Zero group elements are known
\( a s \)
A. alkali metals
B. alkaline earth metals
C. transition metals
D. inert gases


The distance between (-4,-5) and (-4,-10) is
units.
A . 15
B. 10
\( c .5 \)
D.


Let \( \alpha, \beta, \gamma \) be the distinct real numbers. The vectors \( \boldsymbol{\alpha} \hat{\boldsymbol{i}}+\boldsymbol{\beta} \hat{\boldsymbol{j}}+\boldsymbol{r} \hat{\boldsymbol{k}} \)
\( \beta \hat{i}+r \hat{j}+\alpha \hat{k} ; \gamma \hat{i}+\alpha \hat{j}+\beta \hat{k} \) are
A. collinear
B. form an isosceles triangle
c. right angled triangle
D. equilatetral triangle


Calculate the mode for the following
data:
Distance(km) 11 Number of
persons \( \quad 4 \quad 6 \quad 10 \quad 20 \)
A. 41
B. 31
c. 21
D. 1


The figure shows capillary tube of
radius \( r \) dipped into water. The
atmospheric pressure is \( P_{0} \) and the
capillary rise of water is \( h . s \) is the
surface tension for water-glass. Initially, \( h=10 \mathrm{cm} . \) If the capillary tube
is now inclined at \( 45^{\circ}, \) the length of water rising in the tube will be
\( \mathbf{A} \cdot 10 \mathrm{cm} \)
в. \( 10 \sqrt{2} \mathrm{cm} \)
c. \( \frac{10}{\sqrt{2}} c m \)
D. None of these


A compound microscope has an objective of focal length \( 1 \mathrm{cm} \) and an
eyepiece of \( 4 \mathrm{cm} . \) If the tube length is 20 \( \mathrm{cm} . \) Then the magnification of the compound microscope is : (final image is at D
A . 145
B. 14.5
\( c \cdot 1.45 \)
D. None of these


ADH deficiency shows the following condition
A. Only polydipsia
B. Polyuria
c. Polydipsia and polyuria
D. Glucosuria


All vitamins are synthesised by:
A . plants
B. human beings
c. fishes
D. all


Advantages of optical fibres over
electrical wires is:
A. High band width and EM interference
B. Low band width and EM interference
C. High band width low transmission capacity and no EM interference
D. High band width, high data transmission capacity and no EM interference


Name a triangle which has exactly one
line of symmetry. Show line of symmetry in figure.


A coil in a simple generator has 200 turns.Now the number of turns in the
coil increases to \( 500 . \) What will be its
effect:
A. current produced will increase
B. voltage produced will increase
\( c \cdot \) both
D. none


A black body emits heat at the rate of
20 W. When its temperature is 227 \( ^{\circ} \mathrm{C} \)
Another black body emits heat at the rate of \( 15 \mathrm{W} \), when its temperature is 277
\( ^{o} \mathrm{C} . \) Compare the area of the surface of
the two bodies, if the surrounding is at NTP :
A . 16: 1
B. 1: 4
\( c \cdot 12: 1 \)
D. 1:12


If \( \boldsymbol{f}(\boldsymbol{x}) \boldsymbol{\epsilon}[\mathbf{1}, \mathbf{2}] \) when \( \boldsymbol{x} \boldsymbol{\epsilon} \boldsymbol{R} \) and for a fixed
positive real number \( \boldsymbol{p} \) \( \boldsymbol{f}(\boldsymbol{x}+\boldsymbol{p})=1+\sqrt{2 \boldsymbol{f}(\boldsymbol{x})-|\boldsymbol{f}(\boldsymbol{x})|^{2}} \) for al
\( x \epsilon R \) then prove that \( f(x) \) is a periodic function.


A hypothetical reaction \( \boldsymbol{A}_{2}+\boldsymbol{B}_{2} \rightarrow \)
\( 2 A B \) follows the mechanism as given
below:
\( \boldsymbol{A}_{2} \rightleftharpoons \boldsymbol{A}+\boldsymbol{A} \quad(\text { fast }) \)
\( \boldsymbol{A}+\boldsymbol{B}_{2} \rightarrow \boldsymbol{A} \boldsymbol{B}+\boldsymbol{B} \quad(\text { slow }) \)
\( A+B \rightarrow A B \quad(f a s t) \)
The order of the overall reaction is:
\( A \cdot 2 \)
B.
c. 1.5
D.


