (n-1) d^{5} n s^{\text {। }} \)
D. \( (n-1) d^{5} n s^{2} \)


Q Type your question
spriere or radius K are to be balanced al
the edge of a heavy table such that the centre of the sphere remains at the maximum possible horizontal distance
from the vertical edge of the table
without toppling as indicated in the
figure. If the mass of each block is \( \mathrm{M} \)
and of the sphere is \( M / 2, \) then the maximum distance \( x \) that can be
achieved is?
\( \mathbf{A} \cdot 8 L / 15 \)
в. \( 5 L / 6 \)
c. \( (3 L / 4+R) \)
\( D \)


The product of resistivity and conductivity of a conductor is constant.
Explain it.


the following reaction not used if the \( z \)
is:
A. alcoho
B. halogen
\( c . \) ether
D. all of these


Subtract \( 2.5 \times 10^{4} \) from \( 3.9 \times 10^{5} \) and
give the answer to correct number of significant figures.
A. \( 3.6 \times 10^{6} \)
B. \( 3.6 \times 10^{5} \)
c. \( 36 \times 10^{5} \)
D. \( 36 \times 10^{6} \)


\( 0.39 g \) of a liquid on vapourization gave \( 112 \mathrm{ml} \) of vapor at STP. Its molecular
weight is:
A . 39
B. 18.5
\( c \cdot 112 \)
D. None of the above


Three point charges of \( 2 q,-q \) and \( -q \) are placed at the corner of an equilateral triangle of side a. Then:
This question has multiple correct options
A. the potential at the centroid of the triangle is zero
B. the electric field at the centroid of triangle is zero
c. the dipole moment of the system is \( \sqrt{2} q a \hat{j} \)
D. the dipole moment of the system is \( \sqrt{3} q a \hat{j} \)


ff \( (x)=\log _{x} 1 / 9-\log _{3} x^{2}(x>1) \)
then \( \max f(x) \) is equal to


One mole of calcium phosphide on reaction with an excess of water gives:
A. one mole of phosphine
B. two moles of phosphoric acid
c. two moles of phosphine
D. one mole of phosphorous oxide


The altitudes of \( \Delta A B C, A D, B E \) and \( C F \)
are equal. Prove that \( \Delta A B C \) is an
equilateral triangle.


Two equal circles in the same plane can have at the most the following numbers of common tangents
\( A \cdot 3 \)
B . 2
\( c \cdot 4 \)
D.


In a survey it was found that 21 persons
liked product \( P_{1}, 26 \) liked product \( P_{2} \)
and 29 liked product \( P_{3} \). If 14 persons
liked products \( P_{1} \) and \( P_{2} ; 12 \) persons
liked product \( P_{3} \) and \( P_{1} ; 14 \) persons
liked products \( P_{2} \) and \( P_{3} \) and 8 liked all
the three products. Find how many liked
product \( P_{3} \) only.


A plane passes through (1,-2,1) and is
perpendicular to the planes \( 2 x-2 y+ \)
\( z=0 \) and \( x-y+2 z=4 . \) Then the
distance of the plane from the point
(1,2,2) is
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot \sqrt{2} \)
\( D \cdot 2 \sqrt{2} \)


Which of the following metal is purified by using Monds process?
A . \( N i \)
в. \( Z r \)
c. \( T i \)
D. \( C u \)


If \( S_{n} \) denotes the sum of the first \( n \)
terms of an A.P., prove that \( S_{30}= \)
\( \mathbf{3}\left(\boldsymbol{S}_{\mathbf{2 0}}-\boldsymbol{S}_{\mathbf{1 0}}\right) \)


Kepler's law of area is based on
A. Conservation of linear momentum
B. Conservation of angular mementium
c. conservation of energy
D. both(1) and \( \mid(2) \)


A electron at rest is accelerated by
applying a \( P . D . \) of \( 250 \mathrm{V} \). What is its
\( K . E . \) in electron volt ?
A \( .250 e V \)
B. 225 eV
c. 200 eV
D. 150 eV


