A line in the \( x y \) -plane passes through the origin and has a slope of \( \frac{1}{7} . \) Which of the following points lies on the line?
\( \mathbf{A} \cdot(0,7) \)
В \( \cdot(1,7) \)
c. (7,7)
D \cdot (14,2)


The force of attraction between two
charges \( 8 \mu C \) and \( 0.2 N . \) Find the
distance of separation.
A. 412 meter
B. 1.2 meter
c. 120 meter
D. 0.12 meter


The technique of protecting a metal from corrosion by connecting it to a second metal (that is more easily oxidised) is called:
A. annealing
B. galvanisation
c. cathodic protection
D. anodic protection


If the heat of formation of \( N O_{2} \) is 'x'
\( \left[1 / 2 N_{2(g)}+O_{2(g)} \rightarrow N O_{2(g)}\right] \) the heat of
reaction \( N_{2(g)}+O_{2(g)} \rightarrow 2 N O_{(g)} \) is y
and the heat of reaction \( 2 N O_{(g)}+ \) \( O_{2(g)} \rightarrow 2 N O_{2(g)} \) is z, then:
A. \( 2 x+z=y \)
в. \( 2 y+z=x \)
c. \( 2 x-z=y \)
D. \( 2 z+x=y \)


Which of the following compounds will
not give \( +v e \) chromyl chloride test?
A. \( C u C l_{2} \)
в. \( H g C l_{2} \)
c. \( Z n C l_{2} \)
D. \( C_{6} H_{5} N H_{2} H C l \)


Define the terms conductivity and
molar conductivity for the solution of an electrolyte. Comment on their variation
with temperature.


The demand for different shirt sizes is
given in the table.
38 39 40 Size 4
No of
Persons 26 \( \begin{array}{lll}\text { 36 } & \text { 20 } & \text { 15 }\end{array} \)
Find the modal shirt size.
A . 39
B . 40
c. 44
D. 42


The dimensions of a rectangular
parallelepiped are \( 1 \mathrm{cm} \times 1 \mathrm{cm} \times \)
\( 100 \mathrm{cm} . \) If its specific resistance is \( 3 x \)
\( 10^{-7} \Omega m \) then the resistance between
its rectangular faces will be
A \( \cdot 3 \times 10^{-9} \Omega \)
В. \( 3 \times 10^{-7} \Omega \)
c. \( 3 \times 10^{-5} \Omega \)
D. \( 3 \times 10^{-3} \Omega \)


A toroid wound with 100 turns/m of wire
carries a current of \( 3 A \). The core of
toroid is made of iron having relative
magnetic permeability of \( \mu_{r}=5000 \) under given conditions. The magnetic field inside the iron is
\( \left(\text { Take } \mu_{o}=4 \pi \times 10^{-7} T m A^{-1}\right) \)
A \( .0 .15 T \)
в. \( 1.5 \times 10^{-2} T \)
c. \( 0.47 T \)
D. \( 1.88 T \)


The correct arrangement for the ions in the increasing order of their radiiis:
\( \mathbf{A} \cdot C a^{+2}, K^{+}, S^{-2} \)
в. \( C l^{-}, F^{-}, S^{-2} \)
C. \( N a^{+}, C l^{-}, C a^{+2} \)
D. \( N a^{+}, A l^{+3}, B e^{+2} \)


Show that \( \lim _{x \rightarrow 0} \frac{e^{1 / x}-1}{e^{1 / x}+1} \) does not exist.


Find the area bounded by \( y=x+\sin x \)
and its inverse between \( \boldsymbol{x}=\mathbf{0} \) and \( \boldsymbol{x}= \)
\( 2 \pi \)
A .2
B. 4
\( c .6 \)
D. 8


Find \( ^{\prime} x^{\prime} \) if \( \sec ^{2} 2 x=1-\tan 2 x \)


A resistance of \( 2 \Omega \) is connected across
one gap of a metrebridge ( the length of the wire is \( 100 \mathrm{cm} \) ) and an unknown
resistance, greater than \( 2 \Omega, \) is connected across the other gap. When
these resistance's are interchanged, the balance point shifts by \( 20 \mathrm{cm} \) Neglecting any corrections, the unknown resistance is:
A . \( 3 \Omega \)
B. \( 4 \Omega \)
\( c .5 \Omega \)
D. \( 6 \Omega \)


What will be the molality of a solution of glucose in water which is \( 10 \% \boldsymbol{w} / W ? \)
\( \mathbf{A} \cdot 0.01 m \)
в. 0.617 т
\( c .0 .668 m \)
D. 1.623 m


\( 0.02 M \) solution of \( N H_{4} O H \) is \( 3 \% \)
dissociated. Calculate the dissociation
constant of \( \boldsymbol{N} \boldsymbol{H}_{\mathbf{4}} \boldsymbol{O} \boldsymbol{H} \)


State two differences between the
specific heat capacity and the heat capacity of a substance.


The moon takes \( _{--}-_{-}- \) days to
complete one spin
A . 25
B . 26
c. 27
D . 28


\( \frac{\sec 8 \theta-1}{\sec 4 \theta-1}=\frac{\tan r \theta}{\tan 2 \theta} \cdot \) Find \( r \)


Besides the flagellary movement, euglenoids can also perform special movement by membrane undulations, called as "euglenoid movement". Euglenoids are included in
A. Monera
B. Metazoa
c. Metaphyta
D. Protistata


The \( \% \) of \( \alpha- \) anomer in the mixture is:
A . 32.6
B. 67.4
c. 42.6
D. 57.4


What is the difference in number of
neutrons in Protium and Deuterium?
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot 3 \)
\( D \)


Two wave-fronts are emitted from
coherent sources of path difference between them is 2.1 micron. Phase
difference between the wave-fronts at
that point is \( 7.692 \pi . \) Wavelength of light emitted by sources will be :
в. 5400 月
c. \( 5460 \hat{h} \)
D. 5892 月


Which of the following is a respiratory disease?
A. Polio
B. Arthritis
c. Asthma
D. cancer


What is the density of solution of sulphuric acid used as an electrolyte in lead accumulator?
\( \mathbf{A} \cdot 1.5 \mathrm{gm} L^{-1} \)
B. \( 1.2 \mathrm{gm} L^{-1} \)
c. \( 1.8 \mathrm{gm} L^{-1} \)
D. \( 2.0 \mathrm{gm} L^{-1} \)


Water falls from a tap, down the streamline
A. Area decreases
B. Area increases
c. velocity remains same
D. Area remains same


The positive root \( x^{2}+b x+8=0 \) is
twice the other root then \( b= \)
A. 6
B. - -
c. 12
D. -12


Two blocks of mass \( 10 \mathrm{kg} \) and \( 30 \mathrm{kg} \) are
placed along a vertical line the first block of mass \( 10 \mathrm{kg} \) is raised through a height of \( 7 \mathrm{cm} \) by what distance should the second block of mass 30


A group of population, which are
capable of is called as species.
A. Interbreeding
B. Linkingg
c. Both A and B
D. None of the above


A hydrogen atom initially in the ground level absorbs a photon, which excites it
to the \( n=4 t h \) level. Determine the
wavelength and frequency of photon.


Which of the following causes biomagnification?
\( A \cdot S O_{2} \)
B. Mercury
c. DDT
D. Both (b) and (c)


A positively charged croquet ball rolls at
\( 4.0 m / s \) northward through a \( 2.00 T \)
magnetic field which points westward.
If the charge on the croquet ball is \( 1.0 C \)
how much force acts on the croquet ball
due to the magnetic field and in what
direction?
A. Amount of Force \( -2.00 N \), Direction of Force - up
B. Amount of Force \( -8.00 N \), Direction of Force - south
C. Amount of Force \( -8.00 N \), Direction of Force - down
D. Amount of Force \( -0.500 N \), Direction of Force - up
E. Amount of Force \( -8.00 N \), Direction of Force - up


A small metal sphere of radius a is falling with a velocity \( v \) through a
vertical column of a viscous liquid. If the coefficient of viscosity of the liquid
is \( \eta \), then the sphere encounters an opposing force of
A \( .6 \pi \eta a^{2} v \)
в. \( \frac{6 \eta v}{\pi a} \)
c. \( 6 \pi \eta a v \)
D. \( \frac{\pi \eta v}{6 a^{3} v} \)


Verify:
\( \boldsymbol{x}^{3}+\boldsymbol{y}^{3}=(\boldsymbol{x}+\boldsymbol{y})\left(\boldsymbol{x}^{2}-\boldsymbol{x} \boldsymbol{y}+\boldsymbol{y}^{2}\right) \)


If each angle of a triangle is less than the sum of the other two angles of it then the triangle is right-angled. State
true or false
A. True
B. False


A solid cylinder of mass \( \mathrm{m} \) and radius \( \mathrm{r} \) is rolling on a rough inclined plane of inclination \( \theta . \) The coefficient of friction
between the cylinder and incline is \( \mu \) Then:
This question has multiple correct options
A. frictional force is always \( \mu \) mg \( \cos \theta \)
B. friction is a dissipative force.
c. by decreasing \( \theta \), frictional force decreases
D. friction opposes translation and supports rotation


Assertion
Ammonia can be liquefied by applying
high pressure
Reason
Ammonia is highly soluble in water
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


Dramatic changes of body features
associated with puberty are mainly
because of secretion of
A. Oestrogen from testes and testosterone from ovary
B. Estrogen from adrenal gland and testosterone from pituitary gland
c. Testosterone from testes and estrogen from ovary
D. Testosterone from thyroid gland and estrogen from pituitary gland


\( \int \frac{\cos x+\sin x}{\cos x-\sin x} d x \)
\( \mathbf{A} \cdot \log \sin (\pi / 4+x) \)
\( \mathbf{B} \cdot \log \sec (\pi / 4+x) \)
\( \mathbf{C} \cdot \log \cos (\pi / 4+x) \)
D \( \cdot \log \sec (\pi / 4-x) \)


A solid has how many dimensions?


What is true of fluid mosaic model?
A. Phospholipid monolayer is present over protein layer
B. Phospholipid bilayer is present over protein layer
C. Protein embedded in phospholipid bilayer
D. Phospholipid layer is sandwitched between two protein layers.


How many organs or structure in human beings contain oxygenated as well as deoxygenated blood? Lungs, Heart, Kidney, Liver, Pancreas, Gonads, Spleen, Ear, Hypothalamus
A. one
B. Two
c. Three
D. Four


If \( \lim _{n \rightarrow \infty} \frac{n .3^{n}}{n(x-2)^{n}+n .3^{n+1}-3^{n}}=\frac{1}{3} \)
then the range of \( x \text { is (When } n \in N) \)
A. [2,5)
()
B \( \cdot(1,5) \)
c. (-1,5)
\( D \cdot(-\infty, \infty) \)


Which of the following combination of
reagents can bring the
shown transformation?
\( \mathbf{A} \cdot C H_{3} O N a, M g / \)ether\( , C O_{2}, H_{2} O / H^{+} \)
в. \( C H_{3} \) ONa, \( K C N / D M S O, H_{2} O / H_{2} S O_{4}, \) heat
\( \mathbf{c} \cdot M g / \)ether\( , C O_{2}, H_{2} O / H^{+}, C H_{3} O N a \)
D. \( N a O H, M g / \)ether\( , C O_{2}, H_{2} O / H^{+}, C H_{3} I \)


We define p value of a term (say \( x \) ) as
\( \boldsymbol{p}_{\boldsymbol{x}}=-\log \boldsymbol{x} \)
Calculate \( \boldsymbol{p}_{\left(C l^{-}\right)} \) value as \( \boldsymbol{x} \times \mathbf{1 0}^{-1} \) in a
solution that is \( 2.00 \times 10^{-3} \mathrm{Min} \) NaCl
and \( 5.4 \times 10^{-4} \) M \( H C l \)


Give balanced chemical equations for the following reactions:

Fluorine treated with dilute sodium
hydroxide solution


The terms active water absorption and passive water absorption were given by
A. Renner
B. Atkins
c. Priestley
D. Kramer


The mass number of an atom is the
sum of the number of protons and number of neutrons in an atom.
If it is true enter 1 else 0


The point on the line \( 4 x-y-2=0 \)
which is equidistant from the points (-5,6) and (3,2) is
A . (2,6)
в. (4,14)
c. (1,2)
D. (3,10)


Which of the following is a type of deformation?

This question has multiple correct options
A. Strain
B. Stress
c. Fracture
D. All of the above


S-block elements are:
A. Elements of group I-A and III-B.
B. Elements of group I-A and II-A.
C. Elements of group I-A and I-B.
D. Elements of group I-A and II-B.


1,3,9,27,81 is a
A. geometric sequence
B. arithmetic progression
C. harmonic sequence
D. geometric series


llium is a term applied to structure like
A. Part of the small intestine
B. Part of the pelvic girdle
c. Pectoral girdle
D. A particular region of pulmonary tract


Eutrophication is a
A. Neutral sign for ecosystem
B. Dual-sided sign for ecosystem
C. Bad sign for ecosystem
D. Good sign for ecosystem


\( \left(2,30^{\circ}\right) \) and \( \left(4,120^{\circ}\right) \)


A coin is tossed 100 times with the
following frequencies: Head : 20. Find the probability for event having heads only.
A . 0.2
B. 0.5
c. 0.65
D. 1.5


What happens to the pH of a buffer system if one halves the concentration
of both the acid and the salt?
A. Nothing happens
B. pH goes up because there is less total acid in the solution.
c. pH goes down because there is less conjugate base to mask the presence of the
D. It depends upon the original concentration of acid and salt
E . It is impossible to predict


Using the equation of state \( \boldsymbol{p} \boldsymbol{V}=\boldsymbol{n} \boldsymbol{R} \boldsymbol{T} \)
show that, at a given temperature the density of a gas is proportional to its
gas pressure \( \boldsymbol{p} \)


In convectional currents,
A. Warmer molecules move up and colder molecules sink down.
B. Heat energy moves up by infrared waves.
C. There is no motion of molecules.
D. It is dominant in solids


During evolution of man, many changes
have taken place in his ancestral character. Which one of the following is an unsignificant change?
A. change of diet from hard tough fruits and roots into soft food
B. Qualitative improvement in the structure of hands skills for making tools
c. Disappearance of tail.
D. Improvement in speech for communication and social behaviour


In the above sided figure,if
\( Q T \perp P R ., \angle T Q R=40^{\circ} \) and \( \angle S P R= \)
\( 30^{\circ} \),find \( x \) and \( y \)


The correct energy level diagram for \( \left.\boldsymbol{\operatorname { C o }}(\boldsymbol{C N})_{6}\right]^{3-} \)
\( c \)


Termination of chain growth in protein synthesis is brought about by the
codons
A. UAA, UAG and UGA
в. UCG, АСС аnd GсG
c. UUG, UAG and UGA


Select the wrong option about rancidity.
A. Aerial oxidation of fats
B. Aerial oxidation of oils
C . Oils left in refrigerator gets rancid
D. Chips exposed to air gets rancid


Focal length of a convex lens is \( 15 \mathrm{cm} \)
Where should an object be placed so that real and three times larger image
is formed?


