When aluminium phosphide is reacted
with dil. \( \boldsymbol{H}_{2} \boldsymbol{S O}_{4}: \)
\( A \cdot S O_{2} \) is liberated
B. \( P H_{3} \) is evolved.
c. \( H_{2} S \) is evolved
D. \( H_{2} \) is evolved


Find out the volume of gasses evolved by
passing 0.965 A current for 1 hr through
an aqueous solution of \( C H_{3} C O O N a \) at
\( 25^{0} C \) and 1 atm:
A . \( 0.036 L \)
B. 1.76 L
c. \( 0.072 \mathrm{L} \)
D. 1.12 L


Solutions which distill without change in composition or temperature are called:
A. amorphous
B. azeotropic mixture
c. ideal
D. super saturated


If \( |2-|[x]-||1 \leq 2, \) then \( x \) belongs to
the solution set (where [.] represents greatest integer function)
A. [-3,6)
()
в. [-4,6)
c. [-3,7)
D. [-3,6]


\( \int_{0}^{1} \frac{d x}{x+\sqrt{x}}= \)
\( A \cdot \log 2 \)
B. 2 log 2
c. \( 3 \log 3 \)
D. \( \frac{1}{2} \log 2 \)


A dipole is placed in a shell as shown
Find the electric flux emerging out of
the shell and in a hypothetical sphere of
radius r as shown.
A. \( \frac{2 q}{8} \)
В \( \cdot \frac{q}{\varepsilon_{0}}, \frac{-q}{\varepsilon_{0}} \)
c. \( \frac{-q}{\varepsilon_{0}}, \frac{q}{\varepsilon_{0}} \)
0.0


If \( \boldsymbol{y}=\boldsymbol{e}^{\boldsymbol{a} \cos ^{-1} \boldsymbol{x}} \) then \( \left(\boldsymbol{1}-\boldsymbol{x}^{2}\right) \boldsymbol{y}^{\prime \prime}-\boldsymbol{x} \boldsymbol{y}^{\prime}= \)
A . \( a y \)
B. \( -a^{2} y \)
c. \( -a y \)
D \( \cdot a^{2} y \)


First true land plants are
A. Mosses
B. Ferns
c. Amphibians of plant kingdom
D. Produce flowers


Morning sun is not so hot as the mid
day sun because:
A. sun is cooler in the morning
B. heat rays travel slowly is the morning
C . it is God gift
D. the sun's rays travel a longer distance through atmosphere in the morning


State and explain Dalton's atomic theory.


Assertion
Reduction of a metal oxide is easier if
the metal formed is in liquid state at
the temperature of the reduction
Reason
The entropy is higher if the metal is in
liquid state.
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


From the following,pick a property that is associated to ferromagnetic
materials only:
A. attracting magnetic substance
B. hysterisis
c. directional property
D. susceptibility independent of temperature


In which city number of people
watching T.V is same as people reading
newspaper?
\( \mathbb{Z} \) people reading newspaper
\( A \). Delhi
B. Mumbai
C. Kolkata
D. Patna


Match the Column I with Column II
Column n II
nion Column
I
(Units) (Dimensional formulae)
(A) Pas Pas
\( (p) \)
\( \left[M^{0} L^{2} T^{-2} K^{-1}\right] \)
(B) \( \mathrm{Nm} \mathrm{K}^{-1} \)
\( (q) \)
\( \left[M L T^{-3} K^{-1}\right] \)
\( (C) \)
\( \mathrm{J} \mathrm{kg}^{-1} \mathrm{K} \)
-1
\( (r) \)
\( \left[M L^{-1} T^{-1}\right] \) "
(D) \( \mathrm{W} \mathrm{m}^{-1} \)
\( \mathrm{K}^{-1} \)
(s) \( \left[M L^{2} T^{-2} K^{-1}\right] \)
\( A \cdot A-q, B-p, C-r, D-s \)
B. \( A-p, B-q, C-s, D-r \)
C. \( A-r, B-s, C-p, D-q \)
D. \( A-s, B-r, C-q, D-p \)


Strongest reducing agent of the following is :
\( A \cdot H_{2} O \)
в. \( \mathrm{H}_{2} \mathrm{s} \)
c. \( \mathrm{H}_{2} \mathrm{Se} \)
D. \( \mathrm{H}_{2} \mathrm{Te} \)


A substance which burn in air is
(combustible/ non-
combustible) substance such as
(hydrogen/ ammonia/ chlorine).
A. Non-combustible, chlorine
B. Combustible, hydrogen
c. Combustible, ammonia
D. combustible, chlorine


Find out the word pair relation and fill in the blanks.
Cerebrum - Thought
Cerebellum -


The drift current in a \( p-n \) junction
diode is
This question has multiple correct options
A. motion of charge carriers due to the electric field
B. motion of charge carriers due to the charge concentration gradient
C. in same direction as the diffusion current
D. opposite in direction to the diffusion current


\( \mathbf{S i O}_{2} \) can react with:
\( \mathbf{A} \cdot N a O H \) only
B. \( H F \) only
C. Neither \( H F \) nor \( N a O H \)
D. Both \( H F \) and \( N a O H \)


A group of 10 observations has mean 5 and \( \operatorname{s.D.} 2 \sqrt{6} . \) Another group of 20 observations has mean 5 and \( \mathrm{S.D.} 3 \sqrt{2} \)
then the S.D. of combined group of 30 observations is
A . \( \sqrt{5} \)
B. \( 2 \sqrt{5} \)
\( c \cdot 3 \sqrt{5} \)
D. None of these


Suppose \( f^{\prime}(x) \) exists for each \( x \) and
\( \boldsymbol{h}(\boldsymbol{x})=\boldsymbol{f}(\boldsymbol{x})-(\boldsymbol{f}(\boldsymbol{x}))^{2}+(\boldsymbol{f}(\boldsymbol{x}))^{3} \) for
every real number \( x \). Then
This question has multiple correct options
A. \( h \) is increasing whenever fis increasing
B. \( h \) is increasing whenever fis decreasing
c. \( h \) is decreasing whenever fis decreasing
D. nothing can be said in general.


Velocity-time graph of a body with uniform velocity is a straight line:
A. parallel to x-axis
B. parallel to y-axis
c. inclined to \( x \) - axis
D. inclined to y-axis


The number of \( 3 \times 3 \) non-singular
matrices with four entries as 1 and all
other entries as 0 is
A. at least 7
B. less than 4
\( c .5 \)
D. 6


Rays of light fall on a glass plate of refractive index \( =\sqrt{3} . \) If the
angle between refracted ray and
reflected ray is \( 90, \) the angle of incidence is :
A . 90
B . 45
c. 135
D. 60


A girl stands on a box having \( 60 \mathrm{cm} \) length, \( 40 \mathrm{cm} \) breadth and \( 20 \mathrm{cm} \) width in three ways. The pressure exerted by the box will be:
A. maximum when length and breadth form the base
B. maximum when breadth and width form the base
c. maximum when width and length form the base
D. the same in all the above three cases


Assertion
A soft iron core is used in a moving coil galvanometer to increase the strength of magnetic field.
Reason
From soft iron more number of the
magnetic lines of force passes.
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


Benzoyl chloride on reduction with
\( \boldsymbol{H}_{2} / \boldsymbol{P} \boldsymbol{d}-\boldsymbol{B} \boldsymbol{a} \boldsymbol{S} \boldsymbol{O}_{4} \)
produces
A. Benzoic acid
B. Benzyl alcohol
c. Benzoyl sulphate
D. Benzaldehyde


Find the vector equation of the plane whose cartesian form of equation is \( 3 x- \) \( 4 y+2 z=5 \)


In the figure given below \( \square P Q R S \) is a
trapezium. seg \( \boldsymbol{P Q}\|\operatorname{seg} \boldsymbol{M} \boldsymbol{N}\| \operatorname{seg} \boldsymbol{S} \boldsymbol{R} \)
If \( \boldsymbol{P} \boldsymbol{M}=\mathbf{8}, \boldsymbol{M} \boldsymbol{S}=\mathbf{1 0} \) and \( \boldsymbol{N} \boldsymbol{R}=\mathbf{5} \)
then find \( Q N \)


Assertion
lonic compounds have high melting points
Reason lonic compounds have strong electrostatic forces of attraction
between the ions. Therefore, it requires a lot of energy to overcome these forces.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


\( \boldsymbol{I}=\int \frac{1}{2 x^{2}+3 x+4} d x \)


Write the principle on which the
working of a metre bridge is based. In an experiment on meter bridge, student obtains the balance point at the point \( J \)
such that \( A J=40 c m \), as shown in
figure. The values of \( \boldsymbol{R} \) and \( \boldsymbol{X} \) are both
doubled and then interchanged. Find the new position of the balance point. If the galvanometer and battery are also interchanged how will the position of
balance point be affected


Suppose a machine produces metal parts that contain some defective parts
with probability \( 0.05 . \) How many parts should be produced in order that the probability of atleast one part being defective is \( \frac{1}{2} \) or more?
(Given that, log \( _{10} 95=1.977 \) and
\( \left.\log _{10} 2=0.3\right) \)
This question has multiple correct options
A . 11
в. 12
\( c \cdot 15 \)
D. 14


A \( 90 \mathrm{gm} \) ball moving at \( 100 \mathrm{cm} / \mathrm{s} \) collide head on with a stationary 10 gm ball. The coefficient of restitution is \( 0.5 . \) Their
respective velocities after collision are
A \( \cdot 135 \mathrm{cm} / \mathrm{s}, 85 \mathrm{cm} / \mathrm{s} \)
B. \( 85 \mathrm{cm} / \mathrm{s}, 135 \mathrm{cm} / \mathrm{s} \)
\( c .-85 \mathrm{cm} / \mathrm{s}, 135 \mathrm{cm} / \mathrm{s} \)
D. \( 85 \mathrm{cm} / \mathrm{s},-135 \mathrm{cm} / \mathrm{s} \)


Moment of inertia of a uniform circular
disc about a diameter is \( l \). Its moment
of inertia about an axis perpendicular
to its plane and passing through a point on its rim will be:


Find the place value of 5 in 17805


Coracoid is component of
A. Fore limb
B. Skull
c. scapula
D. Pelvic girdle


Which of the following has the maximum value of mean free path?
A. \( C O_{2} \)
в. \( H_{2} \)
\( c \cdot O_{2} \)
D. \( N_{2} \)


Name the part of plant which helps in holding the plant in the soil.


How many consecutive odd numbers are required to form \( 10^{3} \) as their sum?
A . 10
B. 11
\( c .9 \)
D. 20


Match list I with list II and tick the
correct one from codes given below.
c. \( A-\| I, B-11, C-1, D-1 V \)
D. A-IV, B-III, C-II, D-


Let \( A \) and \( B \) be two independent events.
The probability that both \( A \) and \( B \) happen is \( \frac{1}{12} \) and the probability that neither \( A \) nor \( B \) happen is \( 1 / 2 \).If the sum of probabilities of occurence of \( \boldsymbol{A} \) and \( B \) is \( \frac{k}{12}, \) then the value of \( k \) is


Which element of 2nd period forms most acidic oxide?
A. Flourine
B. Nitrogen
c. Boron
D. Carbon


If the relation between the cost charged
by a game shop is shown by the given
graph, then the \( y- \) intercept of this
graph represents
A. The cost of playing 5 games
B. The cost per game, which is \( \$ 5 \)
C. The entrance fee to enter the arcade
D. The number of games that are played


Find the number of sides of a regular
polygon if each exterior angle is equal to its adjacent interior angle


Solution of the differential equation \( \left(x^{2}+y^{3}\right)\left(2 x^{2} d x+3 y d y\right)=12 x d x+ \)
\( 18 y^{2} d y \) is
A \( \cdot \frac{2}{3} x^{3}+\frac{3}{2} y^{2}=6 \ln \left(x^{2}+y^{3}\right)+c \)
в. \( x^{2}+y^{3}=9 \ln \left(x^{2}+y^{3}\right)+c \)
c. \( \frac{2}{3} x^{3}+\frac{3}{2} y^{2}=6 \ln \left(x^{3}+y^{2}\right)+c \)
D. \( x^{3}+y^{2}=6 \ln \left(x^{2}+y^{3}\right)+c \)


An electric dipole is placed at the centre
of a sphere. Mark the correct options:
A. The electric field is zero at every point of the sphere
B. The flux of the electric field through the sphere is nonzero
c. The electric field is zero on a circle on the sphere
D. The electric field is not zero anywhere on the sphere


Find the coordinates of the points which divide the line segment joining the points (-4,0) and (0,6) in 4 equal
parts This question has multiple correct options
A \( \cdot\left(-3, \frac{3}{2}\right) \)
в. (-2,3)
\( ^{c} \cdot\left(-1, \frac{9}{2}\right) \)
D. All of the above


Write the difference between
electrolytic and galvanic cell?


Solve the following:
\( \tan \left(\frac{1}{2} \sin ^{-1} \frac{3}{4}\right) \)


Area enclosed between the curves \( y^{2}= \)
\( x \) and \( x^{2}=y \) is equal to
This question has multiple correct options
A \( \cdot_{2} \int_{0}^{1}\left(x-x^{2}\right) d x \)
B.
c. area of region \( \left\{(x, y): x^{2} \leq y \leq|x|\right\} \)
D. \( \frac{2}{3} \)


The vitamin which is water soluble and
antioxidant is :
A. vitamin B \( _{6} \)
B. vitamin Biz.
c. vitamin c.
D. vitamin E.


A water hose of cross sectional area 4
\( \mathrm{cm}^{2} \) is used to fill a 30 Iit vessel. If it
takes 1 minute to fill that vessel, the speed at which water leaves the hose is:
\( \mathbf{A} \cdot 250 \mathrm{cms}^{-1} \)
B. \( 62.5 \mathrm{cms}^{-1} \)
c. \( 125 \mathrm{cms}^{-1} \)
D. \( 500 \mathrm{cms}^{-1} \)


Find the solution set of the inequality
\( |\boldsymbol{y}-\mathbf{5}| \leq \mathbf{1} \)
A. \( 4 \leq y \leq 6 \)
в. \( 4 \leq y \geq-6 \)
c. \( 4 \geq y \leq 6 \)
D. \( -4 \leq y \leq 6 \)


Four charges are kept at the corners of a
square \( A B C D \) as shown. The force on a
positive charge placed at the centre of
the square is
\( A \)
B. Along diagonal ACC
c. Along diagonal BD
D. perpendicular to side AB


If the total surface area of a solid
hemisphere is \( 46 c m^{2}, \) find its volume


Chiasmata appears during which of the following phase?
A . Diakinesis
B. Synaptotene
c. Diplotene
D. Leptotene


A car is moving on a straight road. The velocity of the car varies with time as
shown in figure. Initially \( (a t t=0), \) the
car was at \( \boldsymbol{x}=\mathbf{0}, \) where, \( \boldsymbol{x} \) is the
position of the car at any time \( t \)
The time interval during which the car
is retarding can be:
\( \mathbf{A} \cdot t=50 s \) to \( t=70 s \)
B. \( t=30 s \) to \( t=50 s \)
\( \mathbf{c} \cdot t=30 s \) to \( t=60 s \)
\( \mathbf{D} \cdot t=10 s \) to \( t=20 \)


Major source of protein among the following is
A. Oryza sativa
B. Cicer arietinum
c. Beta vulgaris
D. Rhizobium leguminosarum


Find \( x^{3}-y^{3} \) if \( x-y=5 \) and \( x y=16 \)


Which of the following is an equivalence relation?
1) \( x<y \)
2) \( x>y \)
3) \( x-y \) is divisible by 5
4) \( x \) divides \( y \)


The lightest gas on earth is?
A. Hydrogen
B. Oxygen
c. Helium
D. Chlorine


How does the ionization energy of an atom vary along a period and a group of the periodic table?


