If amplitude of particle executing SHM is doubled,which of the following quantities are doubled
a) Time period
b) Maximum velocity
c) Maximum acceleration
d) Total energy
A. b and c
B. a, band
c. a and \( c \)
D. a, b, c and d


Which among the equations of the nitrogenous base content in the DNA is
not true?
A \( \cdot A+G=T+C \)
B. \( A+T=G+C \)
\( c \cdot G=c \)


A car acquires a velocity of 72 kmph in
10 \( s \) starting from rest. Calculate its
average velocity :
\( A \cdot 0 \)
B. \( 5 m s^{-1} \)
\( \mathrm{c} \cdot 10 \mathrm{ms}^{-1} \)
D. \( 15 \mathrm{ms}^{-1} \)


If \( W_{1} \) work is done against gravitational
attraction to carry \( 10 \mathrm{kg} \) mass from earth's surface to infinity, then the magnitude of work done by the gravitational attraction in bringing 20 kg mass from infinity to the centre of earth is
\( \mathbf{A} \cdot 2 W_{1} \)
в. \( 3 W_{1} \)
\( c \cdot \frac{w_{1}}{2} \)
D. \( 4 W_{1} \)


The standard potential of the following
cell is \( 0.23 V \) at \( 15^{\circ} C \) and \( 0.21 V \) at
\( 25^{\circ} C \)
\( \boldsymbol{P t H}_{2}(\boldsymbol{g})|\boldsymbol{H} \boldsymbol{C l}(\boldsymbol{a q} .) \| \boldsymbol{A} \boldsymbol{g} C l(s)| \boldsymbol{A} \boldsymbol{g}(s) \)
(i) Write cell reaction.
(ii) Calculate \( \triangle H^{\circ} \) and \( \triangle S^{\circ} \) for the cell
reaction by assuming that these quantities remain unchanged in the range \( 15^{\circ} \mathrm{C} \) to \( 35^{\circ} \mathrm{C} \)
(iii) Calculate the solubility of \( A g C l \) in
water at \( 25^{\circ} C . \) Given the standard
reduction potential of the \( \boldsymbol{A} \boldsymbol{g}^{+} / \boldsymbol{A} \boldsymbol{g} \)
couple is 0.80 volt at \( 25^{\circ} \mathrm{C} \)


At \( 0 K \) temperature, a p-type
semiconductor
A. has equal number of holes and free electrons
B. has few holes but no free electrons
c. has few holes and few free electrons
D. does not have any charge carriers


The adjacent sides of a parallelogram \( 36 \mathrm{cm} \) and \( 27 \mathrm{cm} \) in length. If the perpendicular distance between the
shorter sides is \( 12 \mathrm{cm}, \) find the distance between the longer sides.


Consider the given statements.
I. Dextrin and glycogen are polysaccharides
Il. Lactose and glucose are disaccharides

III.Sucrose and maltose are
disaccharides
IV. Raffinose is oligosaccharide The incorrect statements is/are:
A. only II
B. I and II
C. I, II and III
D. IV only


If \( \boldsymbol{y}=\sec ^{-1}\left(\frac{\boldsymbol{x}+\mathbf{1}}{\boldsymbol{x}-\mathbf{1}}\right)+\sin ^{-1}\left(\frac{\boldsymbol{x}-\mathbf{1}}{\boldsymbol{x}+\mathbf{1}}\right) \)
then \( \frac{d y}{d x} \) is equal to
A .
B. \( x+1 \)
\( c \cdot 1 \)
D. -


Fill in the empty values of the cells in
the table:
\( \begin{array}{cccc} & \boldsymbol{V}_{1} & \boldsymbol{T}_{1} & \boldsymbol{V}_{2} & \boldsymbol{T}_{2} \\ \mathrm{A} & & 840 & 1070 & 147 \\ \mathrm{B} & \begin{array}{l}3250 \\ \mathrm{ml}\end{array} & \mathrm{K} & \mathrm{m} 1 & \mathrm{K} \\ \mathrm{C} & 10 \mathrm{Litre} & & 15 \text { Litre } & 50^{0}\end{array} \) Use Charles Law to fill the following
table:


A point on the parabola \( y^{2}=18 x \) at which the ordinate increases at twice
the rate of the abscissa is:
в. (2,-4)
c. \( \left(\frac{-9}{8}, \frac{9}{2}\right) \)
D. \( \left(\frac{9}{8}, \frac{9}{2}\right) \)


In the soap micelles:
A. the ionic end of soap is on the surface of the cluster while the carbon chain is in the interior of the cluster
B. ionic end of soap is in the interior of the cluster and the carbon chain is out of the cluster
C. both ionic end and carbon chain are in the interior of
the cluster
D. both ionic end and carbon chain are on the exterior of
the cluster


The fermentation of starch into alcohols
is carried by the action of :
A. Enzymes
в. \( O_{2} \)
c. Hormone
\( D \cdot C O_{2} \)


Represent on number line \( \frac{\mathbf{3}}{\mathbf{4}} \)


For an ideal solution of two components
A and B, which of the following is true?
\( \mathbf{A} \cdot \Delta H_{m i x i n g}<0(z e r o) \)
B. \( \Delta H_{\text {mixing}}>0(z \text {ero}) \)
C. \( A \) - \( B \) interaction is stronger than \( A-A \) and \( B-B \) interactions
D. \( A-A, B-B \) and \( A-B \) interactions are identical


Ammonia is used as a:
A. fire extinguisher
B. fertilizer
C. refrigerant
D. fungicide


The water gas when used for the formation of methanol is called:
A. Fuel gas
B. syngas
c. Natural gas
D. Producer gas


What is the correct order of the covalent
size of Cr and Mo?
A. \( \mathrm{cr}=\mathrm{Mo} \)
B. CrsMo
\( c \cdot c r>M o \)
D. None of these


The correct value for the relative
lowering of vapour pressure of a
very dilute solution is equal to:
This question has multiple correct options
A. mole fraction of solute
B. mole fraction of solvent
C. ratio of moles of solute to moles of solvent
D. ratio of moles of solvent to moles of solute


Let \( \boldsymbol{A}=\{1,2,3,4\} ; B=\{3,5,7,9\} \)
\( C=\{7,23,47,79\} \) and \( f: A \rightarrow B, g: \)
\( B \rightarrow C \) be defined as \( f(x)=2 x+1 \)
and \( g(x)=x^{2}+x . \) Express \( (g \circ f)^{-1} \)
and \( f^{-1} \circ g^{-1} \) as the sets of ordered
pairs and verify and \( (\boldsymbol{g} \circ \boldsymbol{f})^{-1}=\boldsymbol{f}^{-1} \circ \)
\( \boldsymbol{g}^{-1} \)


Assertion
Achlorophyllous, multicellular and
eukaryotic decomposers are fungi.
Reason
Fungi have cell wall rich in cellulose and specialized chitin.
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.


Identify the correct sequence of
taxonomical category
A. Species \( \rightarrow \) order \( \rightarrow \) phylum \( \rightarrow \) kingdom
B. Genus \( \rightarrow \) species \( \rightarrow \) order \( \rightarrow \) kingdom
C. Genus \( \rightarrow \) species \( \rightarrow \) phylum \( \rightarrow \) order
D. Genus \( \rightarrow \) species \( \rightarrow \) kingdom \( \rightarrow \) phylum


The resistance of a wire is 5 ohm at \( 50^{\circ} \)
\( \mathrm{C} \) and 6 ohm at \( 100^{\circ} \mathrm{C} \). The resistance of
the wire at \( 0^{\circ} \mathrm{C} \) will be:
\( A \cdot 2 \) ohm
B. 1 ohm
c. 4 ohm
D. 3 ohm


When the same amount of electricity is passed through solution of silver nitrate and copper sulfate, 0.4 g copper is deposited. The amount of silver deposited is:
A. \( 1.36 \mathrm{g} \)
в. 2.78
c. \( 5.1 \mathrm{g} \)
D. 5.48


Amoung the componds, \( P C I_{4}^{+} \) and
\( P C I_{4}^{-} \);which one is not likely to exist
and why?


5
8
8


Calculate the flux through the base of
the cone of radius \( r \)
\( \mathbf{A} \cdot 2 \pi r^{2} E \)
\( \mathbf{B} \cdot 4 \pi r^{2} E \)
\( \mathbf{c} \cdot 0.5 \pi r^{2} E \)
\( \mathbf{D} \cdot \pi r^{2} E \)


Fermentation is represented by the
equation
\( \mathbf{A} \cdot C_{6} H_{12} O_{6}+6 O_{2} \rightarrow 6 C O_{2}+6 H_{2} O+673 \mathrm{k} \) cal
B \( \cdot C_{6} H_{12} O_{6} \rightarrow 2 C_{2} H_{5} O H+2 C O_{2}+18 k \) cal
\( \mathbf{c} \cdot 6 C O_{2}+12 H_{2} O \rightarrow C_{6} H_{12} O_{6}+6 H_{2} O+6 O_{2} \)
\( \mathbf{D} \cdot 6 C O_{2}+6 H_{2} O \rightarrow C_{6} H_{12} O_{6}+6 O_{2} \)


When a bullet is fired from a rifle its
momentum become \( 20 \mathrm{kg} \) m/s. If the
velocity of the bullet is \( 1000 m / s \) what
will be its mass?
A . \( 30 g \)
B. \( 5 \mathrm{kg} \)
c. \( 20 g \)
D. \( 500 g \)


Sum of number of \( 1^{\circ} \) alcoholic group in
product \( (P) \) and \( (Q) \) is:
\( A \)
B. 2
\( c .3 \)
\( D \)


Which of the following statements
regarding orbitals is false?
A. \( 1 s \) orbital has one nodal region.
B. \( 2 s \) orbital is spherical with one nodal region.
C \( .2 p_{x} \) orbital is dumb bell with one nodal plane.
D. \( 3 d_{x y} \) orbital has two nodal planes.


Q Type your question
\( y \)
Development Houses
\( 2 \mathrm{Br} \quad 3 \mathrm{Br} \quad 4 \mathrm{Br} \quad \) Total
single-Family \( 5 \quad 19 \quad 34 \)
58
Townhouse
\( 24 \quad 42 \quad 30 \)
96
Total
\( 29 \quad 61 \quad 64 \)
A daycare centre is planning to distribute pamphlets to the families with children living houses with three or more bedrooms, due to budget. In addition to sending out flyers, it also decides to send out invitations for a free
day of daycare, to the family residing in two categories with the most houses. If
a house that already received a flyer is chosen at random to receive the second
stage of the marketing, then the probability that the house belongs to one of these two groups is \( \frac{p}{q}, \) where \( p, q \) are co-primes.What is the value of \( \boldsymbol{q}- \)
\( \boldsymbol{p} ? \)


The kinetic energy of a body of mass \( \boldsymbol{m} \)
moving with a velocity \( v \) is given by:
A \( \cdot m v^{2} \)
в. \( \frac{1}{2} m v^{2} \)
\( \mathrm{c} \cdot 2 \mathrm{mv}^{2} \)
D. \( \frac{1}{2} m^{2} v^{2} \)


Carbon monoxide (CO) causes:
A. numbness of brain
B. secretion of adrenaline
C. weakening of the wall of alveoli
D. risk of atherosclerosis


If in the expansion of \( (1+y)^{n}, \) the
coefficient of \( 5^{t h}, 6^{t h} \) and \( 7^{t h} \) terms are
in A.P., then \( n \) is equal to:
A .7,11
в. 7,14
\( c \cdot 8,16 \)
D. none of the above


Air that remains in lung after most powerful expiration is
A. Inspiratory air
B. Dead space air
c. Tidal air
D. Residual air


Which of the following is a cubic polynomial?
A \( \cdot p(x)=x^{3}-3^{3} \)
в. \( p(x)=x-3 \)
c. \( p(x)=3 \)
D \( \cdot p(x)=3^{3} \)


When \( I_{2} \) dissociated to its form the
following reaction occurs:
\( \boldsymbol{I}_{2(g)} \rightleftharpoons 2 \boldsymbol{I}_{(g)} ; \triangle \boldsymbol{H}^{0}=+\mathbf{1 5 0 k J} \)
The reaction is favoured at ?
A. low temperature
B. high temperature
c. no change with temperature
D. high pressure.


The value of \( \sin ^{-1} \)
\( \left\{\tan \left(\cos ^{-1} \sqrt{\frac{2+\sqrt{3}}{4}}+\cos ^{-1} \frac{\sqrt{12}}{4}-\right.\right. \)
is
\( \mathbf{A} \cdot \mathbf{0} \)
в. \( \frac{\pi}{2} \)
\( c \cdot-\frac{\pi}{2} \)
D.


In the given figure, \( A B \) is a chord of
length \( 16 \mathrm{cm} \) of a radius \( 10 \mathrm{cm} . \) The
tangents at \( A \) and \( B \) intersect at point
\( P . \) Find the length of \( P A \)


A freely falling object eventually stops on reaching the ground. What happens to its kinetic energy?


The graph between the resistive force
acting on a body and the position of
the body travelling in a straight line is
shown in the figure. The mass of the
body is \( 25 \mathrm{kg} \) and initial velocity is 2 m/s.When the distance covered by the
bodyi \( s 4 \mathrm{m}, \) its kinetic energy would be
A. 50
B . 40 J
c. 20
D. 10


Oxalic acid can donate two protons to water in successive reactions:
(1) \( \boldsymbol{H}_{2} \boldsymbol{C}_{2} \boldsymbol{O}_{4}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l}) \rightleftharpoons \boldsymbol{H}_{3} \boldsymbol{O}+ \)
\( (a q)+H C_{2} O_{4}^{-}(a q) \)
(2) \( H C_{2} O_{4}^{-}(a q)+H_{2} O(l) \rightleftharpoons H_{3} O+ \)
\( (a q)+C_{2} O_{4}^{2-}(a q) \)
f \( \boldsymbol{K}_{c 1}=\mathbf{5 . 9} \times \mathbf{1 0}^{-2} \) and \( \boldsymbol{K}_{c 2}=\mathbf{6 . 4} \times \)
\( 10^{-5} \) at \( 25^{0} C, \) what is the value of \( K_{c} \)
for reaction (3)\( ? \)
(3) \( \boldsymbol{H}_{2} \boldsymbol{C}_{2} \boldsymbol{O}_{4}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{2} \boldsymbol{H}_{2} \boldsymbol{O}(l) \rightleftharpoons \)
\( \mathbf{2} \boldsymbol{H}_{3} \boldsymbol{O}+(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{C}_{2} \boldsymbol{O}_{4}^{2-}(\boldsymbol{a} \boldsymbol{q}) \)
A \( \cdot 3.8 \times 10^{-6} \)
B. \( 1.1 \times 10^{-3} \)
D. \( 9.2 \times 10^{2} \)


Find the square root of \( 4 a b-2\left(a^{2}-\right. \)
\( \left.b^{2}\right) i \)


If \( f(x)=\max \left\{\sin x, \cos ^{-1} x\right\}, \) then
A. \( f \) is differentiable everywhere
B. \( f \) is continuous everywhere but not differentiable
C tis discountinuous at \( x=\frac{n \pi}{2}, n \in N \)
D. \( f \) is non-differentiable at \( x=\frac{n \pi}{2}, n \in N \)


If an electron is released from rest at
point \( p \) in the diagram, what will it do?
A. Move to the right
B. Move to the left
C. Move toward the top of the screen
D. Move toward the bottom of the screen


A satellite orbiting around earth in an
orbit of radius \( R \) is shifted to an orbit of
radius \( 2 R \). Times the time taken for one
revolution will become.
A. 8 times
B. 2 times
c. 2.5 times
D. 2.8 times


It is hotter at the same distance over
the top of a fire than it is on the side of
it mainly because:
A. Heat is radiated upwards
B. Air conducts heat upwards
c. convection takes more heat upwards
D. conduction, convection and radiation all contribute significantly in transferring heat upwards.