Evaluate:
\( \int \frac{\sin x-\cos x}{\sqrt{\sin 2 x}} d x \)


Choose the correct answer among the alternatives given :
What is true for lactational
amenorrhea?
(i) It means absence of menstruation.
(ii) Ovulation does not occur during the lactational period.
(iii) Chances of contraception are almost nil upto six months following parturition.
(iv) Side effects are almost nil
(v) Contraceptive efficiency reduces after the period of intense lactation.
(vi) It is a natural method of
contraception.
(vii) It increases phagocytosis of
sperms.
A . (ii), (iii), (iv), (v) and (vi)
B. (i), (ii), (iii) and (iv)
\( c . \) (ii), (iii), (iv), (v) and (vii)
\( D \cdot(i),(\text { ii) }, \) (iii), (iv), (v) and (vi)


If \( \frac{5}{8} x+\frac{2}{3}=\frac{7}{12}, \) then \( \frac{1}{2} x= \)
A \( \cdot \frac{-1}{15} \)
B. \( \frac{-2}{15} \)
c.
D.


Degree of which of the following polynomial is zero?
\( A \cdot x \)
B . 15
c. \( y \)
D. \( _{x+\frac{1}{x}} \)


Assertion
The minimum distance between an
object and its real image formed by a convex lens is '2 \( f^{\prime} \)
Reason
The distance between object and its
real image is minimum when its
magnification is one.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is incorrect but Reason is correct
D. Both Assertion and Reason are incorrect


The post-fertilization change involves
A. Haploid gametic maturation
B. Introduction of centrioles in the ovum
C. Inhibition of Meiosis-II
D. Formation of vitelline membrane


Give the nature of V-I graph for
(i)ohmic
(ii)non-ohmic
circuit elements. Give an example of
each


Assertion
\( f(x) \) is increasing with concavity
upwards, then concavity of \( \boldsymbol{f}^{-1}(\boldsymbol{x}) \) is
also upwards.
Reason
If \( \boldsymbol{f}(\boldsymbol{x}) \) is decreasing function with
concavity upwards, then concavity of
\( f^{-1}(x) \) is also upwards
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is
not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect and Reason are correct


A particle of mass \( m \) moving with
velocity \( v \) collides with a stationary
particle of mass \( 2 m . \) Then the speed of
the system after collision is:
A .22
в. \( \frac{v}{2} \)
c. \( 3 v \)
D. \( \frac{v}{3} \)


0.002 molar solution of NaCl having
degree of dissociation of \( 90 \% \) at \( 27^{\circ} C \)
has osmotic pressure equal to
A. 0.94 bar
B. 9.4 bar
c. 0.0934 bar
D. \( 9.4 \times 10^{-4} \) bar


If the lines \( 2 x+3 y+1=0 \) and \( 3 x- \)
\( \mathbf{y}-\mathbf{4}=\mathbf{0} \) lie along diameters of a circle
of circumference \( 10 \pi, \) then the
equation of the circle is:
A \( \cdot x^{2}+y^{2}-2 x+2 y-23=0 \)
B. \( x^{2}+y^{2}-2 x-2 y-23=0 \)
C. \( x^{2}+y^{2}+2 x+2 y-23=0 \)
D. \( x^{2}+y^{2}+2 x-2 y-23=0 \)


Which of the following is used to absorb
\( \boldsymbol{S} \boldsymbol{O}_{2} ? \)
A . conc. \( H_{2} S O_{4} \)
B. \( K O H \) solution
c. water
D. Anhydrous \( C a C l_{2} \)


When \( 24.25 \times 10^{3} \) is rounded off to
three significant figures, it becomes:
A .242
B. 243
c. \( 244 \times 10^{2} \)
D. \( 24.2 \times 10^{3} \)


A rectangular loop carrying current \( \boldsymbol{I}_{1} \) is placed near a long straight wire such that the wire is parallel to one of the sides of the loop as shown in the figure. If the straight wire carries a current of
\( I_{2} \) the loop will
A. Move away from the wire
B. Move towards the wire
c. Not move at all
D. Move only if the two currents are equal


Which of the following is an advantage of building dams?
A. The dams disturbs aquatic life
B. Dams lead go large scale disturbance of aquatic life
c. It disturbs the natural ecosystem
D. None


\( 42000 J \) of heat energy is supplied to \( 175 g \) of iron at \( 30^{\circ} C, \) when the final temperature recorded is \( 430^{\circ} . \) Calculate
specific heat capacity of iron
A \( \cdot 600 J g^{-1} \circ C^{-1} \)
B. \( 0.6 J g^{-1} \) о \( C^{-1} \)
c. \( 60 J g^{-1} \) о \( C^{-1} \)
D. \( 6 J g^{-1} \) о \( C^{-1} \)


Which of the following has an equal
number of neutrons and protons?
A. Hydrogen
B. Deuterium
c. Fluorine
D. Chlorine


An object is placed at a distance of \( 10 \mathrm{cm} \) from the curved surface of a glass hemisphere of radius \( 10 \mathrm{cm} \). Find the position of the image from the flat surface.
A \( .26 .67 \mathrm{cm} \)
в. 2.67 ст
\( c \cdot 2 c m \)
D. \( 19.67 \mathrm{cm} \)


How many 4 digit numbers are there
which contain not more than 2 different
digits?


In the figure shown an ideal liquid is flowing through the tube which is of uniform area of cross-section. The
liquid has velocities \( \boldsymbol{v}_{A} \) and \( \boldsymbol{v}_{B}, \) and
pressures \( P_{A} \) and \( P_{B} \) at points \( A \) and \( B \) respectively. Then it going to be
A \( \cdot v_{B}>v_{A} \)
\( \mathbf{B} \cdot v_{B}=v_{A} \)
\( \mathbf{c} \cdot P_{B}<P_{A} \)
\( \mathbf{D} \cdot P_{B}=P_{A} \)


Whats the potential of the reaction below given the half-reaction potentials:
\( 2 F e_{2}++C l_{2} \rightarrow 2 F e^{3+}+2 C l^{-} \)
\( \boldsymbol{F} \boldsymbol{e}^{\boldsymbol{3}+}+\boldsymbol{e}^{-} \rightarrow \boldsymbol{F} \boldsymbol{e}^{2+} ; \boldsymbol{E}=\mathbf{0 . 7 7} \boldsymbol{V} \)
\( \boldsymbol{C l}_{2}+\mathbf{2} \boldsymbol{e}^{-} \rightarrow \mathbf{2} \boldsymbol{C l}^{-} ; \boldsymbol{E}=\mathbf{1 . 3 6} \boldsymbol{V} \)
A . \( 0.18 V \)
B . \( 0.59 V \)
c. \( 1.05 V \)
D. \( 2.13 V \)
E \( .2 .90 V \)


What are the merits of Dalton's atomic
theory?
A. Explains laws of chemical combination
B. Distinguishes between fundamental particles of element
c. Both A and B
D. Proves individuality


A student moves \( \sqrt{2 x} k m \) east from his
residence and then moves \( x \) km north.
He then goes \( x \) km north east and finally he takes a turn of \( 90^{\circ} \) towards right and
moves a distance \( x \mathrm{km} \) and reaches his
school. What is the shortest distance of
the school from his residence?
A. \( (2 \sqrt{2}+1) x k m \)
B. \( 3 x \) km
\( \mathbf{c} \cdot 2 \sqrt{2} x k m \)
D. \( 3 \sqrt{2} x \) km


The sum of \( 2 n \) terms of a geometric
progression whose first term is ' \( a^{\prime} \) and
common ratio \( ^{\prime} r^{\prime} \) is equal to the sum of
\( n \) terms of a geometric progression
whose first term is 'b' and common ' \( r^{2} \) '
then \( b \) is equal to
A. The sum of the first two terms of the first series
B. The sum of the first and last terms of the first series.
c. The sum of the last two terms of the first series
D. None of these


An object of mass \( 0.2 \mathrm{kg} \) executes SHM along the \( x \) -axis with frequency
\( (25 / \pi) H z . A t \) the point \( x=0.04 m \) the
object has \( \mathrm{KE} 0.5 \mathrm{J} \) and PE 0.4 J.The amplitude of oscillation (in cm) is


\( \lim _{x \rightarrow 0}\left(\frac{\sqrt{a+2 x}-\sqrt{3 a}}{\sqrt{3 a+x}}\right) \)


A particle of charge \( q \) and mass \( m \) is
moving at a speed \( v \) enters a uniform
magnetic field of strength \( B \) as shown
below.
How much work is done by the magnetic field on the charge as the field accelerates the charge into a circle
of radius \( r ? \)
\( r \)
9
\( A \)
B.
\( \mathbf{c} \cdot q v B r \)
D. \( m v^{2} \)
E. Cannot be determined


In a small town, the number of water
pumps, concrete houses and
roads increased. The water table of that
place will :
A. get lower
B. get higher
c. remain unaffected
D. none of these


The dimensional formula for electric
flux density is given by
A \( \cdot\left[M L T^{-3} A-1\right] \)
B . \( \left[M L T^{3} A-1\right] \)
c. \( \left[M L T^{-3} A 1\right] \)
D. \( \left[M L T^{3} A 1\right] \)


If \( \vec{a} \) and \( \vec{b} \) are mutually perpendicular unit vectors, then \( (3 \vec{a}+2 \vec{b}) \cdot(5 \vec{a}- \)
\( \mathbf{6} \overrightarrow{\boldsymbol{b}})=? \)
\( \mathbf{A} \cdot \mathbf{5} \)
B. 3
\( c \cdot 6 \)
D. 12


A biconvex lens has a focal length \( 2 / 3 \) times the radius of curvature of either
surface. The refractive index of the lens
material is :
A . 1.7
B. 1.33
\( c \cdot 1.5 \)
D. 1.0


Evaluate the given integral.
\( \int \frac{2}{1-\cos 2 x} d x \)


A wooden plank of length \( 1 \mathrm{m} \) and uniform cross-section is hinged at one
end to the bottom of a tank as shown.
The tank is filled with water upto a
height of \( 0.5 \mathrm{m} . \) The specific gravity of
the plank is \( 0.5 . \) The angle \( \theta \) made by
the plank in equilibrium position is
A . \( 30^{\circ} \)
B . \( 45^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 90^{\circ} \)


If the threshold wavelength \( \left(\lambda_{0}\right) \) for the
ejection of an electron from metal is \( 330 \mathrm{nm}, \) then work function for the photoelectric emission is:
B. \( 1.2 \times 10^{-20} \) 」
D. \( 6 \times 10^{-12} \) J


Pick up the odd one out.
A. Chelone, Calotes, Naja
B. Pavo, Psittacula, Ornithorhyncus
C. Canis, Felis, Rattus
D. Bufo, Rana, Hyla


Assertion
Reversible processes are always
quasistatic
Reason
Quasistatic process is always
reversible
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


The displacement of centre of mass of
\( A+B \) system till the string becomes
vertical is :
A. zer
в. \( \frac{L}{2}(1-\cos \theta) \)
c \( \cdot \frac{L}{2}(1-\sin \theta) \)
D. none of these


After contact with first sphere, sphere \( C \) is brought in contact with the second sphere then find the charge left on
sphere B.
A \( \cdot 4.87 \times 10^{-7} C \)
B. \( 0 C \)
c. \( 6.5 \times 10^{-7} C \)
D. \( 3.25 \times 10^{-7} C \)


Chromium plating can involve the
electrolysis of an electrolyte of an
acidified mixture of chromic acid and
chromium sulphate. If during electrolysis the article being plated
increases in mass by \( 2.6 \mathrm{g} \) and \( 0.6 \mathrm{dm}^{3} \) of oxygen are evolved at an inert anode,
the oxidation state of chromiumions
being discharged must be : (assuming atomic weight of \( \mathrm{Cr}=52 \) and 1 mole of
gas at room temperature and pressure
occupies a volume of \( \left.24 d m^{3}\right) \)
A . -1
в. Zero
\( c \cdot+1 \)
D. +2


If the system of equations \( 2 x+3 y=7 \)
\( 2 a x+(a+b) y=28 \)
has infinitely many solutions, then
A \( . a=2 b \)
B. \( b=2 a \)
c. \( a+2 b=0 \)
\( \mathbf{D} \cdot 2 a+b=0 \)


Find the value of \( \frac{\cos 70^{0}}{\sin 20^{0}}+ \)
\( \cos 57^{0} \operatorname{cosec} 33^{0}-2 \cos 60^{0} \)


One of them is absent in closed
vascular bundles.
A. Cambium
B. Pith
c. Ground tissue
D. All of the above


\( 40 m l \) of hydrocarbon on combustion
gave \( 120 m l C O_{2} \) and \( 80 m l \) water vapour. The molecular formula of
hydrocarbon is:
\( \mathbf{A} \cdot C_{2} H_{6} \)
в. \( C_{3} H_{6} \)
\( \mathbf{c} \cdot C_{3} H_{8} \)
D. \( C_{3} H_{4} \)


The only element that exhibits positive SRP value is
A.
B. zn
c. \( \mathrm{Fe} \)
D. cu


If \( A A^{T}=I \) and \( \operatorname{det}(A)=1, \) then
A. Every element of \( A \) is equal to it's co-factor
B. Every element of A and it's co-factor are additive inverse of each other
C. Every element of A and it's co-factor are multiplicative inverse of each other
D. None of these


The area bounded by curve \( y=|x-1| \)
and \( y=1 \) is
A .
B. 2
c. \( 1 / 2 \)
D. None of these


Differentiate between the following:
Ascending and descending limbs of
Henle's loop.


A travelling wave has a velocity of 400 \( \mathrm{m} / \mathrm{s} \) and has a wavelength of \( 0.5 \mathrm{m} \) What is the phase difference between two points in the wave that are 1.25 milli
secs apart
A \( .2 \pi \)
в. \( 2 \pi / 3 \)
c. \( 2 \pi / 5 \)
D. \( \pi / 6 \)


\( \frac{\frac{\pi}{2}}{\frac{2}{2}} \)


If the equation, \( 1+\sin ^{2} x \theta=\cos \theta \) has
a non-zero solution in \( \theta \), then \( x \) must be
\( A \). an integer
B. a rational number
C. an irrational number
D. strictly between 0 and 1 .