For which values of ' \( a \) ' the different
vectors \( \bar{x}=(2 a, 3 a, 0) \) and \( \bar{y}= \)
\( (0,0,4 a) \) are orthogonal vectors
\( \mathbf{A} \cdot a \in R \)
B . \( a \in N \cup\{0\} \)
\( \mathbf{c} \cdot a \in R-\{0\} \)
\( \mathbf{D} \cdot a=0 \)


The slope of the line, \( l_{1} \) is \( \frac{-3}{5} \) and \( l_{1} \) and
\( l_{2} \) are parallel. Find the slope of \( l_{2} \)
A \( \cdot \frac{-5}{3} \)
в. \( \frac{-1}{5} \)
c. \( \frac{-3}{5} \)
D. \( \frac{3}{5} \)


Find 'c' of Lagrange's mean-value
theorem for
(i) \( f(x)=\left(x^{3}-3 x^{2}+2 x\right) \) on \( \left[0, \frac{1}{2}\right] \)
(ii) \( \boldsymbol{f}(\boldsymbol{x})=\sqrt{\mathbf{2 5}-\boldsymbol{x}^{2}} \) on \( [\mathbf{0}, \mathbf{5}] \)
(iii) \( \boldsymbol{f}(\boldsymbol{x})=\sqrt{\boldsymbol{x}+\boldsymbol{2}} \) on \( [\boldsymbol{4}, \boldsymbol{6}] \)


(a) Define wave-front. Use Huygen's
principle to verify the laws of refraction.
(b) How is linearly polarised light obtained by the process of scattering of light? Find the Brewster angle for airglass interface, when the refractive
index of glass \( =1.5 \)


Robert was asked to made a 5 digit number from the digits 2 and 4 such that first digit cannot be \( 4 . \) Find the number of such 5 digit numbers that can be formed.
A . 10
в. 12
c. 16
D. 18
E. None of these


There is a hole in the ozone layer. What
do you understand by this?


Solve the system of inequalities
graphically:
\( 5 x+4 y \leq 20, x \geq 1, y \geq 2 \)


A long straight wire (radius \( =3.0 \mathrm{mm}) \)
carries a constant current distributed
uniformly over a cross section perpendicular to the axis of the wire. If
the current density is \( 100 \mathrm{A} / \mathrm{m}^{2} \). The magnitudes of the magnetic field at (a) 2.0mm from the axis of the wire and 4.0
mm from the axis of the wire is
A. \( 1.4 e-7 T \)
B . \( 4 \pi \times 10^{-8} \mathrm{T}, \frac{\pi}{2} \times 10^{-8} \mathrm{T} \)
C \( \cdot 4 \pi \times 10^{-8} \mathrm{T}, \frac{9 \pi}{2} \times 10^{-8} \mathrm{T} \)
D・ \( \pi 10^{-4} \mathrm{T}, \frac{9 \pi}{2} \times 10^{-8} \mathrm{T} \)


If \( \boldsymbol{f}(\boldsymbol{x})=\sqrt{\boldsymbol{x}+\boldsymbol{2} \sqrt{\boldsymbol{2} \boldsymbol{x}-\boldsymbol{4}}}+ \)
\( \sqrt{x-2 \sqrt{2 x-4}} \), then the value of
\( \mathbf{1 0} \boldsymbol{f}^{\prime}\left(\mathbf{1 0 2}^{+}\right) \) is
A . -1
B.
c. 1
D. Does not exist


In anaerobic respiration, acetaldehyde is reduced to form alcohol by utilising
\( N A D H_{2} \) obtained from
A. Glycolysis
B. Terminal oxidation
c. Krebs cycle
D. Acetylation


Carbohydrates are stored in human body as the polysaccharide?
A . starch
B. glycogen
c. cellulose
D. amylose


Assertion
Transmission of the nerve impulse across a synapse is accomplished by neurotransmitters.
Reason
Transmission across a synapse usually
requires neurotransmitters because
there is small space i.e., synaptic cleft,
that separates one neuron from another.
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.


Which of the following sequences is
correct?
\( \mathbf{A} \cdot p K_{a}\left(p-O_{2} N C_{6} H_{4} C O O H\right)>p K_{a} \)
\[
\left(C_{6} H_{5} C O O H\right)>p K_{a}\left(p-H O C_{6} H_{4} C O O H\right)
\]
B \( \cdot p K_{a}\left(p-O_{2} N C_{6} H_{4} C O O H\right)<p K_{a} \)
\[
\left(C_{6} H_{5} C O O H\right)<p K_{a}\left(p-H O C_{6} H_{4} C O O H\right)
\]
\( \mathbf{c} \cdot p K_{a}\left(p-O_{2} N C_{6} H_{4} C O O H\right)>p K_{a} \)
\[
\left(C_{6} H_{5} C O O H\right)<p K_{a}\left(p-H O C_{6} H_{4} C O O H\right)
\]
\( \mathbf{D} \cdot p K_{a}\left(p-O_{2} N C_{6} H_{4} C O O H\right)<p K_{a} \)
\[
\left(C_{6} H_{5} C O O H\right)>p K_{a}\left(p-H O C_{6} H_{4} C O O H\right)
\]