The total angular momentum of a rigid
body can be written as
A. \( I \times \omega \); where I: moment of inertia of body, : angular velocity
B. \( I^{2} \times \omega ; \) where I: moment of inertia of body, : angular velocity
C \( \cdot I^{2} \times \omega^{2} ; \) where I: moment of inertia of body, : angular
velocity
D. \( I \times \omega^{2} \); where I: moment of inertia of body, : angular
velocity


Assertion(A): The difference of the focal
distances of any point on the hyperbola \( \frac{\boldsymbol{x}^{2}}{\mathbf{3 6}}-\frac{\boldsymbol{y}^{2}}{\mathbf{9}}=\mathbf{1} \) is 12
Reason(R): The difference of the focal
distances of any point on the hyperbola is equal to the length of it transverse axis
A. Both A and R are true and R is the correct
explanation of \( A \)
B. Both A and R are true but R is not the correct
explanation of \( A \)
C. A is true but R is false.
D. A is false but R is true.


\( \boldsymbol{I}=\int \boldsymbol{x}^{9} \boldsymbol{d} \boldsymbol{x} \)


Say true or false
Points (1,7),(4,2),(-1,-1) and
(-4,4) are the vertices of a square
A. True
B. False


Solve the following \( \left(6 x^{4}+4 x^{2}+9 x+5\right) \div(2 x+3) \)


Name the gland that secretes the
emergency hormone!


The electrode with reaction:
\( \boldsymbol{C r}_{2} \boldsymbol{O}_{7}^{2-}(\boldsymbol{a q})+\mathbf{1 4 H}^{\oplus}(\boldsymbol{a q})+\boldsymbol{6} \boldsymbol{e}^{-} \rightarrow \)
\( 2 C r^{3+}(a q)+7 H_{2} O \) can be
represented as:
A \( \cdot P t \mid H^{\oplus}(a q), C r_{2} O_{7}^{2-}(a q) \)
B. \( P t \mid H^{\oplus}(a q), C r_{2} O_{7}^{2-(a q)}, C r^{3+}(a q) \)
C. \( P t_{H_{2}} \mid H^{\oplus}(a q), C r_{2} O_{7}^{2} \)
D. \( P t_{H_{2}} \mid H^{\oplus}(a q), C r_{2} O_{7}^{2-}(a q), C r^{3+}(a q) \)


In the given figure, \( \Delta X Y Z \) is inscribed
in a circle with centre 0. If the length of chord YZ is equal to the radius of the
circle OY then \( \angle \boldsymbol{Y} \boldsymbol{X} \boldsymbol{Z}= \)
A \( \cdot 60^{\circ} \)
B. \( 30^{\circ} \)
\( c \cdot 80^{\circ} \)
D. \( 100^{\circ} \)


The \( d \) -orbital having two lobes and one
doughnut is:
\( \mathbf{A} \cdot d_{x^{2}-y^{2}} \)
B. \( d_{z} \)
c. \( d_{x y} \)
D. \( d_{y z} \)


Taj Mahal is being slowly disfigured and discoloured. this is primarily due to:
A. Water pollution
B. Global warming
c. soil pollution
D. Acid rain


Which of the following set is isostructural?
\( \mathbf{A} \cdot \mathrm{XeF}_{2}, \mathrm{IF}_{2}^{-} \)
В. \( \mathrm{NH}_{3}, \mathrm{BF}_{3} \)
\( \mathrm{c} \cdot \mathrm{CO}_{3}^{2-}, \mathrm{SO}_{3}^{2} \)
D. \( \mathrm{PCl}_{5}, \mathrm{Cl}_{5} \)


The magnitude of the impulse developed by a mass of \( 0.2 \mathrm{kg} \) which changes its velocity from \( 5 \hat{i}+3 \hat{j}+7 \hat{k} \) \( \mathrm{m} / \mathrm{s} \) to \( 2 \hat{\boldsymbol{i}}+\boldsymbol{3} \hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} \)
A . \( 2.7 \mathrm{N}-\mathrm{s} \)
B. 1.3N-s
c. \( 0.9 N- \) s
D. 3.6N-s


In the load-extension graph for a wire, the elastic limit lies between the points
A. \( Q \) and \( R \)
B. P and Q
c. P and R
D. None of these


The process is spontaneous at the given temperature, if
A. \( \Delta H \) is \( +v e \) and \( \Delta S \) is \( -v e \)
B. \( \Delta H \) is \( -v e \) and \( \Delta S \) is \( +v e \)
\( \mathrm{c} . \Delta H \) is \( +v e \) and \( \Delta S \) is \( +v e \)
D. \( \Delta H \) is \( +v e \) and \( \Delta S \) is equal to zero


A charge 'Q' is placed at the centre of a hemispherical surface of radius ' \( \boldsymbol{R} \). The
flux of electric field due to charge ' \( Q^{\prime} \) through the surface of hemisphere is
\( \mathbf{A} \cdot Q / 4 \varepsilon_{0} \)
в. \( Q / 4 \pi \varepsilon_{0} \)
c. \( Q / 2 \varepsilon_{0} \)
D. \( Q / 2 \pi \varepsilon_{0} \)


The lines \( p\left(p^{2}+1\right) y-x+q=0 \) and
\( \left(p^{2}+1\right) x+\left(p^{2}+1\right)^{2} y+2 q=0 \) are
perpendicular to a common line for
A. exactly one value of \( p \)
B. exactly two values of \( p \)
c. more than two values of \( p \)
D. no value of \( p \)


Which of the following conversions involve ATP synthesis during glycolysis?
A. Glucose \( \rightarrow \) Glucose- 6 -phosphate
B. Fructose-6-phosphate\rightarrowFructose-1,6-biphosphate
c. 1,3 -bisphosphoglyceric acid (BPGA) \( \rightarrow 3- \) phosphoglyceric acid (PGA)
D. All of these


Find the nature of the roots of the
following quadratic equations. If the real roots exist, find them:
(i) \( 2 x^{2}-3 x+5=0 \)
(ii) \( 3 x^{2}-4 \sqrt{3} x+4=0 \)
(iii) \( 2 x^{2}-6 x+3=0 \)


The excess pressure inside a spherical soap bubble of radius \( 1 \mathrm{cm} \) is balanced
by a column of oil (specific gravity \( = \) 0.8)\( , 2 m m \) high, the surface tension of
the bubble is :
A. \( 3.92 \mathrm{N} / \mathrm{m} \)
в. 0.0392 N / \( m \)
c. \( 0.392 \mathrm{N} / \mathrm{m} \)
D. \( 0.00392 \mathrm{N} / \mathrm{m} \)


A charged oil drop is held stationary in an electric field. The space surrounding the drop is exposed to a radioactive source and the drop moves with different terminal velocities \( \mathbf{v}, 2 \mathbf{v} \)
\( 3 v \) etc. It is inferred that
A. Charge is conserved.
B. Drop carries negative charge.
c. charge is quantized.
D. Drop carries positive charge.


Does the charge given to a metallic sphere depends on whether it is hollow or solid? Given reason for your answer.


The rms speed of hydrogen is \( \sqrt{7} \) times the rms speed of nitrogen. If T is the temperature of the gas, then:
\( \mathbf{A} \cdot T_{H_{2}}=T_{N_{2}} \)
B \( \cdot T_{H_{2}}>T_{N_{2}} \)
\( \mathbf{c} \cdot T_{H_{2}}<T_{N_{2}} \)
D. \( T_{H_{2}}=\sqrt{7} T_{N_{N}} \)


The air spaces in the leaf is created by
A. Chlorenchyma
B. Aerenchyma
c. Palisade parenchyma
D. None of the above


Find area of \( \boldsymbol{y}=\boldsymbol{x}^{2} \) from \( \boldsymbol{x}=\boldsymbol{2} \) to \( \boldsymbol{x}=\boldsymbol{4} \)


A metal reacts with chlorine to form two
chlorides \( A \) and \( B . A \) has \( 77.45 \% \) while
\( B \) has \( 84.93 \% \), by mass of chlorine. This
data is in accordance with the:
A. law of conservation of mass
B. law of multiple proportions
c. law of definite proportions
D. law of reciprocal proportions


There is 10 units of charge at the centre of a circle of radius 10m. The work done in
moving 1 unit of charge around the circle
once is:
A . zero
B. 10 units
c. 100 units
D. 1 unit


Which molecule binds to uracil in RNA?
A. Thymine
B. Guanine
c. cytosine
D. Adenine
E. Uraci


f a point is in the \( X Z \) -plane. What can
you say about its \( y \) -coordinate?


In theatres, big halls., the reverberation of sound is a common problem.
A. True
B. False


The process in which the state of
a substance changes from solid to liquid is called:
A. boiling
B. condensation
c. freezing
D. melting


Which one of the following pairs of codons is correctly matched with their function or the signal for the the particular amino acid?
A. AUG, ACG - Start/methionine
B. UUA, UCA - Leucine
c. GUU - Alanine
D. UAG, UGA - Stop


When a metallic sphere is dropped in a long column of a liquid, the motion of the sphere is opposed by the viscous force of the liquid. If the apparent weight of the sphere equals to the retarding forces on it, the sphere moves down with a velocity called:
A. critical velocity
B. terminal velocity
c. velocity gradient
D. constant velocity


Consider the function \( \left\{\begin{array}{c}x \sin \frac{\pi}{x} \text { for } x>0 \\ \text { 0 for } x=0\end{array} \) then the number \right.
of points in (0,1) where the derivative \( f^{\prime}(x) \) vanishes, is
A . 0
B. 1
\( c \cdot 2 \)
D. infinite


An object and its real image are located at distances \( 25 \mathrm{cm} \) and \( 40 \mathrm{cm} \)
respectively from the two principal focii of a convex lens. The linear
magnification of the image is near to
A . +1.3
в. -1.3
\( c .+1.8 \)
D. -1.8.8. -1.8


A uniform electric field \( \boldsymbol{E}=\mathbf{2} \times \)
\( 10^{3} N C^{-1} \) is acting along the positive \( x \)
axis. The flux through the same square if the line normal to tis plane makes a
\( 60^{\circ} \) angle with the \( x \) -axis is
\( \begin{array}{lll}\text { A. } 30 N & C^{-1} m^{2}\end{array} \)
B. \( 10 N \quad C^{-1} m^{2} \)
\( \begin{array}{lll}c \cdot 20 N & C^{-1} m^{2} & ^{2}\end{array}^{C^{2}} \)
D. \( 25 N \quad C^{-1} m^{2} \)


The angle between the lines, whose direction ratios are 1,1,2 and \( \sqrt{3}- \) \( 1,-\sqrt{3}-1,4, \) is
A . \( 45^{\circ} \)
B. \( 30^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 90^{\circ} \)


f 0 is a point on the circle and \( P \) is a
point in the exterior of the circle. Length
of \( \boldsymbol{O} \boldsymbol{P}=7.5 \mathrm{cm} \) and radius of the circle
is \( 5.5 \mathrm{cm} . \) What will be the length of \( Q P \) if \( Q \) is the centre?
A. \( 5.5 \mathrm{cm} \)
B. \( 13 \mathrm{cm} \)
\( c .7 .5 \mathrm{cm} \)
D. \( 13.5 \mathrm{cm} \)


The depletion region in a semiconductor diode is formed at the
A. thermonic emitter
B. junction
c. diode
D. forbidden zone


Integrate with respect to \( x \)
\( x \ln x \)


State and explain Ohm's law.


f \( \boldsymbol{y}=\cot ^{-1}\left[\frac{\sqrt{1+x^{2}}+1}{x}\right], \) then find
the value of \( \frac{d y}{d x} \)


Burying of waste for their disposal is
seen in case of
A. Landfill
B. Incinerations
c. Dumps
D. None of the above


In the circuit shown, assume the diode
to be ideal. When \( V_{i} \) increases from \( 2 V \)
to \( 6 V \), the change in the current is (in
\( \boldsymbol{m} \boldsymbol{A}) \)
A . zero
B . 20
\( c \cdot 80 / 3 \)
D. 40


Suppose \( f \) is the collection of all ordered pairs of real numbers and \( x=6 \) is the
first element of some ordered pair in \( f \) Suppose the vertical line through \( x=6 \) intersects the graph of \( f \) twice. Is \( f \) a function? Why or why not?


A ball is dropped from an elevator
moving upward with acceleration \( ^{\prime} a^{\prime} \) by
a boy standing in it. The acceleration of ball with respect to [Take upward direction positive \( ] \)
A. Boy is \( -g \)
B. Boy is \( -(g+a) \)
c. Ground is \( -g \)
D. Both (2) \& (3)


Which inert gas having higher boiling point?
A . \( x_{e} \)
B. Ar
c. \( \mathrm{kr} \)
D. не


By the process of convection, the transfer of heat is always
A. Vertically downwards
B. Vertically upwards
c. Both
D. None


The conversion of benzaldehyde into benzyl alcohol takes place by:
A. Fittig reaction
B. Wurtz -Fittig reaction
c. wurtz reaction
D. Cannizzaro's reaction


\( |\vec{a}+\vec{b}|^{2}+|\vec{a}-\vec{b}|^{2} \) is equal to \( 2\left(|\vec{a}|^{2}\right. \)
\( \left.|\vec{b}|^{2}\right\rangle \)
If true enter 1 else enter 0


For what values of a does the minimum
value of the function \( y=x^{2}-4 a x- \)
\( a^{4} \) assume the greatest value?