Simplify \( (a+b)^{2} \)


If the pH of \( 0.2 M \) dibasic acid \( \left(H_{2} A\right) \)
is \( 1.699, \) than its osmotic pressure at \( T \) K temperature will be?
в. \( 0.02 R T \)
c. \( 0.4 R T \)
D. \( 0.1 R T \)


Complete the following reaction and identify the products formed


\( \Delta H^{0} \quad \) and \( \quad \Delta S^{0} \quad \) for \( \quad C C l_{4} \) are
\( 2.5 K J^{-1} m o l^{-1} \quad \$ \quad 9.99 J K^{-1} m o l^{-1} \)
respectably at \( 298^{0} K \) find the
temperature at which solid \( C C l_{4} \) and
its liquid are in equilibrium at one atmosphere.


A beaker containing water is balanced on the pan of a common balance. A solid of specific gravity 1 and mass 5 g is tied to the arm of the balance and immersed
in water contained in the beaker.The
scale pan with the beaker
A. goes down
B. goes up
c. remains unchanged
D. none of these


Pituitary is popularly called the master gland.
A. True
B. False


If \( A C \) passes through the centre of the
circle, then the area of the shaded
region in the given figure is
A \( \cdot \frac{a^{2}}{2}(3-\pi) \)
B \( \cdot a^{2}\left(\frac{\pi}{2}-1\right) \)
\( \mathbf{c} \cdot 2 a^{2}(\pi-1) \)
\( ^{\mathrm{D}} \cdot \frac{a^{2}}{2}\left(\frac{\pi}{2}-1\right) \)


If \( A \) and \( B \) are two events, the
probability that exactly one of them occurs is given by
This question has multiple correct options
A. \( P(A)+P(B)-2 P(A \cap B) \)
В \( \cdot P\left(A \cap B^{\prime}\right)+P\left(A^{\prime} \cap B\right) \)
c. \( P(A \cap B)-P(A \cap B) \)
D. \( P\left(A^{\prime}\right)+P\left(B^{\prime}\right)-2 P\left(A^{\prime} \cap B^{\prime}\right) \)


Which of the following statements is/are correct?
i. \( H N O_{3} \) solution is not obeying the
Raoult's law.
ii. More the difference in vapour
pressure of pure compounds forming a
mixture,easier to separate them
through distillation.
iii. In Fig. \( 2.36(a), T_{2} \) is less than \( T_{1} \)
because the liquid of composition \( \mathrm{Q} \) is richer in more volatile component.
A. (ii) and (iii)
B. (ii)
\( c \cdot \) (i) and (ii)
D. (i), (ii) and (iii)


Two waves of amplitudes \( A_{0} \) and \( x A_{0} \)
pass through a region.If \( x>1, \) what is the difference in the maximum and
minimum resultant amplitude is :
A \( \cdot(x+1) A_{0} \)
в. \( (x-1) A_{0} \)
c. \( 2 x A_{0} \)
D. \( 2 A_{0} \)


In Liebig's method for the estimation of C and H, if the compound also contains
N, which of the following is kept near the exist of the combustion tube?
A. Silver wire
в. \( P b C r_{4} \)
c. Both (a) and (b)
D. cuo gauze


For a real number \( x \) let \( [x] \) denote the
largest number less than or equal to \( x \) for \( \boldsymbol{x} \epsilon \boldsymbol{R} \) let \( \boldsymbol{f}(\boldsymbol{x})=[\boldsymbol{x}] \sin \pi \boldsymbol{x} . \) Then
A. fis differentiable on R
B. fis symmetric about the line \( x=0 \)
\( ^{\mathbf{c}} \cdot \int_{-3}^{3} f(x) d x=0 \)
D. For each real \( \alpha \), the equation \( f(x)-\alpha=0 \) has infinitely many roots.


Secondary growth occurs in
A. All plants
B. Only dicots
C. Only monocots
D. Both dicots and monocots


Find \( x \) for which \( f(x)=0 \) when \( f(x)= \)
\( x^{2}-64 \)


To pour water on calcium oxide."which
is another way to classify this reaction? Explain


\( \left(1+i+i^{2}+i^{3}+i^{4}+i^{5}\right)(1+i)= \)
\( \mathbf{A} \cdot i \)
B . \( 2 i \)
\( c .3 i \)
D. 4


A solid copper sphere has a charge of \( +\mathrm{Q} \)
on it. Where on the sphere does the
charge reside?
A. \( +Q \) at the center of the sphere
B. \( \mathrm{Q} / 2 \) at the center of the sphere and \( \mathrm{Q} / 2 \) on the outer surface
c. \( \mathrm{Q} \) at the center of the sphere and \( +2 \mathrm{Q} \) on the outer surface
D. \( + \) Q on the outer surface
E. The charge is spread evenly throughout the sphere


The single median nostril is characteristic of
A. Birds
B. Cyclostomes
c. Bony fishes
D. Protochordates


The total number of podomeres in each leg of cockroach is
A . 5
B. 6
\( c \cdot 7 \)
\( D \)


An equilateral prism deviates a ray
through \( 45^{\circ} \) for the two angles of
incidence differing by \( 20^{\circ} . \) The angle of incidence is
A . \( 62.5^{\circ} \)
в. \( 42.5^{\circ} \)
c. Both are correct
D. Both are wrong


On heating with concentrated NaOH
solution in an inert atmosphere of \( \boldsymbol{C O}_{2} \)
white phosphorus gives a gas. Which of the following statements is incorrect about the gas?
A. It is highly poisonous and has smell like rotten fish.
B. Its solution in water decomposes in the presence of light
c. It is more basic than \( N H_{3} \)
D. It is less basic than \( N H_{3} \)


The value of \( \sqrt[3]{5 \times 25} \) is
A. 5
B. 25
\( c \cdot 125 \)
D. none of these


In how many forms did the earlier Indian philosophers classify matter?
A .2
B. 6
c. 7
D.


Which factors do not effect the vapour pressure of a liquid at equilibrium?
I. Intermolecular forces of attraction
II. The volume of liquid present
III. The temperature of the liquid.
A. Onlyı
c. I and II
D. II and III


What are carbohydrates? Classify them and also write their characteristics.


Why is organic matter (humus) an
important part of soil?
A. It helps to improve water infiltration
B. It can break down organic pollutants
C. It converts nitrogen in the air into nitrates used by plants
D. It is rich in nutrients, which is important for fertility


This particle balances the charges from the protons to make the atom neutral-
A. neutron
B. electron
c. nucleus
D. none of these


Which of the following element exhibits maximum oxidation state?
A. Mn
B. co
c. \( \mathrm{Fe} \)
D. zn


Short / Long answer type questions. Mention a cause and symptom of
constipation.


In the expansion of \( (x+\sqrt{x^{2}-1})^{6}+ \)
\( (x-\sqrt{x^{2}-1})^{6}, \) the number of terms is
A. 7
B. 14
\( c \cdot 6 \)
D.


\( A B C \) is a triangle right-angled at \( B \)
and \( D \) is a point on \( B C \) produced
\( (B D>B C), \) such that \( B D=2 D C \)
Which one of the following is correct?
A. \( A C^{2}=A D^{2}-3 C D^{2} \)
B. \( A C^{2}=A D^{2}-2 C D^{2} \)
c. \( A C^{2}=A D^{2}-4 C D^{2} \)
D. \( A C^{2}=A D^{2}-5 C D^{2} \)


\( 700 \mathrm{m} \) of the road which is \( 1 \mathrm{km} \) long has been repaired. Find the percentage of the road which is yet to be repaired.


Which of the following is best insulator?
A. carbon
B. paper
c. ebonite
D. graphite


The distance from origin to (5,12) is
A . 13
B. 17
c. 10
D. 7


The forbidden gap in germanium crysta
is
A . 0.7 ev
B. \( 1.12 X 10^{19} J \)
c. Both 1 and 2
D. \( 1.1 e V \)


The near point of a myopic eye is \( 15 \mathrm{cm} \) What should be the power of the lens which will enable the eye to read a book
placed at \( 30 \mathrm{cm} ? \)
A. 3.33 dioptre
B. -3.33 dioptre
c. 2.22 dioptre
D. -2.22 dioptre


Calculate the angle between two vectors 2F and \( \sqrt{2} \mathrm{F} \) so that the resultant force is \( \mathrm{F} \sqrt{10} \)
A. 120 degrees
B. 90 degrees
c. 60 degrees
D. 45 degrees


Gaseous pollutants are controlled
through
A. Adsorption
B. ESP
c. Arrestors
D. Pyrolysis
E. Incineration


The areas of two similar triangles are
\( 121 \mathrm{cm}^{2} \) and \( 81 \mathrm{cm}^{2} \) respectively. Find the ratio of their corresponding heights.
A \( \cdot \frac{11}{9} \)
в. \( \frac{10}{9} \)
\( c \cdot \frac{9}{11} \)
D. \( \frac{9}{10} \)


Carbonic acid, \( \boldsymbol{H}_{2} \boldsymbol{C} \boldsymbol{O}_{3}, \) is a diprotic
acid for which \( \boldsymbol{K}_{1}=\mathbf{1 0}^{-\mathbf{7}} \) and \( \boldsymbol{K}_{\mathbf{2}}= \)
\( 10^{-11} . \) Which solution will produce a pH
closet to \( 9 ? \)
A. \( 0.1 \mathrm{M} \mathrm{H}_{2} \mathrm{CO}_{3} \)
в. 0.1 М \( N a_{2} \) СО \( _{3} \).
c. 0.1 М NaHCO\( _{3} \)
D. 0.1 М \( N a H C O_{3} \) and 0.1 М \( N a_{2} C O_{3} \)


A steel wire of mass \( 3.16 K g \) is
stretched to a tensile strain of \( 1 \times 10^{-3} \) What is the elastic deformation energy
if density \( \rho=7.9 g / c c \) and \( Y=2 \times 10^{11} \)
\( \mathrm{N} / \mathrm{m}^{2} ? \)
A. \( 4 K J \)
в. \( 0.4 K J \)
c. \( 0.04 K J \)
D. \( 4 J \)


Convert each of the following
temperature in \( ^{\circ} \boldsymbol{F} \) to the celsius and
kelvin scale \( 68^{\circ} F, 5^{\circ} F, 176^{\circ} F \)


Which of the following statement is
incorrect about chemical equilibrium?
A. There is no change in the concentrations of reactants and products with time
B. Equilibrium can be attained by starting with either reactants or products
C . Equilibrium is dynamic
D. The position of equilibrium cannot be disturbed by changing the concentrations of reactants or products


What is the voltage gain in a common emitter amplifier, when input resistance is \( 3 \Omega \) and load resistance is
\( 24 \Omega \) with \( \beta=60 ? \)
A. 480
в. 2.4
\( c .4 .8 \)
D. 8.4


If \( \boldsymbol{y}=\boldsymbol{A}+\boldsymbol{B} \boldsymbol{x}^{2} \) then:
A \( \cdot \frac{d^{2} y}{d x^{2}}=2 x y \)
B. \( x \frac{d^{2} y}{d x^{2}}=y_{1} \)
c. \( x \frac{d^{2} y}{d x^{2}}-\frac{d y}{d x}+y=0 \)
D. \( x \frac{d^{2} y}{d x^{2}}+\frac{d y}{d x}+y=0 \)


Find the solution of \( 2 x-3>7 \)


A vessel containing \( 50 k g \) of water is placed at a height \( 15 m \) above the ground. Assuming the gravitational potential energy at ground to be zero, what will be the gravitational potential energy of water in the vessel? Consider
\( \boldsymbol{g}=\mathbf{1 0 m} \boldsymbol{s}^{-2} \)
\( \mathbf{A} \cdot 5.0 k J \)
B. \( 7.5 k J \)
c. \( 10.0 k J \)
D. \( 12.5 k J \)


Vulcanization of rubber helps to make
rubber hard and resistant to hot and
cold conditions.
A. True
B. False


If \( y=a \cos (\log x)+b \sin (\log x), \) then
A. \( x^{2} \frac{d^{2} y}{d x^{2}}+x \frac{d y}{d x}+y=0 \)
B. \( \quad x^{2} \frac{d^{2} y}{d x^{2}}-x \frac{d y}{d x}-y=0 \)
c. \( x^{2} \frac{d^{2} y}{d x^{2}}+x \frac{d y}{d x}-y=0 \)
D. \( x^{2} \frac{d^{2} y}{d x^{2}}+x \frac{d y}{d x}+x y=0 \)


When light enters from denser medium to rarer medium at an angle greater than critical angle, it reflects back. This phoenomenon is called
A. Reflection at plane surface
B. Total internal reflection
c. Refraction at plane surface
D. None of above


Which statement(s) is/are correct
about hydrogen spectrum?
A. Energy of 2 nd orbit is different for \( H_{1}^{1}, H_{1}^{2} \) and \( H_{1}^{3} \)
B. Visible spectrum can be obtained in Lyman series and B
C. Infrared spectrum is obtained in Paschen, Brackett and
D. Total number of emission lines obtained in Balmer serie where \( n \) is principal quantum number and \( n>2 \)


A square matrix \( \left(a_{i j}\right) \) in which \( a_{i j}=0 \)
for \( i \neq j \) and \( a_{i j}=k(\text { constant }) \) for \( i= \)
\( j \) is a
A. Unit matrix
B. Scalar matrix
c. Null matrix
D. none


When a body moves with a constant
speed along a circle:
A. no work is done on it
B. no acceleration is produced in the body
C. no force acts on the body
D. its velocity remains constant


Construct a \( 4 \times 3 \) matrix \( A=\left[a_{i j}\right] \) whose element \( a_{i j} \) is \( a_{i j}=2 i+\frac{i}{j} \)


The vapour pressure of two miscible liquids \( (A) \) and \( (B) \) are 300 and 500 mm of Hg respectively. In a flask, 10 moles of
(A) is mixed with 12 moles of \( (\mathrm{B}) \)
However, as soon as (B) is added, (A)
starts polymerising into a completely insoluble solid. The polymerization follows first-order kinetics. After 100
minutes, 0.525 moles of a solute is dissolved which arrests the
polymerisation completely. The final vapour pressure of the solution is 400 \( \mathrm{mm} \) of Hg. The rate constant of the
polymerisation reaction is Assume negligible volume change on
mixing and polymerisation and ideal behaviour for the final solution:
A \( .1 .0 \times 10^{-4} \)
В. \( 3.0 \times 10^{-4} \)
c. \( 2.0 \times 10^{-4} \)
D. None of these


The angular velocity of the earth's rotation about its axis is \( \omega . \) An object
weighed by a spring balance gives the same reading at the equator as at height \( h \) above the poles, the value of \( h \)
will be:
\( ^{\mathrm{A}} \cdot \frac{\omega^{2} R^{2}}{g} \)
В. \( \frac{\omega^{2} R^{2}}{2 g} \)
c. \( \frac{2 \omega^{2} R^{2}}{g} \)
D. \( \frac{2 \omega^{2} R^{2}}{3 g} \)


\( \int \frac{d x}{\sin x-\cos x+\sqrt{2}} \) is equal to.
A \( \cdot-\frac{1}{\sqrt{2}} \tan \left(\frac{x}{2}+\frac{\pi}{8}\right)+C \)
B. \( \frac{1}{\sqrt{2}} \tan \left(\frac{x}{2}+\frac{\pi}{8}\right)+C \)
c. \( \frac{1}{\sqrt{2}} \cot \left(\frac{x}{2}+\frac{\pi}{8}\right)+C \)
D. \( -\frac{1}{\sqrt{2}} \cot \left(\frac{x}{2}+\frac{\pi}{8}\right)+C \)


Study the following diagram carefully
and then answer the questions that follow. The diagram is depicting a
defect of the human eye.
(i) Identify the defect shown in the
diagram.
(ii) Give two possible reasons for the
above defect.
(iii) Draw a neat labelled diagram to
show how the above defect can be
rectified.