What is the geometric mean of the
sequence \( 1,2,4,8, \dots \dots 2^{n} ? \)
\( \mathbf{A} \cdot 2^{n / 2} \)
B. \( 2^{(n+1) / 2} \)
c. \( 2^{(n+1)}-1 \)
D. \( 2^{(n-1)} \)


A bolt of mass \( 0.3 \mathrm{kg} \) falls from the ceilling of an elevator moving down with an uniform speed of \( 7 m / s . \) It hits the floor of the elevator ( length of the elevator \( =3 \mathrm{m} \) ) and does not rebound.
What is the heat produced by impact?
A . 8.82
B . 7.72 J
c. 6.62 J
D. 5.52


The law of conservation of angular
momentum is obtained from Newton's II
law in rotational motion when:
A. External torque is maximum
B. External torque is minimum
c. External torque is zero
D. External torque is constant


The adjoining bar graph shows the numbers of book sold by a bookstore during 5 consecutive years. Read the bar graph and answer the following
question:

About how many books were sold in
2008,2009 and 2011 years?


From the sum of \( 3 x-y+11 \) and \( -y- \)
11 subtract \( 3 x-y-11 \)


Every rational number is
A. A natural number
B. An integer
C. A real number
D. A whole number


How much \( C a\left(N O_{3}\right)_{2}, \) in \( m g, \) must be
present in 50 ml of a solution with
2.35 ppm of Ca ?
A . 0.1175
B. 770.8
c. 4.7
D. 0.48


How much heat is required to raise 1 gram of copper at \( 1^{\prime} \mathrm{C} ? \)
A. 0.385 Joules
B. 0.485 Joules
c. 1.02 Joules
D. 2.045 Joules


Increase in the concentration of
pollutants (toxicant) in higher trophic levels is called as
A. Recycling
B. Eutrophication
c. Biodegradation
D. Biomagnification


Q Type your question.
Iong ana reacnes the potrom \( 3 s \) later. \( A \) t
the instant when \( A \) is released, a
second mass \( B \) is projected upwards
along the plate from the bottom with a
certain initial velocity. Mass \( B \) travels a
distance up the plane, stops and
returns to the bottom so that it arrives
simultaneously with \( A \). The two masses
do not collide. Initial velocity of \( B \) is
A \( \cdot 4 m s^{-1} \)
B. \( 5 m s^{-1} \)
\( c \cdot 6 m s^{-1} \)
D. \( 7 \mathrm{ms}^{-} \)


The contents of three bags \( I, I I \) and \( I I I \)
are as follows:
Bag \( I: 1 \) white, 2 black 3 red balls
Bag \( I I: 2 \) white, 1 black 1 red balls
Bag III : 4 white, 5 black 3 red balls A bag is chosen at random and two
balls are drawn. What is the probability that the balls are white and red


Integrate the function
\( \frac{6 x+7}{\sqrt{(x-5)(x-4)}} \)


The light waves from two independent monochromatic light sources are given
by-
\( \boldsymbol{y}_{1}=\mathbf{2} \sin \omega \boldsymbol{t} \) and \( \boldsymbol{y}_{2}=\mathbf{2} \cos \boldsymbol{\omega} \boldsymbol{t} \)
then the following statement is correct
A. Both the waves are coherent
B. Both the waves are incoherent
c. Both the waves have different time periods
D. None of the above


\( a b c d=81 \) find minimum value of \( a+ \)
\( \boldsymbol{b}+\boldsymbol{c}+\boldsymbol{d} ? \)
A . 12
B.
\( c \cdot-1 \)
D. -12


The formal potential of \( \boldsymbol{F e}^{3+} / \boldsymbol{F e}^{2+} \) in a sulphuric acid and phosphoric acid
mixture \( \left(\boldsymbol{E}^{o}=+\mathbf{0 . 6 1} \boldsymbol{V}\right) \) is much lower
than the standard potential
\( \left(\boldsymbol{E}^{o}=+\mathbf{0 . 7 7} \boldsymbol{V}\right) . \) This is due to:
This question has multiple correct options
A \( \cdot \) formation of the species \( \left[F e H P O_{4}\right]^{+} \)
B. lowering of potential upon complexation
C . formation of the species \( \left[\mathrm{FeSO}_{4}\right]^{-} \)
D. high acidity of the medium


Which sub-atomic particle(s) in the 3 isotopes of \( ^{\prime} \boldsymbol{H}^{\prime} \) are the same?
A. Proton and electron
B. Neutron
c. Both \( A \) and \( B \)
D. None of the above


Decomposition of \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) is a first order
reaction. A 16 volume solution of \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \)
of half life 30 min is present at start. When will the solution become one
volume?
A. After 120 min
B. After 90 min
c. After 60 min
D. After 150 min