Prove that the sum of angles of a
triangle is 180


Assertion
Liquids and gases are largely incompressible and densities are therefore, nearly constant at all
pressures.
Reason
Liquids exhibits large variation in
densities with pressure but gases do
not.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


In the following diagram if \( V_{2}>V_{1} \) then
\( \mathbf{A} \cdot \lambda_{1}=\sqrt{\lambda_{2}} \)
B \( \cdot \lambda_{1}<\lambda_{2} \)
\( c \cdot \lambda_{1}=\lambda_{2} \)
D. \( \lambda_{1}>\lambda_{2} \)


A beam of light of wavelength 600 nm from a distant source falls on a single
slit \( 1.0 \mathrm{mm} \) wide and the resulting diffraction pattern is observed on
a screen \( 2 \mathrm{m} \) away. The distance between the first dark fringes on either
side of the central bright fringe is:
A . \( 1.2 \mathrm{cm} \)
B. 1.2 \( \mathrm{mm} \)
c. \( 2.4 \mathrm{cm} \)
D. 2.4 mm


Coefficient of range 5,2,3,4,6,8,10 is?
A \( \cdot \frac{2}{3} \)
B. \( \frac{1}{3} \)
\( c \cdot \frac{3}{5} \)
D.


The type of reactions considered to be the principal sources of energy in stars is \( _{-}--_{-}- \) when hydrogen is converted to helium.
A. nuclear fission
B. nuclear fusion
c. radioactive decay
D. none of the above


A straight line conductor of length
\( 0.4 m \) is moved with a speed of \( 7 m / s \) perpendicular to a magnetic filed of
intensity \( 0.9 W b / m^{2} . \) The induced e.m.f. across the conductor is
A . \( 5.04 V \)
B . \( 1.26 V \)
c. \( 2.52 V \)
D. 25.2 \( V \)


What are the products of hydrolysis of
maltose?


Assertion
Brittle materials do not exhibit an
identifiable yield point; rather, they fail by brittle fracture.
Reason
The value of the largest stress in tension and compression defines the ultimate strength.
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


Calculate the number of fringes.
A . 10
B. 20
\( c .30 \)
D. 40


Rubber is hardened for making tyres by:
\( \mathbf{A} \cdot \) adding \( H_{2} \)
B. adding carbon black
c. saturating it
D. All of the above


What is the second component of an ordered pair \( (\mathbf{3},-\mathbf{0 . 2}) ? \)
\( A \cdot 3 \)
B. 0.2
c. 1
D. - 0.2


If temperature is decreased, then
relaxation time of electrons in metals
will
\( A \). increase
B. decrrease
C. fluctuate
D. remains constant


A hammer weighing \( 3 \mathrm{kg}, \) moving with a velocity of \( 10 \mathrm{m} / \mathrm{s}, \) strikes against the head of a spike and drives it into a block of wood. If the hammer comes to
rest in 0.025 s, the impulse associated with the spike will be :
\( A \cdot \) 30 Ns
B. -30Ns
c. 15 Ns
D. -15 Ns


A weak acid \( \boldsymbol{H} \boldsymbol{X}\left(\boldsymbol{K}_{\boldsymbol{a}}=\mathbf{1} \times \mathbf{1 0}^{-\mathbf{5}}\right) \) on
reaction with NaOH gives NaX. For \( 0.1 \mathrm{M} \) aqueous solution of NaX, the \% hydrolysis is:
A . 0.001\%
B . 0.01\%
c. \( 0.15 \% \)
D. 1\%


while travelling by train, when the train passes through the tunnel, why does our ear ache?
A. atmospheric pressure
B. tunnel pressure
c. inner pressure
D. none of the above


The possible relationship between
magnitudes of " \( V_{1} \) " and " \( V_{2} \) " is:
A \( \cdot V_{1}>V_{2} \)
в. \( V_{1}<V_{2} \)
\( c \cdot V_{1}=V_{2} \)
D. Both (A) and (C)


A ball of radius \( \boldsymbol{R}=\mathbf{1 0 . 0} \) cm rolls
without slipping on a horizontal plane
so that its centre moves with constant
acceleration \( a=2.50 \mathrm{cm} / \mathrm{s}^{2} ; t=2.00 s \)
after the beginning of motion its portion corresponds to that shown in Fig. Find:
(a) the velocities of the points \( A, B \) and
\( O \)
(b) the accelerations of these points.


When a certain metal is irradiated with
a radiation of frequency \( 3.2 \times 10^{16} S^{-1} \) the photo electrons emitted had twice the kinetic energy as did the phototelectrons emitted when the same
metal was irradiated with radiation of
frequency \( 2 \times 10^{16} S^{-1} . \) Calculate
threshold frequency of metal.


Fossils are mostly present in which of the following rocks?
A. Igneous rocks
B. Sedimentary rocks
c. Metamorphic rocks
D. coarse-grained rocks


The U tube having identical limbs
contains mercury (density \( \rho_{m} \) ) to a level as shown in the figure. If the left limbs
is filled to the top with water \( \left(\rho_{w}\right), \) then
the rise of mercury level in the right
limb will be
A . 12 pm 12pm
в.
c. \( \frac{\rho_{m} l}{\rho_{w}} \)
D.


Which of the following is the correct match?
(a) Eka silicon - Ge
(b) Eka aluminum - Ga
(c) Eka manganese - Tr
(d) Eka boron - Sc
\( A \cdot b, c \)
B. a, b, d
\( c \cdot a, d \)
D. All of above


Calculate \( [\boldsymbol{O} \boldsymbol{H}] \) which would be produced by each equilibrium concentration of \( N H_{3} \) in part
(a). Predict whether \( Z n(O H)_{2} \) or \( Z n(O H)_{4}^{2-} \) would form in prefemce to \( Z n\left(N H_{3}\right)_{4}^{2+} \) upon addition of sufficient
\( N H_{3} \) to produce the equilibrium concentration calculated in part (a).
A \( \cdot 3.33 \times 10^{-4} M \)
В. \( 2.5 \times 10^{-4} M \)
c. \( 4.5 \times 10^{-4} M \)
D. \( 9.0 \times 10^{-4} M \)


Pressure exerted by liquid depends on
A. Depth of liquid
B. Gravity
c. Density of liquid
D. All of these


Assertion
Higher yields in case of bell pepper can
be achieved by growing them in carbon dioxide enriched green houses.
Reason
In the case of bell pepper, due to higher
intracellular \( \mathrm{CO}_{2} \) concentration in
bundle sheath cells RuBisCo mainly
acts as carboxylating enzyme.
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.


locate the point representing the
complex numbers \( z \) on the Argand diagram for which
\( |z|-4=|z-i|-|z+5 i|=0 \)


If \( \theta \) is the angle between the lines
\( A B, A C \) where \( A, B, C \) are the three points with coordinates (1,2,-1),(2,0,3),(3,-1,2)
respectively, then \( \sqrt{462} \cos \theta \) is equal to
A . 20
в. 2
c. 22
D. 26


The oxides of nitrogen and sulfur, when mixed with water in the air, are the chief components of acid rain.
A. True
B. False
c. Either
D. Neither


Show how would you synthesize the given alcohol from appropriate alkenes.


Find sum of stereoisomer of following
compound
\( A \cdot 2^{6} \)
B . \( 2^{3} \)
\( c \cdot 2^{5} \)
D. None of these


An item was sold for \( R s .540 \) at a loss of
\( 5 \% . \) what was its cost price.


\( \mathbf{f}\left[\begin{array}{ccc}\mathbf{9} & -\mathbf{1} & \mathbf{4} \\ -\mathbf{2} & \mathbf{1} & \mathbf{3}\end{array}\right]=\boldsymbol{A}+\left[\begin{array}{ccc}\mathbf{1} & \mathbf{2} & -\mathbf{1} \\ \mathbf{0} & \mathbf{4} & \mathbf{9}\end{array}\right] \)
then find the matrix \( A \)


A metal rod \( \frac{1}{\sqrt{\pi}} m \) long rotates about one of its ends perpendicular to a plane whose magnetic induction is \( 4 \times \) \( 10^{-3} T . \) Calculate the number of
revolutions made by the rod per second if the e.m.f induced between the ends of
the rod is \( 16 m V \)


If the chord \( y=m x+1 \) of the circle
\( x^{2}+y^{2}=1 \) subtends an angle of
measure \( 45^{\circ} \) at the major segment of
the circle then the value of \( m \) is
A \( .2 \pm \sqrt{2} \)
B. \( -2 \pm \sqrt{2} \)
c. \( -1 \pm \sqrt{2} \)
D. none of these


Construct a \( 2 \times 2 \) matrix \( A=\left[a_{i j}\right] \)
whose element \( a_{i j} \) is \( a_{i j}=\frac{(i-j)^{2}}{2} \)


The reading of the voltmeter connected
across \( 20 \Omega \) resistance is
\( A \cdot 15 V \)
В. \( 10 V \)
\( c .5 V \)
D. \( 22.5 V \)


Coupling factor- F occurs over
A. Ribosome
B. Stroma
c. Matrix
D. Thylakoids


Consider the matrix \( A, B, C, D \) with
order \( 2 \times 3,3 \times 4,4 \times 4,4 \times 2 \)
respectively. Let \( \boldsymbol{x}=\left(\boldsymbol{\alpha} \boldsymbol{A} \boldsymbol{B} \boldsymbol{\gamma} \boldsymbol{C}^{2} \boldsymbol{D}\right)^{3} \)
where \( \alpha \) and \( \gamma \) are scalars. Let \( |x|= \)
\( k\left|A B C^{2} D\right|^{3} . \) Then the value of \( k \)
A \( \cdot \alpha^{6} \gamma^{6} \)
в. \( \alpha \gamma \)
c. \( \alpha^{3} \gamma^{3} \)
D. \( \alpha^{6} \gamma^{12} \)


\( \boldsymbol{K}_{s p} \) of a salt \( \boldsymbol{N} \boldsymbol{i}(\boldsymbol{O} \boldsymbol{H})_{2} \) is \( \boldsymbol{2} \times \mathbf{1 0}^{-15} \)
then molar solubility of \( N i(O H)_{2} \) in
\( \mathbf{0 . 0 1} \boldsymbol{M} \mathbf{N a O H} \mathbf{~ i s : ~} \)
A \( \cdot 2 \times 10^{-15} \mathrm{M} \)
B . \( 2^{-1 / 3} \times 10^{-5} M \)
c. \( 2 \times 10^{-11} M \)
D. \( 10^{-7} M \)


The element whose electronic
conguration is \( 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} \) is :
A. non-metal
B. noble gas
c. metalloid
D. metal


One heartbeat in an average man lasts
A . 0.8 second
B. 0.2 second
c. 0.5 second
D. 1 minute


\( C a C_{2} \) and \( H_{2} O \) react to produce:
A \( \cdot C H_{4} \)
в. \( C_{2} H_{4} \)
c. \( C_{2} H_{2} \)
D. \( C_{2} H_{6} \)


If \( \frac{\mathbf{x}^{2}}{\left(\mathbf{x}^{2}+\mathbf{1}\right)\left(\mathbf{x}^{2}+\mathbf{2}\right)}=\frac{\mathbf{A} \mathbf{x}+\mathbf{B}}{\mathbf{x}^{2}+\mathbf{1}}+ \)
\( \frac{\mathbf{C x}+\mathbf{D}}{\mathbf{x}^{2}+\mathbf{2}} \operatorname{then}(\boldsymbol{A}, \boldsymbol{C})= \)
A. (1,-1)
в. (1,1)
D. (1,2)


Calculate the \( \% \) p-character in the orbital occupied by the lone pairs in water molecules:
[Given : \( \angle H O H \) is \( 104.5^{\circ} \) and \( \cos \) \( (\mathbf{1 0 4 . 5})=-\mathbf{0 . 2 5}] \)
A . \( 80 \% \)
B . 20\%
c. \( 70 \% \)
D. 75\%


Fill in the blanks:
Open chain compounds are also called


\( A \) and \( B \) are two sets having 3 and 5
elements respectively and having 2
elements in common. Then the number
of elements in \( \boldsymbol{A} \times \boldsymbol{B} \) is
\( A \cdot 6 \)
B . 36
c. 15
D. none of these


What is the oxidation state of \( C r \) in
\( \boldsymbol{C r} \boldsymbol{O}_{5} ? \)


\( H_{2} O \) is polar, whereas \( B e F_{2} \) is not
because:
A. electronegativity of F is greater than that of 0
B. \( H_{2} O \) involves H-bonding , whereas \( B e F_{2} \) is a discrete molecule
c. \( H_{2} O \) is angular and \( B e F_{2} \) is linear
D. \( H_{2} O \) is linear and \( B e F_{2} \) is angular.


Based on the information in each choice
below, which of the noble gases would
have the greatest density for a \( 1.00 L \)
sample at room temperature and
pressure?
A. Krypton molar mass \( 83.8 g / \)mol , atomic radius 111 picometers
B. Argon molar mass \( 39.9 g / \)mol , atomic radius 94 picometers
c. Neon molar mass \( 20.2 g / \)mol , atomic radius 70 picometers
D. Helium molar mass \( 4.0 g / \mathrm{mol} \) atomic radius 50 picometers


Peptisation involves:
A. precipitation of colloidial particles
B. disintegration of colloidal aggregates
C . evaporation of dispersion medium
D. impact of molecules of the dispersion medium on the colloidal particles


What are the causes of water pollution?
Discuss how can you contribute in
reducing the water pollution.


The transformer voltage induced in the secondary coil of a transformer is mainly due to:
A. a varying electric field
B. a varying magnetic field
c. the vibrations of the primary coil
D. the iron core of the transformer


A charged oil drop weighing \( 1.6 \times \) \( 10^{-15} N \) is found to remain suspended
in a uniform electric field of intensity
\( 2 \times 10^{3} N C^{-1} . \) Find the charge on the
drop.