Why do the tyres of a bicycle feel hard
when air is filled in the tubes inside
them.


All alkane forming isomers if the number of least carbon atom is :
A . 1
B. 2
\( c .3 \)
\( D \)


If \( g \) is the acceleration due to gravity on the earth's surface, the gain of the potential energy of an object of mass \( \boldsymbol{m} \)
raised from the surface of the earth to a
height equal to the radius \( R \) of the earth
will be :
A. \( 2 m g R \)
в. \( m g R \)
c. \( \frac{1}{2} m g R \)
D. \( \frac{1}{4} m g R \)


A ball hits the ground and loses \( 20 \% \) of
its momentum. Coefficient of
restitution is
A. 0.2
B. 0.4
\( c \cdot 0.6 \)
D. 0.8


The electron configuration
\( 1 s^{2} 2 s^{2} p^{6} 3 s^{2} p^{6} 4 s^{2} 3 d^{7} \) represents an
atom of the element
A. \( B r \)
в. \( C o \)
c. \( C d \)
D. \( G a \)
E . \( M g \)


Which of the following has zero electronegativity?
A . \( A r \)
B. \( S \) i
c. \( N \)
D. \( F \)


A hot and a cold body are kept in
vacuum separated from each other. Which of the following causes decrease in temperature of the hot body?
A. Radiation
B. Convection
c. conduction
D. Temperature remains unchanged


The sum of the outer angles of polygon is twice the sum of the inner angles.
(i) How many sides does it have?
(ii) What if the sum of outer angles is half the sum of inner angles?
(iii) If the sums are equal?
A. (i) 3 (ii) 4 (iii) 6
B. (i) 6 (ii) 4 (iii) 3
c. (i) 4 (ii) 3 (iii) 6
D. (i) 3 (ii) 6 (iii) 4


Which congruence criterion do you use
in the following?
Given: \( \mathrm{EB}=\mathrm{BD}, \mathrm{AE}=\mathrm{CB}, \angle \mathrm{A}=\angle \mathrm{C}=90^{\circ} \)
So \( \Delta A B E \equiv \Delta C D B \)


Define water harvesting.


How many POP bonds appear in cyclic metaphosphoric acid?
A. Four
B. Three
c. Two
D. one


State which quadrants or on which axis do the following points line?
1. \( \boldsymbol{A}(-\mathbf{3}, \mathbf{2}) \)
2. \( B(5,3) \)
3. \( C(0,4) \)
4. \( \boldsymbol{D}(-\mathbf{3}, \mathbf{0}) \)


Find an A.P. in which sum of any number
of terms is always three times the squared number of these terms.


Evaluate the following question. \( \lim _{x \rightarrow a} \frac{(x)^{3 / 2}-(a)^{3 / 2}}{x-a} \)


When stem of a herbaceous plant is cut water or sap oozes out, this is due to?
A. Guttation
B. Transpiration pull
c. Root pressure
D. Imbibition


If \( a, b, c, d \epsilon R \) are such that \( a^{2}+b^{2}=4 \)
and \( c^{2}+d^{2}=2 \) and if \( |a+i b|^{2}=\mid c+ \)
\( \left.i d\right|^{2}|x+i y| \operatorname{then} x^{2}+y^{2}= \)
\( A \cdot 4 \)
B. 3
\( c \cdot 2 \)
\( D \)


Define pseudio first order reaction Show that half life of zero order reaction
is directly proportional to concentration of reactant.


Assertion
Centre of mass of a rigid body always lies inside the body.
Reason
Centre of mass and centre of gravity coincide if gravity is uniform.
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


Match the items of Column I with
Column II


Assuming a person could survive in all of the following locations, where would this person have the most mass?
A. on the surface of the earth
B. on the surface of the moon
c. on the surface of Jupiter
D. on the surface of the sun
E. same mass at all locations


Which of the following quantity is always positive for a spontaneous chemical reaction?
A. Standard voltaic potential
B. Entropy
c. Enthalpy
D. Reaction rate
E. Gibbs free energy


a) A solution containing \( 18 g \) of nonvolatile non-electrolyte solute is dissolved in 200 g of water freezes at 272.07 K. Calculate the molecular mass
of the solute.
Given \( : \boldsymbol{K}_{\boldsymbol{f}}=\mathbf{1 . 8 6} \mathrm{K} \mathrm{kg} / \mathrm{mol} \)
The freezing point of water \( =273 \mathrm{K} \)
b) Define the isotonic solution. What
happens when the blood cell is dipped in a solution containing more than normal saline concentration?


The position of an object moving along \( x- \) axis is given by \( x=a+b t^{2} \) where
\( \boldsymbol{a}=\mathbf{8 . 5} \boldsymbol{m}, \boldsymbol{b}=\mathbf{2 . 5} \boldsymbol{m} \boldsymbol{s}^{-2} \) and \( \boldsymbol{t} \) is
measured in seconds. What is its
velocity at \( t=0 s \) and \( t=2.0 s . \) What is
the average velocity between \( t=2.0 s \)
and \( t=4.0 s \)


Say true or false:
\( \mathrm{C}=\{\text { even numbers between } 6 \text { and } 10\} \) is
not an empty set.
A. True
B. False


Which of the following occurs in grass and regenerates the part removed by the grazing herbivores?
A. Promeristem
B. Primary meristem
c. Secondary meristem
D. Lateral meristem


What is the main difference between
isotopes of the same element?


Jupiter has a thick atmosphere of which reflects most of
the sun light falling on it.
A. Oxygen
B. Helium
c. Nitrogen
D. Hydrogen


Abhirami runs to her class rooms as the
school ball rang. What will be the probable rate of breathing in her lungs due to this vigorous act?
A \( \cdot \) 15 to 18 times per minute
B. 16 to 20 times per minute
c. 18 to 25 times per minute
D. 20 to 25 times per minute


When magnetic field at \( \mathrm{P} \) and \( \mathrm{Q} \) is same then OP/OQ is:
A \( \cdot \frac{1}{3} \)
B. \( \frac{1}{\frac{1}{3}} \)
\( c \cdot 2 \sqrt{2} \)
D. \( \frac{3}{2} \)


State whether true or false:
A piece of fresh potato does not conduct electricity at all.
A. True
B. False


A man of mass \( 60 k g \) climbs up a \( 20 m \) long staircase on the top of a building
10 \( m \) high. What is the work done by
him? \( \left(\text { Takeg }=10 m s^{-2}\right) \)
A. \( 12 k J \) J 5 J. 12 .
в. \( 6 k J \)
c. \( 3 k J \)
D. \( 18 k J \)


An electric heater of resistance \( 8 \Omega \)
draws \( 15 A \) from the service mains in 2
hrs.Calculate the rate at which heat is
developed in the heater


When alpha particles are sent through a thin metal foil, most of them go straight through the foil because:
A. alpha particles are much heavier than electrons
B. alpha particles are positively charged
c. most part of the atom is empty space
D. alpha particle move with high velocity


Which of the following act as both hormone and enzyme?
A. ADH hormone
B. Acetylcholinesterase
c. Angiotensinogen
D. Renin


The weight of Rahul is \( 5 k g \) more than
Sachin.The weight of Samir is 12 kg less than double the weight of Sachin.lf the total weight of all the three is 93 find the weight of each one of them.
A. Sachin-25 kg, Rahul - 30 kg, Samir 38kg
B. Sachin-25 kg, Rahul -30 kg, Samir 40 kg
c. Sachin- -25 kg, Rahul - 38 kg, Samir -25 kg
D. Sachin- -25 kg, Rahul -38 kg, Samir 38kg


Consider the following statements.
(a) Sudden action in response to something in the environment is called
reflex action.
(b) Sensory neurons carry signals from spinal cord to muscles.
(c) Motor neurons carry signals from receptors to spinal cord.
(d) The path through which signals are transmitted from a receptor to a muscle or a gland is called reflex arc. Which of the above statements are
correct?
\( A \cdot(a) \) and \( (b) \)
B. (a) and (c)
c. (a) and (d)
D. \( (a),(b) \) and \( (c) \)


Which product will be obtained in the following reaction? \( \boldsymbol{P}_{4}(s)+\mathbf{3} N \boldsymbol{a} \boldsymbol{O} \boldsymbol{H}(\boldsymbol{a} \boldsymbol{g})+\boldsymbol{3} \boldsymbol{H}_{2} \boldsymbol{O}(l) \rightarrow \)
A \( \cdot P H_{3}(g)+3 N a H_{2} P 0_{2}(a q) \)
B . \( P H_{3}(g)+3 N a_{2} H P O_{2}(a q) \)
c. \( 2 P H_{3}(g) 3 N a_{2} H P O_{2}(a q) \)
D \( \cdot 2 P H_{3}(g)+3 N a H_{2} P O_{2}(a q) \)


If \( \overrightarrow{\boldsymbol{a}}=\boldsymbol{x} \hat{\boldsymbol{i}}+\boldsymbol{2} \hat{\boldsymbol{j}}-\boldsymbol{z} \hat{\boldsymbol{k}} \) and \( \overrightarrow{\boldsymbol{b}}=\boldsymbol{3} \hat{\boldsymbol{i}}- \)
\( y \hat{j}+\hat{k} \) are two equal vectors, then write
the value of \( \boldsymbol{x}+\boldsymbol{y}+\boldsymbol{z} \)


What are the ill effects of algal blooms?


A girl with two normal eyes wants to see the full width of her face using a plane
mirror. The eye to eye and ear to ear distances of her face are 4 inch and 6
inch respectively. The minimum width of the required mirror is:
A. 1 inch
B. 2 inch
\( c .2 .5 \) inch
D. 5 inch


Means of perennation in club mosses
are
A . Gemmae
B. Tubers
c. Bulbils
D. Both A and C


Choose the correct relation between
\( u, v \) and \( r \) for a spherical mirror, where
\( r \) is radius of curvature.
A \( \cdot r=\frac{2 u v}{u+v} \)
B. \( r=\frac{2}{u+v} \)
c. \( r=\frac{2(u+v)}{(u v)} \)
D. \( r=\frac{2 u v}{u-v} \)


Hypochondria commonly occurs in adolescents with
A. Perceptual disturbance
B. Late development
c. Physiological aberration
D. Chronic mental and physical weakness


Which of the following class of forces is different from others?
A. Pulling of a cart
B. Stretching of a coiled spring
c. Kicking of a football
D. weight of the body


If the \( z x \) -plane divides the line segment
joining (1,-1,5) and (2,3,4) in the ratio \( \boldsymbol{p}: 1, \) then \( \boldsymbol{p}+\mathbf{1}= \)
A \( \cdot \frac{1}{3} \)
B.
\( c \cdot \frac{3}{4} \)
D. \( \frac{4}{3} \)


Find the sum of the series:
\( \mathbf{5}+\mathbf{1 3}+\mathbf{2 1}+\dots+\mathbf{1 8 1} \)


10 g fairly concentrated solution of
\( \boldsymbol{C u} \boldsymbol{S O}_{4} \) is electrolyzed using 0.01 \( \mathrm{F} \) of electricity. Calculate:
(a) The weight of resulting solution(g) (write the value to the nearest integer).


A length is measured as \( 7.60 \mathrm{m} \). This is
the same as
A. \( 760 \mathrm{mm} \)
B. \( 0.0076 \mathrm{mm} \)
\( c .760 \mathrm{cm} \)
D. \( 0.76 d m \)


Zero can be written in the form of \( \frac{\boldsymbol{p}}{\boldsymbol{q}} \) where p and q are integers and \( \mathrm{q} \neq 0 ? \) If above statement is true then enter 1
and if false then enter 0


If \( z^{2}+z+1=0, \) then \( \sum_{r=1}^{6}\left(z_{1}+\frac{1}{z_{2}}\right)^{2} \)
is equal to
\( A \cdot 6 \)
B. 12
\( c \cdot 18 \)
D. 24


The angle made by the tangent at any
point on the curve \( \boldsymbol{x}=\boldsymbol{a}(\boldsymbol{t}+ \)
\( \sin t \cos t), y=a(1+\sin t)^{2} \) with \( x \) -axis
is
A \( \cdot \frac{\pi}{2} \)
B. \( \frac{\pi}{4} \)
c. \( _{\pi+\frac{t}{2}} \)
D. \( \frac{\pi}{4}+\frac{t}{2} \)


A car which costs Rs. 3,50,000 depreciates by \( 10 \% \) every year. What will be the worth of the car after three years?
A .2,55,150
В. 1,65,150
c. 2,25,350
D. 1,55,350


What is a wavefront? How does it
propagate ? Using Huygens' principle, explain reflection of a plane wavefront
from a surface and verify the laws of
reflection.


State two factors upon which the heat
absorbed by a body depends.


What is the type of polynomial \( 11= \) \( -4 x^{2}-x^{3} ? \)
A. Cubic
B. Quadratic
c. Linear
D. None of these


What are the programmes listed under the maternity and child health and
family planning.