\( \sin \left[2 \cos ^{-1} \cot \left(2 \tan ^{-1} x\right)\right]=0 \) if
This question has multiple correct options
\( \mathbf{A} \cdot x=-1-\sqrt{2} \)
B. \( x=1+\sqrt{2} \)
\( \mathbf{c} \cdot x=1-\sqrt{2} \)
D. \( x=\sqrt{2}-1 \)


If \( (x-1),(x+1) \) and \( (x-2) \) are
factors of \( \boldsymbol{x}^{4}+(\boldsymbol{p}-\boldsymbol{3}) \boldsymbol{x}^{3}-(\boldsymbol{3} \boldsymbol{p}- \)
5)\( x^{2}+(2 p-9) x+6, \) what is the value
of p?
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c \cdot 3 \)
D.


\( 20 m L \) solution of \( 0.1 ~ M \) ferrous
sulphate was completely oxidised using a suitable oxidising agent. What is the number of electrons exchanged?
A. \( 1.204 \times 10^{22} \)
в. 193
c. 1930
D. \( 1.204 \times 10^{2} \)


Entry to a certain University is determined by a national test. The scores on this test are normally
distributed with a mean of 500 and a
standard deviation of \( 100 . \) Tom wants to
be admitted to this university and he knows that he must score better than at
least \( 70 \% \) of the students who took the
test. Tom takes the test and scores 585
Tom does better than what percentage
of students?
A. \( 89.23 \% \)
B. \( 77.26 \% \)
c. \( 70.23 \% \)
D. \( 80.23 \% \)


Calculate the oxidation number of \( M n \)
in the product formed on strongly
heating \( M n_{2} O_{7} \)
(write absolute value of an answer)


In a semiconductor, \( 2 / 3 r d \) of the total
current is carried by electrons and
remaining \( 1 / 3 r d \) by the holes. If at this temperature, the drift velocity of
electrons is 3 times that of holes, the
ratio of number density of electrons to that of holes is
\( A \cdot \frac{3}{2} \)
B. \( \frac{2}{3} \)
c. \( \frac{5}{3} \)
D. \( \frac{3}{3} \)
\( E \cdot \frac{1}{3} \)


Anhydrous sodium carbonate is commonly known as:
A. baking soda
B. washing soda
c. chalk
D. paris white


The correct relation between the
impedance of secondary coil with that of primary coil is
\( \mathbf{A} \cdot Z_{S}=Z_{P} \)
в. \( Z_{S}=Z_{P} \frac{N_{S}}{N_{P}} \)
\( ^{\mathrm{c}} Z_{S}=Z_{P}\left(\frac{N_{S}}{N_{P}}\right)^{2} \)
D. \( _{Z_{S}}=Z_{P}\left(\frac{N_{P}}{N_{S}}\right)^{2} \)


\( \int e^{\tan ^{-1} x}\left(1+x+x^{2}\right) d\left(\cot ^{-1} x\right) \) is
equal to
A \( \cdot-e^{\tan ^{-1} x}+c \)
B - \( e^{\tan ^{-1} x}+c \)
C. \( _{-x e^{\tan ^{-1} x}+c} \)
D. \( x e^{\tan ^{-1} x}+c \)


A particle of mass \( m \) moves according
to the equation \( \boldsymbol{F}=- \)amr where \( \boldsymbol{a} \) is a
positive constant, \( r \) is radius vector.
\( \boldsymbol{r}=\boldsymbol{r}_{0} \hat{\boldsymbol{i}} \) and \( \boldsymbol{v}=\boldsymbol{v}_{0} \hat{\boldsymbol{j}} \) at \( \boldsymbol{t}=\mathbf{0} . \) Describe
the trajectory.
\( ^{\mathbf{A}} \cdot\left(\frac{x}{r_{0}}\right)^{2}+a\left(\frac{y}{v_{0}}\right)^{2}=1 \)
\( ^{\mathbf{B}} \cdot\left(\frac{x}{r_{0}}\right)^{2}+a\left(\frac{y}{v_{0}}\right)^{2}=0 \)
\( \left(\frac{x}{r_{0}}\right)^{2}+\left(\frac{y}{v_{0}}\right)^{2}=\frac{1}{\alpha} \)
D. none of these