Azeotropic mixture:
A. Boil at different temperature
B. Are mixture of solids
C. Are constant boiling mixture
D. Gaseous mixture


Write equations for the reaction of dil HCl with each of the following. Sodium sulphite
A \( \cdot 2 H C l+N a_{2} S O_{3} \rightarrow 2 N a C l+S O_{2}+H_{2} O \)
в. \( 4 H C l+N a_{2} S O_{3} \rightarrow 2 N a C l+S O_{2}+2 H_{2} O \)
c. \( 2 H C l+N a_{2} S O_{3} \rightarrow N a C l+S O_{2}+H_{2} O \)
D. \( 2 H C l+N a_{2} S O_{3} \rightarrow 2 N a C l+S O_{3}+H_{2} O \)


The linear magnification for a spherical mirror is the ratio of the size of the
image to the size of the object, and is
denoted by m. Then \( m \) is equal to (symbols have their usual meanings)
A \( \cdot \frac{u}{u-f} \)
B. \( \frac{u f}{u-f} \)
c. \( \frac{f}{u+f} \)
D. None of these


Match the following and choose the correct combination from the options
given
\( \begin{array}{llll} & \text { Column I } & & \text { Column II } \\ \text { A } & \text { DDT } & 1 & \text { N0 }_{x} \text { , CO } \\ \text { B } & \text { PAN } & 2 & \text { Smog } \\ \text { C } & \text { Acid rain } & 3 & \begin{array}{l}\text { Biological } \\ \text { magnification }\end{array} \\ \text { D } & \begin{array}{l}\text { Global } \\ \text { warming }\end{array} & 4 & \text { so }_{2}\end{array} \)
A. A- \( 4, \) B- \( 3, \) C- \( 2, \) D-
B. A-1, B- 3, C- 2, D-4
c. \( A-2, B-3, C-4, D-1 \)
D. A- 3, B-2, C-4


For the equilibrium, \( M g C O_{3}(s) \Leftrightarrow \)
\( M g O(s)+C O_{2}(g), \) which of
the following expression is correct?
\( ^{\mathrm{A}} \cdot_{K_{p}}=\frac{P_{M g} o+P_{C O_{2}}}{P_{M g C O_{3}}} \)
в. \( _{K_{p}}=\frac{[M g O]+\left[C O_{2}\right]}{\left[M g C O_{3}\right]} \)
\( ^{\mathrm{c}} \cdot_{K_{p}}=\frac{P_{M g} o \cdot P_{C O_{2}}}{P_{M g C O_{3}}} \)
D. \( K_{p}=P_{C O_{2}} \)


The IUPAC name of tertiary butyl chloride is:
A. 4-chlorobutane
B. 2-chlorobutane
c. 1-chloro-3-methylpropane
D. 2-chloro-2-methylpropan


Assertion
Low temperature destroys enzymes by causing their denaturation.
Reason
High temperature preserves the enzymes in their inactive stage.
A. Both statements 1 and 2 are correct
B. Statement 1 is correct but statement 2 is incorrect
c. statement 1 is incorrect but statement 2 is correct
D. Both statements1 and 2 are incorrect.


topp 5
Q type your question
4
\( B \)
\( c \)
\( D \)


Three ants on the floor of a moving bus along a straight line with a uniform speed of \( 2 \mathrm{cm} / \mathrm{s} \) also moves with the
same velocity with respect to the ground along the straight line. Then
A. The collection of three ants can be considered as a rigid body with respect to the bus frame of reference
B. The collection of three ants can be considered as a rigid body with respect to the ground frame of reference
c. The collection of three ants is not a rigid body, since they are moving
D. The first ant can be considered as a rigid body, while the others are moving relative to first ant


Multiple Correct Answers Type:
The body will speed up if

This question has multiple correct options
A. Velocity and acceleration are in the same direction.
B. Velocity and acceleration are in opposite directions.
C. Velocity and acceleration are in the perpendicular direction.
D. Velocity and acceleration are acting at acute angle
w.r.t each other.


Glycogen is stored in
A . Liver
B. Muscles
c. Pancreas
D. Liver and muscles


\( \boldsymbol{n} \) is a whole number which when
divided by 4 gives 3 as remainder.
What will be the remainder when \( 2 n \) is
divided by \( 4 ? \)
\( A \cdot 7 \)
B. 5
\( c \cdot 4 \)
D. 2


In the options below which one of the isotope of the uranium can cause fission reaction?
A \( \cdot U_{234} \)
B. \( U_{235} \)
c. \( U_{23} \)
D. \( U_{238} \)


\( \boldsymbol{A}(\boldsymbol{g}) \rightarrow \boldsymbol{B}(\boldsymbol{g})+\boldsymbol{C}(\boldsymbol{g}) \)
\( \frac{-\boldsymbol{d}[\boldsymbol{A}]}{\boldsymbol{d} t}=\boldsymbol{k}[\boldsymbol{A}] \)
At the start, the pressure is \( 100 \mathrm{mm} \) and after 10 min, the pressure is 120
mm. Hence, rate constant \( \left(\min ^{-1}\right) \) is:
A \( \cdot \frac{2.303}{10} \log \left(\frac{120}{100}\right) \)
В. \( \frac{2.303}{10} \log \left(\frac{100}{20}\right) \)
c. \( \frac{2.303}{10} \log \left(\frac{100}{80}\right) \)
D. \( \frac{2.303}{10} \log \left(\frac{100}{120}\right) \)


The perimeter of rhombus is 52 sq. cm. If one of its diagonal is \( 24 \mathrm{cm} ; \) find the length of its other diagonal.


The function of potassium ethyl xanthate in froth floatation process is to make the ore:
A. attracted towards water
B. water repellant
c. lighter
D. heavier


If a body moves back and forth
repeatedly about a mean position, it is said to possess
A. rotatory motion
B. projectile motion
c. oscillatory motion
D. Reciprocating motion


Find the resistance of \( 1000 \mathrm{W}-250 \mathrm{V} \)
heater wire.


000
following


The \( x-y \) plane is the boundary
between two transparent media. Medium-1 with \( z>0 \) has refractive
index \( \sqrt{2} \) and medium- 2 with \( z<0 \) has a refractive index \( \sqrt{3} . \) A ray of light in medium-1 given by the vector \( \overrightarrow{\boldsymbol{A}}= \) \( 6 \sqrt{3} \hat{i}+8 \sqrt{3} \hat{j}-10 \hat{k} \) is incident on the
plane of separation. Find the unit vector
in the direction of refracted ray in medium-2.
\( \mathbf{A} \cdot 45^{\circ} \)
B. \( 60^{\circ} \)
\( \mathbf{c} \cdot 75^{\circ} \)
D. 30 \( ^{\circ} \)


The number of ions given by one
molecule of \( \boldsymbol{K}_{4} \boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{6} \) after complete
dissociation is
\( \mathbf{A} \cdot \mathbf{5} \)
B. 11
\( c \cdot 2 \)
D. 10


The value of \( \frac{\boldsymbol{f}(\boldsymbol{t})}{\boldsymbol{f}^{\prime}(\boldsymbol{t})} \cdot \frac{\boldsymbol{f}^{\prime \prime}(-\boldsymbol{t})}{\boldsymbol{f}^{\prime}(-\boldsymbol{t})}- \)
\( \frac{f(-t)}{f^{\prime}(-t)} \cdot \frac{f^{\prime \prime}(t)}{f^{\prime}(t)} \forall t \epsilon R \) is equal to
A . -2
B. 2
c. -4
\( D \)


IUPAC name is 3-phenylpropan-1-ol.
A. True
B. False


Which molecule contains both polar
and nonpolar covalent bond?
A \( . N H_{4} C l \)
в. \( H C N \)
\( \mathrm{c} \cdot \mathrm{CH}_{4} \)
D. \( H_{2} O_{2} \)


Assertion: Anterior lobe of pituitary is attached to hypothalamus by a vein
Reason: This attachment is done
through a portal vein
A. If both the assertion and the reason are true and the reason is the correct explanation of the assertion
B. If both the assertion and the reason are true and the reason is not the correct explanation of the assertion
c. If the assertion is true and the reason is false
D. If both the assertion and the reason is false
E. If the assertion is false but the reason is true


Evaluate the following integral
\( \int \frac{\sec x \operatorname{cosec} x}{\log (\tan x)} d x \)


If Set B has 200,000 elements,
calculate the difference between
number of negative and even numbers
of set B.

Negative and Even Number Distributions
Numbers
A .25,000
В. 140,000
\( c .50,000 \)
D. 155,000


The characteristic inflorescence of
family Cruciferae is
A. Umbel
B. Racemose
c. cymose
D. catkin


The rate of the reaction, \( \boldsymbol{A}+\boldsymbol{B}+\boldsymbol{C} \longrightarrow \)
Products, is given by, \( -\frac{\boldsymbol{d}[\boldsymbol{A}]}{\boldsymbol{d} t}= \)
\( \boldsymbol{k}[\boldsymbol{A}]^{1 / 2}[\boldsymbol{B}]^{1 / 3}[\boldsymbol{C}]^{1 / 4} \)
The order of the reaction is:
A \( \cdot \frac{1}{2} \)
в. \( \frac{13}{12} \)
c. 1
D. 2


In Thomson experiment of finding \( \frac{e}{m} \)
for electrons, beam of electrons is
replaced by that of muons (particle with same charge as of electrons but mass 208 times that of electrons).

No deflection condition in this is case
satisfied, if :
A. B is increased 208 times
B. E is increased 208 times
c. \( B \) is increased 14.4 times
D. None of the above


\( \boldsymbol{N} \boldsymbol{H}_{3}+\boldsymbol{O}_{2} \stackrel{P t}{\rightarrow} \boldsymbol{A}+\boldsymbol{H}_{2} \boldsymbol{O} \)
Identify the compound \( A \)
A . \( N O \)
в. \( N O_{2} \)
\( c \cdot N O_{3} \)
D. \( H N O_{3} \)


A blueliquid among the following is :
A. \( \mathrm{N}_{2} \mathrm{O}_{3} \)
в. \( \mathrm{N}_{2} \mathrm{O} \)
\( \mathrm{c} \cdot \mathrm{N}_{2} \mathrm{O}_{4} \)
D. NO


Write uses of plastic in medical?


The tissue that brings about an increase in the height of the plant is
A . Lateral Meristem
B. Apical Meristem
c. Intercalary Meristem
D. None of the above


If the roots of the equation \( p x^{2}+q x+ \)
\( \boldsymbol{r}=\mathbf{0} \) are in the ratio \( l: \boldsymbol{m} \) prove that
\( (l+m)^{2} p r=l m q^{2} \)


An object of mass \( m \) is tied to a string
of length \( l \) and a variable force \( F \) is
applied on it which brings the string
gradually at an angle \( \theta \) with the vertical
Find the work done by the force \( F \)
A. \( m g l(1-\cos \theta) \)
в. \( m g l(2-\cos \theta) \)
c. \( _{m g l}\left(1-\frac{\cos \theta}{2}\right) \)
D \( \cdot \operatorname{mgl}\left(2-\frac{\cos \theta}{2}\right) \)


How will you prepare ethane from
methyl chloride?
A. Williamson's synthesis
B. Wurtz synthesis
C. Hydrogenation of methyl chloride
D. Dehydrohalogenation of methyl chloride


Which of the following statements are true regarding Werner's theory are true?
(1) Ligands are connected to the metal ions by covalent bonds
(2) Secondary valencies have directional properties
(3) Secondary valencies are non- ionizable
A. 1,2 and 3 are correct
B. 2 and 3 are correct
c. 1 and 3 are correct
D. 1 and 2 are correct


A body falls from rest. In the last second of its fall it covers half of the total
distance. If \( g \) is \( 9.8 m / s^{2}, \) then the total
time of its falls is (in second)?
A . 2
B. \( 2+\sqrt{2} \)
\( c \cdot 4-\sqrt{2} \)
D. 3


Length of the latus rectum of the parabola \( \sqrt{\boldsymbol{x}}+\sqrt{\boldsymbol{y}}=\sqrt{\boldsymbol{a}} \) is
\begin{tabular}{l}
A \( \cdot a \sqrt{2} \) \\
\hline
\end{tabular}
B. \( \frac{a}{\sqrt{2}} \)
\( c \)
D. 2a


The elements \( A \) and \( B \) obey
Newland's law of octave. How many
elements are there between \( A \) and \( B ? \)
A. 7
B. 8
\( c .5 \)
D. 6


The value of \( g \) at a particular point is 9.8
\( m s^{-2} . \) Suppose the earth suddently shrinks uniformly to half its present size without losing any mass. The value of \( g \) at the same point (distance of the point from the centre of earth does not change) will now be
A. \( 9.8 m s^{-2} \)
B. \( 4.9 m s^{-2} \)
\( \mathbf{c} \cdot 19.6 \mathrm{ms}^{-2} \)
D. \( 39.2 \mathrm{ms}^{-2} \)


Heating benzene in a large excess of
\( 80 \% D_{4} S O_{2} \) in \( D_{2} O \) results in what
product?
A. \( C_{6} H_{5} S O_{3} D \)
в. \( C_{6} H_{5} \) О О
c. \( C_{6} H_{5} \) D
D. \( C_{6} D_{6} \)


In an electric motor, wires carrying a
current of \( 5 A \) are placed at right angles to a magnetic field of induction 0.8 T. If
each wire has length of \( 20 \mathrm{cm} \), then the
force acting on each wire is :
A \( .0 .2 N \)
в. 0.4 N
\( c \cdot 0.6 N \)
D. \( 0.8 N \)


Complete the following statements with an appropriate word /term be filled in the blank space(s).

The equivalent capacitance \( C \) for the parallel combination of three
capacitance \( C_{1}, C_{2} \) and \( C_{3} \) is given by
\( C=\dots \)
A \( \cdot C_{1}+C_{2}+C_{3} \)
B. \( \frac{1}{C_{1}+C_{2}+C_{3}} \)
\( ^{c}\left(\frac{1}{\frac{1}{C_{1}}+\frac{1}{C_{2}}+\frac{1}{C_{3}}}\right) \)
\( ^{\mathrm{D}} \cdot\left(\frac{1}{C_{1}}+\frac{1}{C_{2}}+\frac{1}{C_{3}}\right) \)


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


The equation of a progressive wave is \( \boldsymbol{y}=\mathbf{8} \sin \left[\boldsymbol{\pi}\left(\frac{\boldsymbol{t}}{\mathbf{1 0}}-\frac{\boldsymbol{x}}{\mathbf{4}}\right)+\frac{\boldsymbol{\pi}}{\mathbf{4}}\right] . \) The
wavelength of the wave is
\( \mathbf{A} \cdot 8 m \)
B. \( 4 m \)
c. \( 2 m \)
D. \( 10 \mathrm{m} \)


If \( \vec{r} . \hat{\boldsymbol{i}}=\overrightarrow{\boldsymbol{r}} \cdot \hat{\boldsymbol{j}}=\overrightarrow{\boldsymbol{r}} \cdot \hat{\boldsymbol{k}} \) and \( |\overrightarrow{\boldsymbol{r}}|=\boldsymbol{3}, \) then
\( \vec{r}= \)
\( \mathbf{A} \cdot \pm 3(\hat{i}+\hat{j}+\hat{k}) \)
B. \( \pm \frac{1}{3}(\hat{i}+\hat{j}+\hat{k}) \)
c. \( \pm \frac{1}{\sqrt{3}}(\hat{i}+\hat{j}+\hat{k}) \)
D. \( \pm \sqrt{3}(\hat{i}+\hat{j}+\hat{k}) \)


Find the least number of terms of an
A.P., \( 64+49+34+\dots \dots \) to be added
so that the sum is less than 36


Colocasia also known as taro, is an
example of a modified
A. Corm which is a stem modification
B. Bulb which is a stem modification
c. Bulb which is a root modification
D. Corm which is a root modification


Read the given statements that describe certain infectious particle.
(i) It was discovered by T.O. Diener and
was found to be smaller than viruses.
(ii) It causes potato spindle tuber
disease.
(iii) It is a free RNA particle which lacks the protein coat.
(iv) It has low molecular weight RNA as genetic material.
Which of the following is referred to here?
A. Virus
B. Viroid
c. virion
D. Bacteriophage


Calculate the emf of the following
concentration cell at \( 25^{\circ} C \)
\( \boldsymbol{A} \boldsymbol{g}(\boldsymbol{s}) \mid \boldsymbol{A} \boldsymbol{g} \boldsymbol{N} \boldsymbol{O}_{3}(\mathbf{0} . \boldsymbol{0} \mathbf{1} \boldsymbol{M}) \)
\( \boldsymbol{A} \boldsymbol{g} \boldsymbol{N} \boldsymbol{O}_{3}(\boldsymbol{0} . \boldsymbol{0} \boldsymbol{5} \boldsymbol{M}) \mid \boldsymbol{A} \boldsymbol{g}(\boldsymbol{s}) \)
A. \( -0.414 V \)
в. \( 0.828 V \)
c. \( 0.414 V \)
D. \( 0.0414 V \)


A 150 g cricket ball moving at a speed of \( 12 m s^{-1} \) is hit by a bat and turned back at a speed of \( 20 m s^{-1} . \) The duration of
impact is 0.01 s. What is the average force exerted on the ball by the bat?