Standard free energies of formation(in
\( k J / m o l \) ) at \( 298 \mathrm{K} \) are -237.2,-394.4
and -8.2 for \( H_{2} O(I), C O_{2}(g) \) and pentane(g) respectively. The value of \( E_{c e l l}^{o} \) for the pentane-oxygen fuel cell is:
A . \( 1.968 \mathrm{v} \)
в. 2.0968 V
c. \( 1.0968 \mathrm{v} \)
D. \( 0.0968 \mathrm{V} \)


A storage battery contains a solution of
\( H_{2} S O_{4} 38 \% \) by weight. What will be the
Vant Hoff factor if the \( \Delta T_{f(e x p e r i m e n t)} \) in \( \mathbf{2 9 . 0 8} .\left[\text {Given } \boldsymbol{K}_{\mathbf{1}}=\mathbf{1 . 8 6 m o l}^{-\mathbf{1}} \mathbf{K} \boldsymbol{g}\right] \)


A positively charged ball hangs from a silk thread. We put a positive test
charge \( q_{0} \) at a point and measure \( F / q_{0} \) then it can be predicted that the electric field strength E.
\( A \cdot>F / q_{0} \)
в. \( =F / q \)
c. \( <F / q_{0} \)
D. Cannot be estimated


Select the correct statement(s) among
the following.
a. Electron gain enthapy of \( A s \) is more
negative than \( C l \)
b. (+3) oxidation state are shown by \( \boldsymbol{S} \boldsymbol{b} \)
and \( B i \) both
c. \( \boldsymbol{P} \) is more electronegative than \( \boldsymbol{N} \)
\( A \cdot a, b \) and \( c \)
B. b only
c. a and bonly
D. b and conly


Violet coloured complex obtained in the
detection of sulphur is :
\( \mathbf{A} \cdot N a_{2}\left[F e(N O)(C N)_{5}\right] \)
B . \( \operatorname{Na}_{3}\left[\mathrm{Fe}(\mathrm{ONSNa})(\mathrm{CN})_{5}\right. \)
c. \( N a_{4}\left[F e(C N)_{5} N O S\right. \)
D. Both (B) and (C)


If the kinetic energy of the moving
particle is \( \boldsymbol{E} \), then the de Broglie wavelength is
A \( \cdot \lambda=\frac{h}{\sqrt{2 m E}} \)
B. \( \lambda=\frac{\sqrt{2 m E}}{h} \)
c. \( \lambda=h \sqrt{2 m E} \)
D. \( \lambda=\frac{h}{E \sqrt{2 m}} \)


Bulk modulus of water is \( 2 \times 10^{9} \) Pa. Air
is \( _{--}- \) - times more compressible than
water
A . 200
B . \( 2 \times 10^{3} \)
c. \( 2 \times 10^{5} \)
D . \( 2 \times 10^{4} \)


Why hard water does not form later with
soap? What advantages has soap over detergents.


Value of \( g \) on the surface of earth is
\( 9.8 m / s^{2} . \) Value of \( g \) on the surface of earth is \( 9.8 m / s^{2} . \) At height \( h=R \) from the surface the value of \( g \) is \( \frac{g}{x} . \) Find \( x \)


Select the correct matching of a
hormone, its source and function.
\( \mathbf{A} \)
B.
\( c \cdot 3 \)
D.


True or False.
The components of a mixture can never
be separated by physical methods.


Radius of circle is \( 7 \mathrm{cm} \) Find Perimeter
and area of circle


The centre of a circle is (2,-3) and the circumference is \( 10 \pi . \) Then, the equation of the circle is
A. \( x^{2}+y^{2}+4 x+6 y+12=0 \)
B . \( x^{2}+y^{2}-4 x+6 y+12=0 \)
c. \( x^{2}+y^{2}-4 x+6 y-12=0 \)
D. \( x^{2}+y^{2}-4 x-6 y-12=0 \)


Isodiaphers are the atoms of two elements having same values of:
A \( \cdot p / n \)
B . \( (p-n) \)
c. \( (n-p) \)
D . \( n \times p \)


Do you think an electromagnet can be used for separating plastic bags from a garbage heap? Explain


For a normal eye, the near point is 25 \( \mathrm{cm} \) from the eye lens.The distance between eye lens and retina of the eye is
2.5 cm. What is the power of the eye
lens?
A . \( 4 D \)
в. \( 40 D \)
\( c .36 D \)
D. \( -44 D \)


For which of the following reactions at equilibrium at constant temperature, doubling the volume will cause a shift to the right? This question has multiple correct options
A \( \cdot N_{2} O_{4}(g) \rightleftharpoons 2 N O_{2}(g) \)
в. \( C a C O_{3}(s) \rightleftharpoons C a O(s)+C O_{2}(g) \)
\( \mathbf{c} \cdot 2 C O(g)+O_{2}(g) \rightleftharpoons 2 C O_{2}(g) \)
D. \( N_{2}(g)+O_{2}(g) \rightleftharpoons 2 N O(g) \)


In the above given chemical reaction,
the compounds \( A \) and \( B \) respectively,
are :
A. Nitrobenzene and chlorobenzene
B. Nitrobenzene and fluorobenzene
c. Phenol and benzene
D. Benzene diazonium chloride and fluorobenzene


Assertion
More force is required to push a body up
a rough inclined plane than that to
move the same body down the same
plane
Reason
The friction always acts parallel to
inclined plane downwards
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A metal string is fixed between rigid supports. It is initially at negligible tension. Its Young's modulus is \( Y \) density is \( \rho \) and coefficient of linear
expansion is \( \alpha \). It is now cooled
through a temperature \( t, \) transverse
waves will move along it with a speed of
A \( \cdot \sqrt{\frac{Y \alpha t}{\rho}} \)
B \( \cdot Y \sqrt{\frac{\alpha t}{\rho}} \)
c. \( \alpha \sqrt{\frac{Y t}{\rho}} \)
D \( \cdot t \sqrt{\frac{\rho}{Y \alpha}} \)


R.Q. of anaerobic respiration is
A. zero
B. Less than 1
\( c \cdot 1 \)
D. More than 1


Which of the following represents a
detergent?
A. Sodium salt of alkyl hydrogen sulphate of alcohol or alkyl benzene sulphonate
B. Sodium salt of long chain carboxylic acid
C. Potassium salt of long chain carboxylic acid
D. All of these


If \( \boldsymbol{A}=\left[\begin{array}{cc}\mathbf{3} & \mathbf{1} \\ -\mathbf{1} & \mathbf{2} \\ \mathbf{0} & \mathbf{6}\end{array}\right] \) and \( \boldsymbol{B}= \)
\( \left[\begin{array}{ccc}5 & 4 & 6 \\ 4 & 1 & 2 \\ -5 & -1 & 1\end{array}\right], \) then
A. \( A+B \) exists
B. \( A B \) exists
c. \( B A \) exists
D. none of these


If you are traveling on a spaceship close to the speed of light (pick a number e.g.
0.95c), With or without constant acceleration whichever works for the
question. Time will slow down relative to earth
and you will be able to travel a greater distance than you would be able to without relativistic effects. You would
also be able to return to earth with
significant time passed relative to your experience. My question is, what would it feel like on the spaceship...I know the standard answer is you wouldn't feel anything, but logically, if you were traveling through galaxy after galaxy in a relativistic time of human life then
intuition says everything would look like it whizzing past. Basically, what is the human experience of being able to trave interstellar distances?


Two Particles are dropped simultaneously from the top of a tall
building. Particle 1 has mass \( M_{1} \) and
particle 2 has mass \( M_{2} . \) Find out the
ratio of their momentum just before
they hit the ground? Neglect the air
resistance
A \( \cdot \frac{\sqrt{M_{1}}}{M_{2}} \)
в. \( \frac{M_{1}}{M_{2}} \)
\( \left(\frac{M_{1}}{M_{2}}\right)^{2} \)
D. 1
E. None of the above


A South pole and North pole of each strength 'm' are placed at the two corners of an equilateral triangle of side 'a'. The resultant magnetic induction field
strength at the third vertex is :
A. o (zero)
в. \( \frac{2 \mu_{0}}{4 \pi} \frac{m}{d^{2}} \)
c. \( \frac{\mu_{0}}{4 \pi} \frac{m}{d^{2}} \)
D. \( \frac{3 \mu_{0}}{4 \pi} \frac{m}{d^{2}} \)


Which reagent is used in
Rosenmund reduction?
\( \mathbf{A} \cdot H_{2} / P d-B a S O_{4} \)
\( \mathbf{B} \cdot L i A I H_{4} \)
\( \mathbf{c} \cdot N H_{2}-N H_{2} / K O H / C H_{2} O H-C H_{2} O H \)
\( \mathbf{D} \cdot Z n-H g / H C l \)


If the ratio of the perimeter of two
similar triangles is \( 4: 25, \) then find the
ratio of the areas of the similar
triangles


A particle is moving with a velocity of \( \boldsymbol{v}=\left(\mathbf{3}+\mathbf{6} \boldsymbol{t}+\mathbf{9} \boldsymbol{t}^{2}\right) \boldsymbol{m} / \boldsymbol{s} . \) This
displacement of the particle in the interval \( t=5 s \) to \( t=8 s \) is
\( \mathbf{A} \cdot 1287 m \)
в. \( 1285 \mathrm{m} \)
c. \( 1280 m \)
D. \( 1290 m \)


A spontaneous reaction occurs:
A. by itself and quickly
B. with outside intervention and quickly
C . by itself and slowly
D. with outside intervention and slowly
E. by itself but it has now effect on how fast the reaction
takes


The temperature of an isolated black
body falls from \( T_{1} \) to \( T_{2} \) in time \( t, \) then \( t \)
is (Let \( c \) be a constant)
A \( \cdot t=c\left(\frac{1}{T_{2}}-\frac{1}{T_{2}}\right) \)
B \( t=c\left(\frac{1}{T_{2}^{2}}-\frac{1}{T_{1}^{2}}\right) \)
\( ^{\mathrm{c}} \cdot_{t=c}\left(\frac{1}{T_{2}^{3}}-\frac{1}{T_{1}^{3}}\right) \)
D \( t=c\left(\frac{1}{T_{2}^{4}}-\frac{1}{T_{1}^{4}}\right) \)


Calculate combined resistance.


A compound of relative molecular mass
34 and empirical formula \( H O \) has the molecular formula:
A \( . H O_{2} \)
в. \( H O \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{O} \)
D. \( H_{2} O_{2} \)


Assertion
Integrated pest management programme involves harmonious
application of various 'cuture controls'
to insure minimum environmental
pollution and proper maintenance of ecological balance.
Reason
Integrated pest management programme is an important step taken by Government of India.
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 \( f(x)=\frac{2}{3} x+7, \) find the value of \( f(x) \)
if \( \boldsymbol{x}=\mathbf{3} \)
A. - -
B . - -
\( c \cdot 6 \)
D.


Copper reacts with \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \) to give \( \boldsymbol{N} \boldsymbol{O} \)
and \( N O_{2} \) in molar ratio of 1: 2
\( \boldsymbol{C u}+\boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \longrightarrow \ldots \ldots+\boldsymbol{N} \boldsymbol{O}+ \)
\( N O_{2}+\dots \dots \)
If true enter 1 , if false enter 0 .


Which one of the following products is formed when a mixture of steam,
sulphur dioxide gas and oxygen gas (from air) is passed over dry lumps of common salt, the sodium chloride?
A. \( N a_{2} S O_{3} \)
в. \( C l_{3} \)
\( \mathbf{c} \cdot \operatorname{NaH} S O_{3} \)
D. \( N a_{2} S O_{4} \)


If the supplement of an angle is \( 65^{\circ} \) then find its complement.


If the matrices \( A, B,(A+B) \) are non singular then \( \left[\boldsymbol{A}(\boldsymbol{A}+\boldsymbol{B})^{-1} \boldsymbol{B}\right]^{-1} \) is
equal to-
\( \mathbf{A} \cdot A+B \)
B. \( A^{-1}+B^{-1} \)
c. \( A(A+B)^{-1} \)
D. None


Using integration, find the area bounded by the curve \( x^{2}=4 y \) and the
line \( x=4 y-2 \)


The value of the total energy of an electron in the hydrogen atom is given by:
A \( \cdot m v^{2} \)
B . \( 1 / 2 m v^{2} \)
c. \( -e^{2} / 2 r \)
D. \( -m v / r^{2} \)


Simplify: \( \left(-80 m^{4} n p q\right) \div 10 m^{3} p q n^{2} \)
\( \mathbf{A} \cdot-8 m n \)
в. -8 тпр\( q \)
\( c .-8 m \)
D. \( \frac{-8 m}{n} \)


The middle term in the expansion of \( \left(\frac{a}{x}+b x\right)^{12} \)
A \( \cdot 924 a^{6} b^{6} \)
B. \( 924 a^{6} b^{5} \)
\( \mathbf{c} \cdot 924 a^{5} b^{5} \)
D. \( 924 a^{5} b^{6} \)


Write down the number of significant figures in the following value. \( \mathbf{1 2 0 0} \boldsymbol{N} \)
A .4
B. 3
\( c \cdot 2 \)
D.


Which of the following is not a compound?
A. Sugar
B. Common Salt
c. Diamond
D. Plaster ofParis


If \( (x+i y)^{3}=u+i v, \) then show that
\( \frac{u}{x}+\frac{v}{y}=4\left(x^{2}-y^{2}\right) \)


Hydrogen occupies a unique position in Modern Periodic Table.
A. True
B. False


The most common oxidation state of
lanthanides is:
\( A \cdot+2 \)
B. +3
\( c \cdot+4 \)
D. +5


Which part has maximum attraction in a magnet?
A. In the centre
B. on the sides
c. on the poles
D. on the surface


The coordinates of \( B \) is \( (3,-2) . \) If true
enter 1 or else.


Calculate the heat needed to raise the
temperature of \( 20 g \) iron from \( 25^{\circ} C \) to
\( 500^{\circ} \mathrm{C}, \) if specific heat capacity of iron is \( 0.45 J K^{-1} g^{-1} \)
\( \mathbf{A} \cdot 6732 J \)
в. \( 225 . J \)
c. \( 15.66 . \)
D. 2250J


The \( 3 r d, 4 t h \) and 5 th terms in the
expansion of \( (1+x)^{n} \) are 60,160 and
240 respectively, then \( x= \)
\( A \cdot 2 \)
B. 4
\( c .5 \)
D. 6


Polygons that have any portions of their diagonals in their exterior are called
A. squares
B. convex polygons
c. concave polygons
D. triangles


Find the modulus of the complex number \( \sqrt{\mathbf{2}} \boldsymbol{i}-\sqrt{-\mathbf{2}} \boldsymbol{i} \)


If \( \frac{2}{11} \) is the probability of an event.
What is the probability of the event 'not
\( \boldsymbol{A}^{\prime} \)


Consider a light beam incident from air to a glass slab at Brewster's angle as
shown in figure. A polaroid is placed in the path of the emergent ray at point \( \mathrm{P} \)
and rotated about an axis passing
through the centre and perpendicular to
the plane of the polaroid.
A. For a particular orientation there shall be darkness as observed through the polaroid
B. The intensity of light as seen through the polaroid shall be independent of the rotation
c. The intensity of light as seen through the polaroid shall go through a minimum but not zero for two orientations of the polaroid
D. The intensity of light as seen through the polaroid shall go through a minimum for four orientations of the polaroid.