The products of respiration is
A. water
B. Carbon dioxide
c. Energy
D. All of the above


A charge 'q' moves in a region where electric field and magnetic field both exist, then force on it is : -
\( \mathbf{A} \cdot q(\vec{V} \times \vec{B}) \)
B \( \cdot q \vec{E}+q(\vec{V} \times \vec{B}) \)
\( \mathbf{c} \cdot q \vec{E}+q(\vec{B} \times \vec{V}) \)
\( \mathbf{D} \cdot q \vec{B}+q(\vec{E} \times \vec{V}) \)


Draw a structural formula for the
product of each \( S N_{1} \) reaction. Where the configuration of the starting material is given, show the configuration of the product


The value of \( (\Delta H-\Delta U) \) the formation
of carbon monoxide from its elements
at \( 298 K \) is:
A. \( -2477.57 \mathrm{J} \) mol \( ^{-1} \)
1
В. \( +2477.57 \mathrm{J} \) mol \( ^{-1} \)
c. \( -1238.78 \mathrm{J} \mathrm{mol}^{-1} \)
D. \( +1238.78 \mathrm{J} \mathrm{mol}^{-1} \)


Inability of the eye to focus on both far and near objects with advancing age is:
A. Astigmatism
B. Presbyopia
c. Myopia
D. Hypermetropia


\( \sin ^{-1}\left(\frac{\sqrt{1+x}+\sqrt{1-x}}{2}\right) \)


The value of \( 2 \sqrt{-49} \) is equal to
A . -14
B. None of these
c. 14
D. 14


Absolute value of sum of all integers in the domain of \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \cot ^{-1} \sqrt{(x+3) x}+\cos ^{-1} \sqrt{x^{2}+3 x+1} \)
is


The species \( N e, N a^{+} \) and \( F^{-} \) have the
same:
A. number of protons
B. number of nucleons
c. number of electrons
D. mass number


The figure shows the graphical
variation of the reactance of a capacitor
with frequency of ac source

Find the capacitance of the capacitor


A simple microscope has
A. 2 convex lens
B. 2 concave lens
c. 1 convex lens
D. 1 concave lens


The value of integral \( \int_{\pi / 4}^{3 \pi / 4} \frac{x}{1+\sin x} d x \)
is :
A \( \cdot \pi \sqrt{2} \)
B . \( \frac{\pi}{2}(\sqrt{2}+1) \)
c. \( \pi(\sqrt{2}-1) \)
D. \( 2 \pi(\sqrt{2}-1) \)


A stone is dropped from the \( 16^{t h} \) storey
of a multi-storeyed building and it
reaches the ground in 4 s. In the first second, it passes through how many
storeys of the building \( \left(\boldsymbol{g}=\mathbf{1 0 m s}^{-2}\right) \) ?
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot 3 \)
D. None


Identify the equations involved in
bleaching action of \( \boldsymbol{S O}_{2}: \) This question has multiple correct options
A. \( S O_{2}+H_{2} O \rightarrow H_{2} S O_{3} \)
в. \( S O_{2}+O_{2} \rightarrow S O_{3} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{SO}_{3}+\mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{H}_{2} \mathrm{SO}_{4}+2[\mathrm{H}] \)
\( \mathrm{D} \cdot S O_{3}+H_{2} O+H_{2} S O_{4} \)