When lead \( (P b) \) is reacted with the
hydrochloric acid a gas is evolved.
Name the gas.
A. Hydrogen gas
B. Chlorine gas
c. Both hydrogen gas and chlorine gas
D. None of them


If the lowest energy X-rays have \( \lambda= \)
\( 3.055 \times 10^{-8} m, \) estimate the
minimum difference in energy between
two Bohr's orbits such that an
electronic transition would correspond
to the emission of an X-ray. Assuming that the electrons in other shells exert
no influence, at what \( Z(\text { minimum }) \) would a transition from a second energy
level to the first result in the emission
of an X-ray?
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot 3 \)
D. 4


A current carrying loop is placed in a
uniform magnetic field in four different
orientations as shown in figure. Arrange them in the decreasing order of
potential energy
\( \widehat{Q} \)
2
3
A. 4,2,3,1
В. 1,4,2,3
\( \mathbf{c} \cdot 4,3,2,1 \)
D. 1,2,3,4


The Sl unit of atmospheric pressure is
A. Barye
B. Pascal
c. Dyne
D. None of the above


Which of the following statements can
be suitable?
A. Rotational motion is a type of circular motion.
B. Circular motion is similar to rotational motion.
C. Rotational and circular motion are fundamentally unrelated.
D. None of these


Find the measure of an angle, if seven
times its complement is \( 10^{\circ} \) less than
three times its supplement
A .40
B . 25
\( c \cdot 30^{\circ} \)
D. 15


(a) Account for the following:
(i) \( N H_{3} \) acts as a Lewis base.
(ii) \( P C l_{3} \) fumes in moist air
(iii) Fluorine shows only - 1 oxidation
state.
(b) (i) Suggest any two fluorides of Xenon.
(ii) Write a method to prepare any
one of the above mentioned Xenon
fluorides.


Which of the following is/are the feature of vertebra of mammals?
A. Centrum is amphiplatyan
B. Zygapophyses present
c. Inter vertebral disc present between two bone
D. All of the above


A sitar wire vibrates with frequency of 330 vibrations per second. If its length is increased three times and tension is
increased four times then the frequency of the wire will be
A . \( 110 \mathrm{Hz} \)
в. 220 Н
c. \( 330 H z \)
D. \( 440 \mathrm{Hz} \)


Write the marks wise frequencies in the following frequency distribution table.
Marks \( \begin{array}{cccc}\text { Up } & \text { Up } & \text { Up } & \text { Up } \\ \text { to } & \text { to } & \text { to } & \text { to } \\ \mathbf{5} & \mathbf{6} & \mathbf{7} \$ & \mathbf{8}\end{array} \)
No of
11
student


Which of the following statement is
correct?
A. The earth's surface is negatively charged
B. The earth's surface is positively charged
C. The earth's surface is neutral
D. None of the above


Secretion of gastric juice is stopped by
A. Gastrin
B. Secretin
c. Enterogastrone
D. cholecystokinin


The \( 11^{t h} \) term and the \( 21^{s t} \) term of an
A.P. are 16 and 29 respectively, then find
the \( 34^{t h} \) term


Which one has the highest boiling point?
A \( \cdot H_{2} O \)
в. \( H_{2} \) Те
c. \( H_{2} \)
D. \( H_{2} S e \)


In a long hollow vertical metal pipe a magnet is dropped. During its fall, the acceleration of magnet
A. will decrease linearly
B. will decrease upto a value which is less than \( g \).
c. will decrease to zero and will attain a terminal speed
D. may increase or decrease


Select the correct statements about
enzymes.
This question has multiple correct options
A. Enzymes are biological catalysts found in organisms
B. All enzymes are protein
C. Enzymes can catalyse any reaction
D. Enzyme's activity is optimum at \( 27^{\circ} \mathrm{C} \)


If you multiply a number by 3 and then add \( 40, \) the result is the same as if you
first add 17 and then multiply by 2 What is the result if you subtract 9 from
the number and then multiply by \( 4 ? \)
A. -60
B. -72
c. -84
D . -108


Differentiate the following functions
with respect to \( \boldsymbol{x} \) \( \sin ^{-1}\left(2 x^{2}-1\right), 0<x<1 \)


\( (x-4) \) is geometric mean of \( (x-5) \)
and \( (x-2) \) find \( x \)


\( A M \) is a median of a triangle \( A B C . \) Is \( A B+B C+C A>2 A M ? \)
(Consider the sides of triangles \( \Delta A B M \text { and } \Delta A M C) \)
A. True
B. False


What is the value of \( y \) if \( (y, 3),(-5,6) \)
and (-8,8) are collinear?
A . -1
B . 2
c. \( \frac{1}{2} \)
D. \( -\frac{1}{2} \)


Compounds which contains only carbon and hydrogen are termed as:
A. hydrocarbons
B. organic compounds
c. inorganic compounds
D. carbohydrogens


Calculate the mean free path in \( C O_{2} \) at
\( 27^{\circ} \mathrm{C} \) and a pressure of \( 10^{-9} \) bar.

Molecular diameter of \( C O_{2} \) is 500 pm. Given \( : \mathrm{R}=\frac{25}{3} J . m o l^{-1} K^{-1}, \sqrt{2}= \)
\( \mathbf{1} . \mathbf{4}, \boldsymbol{\pi}=\frac{\mathbf{2 2}}{\mathbf{7}}, \boldsymbol{N}_{\boldsymbol{A}}=\mathbf{6} \times \mathbf{1 0}^{\mathbf{2 3}} \mathbf{j} \)
A \( \cdot 3.788 \times 10^{3} \mathrm{cm} \)
В . \( 7.47 \times 10^{3} \mathrm{cm} \)
\( \mathbf{c} \cdot 6.43 \times 10^{5} \mathrm{cm} \)
D. None of these


Match the items in Column I with
Column II and choose the correct
alternative.
\( \begin{array}{ll}\text { Column I } & \text { Column II } \\ \text { A. Tubercular storage roots } & \text { 1. Tinospora } \\ \text { B. Pneumatophores } & \text { 2. Heritiera } \\ \text { C. Haustoria } & \text { 3. Asparagus } \\ \text { D. Prop-roots } & \text { 4. Viscum } \\ \text { E Assimilatory roots } & \text { 5. Screwpine }\end{array} \)
A . A- 2, B- 3, C- 4, D- 5, E- -
B. A- \( 3, \) B-4, C- 5, D-1, E-2
c. \( A-3, \) В- \( 1, \) С- \( 2, \) D- \( 5, \) Е- 4
D. A- 5, B- 4, C- 3, D- 2, E- -
E. \( A-3, B-2, C-4, D-5 \)


Plant shows adaptations to hot and dry
climates is
I. CAM
II. Mycorrhizae
III. \( C_{4} \) photosynthesis
A. I only
B. II only
c. I and ॥
D. I and III
E . ।, ॥।, and III


A pack of coffee powder contains a mixture of \( x \) gms of coffee and \( y \) gms of choco. The amount of coffee powder is greater than that of chocolate and each
pack weights at least 10 g. Which of the following inequalities describe the given condition? This question has multiple correct options
A. \( x<y \)
в. \( x+y \geq 10 \)
c. \( x+y \leq 10 \)
D. \( x>y \)


Find the term independent of \( x \) in the
expansion of
\( \left(1+x+2 x^{2}\right)\left(\frac{3 x^{2}}{2}-\frac{1}{3 x}\right)^{9} \)


Which of the following reactions is used
to make a fuel cell?
\( \mathbf{A} \cdot 2 H_{2}(g)+O_{2}(g) \rightarrow 2 H_{2} O(l) \)
B. \( 2 F e(s)+O_{2}(g)+4 H^{+}(a q) \rightarrow 2 F e^{2+}(a q)+2 H_{2} O(l) \)
\( \mathbf{c} \cdot P b(s)+P b O_{2}(s)+2 H_{2} S O_{4}(a q) \rightarrow 2 P b S O_{4}(s)+ \)
\( H_{2} O(l) \)
D. \( C d(s)+2 N i(O H)_{3}(s) \rightarrow C d O(s)+2 N i(O H)_{2}+ \)
\( 2 H_{2} O(l) \)


Nuclidic masses of \( _{7}^{14} \mathrm{N} \) and \( _{7}^{15} \mathrm{N} \) are mixed to give average atomic mass of
14.1. The ratio of \( 14 \mathrm{N} \) and \( 15 \mathrm{N} \) mixed is : 7 7


Integrate \( \int \frac{1}{\sqrt{4-x^{2}}} d x \)


The higher concentration of which gas in air can cause stiffness of flower
buds?
\( A \cdot S O_{2} \)
в. \( N O_{2} \)
\( c \cdot C O_{2} \)
D. \( C O \)


From the given venn diagram, is \( \boldsymbol{A} \cap \boldsymbol{B}^{\prime} \)
and \( A-B \) are equal. \( (\text { Enter } 1 \) if true or
otherwise


Plants excrete gases through
A. Microscopic pores in leaves.
B. Small porous roots
c. Flowers
D. Seeds


If concentration of two weak acids are
different and degree of ionization \( (\alpha) \) is very less, then their relative strength can be compared by:
This question has multiple correct options
\( \mathbf{A} \cdot \frac{\left[H^{+}\right]_{1}}{\left[H^{+}\right]_{2}} \)
в. \( \frac{\alpha_{1}}{\alpha_{2}} \)
c. \( \frac{C_{1} \alpha_{1}}{C_{2} \alpha_{2}} \)
D. \( \frac{K_{a_{1}} C_{1}}{K_{a_{2}} C_{2}} \)


In autogenic succession,
A. The community itself modifies its own environment thus causing its own replacement by a new community.
B. Early dominance of heterotrophs.
C. Replacement of existing communities due to external conditions.
D. Early and continued dominance of autotrophic organisms.
E. There is previously built substratum with already existing matter.


A particle is acted upon by a force of
constant magnitude which is always perpendicular to the velocity of the
particle The motion of he particle takes place in a plane It follows that
A. Its velocity is constant
B. Its acceleration is constant
C. Its kinetic energy is conserved
D. None of these


A plane is flying horizontally at \( 98 m s^{-1} \) and releases an object which reaches the ground in \( 10 s . \) The angle made by it while hitting the ground is:
A . 55
B . 45
c. 60
D. 75


A man crosses a river in a boat. If he
crosses the river in minimum time he
takes 10 minutes with a drift \( 120 \mathrm{m} \). If he
crosses the river taking shortest path, he takes 12.5 minute, find
(i) width of the river,
(ii) velocity of the boat with respect to water, (iii) speed of
the current
Assume \( \boldsymbol{v}_{\boldsymbol{b} / \boldsymbol{r}}>\boldsymbol{v}_{\boldsymbol{r}} \)


The combined state of metals are
called:
A. Mineral
B. Gangue
c. Flux
D. Native form


What is the measure of complementary
angle of \( 32^{\circ} ? \)
A \( \cdot 48^{\circ} \)
B. 78
\( c \cdot 58 \)
\( D \cdot 68 \)


If 30 men can reap a field in 14 days, in
how many days will 20 men reap it?


Three concentric spherical conductors
are shown in figure. Determine the
equivalent capacitance of the system
between \( B \) and \( C \).


Which symbol is used for the element hydrogen?
A . \( H g \)
в. \( H e \)
c. \( H \)
D. Но
E. \( H f \)


The average weight of 40 balls is 5 grams. When the weight of the basket is added to the weight of balls, the average
increased by 0.5 grams. Find the weight of the basket.


In an experiment, setup \( A \) consists of two parallel wires which carry currents
in opposite directions as shown in the figure. \( A \) second setup \( B \) is identical to
setup \( A \), except that there is a metal
plate between the wires.

Let \( F_{A} \) and \( F_{B} \) be the magnitude of the
force between the two wires in setup \( \boldsymbol{A} \)
and \( B, \) respectively, then which of the following condition is correct:
\( \mathbf{A} \cdot F_{A}>F_{B} \neq 0 \)
B . \( F_{A}<F_{B} \)
c. \( F_{A}=F_{B} \neq 0 \)
D. \( F_{A}>F_{B}=0 \)


A solid sphere of mass \( M, \) radius \( R \) and
having moment of inertia about an axis passing through the centre of mass as
\( I, \) is recast into a disc of thickness \( t \)
whose moment of inertia about an axis
passing through its edge and perpendicular to its plane remains \( \boldsymbol{I} \) Then, radius of the disc will be:
A \( \cdot \frac{2 \mathrm{R}}{\sqrt{15}} \)
B \( \cdot R \sqrt{\frac{2}{15}} \)
c. \( \frac{4 \mathrm{R}}{\sqrt{15}} \)
D. \( \sqrt{\frac{2 R}{15}} \)


Derive the relationship showing
variation in rate constant with
temperature


\( \left|\begin{array}{ccc}1+a & 1 & 1 \\ 1 & 1+b & 1 \\ 1 & 1 & 1+c\end{array}\right|= \)
\( \boldsymbol{X} \boldsymbol{a b c}\left(1+\frac{1}{\boldsymbol{a}}+\frac{1}{\boldsymbol{b}}+\frac{1}{c}\right) . \) Find the value
of \( \boldsymbol{X} \)


The displacement \( x(\text { in } m), \) of a particle of mass \( m(\text { in } K g) \) is related to time \( t \) (in
\( \sec ) \) by \( t=\sqrt{x}+3 . \) Find the work done
in the first six seconds. (in mJ)


Find the smallest number by which a
given number must be multiplied to obtain a perfect cube 72


Write the IUPAC name of the given
compound.