A manufacturer of a certain item can
sell all he can produced at the selling price of Rs 60 each. It cost him Rs 40 in materials and labour to produce each item and he has overhead expenses of Rs 3000 per week in order to operate that plant. The number of units he should produce and sell in order to make a profit of at least Rs 1000 per weeks is
A . 250
в. 300
\( c .400 \)
D. 200


Explain emission and absorption
spectra


Q Type your question-
of water, but in the presence of a strong
\( \operatorname{acid}\left(H^{+}\right) \) with a non-nucleophilic
counterion. If this reaction follows a
typical mechanism of electrophilic
addition, what would be the expected
product?
\( A \)
B.
\( c \)
\( D \)


Which electronic level would allow the
hydrogen atom to absorbs a photon but not to emit a photon?
A . \( 3 s \)
B . \( 2 s \)
c. \( 1 s \)
D. \( 4 s \)


The structure of Nylon-6 is:
\( \left[\begin{array}{rr}0 & \mathrm{H} \\ -\mathrm{c} \mathrm{H}_{2} & -\mathrm{C}-\mathrm{N}\end{array}\right] \)
B. \( \left[\begin{array}{rr}0 & H \\ \| & I \\ \left(C H_{2}\right)_{4}-C-N & -\end{array}\right] \)
\( \left[\begin{array}{cc}0 & H \\ \| & I \\ -C-\left(C H_{2}\right)_{5}-N & -\end{array}\right] \)
\( D \)
\( \left[\begin{array}{cc}\mathbf{o} & \mathbf{H} \\ \| & \mathbf{I} \\ -\mathbf{c}-\left(\mathbf{C H}_{2}\right)_{\mathbf{6}}-\mathbf{N} & \mathbf{-}_{\mathbf{n}}\end{array}\right. \)


The value of \( \cos \left\{\cos ^{-1}\left(-\frac{\sqrt{3}}{2}\right)+\frac{\pi}{6}\right\} \)
is-
\( \mathbf{A} \cdot \mathbf{1} \)
B. -
\( c \cdot 0 \)
D.


Find the product of \( (\sqrt{2}+\sqrt{3})(\sqrt{2}+\sqrt{5})(\sqrt{2}+\sqrt{7}) \)


Write the names of any two excretory organs in human beings.


Take a look at the image below:
What type of reaction is being represented?
\[
+0 \Rightarrow
\]
A. Combination
B. Combustion
c. Net ionic equation
D. single replacement reaction


Three compounds \( (A),(B), \) and \( (C) \) are
given.Which statements are correct about \( (A),(B) \) and \( (C) ? \)
This question has multiple correct options
A. The rate of catalytic hydrogenation is faster in (A) than in
(B) and (C).
B. The rate of catalytic hydrogenation is faster in (B) than in
\( (c) \)
c. (A) has a cyclopropane ring whose strain on going to less-strained cyclopropane ring is reduced on hydrogenation. Similarly, cyclobutene ring in (B) on hydrogenenation is reudced to less-strained cyclobutane ring. But, cyclopropene ring is more strained than cyclobutene ring, so faster hydrogenation is in (A) than in (B).
D. There is a little change in the ring strain when the cyclohexene ring is reduced.


Which of the following will give a pleasant smell of ester when heated with ethanol and a small quantity of sulphuric acid?
A \( \cdot C H_{2} C H_{2} O H \)
в. \( C H_{3} O H \)
c. \( C H_{3} \) СООН
D. \( C H_{3} C H O \)


If \( f(x) \) is differentiable in the interval
\( [2,5], \) where \( f(2)=\frac{1}{5} \) and \( f(5)=\frac{1}{2} \)
then there exists a number \( c, 2<c< \)
5 for which \( f^{\prime}(c)= \)
A \( \cdot \frac{1}{2} \)
B. \( \frac{1}{5} \)
\( c \cdot \frac{1}{10} \)
D. None


The coeffcient of \( x^{10} \) in the expansion of
\( (1+x)^{2}\left(1+x^{2}\right)^{3}\left(1+x^{3}\right)^{4} \) is equal to
A . 52
B. 44
c. 50
D. 56


Given that \( \boldsymbol{K}_{s p} \) of \( \boldsymbol{C a} \boldsymbol{F}_{2} \) is \( \mathbf{1 . 7} \times \mathbf{1 0}^{-\mathbf{1 0}} \)
how many grams of it can be dissolved in:
a) \( 0.1 M N a F \)
b) \( 0.1 M C a C l_{2} \)


Biodiversity must be conserved as it
plays an important role in many ecosystem services that nature provides. Explain any two services of the ecosystem


The rotting dead matter in the soil is called as
A. Decomposition
B. Humus
c. Petrification
D. Minerals


Classify the given curves are (i) Open or
(ii) Closed.


Corpuscles are the tiny particles of
A. Light
B. Sound
c. waves
D. Radiation


A transmitter transmits at a
wavelength of \( 300 m . \) A condenser of
capacitance \( 2.4 \mu F \) is being used. The
value of the inductance for the resonant
circuit is approximately
\( \mathbf{A} \cdot 10^{-4} H \)
в. \( 10^{-6} H \)
c. \( 10^{-8} H \)
D. \( 10^{-10} \mathrm{H} \)


If the half-life period of a first-order
reaction is 138.6 min, then the value of
decay constant for the reaction will be:
A \( .5 \mathrm{min}^{-1} \)
B. 0.5 min \( ^{-1} \)
c. 0.05 min \( ^{-1} \)
D. \( 0.005 \min ^{-1} \)


Calculate the heat energy that will be
released when \( 5.0 \mathrm{kg} \) of steam at \( 100^{\circ} \mathrm{C} \)
condenses to form water at \( 100^{\circ} \mathrm{C} \)
Express your answer in S.I. unit (specific heat of vapourisation of steam is \( 2268 \mathrm{kJ} / \mathrm{kg} \) )


Two object collides elastically mass \( 2 m \)
is moving with velocity \( U \) and mass \( m \) is initially at rest. After the collision, the
objects move away with velocities \( u \)
and \( v, \) as shown in above figure.
Find the relation between \( u \) and \( v ? \)
A \( \cdot 2 u \cos 30^{\circ}=v \cos 60^{\circ} \)
B \( \cdot u \cos 30^{\circ}=2 v \cos 60^{\circ} \)
c. \( 2 u \sin 30^{\circ}=v \sin 60^{\circ} \)
D. \( u \sin 30^{\circ}=2 v \sin 60^{\circ} \)
E \( \cdot u \sin 30^{\circ}=v \cos 60^{\circ} \)


The adsorption of a gas, on a solid surface, varies with pressure of the gas in which of the following manner?
A. Slow, fast independent of the pressure
B. Fast slow independent of the pressure
c. Independent of the pressure slow fast
D. Independent of the pressure fast slow


What is the PAR range?
A. \( 200 n m-800 n m \)
B. 400nm - 700nm
c. \( 350 n m-550 n m \)
D. \( 600 n m-100 n m \)


State and prove Baye's theorem.


The direction of torque produced due to
induced current is
A . counter-clockwise
B. clockwise
C. lateral to produce precession
D. none of these


Two cells of unequal e.m.fs. \( E_{1} \) and \( E_{2} \)
and internal resistance \( r_{1} \) and \( r_{2} \) are
joined as shown. \( V_{A} \) and \( V_{B} \) are the
potentials at \( A \) and \( B \) respectively:
This question has multiple correct options
A. one cell will continuously supply energy to the other
B. the potential difference across both the cells will be equal
c. the potential difference across one cell will be greater than its e.m.f.
\( V_{A}-V_{B}=\frac{\left(E_{1} R_{2}+E_{2} R_{1}\right)}{\left(r_{1}+r_{2}\right)} \)


\( \int_{0}^{1} \frac{\boldsymbol{d} \boldsymbol{x}}{\sqrt{1+\boldsymbol{x}-\sqrt{\boldsymbol{x}}}}= \)
\( A \cdot \frac{2 \sqrt{2}}{3} \)
B. \( \frac{4 \sqrt{2}}{3} \)
\( c \cdot \frac{8 \sqrt{2}}{3} \)
D. None of these


Two spheres of the same metal have
radii \( 1 \mathrm{m} \) and \( 4 \mathrm{m} \) and temperature \( 4000 K \) and \( 2000 K \) respectively. The
ratio of the energy radiated per second by the first to the second is :
A . 1:
B. 1:
c. 2:
D. 1:


Give all possible isomers of alkane with
formula \( C_{4} H_{10} \)


Find the sum of all two digit numbers which when divided by \( 4, \) yield unity as remainder.


Find the position vector of a point \( \boldsymbol{R} \)
which divides the line joining two
points \( P \) and \( Q \) whose position vectors \( \operatorname{are} \hat{\boldsymbol{i}}+\boldsymbol{2} \hat{\boldsymbol{j}}-\hat{\boldsymbol{k}} \) and \( -\hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} \)
respectively, in the ratio 2: 1
(i) internally
(ii) externally


A marble starts falling from rest on a
smooth inclined plane of inclination \( \alpha \)
After covering distance \( h \) the ball
rebounds off the plane. The distance
from the impact point where the ball rebounds for the second time is :
\( A \cdot 8 h \cos \alpha \)
B. \( 8 h \sin \alpha \)
\( c \cdot 2 h \tan \alpha \)
D. \( 4 h \sin \alpha \)


The pH of pure water at \( 25^{\circ} \mathrm{C} \) and \( 35^{\circ} \mathrm{C} \)
are 7 and 6 respectively. The heat of
formation of \( \boldsymbol{H}^{+} \) and \( \boldsymbol{O H}^{-} \) ions in
\( k c a l m o l^{-1} \) is :
A . -84.5
B. +84.5
c. +184.5
D. -184.5


Fill in the blanks.
Name of an optical instrument which is used to see erect image of distant object is


If \( C a O \) caustic soda then which of the
following option is correct?
A \( \cdot M g\left(C r O_{4}\right)_{2}: \) Refractory metal
B. \( C a H_{2} \) :Radioactive element
c. Radium: Do not impart any colour
D. \( M g O: \) constituent of sorel cement


The first ionization energy for \( L i \) is 5.4 eV and electron affinity of \( C l \) is \( 3.61 \mathrm{eV} \) The \( \Delta H \) (in \( \mathrm{kJ} / \mathrm{mol} \) ) for the reaction
\( \boldsymbol{L} \boldsymbol{i}(\boldsymbol{g})+\boldsymbol{C l}(\boldsymbol{g}) \rightarrow \boldsymbol{L} \boldsymbol{i}^{+}(\boldsymbol{g})+\boldsymbol{C l}^{-}(\boldsymbol{g}) \) is:
(If the resulting ions do not combine with each other)
\( A \cdot 70 \)
в. 100
c. 172
D. 270


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


What is the unit of latent heat of a
body?
A. Joule/kg
B. Calorie/'c
c. Joules/'c
D. Kg/Joules


Which compound is formed when
excess of \( K C N \) is added to an aqueous
solution of copper sulphate?
\( \mathbf{A} \cdot C u(C N)_{2} \)
в. \( K_{2}\left[C u(C N)_{2}\right] \)
c. \( K\left[C u(C N)_{2}\right] \)
D. \( K_{3}\left[C u(C N)_{4}\right] \)


Find the distance between the points whose position vectors are given as follows \( -2 \hat{i}+3 \hat{j}+5 \hat{k}, 7 \hat{i}-\hat{k} \)
A. \( 3 \sqrt{14} \)
(i) 144
B. \( \sqrt{54} \)
c. \( 3 \sqrt{19} \)
D. \( \sqrt{57} \)


A ball of mass m approaches a wall of \( \operatorname{mass} M(>>m) \) with the speed \( 4 \mathrm{m} / \mathrm{s} \)
along normal to the wall. The speed of wall is \( 1 \mathrm{m} / \mathrm{s} \) towards the ball. The speed of the ball after an elastic collision with
the wall is-
A. \( 5 \mathrm{m} / \mathrm{s} \) away from the wall
B. 3 m/s away from the wall
c. \( 9 \mathrm{m} / \mathrm{s} \) away from the wall
D. \( 6 \mathrm{m} / \mathrm{s} \) away from the wall


Among the following, identify the species with an atom in +6 oxidation
state
A. \( M n O_{4}^{\text {ह }} \)
В \( \cdot\left[C r(C N)_{6}\right]^{3-} \)
\( \mathbf{c} \cdot\left[N i F_{6}\right]^{2-} \)
D. \( \operatorname{Cr} \mathrm{O}_{2} \mathrm{Cl}_{2} \)


If function \( \boldsymbol{f}(\boldsymbol{x})=\frac{1}{2}- \)
\( \tan \left(\frac{\pi x}{2}\right) ;(-1<x<1) \) and \( g(x)= \)
\( \sqrt{3+4 x-4 x^{2}}, \) then the domain of
\( (g o f) \) is


Zig-zag development of flower on
inflorescence axis is
A. Cyathium
B. Capitulum
C. Helicoid cyme
D. Scorpioid cyme


The population of a city increases at the rate \( 3 \% \) per year. If at time \( t \) the population of city is \( p, \) then find equation of p in time t.
A. \( _{p=c e} \frac{3 t}{100} \)
в. \( \quad p=3 e^{\frac{3 t}{100}} \)
D. \( p=\frac{3}{100} e^{3 t} \)


A solid spherical ball rolling without slipping collides elastically with an identical ball at rest, as shown in the figure. Assuming that the frictional forces are small enough to have
negligible effect during the instant of collision, calculate, the velocity of each ball along enough time after the collision when each ball is again rolling without slipping.