If the bond dissociation energies of \( \boldsymbol{X} \boldsymbol{Y} \)
\( X_{2} \) and \( Y_{2} \) (all diatomic molecules) are
in the ratio of 1: 1: 0.5 and \( \Delta H_{f} \) for the formation of \( \boldsymbol{X} \boldsymbol{Y} \) is \( -\mathbf{2 0 0} \) kJ/mol. The
bond dissociation energy of \( X_{2} \) will be :
\( \mathbf{A} \cdot 100 \mathrm{kJ} / \mathrm{mol} \)
B. 800 kJ/mol
c. 300 kJ/mol
D. 400 kJ/mol


Two coins are tossed simultaneously.
Write the sample space \( ^{\prime} S^{\prime} \) and the
number of sample point \( n(S) . A \) is the
event of getting no head. Write the event \( A \) in set notation and find \( n(A) \)


Among.the metals \( \mathrm{Cr}, \mathrm{Fe}, \mathrm{Mn}, \mathrm{Ti}, \mathrm{Ba}, \) and
Mg, the one that cannot be obtained by reduction of its metal oxide by
aluminium is :
A. \( c r \)
B. Fe
\( c . \) мп
D. Ba


Plant succession is a \( \ldots \) mess.
A. Definite
c. Unimportant
D. None of the above


Evaluate:
\( \int \frac{\sin ^{6} x+\cos ^{6} x}{\sin ^{2} x \cos ^{2} x} d x \)


The potential energy function for a
particle executing linear simple
harmonic motion is given by \( U(x)= \)
\( \frac{1}{2} k x^{2}, \) where \( k \) is the force constant. For
\( k=0.5 N m^{-1}, \) the \( \operatorname{graph} \) of \( U(x) \)
versus \( x \) is shown in figure. Show that a
particle of total energy \( 1 J \) moving
under this potential' turns back' when
it reaches \( \boldsymbol{x}=\pm \mathbf{2} \boldsymbol{m} \)


Three concentric conducting spherical shells of radii \( \boldsymbol{R}, 2 \boldsymbol{R} \) and \( \boldsymbol{3} \boldsymbol{R} \) carry
charges \( Q,-2 Q \) and \( 3 Q, \) respectively. Compute the electric field at \( r=\frac{5}{2} R \)
\( A \)
B.
\( c \)
D.


\( H C l \) is added to the following oxides,
which one would give \( H_{2} O_{2} ? \)
\( \mathbf{A} \cdot B a O_{2} \)
в. \( M n O_{2} \)
\( \mathbf{c} \cdot P b O_{2} \)
D. \( N O_{2} \)


Which of the following is not a thermodynamic coordinate?
A. Gas constant (R)
B. Pressure (P)
c. volume (v)
D. Temperature (T)


Find the equation of the ellipse whose
foci are (0,±4) and length of the minor
axis is 18


The direction cosine of a line equally inclined to the axes are
A \( \cdot \frac{1}{3}, \frac{1}{3}, \frac{1}{3} \)
B. \( -\frac{1}{3},-\frac{1}{3},-\frac{1}{3} \)
c. \( \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}} \)
D. none of these


Bilateral symmetry is found in
A. Cindaria
B. Platyhelminthes
c. Mollusca
D. Both B and C


Which is synthesized in G_phase?
A. DNA polymerase
B. Histones
c. Nucleolar DNA
D. Tubulin protein


An alpha-particle (charge 2e) moves
along a circular path of radius \( 1 A \) with
a uniform speed of \( 2 \times 10^{6} m s^{-1} \)

Calculate the magnetic field produced at the centre of the circular path


Haemodialysis is also called artificial
A . Liver
B. Lung
c. Heart
D. Kidney


Working of radars in oceans is based on
the principle of
A . geo-positional system
B. reflection of sound
c. locus of sound waves
D. none


After mitosis, the chromosome number
of a daughter cell is \( \ldots \ldots \ldots \) that of the parent cells
A. Doubled compared to
B. One-half
c. The same as
D. Rearranged compared to