If \( \left(2 x^{2}-3 x+1\right)\left(2 x^{2}+5 x+1\right)=9 x^{2} \)
A. For real root
B. Two real and two imaginary root
c. Four imaginary roots
D. None of the above


Assertion
Let \( \boldsymbol{f}: \boldsymbol{X} \rightarrow \boldsymbol{Y} \) be a function defined by \( f(x)=2 \sin \left(x+\frac{\pi}{4}\right)-\sqrt{2} \cos x+c \)
Statement I: For set \( \boldsymbol{X}, \boldsymbol{x} \in\left[\mathbf{0}, \frac{\boldsymbol{\pi}}{\mathbf{2}}\right] \cup \)
\( \left[\pi, \frac{3 \pi}{2}\right], f(x) \) is one-one function
Reason Statement II: \( \boldsymbol{f}^{\prime}(\boldsymbol{x}) \geq \mathbf{0}, \boldsymbol{x} \in\left[\mathbf{0}, \frac{\boldsymbol{\pi}}{\mathbf{2}}\right] \)
A. Statementl is true, statement II is also true:
Statement II is the correct explanation of Statement
B. Statement I is true, Statement II is also true:
Statement II is not the correct explanation of Statement
c. Statement I is true, Statement II is false
D. Statement l is false, Statement II is true


What will be the electric flux through
the sphere \( S_{1} \) if a medium of dielectric
constant \( \epsilon_{r} \) is introduced in the
space inside \( S_{1} \) in place of air
A. \( \frac{20}{\epsilon \epsilon_{n}} \)
в. \( \frac{40}{\epsilon_{0} \epsilon_{r}} \)
c. \( \frac{20 \epsilon_{c}}{\epsilon_{0}} \)
D. \( \frac{406}{6} \)


The component of a vector \( \vec{a} \) along and perpendicular to a nonzero vector \( \overrightarrow{\boldsymbol{b}} \) is:


Among \( L i C l, R b C l, B e C l_{2} \) and \( M g C l_{2} \)
which two are the highest and the lowest ionic compounds?
A. \( L i C l \) \& \( R b C l \)
в. \( R b C l \& B e C l_{2} \)
c. \( R b C l \& M g C l_{2} \)
D. \( M g C l_{2} \& B e C l_{2} \)


The value of the magnetic moment of a
particular ion is 2.83 Bohr magneton. The ion is :
A \( \cdot F e^{2} \)
B. \( N i^{2} \)
\( \mathbf{c} \cdot M n^{2+} \)
D. \( C o^{3} \)


In absence of sunlight,chlorine is dissolved in water.Oxidation state of
chlorine is changed to:
This question has multiple correct options
A . -1
B. +1
\( c \cdot+3 \)
D. +5


Figure shows the stress-strain graphs
for materials \( A \) and \( B \).
From the graph it follows that:
This question has multiple correct options
A. material A has a higher Young's modulus
B. material B is more ductile
\( c . \) material A is more brittle
D. material A can withstand a greater stress


On boiling an aqueous solution of
\( K C l O_{3} \) with \( I_{2} \) the products obtained
are:
A \( . K I O_{3}+C l \)
в. \( K C l+I_{2} O_{5} \)
c. \( K I O_{4}+C l_{2} \)
D. none of the above


Three capacitors each of capacitance
\( 9 p F \) are connected in series as shown
in figure.
(a) What is the total capacitance of the
combination?
(b) What is the potential difference across each capacitor, if the
combination is connected to a 120 volt
supply?


Complete oxidation of \( 1 \mathrm{gm} \) of glucose molecule gives rise to
A. 68,60,000 cal
B. 6,86,000 cal
c. 68,600 cal
D. 6,800 cal


Which one is the correct option for the structure and function of a
nephron?
A . Glomerulus- filtration
B. Proximal convoluted tubule- reabsorption
c. Both A and B
D. Distal convoluted tubule- filtration


Four pieces of wooden sticks \( P, Q, R \) and S are placed along the length of \( 15 \mathrm{cm} \) long scale as shown in figure. What is the average length of these sticks?
A . 2.0
B. 2.5 \( \mathrm{cm} \)
c. \( 2.6 \mathrm{cm} \)
D. 2.9 \( \mathrm{cm} \)


IUPAC name of given compound is :
A. 5,6 -diethyldec- 4 -ene
B. 5,6 -diethyldec- 5 -ene
c. 5,6 -diethyldec-3-ene
D. 5,6 -diethyldecene


Assuming the earth to be a sphere of uniform mass density, how much would a body weigh (in \( \mathrm{N} \) ) half way down to the center of the earth if it weighed 250 N on the surface?


The force of cohesion tension exceeds
root pressure on a
A. Rainy day
B. Foggy morning
c. sunny day
D. Full moon night


In glycolysis, the rate limiting enzyme
is
A. Glucokinase
B. Phosphofructokinase
c. Phosphohexose isomerase
D. Aldolase


An example of solid-solid system is:
A. smoke
B. coke
c. synthetic gems
D. pumice stone


A sphere of density \( d \), specific heat
capacity \( c \) and radius \( r \) is hung by a
thermally insulating thread in an enclosure which is kept at lower
temperature than the sphere. The temperature of the sphere starts to drop at a rate which is proportional to:
A \( \cdot c / r^{3} d \)
B . \( 1 / r^{3} d c \)
\( \mathbf{c} \cdot 3 r^{3} d c \)
D. \( 1 / r d c \)


A diver stands at the top of a platform
that is 15 meters high.After diving, she challenges herself from a cliff that is 30
meters high.since she is twice as far
from the surface of the earth when she
is on the cliff as compared with the diving board, how does her weight on the cliff compare with her weight on the
diving board?
A. Her weight on the cliff is half as much
B. Her weight on the cliff is one-fourth as much
C. Her weight on the cliff is about the same
D. Her weight on the cliff is twice as much
E. Her weight on the cliff is four times as much


If the distance between the earth and
sun were to be doubled from its present value, the number of days in a year
would be :
A . 64.5
в. 1032
\( c \cdot 182.5 \)
D. 730


Equation 1:
and 2 \( \boldsymbol{x} \) ; -2 \( \mathbf{0} \) 4
\( 4 \quad 2 \)
Equation 2:
\( \boldsymbol{x} \) \( -8 \quad-4 \) \( \mathbf{0} \) What is and 4
-8 -7 7 -6 -5
The linear equations represented by the data shown in the above tables form a
system, what is the \( x- \) coordinate of
the solution to that system?
\( \mathbf{A} \cdot 4 \)
B. 8
\( \mathbf{c} .0 \)
D. -6


The vector \( (\cos \alpha \cos \beta) \vec{i}+ \)
\( (\cos \alpha \sin \beta) \vec{j}+\sin \alpha \vec{k} \) is
A. Null vector
B. unit vector
C . parallel to \( (\vec{i}+\vec{j}+\vec{k}) \)
D. a vector parallel to \( (2 \vec{i}+\vec{j}-\vec{k}) \)


What is transcription?


locate the point representing the
complex numbers \( z \) on the Argand diagram for which
\( |z-1|=|z-3|=|z-i| \)


Explain Werner's theory of coordinate compounds with suitable examples?


If \( \boldsymbol{a}=\boldsymbol{x} \boldsymbol{i}+(\boldsymbol{x}-\mathbf{1}) \boldsymbol{j}+\boldsymbol{k} \) and \( \boldsymbol{b}=(\boldsymbol{x}+ \)
1) \( i+j+a k \) always make an acute
angle with each other for every value of
\( \boldsymbol{x} \boldsymbol{\epsilon} \boldsymbol{R}, \) then
A \( . a \epsilon(-\infty, 2) \)
В. \( a \epsilon(2,-\infty) \)
c. \( a \epsilon(-\infty, 1) \)
D. \( a \epsilon(1,-\infty) \)


An oxide \( X \) in its normal form is almost
non-reactive due to very high \( X-0 \) bond enthalpy. It resists the attack by halogens, hydrogen and most of acids and metals even at elevated
temperatures. It is only attacked by HF and NaOH. The oxide X is :
A. \( \operatorname{si} 0_{2} \)
в. \( C O_{2} \)
\( \mathrm{c} \cdot \operatorname{sn} \mathrm{O}_{2} \)
D. \( P b O_{2} \)


For emission line of atomic hydrogen
from \( n_{i}=8 \) to \( n_{f} \) - the plot of wave number \( (\bar{v}) \) against \( \left(\frac{1}{n^{2}}\right) \) will be: (The Rydberg constnt, \( R_{H} \) is in wave number
unit).
A . linear with slope \( -R_{H} \)
B. linear with intercept - \( R_{H} \)
c. non linear
D. linear with slope \( R_{H} \)


Consider the situation of figure. The
work done in taking a point charge from
\( P \) to \( A \) is \( W_{A}, \) from \( P \) to \( B \) is \( W_{B} \) and from
\( P \) to \( C \) is \( W_{C} . \) Then :
\( \mathbf{A} \cdot W_{A}<W_{B}<W_{C} \)
\( \mathbf{B} \cdot W_{A}>W_{B}>W_{C} \)
\( \mathbf{c} \cdot W_{A}=W_{B}=W_{C} \)
D. None of these


The top of a water tank is open to air
and its water level is maintained. It is
giving out \( 0.74 m^{3} \) water per minute through a circular opening of \( 2 \mathrm{cm} \) radius in its wall. The depth of the
centre of the opening from the level of
water in the tank is close to :
A. \( 9.6 m \)
в. \( 4.8 \mathrm{m} \)
\( c .2 .9 m \)
D. \( 6.0 m \)


Which one shows the correct
hierarchical arrangement
A. Kingdom \( \leftarrow \) Division \( \leftarrow \) Class \( \leftarrow \) Order Family \( \leftarrow \) Species \( \leftarrow \) Genus
B. Kingdom \( \leftarrow \) Division \( \leftarrow \) Order \( \leftarrow \) Class \( \leftarrow \) Family \( \leftarrow \) Genus \( \leftarrow \) Species
C. Kingdom \( \rightarrow \) Division \( \rightarrow \) Order \( \rightarrow \) Class \( \rightarrow \) Family \( \rightarrow \) Genus \( \rightarrow \) Species
D. Kingdom \( \rightarrow \) Division \( \rightarrow \) Class \( \rightarrow \) Order \( \rightarrow \) Family \( \rightarrow \) Genus \( \rightarrow \) Species
E. Kingdom \( \rightarrow \) Division \( \rightarrow \) Family \( \rightarrow \) Order \( \rightarrow \) Class \( \rightarrow \) Genus \( \rightarrow \) Species


In the given figure, \( p \| q \) and \( r \| s . \) Find
the values of \( x, y \) and \( z \)


Electronic configurations of few
elements are given below. Mark the
incorrect match.
A \( \cdot l s^{2} 2 s^{2} 2 p^{5} \) - Most electronegative element
B. \( l s^{2} 2 s^{2} 2 p^{3}- \) An element belonging to 3rd period and 5 th
group
C \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 3 d^{8} 4 s^{2}- \) A d-block element
D. \( 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} \) - An element from 18th group


Organic compounds will always contain:
A. carbon
B. hydrogen
c. nitrogen
D. sulphur


Which is true regarding an aqueous
Solution of \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4} \) at \( \boldsymbol{2} \boldsymbol{5}^{\boldsymbol{O}} \boldsymbol{C} \boldsymbol{?} \)
A. It has a very large acid ionization constant
B. It has a bitter taste
C. The concentration of \( \left[O H^{-}\right]>1.0 \times 10^{-7} \mathrm{M} \)
D. It is a weak electrolyte
E. It can be formed by the reaction of a metal oxide and water


Which pollutant gas is produced by the decomposition of vegetation?
A. Carbon monoxide
B. Methane
c. Nitrogen dioxide
D. Sulfur dioxide


In cyclotron the resonance condition is:
A. the frequency of revolution of charged particle is equal to the frequency of A.C. voltage sources
B. the frequency of revolution of charged particle is equal to the frequency of applied magnetic field
C. the frequency of revolution of charged particle is equal to the frequency of rotation of earth
D. the frequency of revolution of charged particle, frequency of A.C. source and frequency of magnetic field are equal


Assertion
The gas is heated, if its temperature is less than its inversion temperature in
Joule-Thomson effect.
Reason
Heating effect in gas is noticed during
Joule-Thomson effect when \( \boldsymbol{T}>\boldsymbol{T}_{i} \)
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


Fill in the blanks:
A quantity which can be completely represented by magnitude alone is called


Find the derivatives of the following
functions.
\( \log _{2}\left(2 x^{2}-3 x+1\right) \)


A magnetic needle free to rotate in a vertical plane parallel to the magnetic meridian has its north tip pointing
down at \( 22^{\underline{0}} \) with the horizontal. The
horizontal component of the earth's magnetic field at the place is known to be 0.35 G. Determine the magnitude of the earth's magnetic field at the place.


Which of the following shall form an octahedral complex?
This question has multiple correct options
A \( \cdot d^{4} \) (low spin)
B. \( d^{8} \) (high spin)
c. \( d^{6} \) (low spin)
D. None of these


\( \frac{41 x-12}{x^{2}-16}=\frac{4 x+3}{x-4} \)


\( \Delta A B C \quad \) and \( \Delta D B C \quad \) are two
isosceles triangle on the same base BC
and vertices \( A \) and \( D \) are on the same
side of BC. if AD is extended to intersect
\( \mathrm{BC} \) at \( \mathrm{p}, \) show that AP is the perpendicular bisector of BC


An \( \alpha \) -particle describes a circular path of radius \( r \) in a magnetic field \( B \). The
radius of the circular path described by the proton of same energy in the same magnetic field is :
A \( \cdot \frac{r}{2} \)
B.
\( c \cdot \sqrt{2} r \)
D. \( 2 r \)


Which is not one of the laws of chemical
combinations?
A. Law of multiple proportion
B. Law of conservation of mass
C. Law of conservation of energy
D. Law of definite proportion


Fill in the blank:
Meteors are also known as
stars.
A. twinkling
B. pole
c. shooting
D. dwarf


A particle of mass \( 2 \mathrm{kg} \) is on a smooth
horizontal table and moves in a circular
path of radius 0.6m. The height of the table from the ground is \( 0.8 \mathrm{m} \) If the angular speed of the particle is
12rads \( ^{-1} \), the magnitude of its angular momentum about a point on the ground right under the centre of the circle is:
A. \( 8.64 \mathrm{kg} \mathrm{m}^{2} s^{-1} \)
B. \( 11.52 \mathrm{kg} \mathrm{m}^{2} \mathrm{s}^{-1} \)
c. \( 14.4 \mathrm{kg} \mathrm{m}^{2} s^{-1} \)
D. \( 20.16 \mathrm{kg} \mathrm{m}^{2} \mathrm{s}^{-1} \)


Rocket-powered sleds are used to test the human response to acceleration. If a rocket-powered sled is accelerated to a speed of \( 444 m / s \) in 1.83 seconds, then
what is the acceleration? \( \left(\operatorname{in} m / s^{2}\right) \)
A. \( 243 m / s / s \)
B. \( 24 m / s / s \)
c. \( 23 m / s / s \)
D. \( 43 m / s / s \)


\( g(x)=\log \left(\frac{2+x}{2-x}\right) \) for \( 0<x<2 \)
find the value of \( \frac{1}{2} g\left[\frac{8 x}{4+x^{2}}\right] \)


Assertion: Increasing the temperature increases the reaction rate.
Reason: At high temperatures, molecules or atoms tend to be further
apart.
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
E. Both Assertion and Reason are false


In a AC circuit the voltage and current are described by \( V= \) \( 200 \sin \left(319 t-\frac{\pi}{6}\right) v o l t s \) and \( i= \)
\( \mathbf{5 0} \sin \left(\mathbf{3 1 4 t}+\frac{\boldsymbol{\pi}}{\mathbf{6}}\right) \boldsymbol{m} \boldsymbol{A} \) respectively. The
average power dissipated in the circuit
is
A. 2.5 watts
B. 5.0 watts
c. 10.0 watts
D. 50.0 watts


Using VBT theory describe shape of
\( \boldsymbol{X} \boldsymbol{e} \boldsymbol{O}_{4} \)


The compound statement, "If you won
the race; then you did not run faster
than others" is equivalent to
A. "If you won the race, then you ran faster than others""
B. "If you ran faster than others, then you won the race""
C. "If you did not win the race, then you did not run faster than others""
D. "If you ran faster than others, then you did not win the race"


A coin is tossed three times. Find
\( \boldsymbol{P}(\boldsymbol{A} / \boldsymbol{B}) \) in given cases:
\( A=A t \) most two tails, \( B=A t \) least one
tail.