State whether given statement is True
or False

When a point object is at the principal focus of a convex lens, it forms a parallel beam of light after refraction.
A. True
B. False


A calorimeter contains \( 70.2 g \) of water
at \( 15.3^{\circ} \mathrm{C} \). If \( 143.7 g \) of water \( \operatorname{at} 36.5^{\circ} \mathrm{C} \)
in mixed it with the common
temperature is \( 28.7^{\circ} \mathrm{C} \). The water
equivalent of the calorimeter is:
A. \( 15.6 g \)
в. \( 9.4 g \)
\( c .6 .3 g \)
D. \( 13.4 g \)


The charge \( Q \) and \( -2 Q \) are placed at some distance. What is the locus of
point in the plane of the charges where the potential is zero?
1. Parabola
2. Circle
3. Ellipse
Write your answer in terms 1,2 and 3
only.


\( \boldsymbol{y}=\frac{\boldsymbol{x}}{2 \sqrt{2}} \) find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \)


What is aestivation ? Describe various
types of aestivation.


The sides of a triangle are equal and have equations \( 2 x-y=0,3 x+y=0, x \)
\( 3 y+10=0, \) respectively find the equation of three medians of the triangle and verify that they are concurrent


Evaluate the following limit \( \lim _{x \rightarrow 0} \frac{(1+x)^{6}-1}{x} \)


Chlorine is the main factor to damage ozone layer. CFC is considered
responsible for \( 80 \% \) of total decrease in
ozone layer. If the pollution in the atmosphere increases, which of the following is possible in future?
P. The ice at poles will melt and all the organisms will die living at the island.
Q. Many organisms living at island may migrate.
R. The existence of forests on the Earth
will be no more.
A . Only Q
B. Only P and Q
c. All P, Q and R
D. only Q and R


If the integers \( m \) and \( n \) are chosen at
random from 1 to 100 then the
probability that \( 7^{m}+7^{n} \) is divisible by
5 is \( ? \)
A. \( 1 / 5 \)
B. 1/7
c. \( 1 / 4 \)
D. 1/49


The formal charge on the 0 atoms in the ion \( [: \ddot{O}=N=\ddot{O}:]^{+} \) is:
A . -2
B. - 1
c. 0
D. +1


Choose the correct answer from the
alternatives given:
The sum of \( \frac{1}{\sqrt{2}+1}+\frac{1}{\sqrt{3}+\sqrt{2}}+ \)
\( \frac{1}{\sqrt{4}+\sqrt{3}}+\ldots . .+\frac{1}{\sqrt{100}+\sqrt{99}} \) is
\( \mathbf{A} \cdot \mathbf{9} \)
B . 10
c. 11
D. None of these


Female sex organ of a Bryophyte differs
from that of a Fungus in structure in
having
A. A unicellular stalk
B. A sterile jacket
c. A single cell only
D. A multicellular gametophyte


In the diagram above, what is the half
reaction that occurs at the cathode?
A \( \cdot A l \rightarrow A l^{3+}+3 e^{-} \)
B. \( N i^{2+}+2 e^{-} \rightarrow N i \)
\( \mathbf{C} \cdot N i \rightarrow N i^{2+}+2 e^{-} \)
\( \mathbf{D} \cdot 2 A l^{3+}+6 e^{-} \rightarrow 2 A l \)
E. None of these


A constant current i is maintained in a
solenoid. Which of the following
quantities will increase if an iron rod is inserted in the solenoid along its axis? This question has multiple correct options
A. Magnetic field at the centre
B. Magnetic flux linked with the solenoid
c. self-inductance of the solenoid
D. Rate of Joule heating


If
\( M_{e} \) is the mass of earth and \( M_{m} \) is
the mass of moon \( \left(M_{e}=81 M_{m}\right) \). The
potential energy associated with object of mass \( m \) situated at a distance \( R \)
from the centre of earth and \( r \) from
the centre of moon, will be :
\( ^{\mathbf{A}} \cdot_{-G m M_{m}}\left[\frac{R}{81}+r\right] \frac{1}{R^{2}} \)
в. \( -G m M_{m}\left[\frac{81}{r}+\frac{1}{R}\right] \)
\( ^{\mathrm{c}} \cdot_{-G m M_{m}}\left[\frac{81}{R}+\frac{1}{r}\right] \)
D. \( -G m M_{m}\left[\frac{81}{R}-\frac{1}{r}\right. \)


\( (\boldsymbol{P} \cap \boldsymbol{Q}) \cup(\boldsymbol{Q} \cap \boldsymbol{R}) \)
A \( \cdot\{b, c, f\} \)
в. \( \{b, c, d\} \)
\( \mathbf{c} \cdot\{b, c, d, f\} \)
\( \mathbf{D} \cdot\{b, c, f, g\} \)


Sum of a \( \alpha \) hydrogen in \( A+B+C=? \)
A . 17
B. 18
\( c \cdot 19 \)
D. 20


An n-type semiconductor is
A. Positively charged
B. Negatively charged
C . Electrically neutral
D. None of the above


Two people can hear the sound of each
other on the moon's surface.
A. True
B. False


Given 3 vectors: \( \vec{V}_{1}=a \hat{i}+b \hat{j}+c \hat{k} \)
\( \vec{V}_{2}=b \hat{i}+c \hat{j}+a \hat{k} \) and \( \vec{V}_{3}=c \hat{i}+a \hat{j}+ \)
b \( \hat{k} . \) In which of the following conditions
\( \vec{V}_{1}, \vec{V}_{2} \) and \( \vec{V}_{3} \) are linearly independent?
A \( \cdot a+b+c=0 \) and \( a^{2}+b^{2}+c^{2} \neq a b+b c+c a \)
B . \( a+b+c=0 \) and \( a^{2}+b^{2}+c^{2}=a b+b c+c a \)
C \( \cdot a+b+c \neq 0 \) and \( a^{2}+b^{2}+c^{2}=a b+b c+c a \)
D . \( a+b+c \neq 0 \) and \( a^{2}+b^{2}+c^{2} \neq a b+b c+c a \)


Calculate the freezing temperature of
an aqueous solution having its boiling
temperature \( 100.1^{\circ} \mathrm{C} \). The mola
ebullioscopic constant and the molal cryoscopic constant are 0.513 deg and 1.86 deg, respectively. The answer is
\( -0 . m n \) then \( m+n= \)


A compound contains \( N=25.94 \% \) and 0
\( =74.06 \% . \) If its vapour density is 54.2 calculate its molecular formula.
A . \( N O \)
в. \( N O_{2} \)
\( \mathrm{c} \cdot N_{2} \mathrm{O} \)
D. \( N_{2} O_{5} \)


In the \( \ln \boldsymbol{K} \boldsymbol{v} \boldsymbol{s} \cdot \frac{\boldsymbol{1}}{\boldsymbol{T}} \) plot of chemical
process having \( \Delta S^{\circ}>0 \) and \( \Delta H^{\circ}<0 \)
the slope is proportional to (where Kis equilibrium constant)
A . \( -\left|\Delta H^{\circ}\right| \)
в . \( \left|\Delta H^{\circ}\right| \)
\( \mathrm{c} \cdot-\Delta S^{\circ} \)
D. \( \Delta G^{\circ} \)


A light source is placed \( 100 \mathrm{cm} \) away from a screen. A converging lens placed at a certain position between the source and the screen focuses the image of the source on the screen. The lens is moved
a distance of \( 40 \mathrm{cm} \) and it is found that
it again focuses the image of the source on the screen. The focal length of the lens is :
\( A \cdot 21 \mathrm{cm} \)
B. 30 cm
c. \( 40 \mathrm{cm} \)
D. \( 67 \mathrm{cm} \)


Lines \( L_{1}: x+\sqrt{3} y=2, \) and \( L_{2}: a x+ \)
\( b y=1 \) meet at \( P \) and enclose an angle
of \( 45^{\circ} \) between them. A line \( L_{3}: y= \)
\( \sqrt{3} x, \) also passes through \( P \) then
\( \mathbf{A} \cdot a^{2}+b^{2}=1 \)
B \( \cdot a^{2}+b^{2}=2 \)
c. \( a^{2}+b^{2}=3 \)
\( \mathbf{D} \cdot a^{2}+b^{2}=4 \)


Chain and position isomerism are shown in:
A . alkane
B. alkene
c. alkynes
D. all of the above


A diatomic ideal gas is expanded at constant at pressure. If work done by the system is \( 10 J \) then calculate heat
absorbed.
A . \( 40 J \)
в. \( 20 J \)
\( c .35 J \)
D. \( 15 J \)


For the following AP, write the first term
and the common difference
-5,-1,3,7
A. First term: 7 and Common difference: 7
B. First term: 3 and Common difference: -1
C. First term: -5 and Common difference: 4
D. First term: 3 and Common difference: -2


The molar mass of \( \boldsymbol{O}_{3} \) is 48 gram per
mole. How many moles are there in 480
grams of ozone?
A . \( 0 . \)
B. 1
\( c \cdot 10 \)
D. 4.8


Evaluate the following limits. \( \lim _{x \rightarrow a} \frac{\sin \sqrt{x}-\sin \sqrt{a}}{x-a} \)


Washing soda on strong heating gives sodium oxide and carbon dioxide.
A. True
B. False


How many ATP molecules will be produced in a brain cell (neuron) from a glucose molecule involving electron transport chain only?
A . 32
B. 16
\( c \cdot 38 \)
D. 34


A circular loop of radius \( \boldsymbol{R} \), carrying
current \( I, \) lies in \( x \) -y plane with its
center at origin. The total magnetic flux through x-y plane is
A. directly proportional to \( I \)
B. directly proportional to \( R \)
c. inversely proportional to \( R \)
D. inversely proportional to \( I \)
E. zero


A lightning rocket is a device used to
control
A. time and location of a lighting strike.
B. fuel and location of a lighting strike.
C. the lighting of the strom
D. none of the above


Which of the following are polycarbamate ester polymers? This question has multiple correct options
A. Polyurethane
B. Perlon-U
c. Melamine
D. Saran


when \( \boldsymbol{x} \in \boldsymbol{R} \)
Are the following pairs of the
statements are negative of each other:
The number \( x \) is a rational number.
The number \( x \) is not an irrational
number.
If Yes put 1 else 0.


In an experiment, the refractive index of glass was observed to be
1.45,1.56,1.54,1.44,1.54 and 1.53
Calculate relative error.


Assertion
FrCl has \( C \)s \( C l \) structure with
coordination number 8
Reason
\( C N 8 \) is favoured by the large cation size.

Read the above assertion and reason
and choose the correct option regarding
¡t.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


If \( \boldsymbol{x}^{\boldsymbol{m}} \cdot \boldsymbol{y}^{\boldsymbol{n}}=(\boldsymbol{x}+\boldsymbol{y})^{\boldsymbol{m}+\boldsymbol{n}} \) then \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}= \)
A. \( \frac{y}{x} \)
B. \( -\frac{y}{x} \frac{y}{x} \)
c. \( \frac{m y}{x} \)
D. \( \frac{n y}{x} \)


The heat pump is also called as the :
A. Reverse motor
B. Reverse refrigerator
c. Reverse oscillator
D. Reverse engine


A ceiling fan is rotating at the rate of
\( 3.5 r p s \) and its moment of inertia is
\( 1.25 k g m^{2} . \) If the current is switched off
the fan comes to rest in \( 5.5 s . \) The torque acting on the fan due to friction is:
A . \( 2.5 \mathrm{Nm} \)
B. \( 5 \mathrm{Nm} \)
\( \mathrm{c} .7 .5 \mathrm{Nm} \)
D. 10 Nm


Photosynthesis of a carbohydrate in plants is given by chemical equation:
\( 6 C O_{2}+6 H_{2} O \longrightarrow C_{6} H_{12} O_{6}+6 O_{2} \)
If you have net result as:
\( 6 C O_{2}+6 H_{2} O \longrightarrow C_{6} H_{12} O_{6}+6 O_{2} \)
Check whether this reaction is correct
or not.


Consider the following gas phase
reaction:
\( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{B r}_{2}(\boldsymbol{g}) \rightleftharpoons 2 \boldsymbol{H} \boldsymbol{B} \boldsymbol{r}(\boldsymbol{g}) \)
The concentrations of \( \boldsymbol{H}_{2}, \boldsymbol{B} \boldsymbol{r}_{2}, \) and
HBr are \( 0.05 M, 0.03 M, \) and \( 500.0 M \)
respectively. The concentration equilibrium constant for this reaction
\( \operatorname{at} 400^{\circ} \mathrm{C} \) is \( 2.5 \times 10^{3} . \) Is this system at
equilibrium?
A. Yes, the system is at equilibrium.
B. No, the reaction must shift to the right in order to reach equilibrium.
c. No, the reaction must shift to the left in order to reach equilibrium.
D. It cannot be determined


Suppose a pool begins with a population of only 1 bacterium. What would be the mass of the population
after 30 hours?


\( \angle C E D \)


Centrosomes occurs in
A. Green plants
B. Bacteria
C. Animal cells
D. All of the above


If \( \int \frac{2^{x}}{\sqrt{1-4^{x}}} d x=K \sin ^{-1}\left(2^{x}\right)+C \)
then \( K \) is equal to
A \( . e n 2 \)
в. \( \frac{1}{2} \ell n 2 \)
\( c \cdot \frac{1}{2} \)
D. \( \frac{1}{\ell n^{2}} \)


A \( 400 \Omega \) resistor and \( 6 \mu F \)
capacitor are connected in parallel to a source of \( V_{r m s}=220 V \)
and angular frequency 360 rad \( / s \)
Find the current in the resistor
and capacitor.
A. 0.55 A 0.475 A
B. 0.65 A , 0.726 A
c. 0.55 А, 0.176 А
D. none of these


\( \left(\left[\begin{array}{ll}\mathbf{8} & \mathbf{4} \\ \boldsymbol{x} & \mathbf{8}\end{array}\right]\right)=\mathbf{4}\left(\left[\begin{array}{ll}\mathbf{2} & \mathbf{1} \\ \mathbf{1} & \mathbf{2}\end{array}\right]\right) \) then the value
of \( x \) is
A .
B. 2
\( c \cdot \frac{1}{4} \)
\( D \)


A force of magnitude 6 in the direction of the vector \( \vec{i}-2 \vec{j}+2 \vec{k} \) acts at the point whose position vector is \( \vec{i}-\vec{j} \). \( A \)
second force acting at the point with position vector \( \vec{j}-\vec{k} \) forms a couple
with the first force. Find the vector
moment of the couple.
\( \mathbf{A} \cdot-(2 \vec{i}+\vec{j}) \)
B . \( -2(2 \vec{i}+\vec{j}) \)
c. \( -4(2 \vec{i}+\vec{j}) \)
D. \( -8(2 \vec{i}+\vec{j}) \)


If the probability of defective bolts is 0.1
find the mean and standard deviation
for the distribution of defective bolts in
a total of 500 bolts.