A polnt sources \( \boldsymbol{s} \) emicting IIght of
wavelength 600 nm is placed at a very
small height \( h \) above a flat reflecting
surface \( \boldsymbol{A B} \) (see figure). The intensity
of the reflected light is \( 36 \% \) of the
incident intensity. Interference fringes
are observed on a screen placed parallel
to the reflecting surface at a very large
distance \( D \) from it.What is the shape of
the interference fringes on the screen?
A. Circular
B. helical
C . eliptical
D. spiral


Esters are functional group isomers of:
This question has multiple correct options
A. Hydroxy aldehydes
B. ketones
c. Diketones
D. Alkanoic acid


f you want to hear a train approaching from far away then you should:
A. put the ear to the track.
B. put the ear away from the track
c. both can be true
D. none is true


A metal ball of radius \( 2 \mathrm{mm} \) and
density \( 10.5 \mathrm{gmcm}^{-3} \) is dropped in glycerine of coefficient of viscosity 9.8 poise and density \( 1.5 \mathrm{gm} \mathrm{cm}^{-3} \). The
terminal velocity of the ball in \( \mathrm{cm} s^{-1} \) is:
\( A \cdot 2 \)
B. 4
\( c \cdot 6 \)
D. 8


Agonist can inhibit the catalytic
activity of the enzyme If this is true enter 1 , if false enter 0 .


When we suck using a straw, the liquid travels up into it. Explain why?


A solution is prepared by addition of
excess of \( A g N O_{3} \) solution in \( K I \) solution. The charge likely to develop on colloidal particles is?
A. Positive
B. Negative
c. No charge
D. Both charges


Match the Column-I with the graph of Column-II which is most close to the
answer


If \( \boldsymbol{A}=\{\mathbf{2}, \boldsymbol{4}\} \) and \( \boldsymbol{B}=\{\mathbf{3}, \mathbf{4}, \mathbf{5}\} \) then
\( (\boldsymbol{A} \cap \boldsymbol{B}) \times(\boldsymbol{A} \cup \boldsymbol{B}) \) is
A \( \cdot\{(2,2),(3,4),(4,2),(5,4)\} \)
в. \{(2,3),(4,3),(4,5)\}
\( \mathbf{c} \cdot\{(2,4),(3,4),(4,4),(4,5)\} \)
D. \{(4,2),(4,3),(4,4),(4,5)\}


Solve the simultaneous equation:
\( \frac{2}{x}+\frac{2}{3 y}=\frac{1}{6} ; \frac{3}{x}+\frac{2}{y}=0 \)


The
\( 1921, \) thus, it has been termed as the
year of the great divide.
A. partition between India and Pakistan took place
B. population of India saw a negative growth rate
\( c \cdot \operatorname{both} A \& B \)
D. neither A nor B


The radioactivity of a sample is \( \boldsymbol{R}_{1} \) at a
time \( T_{1} \) and \( R_{2} \) at a time \( T_{2} \). If the half-
life of the specimen is \( T, \) the number of atoms that have disintegrated in the
\( \operatorname{time}\left(T_{2}-T_{1}\right) \) is equal to
\( \frac{\boldsymbol{n}\left(\boldsymbol{R}_{1}-\boldsymbol{R}_{2}\right) \boldsymbol{T}}{\ln 4} . \) Here \( \boldsymbol{n} \) is some integral
number. What is the value of \( n \) ?


Which of the following reactions are disproportionation reactions?
(।) \( C u^{+} \rightarrow C u^{2+}+C u \)
(II) \( 3 M n O_{4}^{-}+4 H^{+} \rightarrow 2 M n O_{4}^{-}+ \)
\( M n O_{2}+2 H_{2} O \)
(III) \( 2 K M n O_{4} \rightarrow K_{2} M n O_{4}+ \)
\( M n O_{2}+O_{2} \)
\( (\mathrm{IV}) 2 M n O_{4}^{-}+3 M n^{2+}+2 H_{2} O \rightarrow \)
\( \mathbf{5} M n O_{2}+4 H^{+} \)
\( A \cdot(1),(1) \)
B. (I), (II), (III)
\( c \cdot(11),(11),(1 v) \)
\( D .(1),(1 v) \)