\( f\left(a_{1}, a_{2}, a_{3}, \dots \dots a_{n} \) are in A.P then \right.
\( \frac{1}{a_{1} a_{n}}+\frac{1}{a_{2} a_{n-1}}+\frac{1}{a_{3} a_{n-2}}+\dots+ \)
\( \frac{1}{a_{n} a_{1}}= \)
\( \frac{\mathbf{2}}{\boldsymbol{a}_{1}+\boldsymbol{a}_{\boldsymbol{n}}}\left(\frac{\mathbf{1}}{\boldsymbol{a}_{\mathbf{1}}}+\frac{\mathbf{1}}{\boldsymbol{a}_{\mathbf{2}}}+\ldots+\frac{\mathbf{1}}{\boldsymbol{a}_{\boldsymbol{n}}}\right) . . \) If this
expression is correct write 1 otherwise
0


Mention any two examples of anthropogenic acid. Distinguish
between homozygous and heterozygous
plants.


The speed at which a source of sound
should move so that a stationary observer finds the apparent frequency equal to half of the original frequency
A \( \cdot \frac{V}{2} \)
B. 2
c. \( \frac{V}{4} \)
D. \( V \)


Which of the following combination of characters is true for slime moulds?
A. Parasitic, plasmodium with true walls, spores dispersed by air currents.
B. Saprophytic, plasmodium without walls, spores dispersed by water.
c. Parasitic, plasmodium without walls, spores dispersed by water.
D. Saprophytic, plasmodium without walls, spores dispersed by air currents.


Four resistances of \( 100 \Omega \) are connected
in the form of square. Then the effective resistance along the diagonal points is
\( \mathbf{A} \cdot 200 \Omega \)
в. \( 400 \Omega \)
c. \( 100 \Omega \)
D. \( 150 \Omega \)


Find the value of:
(i) \( \left(3^{0}+4^{-1}\right) \times 2^{2} \)
(ii) \( \left(2^{-1} \times 4^{-1}\right) \div 2^{-2} \)
(iii) \( \left(\frac{1}{2}\right)^{-2}+\left(\frac{1}{3}\right)^{-2}+\left(\frac{1}{4}\right)^{-2} \)
(iv) \( \left(3^{-1}+4^{-1}+5^{-1}\right)^{0} \)
\( (v)\left[\left(\frac{-2}{3}\right)^{-2}\right]^{2} \)
\( (v i) 7^{-20}-7^{-21} \)


Show that the total kinetic energy of a
sphere of mass \( m \) rolling along
horizontal plane with velocity \( \boldsymbol{v} \) is
\( 7 / 10 m v^{2} \)


A burning substance will be if the temperature falls below its ignition temperature.
A. extinguished
B. burning brightly
c. burning dimly
D. burning with smoke


The velocity ' \( V \) ' of a particle varies with distance ' \( x \) ' and time 't' as \( \boldsymbol{V}= \)
\( \boldsymbol{A} \sin (\boldsymbol{B} \boldsymbol{x}) \cos (\boldsymbol{C} \boldsymbol{t}) \) when \( \boldsymbol{A}, \boldsymbol{B}, \boldsymbol{C} \) are
constants, then \( \frac{\boldsymbol{A} \boldsymbol{B}}{\boldsymbol{C}} \) will have the dimensions of:
A. velocity
B. acceleration
c. pressure
D. strain


The intermolecular interaction
dependent on the inverse cube of between the molecules is:
A. ion-ion interaction
B. ion-dipole interaction
c. london force
D. none of the above


A brick whose length, breadth and height are \( 5 \mathrm{m}, 6 \mathrm{m}, \) and \( 7 \mathrm{m} \) respectively. Find the surface area of the brick.
A . 214 \( m^{2} \)
B . 202 \( m^{2} \)
c. \( 201 m^{2} \)
D. 210 \( m^{2} \)


In Wedge-Dash Notation for threeDimensional Representation of an organic molecule, the wedged bond
represents
A. a bond below the plane of the paper
B. a bond above the plane of the paper
c. a bond in the plane of the paper
D. a bond either above or below the plane of the paper


An electric field of \( 1000 \mathrm{V} / \mathrm{m} \) is applied
to an electric dipole at angle of \( 45^{\circ} . \) The
value of electric dipole moment is \( 10^{-29} \)
C.m. What is the potential energy of the electric dipole?
B. \( -7 \times 10^{-27} \) j
\( c \cdot-10 \times 10^{-29} \)
D. \( -20 \times 10^{-18} \mathrm{J} \)


If you place pivot at center of a meter rule, weight has no
A. property
B. Concern
c. Turning effect
D. Magnitude


The primary coil of a step-down transformer has number of
turns
A. more
B. less
c. same
D. None of the above


\( 21-3(b-7)=b+20 \)


Which of the following cells gets activated during bleeding?
A. RBC
в. wвс
c. Platelets
D. None of the above


Railway tracks are banked on curves
A. necessary centrifugal force may be obtained from the horizontal component weight of the train
B. to avoid frictional force between the tracks and wheels
C. necessary centripetal force may be obtained from the horizontal component of the weight of the train
D. the train may not fly off in the opposite direction


Find the equation of a plane which passes through the point (1,2,3) and which is equally inclined to the planes \( x-2 y+2 z-3=0 \) and \( 8 x-4 y+ \)
\( \boldsymbol{z}-\mathbf{7}=\mathbf{0} \)


What will be the values of \( \theta \) between \( 0^{\circ} \)
and \( 360^{\circ} \) if \( \sin \theta=-\frac{\sqrt{3}}{2} \)
A \( \cdot 30^{\circ}, 330^{\circ} \)
В. \( 60^{\circ}, 120^{\circ} \)
c. \( 135^{\circ}, 315^{\circ} \)
D . \( 240^{\circ}, 300^{\circ} \)


The temperature, at which a
ferromagnetic material entirely loses its magnetic properties, is referred as
A. non magnetic point
B. curie point
c. van revolt point
D. none


If 10 liters of \( \mathrm{CO} \) gas react with sufficient amount of oxygen for a complete reaction, how many liters of
\( C O_{2} \) gas will be formed?
A . 5
B. 10
c. 15
D. 20
E . 40


A home-owner pushes a lawn mower
across a horizontal patch of grass with
a constant speed by applying a force \( P \)
The arrows in the diagram correctly
indicate the directions but not
necessarily the magnitudes of the
various forces on the lawn mower.
Which of the following relations among
the various force magnitudes, \( \mathbf{W}, \mathbf{f}, \mathbf{N}, \mathbf{P} \)
is correct?
\( A \cdot P>f \) and \( N>W \)
B. \( P<f \) and \( N=W \)
C. \( P>f \) and \( N<W \)
\( D \cdot P=f \) and \( N>W \)


Solve for \( \boldsymbol{x}: \mathbf{2 5}+\mathbf{2 2}+\mathbf{1 9}+\ldots \ldots+\boldsymbol{x}= \)
\( \mathbf{1 1 5} \)
If \( a, b, c \) are in A.P, Prove \( a+b, b+c, c+a \) are
in A.P


The reaction of \( P_{4} \) with \( X \) leads
selectively to \( P_{4} O_{6} . \) The \( x \)
is
\( A \cdot \operatorname{Dry} O_{2} \)
B. A mixture of \( O_{2} \) and \( N_{2} \)
c. Moist \( O_{2} \)
D. \( O_{2} \) in the presence of aqueous \( N a O H \)


The reaction, \( 2 B r^{-}(a q)+ \)
\( \boldsymbol{S} \boldsymbol{n}^{2+}(\boldsymbol{a} \boldsymbol{q}) \rightarrow \boldsymbol{B} \boldsymbol{r}_{2}(\mathbf{1})+\boldsymbol{S} \boldsymbol{n}(\boldsymbol{s}) \) with the
standard potentials, \( \boldsymbol{E}_{\boldsymbol{S n}}^{\circ}= \)
\( -\mathbf{0 . 1 1 4} V, \boldsymbol{E}_{\mathbf{B r}_{2}}^{\circ}=+\mathbf{1 . 0 9} \boldsymbol{V}, \) is:
A. spontaneous in reverse direction
B. spontaneous in forward direction
c. at equilibrium
D. non-spontaneous in reverse direction


(B) is resolvable but \( (A) \) is not.


A ray of light passes through an equilateral prism (refractive index 1.5 ) such that angle of incidence is equal to angle of emergence and the latter is equal to \( 3 / 4^{t h} \) of the angle of prism. The angle of deviation is
A .60
B. \( 30^{\circ} \)
c. 45
D. \( 120^{\circ} \)


Let \( A=\{1,2,3,4,6\} \) and \( R \) be the relation on \( \boldsymbol{A} \) defined by \( \{(\boldsymbol{a}, \boldsymbol{b}): \boldsymbol{a}, \boldsymbol{b} \in \)
\( A, b \text { is exactly divisible by } a\} \)
(i) Write \( R \) in roster form
(ii) Find the domain of \( \boldsymbol{R} \)
(iii) Find the range of \( \boldsymbol{R} \)


The IUPAC name of the compound
\( \boldsymbol{C H}_{3}-\boldsymbol{C H}\left(\boldsymbol{C H}_{3}\right)-\boldsymbol{C H}_{2}-\boldsymbol{C} \equiv \boldsymbol{C}- \)
\( C H_{3} \) is 2 -methyl-4-hexyne.
A. True
B. False


If maximum and minimum values of
the determinant
\( \left|\begin{array}{ccc}1+\sin ^{2} x & \cos ^{2} x & \sin 2 x \\ \sin ^{2} x & 1+\cos ^{2} x & \sin 2 x \\ \sin ^{2} x & \cos ^{2} x & 1+\sin 2 x\end{array}\right| \) are
\( \alpha \) and \( \beta, \) then
This question has multiple correct options
\( \mathbf{A} \cdot \alpha+\beta^{99}=4 \)
B \( \cdot \alpha^{3}-\beta^{17}=26 \)
C \( \cdot\left(\alpha^{2 n}-\beta^{2 n}\right) \) is always an even integer for \( n \in N \)
D. a triangle can be constructed having its sides as \( \alpha- \) \( \beta, \alpha+\beta \) and \( \alpha+3 \beta \)


Which of the following is strongly acidic?
A. Phenol
B. O-cresol
c. p-nitrophenol
D. p-cresol


\( A \) box \( ^{\prime} A^{\prime} \) contains 2 white, 3 red and 2
black balls. Another box ' \( B^{\prime} \) contains 4
white, 2 red and 3 black balls. If two
balls are drawn at random, without
replacement, from a randomly selected box and one ball turns out to be white
while the other ball turns out to be red,
then the probability that both balls are
drawn from box' \( B^{\prime} \) is
A \( \cdot \frac{7}{16} \)
в. \( \frac{9}{32} \)
\( c \cdot \frac{7}{8} \)
D. \( \frac{9}{16} \)


\( C_{2} \) and \( C_{3} \) atoms in \( C H \equiv C-C H= \)
\( C H_{2} \) are respectively \( s p \) and \( s p^{2} \)
hybridised.
A. True
B. False


The association of Nitrogen fixing bacteria (nodule bacteria) with
leguminous roots is known as
A. Saprophytism
B. Symbiosis
c. Epiphytism
D. Parasitism


Which of the following species the
longest \( \boldsymbol{O}-\boldsymbol{O} \) bond length ?
A. \( O_{2} \)
в. \( O_{2}^{+} \)
\( c \cdot O_{2} \)
D. \( O_{2}^{2} \)


For a horizontal rod of moment of inertia
I if a constant force \( F \) acts on the rod at
an angle \( \theta \) with the horizontal, the
torque equation for the rod will be (NOTE: The rod is lying on a floor horizontally)
A \( \cdot I d^{2} \theta / d t^{2}=2 F L \theta \)
B . \( I d^{2} \theta / d t^{2}=F L \theta \)
\( \mathbf{c} \cdot I d^{2} \theta / d t^{2}=(F L / 2) \)
D. None of the above


Define polymerisation.


At \( 80^{\circ} C, \) distilled water \( \left(H_{3} O^{+}\right) \) has
concentration equal to \( 1 \times \)
\( 10^{-6} \) mol/litre. The value of \( K_{w} \) at this
temperature will be:
A \( \cdot 1 \times 10^{-6} \)
B. \( 1 \times 10^{-12} \)
c. \( 1 \times 10^{-9} \)
D. \( 1 \times 10^{-15} \)


The nature of \( _{-1-}-_{--}- \) rays depends upon the nature of the gas in the
discharge tube


Check if given series is \( A P \) or not? If
they form an \( A P \), find the common
difference \( d \) and write three more terms.
\( \mathbf{3}, \mathbf{3}+\sqrt{\mathbf{2}}, \mathbf{3}+\mathbf{2} \sqrt{\mathbf{2}}, \mathbf{3}+\mathbf{3} \sqrt{\mathbf{2}} \)


The probability that a marksman will hit a target is given as \( \frac{1}{5}, \) then his probability of at least one hit in 10 shots is
\( ^{\mathrm{A}} \cdot_{1}-\left(\frac{4}{5}\right)^{10} \)
в. \( \frac{1}{510} \)
c. \( _{1-\frac{1}{5^{10}}} \)
D. None of these


The upper surface of a leaf is dark green in colour when compared to the lower surface of the leaf. The presence of
which tissue near the upper epidermis is responsible for this?
A. Palisade
B. spongy
c. collenchyma
D. vessels


Give an example of zone refining of
metals.