Which one of them catalyzes oxidation-
reduction reactions?
A. Oxidase
B. Oxidoreductase
c. oxygenase
D. All of the above


Replacement of diazo group by other groups is helpful in preparing those substituted aromatic compounds which cannot be prepared by:
A. direct elimination
B. replacement reaction
c. direct substitution
D. addition reaction


Two long parallel wires \( P \) and \( Q \) are held
perpendicular to the plane of the paper at a acceptance of \( 5 \mathrm{m} \) between them. If \( P \)
and \( Q \) carry currents of 2.5 and 5 amp
respectively in the same direction, then
the magnetic field at a point half way
between the wire is
\( \mathbf{A} \cdot \frac{\mu_{0}}{\pi} \)
B. \( \frac{\sqrt{3} \mu_{0}}{\pi} \)
\( c \cdot \frac{\mu_{0}}{2 \pi} \)
D. \( \frac{3 \mu_{0}}{2 \pi} \)


A certain liquid mixture of two liquids \( A \) and B (behaving ideally) has a vapour
pressure 70 torr \( (1 \text { torr }=1 \mathrm{mm}) \) at \( 25^{\circ} \mathrm{C} \) for a certain mole fraction \( X \) of \( A \). For the same mole fraction \( X \) for \( B \) in the
mixture, the vapour pressure of mixture
is 90 torr at \( 25^{\circ} \mathrm{C} . \) If \( \boldsymbol{P}_{A}^{0}-\boldsymbol{P}_{B}^{0}=\mathbf{4 0} \) torr
calculate \( P_{A}^{0}, P_{B}^{0} \) and \( X \)
A . 100 torr, 60 torr, 0.25
B. 120 torr, 80 torr, 0.25
c. 200 torr, 160 torr, 0.25
D. 220 torr, 180 torr, 0.25


If \( n_{r} \) and \( n_{b} \) are the number of photons
of red and blue lights respectively with same energy, then
A \( \cdot n_{r}>n_{b} \)
в. \( n_{r}<n_{b} \)
\( \mathbf{c} \cdot n_{r}=n_{b} \)
D. no relation between \( n_{r} \) and \( n_{b} \)


Read the following statements.
a. Ozone in found mostly in the
stratosphere
b. Ozone layer lies \( 55-75 \) kms above the surface of the earth.
c. 0 zone absorbs ultraviolet radiation
from the Sun
d. Ozone layer has no significance for life on the earth.
Which set of the statements is correct?
A. a and c
B. b and d
\( c . \) b and \( c \)
D. a and d


\( \int \frac{\cos ^{3} x}{\sqrt{\sin x}} d x \)


A bomb of mass \( m=1 \mathrm{kg} \) thrown
vertically upwards with a speed \( u= \)
\( 100 \mathrm{m} / \mathrm{s} \) explodes into two parts after
\( \boldsymbol{t}=\mathbf{5} \) s. \( \mathbf{A} \) fragment of \( \operatorname{mass} \boldsymbol{m}_{\mathbf{1}}=\mathbf{4 0 0} \mathbf{g} \)
moves downwards with a speed \( v_{1}=25 \)
\( \mathrm{m} / \mathrm{s}, \) then speed \( \boldsymbol{v}_{2} \) and direction of
another mass \( m_{2} \) will be?
A. \( 40 \mathrm{m} / \mathrm{s} \) downwards
B. 40 m/s upwards
c. \( 60 \mathrm{m} / \mathrm{s} \) upwards
D. \( 100 \mathrm{m} / \mathrm{s} \) upwards


\( \lim _{h \rightarrow 0} \frac{\sqrt{x+h}-\sqrt{x}}{h} \) is equal to
A \( \cdot \sqrt{x} \)
в. \( \frac{1}{2 \sqrt{x}} \)
\( c \cdot 2 \sqrt{x} \)
D. \( \frac{1}{\sqrt{x}} \)


The molecular weight of an organic compound is 58.0 g/mol. Compute the boiling point of a solution containing \( 24.0 \mathrm{g} \) of the solute and \( 600 \mathrm{g} \) of water when the barometric pressure is such that pure water boils at
\( 99.725^{\circ} \mathrm{C} .\left(K_{6} \text { forwater } 0.513^{\circ} \mathrm{C} / \mathrm{m}\right) \)
\( \mathbf{A} \cdot 50^{\circ} C \)
B . \( 100.08^{\circ} \mathrm{C} \)
\( c \cdot 150.1^{\circ} C \)
D. \( 180.34^{\circ} \mathrm{C} \)


Ge and Si diodes start conducting at 0.3
V and 0.7 V respectively. In the following figure if Ge diode connection are
reversed, the value of \( V_{o} \) changes by :
(assume that the Ge diode has large
breakdown voltage)
A . \( 0.6 v \)
B. 0.8
\( c \cdot 0.4 v \)
\( D, 0.2 \mathrm{v} \)


The weight of one mole of heavy water
is:
A. \( 18 \mathrm{gm} \)
B. \( 20 \mathrm{gm} \)
c. \( 19 \mathrm{gm} \)
D. 21 gm


John and Jivanti together have 45 marbles. Both of them lost 5 marbles
each, and the product of the number of
marbles they now have is \( 124 . \) Form the quadratic equation we can find that John had 36 or 9 marbles.
A. True
B. False


During every financial year, the value of a machine depreeciates by 12\%. Find the original cost of a machine which depreciates to Rs. 2,640 during the second financial year of its purchase.
A. 3409
B. 3333
\( c \cdot 2365 \)
D. 855


The area bounded by \( \mathbf{y}=\sin \mathbf{x}, \mathbf{y}=\cos \mathbf{x} \)
between any two successive intersections is:
A .2
B. \( \sqrt{2} \)
\( c \cdot 2 \sqrt{2} \)
D. 4


Solve the following simultaneous linear equations by method of reduction.
\( \boldsymbol{x}+\mathbf{2} \boldsymbol{y}+\boldsymbol{z}=\mathbf{8} \)
\( 2 x+3 y-z=11 \)
\( 3 x-y-2 z=5 \)


The sum total of the number of
electrons in a system may change. The
statement is :
A. true
B. false
c. ambiguous
D. data insufficient


At \( 25^{\circ} C, \) the vapour pressure of pure benzene is 100 torr, while that of pure
ethyl alcohol is 44 torr. Assuming ideal behaviour, calculate the vapour
pressure at \( 25^{\circ} \mathrm{C} \) of a solution which
contains 10 g of each substance.
A. 33.775 torr
B. 54.775 torr
c. 64.775 torr
D. 60.775 torr


If fifth term of a GP is 2 , then the
product of its 9 terms is:
A .256
в. 512
\( c \cdot 1024 \)
D. None of these


The main reason for showing anomalous properties of the first
member of a group in s or p-block is :
A. maximum chemical reactivity
B. maximum electronegativity and different configurations
c. small size, large charge, /radius ratio
D. tendency to form multiple bonds


Aqueous sodium hydroxide reacts with white phosphorous to form phosphine
and :
A. \( N a H_{2} P O_{2} \)
в. \( P_{2} O_{5} \)
\( \mathbf{c} \cdot N a_{2} P O_{3} \)
D. \( P_{2} O_{3} \)


When magnesium wire is lighted in an air, it burns with bright light and gives powder as a residue.
A . black
B. white
c. yellow
D. blue


A fascinating behaviour of the series RLC circuit is the phenomenon of resonance.
a) Explain Resonance in an LCR circuit.
b) Draw a graphical representation of
variation of current amplitude \( i_{m} \) with
frequency \( \omega \)
c) What do you mean by sharpness of resonance? Explain it.


P-V diagram of a diatomic gas is a straight line passing through origin. The molar heat capacity of the gas in
the process will be
A. \( 4 R \)
в. \( 2.5 R \)
\( c .3 R \)
D. \( \frac{4 R}{3} \)


Consider two events \( A \) and \( B \) of an
experiment where \( P(A \cap B)=\frac{1}{4} \) and \( P(B)=\frac{1}{2}, \) then \( P(A) \) cannot exceed
\( A \cdot \frac{1}{2} \)
B. \( \frac{2}{3} \)
\( c \cdot \frac{3}{4} \)
D.


The temperature of stars is determined
by
A. Stefan's law
B. Wien's displacement law
c. Kirchhoff's law
D. Ohm's law


A weak acid react with strong base, ionisation constant of weak acid is \( 10^{-4} \)
Find out equilibrium constant for this reaction.
A \( \cdot 10^{-10} \)
B. \( 10^{10} \)
\( c \cdot 10^{-9} \)
\( D \cdot 10^{9} \)


Find \( y=\left(\sin ^{-1} x\right)^{x^{2}}, \) then \( y^{\prime}(0)=? \)


According to Maxwell's hypothesis,
changing of electric field give rise to
A. Magnetic field
B. Pressure gradient
c. charge
D. voltage


Which one of the following diagrams best represents the path followed by a projectile that has been launched horizontally from a countertop?
\( A \)
в.
\( c \)
D.


Which of the following forms cationic
micelles above a certain minimum
concentration?
A. Sodium dodecyl sulphate
B. Sodium acetate
c. urea
D. cetyl trimethyl ammonium bromide


How did Rutherford conclude that \( \alpha \)
particles were not deflected by the attraction of electrons inside the atom?


Two solid spheres of same size of a
certain metal are placed in contact with
each other. Prove that the gravitiational
force acting between them is directly
proportional to the fourth power of their
radius.


A bird flies with a speed of \( 10 \mathrm{km} / \mathrm{h} \)
and a car moves with a uniform speed
of \( 8 k m / h . \) Both start from \( B \) toward \( \boldsymbol{A}(\boldsymbol{B} \boldsymbol{A}=\mathbf{4 0} \boldsymbol{k} \boldsymbol{m}) \) at the same instant.
The bird having reached \( A \), flies back immediately to meet the approaching car. As soon as it reaches the car, it flies
back to \( A \). The bird repeats this till both
the car and the bird reach \( \boldsymbol{A} \)
simultaneously. Find the total distance flown by the bird.


Rural population in India is higher, as compared to its urban population, since it is a developing country
A. True
B. False


A bag contains some white and some black balls, all combinations of balls
being equally likely. The total number of
balls in the bag is \( 10 . \) If three balls are drawn at random without replacement and all of them are found to be black,
the probability that the bag contains 1
white and 9 black balls is
A \( \cdot \frac{14}{55} \)
B. \( \frac{12}{55} \)
\( c \cdot \frac{2}{55} \)
D. \( \frac{8}{55} \)


Among the following, the most stable complex is:
\( \mathbf{A} \cdot\left[F e\left(H_{2} O\right)_{6}\right]^{3} \)
B . \( \left[F e\left(N H_{3}\right)_{6}\right]^{3+} \)
c. \( \left[F e\left(C_{2} O_{4}\right)_{3}\right]^{3} \)
D. \( \left[F e C I_{6}\right]^{3-} \)


The total kinetic energy of 1 mole of \( N_{2} \) at \( 27 \mathrm{C} \) will be approximately
A . 3739.662
B. 1500 calorie
c. 1500 kilo calorie
D. 1500 erg.


A body of mass \( m \) is moving in a circular orbit of radius \( \boldsymbol{R} \) about a planet
of mass \( M . \) At some instant, it splits into two equal masses. The first mass moves in a circular orbit of radius \( \frac{\boldsymbol{R}}{\longrightarrow} \) \( \overline{2} \)
and the other mass, in a circular orbit of radius \( \frac{3 R}{2} . \) The difference between the final and initial total energies is:
A. \( -\frac{G M m}{2 R} \)
в. \( +\frac{G M m}{6 R} \)
c. \( \frac{G M m}{2 R} \)
D. \( -\frac{G M m}{6 R} \)


Which of the following halides cannot be hydrolyzed?
(I) \( \boldsymbol{T} \boldsymbol{e} \boldsymbol{F}_{6},(\|) \boldsymbol{S} \boldsymbol{F}_{6} \)
(III) \( N C l_{3}, \) and \( (I V) \)
\( N F_{3} \)
\( \mathbf{A} \cdot\|\| \) and \( I \mathbf{V} \)
B. I, II and III
c. ।, ॥ and IV
D. II and IV


Expand the binomial \( \left(\frac{2 x}{3}+\frac{3 y}{2}\right)^{20} u p \) to four terms


State the following statement is True or
False
f \( p, q, r \) are statements, with truth
values \( \mathrm{T} \), \( \mathrm{F} \), \( \mathrm{T} \) respectively, then the truth value of \( (\sim p \vee q) \wedge \sim r \Rightarrow p \) is \( T \)
A. True
B. False


A ray of light from air suffers partia reflection and refraction at the
boundary of water as shown in the
figure. In Fig, which of the ray is the correct partially reflected ray?
\( A \cdot D \)
в. \( B \)
\( c \)
\( D \)


Find the values of \( x, \) if
\( \left|\begin{array}{ll}\boldsymbol{x}+\mathbf{1} & \boldsymbol{x}-\mathbf{1} \\ \boldsymbol{x}-\mathbf{3} & \boldsymbol{x}+\mathbf{2}\end{array}\right|=\left|\begin{array}{ll}\boldsymbol{4} & -\mathbf{1} \\ \mathbf{1} & \mathbf{3}\end{array}\right| \)


Find \( \boldsymbol{m} \) if \( \operatorname{cosec} \boldsymbol{C} \) is equal to \( \frac{\mathbf{5}}{m} \)


\( \vec{a} \) and \( \vec{b} \) form the consecutive sides of a
regular hexagon ABCDEF. \( \overrightarrow{A B}=\vec{a}, \overrightarrow{B C}=\vec{b} \)


Pen, book, needle belong to which states
of matter?
A. Solid
B. Liquid
c. Gas
D. Plasma


Express \( \$ \$ 5: 8 \$ \$ \) as percent


The current \( I \) drawn from the \( 5 V \) source
in the given circuit will be :
A. 0.33 A
B. \( 0.5 \mathrm{A} \)
c. \( 0.67 \mathrm{A} \)
D. 0.17 A


The law of conservation of mass was
given by :
A. Dalton
B. Proust
c. Lavoisier
D. Berzelius


Out of the total at any time, water present in the atmosphere is
A . \( 0.01 \% \)
B. 0.02\%
c. 0.001\%
D. 0.005\%