A sample of H-atoms containing all the
atoms in some excited state is
irradiated with light of wavelength \( \lambda \) and the atoms get re-excited to further
higher orbit. On removing the light source, atoms de-excite to ground state
with emission of radiations. The
emission spectrum thus obtained
consists of ten spectral lines corresponding to ten different wavelengths. Out of the ten spectral lines, seven lines have the wavelength
smaller than the incident llambda,
while only two of them have
wavelengths longer than the incident wavelength. The orbit number in which electrons were present initially is:
A. 3
B. 4
\( c \cdot 5 \)
\( D .6 \)


\( f(x)= \)
\[
\begin{array}{ccc}
\cos ^{x} & \cos x \sin x & -\sin x \\
\cos x \sin x & \sin ^{x} & \cos x \\
\sin x & -\cos x & 0
\end{array}
\]
Prove that \( f(x)=1 \) is an identity


Which gates are called universal gates?


Divide and write the quotient and the remainder.
\( \left(p^{2}+7 p-5\right) \div(p+3) \)


Assertion
Power of the lens is larger if its focal length is smaller.
Reason
Power of the lens measures the ability to converge or diverge the refracted
rays.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


What is derivative of \( \left[\frac{1}{x}\right]^{x} \)


One pendulum ticks 57 times in 58 seconds and another 608 times in 609
seconds. If they start simultaneously, find the time after which will they tick
together?
A \( \cdot \frac{211}{19} \)
в. \( \frac{1217}{19} s \)
c. \( \frac{1218}{19} s \)
D. \( \frac{1018}{19} s \)


A ray of light travelling in impure water is incident on a glass plate immersed in
it. When the angle of incidence is \( 51^{\circ} \) the reflected ray is totally plane polarized. Given that refractive index of impure water if \( 1.4 . \) The refractive index
of glass should be
\( \left(\tan 51^{\circ}=1.235\right) \)
A . 1.64
в. 1.34
c. 1.53
D. 1.73


The Point \( (s) \) on the cure \( y^{3}+3 x^{2}= \)
\( 12 y \) where the tangent is vertical
(parallel to y-axis), is/are.
\( \mathbf{A} \cdot\left[\pm \frac{4}{\sqrt{3}},-2\right] \)
B \( \cdot\left(\pm \frac{\sqrt{11}}{3}, 1\right) \)
D \( \cdot\left(\pm \frac{4}{\sqrt{3}}, 2\right) \)


Solve:
\( x^{3} \frac{d y}{d x}=y^{3}+y^{2} \sqrt{y^{2}-x^{2}} \)
A \( . x y=c(x-\sqrt{y^{2}-x^{2}}) \)
B . \( x=c\left(y+y^{2}-x^{2}\right) \)
c. \( y=c\left(x+y^{2}-x^{2}\right) \)
D. \( x y=c(y+\sqrt{y^{2}-x^{2}}) \)


Which of the following is correct?
A. Determinant is a square matrix
B. Determinant is a number associated to a matrix
C. Determinant is a number associated to a square
matrix
D. None of these


In given figure of cube and cuboid, which one has a greater surface area?
A. cube
B. Cuboid
c. cant compose
D. None


The total number of distinct terms in
the expansion of \( (x+a)^{100}+(x-a)^{100} \)
after simplification is
\( \mathbf{A} \cdot 50 \)
в. 202
c. 51
D. none of these


What is \( \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}|\sin x| d x \) equal to \( ? \)
\( A \cdot 2 \)
B. 1
\( c . \pi \)
D.