What should be the new radius of the
earth in order to make the escape velocity to double of the present value without changing the mass of the earth, if the actual radius of the earth is equal
to R?
A \( \cdot \frac{2}{R} \)
в. \( \frac{4}{R} \)
c. \( \frac{R}{4} \)
D. \( R^{2} / 2 \)


In Millikan's oil drop experiment, an oil drop is held stationary by a potential deference of \( 400 \mathrm{V} \). If another drop of double the radius, but carrying the same charge, is to be held stationary, the potential difference required will be
A . \( 800 \mathrm{v} \)
B. 1600
c. 3200
D. 400


If \( \sin ^{-1} x+\sin ^{-1} y+\sin ^{-1} z=\pi, \) prove
that \( x \sqrt{1-x^{2}}+y \sqrt{1-y^{2}}+ \)
\( z \sqrt{1-z^{2}}=2 x y z \)


Mimosa pudica displays
movement.
A. Phototropic
B. Photonastic
c. Thigmonastic
D. Thermonastic


Calculate the height through which a
body of mass \( 0.5 k g \) is lifted if the
energy spent in doing so is \( 1.0 J . \) (Take
\( \boldsymbol{g}=\mathbf{1 0 m} \boldsymbol{s}^{-2} \mathbf{)} \)
\( A \cdot 2 m \)
в. \( 0.2 m \)
\( c .20 m \)
D. \( 0.4 m \)


Let, paramagnetism is given by the relation \( \mu=2 \sqrt{s(s+1)} \) magnetons
where 's' is the total spin. On this basis,
the pramagnetism of \( C u^{+} \) ion is:
A . 3.88 magnetons
B. 2.83 magnetons
c. 1.41 magnetons
D. zero


Ducts of Bellini are found in
A . Liver
B. Intestine
c. Medulla oblongata
D. Kidney


Identify which of the following equations represents alpha decay in a nuclear fission reaction?
\( \begin{array}{ll}\text { A } \cdot & \frac{2}{1} H+_{1}^{2} H \rightarrow \quad_{1}^{3} H+_{1}^{1} H+\text { energy } \\ & \text { y } H\end{array} \)
B \( \cdot \frac{226}{88} R a \rightarrow \quad \frac{222}{86} R n+_{2}^{4} H e \)
\( \begin{array}{ll}\text { C. }_{83}^{209} B i \rightarrow & \frac{209}{84} P o+_{-1}^{0} e \\ & e\end{array} \)
D \( \cdot \frac{235}{92} U+_{0}^{1} n \rightarrow \quad \frac{140}{54} X e+_{38}^{94} S r+_{2}^{1} n \)
E \( \cdot \frac{4}{2} \mathrm{He}+_{13}^{27} \mathrm{Al} \rightarrow \quad_{15}^{30} \mathrm{P}+_{0}^{1} n \)


A real image occurs when rays converge. A virtual image occurs when
rays
A. converge
B. diverge
c. appear to converge
D. appear to diverge


Limestone sand, gypsum, and coal dust are the materials required for the
manufacture of cement.
A. True
B. False


Which one of the following can exist in optically active forms?
A. Trans-1,3-Dichlorocyclohexane
B. Cis-1,3-Dichlorocyclohexane
C. Cis-1,4-Dichlorocyclohexane
D. Cis-1,2-Dichlorocyclohexane


When unpolarised light is incident on a plane glass plate at Brewster's angle, then which of the following statements
is correct?
A. Reflected and refracted rays are completely polarised with their planes of polarisation parallel to each other
B. Reflected and refracted rays are completely polarised with their planes of polarisation perpendicular to each other
c. Reflected light is plane polarised but transmitted light is partially polarised
D. Reflected light is partially polarised but refracted light is plane polarised


When you add sodium hydrogen
carbonate to acetic acid in a test tube, a gas liberates immediately with brisk effervescence. Name this gas. Describe the method of testing this gas.


Grave's disease is caused due to
A. Hyposecretion of adrenal gland
B. Hypersecretion of adrenal gland
C. Hyposecretion of thyroid gland
D. Hypersecretion of thyroid gland


For the network shown in the figure the
value of the current i is
A \( \cdot \frac{18 V}{5} \)
B. \( \frac{5 v}{9} \)
\( c \cdot \frac{9 V}{355} \)
D. \( \frac{5 V}{18} \)


\( B F_{3} \) dimerizes to form stable molecule.
Enter 1 if true else enter 0


Lateral meristem is responsible for
A. Growth in length
B. Growth in parenchyma
c. Growth in thickness
D. Growth in cortex


Describe the interaction of \( t-R N A, m \)
RNA and ribosomes during the events of translation.


If \( A \) is a square matrix of order \( n \times n \)
and \( k \) is a scalar, then \( a d j(k A) \) is equal
to
A \( \cdot k^{n-1} a d j A \)
в. \( k^{n} \) adj \( A \)
c. \( k^{n+1} a d j A \)
D. kadj A


In the figure shown, if the diode forward
voltage drops is \( 0.2 V \), the voltage difference between \( A \) and \( B \) is
A \( .1 .3 V \)
В. \( 2.2 V \)
\( c .0 .5 V \)
\( D \)


What is latent heat of evaporation?


\( \frac{\boldsymbol{x}+\mathbf{1}}{(\mathbf{2} \boldsymbol{x}-\mathbf{1})(\mathbf{3} \boldsymbol{x}+\mathbf{1})}=\frac{\boldsymbol{A}}{\mathbf{2} \boldsymbol{x}-\mathbf{1}}+ \)
\( \frac{B}{3 x+1} \Rightarrow 16 A+9 B= \)
\( A \)
B. 5
\( c \cdot 6 \)
\( D \)


Hydrogen bond energy (per mole) is about:
A . 10 kcal
B. 10 Joules
c. 10 ergs
D. 10 ev


A double ordinate of the parabola \( y^{2}= \) \( 8 p x \) is of length \( 16 p . \) The angle
subtended by it at the vertex of the parabola is
A.
в. \( \frac{\pi}{2} \)
c. \( \frac{\pi}{3} \)
D. none of these


Which of the following cranial nerves are involved in the movement of eye?
A. Optic, occulomotor, abducens
B. Occulomotor, abducens, trochlear
C. Trochlear, abducens, optic
D. Abducens, optic, trochlear, occulomotor


Check continuity of the function \( x^{2}|x| \) at the origin.


In a buffer solution, the concentration of
\( \boldsymbol{X}^{-} \) and \( \mathrm{HX} \) are equivalent. If \( \boldsymbol{K}_{\boldsymbol{b}} \) for \( \boldsymbol{X}^{-} \)
is \( 10^{-10} \) then pH of the solution would
be:
(PMT, Rajasthan, 1997)
A \( \cdot 14 \)
B. 10
\( c \cdot 4 \)
D. 8


A dip circle shows an apparent dip of \( 60^{0} \) at a place where the true dip is \( 45^{0} \)
If the dip circle is rotated by \( 90^{0}, \) what will be the apparent dip?
\( ^{\mathbf{A}} \cdot \cos ^{-1} \sqrt{\frac{2}{3}} \)
B. \( \tan ^{-1} \sqrt{\frac{2}{3}} \)
\( c \cdot \sin ^{-1} \sqrt{\frac{2}{3}} \)
D. \( \cot ^{-1} \sqrt{\frac{2}{3}} \)


In the core of nuclear fusion reactor, the
gas becomes plasma because of
A. strong nuclear force acting between the deuterons
B. coulomb force acting between the deuterons
c. coulomb force acting between deuteron-electron pairs
D. the high temperature maintained inside the reactor \( \operatorname{cor} \)


Region of nephron found in renal
medulla is
A. Malpighian corpuscle
B. Proximal convoluted tubule
c. Distal convoluted tubule
D. Henle's loop
E. Glomerulus


To obtain a good quality DC from AC we
shall use
This question has multiple correct options
A . RC filter
B. LC filter
c. \( \pi \) filter
D. Butterworth filter


To get line spectrum, the substances are excited in their
A. Solid state
B. Molecular state
c. Gaseous state
D. Atomic state


Match list I with List II and select the
correct answer using the codes given
below the lists:
List I
(A) Coagulation
(1) Scattering
(B) Lyophilization
(2) Washing of precipitates
(C) Peptization
(3) Purification of colloids
(D) Tyndall
(4) Electrolyte
A. A-4; B-3; C-2; D-1
B. A-2; B-1; C-3; D-4
c. \( A-3 ; B-4 ; C-2 ; D-1 \)
D. A-4; B-3; C-1; D-1 -


Assertion
Average velocity of the body may be equal to its instantaneous velocity at all
points of time.
Reason
If a body is having uniform motion in
one dimension, then velocity is constant
and average velocity can be equal to instantaneous velocity
A. Both Assertion and Reason are true and Reason is the correct explanation for Assertion.
B. Both Assertion and Reason are true but Reason is not the correct explanation for Assertion.
C. Assertion is true, but Reason is false.
D. Assertion is false, but the Reason is true.


Which of the following statements is
not correct regarding algal blooms?
A. Algal blooms are formed by blue-green algae
B. Growth of Eichhornia crassipes causes colouration of water during algal blooms
C. Increased growth of algae causes depletion of \( O_{2} \) in water
D. Algal blooms cause deterioration of water quality and fish mortality


A carrier protein transfers a solute across the phospholipid bilayer via facilitated diffusion behaves much like
an enzyme-substrate reaction. A distintction between the process by
which an enzyme converts substrate to product and facilitated transport is
A. Solutes are able to undergo transport without chemical modification
B. Solutes are restricted to flow in one direction depending on the orientation of the carrier protein.
C. Solutes are directly transported without interacting with or influencing the conformational state of the carrier protein.
D. Solutes are transported whether or not there is a competitive or noncompetitive inhibitor present.


Write the equation that formed by increasing each root of the equation \( 2 x^{2}-3 x-1=0 \) by 2


In 1911 came to the
conclusion that the atom had a dense
nucleus because most of the particles shot straight through, but some of the particles were deflected due to the dense nucleus of the gold atoms.
A. Thompson
B. Chadwick
c. Rutherford
D. none of the above


Consider a jet traveling at \( 1000 \mathrm{km} / \mathrm{hr} \). If the jet shoots a laser in the same direction it is traveling, how fast will the laser be traveling relative to the ground?
A. \( 300,000 \mathrm{km} / \mathrm{sec} \)
B. 300,000 km/sec plus 1000 km/hr
c. \( 300,000 \mathrm{km} / \mathrm{sec} \) minus \( 1000 \mathrm{km} / \mathrm{hr} \)
D. 1000 km/hr minus 300,000 km/sec
E. cannot be determined with information providede


Which salt can be classified as acid
salt?
A \( \cdot N a_{2} S O_{4} \)
в. В гОС
c. \( P b(O H) C l \)
D. \( N a_{2} H P O_{4} \)


Calculate the scalar product of the following vectors. Given three forces \( M= \)
\( \{3,-4,2\}, W= \)
\( \{2,3,-5\}, \) and \( P=\{-3,-2,4\} \)
applied to the same point. Calculate the work performed by the resultant of these three forces when the point of application of the resultant moves along a straight line and is displaced
from the position \( M_{1}\{5,3,-7\} \) to the
position \( M_{2}\{4,-1,-4\} \)


The thin filaments of myofibril contain
(A) \( _{--} \) actin and two filaments of
(B) \( _{-} \) protein along with
(C) \( _{--} \) protein for masking binding site for myosin.
A. A - 1F B - troponin C - Tropomyosin
B. A - 1F B - tropomyosin C - troponin
c. A - 2F B - troponin C - tropomyosin
D. A - 2F B - tropomyosin C - troponin


Which is a saturated compound?
A. alkanes
B. alkenes
c. alkynes
D. cycloalkenes


The bleaching action of bleaching
powder is due to:
A . oxidation
B. reduction
c. both A and B
D. none of these


Which of the following will respond to sublimation?
1.Sodium chloride 2. Dry ice 3.
Naphthalene 4. Ammonium chloride
A. 1,2 and 3
B. 1,3 and 4
\( c \cdot 3 \) and 4
D. 2, 3 and 4


Hydra reproduces by budding. This is an example of
A. Asexual reproduction
B. Sexual reproduction
c. Regeneration
D. Parthenocarpy


Which one of the following is a tertiary alcohol?
A. \( C H_{3} C H_{2} C H_{2} O H \)
в. \( C H_{3} C H(O H) C H_{3} \)
c. \( \left(C H_{3}\right)_{2} \) СНСН\( _{2} \) ОН
D. \( \left(C H_{3}\right)_{3} C O H \)


An equation in which the highest index
of the variables present is one is called
A. simple equation
B. linear equation
c. multicquation
D. none of these


Assertion
Smaller the orbit of the planet around
the sun, shorter is the time it takes to
complete one revolution.
Reason
According to Kepler's third law of
planetary motion, square of the time period is proportional to the cube of the mean distance from the sun.
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


Write the relation between \( ^{0} C \) and
Kelvin (K)


Work done by kinetic friction on a body
is never zero.
A. True
B. False
c. Ambiguous
D. Data insufficient


In the above diagram, the teeth marked
B represent
A. Incisors
B. Canines
c. Molars
Dremolars


In the circuit shown the resistance of
voltmeter is 10,000 ohm and that of ammeter reading is 0.10 Amp and
voltmeter reading is 12 volt. Then \( R \) is
equal to
A . \( 120 \Omega \)
в. \( 140 \Omega \)
\( c \cdot 116 \Omega \)
D. 100\Omega


If two dice are rolled 12 times, obtain the mean and the variance of the
distribution of successes, if getting a total greater than 4 is considered a
success.


Energy can be extracted by creating a reservoir or basin behind a barrage and then passing tidal waters through turbines in the barrage to generate electricity. This form of energy is known
as
A. solar energy
B. wind energy
c. hydro energy
D. tidal energy


A man in a minivan rounds a circular
turn at a constant speed.

Which of the following would cause the
minivan to experience less
acceleration?
A. Traveling faster
B. Traveling around a turn with a smaller circular radius
C. Traveling with more weight in the van
D. Traveling around a turn with a greater circular radius
E. Traveling the opposite direction around the same turn


Maximum prescribed limit of Al in drinking water is:
\( A \cdot 5 \) ppm
B. 2 ppm
c. \( 0.2 \mathrm{ppm} \)
D. 0.5 ppm


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


What is metamerism?


A container having a hole at the bottom
is free to move on a horizontal
surface. As the liquid comes out, the container moves in a backward
direction
with an acceleration \( \alpha \) and finally
acquires a velocity v (when all the liquid has drained out). Neglect the mass of the container. The correct option out of the following is :
A. Only v vepends on \( h \)
B. Only \( \alpha \) depends on h
c. Both v and \( \alpha \) depend on \( n \)
D. Neither v nor \( \alpha \) depends on \( h \)


There is no change in the volume of a wire due to change in its length on stretching. The Poisson's ratio of the material of the wire is :
\( \mathbf{A} \cdot+0.50 \)
B . -0.50
c. 0.25
D. -0.25


Soil suitable for cultivation of tobacco,
vegetables and paddy
A. Black soil
B. Red soil
c. Alluvial soil
D. All of the above


Two conducting spheres, each given a
charge \( q \) are kept far apart as shown. The amount of charge that crosses the
switch \( S_{1}, \) where it is closed, is (the
connection between the spheres is
conducting)
A . \( \underline{q} \) 3
в. \( \frac{2 q}{3} \)
\( c \cdot \frac{3 q}{4} \)
D. Zero


A five carbon sugar with molecular
formula \( C_{5} H_{10} O_{4} \)
A. Deoxyribose
B. Ribose
c. Glucose
D. Lactose


If \( x^{3}+y^{3}=3 a x y, \) then \( \frac{d y}{d x} \) is
A \( \cdot \frac{a y-y^{2}}{x^{2}-a x} \)
В. \( \frac{a y-x^{2}}{y^{2}-a x} \)
c. \( \frac{b y-x^{2}}{y^{2}-b x} \)
D. None of these


Statement 1: correct order of acidic
strength is \( \boldsymbol{C H}_{3} \boldsymbol{C H}_{3}>\boldsymbol{C H}_{2}= \)
\( \boldsymbol{C H}_{2}>\boldsymbol{H C}=\boldsymbol{C h} \)
Statement 2:- C-H bond energy in ethene is more than ethane but less than
ethyne
A. Statement 1 is true, Statement 2 is true and Statement 2 is correct explanation for Statement 1
B. Statement 1 is true, Statement 2 is true and Statement 2 is NOT the correct explanation for Statement 1.
c. statement 1 is true, Statement 2 is false
D. Statement 1 isfalse, Statement 2 is true


Examples of radiations are:
A. a microwave oven
B. refrigeration
c. monsoon
D. none of the above


The diagram given represents a certain
stage of mitosis.
(i) Identify the stage of cell division.
\( (i i) \) Name the parts labelled \( A \) and \( B \)
(iiii) What is the unique feature
observed in this stage?
\( (i v) \) How many daughter cells formed
from this type of cell division?