Name the element in the periodic table forming a maximum number of
compounds?
A. carbon
B. Hydrogen
c. oxygen
D. Fluorine


toppr
Q Type your question.
experiment to verify the value of \( \Delta H_{\text {solution}} \) for ammonium nitrate. She
places a known amount of water in a coffee-cup calorimeter and adds a known quantity of solid ammonium nitrate. She traces the course of the
reaction by use of a digital thermometer
Using \( \boldsymbol{q}_{\text {solute}} \) and \( \boldsymbol{q}_{\text {water}} \) to represent the quantity of heat gained or lost by the ammonium nitrate solute itself and the
water in the calorimeter, and using \( \triangle \boldsymbol{T} \)
to represent the temperature change that she expects to observe, which combination below correctly describes
the signs for \( q_{\text {solute}}, \boldsymbol{q}_{\text {water}}, \) and \( \Delta \boldsymbol{T} \) ?
\( A \)
\begin{tabular}{|c|c|}
\hline Variable & Sign \\
\hline q \( _{\text {solute }} \) & \( + \) \\
qwater & \( - \) \\
\( \Delta \mathbf{T} \) & \( + \) \\
\hline
\end{tabular}
в. \begin{tabular}{|c|c|}
\hline Variable & Sign \\
\hline q \( _{\text {solute }} \) & \( - \) \\
qwater & \( + \) \\
\( \Delta \mathbf{T} \) & \( + \) \\
\hline
\end{tabular}
\( c \)
\begin{tabular}{|c|c|}
\hline Variable & Sign \\
\hline q solute & \( + \) \\
qwater & \( - \) \\
\( \Delta \mathbf{T} \) & \( - \) \\
\hline
\end{tabular}
D. \begin{tabular}{|c|c|}
\hline Variable & Sign \\
\hline q \( _{\text {solute }} \) & \( - \) \\
qwater & \( + \) \\
\( \Delta \mathbf{T} \) & \( - \) \\
\hline
\end{tabular}


Using general logic for electric field, the flux of \( \vec{g} \) through any closed surface is given by :
A \( \cdot \oint \vec{g} \cdot d \vec{s}=4 \pi G m_{\text {endosed }} \)
в. \( \oint \vec{g} \cdot d \vec{s}=-4 \pi G m_{\text {endosed }} \)
c. \( \oint \vec{g} \cdot d \vec{s}=G m_{\text {enclosed}} \)
D \( \cdot \oint \vec{g} \cdot d \vec{s}=-G m_{\text {endose}} \)


The area of trapezium shaped field is
\( 480 m^{2}, \) the distance between two
parallel sides is \( 15 \mathrm{cm} \) and one of the
parallel sides is 20 m. Find the other
parallel side.
A. \( 44 m \)
в. 42 т
\( c .43 m \)
D. None of these


Eri silk moth feeds on
A. Mulberry leaves
B. Arandi leaves
c. Ficus leaves
D. Neem leaves


PQRS is a parallelogram and \( \angle 1 \) and \( \angle 2 \) are two exterior,angles, then \( \angle 1= \)
\( \angle 2=\angle 3=\angle 4 \)
A. True
B. False


Find the speed of the proton at the final
point.
A \( \cdot 2.7 \times 10^{-6} \mathrm{m} / \mathrm{s} \)
В. \( 3 \times 10^{8} m / s \)
c. \( 3 \times 10^{-8} m / s \)
D. \( 2.7 \times 10^{6} \mathrm{m} / \mathrm{s} \)


A watch shows time as 3: 25 when seen
through a mirror, time appeared will be
then
\( A \cdot 8: 35 \)
B. 9: 35
\( c \cdot 7: 35 \)
D. 8: 25


Students of a school staged a rally for a
cleanliness campaign. They walked
through the lanes in two groups. One
group walked through the lanes \( A B, B C \) and CA; where the Other through \( A C, C D \)
and DA. Then they cleaned the area
enclosed within their lanes. If \( \boldsymbol{A B}= \)
\( \mathbf{9} \boldsymbol{m}, \boldsymbol{B} \boldsymbol{C}=\mathbf{4 0 m}, \boldsymbol{C D}=\mathbf{1 5 m}, \boldsymbol{D} \boldsymbol{A}= \)
\( 28 m \) and \( \angle B=90^{0}, \) which group cleaned
more area and by how much? Find the
total area cleaned by the students.


Sl unit of electric polarisation is
A \( \cdot C m^{-2} \)
B. coulomb
c. ampere
D. volt


The presence or absence of hydroxy group on which carbon atom of sugar differentiative RNA and DNA?
\( \mathbf{A} \cdot 1^{s t} \)
B . \( 2^{n} \)
\( c \cdot 3^{r d} \)
\( D \cdot 4^{t h} \)


A alatnermıc piscon alvıaes aalapatıc
cylinder of volume \( V_{0} \) into two equal
parts as shown in the figure.Both the parts contain ideal monoatomic gases.
The initial pressure and temperature of
gas in left compartment are \( P_{0} \) and \( T_{0} \)
while that in right compartment are
\( 2 P_{0} \) and \( 2 T_{0} . \) Initially the piston is kept
fixed and the system is allowed to
acquire a state of thermal equilibrium. The pressure in left compartment after
thermal equilibrium is achieved is:
\( A \cdot P_{o} \)
B. \( \frac{3}{2} P \)
\( c \cdot \frac{4}{3} P \)
D. None


In a magnetic field of \( 0.05 T \) area of coil
changes from \( 101 c m^{2} \) to \( 100 c m^{2} \)
without changing the resistance which is \( 2 \Omega . \) The amount of charge that flow during this period is
A \( \cdot 2.5 \times 10^{-6} C \)
B . \( 2 \times 10^{-6} C \)
c. \( 10 \times 10^{-6} C \)
D. \( 8 \times 10^{-6} C \)


The equation to the sides \( A B, B C, C A \)
of a \( \triangle \operatorname{are} \boldsymbol{x}+\boldsymbol{y}=\mathbf{1} ; \mathbf{4} \boldsymbol{x}-\boldsymbol{y}+\mathbf{4}= \) and
\( 2 x+3 y=6 . \) Circle are drawn on
\( A B, B C, C A \) as diameter. The point of
concurrence of the common chord is
A. centroid of the triangle
B. orthocenter
c. circumcenter
D. incenter


Area of region \( \left\{(x, y) \in R^{2}: y \geq \sqrt{|x+3|}, 5 y \leq x+9\right. \)
is equal to
A \( \cdot \frac{1}{6} \)
B. \( \frac{4}{3} \)
\( c \cdot \frac{3}{2} \)
D.


A bulbs is connected to a battery of p.d. \( 4 \mathrm{V} \) and internal resistance \( 2.5 \Omega . A \)
stedy current of \( 0.5 \mathrm{A} \)
(i) the total energy supplied by the battery in 10 minutes,
(ii) the resistance of the bulb,and
(iii) the energy displated in the bulb in
10 minutes


\( P \) is a variable points which moves
such that \( 3 P A=2 P B . \) If \( A= \)
(-2,2,3) and \( B=(13,-3,13) \) prove
that \( P \) satisfies the equation \( x^{2}+y^{2}+ \)
\( z^{2}+28 x-12 y+10 z-247=0 \)


A magnetic field of flux density \( 1.0 W b m^{-2} \) acts normal to a 80 turn
coil of \( 0.01 m^{2} \) area. The e.m.f. induced
in it, if this coil is removed from the
field in 0.1 second is
A . \( 8 V \)
в. \( 4 V \)
\( c \cdot 10 V \)
D. \( 6 V \)


When two waves of the same amplitude and frequency but having a phase difference of \( \phi \) travelling with the same speed in the same direction (positive \( x \) ) meets at a point then
A. their resultant amplitude will be twice that of a single wave but the frequency will be same
B. their resultant amplitude and frequency will both be twice that of a single wave
c. their resultant amplitude will depend on the phase angle while the frequency will be the same
D. the frequency and amplitude of the resultant wave will depend upon the phase angle


What type of polymer is a protein?
A. Structure
B. Mode of Polymerization
c. Molecular forces
D. None


Find the number of words that can be
formed by consider of thing all the possible permutations of the word FATHER. How many of these words begin
with \( A \) and end with \( R \)


A bag contains four tickets marked
with \( 112,121,211,222, \) one ticket is
drawn at random from the bag. Let
\( \boldsymbol{E}_{i}(\boldsymbol{i}=\mathbf{1}, \mathbf{2}, \mathbf{3}) \) denote the event that \( \boldsymbol{i}^{t h} \)
digit on the ticket is 2 then :
This question has multiple correct options
A \( . E_{1} \) and \( E_{2} \) are independent
B. \( E_{2} \) and \( E_{3} \) are independent
C \( . E_{3} \) and \( E_{1} \) are independent
D. \( E_{1}, E_{2}, E_{2} \) are independent


The mass of ice (in dag to the nearest
integer) that will separate out on cooling a solution containing 50 g ethylene glycol in 200 g water to \( -9.3^{\circ} \mathrm{C}\left(\mathrm{K}_{f} \text { for water }=\right. \)
\( \left.1.86 K m o l^{-1} k g\right) \) is


Find the square root of 2 correct to two
places of decimal.


If \( a x^{3}+b x^{2}+c x+d \) is divided by \( x \)
2, then the remainder is equal
A \( . d \)
B. \( a-b+c-d \)
c. \( 8 a+4 b+2 c+d \)
D. \( -8 a+4 b-2 c+d \)


Let \( \boldsymbol{f}(\mathbf{1})=-\mathbf{2} \) and \( \boldsymbol{f}^{\prime}(\boldsymbol{x}) \geq \mathbf{4 . 2} \) for \( \mathbf{1} \leq \)
\( \boldsymbol{x} \leq \mathbf{6 .} \) The smallest possible value of
\( \boldsymbol{f}(\boldsymbol{6}) \) is
\( \mathbf{A} \cdot \mathbf{9} \)
B. 12
c. 15
D. 19


Solve the following equation:
\( \sin x=\frac{\sqrt{2}}{2} \)


Find \( \rho \) using \( a=\frac{-n}{T} \)
\( \mathbf{A} \cdot \rho \propto T^{n} \)
B \( \cdot \rho \propto T^{n-1} \)
c. \( \rho \propto T^{-n} \)
D. \( \rho \propto \frac{n}{T} \)


STATEMENT-1:
The plot of atomic number (y-axis) versus number of neutrons (x-axis) for
stable nuclei shows a curvature
towards \( x \) -axis from the line of \( 45^{\circ} \) slope as the atomic number is increased.
STATEMENT-2:
Proton-proton electrostatic repulsions begin to overcome attractive forces involving protons and neutrons and neutrons in heavier nuclides.
A. STATEMENT-1 is True, STATEMENT-2 is True:
STATEMENT-2 is correct explanation for STATEMENT-
B. STATEMENT-1 is True, STATEMENT-2 is True STATEMENT-2 is NOT a correct explanation for STATEMENT-1
C. STATEMENT-1 is True, STATEMENT-2 is False
D. STATEMENT-1 is False, STATEMENT-2 is True


The sum of the infinite series \( 1+ \) \( \left(1+\frac{1}{5}\right)\left(\frac{1}{2}\right)+ \)
\( \left(1+\frac{1}{5}+\frac{1}{5^{2}}\right)\left(\frac{1}{2^{2}}\right)+\dots \dots \)
A \( \cdot \frac{20}{9} \)
в. \( \frac{10}{9} \)
\( c \cdot \frac{5}{9} \)
\( D \cdot \frac{5}{3} \)


In the reaction sequence:
Cyclohexane \( \frac{h \nu / C l_{2}}{\longrightarrow}(X) \frac{a l c . K O H / \Delta}{\longrightarrow} \)
\( (\boldsymbol{Y}) \frac{(i) \boldsymbol{O}_{3}}{(i i) \boldsymbol{H}_{2} \boldsymbol{O} / \boldsymbol{Z} \boldsymbol{n}}(\boldsymbol{Z}) \)
\( (Z) \) will be :
A. Hexanal
B. 2- Hexanone
c. 3 - Hexanone
D. Hexanedial


Ammonia will not form complex with:
A \( \cdot A g^{2} \)
B. \( P b^{2} \)
\( c \cdot C u^{2} \)
D. \( C d^{2} \)


Two integers are selected at random
from the set \( 1,2, \ldots, 11 . \) Given that the sum of selected numbers is even, the
conditional probability that both the
numbers are even is:
A \( \cdot \frac{2}{5} \)
B. \( \frac{1}{2} \)
\( c \cdot \frac{3}{5} \)
D. \( \frac{7}{10} \)


The reaction of toluene with \( C l_{2} \) in
presence of \( F e C l_{3} \) gives predominantly:
A. benzoyl chloride
B. benzyl chloride
c. \( o \) -and \( p \) -chlorotoluene
D. \( m \) -chlorotoluene


lonisation potential of boron is less than that of beryllium. This is because:
A . B has \( 1 s^{2} 2 s^{2} 2 p^{1} \) configuration
B. B has small atomic size
c. B has higher nuclear charge
D. B has more number of shells


A circular coil of one turn and area \( \boldsymbol{A} \)
carrying a current has a magnetic dipole moment \( M . \) The current through
the coil is :
\( A \cdot M A \)
в. \( \frac{A}{M} \)
c. \( \frac{M}{A} \)
D. \( \frac{M}{A^{2}} \)


It is observed in a potentiometer
experiment that no current passes through the galvanometer across when
the terminals of a cell are connected
across a certain length of the potentiometer wire. On shuting the cell by a \( 2 \Omega \) resistance, the balancing length is reduced to half. The internal resistance of the cell is :-
A . \( 4 \Omega \)
B. 2\Omega
c. \( 1 \Omega \)
D. 8\Omega


R.Q. of sprouting potato tubers is
\( A \)
B. \( <1 \)
\( c \cdot>1 \)
D.


Verify \( t=1 \) is a zero of the polynomial
\( 2 t^{3}-3 t^{2}+7 t-6 \)


Air pollution is caused by:
A. human.
B. nature.
C. both nature and man.
D. forestation.