A plane meets the axes in \( A, B \) and \( C \)
such that centroid of the \( \triangle A B C \) is
\( (1,2,3) . \) The equation of the plane is
A \( \cdot x+\frac{y}{2}+\frac{z}{3}=1 \)
В \( \cdot \frac{x}{3}+\frac{y}{6}+\frac{z}{9}=1 \)
c. \( x+2 y+3 z=1 \)
D. None of these


The graph of the linear equation \( 2 x- \)
\( y=4 \) cuts \( x \) -axis at
A \( .(2,0) \)
в. (-2,0)
c. (0,-4)
D. (0,4)


Calculate the extension of the steel wire
and the energy stored in it.
A . 45 J
в. 4.5 Л
c. \( 0.45 J \)
D. 0.045


Fill in the blanks
If nitrogen and sulphur both are present in an organic compound and it is fused with sodium. The sodium compound formed is


When the source voltage increases in a zener regulator, which of these currents
remains approximately constant?
A. Series current
B. zener current
c. Load current
D. Total current


A unit cube is cut into two equal halves by a plane section parallel to one of its faces. The total surface area of both the
halves is
A. 6 sq, units
B. 7 sq, units
c. 8 sq, units
D. 9 sq, units


Draw a circle of radius \( 6 \mathrm{cm} \) and
construct tangents to it from an external point \( 10 \mathrm{cm} \) away from the
centre. Measure and verify the length of
the tangents.


The reacting surface is reduced when the particle size is:
A . small
B. large
c. moderate
D. both a and c


An automobile travelling with a speed of \( 60 k m / h, \) can brake to stop within a
distance of \( 20 m . \) If the car is going
twice as fast, i.e. \( 120 k m / h \), the
stopping distance will be:
A . \( 20 m \)
в. \( 40 m \)
\( c .60 m \)
D. \( 80 m \)


Which one of the following is an emulsion?
A. Milk
B. Soap lather
c. Butter
D. Vanishing Cream


The splitting of white light into constituent colors is called


Body cavity of animals derived from Blastocoel is known as
A. Pseudocoelom
B. Schizocoelom
c. Enterocoelom
D. Haemocoel


Find the number of molecule(s) which
do not exist
\( \boldsymbol{N} \boldsymbol{C l}_{3}, \quad \boldsymbol{P C l}_{3}, \quad \boldsymbol{P C l}_{5}, \quad \boldsymbol{N C l}_{5} \)


Which one of the following is an elementary symmetric function of
\( \boldsymbol{x}_{1}, \boldsymbol{x}_{2}, \boldsymbol{x}_{3}, \boldsymbol{x}_{4} \)
A. \( x_{1} x_{2} x_{3}+x_{2} x_{3} x_{4} \)
в. \( x_{1} x_{2}+x_{2} x_{3}+x_{3} x_{1} \)
C \( \cdot x_{1}^{2}+x_{2}^{2}+x_{3}^{2}+x_{4}^{2} \)
D. \( x_{1} x_{2}+x_{1} x_{3}+x_{1} x_{4}+x_{2} x_{3}+x_{2} x_{4}+x_{3} x_{4} \)


A sample of ammonium phosphate, \( \left(N H_{4}\right)_{3} P O_{4}, \) contains 6 moles of
hydrogen atoms. The number of moles of oxygen atoms in the sample is:
A.
B. 2
\( c \cdot 4 \)
\( D \cdot 6 \)


At \( 25^{\circ} C,_{-}-_{-}-- \) produces an aqueous
solution with \( p H>7 \)
A. Arrhenius acid
B. Arrhenius base
c. Buffer
D. Indicator
E. Salt


\( \left|\begin{array}{lll}\boldsymbol{a}+\boldsymbol{b} & \boldsymbol{b}+\boldsymbol{c} & \boldsymbol{c}+\boldsymbol{a} \\ \boldsymbol{b}+\boldsymbol{c} & \boldsymbol{c}+\boldsymbol{a} & \boldsymbol{a}+\boldsymbol{b} \\ \boldsymbol{c}+\boldsymbol{a} & \boldsymbol{a}+\boldsymbol{b} & \boldsymbol{b}+\boldsymbol{c}\end{array}\right|=\boldsymbol{K}\left|\begin{array}{lll}\boldsymbol{a} & \boldsymbol{b} & \boldsymbol{c} \\ \boldsymbol{b} & \boldsymbol{c} & \boldsymbol{a} \\ \boldsymbol{c} & \boldsymbol{a} & \boldsymbol{b}\end{array}\right| \)
\( \operatorname{then} K= \)
A . 1
B. 2
\( c \)
\( D \)


A passenger in moving train tosses a coin which falls behind him. It means
that the motion of the train is
A. Accelerated
B. Uniform
C. Retarded
D. Circular motion


If \( \boldsymbol{y}=\sin ^{-1}\left(3^{-x}\right), \) then \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}= \)
A \( \cdot \frac{-\log 3}{\sqrt{3^{2 x}-1}} \)
в. \( \frac{3^{x} \log 3}{\sqrt{3^{2 x}-1}} \)
c. \( \frac{-3^{-x} \log 3}{\sqrt{3^{2 x}-1}} \)
D. \( \frac{\log 3}{3^{x} \sqrt{3^{2 x}-1}} \)


Which is expected to be more stable, (I)
\( \boldsymbol{O}_{2} \boldsymbol{N} \boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{O}^{-} \) or \( (\|) \boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{O} \)
and why?
A. (I) due to resonance
B. (II) due to resonance
c. (I) due to inductive effect
D. (II) due to inductive effect


For energy density, power and intensity of any wave choose the correct options.
A \( \cdot u= \) energy density \( =\frac{1}{2} \rho \omega^{2} A^{2} \)
B. \( P= \) power \( =\frac{1}{2} \rho \omega^{2} A^{2} v \)
c. \( _{I}= \) intensity \( =\frac{1}{2} \rho \omega^{2} A^{2} S v \)
D. \( _{I}=\frac{P}{S} \)


Which of the following substance can be used as a raw material for obtaining
alcohol?
A. Potatoes
B. Molasses
c. Maize
D. All of the above


Two metallic plates are kept parallel to
one another and charges are given to
them as shown in figure. Find the charge on all the four faces


A body is said to be in static
Equilibrium?
A. When it is moving around a circular path
B. When it is a. rest
C. When it is moving with uniform velocity
D. When it is accelerated by the external force


Find the solution of the equation \( x+ \)
\( 2 y=6 \) from the options given below:
B. (0,2),(6,0),(2,2) and (4,1)
D. (0,3),(6,0),(1,2) and (4,1)


Nylon is not a
A. condensation polymer
B. polyamide
C. copolymer
D. homopolymer


Comment on the hole and electron
concentration in an intrinsic
semiconductor?


If the temperature scale is changed
from \( ^{\circ} \boldsymbol{F} \) to \( ^{\circ} \boldsymbol{C} \), the numerical value of
specific heat will
\( A \). increase
B. decrease
c. remain unchanged
D. Nothing can be said


Assertion
A body can have acceleration even if its velocity is zero at a given instant of time.
Reason
A body is numerically at rest when it reverses its direction.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


If \( \int \log (\sqrt{1-x}+\sqrt{1+x}) d x= \)
\( \boldsymbol{x} \boldsymbol{f}(\boldsymbol{x})+\boldsymbol{A} \boldsymbol{x}+\boldsymbol{B} \sin ^{-1} \boldsymbol{x}+\boldsymbol{c}, \) then
A \( . f(x)=\log (\sqrt{1-x}+\sqrt{1+x}) \)
B. \( _{A}=-\frac{1}{3} \)
\( c \cdot_{B}=\frac{2}{3} \)
D. \( _{B}=-\frac{1}{2} \)


A uniform electric field of magnitude \( \mathbf{1 0 0} V / \boldsymbol{m} \) in space is directed along the
line \( y=3+x . \) Find the electric
potential difference between (1,3) and (3,1)
A. \( 100 V \)
в. \( 200 \sqrt{2} V \)
c. \( 200 V \)
D.


Assertion
Presence of connective tissue inside the
brain is essential for conduction of
nerve impulse
Reason
Connective tissue hold together the
nerve cells of brain
A. If both the assertion and the reson are true and the reason is correct explanation of the assertion.
B. If both the assertion and the reson are true but the reason is not correct explanation of the assertion
c. If the assertion is true but the reason is false
D. If both the assertion and reason are false


The closest relative of modern man is co
nsidered to be
A. Chimpanzee
B. Orangutan
c. Apes
D. Gibbon


1-Pentene and 3-methyl-1-butene are
A. chain isomers
B. position isomers
c. functional isomers
D. metamers


Let three matrices \( A=\left[\begin{array}{ll}2 & 1 \\ 4 & 1\end{array}\right] ; B= \)
\( \left[\begin{array}{ll}\mathbf{3} & \mathbf{4} \\ \mathbf{2} & \mathbf{3}\end{array}\right] \) and \( C=\left[\begin{array}{cc}\mathbf{3} & -\mathbf{4} \\ -\mathbf{2} & \mathbf{3}\end{array}\right] \) then
\( \boldsymbol{t}_{\boldsymbol{r}}(\boldsymbol{A})+\boldsymbol{t}_{\boldsymbol{r}}\left(\frac{A B C}{2}\right)+\boldsymbol{t}_{\boldsymbol{r}}\left(\frac{\boldsymbol{A}(\boldsymbol{B C})^{2}}{4}\right)+ \)
\( \boldsymbol{t}_{\boldsymbol{r}}\left(\frac{\boldsymbol{A}(\boldsymbol{B} C)^{3}}{\boldsymbol{8}}\right)+\ldots+\infty \)
\( A \cdot 6 \)
B.
c. 12
D. none of these


When the temperature is increased:
A. speed with which the molecules vibrate increases
B. speed with which the molecules vibrate decreases
C. there is no change in the speed of the molecules
D. the speed of the molecules remains constant


A projectile is fired with an initial speed
of \( 500 \quad m s^{-1} \) horizontally from the top
of a cliff of height \( 19.6 \mathrm{m} \). At what distance from the foot of the cliff does it
strike the ground?


Define R.Q. What is its significance?


Phosphodiesterases rapidly catalyze hydrolysis of sugar phosphate bond in nucleic acids.

The first digit of their E,C number can be
A . 1
B. 2
\( c .3 \)
D. 6


A uniform electric field of magnitude \( 290 V / m \) is directed in the positive \( x \) direction. \( A+13.0 \mu C \) charge moves from the origin to the point \( (x, y)= \) \( (20.0 c m, 50.0 c m) \)
What is the change in the potential
energy of the charge field system?
A . \( -754 J \)
в. \( -754 m J \)
c. \( -754 k J \)
D. \( -754 \mu J \)


Which value of \( x \) is in the solution set of
the inequality \( :-2 x+5>17 ? \)
A \( . x>-8 \)
в. \( x<-6 \)
c. \( x>-4 \)
D. \( x<12 \)


Complete the following sentence:
The potential energy of a body is the energy by virtue of its
A. motion
B. position
c. Both A and B
D. None of these


If one litre of water at \( 25^{\circ} C \) is mixed
with one litre of water at \( 45^{\circ} \mathrm{C} \) the
temperature of the water will be
\( \mathbf{A} \cdot 70^{\circ} \mathrm{C} \)
B \( \cdot 20^{\circ} \mathrm{C} \)
\( \mathrm{c} \cdot<25^{\circ} \mathrm{C} \)
\( \mathrm{D} \cdot>25^{\circ} \mathrm{C\&}<45^{\circ} \mathrm{C} \)


A man A is sitting in a car at rest
observes a man B on bike moving away
from him with velocity \( 16 m s^{-1}, \) a man
walking on road with velocity \( 2 m s^{-1} \) towards him and a bird flying with
speed \( 20 m s^{-1} \) at angle \( 37^{\circ} \) with
horizontal as shown in Fig. Find the
a. velocity of car, bird, and man C as
seen by man B.
b. velocity of car, bird and man B as
seen by man \( \mathrm{C} \)
c. velocity of car, than \( \mathrm{B} \), and man \( \mathrm{C} \) as
seen by bird:


Why are electric field lines always emanate perpendicular to a charged surface?
A. To prevent surface potential
B. To prevent surface current
c. To prevent surface polarisation
D. All of the above


A steel wire of length \( 64 \mathrm{cm} \) weighs \( 5 \mathrm{g} \). It
is stretched by a force of \( 8 N, \) what
would be the speed of transverse wave passing on it?


Which of the following has two sterioisomers?
A. None of these
B. Only I
c. only \( I I I \)
D. \( I \) and \( I I I \)


Find the place value of 4 in 543.67
A. 4000
B. 400
\( c \cdot 40 \)
D. 4


Find the derivative of \( |x|+a_{0} x^{n}+ \)
\( \boldsymbol{a}_{1} \boldsymbol{x}^{\boldsymbol{n}-1}+\boldsymbol{a}_{2} \boldsymbol{x}^{\boldsymbol{n}-\boldsymbol{2}}+\ldots+\boldsymbol{a}_{\boldsymbol{n}-1} \boldsymbol{x}+\boldsymbol{a}_{\boldsymbol{n}} \)
A \( \cdot \frac{x}{|x|}+n a_{0} x^{n-1}+(n-1) a_{1} x^{n-2}+(n-2) a_{2} x^{n-3}+\ldots .+ \)
\( a_{n-1} \)
B \( \cdot 1+n a_{0} x^{n-1}+(n-1) a_{1} x^{n-2}+(n-2) a_{2} x^{n-3}+\ldots .+ \)
\( a_{n-1} \)
C \( \cdot \frac{x}{|x|}+n a_{0} x^{n-1}+(n-1) a_{1} x^{n-2}+(n-2) a_{2} x^{n-3}+\ldots .+ \)
\( a_{n} \)
D. None of these


Give a relation \( \mathrm{R}=\{(1,2),(2,3)\} \) on the set
of natural numbers, add a minimum number of ordered pairs.
This question has multiple correct options
A. enlarged relation is symmetric
B. enlarged relation is transitive
c. enlarged relation is reflexive.
D. enlarged relation is equivalence relation


The muscular contraction in the
alimentary canal is known as
A. systole
B. Diastole
c. Peristalsis
D. Metachronal


A wire of length \( l \) carries a current \( i \) along the \( x \) -axis.A magnetic field \( \vec{B}= \) \( B_{o}(\hat{j}+\hat{k}) \) exists in the space.Find the
magnitude of the magnetic force acting on the wire.