Gravitational potential difference between surface of a planet and a point
situated at a height of \( 20 m \) above its
surface is 2 joule/kg. If gravitational field is uniform, then the work done in
taking a \( 5 k g \) body of height 4 meter above surface will be :-
\( A \cdot 2 J \)
B. \( 20 J \)
c. \( 40 J \)
D. \( 10 J \)


Among the metals \( F e ; Z n ; P b ; A g \) and
\( P t, \) which do not give a metal nitrate on
treatment with concentrated \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \) ?
A . Fe and \( P t \)
B. Fe and \( Z n \)
\( \mathrm{c} \cdot F e, A g \) and \( P t \)
D. \( P b, A g \) and \( P t \)


Methylamine reacts with \( H N O_{2} \) to
form:
A \( \cdot C H_{3}-O-N=O \)
В. \( C H_{3}-O-C H_{3} \)
\( \mathbf{c} \cdot C H_{3} O H \)
D. \( C H_{3} C H O \)


The value of \( \int \frac{\cos \sqrt{x}}{\sqrt{x}} d x \) is
\( A \cdot 2 \cos \sqrt{x}+C \)
B. \( \sqrt{\frac{\cos x}{x}}+C \)
\( c \cdot \sin \sqrt{x}+C \)
D. \( 2 \sin \sqrt{x}+C \)


If three wires of equal resistance are given then number of combinations they can be made to give difference resistance is
A . 4
B. 3
\( c .5 \)
D.


A charged oil drop od mass \( 2.5 \times \) \( 10^{-7} k g \) is in space between the two
plates, each of area \( 2 \times 10^{-2} m^{2} \) of a
parallel plate capacitor. When the upper plate has a charge of \( 5 \times 10^{-7} C \) and the
lower plate has an equal negative
charge then the oil remains stationery. The charge of the oil drop is (take, \( g= \) \( 10 m / s^{2} \)
A \( \cdot 9 \times 10^{-1} C \)
В \( \cdot 9 \times 10^{-6} C \)
C \( .8 .85 \times 10^{-13} C \)
D. \( 1.8 \times 10^{-14} C \)


A stone projected vertically upwards reaches to the level of window \( 10 \mathrm{m} \) from
the ground. Find the magnitude of velocity of the stone at the time of its projection.
\( \begin{array}{ll}\text { A. } 7 & \text { ms }^{-1}\end{array} \)
В. 36 ms\( ^{-1} \)
\( \begin{array}{ll}\text { c. } 28 & \text { ms }^{-1}\end{array} \)
\( \begin{array}{ll}\text { D. } 14 & m s^{-1}\end{array} \)


A current of 3 A has to be passed through a solution of silver nitrate for
\( t^{\prime} \) sec to coat a metal surface of \( 80 \mathrm{cm}^{2} \)
with a 0.005 -mm-thick layer, then \( t \) is:
(density of silver is 10.5 g \( c m^{-3} \) ) (write
your answer to nearest integer)


In the reaction: \( S_{2} O_{8}^{2-}+2 I^{-} \rightarrow \)
\( 2 S O_{4}^{2-}+I_{2} \)
A. oxidation of iodide into iodine takes place
B. reduction of iodine into iodide takes place
c. both oxidation and reduction of iodine takes place
D. none of the above


Construct a quadrilateral \( \boldsymbol{V} \boldsymbol{A} \boldsymbol{B} \boldsymbol{N} \)
where \( \boldsymbol{V} \boldsymbol{A}=\mathbf{7} \boldsymbol{c m}, \boldsymbol{A B}=\boldsymbol{8} \boldsymbol{c m}, \boldsymbol{B} \boldsymbol{N}= \)
\( \mathbf{1 0} c \boldsymbol{m}, \boldsymbol{A} \boldsymbol{N}=\mathbf{1 2} \boldsymbol{c m} \) and \( \boldsymbol{V} \boldsymbol{B}=\mathbf{1 1} \boldsymbol{c m} \)
The perimeter (in cm.) of \( \square V A B N \) is


What kind energy change takes place when a magnet is moved towards a coil having a galvanometer at its ends?
A. Mechanical energy changes to the magnetic energy.
B. Mechanical energy changes to the electric energy
c. electric energy changes to the magnetic energy.
D. None of these.