In a leaf with parallel venation
A. Veins form a network on the leaf
B. Veins run parallel to the midrib
C. Veins run horizontal to the midrib
D. Veins crisscross each other to from an irregular
pattern


Find the volume of a sphere-shaped metallic shotput having a diameter of
\( 8.4 \mathrm{cm}\left(\text { Take } \pi=\frac{22}{7}\right) \)


In a right-angled triangle \( A B C \) with
\( \angle C=90^{\circ} \) and \( \angle A=2 \angle B, \angle B \) is
A \( \cdot 15^{\circ} \)
В. \( 60^{\circ} \)
\( c \cdot 45^{\circ} \)
D. \( 30^{\circ} \)


Choose the correct statement with
respect to the graph given(consider the
case of simple mass spring, \( ) \)
A. A force must be acting on the system
B. B represent kinetic energy
C. A represent potential energy
D. none of the above


When a 1 ohm resistor is connected
across the potential difference of \( 20 \mathrm{V} \) what will be power dissipation in it?
\( \mathbf{A} \cdot 200 W \)
в. \( 20 W \)
c. \( 400 W \)
D. \( 10 W \)


Pneumatophores take part in, which of the following functions?
A. Excretion
B. Feeding
c. Respiration
D. Reproduction


n \( \triangle A B C, \angle A B C=90^{\circ}, B D \perp A C \) If
\( \boldsymbol{B} \boldsymbol{D}=\boldsymbol{8} \mathbf{c m}, \boldsymbol{A} \boldsymbol{D}=\boldsymbol{4} \mathrm{cm}, \) find \( \boldsymbol{C} \boldsymbol{D} \)


Use Euclid's division lemma to show
that the cube of any positive integer is of the form \( 9 m, 9 m+1 \) or \( 9 m+8 \)


If \( A \) is a skew-symmetric matrix, then trace of \( A \) is
\( \mathbf{A} \cdot \mathbf{1} \)
B. - -
\( c \cdot 0 \)
D. none of these


Find the domain of \( f(x)=\sqrt{\log _{16} x^{2}} \)


All metals react with other substance to
form chemical compounds.
A. True
B. False


The maximum value of \( 4 \sin ^{2} x- \)
\( 12 \sin x+7 \) is.
A . 25
B. 4
c. Does not exist
D. None of these


\( f(x)=\frac{\log \frac{1}{2}+\log (2+4 x)}{x} \) for \( x \neq 0 \) at \( x=2 \)


A body of mass \( 10 \mathrm{kg} \) is under a
constant force which causes a
displacement S is in metres given the relation \( s=\frac{2}{3} t^{4}, \) where \( + \) is in seconds.
To find work-done by the force \( 5 s \)


The potential energy of the dipole in the equilibrium position is :
\( \mathbf{A} \cdot+3 \times 10^{-23} J \)
В. \( -3 \times 10^{-23} \mathrm{J} \)
c. \( -6 \times 10^{-23} J \)
D. \( -3 \times 10^{-36} J \)


How do you explain the functionality of
a monomer?


Which of the following match are
correct:
A. Goldschmidt aluminothermite process- \( C r_{2} O_{3} \)
B. Mac Arther cyanide process-Fe
C. Mond process -Ni
D. Van Arkel process-Au


Which of the following indicate proton transfer equilibria within the glycine
molecule shown below?
A \( . I, I I, I I I \) only
B. I and III only
c. \( I \) and \( I I \) only
D. \( I, I I, I I I, I V \)


Cube of any positive integer is of the form \( 9 m, 9 m+1 \) or \( 9 m+8, \) where \( m \) is
a non-negative integer.
A. True
B. False
c. Neither
D. Either


A body has its centre of mass at the
origin. The \( x \) -coordinates of the
particles
A. may be all positive
B. must be positive for some particles and negative in other particles
C. Must be all non- negative
D. may be positive for some particles and negative in other particles


The following is an example of empty
set:
\( \{x: x \) is a point common to any two
parallel lines
A. True
B. False


Any that influences the valence
electrons will affect the chemistry of the clement. Which one of the following
factors does not affect the valence shell
\( ? \)
A. Valence principal quantum number
B. Nuclear charge
c. Nuclear mass
D. Number of core electrons


What quantity of copper (II) oxide will
react with 2.80 litre of hydrogen at NTP
\( ? \)


In the figure shown \( A B C \) is a uniform
wire. If centre of mass of wire lies vertically below point \( A, \) then \( \frac{B C}{A B} \) is
close to:
This question has multiple correct options
\( \mathbf{A} \cdot 1.85 \)
B. 1.5
c. 1.37
D. 3


The perimeter of a parallelogram is 22 cm. If the longer side measures \( 6.5 \mathrm{cm} \) what is the measure of the shorter side?
A. \( 4.5 \mathrm{cm} \)
B. \( 5.5 \mathrm{cm} \)
\( c .6 .5 \mathrm{cm} \)
D. 4.2 \( \mathrm{cm} \)


n the figure if \( \angle B D C=30^{\circ}, \angle \)
\( C B A=110^{\circ}, \) then find \( \angle B C A \)
4.20
3.40
235
; 0


The total magnetic induction at point 0
due to curved portions and straight portion in the following figure, will be
A \( \cdot \frac{\mu_{0} i}{2 \pi r}[\pi-\phi+\tan \phi \)
в. \( \frac{\mu_{0} i}{2 \pi r} \)
c. \( \frac{\mu_{0} i}{\pi r}[\pi-\phi+\tan \phi \)
D.


Find the derivative of \( \operatorname{cosec}^{2} x, \) by using
first principle of derivatives?


A ray of light passes through an equilateral prism (refractive index \( = \)
1.5) such that the angle of incidence is
equal to the angle of emergence and the latter is equal to \( 3 / 4 \) th the angle of the prism. The angle of deviation is:
A \( .20^{\circ} \)
B. \( 39^{\circ} \)
c. \( 5^{\circ} \)
D. \( 30^{\circ} \)


Fibres obtained from plants and
animals are called:
A. man made fibres
B. natural fibres
c. organic fibres
D. none of the above


Draw \( 2^{\circ} \) alkyl halides with the
empirical formula \( C_{5} H_{11} C l \)


(a) State Ampere's circuital law. Use this law to obtain the expression for the magnetic field inside an air cored toroid of average radius r having 'n' turns per unit length and carrying a steady current I
(b) An observer to the left of a solenoid of N terms each of cross section area \( A \)
observes that a steady current lin it flows in the clockwise direction. Depict the magnetic field lines due to the solenoid specifying its polarity and show that it acts as a bar magnet of
magnetic momentum \( \boldsymbol{m}=\boldsymbol{N} \boldsymbol{I} \boldsymbol{A} \)


Balance the following equation and find the values of \( a, b, c, d \) \( \boldsymbol{a} \boldsymbol{P b O}_{2}+\boldsymbol{b C l}^{\ominus} \longrightarrow \boldsymbol{c} \boldsymbol{C l O}^{\ominus}+ \)
\( \boldsymbol{d}\left[\boldsymbol{P b}(\boldsymbol{O H})_{3}\right]^{\ominus}(\text { in basic solution }) \)
В. \( a=1, b=1, c=1, d=1 \)
c. \( a=2, b=1, c=1, d=2 \)
D. \( a=1, b=1, c=2, d=2 \)


If \( f(x)=\sqrt{1-e^{-x^{2}}}, \) then at \( x=0, f(x) \)
is
A. differentiable as well as continuous
B. continuous but not differentiable
c. differentiable but not continuous
D. neither differetiable nor continuous


The drift velocity of electrons in a conductor is :
A. Very small
B. Very large
c. Equal to the velocity of the tight
D. Varies with the conductor


For a reversible reaction, if \( \Delta G^{o}=0 \)
the equilibrium constant of the reaction should be equal to:
A. zero
B.
\( c \cdot 2 \)
D. 10


A person moves towards East for \( 3 m \)
then towards North for \( 4 m \) and then
moves vertically up by \( 5 m . \) What is his distance now from the starting point?


Two inclined friction less tracks, one
gradual and the other steep meet at \( \boldsymbol{A} \)
from where two stones are allowed to
slide down from rest, one on each track.
Will the stones reach the bottom at the
same time? Will they reach there with
the same speed? Explain. Given \( \boldsymbol{\theta}_{\mathbf{1}}= \)
\( \mathbf{3 0}^{0}, \boldsymbol{\theta}_{2}=\mathbf{6 0}^{0}, \) and \( \boldsymbol{h}=\mathbf{1 0} \boldsymbol{m}, \) what are
the speeds and times taken by the two
stones ?


toppr
Q Type your question
drew the following diagrams \( a, b, c \) and among which three were considered
wrong and one correct by the teacher.
Guess the correct potential energy diagram and justify it.
\( A \)
B.
\( c \)
distanc
\( D \)


Calculate \( C-C l \) bond enthalpy from
following reaction:
\( \boldsymbol{C H}_{3} \boldsymbol{C l}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g}) \longrightarrow \)
\( \boldsymbol{C H}_{2} \boldsymbol{C l}_{2}(\boldsymbol{g})+\boldsymbol{H} \boldsymbol{C l}(\boldsymbol{g}) \boldsymbol{\Delta} \boldsymbol{H}^{o}= \)
\( -104 k J . \) If \( C-H, C l-C l \) and \( H-C l \)
bond enthalpies are 414,243 and \( 431 k J m o l^{-1} \) respectively


A radioactive nucleus can decay by two different processes. The mean value
period for the first process is \( t_{1} \) and that
for the second process is \( t_{2} \). The effective mean value period for the two
processes is
A \( \cdot \frac{t_{1}+t_{2}}{2} \)
B . \( t_{1}+t_{2} \)
c. \( \sqrt{t_{1} t_{2}} \)
D. \( \frac{t_{1} t_{2}}{t_{1}+t_{2}} \)


An alternating potential \( V=V_{0} \sin \omega t \)
is applied across a circuit. As a result, the current \( \boldsymbol{I}=\boldsymbol{I}_{0} \sin \left(\boldsymbol{\omega} \boldsymbol{t}-\frac{\boldsymbol{\pi}}{2}\right) \) flows
in it. The power consumed in the circuit per cycle is:
A . zero
в. \( 0.5 I_{0} V_{0} \)
с. \( 0.707 I_{0} V_{0} \)
D. \( 1.414 I_{0} V_{0} \)


If the extension of the spring is \( x_{0} \) at
time \( t, \) then the displacement of the
first block at this instant is :
\( ^{\mathbf{A}} \cdot \frac{1}{2}\left(\frac{F t^{2}}{2 m}+x_{0}\right) \)
B \( \cdot-\frac{1}{2}\left(\frac{F t^{2}}{2 m}+x_{0}\right) \)
c. \( \frac{1}{2}\left(\frac{F t^{2}}{2 m}-x_{0}\right) \)
D. \( \frac{F t^{2}}{2 m}+x_{0} \)


Find out the incorrect statement
A. Ammonia is the most toxic form and requires large amount of water for its elimination
B. Kidneys do not play any important role in ammonia removal
C. Human kidneys can only produce hypertonic urine nearly five timesconcentrated than the initial filtrate
D. Urea may be retained in the kidney matrix of some animals to maintain the desired acidity.


Solve \( \int_{0}^{\frac{\pi}{2}} \sqrt{\sin \phi} \cos ^{5} \phi d \phi \)
A \( \cdot \frac{64}{231} \)
в. \( \frac{24}{231} \)
c. \( \frac{54}{231} \)
D. None of these


A body of mass 2 g, moving along the positive \( x- \) axis in gravity free space
with velocity \( 20 \mathrm{cms}^{-1} \) explodes at \( x= \) \( \mathbf{1} \mathbf{m}, \boldsymbol{t}=\mathbf{0} \) into two pieces of masses \( \frac{\mathbf{2}}{\mathbf{3}} \)
\( \mathrm{g} \) and \( \frac{4}{3} \) g. After \( 5 \mathrm{s} \), the lighter piece is at the point \( (3 m, 2 m,-4 m) . \) Then the position of the heavier piece at this moment, in metres is
в. (1.5,-2,-2)
\begin{tabular}{l}
c. (1.5,-1,-1) \\
\hline
\end{tabular}
D. None of these


The number of revolutions made by a
wheel of diameter \( 56 \mathrm{cm} \) in covering a distance of \( 1.1 k m \) is \( \left(U s e \pi=\frac{22}{7}\right) \)
\( \mathbf{A} \cdot 31.25 \)
B. 56.25
c. 625
D. 62.5


set of rational numbers is \( \left\{-\mathbf{6},-\mathbf{5} \frac{\mathbf{3}}{\mathbf{4}},-\sqrt{\mathbf{4}},-\frac{\mathbf{3}}{\mathbf{5}},-\frac{\mathbf{3}}{\mathbf{8}}, \mathbf{0}, \frac{\mathbf{4}}{\mathbf{5}}, \mathbf{1}, \mathbf{1} \frac{\mathbf{2}}{\mathbf{3}}, \mathbf{3}\right. \)
A. True
B. False


The solution of the differential equation \( \sec ^{2} x \cdot \tan y d x+\sec ^{2} y \cdot \tan x d y=0 \)
is
A. \( \tan x \cdot \cot y=C \)
B. \( \cot x \cdot \tan y=C \)
\( \mathbf{c} \cdot \tan x \cdot \tan y=C \)
\( \mathbf{D} \cdot \sin x \cdot \cos y=C \)


The minimum non-zero distance on
screen from central maxima where both
the wave are going to produce maxima
together
A . \( 2000 \mu \) m
в. \( 3600 \mu \) и
c. \( 4320 \mu \) m
D. \( 2160 \mu \mathrm{m} \)


The unit of \( \sqrt{\boldsymbol{L} \boldsymbol{C}} \) is
A. Henry
B. Farad
c. second
D. Ampere


Find the roots of the following quadratic equation, if they exist, using the quadratic formula of Shridhar Acharya. \( 2 x^{2}-2 \sqrt{2} x+1=0 \)


Find the cost of polishing a circular
table-top of diameter \( 1.6 \mathrm{m}, \) if the rate of polishing is Rs. \( \left.15 / m^{2} . \text { (Take } \pi=3.14\right) \)


Three coins are tossed once. Describe
the following events associated with this ransom experiment. \( A= \) Getting three heads, \( B= \) Getting two heads and one tail
\( \boldsymbol{C}= \) Getting three tails, \( \boldsymbol{D}= \) Getting a head on the first coin.
Which pairs of events are mutually
events


What determines the frequency of a.c.
produced in a generator?
A. The number of rotations of the coil in one second.
B. the speed of rotation of the coil
\( c \cdot \) both \( A \& B \)
D. None of the above


One light year is equal to
\( A \cdot 3.26 \) parsec
B. 3.26km
c. 3.26 A.U.
D. \( \frac{1}{3.26} \) parsec


The angle between the electric dipole moment and the electric field strength due to it, on the equatorial line is :
A \( \cdot 0^{\circ} \)
В. \( 90^{\circ} \)
\( c \cdot 180^{\circ} \)
D. \( 60^{\circ} \)


Evaluate \( \int_{0}^{2} \frac{x}{3} d x \)


The migration of positively charged colloidal particles under an electrical
field towards the cathode is called:
A. cataphoresis
B. electro-osmosis
c. sedimentation
D. electrodialysis


At what temperature will the volume of a gas become twice the volume at \( 2700 \mathrm{C} \) at
a given pressure.
A. \( 327^{\circ} \mathrm{c} \)
B. \( 54^{\circ} \mathrm{C} \)
c. \( 127^{\circ} \mathrm{C} \)
D. \( 100^{\circ} \mathrm{C} \)


An anaerobic bacterium capable of nitrogen fixation is
A. Chlorobium
B. Rhodospirillum
c. clostridium
D. All of the above