Rate law for the following reaction; Ester \( +\boldsymbol{H}^{+} \rightleftharpoons \) Acids \( + \) Alcohol; is
\( \frac{d x}{d t}=k[\text { ester }]^{1}\left[H^{+}\right]^{0} . \) What would be the
effect on the rate if concentration of \( \boldsymbol{H}^{+} \)
ion is doubled?
A. Same
B. Doubled
c. Half
D. Data insufficient


The values of \( L, C \) and \( R \) in an \( L-C- \)
\( R \) series circuit are \( 4 m H, 40 p F \) and
100 \( \Omega \) respectively. The quality factor of the current is
A . 10
B. 100
\( c \cdot 1000 \)
D. 10,000


A \( 1.0 \mathrm{kg} \) box on a horizontal surface
experiences a 3.0 N horizontal frictional force. How much force must be applied horizontally to the box to cause it to accelerate at \( 1.0 \mathrm{m} / \mathrm{s}^{2} \) ?
A . \( 1.0 \mathrm{N} \)
в. 2.0 N
c. 3.0 N
D. 4.0 N
E. \( 5.0 \mathrm{N} \)


Which will be the least stable
resonating structure?
A \( \cdot C H_{2}=C H-C H-C H-O-C H_{3} \)
В \( \cdot \frac{\theta}{C H_{2}}-\frac{\oplus}{C H}-C H=C H-O C H_{3} \)
c. \( \stackrel{\ominus}{C H_{2}}-C H=C H-C H=\stackrel{\oplus}{O}-C H_{3} \)
D. \( C H_{2}=C H-C H-C H=O-C H_{3} \)


In a buffer solution consisting of a weak
acid and its salt, the ratio of the
concentration of salt to acid is
increased tenfold, then the \( p H \) of the solution will:
A. Increase by one
B. Increase tenfold
c. Decrease by one
D. Decrease tenfold


A coil has resistance \( 30 \Omega \) and inductive
reactance \( 20 \Omega \) at \( 50 H z \) frequency.If an
ac source of \( 200 V, 100 H z \) is connected
across the coil, the current in the coil in
the coil will be
A \( \cdot \frac{20}{\sqrt{13}} A \)
в. \( 2.0 A \)
c. \( 4.0 A \)
D. \( 8.0 A \)


If the polynomial \( 6 x^{4}+8 x^{3}-5 x^{2}+ \)
\( a x+b \) is exactly divisible by the
polynomial \( 2 x^{2}-5, \) then find the
product of the values of \( a \) and \( b \)


\( \begin{array}{cc}\boldsymbol{O H} & \boldsymbol{C H}_{3} \\ \boldsymbol{C H}_{3}-\boldsymbol{C H}-\boldsymbol{C} \boldsymbol{H}-\boldsymbol{C H}-\boldsymbol{C H O} & \mid \\ & \boldsymbol{O H}\end{array} \)
The IUPAC name is:
A. 4 -hydroxy-1-methylpentanal
B. 3, 4-dihydroxy-2-methylpentanal
c. 2 -hydroxy- 4 -methylpentanal
D. 2, 3-dihydroxy-4-methylpentanal


A fan is running at 3000 rpm. It is switched off. It comes to rest by
uniformly decreasing its angular speed in 10 seconds. The total number of
revolutions in this period.
A. 150
B. 250
c. 350
D. 300


Which one of the following pairs is correctly matched with regard to the codon and the amino acid coded by it?
A. UUU - Valine
B. AAA - Lysine
c. AUG- - cysteine
D. ccc - Alanine


The equivelent resistance between \( A \)
and \( B \) is
\( ^{A} \cdot \frac{288}{56} \Omega \)
В. \( 12 \Omega \)
\( c \cdot 8 \)
\( D \)


The area of a triangle is 5 sq.unit. If two vertices of the triangle are (2,1),(3,-2) and the third vertex is
\( (x, y) \) where \( y=x+3, \) then find the
coordinates of the third vertex.


I ne rollowıng table represents the
velocity of a moving body at different
instants of time.
Times
\( (s) \)
Velocity
\( \left(m s^{-1}\right) \)
\( 20 \quad 20 \)
The velocity-time graph is as shown in
figure. For which interval of time the
body has a uniform motion? Find the
velocity in this time interval?
\( A \cdot \) from \( t=0 \) s to \( t=5 s ; 10 m / s \)
B. from \( t=5 \) s to \( t=10 s ; 20 m / s \)
C. from \( t=10 \) s to \( t=15 s ; 20 \mathrm{m} / \mathrm{s} \)
D. from \( t=15 \) s to \( t=25 s ; 30 m / s \)


Find the smallest number by which each of the following number must be divided to obtain a perfect cube.
(i) 81
(ii) 128
(iii) 135
(iv) 192
\( \mathbf{7 0 4} \)
(vi) 625


Construct a triangle \( P Q R \) in which
\( \angle Q=60^{\circ} \) and \( \angle R=45^{\circ} \) and \( P Q+ \)
\( Q R+P R=11 \mathrm{cm} \)


\( A \) and \( B \) are events with \( P(A)= \)
\( \mathbf{0 . 5}, \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 4} \) and \( \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B})=\mathbf{0 . 3} \)
Find the probability that neither \( A \) and \( B \) occurs.


A drop of water is an example of :-
A. Micro ecosystem
B. Macro ecosystem
C. Nano ecosystem
D. Both B \& C


Evaluate
\( \int \frac{x^{3}}{\sqrt{1+2 x^{4}}} d x \)


Find the slope of the line that passes through the points (2,0) and (2,4)


For the events \( \boldsymbol{A} \) and \( \boldsymbol{B}, \boldsymbol{P}(\boldsymbol{A})= \)
\( \frac{3}{4}, P(B)=\frac{1}{5}, P(A \cap B)=\frac{1}{20} \) then
\( \boldsymbol{P}(\boldsymbol{A} / \boldsymbol{B})= \)
\( A \cdot \frac{1}{4} \)
B. \( \frac{1}{15} \)
\( c \cdot \frac{3}{4} \)
D.


Three charges, each \( +q, \) are placed at
the corners of an isosceles triangle \( A B C \)
of sides \( \mathrm{BC}, \mathrm{AC} \) and \( \mathrm{AB} \). D and \( \mathrm{E} \) are the
midpoints of BC and CA. The work done in taking a charge \( Q \) from \( D \) to \( E \) is:
(Given \( B C=A C) \)
A \( \cdot \frac{e q Q}{8 \epsilon q} \)
B. \( \frac{q Q}{4 \epsilon_{6} a} \)
C. zero
D. \( \frac{3 q Q}{4 \epsilon_{6} a} \)


One of the angles of a \( \triangle \) is \( 75 . \) If the
difference of the other two other is 35
Find the largest angle of the \( \triangle \)


A charge of \( -1 C \) contains \( n \) electrons,
then \( \boldsymbol{n}=? \)
A \( \cdot 6.25 \times 10^{-20} \)
B . \( 6.25 \times 10^{19} \)
c. \( 6.25 \times 10^{18} \)
D. \( 6.25 \times 10^{-19} \)


Calculate \( p H \) of a \( 1.0 \times 10^{-8} M \)
solution of \( \boldsymbol{H} \boldsymbol{C l} \)


The resistor of resistance \( \boldsymbol{R} \) is
connected between the terminals of a
cell of emf \( \boldsymbol{E} \) and internal resistance \( \boldsymbol{r} \)
The current \( I \) through the circuit is :
A \( \cdot \frac{E}{R r} \)
в. \( \frac{E}{R+r} \)
c. \( \frac{R+r}{E} \)
D. \( \frac{E}{R}+r \)


The colour composition of beetle population is likely to change in the following manner.
A. Both red and green beetles survive equally
B. Only the red beetles survive.
C. More red beetles survive than the green.
D. More green beetles survive than the red


Which cells of the body are responsible for obesity and why?


The given diagram is an apparatus for carbon detection. Fill in the blank of the
labelled diagram.
A. Cupric oxide
B. Anhydrous copper sulphate
c. copper precipitate
D. Calcium carbonate


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


Which of the following adjustments are made by the eye to enable clear vision of distant objects?
A. Relaxation of ciliary muscles
B. Thinning of the eye lens
c. Increasing the focal length
D. All of the above


A police car moving at \( 22 \mathrm{m} / \mathrm{s} \), chase a motorcyclist. The police man sounds his horn at \( 176 \mathrm{Hz} \), while both of them move
towards a stationary siren of frequency \( 165 \mathrm{Hz} . \) Calculate the speed of the motorcyclist, if he does not observe any beats. (velocity of sound in air \( =330 \) \( \mathrm{m} / \mathrm{s}) \)
\[
\begin{array}{l}
\text { Police car } \\
\hline 176 \mathrm{Hz}^{*} 22 \mathrm{m} / \mathrm{s} \frac{\text { Motorcycle }}{\mathrm{V}} \quad \text { Stationary } \\
\qquad \text { Siren }(165 \mathrm{Hz})
\end{array}
\]
\( A .33 \mathrm{m} / \mathrm{s} \)
B. 22 m/s
c. zero
D. \( 11 \mathrm{m} / \mathrm{s} \)


Find the measure of arc \( C D \).
A \( \cdot 105 \)
B . \( 55^{\circ} \)
\( c \cdot 108 \)
D. 75


Position-time graph for a particle is
shown in the figure. Starting from \( t=0 \)
at what time \( t, \) the average velocity is
zero?
4.1
3.3
\( c .6 s \)
2.7


A healthy adult of height \( 1.7 m \) has an
average blood pressure (BP) of 100mm
of \( H g . \) The heart is typically at a height
of \( 1.3 m \) from the foot. Take the density
of blood to be \( 10^{3} \mathrm{kg} / \mathrm{m}^{3} \) and note that
100mm of \( H g \) is equivalent to 13.3 KPa (Kilo pascals). The ratio of Blood

Pressure in the foot region to that in the head regions is close to :
A. one
B. two
c. three
D. four


In a galvanic cell, the salt bridge
(i) does not participate chemically in the cell reaction
(ii) stops the diffusion of ions from one electrode to another
(iii) is necessary for the occurrence of the cell reaction
(iv) ensures mixing of the two electrolytic solutions.
A. (i) and (iii) only
B. (i) and (ii) only
c. (iii) and (iv) only
D. All of these


The electronic configuration of
gadolinium (atomic number 64 ) is ?
\( \mathbf{A} \cdot[X e] 4 f^{3} 5 d^{5} 6 s^{2} \)
В . \( [X e] 4 f^{7} 5 d^{2} 6 s^{1} \)
\( \mathbf{c} \cdot[X e] 4 f^{7} 5 d^{1} 6 s^{2} \)
\( \mathbf{D} \cdot[X e] 4 f^{8} 5 d^{6} 6 s^{2} \)


If \( \boldsymbol{\alpha} \neq \boldsymbol{\beta}, \boldsymbol{\alpha}^{2}=\mathbf{5} \boldsymbol{\alpha}-\mathbf{3}, \boldsymbol{\beta}^{2}=\mathbf{5} \boldsymbol{\beta}-\mathbf{3} \)
then the equation whose roots are \( \boldsymbol{\alpha} / \boldsymbol{\beta} \)
\( \& \boldsymbol{\beta} / \boldsymbol{\alpha} \) is
A \( \cdot x^{2}+5 x-3=0 \)
B. \( 3 x^{2}+12 x+3=0 \)
c. \( 3 x^{2}-19 x+3=0 \)
D. None of these


If \( s_{n}=\sum_{n=1}^{n} \frac{1+2+2^{2}+\ldots t o n t e r m s}{2^{n}} \) then \( s_{n} \)
is equal to
A \( \cdot 2^{n}-(n+1) \)
B. \( 1-\frac{1}{2^{n}} \)
c. \( _{n-1}+\frac{1}{2^{n}} \)
D. \( 2^{n}-1 \)


How many nodes are found in heart of
human?
A. one
B. Two
c. many
D. None of the above


The molecular formula of Rinmann's
green is
A \( . F e S O_{4} 7 H_{2} O \)
в. \( C r C l_{3} \)
c. \( N i S O_{4} 7 H_{2} O \)
D. \( \operatorname{CoOZnO} \)


What is the smallest number by which
1600 must be divided so that the
quotient is a perfect cube?


Static charges in the atmosphere is generated by
A. induction from the earth's surface
B. conduction between clouds
c. friction of the air upon itself
D. No reason


After rounding off 1.235 and 1.225 to two places, the answer will be :
A. 1.23,1.22
B. 1.24, 1.123
c. 1.23,1.23
D. 1.24,1.22


Which of the following is/are characteristics of medicines?
A. They are addictive
B. They are toxic
c. All drugs are medicines
D. None of the above


State whether the given statement is True or False:

The ripples in water waves are created by the oscillatory movement of water
particles.
A. True
B. False


Find the symmetric and skew
symmetric parts of the matrix \( \boldsymbol{A}=\left[\begin{array}{lll}1 & 2 & 4 \\ 6 & 8 & 1 \\ 3 & 5 & 7\end{array}\right] \)


What occurs 15 days after the full moon
day?
A. Half moon day
B. Crescent moon day
c. New moon day
D. None of the above


The name hydrogen was proposed by
A. Lavoisier
B. Rutherford
c. Henry cavandish
D. scheele


If \( A \) and \( B \) be the points (3,4,5) and (-1,3,-7) respectively. Find the equation of the set of points \( \boldsymbol{P} \) such
that \( \boldsymbol{P} \boldsymbol{A}^{2}+\boldsymbol{P} \boldsymbol{B}^{2}=\boldsymbol{K}^{2}, \) where \( \boldsymbol{K} \) is a
constant


The inverse of the proposition \( (p \wedge \sim \)
\( \boldsymbol{q}) \Rightarrow \boldsymbol{r} \) is
A \( . \sim r \Rightarrow(\sim p \vee q) \)
В \( \cdot(\sim p \vee q) \Rightarrow \sim r \)
c. \( r \Rightarrow p(\wedge \sim q) \)
D. None of these


Which one of the liquids, has the highest specific heat capacity?
A. water
B. Ether
c. Alcohol
D. None of the above


Find the amount of water displaced by a solid spherical ball of diameter \( 28 \mathrm{cm} \)
A \( \cdot_{11498} \frac{2}{3} c m^{3} \)
В \( \cdot_{11498} \frac{2}{7} c m^{3} \)
c. \( _{11498} \frac{1}{3} c m^{3} \)
D. \( _{11498} \frac{2}{5} \)cm\( ^{3} \)


As one penetrates through uniformly charged conducting sphere, what happens to the electric field strength:
A. decreases inversely as the square of the distance
B. decreases inversely as the distance
c. becomes zero
D. increases inversely as the square of distance


at a constant temperature of \( \theta \). Assume
that it obeys Newton's law of cooling. Its
temperature \( \theta \) is plotted against time \( t \)
Tangents are drawn to the curve at the
points \( \boldsymbol{P}\left(\boldsymbol{\theta}=\boldsymbol{\theta}_{1}\right) \) and \( \mathrm{Q}\left(\boldsymbol{\theta}=\boldsymbol{\theta}_{2}\right) . \) These
tangents meets the time axis at angles
of \( \phi_{2} \) and \( \phi_{1} \) as shown
\( \mathbf{A} \cdot \frac{\tan \phi_{2}}{\tan \phi_{1}}=\frac{\theta_{1}-\theta_{0}}{\theta_{2}-\theta_{0}} \)
B. \( \frac{\tan \phi_{2}}{\tan \phi_{1}}=\frac{\theta_{2}-\theta_{0}}{\theta_{1}-\theta_{0}} \)
c. \( \frac{\tan \phi_{1}}{\tan \phi_{2}}=\frac{\theta_{1}}{\theta_{2}} \)
D. \( \frac{\tan \phi_{1}}{\tan \phi_{2}}=\frac{\theta_{2}}{\theta_{1}} \)


What is displacement current? Obtain
an expression of displacement current for a charged capacitor. Write AmpereMaxwell's law.