If \( \sec \theta=1 ; 0 \leq \theta<12^{\circ}, \) then the value
of \( \boldsymbol{\theta} \) is
A \( .5^{\circ} \)
B . 0
\( c \cdot 1^{c} \)
D. \( 2^{\circ} \)


Sketch the graph \( y=|x+3| . \) Evaluate \( \int_{-6}^{0}|x+3| d x . \) What does this integral represent on the graph?


Discriminant of the equation \( -3 x^{2}+ \)
\( 2 x-8=0 \) is
A . -92
B. -29
c. 39
D. 49


If \( 2 g \) of hydrogen is converted into 1.986gm Helium in a thermonuclear
reaction, the energy released is
\( A \cdot 63 \times 10^{7} J \)
B. \( 63 \times 10^{10} J \)
c. \( 126 \times 10^{10} J \)
D. \( 6.3 \times 10^{20} J \)


Which reaction represents the oxidising behaviour of \( \boldsymbol{H}_{2} \boldsymbol{S O}_{4} ? \)
A \( \cdot N a C l+H_{2} S O_{4} \rightarrow N a H S O_{4}+H C l \)
в. \( 2 \mathrm{NaOH}+\mathrm{H}_{2} \mathrm{SO}_{4} \rightarrow \mathrm{Na}_{2} \mathrm{SO}_{4}+2 \mathrm{H}_{2} \mathrm{O} \)
\( \mathrm{c} \cdot 2 \mathrm{HI}+\mathrm{H}_{2} \mathrm{SO}_{4} \rightarrow \mathrm{I}_{2}+\mathrm{SO}_{2}+2 \mathrm{H}_{2} \mathrm{O} \)
D. \( 2 P C l_{5}+H_{2} S O_{4} \rightarrow 2 P O C l_{3}+S O_{2} C l_{2}+2 H C l \)


A tank contains 100 liters of fresh water.
A solution containing 1 gm/litre of soluble lawn fertilizer runs into the tank at the rate of 1 lit/min., and the mixture
is pumped out of the tank at the rate of
3 litres/min. Find the time when the
amount of fertilizer in the tank is
maximum.

Enter \( 9 t \) i.e, \( (t \) is time in minutes)


\( i \log \left(\frac{x-i}{x+i}\right) \) is equal to
\( \mathbf{A} \cdot 2 i \log (x-i)-i \log \left(x^{2}+1\right) \)
B. \( 2 i \log (x-i)+i \log \left(x^{2}+1\right) \)
\( \mathbf{c} \cdot 2 i \log (x+i)-3 i \log \left(x^{2}+1\right) \)
D. \( 2 i \log (x-i)-i \log \left(x^{2}+i\right) \)


lleum is characterised by the presence
of
A. Brunner's glands and villi
B. Brunner's gland and Peyer's patches
c. Peyer's patches and villi
D. Brunner's gland and Taeniae coili


Assertion
Contraceptive pills are rich in only
progesterone and estrogen.
Reason
This will stop menstrual cycle for
Sometime.
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


There are 5 doors to a lecture hall. The
number of ways that a student can enter the hall and leave it by a different door is
A . 20
B. 16
c. 19
D. 2


1 \( g \) of same non volatile solute is added
to \( 100 g \) o two different solvents \( A \) and \( B \)
\( \boldsymbol{K}_{\boldsymbol{b}} \) of \( \boldsymbol{A}: \boldsymbol{B}=\mathbf{1}: \mathbf{5} \)
find out \( \frac{\left(\Delta T_{b}\right)_{A}}{\left(\Delta T_{b}\right)_{B}} \)
\( \mathbf{A} \cdot 1: 10 \)
B. 1: 5
c. 1: 20
D. 2: 5


\( C-X \) bond is polar because:
\( \mathbf{A} \cdot X \) is more electronegative than \( C \)
B. \( X \) attracts electron cloud to itself
c. \( X \) gains slight negative charge on it and \( C \) gains slight positive charge on it
D. all of these


The halide ore of sodium is called
as
A. Horn salt
B. cryolite
c. Rock salt
D. Both a and c