Yand Zare
\( \mathbf{A} \cdot N_{2} O_{3} \) and \( H_{3} P O_{4} \)
B. \( N_{2} O_{5} \) and \( H P O_{3} \)
\( \mathbf{c} \cdot N_{2} O_{4} \) and \( H P O_{3} \)
D. \( N_{2} O_{4} \) and \( H_{3} P O_{3} \)


Describe the shape and Magnetic
property of \( \left[\boldsymbol{F e}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{6}\right]^{+2} \)
\( \left[\boldsymbol{C O}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{6}\right]^{+3} \&\left[\boldsymbol{N} \boldsymbol{i} \boldsymbol{C l}_{4}\right]^{-2} \)


For an ideal gas equation of a process for which the heat capacity of the gas varies with temperature as \( \mathrm{C}=\frac{\alpha}{T}(\alpha \) is a constant) is given by
A. \( V I n T= \) constant
в. \( \frac{1}{V T^{(\gamma-1)}} e^{\frac{\alpha}{R T}}= \) constant
c. \( \frac{1}{V^{(\gamma-1)}} T^{\frac{\alpha}{R T}}= \) constant
D. \( V^{\gamma-1} T= \) constant


A cell can be balanced against \( 110 \mathrm{cm} \)
and \( 100 \mathrm{cm} \) of potentiometer wire, respectively with and without being short circuited through a resistance of
\( 10 \Omega \) Its internal resistance is
A. 2.0 ohm
B. zero
c. 1.0 ohm
D. 0.5 ohm


In a series of 3 independent trials, the probability of exactly 2 success is 12 times as large as the probability of 3 successes. The probability of a success in each trail is
A \( \cdot \frac{1}{5} \)
B. \( \frac{2}{5} \)
\( c \cdot \frac{3}{5} \)
D. \( \frac{4}{5} \)


Phosphorus which is used as an impurity to produce an extrinsic semiconductor is a \( _{-}- \) - impurity.
A. Trivalent
B. Divalent
c. Tetravalent
D. Pentavalent


Earth is flattened at poles and bulging
at equator. This is due to
A. revolution of Earth around the Sun in an elliptical orbit
B. angular velocity of spinning about its axis is more at Equator
C . centrifugal force is more at Equator than poles
D. more centrifugal force at poles than Equator


For the reaction system:
\( \mathbf{2} N O(g)+O_{2}(g) \rightarrow 2 N O_{2}(g) \) volume
is suddenly reduced to half its value by increasing the pressure on it. If the reaction is of first order with respect to
\( O_{2} \) and second order with repeat to \( \mathrm{NO} \)
the rate of reaction will:
A. increase to eight times of its initial value
B. increase to four times of its initial value
c. decrease to one-fourth of its initial value
D. decrease to one-eighth of its initial value


Consider the reaction, \( 3 I_{(a q)}^{-}+ \)
\[
S_{2} O_{8}^{2-} \rightarrow I_{3(a q)}^{-}+2 S O_{4(a q)}^{2-} . A t
\]
particular time \( t, \frac{\boldsymbol{d}\left[\boldsymbol{S O}_{4}^{2-}\right]}{\boldsymbol{d} t}=\boldsymbol{2} . \boldsymbol{2} \times \)
\( 10^{-2} M / s . \) What are the values of the
following at the same time?
\[
-\frac{\boldsymbol{d}\left[\boldsymbol{I}^{-}\right]}{\boldsymbol{d} \boldsymbol{t}}=?
\]


A charge of +2 nC is separated from a charge of \( -2 \mathrm{nC} \) by \( 1.5 \mathrm{cm} \) forming an electric dipole. What torque acts on the
dipole moment vector makes an angle
of \( 30^{0} \) in the clockwise sense with the
field of magnitude \( 5000 \mathrm{N} / \mathrm{C} ? \)


Find the rate of change of the area of a circle with respect to its radius \( r \) when
(i) \( r=3 \mathrm{cm} \)
(ii) \( r=4 \mathrm{cm} \)


Among the following which will decrease the rate of the reaction?
i. Using highly concentrated reactants
ii. Decreasing the temperature by \( 25 K \)
iii. Stirring the reactants
A. i only
B. ii only
c. i and iii only
D. ii and iii only
E. i, ii, and iii


Increasing order of reactivity of the
following compounds for \( \boldsymbol{S}_{N} \mathbf{1} \)
substitution is:
\( A \)
(B)
\( \mathbf{C} \)
\( \mathbf{D} \)
A \( \cdot(B)<(C)<(D)<(A) \)
В. \( (A)<(B)<(D)<(C) \)
C. \( (B)<(A)<(D)<(C) \)
D. \( (B)<(C)<(A)<(D) \)


For any \( \theta \), state the value of:
\( \sin ^{2} \theta+\cos ^{2} \theta \)


Aqueous \( N a O H \) solution is labelled as
\( 10 \% \) by weight mole fraction of the
solute in it is:
A . 0.05
B. 0.0476
c. 0.052
D. 0.52


Identical charges -q each are placed at 8 corners of a cube of each side \( b \)
Electrostatic potential energy of a charge +q which is placed at the centre of cube will be :
\( ^{\mathbf{A}} \cdot \frac{-4 \sqrt{2} q^{2}}{\pi \epsilon_{0} b} \)
B. \( \frac{-8 \sqrt{3} q^{2}}{\pi \epsilon_{6} b} \)
\( ^{\mathrm{c}} \cdot \frac{-4 q^{2}}{\sqrt{3} \pi \epsilon_{0} b} \)
D. \( \frac{-8 \sqrt{2} q^{2}}{\pi \epsilon_{0} b} \)


Maizah bought a pair of pants and a briefcase at a departmental store. The
sum of the prices of the pants and the briefcase before sales tax was \( \$ 130.00 \)
There was no sales tax on the pants and a \( 9 \% \) sales tax on the briefcase. The
total Maizah paid, including the sales
\( \operatorname{tax}, \) was \( \$ 136.75 . \) What was the price in
dollars, of the pants?


The strongest reductant among the following is:
A. \( G e C l_{2} \)
в. \( \operatorname{SnCl}_{2} \)
c. \( P b C l_{2} \)
D. \( \operatorname{SnCl}_{4} \)


If \( x \) and \( y \) co-ordinate of a point is \( (3,10), \) then \( y \) co-ordinate is
A . 0
B. 3
c. 10
D. None of the above


In a group, basic nature
from top to bottom.
A. increases
B. decreases
c. remains same
D. none of these


The chief sources of water pollution can
be:
A. point sources
B. non-point sources
c. both A and B
D. none of above


This is a flagellate protist.
Justify it to be a connecting link
between plants and animals.
A. A suggest animal nature and B and C depicts plant nature
B. B suggests animal nature and A and C depicts plant nature
C. \( \mathrm{C} \) suggests animal nature and \( \mathrm{A} \) and \( \mathrm{B} \) depicts plant nature
D' C suggests animal nature and B depicts plant


Assertion: \( B_{2} \) molecule is diamagnetic.
Reason: The highest occupied molecular orbital is of \( \sigma \) type.
A. Assertion and Reason are true and the Reason is a correct explanation of the Assertion
B. Assertion and Reason are true but Reason is not a correct explanation of the Assertion
c. Assertion is true but Reason is false
D. Both the Assertion and Reason are false
E. Assertion is false but the Reason is true


The average induced emf in the circuit
is
\( \mathbf{A} \cdot 0.2 V \)
B. \( 0.1 V \)
\( \mathbf{c} \cdot 1 V \)
D. \( 10 V \)


The given schematic diagram depicts heterodont teeth and its thecodont
arrangement. Find the correct labelling
for \( A-D \) fom the options given below.
A. A - Incisor, B- Canine, C - Premolar
D- Molar
B. A - Molar, B - Premolar, C -Canine, D-Incisor
C. A- Incisors, B-Premolar, C-Canine, D- Molar
D. A - Molar, B- Premolar, C-Incisor, D- Canine


A vector \( \vec{A}=2 \hat{i}+3 \hat{j}+6 \hat{k} \) makes an
angle of \( \beta \) with positive direction of \( x- \) axis. \( \beta \) is equal to:
A \( \cdot \tan ^{-1} \frac{2}{7} \)
B. \( \sin ^{-1} \frac{2}{7} \)
\( c \cdot \cos ^{-1} \frac{2}{7} \)
D. \( \cos ^{-1} \frac{4}{7} \)


State and draw the lines of symmetry for a rhombus.


Find the equation of line equally inclined to coordinate axes and passes
through (-5,1,-2)


Rainbow is due to
This question has multiple correct options
A. scattering of light
B. refraction of light
C . dispersion
D. total internal reflection of light


Algae are autotrophic. Which of the following statement can be related to
autotrophs?
A. Autotrophs prepares their own food
B. Autotrophs depends on others for their food
c. Autotrophs are insectivores
D. None of these


Let \( h(x) \) be differentiable for all \( x \) and
let \( \boldsymbol{f}(\boldsymbol{x})=\left(\boldsymbol{k} \boldsymbol{x}+\boldsymbol{e}^{\boldsymbol{x}}\right) \boldsymbol{h}(\boldsymbol{x}) \) where \( \boldsymbol{k} \) is
some constant. If \( h(0)=5, h^{\prime}(0)=-2 \)
and \( f^{\prime}(0)=18, \) then the value of \( k \) is equal to
\( A \cdot 3 \)
B. 4
c.
D.


A particle performing linear simple
harmonic motion has maximum
velocity \( 25 \mathrm{cm} / \mathrm{s} \) and maximum
acceleration of \( 100 \mathrm{cm} / \mathrm{s}^{2} \). Find the amplitude and period of oscillation. \( (\boldsymbol{\pi}=\mathbf{3 . 1 4 2}) \)


On long standing, bleaching powder undergoes auto-oxidation into:
A \( \cdot C a\left(C l O_{3}\right)_{2}, C a C l_{2} \)
в. \( C a O, C a C l_{2} \)
c. \( c a C l O, C a C l O_{3} \)
D. \( C a C l O_{2}, C a C l_{2} \)


All of the following are bases except:
в. \( N H_{2} O H \)
c. \( N H_{3} \)
D. \( N_{3} H \)


rest on a rough horizontal table. A
horizontal force \( F \) is applied normal to one of the face at a point, at a height \( 3 b / 4 \) above the base. What should be
the coefficient of friction \( (\mu) \) between
cube and table so that it will tip about
an edge before it starts slipping?
' \( \mu>\frac{2}{3} \)
3. \( \mu>\frac{1}{3} \)
\( c_{\mu>\frac{3}{2}} \)
\( D \)


Value based questions. Try to explain the following observations
When \( K^{+} \) ions are removed from the
medium surrounding red blood cells, sodium influx into the cells and
potassium efflux increase dramatically.


Which of the following reaction and products are correctly matched?
This question has multiple correct options
\( A \)
B.
\( c \)
D.


The set of positive integers is
A . Infinite
B. Finite
c. subset
D. Empty


A container having some gas was kept in a moving train. The temperature of the gas in the container will be
A. Increases slightly
B. Remain the same
c. Decrease
D. Infinite


Which unit is equivalent to the coulomb?

This question has multiple correct options
A. ampere - second
B. joule per volt
c. watt per ampere
D. watt per volt


Find the mechanical work to be
performed in order to turn the frame
through \( 180^{\circ} \) about its axis, with the
currents maintained constant.
A. \( 1.0 \mu J \)
B. \( 0.1 \mu J \)
c. \( 10 \mu J \)
D. \( 0 \mu J \)


Calculate the interest on \( R s .800 \) at \( 6 \frac{1}{2} \) \( \% \) per annum, for \( 3 \frac{1}{2} \) years


Which of the following is correct
regarding genetic code?
A. UUU is the initiation codon which also codes for phenylalanie.
B. There are 64 triplet codons and only 20 amino acids.
C. Three random nitrogen bases specify the placement of one amino acid.
D. UAA is the nonsense codon which also codes for
methionine.


Which amine yield \( N- \) nitroso amine
after treatment with nitrous acid
\( \left(N a N O_{2}, H C l\right) ? \)
\( A \)
B.
\( c \)
\( D \)


A solution that obeys Raoult's law is:
A. non-ideal
B. colliod
\( c . \) ideal
D. saturate


The energy of the electron of the
hydrogen atom in the \( n \) th orbit is \( E_{n}= \) \( -\frac{13.6}{n^{2}} e V . \) Draw the energy level
diagram for the hydrogen atom and show transitions corresponding to lives of Lyman and Balmer series.


Suppose the gravitational potential due to a small system is \( k / r^{2} \) at a distance from it. What will be the gravitational field ? Can you think of any such system? What happens if there were negative masses?


Solve the linear equation:
\( 3 x+13=52 \)


Relation between displacement, \( x \) and
time, \( t \) is \( x=2-5 t+t^{2}, \) the initial
acceleration will be
\( \mathbf{A} \cdot-3 m / s^{2} \)
в. \( 12 \mathrm{m} / \mathrm{s}^{2} \)
c. \( 2 m / s^{2} \)
D. \( -5 ~ m / s^{2} \)


For first order reaction as time duration
goes from 10 in to 30min rate of reaction
decreases from \( 0.4 M s^{-1} \) to \( 0.04 M s^{-1} \)
What is the half life of the reaction?
\( A \cdot 8 \min \)
B. 4 min
c. 6 min
D. 2 min


Find the angle of incidence on the surface of a diamond of refractive index
\( 2.4, \) if the angle between the reflected
and refracted rays is \( 90^{\circ} \)
\( \mathbf{A} \cdot \tan ^{-1}(2.4) \)
B. \( \sin ^{-1}\left(\frac{1}{2.4}\right) \)
\( ^{\mathbf{c}} \cdot \tan ^{-1}\left(\frac{1}{2.4}\right) \)
D. \( \cos ^{-1}\left(\frac{1}{2.4}\right) \)


What is the order of the product \( \left[\begin{array}{lll}\boldsymbol{x} & \boldsymbol{y} & \boldsymbol{z}\end{array}\right]\left[\begin{array}{lll}\boldsymbol{a} & \boldsymbol{h} & \boldsymbol{g} \\ \boldsymbol{h} & \boldsymbol{b} & \boldsymbol{f} \\ \boldsymbol{g} & \boldsymbol{f} & \boldsymbol{c}\end{array}\right]\left[\begin{array}{l}\boldsymbol{x} \\ \boldsymbol{y} \\ \boldsymbol{z}\end{array}\right] \)
\( A \cdot 3 \times 1 \)
в. \( 1 \times 1 \)
\( c \cdot 1 \times 3 \)
D. \( 3 \times 3 \)


Extraction of gold and silver involves
leaching the metal with \( C N^{-} \) ion. The metal is recovered by:
A. displacement of metal by some other metal from the complex ion
B. roasting of metal complex
c. calcination followed by roasting
D. thermal decomposition of metal complex