Metal spheres, each of radius \( 2 \mathrm{cm}, \) are
packed into a rectangular box of internal dimensions \( 16 \mathrm{cm} \times 8 \mathrm{cm} \times 8 \)
cm. When 16 spheres are packed the box filled with preservative liquid. Find the volume of this liquid. (Give the answer to the nearest integer value)
\( \mathbf{A} \cdot 482 c m^{3} \)
В. \( 478 \mathrm{cm}^{3} \)
\( \mathrm{c} \cdot 488 \mathrm{cm}^{3} \)
D. \( 490 \mathrm{cm}^{3} \)


The value of
\( \tan \left(\sin ^{-1}\left(\cos \left(\sin ^{-1} x\right)\right)\right) \tan \left(\cos ^{-1}(\sin \right. \)
where \( \boldsymbol{x} \boldsymbol{\epsilon}(\boldsymbol{0}, \boldsymbol{1}), \) is equal to
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot-1 \)
D. none of these


cm carrying a current \( I \) of 12 A is placed
in different orientations as shown in the
figure below.
If there is a uniform magnetic field of
\( 0.3 T \) in the positive z-direction, in which
orientations the loop would be in (i)
stable equilibrium and (ii) unstable
equilibrium:
(1)
(2)
(3)
(4)
A \( \cdot(2) \) and \( (4), \) respectively
B. (2) and
\( (3), \) respectively
C. () 1 and \( (2), \) respectively
D. () 1 and
\( (3), \) respectively


Red wood tree is
A. Cedrus
B. Pinus
C . Dalbergia
D. Sequoia


If \( \mathrm{N} \) is the number of turns in a coil, the value of self inductance varies as
A . \( N^{0} \)
B.
c. \( N^{2} \)
D. \( N^{-2} \)


The carbon resistor has three orange
bands. The maximum value of
resistance offered by the resistor will be
A . \( 39.6 k . \Omega \)
в. \( 49.6 k \Omega \)
\( \mathbf{c} .33 k \Omega \)
D. 26.4k\Omega


The force between two point charges
separated by a certain distance is \( \boldsymbol{F} \). If each charge is double and the distance
between them is also doubled then the
force would be
A \( .2 F \)
в. \( F \)
c. \( F / 2 \)
D. \( 4 F \)


State whether the following triangles
are congruent or not? Give reasons for
your answer


The ratio of specific heat capacity to molar heat capacity of a body
A . is a universal constant
B. depends on the mass of the body
c. depends on the molecular weight of the body
D. is dimensionless


A stone projected at an angle \( \theta \) with horizontal from the roof of a tall
building falls on the ground after three seconds. Two seconds after the
projection it was again at the level of projection. Then the height of the building is:
A . \( 15 \mathrm{m} \)
в. \( 5 m \)
\( c .25 m \)
D. \( 20 m \)


A particle moves along the \( x \) -axis from
\( x=0 \) to \( x=5 m \) under the influence of
a force \( F(\text { in } N) \) given by \( F=3 x^{2}- \)
\( 2 x+7 . \) Calculate the work done by this
force


The Sl unit of electric flux is
A. \( N / C \)
в. \( N m / C \)
c. \( N m^{2} \)
D. \( N m^{2} / C \)


The mode of the following discrete series is:
12 \( \boldsymbol{x}_{i} \quad 1 \quad 3 \quad 5 \quad 6 \)
\( f_{i} \quad 5 \quad 7 \quad 3 \) 8
\( \mathbf{A} \cdot \mathbf{3} \)
B. 12
c. 8
D. 6


In the Bohr model of hydrogen atom, the ratio of the kinetic energy and total
energy of electron in the \( n^{t h} \) quantum
state will be
A . 1
B. - -
c. 2
D. -12


If \( A \) is any event in a sample space, then \( \boldsymbol{P}(\overline{\boldsymbol{A}})=\mathbf{1}+\boldsymbol{P}(\boldsymbol{A}) \)
A. True
B. False
c. Either
D. Neither


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. \( 0 V, 1.4 A \)
\( c .5 .6 V, 1.4 \)
) \( .8 V, 2.0 A \)


A student finds the writing on the
blackboard as blurred and unclear when
sitting on the last desk in the classroom. He however, sees it clearly
when sitting on the front dest at an approximate distance of \( 2 \mathrm{m} \) from the blackboard. Draw ray diagrams to
illustrate the formation of image of the blackboard writting by his eye - lens when he is seated at the
(i) last desk
(ii) front desk
Name the kind of lens that would help
him to see clearly even when he is seated at the last desk. Draw a ray
diagram to illustrate how this lens helps him to see clearly.


In the given figure, if area of parallelogram \( A B E F \) is \( 96 \mathrm{cm}^{2} ; \) state
giving reason, the area of \( \triangle A D B \)
\( \mathbf{A} \cdot 48 \mathrm{cm}^{2} \)
B. \( 38 \mathrm{cm}^{2} \)
\( \mathrm{c} \cdot 58 \mathrm{cm}^{2} \)
\( \mathrm{D} \cdot 68 \mathrm{cm}^{2} \)


Which of the following specie(s) has/have a tetrahedral structure?
This question has multiple correct options
A. \( B_{2} H_{6} \) (around each boron atom)
в. \( B_{3} N_{3} H_{6} \)
\( \mathbf{c} \cdot B H_{4}^{-} \)
D. \( A l C l_{4} \)


The acidic strength of two monobasic
acids may be compared by comparing the hydronium ion concentrations of
their aqueous solution of same molar concentration. The dissociation
constants of acids HA and HB are \( 4 \times \)
\( 10^{-6} \) and \( 2.5 \times 10^{9}, \) respectively. How
many times HA is stronger than HB? Assume that for both the acids, the degree of dissociation at the
concentration taken, is negligible.


The correct order of melting points of
hydrides of group 16 elements is:
\( \mathbf{A} \cdot H_{2} S>H_{2} S e>H_{2} T e \)
B. \( H_{2} S<H_{2} S e<H_{2} T e \)
\( \mathbf{c} \cdot H_{2} S>H_{2} S e<H_{2} T e \)
\( \mathbf{D} \cdot H_{2} S<H_{2} S e>H_{2} T e \)


Valence electrons in the element \( A \) are 3
and that in element \( B \) are \( 6 . \) Most
probable compound formed from \( A \) and
\( B \) is:
A \( . A_{2} B \)
в. \( A B_{2} \)
\( \mathbf{c} \cdot A_{6} B_{3} \)
D. \( A_{2} B_{3} \)


Find the cube root of :
8


Which part of - COOH group is involved in the reaction of acid with metals?
A. C group
B. only -OH group
c. соон group
D. all carboxylic group


A fair coin is tossed \( n \) times. if the
probability that head occurs 6 times is equal to the probability that head
occurs 8 times, then value of \( n \) is
A .24
B. 48
c. 14
D. 16


Find the total number of stereoisomer
for each compound.
\( A \)
B. 4
\( c .5 \)
\( D . \) none


The triad of the nuclei that is isotonic
is:
\( \mathbf{A} \cdot_{6} N^{14}, 7 N^{14},_{9} F^{19} \)
B \cdot \( _{6} C^{14}, 7 N^{15},_{9} F^{17} \)
\( \mathbf{c} \cdot_{6} C^{14}_{7} N^{14},_{9} F^{17} \)
\( \mathrm{D} \cdot_{6} C^{12},_{7} N^{14},_{9} F^{19} \)


Unpolarized red light is incident on the
surface of a lake at incident angle \( \boldsymbol{\theta}_{\boldsymbol{R}} \)
An observer seeing the light reflected from the water surface through a polarizer notices that on rotating the polarizer, the intensity of light drops to
zero at a certain orientation. The red
light is replaced by unpolarized blue light. The observer sees the same effect
with reflected blue light at incident
angle \( \theta_{s} . \) Then :
A \( \cdot \theta_{B}<\theta_{R}<45^{\circ} \)
в. \( \theta_{B}=\theta_{R} \)
\( \mathbf{c} \cdot \theta_{B}>\theta_{R}>45^{\circ} \)
\( \mathbf{D} \cdot \theta_{R}>\theta_{B}>45^{\circ} \)


Two magnetic monopoles are kept apart by a distance 'd'. The magnetic force acting on each pole is 'F'. How much percentage must the distance between
the magnetic poles be changed so that the magnetic force acting on each pole be \( 4 \mathrm{F} \)
A . -10\%
B . -20\%
c. -40\%
D . -50\%


A wire of resistance \( 4 \Omega \) is stretched to
twice its original length. In the process of stretching, its area of cross section gets halved. Now, the resistance of the
wire is:
\( A \cdot 8 \Omega \)
в. 16 \Omega
c. \( 1 \Omega \)
D. \( 4 \Omega \)


How can the rate of the chemical
reaction, namely, decomposition of hydrogen peroxide be increased?


A silver wire of \( 1 \mathrm{mm} \) diameter has a
charge of 90 coulombs flowing in 1 hours and 15 minutes. Silver contains


If \( f(x)=a \cos (b x+c)+d \) then range
of \( \boldsymbol{f}(\boldsymbol{x}) \) is
A \( \cdot[d+a, d+2 a] \)
B . \( [a-d, a+d] \)
c. \( [d+a, a-d] \)
D \cdot \( [d-a, d+a] \)


Identify the products.


In which of the following compounds, the oxidation number of iodine is fractional?
A. \( I F_{7} \)
B . \( I_{3}^{-} \)
c. \( I F_{5} \)
D. \( I F_{3} \)


The instrument by which blood pressure of a man can be determined is
A. Ultrasound
B. Blood pressure meter
c. stethoscope
D. sphygmomanometer


The normal drawn to the surface of a
conductor makes an angle \( \theta \) with the direction of field \( \vec{B}, \) the flux \( \phi \) passing through the area \( \vec{A} \) is given by
A. \( \phi=A B \sin \theta \)
в. \( _{\phi}=\frac{B}{A} \)
c. \( \phi=B A \)
D. \( \phi=B A \cos \theta \)


Given the reaction \( \boldsymbol{A} \rightarrow \boldsymbol{B}+\boldsymbol{C}, \) when
\( \triangle \boldsymbol{H}_{\text {reaction}} \) is negative, what effect
would increase in temperature (at constant pressure) have on the system at equilibrium?
A. No change
B. Cannot be determined
c. Shift to the right
D. Shift to left for \( K<1 \) and to the right for \( K>1 \)
E. Shift to the left


Which of the following cofactor is responsible for the activity of an enzyme leading to the formation of carbonic acid in RBCs?
\( \mathbf{A} \cdot C a^{+} \)
B. \( Z n^{+} \)
c. \( M n^{+} \)
D. \( M g^{+} \)


1.00 g of a hydrated salt contains 0.2014 g of iron, 0.1153 g of sulphur \( 0.2301 \mathrm{g} \) of oxygen and \( 0.4532 \mathrm{g} \) of water of crystallisation. How much water molecules are present in its empirical formula? \( (\boldsymbol{F} \boldsymbol{e}=\mathbf{5} \mathbf{6} ; \boldsymbol{S}= \)
\( \mathbf{3 2} ; \boldsymbol{O}=\mathbf{1 6} \)


The diagram below represents a group of organs in the human body. Urine leaves the urinary bladder by passing
through this structure labeled as
\( A \)
B.
\( c \)
\( D \)


Compound which is added to soap to impart antiseptic properties is:
A. sodium lauryl sulphate.
B. sodium dodecylbenzenesulfonate.
c. rosin
D. bithionol.


30 litre \( H_{2}(g) \) and 30 litre \( N_{2}(g) \) were
taken for the reaction in Haber's
process which yields only \( 50 \% \) of the expected ammonia due to the reversibility of the reaction. What will be the composition of the reaction mixture under the given condition?
A \( \cdot N H_{3}: 20 L ; N_{2}: 20 L ; H_{2}: 20 L \)
B. \( N H_{3}: 10 L ; N_{2}: 25 L ; H_{2}: 15 L \)
c. \( N H_{3}: 20 L ; N_{2}: 10 L ; H_{2}: 30 L \)
D. \( N H_{3}: 20 L ; N_{2}: 25 L ; H_{2}: 15 L \)


For three events \( A, B \) and \( C, P( \) exactly
one of the events \( A \text { or } B \text { occurs })=P( \)
exactly one of the vents \( B \) or \( C \) occurs
\( =P(\text { exactly one of the events } C \text { or } A \) occurs \( )=p \) and \( P( \) all the three events
occur simultaneously \( )=p^{2}, \) where \( 0< \)
\( \boldsymbol{p}<\frac{1}{2} \)
Then the probability of atleast one of the three events \( A, B \) and \( C \) occurring is
A \( \cdot \frac{3 p+2 p^{2}}{2} \)
в. \( \frac{p+3 p^{2}}{2} \)
c. \( \frac{3 p+p^{2}}{2} \)
D. \( \frac{3 p+2 p^{2}}{4} \)


If \( \frac{a}{b}+\frac{b}{a}=1, \) then the value of \( a^{3}+b^{3} \)
is-
A .
B. \( a \)
\( c \cdot b \)
D.


\( \boldsymbol{H}_{2}+\boldsymbol{C l}_{2} \rightarrow \boldsymbol{H} \boldsymbol{C l} \) The above reaction is
an example of which of the following reaction?
A. Combination reaction
B. Decomposition reaction
c. Displacement reaction
D. Double displacement reaction


Which among the following oxoacids of phosphorus shows a tendency of disproportionation?
A. Phosphinic aicd \( \left(H_{3} P O_{2}\right) \)
B. orthophosphoric acid (H \( _{3} P O_{4} \) )
c. Phosphonic acid \( \left(H_{3} P O_{3}\right) \)
D. Pyrophosphoric acid \( \left(H_{4} P_{2} O_{7}\right) \)