A man is pulling a rope attached to a block on a smooth horizontal table. The
tension in the rope will be the same at all points.
A. If and only if the rope is not accelerated
B. If and only if the rope is massless
c. If either the rope is not accelerated or is massless
D. always


Find the value of \( \boldsymbol{x}: \) \( \boldsymbol{x}-\left[\mathbf{2} \boldsymbol{x}-\frac{\mathbf{3} \boldsymbol{x}-\mathbf{4}}{\mathbf{7}}\right]=\frac{\mathbf{4} \boldsymbol{x}-\mathbf{2 7}}{\mathbf{3}}-\mathbf{3} \)


When electrolysis of \( K C l \) is done in
alkaline medium, 10 g of \( K C l O_{3} \) is produced as follows:
\( \boldsymbol{C l}^{\ominus}+\mathbf{6} \stackrel{\ominus}{\boldsymbol{O}} \boldsymbol{H} \rightarrow \boldsymbol{C l} \boldsymbol{O}_{3}^{\ominus}+\mathbf{3} \boldsymbol{H}_{2} \boldsymbol{O}+\boldsymbol{6} \boldsymbol{e}^{-} \)
A current of 2 A is passed for 10.941 hours. The current efficiency (in \%) used in the process is ( \( M w t o f K C l O_{3}= \) 122.5


Which type of bond is not present in
\( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \) molecule?
A. Covalent
B. Ionic
c. Dative
D . \( p_{\pi}-p_{\pi} \)


What is the sum of G.P. \( 1,3,9,27, \dots . . \) up
to 7 numbers?
A. 1093
в. 2093
\( c .3093 \)
D. 4093


Which element is an important component of transistors?
A. sodium
B. copper
c. germanium
D. radium


Two connected charges of \( +q \) and \( -q \)
respectively are at a fixed distance \( \boldsymbol{A B} \)
apart in a non uniform electric field
whose lines of force are shown in the
figure. The resultant effect on the two
charges is
A. a torque in the plane of the paper and no resultant force
B. a resultant force in the plane of the paper and no torque
c. a torque normal to the plane of the paper and no resultant force
D. a torque normal to the plane of the paper and a resultant force in the plane of the paper


\( \boldsymbol{A}_{\boldsymbol{3}(\boldsymbol{g})} \rightleftharpoons \mathbf{3} \boldsymbol{A}_{(\boldsymbol{g})} \)
In the above reaction, the initial moles
of \( A_{3} \) is "a". If \( \alpha \) is degree of
dissociation of \( A_{3} \). The total number of
moles at equilibrium will be:
A \( \cdot a-\frac{a \alpha}{3} \)
B. \( \frac{a}{3}-\alpha \)
c. \( \left(\frac{a-a \alpha}{2}\right) \)
D. None of these


A particle of mass \( 0.1 \mathrm{kg} \) moving with an initial speed v collides with another
particle of same mass kept at rest. If after collision the total energy becomes \( 0.2 \mathrm{J}, \) then:
A. minimum value of v is \( 2 \mathrm{m} / \mathrm{s} \)
B. maximum value v is 4 \( \mathrm{m} / \mathrm{s} \)
c. minimum value v is 3 \( \mathrm{m} / \mathrm{s} \)
D. maximum value of v is \( 6 \mathrm{m} / \mathrm{s} \)


\( A g C l \) is in nature.
A. covalent
B. ionic
c. polar
D. non-polar


A survey conducted on 600 students of
B. A part I classes of a collage gave the
following report. Out of 600 students,
307 took economics, 198 took history,
230 took sociology, 65 took history and
economics, 45 took economics and sociology, 31 took sociology and history and 10 took all the three subjects. The report sounded very impressive, but the surveyor was fired. Why?


Explain the dual function of AUG codon. Give the sequence of bases it is transcribed from and its anticodon.


If an egg is not fertilised,it is expelled from the body during


How many terms of the sequence \( \sqrt{3}, 3,3 \sqrt{3}, \ldots \) must be taken to get the \( \operatorname{sum} 39+13 \sqrt{3} ? \)


In the given figure, find the value of \( x \)


A proton is projected with velocity \( \vec{V}= \) \( 2 \hat{i} \) in a region where magnetic field \( \vec{B}=(\hat{i}+3 \hat{j}+4 \hat{k}) \mu T \) and electric field
\( \vec{E}=10 \hat{i} \mu \mathrm{V} / \mathrm{m} . \) Then find out the net
acceleration of proton.
\( \mathbf{A} \cdot 1400 m / s^{2} \)
B. \( 700 \mathrm{m} / \mathrm{s}^{2} \)
C \( .1000 \mathrm{m} / \mathrm{s}^{2} \)
D. \( 800 \mathrm{m} / \mathrm{s}^{2} \)


Spindle usually persists in the form of
during method of
cytokinesis.
A. phragmoplast, cleavage
B. phragmoplast, cell plate
c. cell plate, cell plate
D. cell plate, cleavage


Find the mean deviation about mean
and median for the following data.
\begin{tabular}{lllll}
\multirow{2}{*} {\( \boldsymbol{C I} \)} & \( \boldsymbol{5}- \) & \( \mathbf{1 0}- \) & \( \mathbf{1 5}- \) & \( \mathbf{2 0}- \) \\
& \( \mathbf{1 0} \) & \( \mathbf{1 5} \) & \( \mathbf{2 0} \) & \( \mathbf{2 5} \)
\end{tabular}
12


Choose the correct answer form the
alternatives given. \( C a^{2+} \) is
isoelectronic with:
A. \( N a \)
B . \( 4 M g^{2+} \)
\( c \cdot B a^{2} \)
D. \( A r \)


Which of following can have vacant \( \boldsymbol{p} \) orbital?
\( \mathbf{A} \cdot \cdot \cdot C H_{3} \)
в. \( _{C H_{3}}^{\oplus} \)
\( \mathrm{c} \cdot \mathrm{CH}_{4} \)
D. Both \( (B) \) and \( (C) \)


Find the position of the object which
when raised in front of convex mirror of
focal length \( 20 \mathrm{cm} \) produces virtual image which is half size of the object.


Write the following steps of an experiment in a sequential order to show that a current carrying conductor sets up a magnetic field around it.
(a) Pass the insulted copper wire through the small hole at the centre of the carboard and perpendicular to it.
(b) Paste a white paper on a rectangular cardboard and make a small hole at its
centre.
(c) Connect this wire to a battery, a
switch and a variable resistor in series.
(d) Clamp this cardboard to a stand in a horizontal position and sprinkle some iron filings over it.
(e) Now, when the circuit is closed, the iron filings on the carboard form concentric circles around the wire.
A. bdace
B. baced
c. adbec
\( \mathbf{D} \cdot e d a b c \)


In the rabbits, the muscles which move
the pinnae are
A. Absent
B. Vestigial
c. Non-functional
D. Functional


Find the center of mass of a uniform \( L \)
shaped lamina (a thin flat plate) with
dimensions as shown in Fig. The mass
of lamina is \( 3 \mathrm{kg} \)


The area bounded by the curves \( \boldsymbol{y}= \)
\( |x|-1 \) and \( y=-|x|+1 \) is
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
c. \( 2 \sqrt{2} \)
D.


Aufbau principle fails to explain the configuration of element with atomic
number:
\( A \cdot 18 \)
B . 21
\( c \cdot 24 \)
D. 27


Hydrated sulphate of a divalent metal of atomic weight 65.4 loses \( 43.85 \% \) of its weight on dehydration. Find the number of molecules of water of crystallisation in the formula of hydrated salt.
A. \( M S O_{4} \cdot 16 H_{2} O \)
в. \( M S O_{4} \cdot 5 H_{2} O \)
\( \mathrm{c} \cdot M S O_{4} \cdot 10 H_{2} O \)
D. \( M S O_{4} \cdot 12 H_{2} O \)


Reaction of sodium ethoxide and ethyl iodide will give:
A. ether
B. ethyl alcohol
c. acetaldehyde
D. acetic acid


Steady current flows in a metallic conductor of non-uniform cross-section.
Which of the following quantities is a constant along the conductor?
A. Current
B. Current density
c. Electric field
D. Drift speed


Which of the following means of transmembrane transport involves the expenditure of energy by the cell and can move materials up a concentration gradient?
A. Osmosis
B. Facilitated diffusion
c. simple diffusion
D. Active transport


Out of photosynthesis and respiration
in plants, which process occurs all the time?


One mole of \( N_{2} O_{5}(g) \) at \( 300 \mathrm{K} \) is left in a closed container under one atm. It is
heated to \( 600 \mathrm{K} \) when \( 20 \% \) by mass of
\( N_{2} O_{5}(g) \) decomposes to \( N O_{2}(g) . \) The resultant pressure is:
A . 1.2 atm
B. 2.4 atm
c. 2.0 atm
D. 1.0 atm


Which of the following sets represent the
normal physical states of the elements
concerned at \( 25^{\circ} \mathrm{C} \) and one bar pressure,
with \( \Delta H^{\circ} \) (formation) \( =0 \)
\( \mathbf{A} \cdot C(\operatorname{diamond}), S_{8}(s), N a(s) \)
B. \( C(\text {diamond}) \) ), \( C(\text { graphite }), B r_{2}(I) \)
c. \( C(\text { graphite }), B r_{2}(g), P_{4}(\text { white }) \)
D. \( C(\text { graphite }), B r_{2}(I), I_{2}(s) \)


A uniform field of \( 30 \mathrm{mT} \) exists in the \( +x \)
direction. A particle of charge +ve and
\( \operatorname{mass} 1.67 \times 10^{-27} \mathrm{kg} \) is projected
through the field in the \( +Y \) direction with
a speed of \( 4.8 \times 10^{6} m / s \)
(a) Find the force on the charged particle in magnitude and direction
(b) Find the force if the particle were negatively charged.
(c) Describe the nature of path followed by the particle in both the cases.


State True or False.
\( 1<\frac{1}{1001}+\frac{1}{1002}+\frac{1}{1003}+\dots \dots+ \)
\( \frac{1}{3001}<1 \frac{1}{3} \)
A. True
B. False


Mr. Albert's gross annual income is Rs. \( \mathbf{5}, \mathbf{0 0}, \mathbf{0 0 0} \) for \( \mathbf{F . Y .} \mathbf{2 0 1 2}-\mathbf{1 3 .} \) His annual
savings in this year are as follows:
(a) L.I.C. premium Rs. 70,000
(b) Contribution towards P.F. Rs. 12,000
(c) P.P.F. Rs. 30,000
(d) N.S.C. Rs. 10,000 Find his taxable income and income tax
for F.Y. \( 2012-13 \)


Which of the following technique is used in the manufacture of aluminium
from bauxite?
A. Reduction with magnesium
B. Reduction with coke
c. Electrolytic reduction
D. Reduction with iron


A light bulb is rated at \( 100 W \) for a
\( 220 V \) supply. Find the rms current through the bulb:
\( \mathbf{A} \cdot 0.25 A \)
в. \( 0.45 A \)
c. \( 0.65 A \)
D. \( 0.85 A \)


If series limit (in \( n m \) ) of a series of
hydrogen spectrum which contains a photon of wavelength 1278.35 nm is expressed as \( \frac{1240}{x}, \) then \( x \) is:
(Given \( : h c=1240 \mathrm{eV}-\mathrm{nm}) \)
A . \( 1.51 e V \)
в. \( 2 e V \)
c. \( 3.4 e V \)
D. \( 0.66 e V \)


The two structures of D-glucopyranose forms are:
A. anomers
B. enantiomers
c. epimers
D. diesterioisomers


Inversion temperature of helium is very
low. So when helium is allowed to
expand into vacuum it gets:
A. cooled
B. Heated
c. Neither cooled, nor heated \( x \)
D. Liquified


A solenoid of length \( 10 \mathrm{cm} \), diameter 1 \( \mathrm{cm}, \) number of turns 500 with relative
permeability of the core
\( 2000, \) is connected to an ac source of
frequency 50 Hz. Then, the reactance is
A . zero
B. \( 55 \Omega \)
c. \( 105 \Omega \)
D. \( 155 \Omega \)


\( \int \frac{5 x+4}{\sqrt{x^{2}+3 x+2}} d x= \)
\( A \sqrt{x^{2}+3 x+2} \)
\( \boldsymbol{B} \ln \left[\left(\boldsymbol{x}+\frac{\boldsymbol{3}}{\mathbf{2}}\right)+\sqrt{\boldsymbol{x}^{2}+\boldsymbol{3} \boldsymbol{x}+\boldsymbol{2}}\right]+\boldsymbol{C} \)
Then \( A+2 B=? \)
\( A \cdot 9 \)
B . 10
c. 11
D. 12


Solve \( 17^{2} \cdot 17^{-5} \)


In some solutions, the concentration of
\( H_{3} O^{+} \) remains constant even when
small amounts of strong acid or strong base are added to them. These solutions
are known as:
A. colloidal solutions
B. buffer solutions
c. true solutions
D. ideal solutions


What all properties are detected on
basis of speed and nature of reflected
ultrasound waves?
A. Shape and position of object
B. Shape and height of object
c. shape and size of object
D. weight and position of object


Draw a labeled diagram of AC generator.Derive the expression for the instantaneous value of the emf induced
in the coil.


A body is dropped from the top of a
tower covers \( \frac{7}{16} \) of total height isn the
last second of its fall. The time of fall is
A \( .2 s \)
B. 4 s
\( \mathbf{c} \cdot<1 s \)
\( \mathbf{D} \cdot>5 s \)


The aquatic organism with prehensile
tail is
A. Mococo
B. Chameleon
c. Exocoetus
D. Hippocampus


Nernst equation is : \( \boldsymbol{E}=\boldsymbol{E}^{o}-\frac{\boldsymbol{R} \boldsymbol{T}}{\boldsymbol{n} \boldsymbol{F}} \boldsymbol{l} \boldsymbol{n} \boldsymbol{Q} \)
If \( Q=K_{c} \), then which one is not
correct?
A \( . E=E^{\circ} \)
в. \( \frac{R T}{n F} \ln Q=E^{c} \)
\( \mathbf{c} \cdot E=z e r o \)
D. \( _{K_{c}=e} \frac{n F E^{o}}{R T} \)


Prove that \( \sqrt{3}+\sqrt{8} \) is an irrational
number.