Maximum acidic character is shown by the oxyacids of halogens with oxidation number of halogens as


In the speed-time graph for a moving car given here, the part which indicates
uniform acceleration
\( A \cdot A B \)
B. вС
\( c \cdot D E \)
D. None


A compound which can be used in
space vehicles both to a absorb \( C O_{2} \)
and liberate \( \boldsymbol{O}_{2} \) is:
A . \( N a O H \)
в. \( N a_{2} O \)
c. \( N a_{2} O_{2} \)
\( \mathbf{D} \cdot C a O+N a O H \)


In the electroysis of \( A g N O_{3} \) solution,
\( 0.7 \mathrm{g} \) of \( \mathrm{Ag} \) is deposited after a certain period of time. Calculate the quantity of electricity required in coulomb. (Molar mass of \( A g \) is \( 107.9 g \) mol \( ^{-1} \) ).


Write chemical reaction of glucose with
\( \boldsymbol{H I} \)


Which of the following statement, is
false?
A. Urea is more toxic than ammonia.
B. Ammonia is converted to urea in liver.
C. Ammonia is produced in the body cells by the metabolism of proteins.
D. Fluid collected in Bowman's capsule is called glomerular fluid.


Two identical coherent sources are
placed on a diameter of a circle of
radius \( R \) at separation \( x(<<R) \)
symmetrically about the centre of the circle. The sources emit identical
wavelength \( \lambda \) each. The number of points on the circle with maximum intensity is \( (x=5 \lambda) \)


If \( \tan \theta+\sec \theta=4, \) then find \( \sin \theta+ \)
\( \cos \theta \)
A .
B. - -
c. \( \frac{23}{17} \)
D. \( \frac{13}{14} \)


In the figure, chords \( B A \) and \( D C \) of a
circle meet at \( P . \) Prove that
\( \boldsymbol{P A} \times \boldsymbol{P B}=\boldsymbol{P C} \times \boldsymbol{P D} \)


A dice is thrown once,what is the
probability of getting an even prime number.
A \( \cdot \frac{1}{2} \)
B. \( \frac{2}{3} \)
\( c \cdot \frac{1}{4} \)
D.


What is called fossil fuel?
A. Mineral coal
B. Petroleum
c. Natural gas
D. All of these


Number of real solutions of the
equation \( \sin a^{x} \cos a^{x}=\frac{a^{x}+a^{-x}}{4} \) is
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c .3 \)
D.


A mass of \( 0.65 g \) of zinc reacts completely with \( H C l \) to produce
hydrogen gas and a zinc chloride compound. The mass of the chlorine in the compound is \( 0.71 g \), what is the empirical formula of this compound?
(At. mass of \( Z n=65 g / \text { mol }) \)
\( \mathbf{A} \cdot Z n C l \)
в. \( Z n C l_{2} \)
c. \( Z n C l_{5} \)
D. \( Z n C l_{4} \)


Primary gaseous fuel among the following is:
A. producergas
B. water gas
c. LPG
D. natural gas


If \( \frac{z+2 i}{z-2 i} \) is purely imaginary then \( |z| \) is
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot \frac{1}{2} \)
D.


The \( 4^{t h} \) term of A.P. is 22 and \( 15^{t h} \) term
is \( 66 . \) Find the first term and the
common difference. Hence find the sum
of the series to 8 terms.


The variance of the first \( n \) natural
number is
A \( \cdot \frac{1}{12}\left(n^{2}-1\right) \)
B \( \cdot \frac{1}{6}\left(n^{2}-1\right) \)
c. \( \frac{1}{6}\left(n^{2}+1\right) \)
D. \( \frac{1}{12}\left(n^{2}+1\right) \)


In a certain town, \( 25 \% \) families own a
phone and \( 15 \% \) own a car, \( 65 \% \) families
own neither a phone nor a car. 2000 families own both a car and a phone. Consider the following statements in this regard.
1) \( 10 \% \) families own both a car and a
phone
Il) \( 35 \% \) families own either a car or a
phone
III) 40,000 families live in the town.
Which of the above statements are
correct ?
A . \( I \& I I \)
в. I \& III
c. II \& III
D. I,II \& III


For the probability distribution function
of random variable \( X, x_{1}, x_{2}, x_{3}, \dots x_{n} \)
are the values \( X \) takes, and \( p\left(x_{i}\right) \)
denote the probability of \( x_{i} \) then which
one of the following is true.? This question has multiple correct options
\( \mathbf{A} \cdot p\left(x_{i}\right)>0 \)
в. \( p\left(x_{i}\right)<0 \)
\( \mathbf{c} \cdot \sum p\left(x_{i}\right)=1 \)
D. \( \sum x_{i}=1 \)


The increasing order of basic strength for the following compounds is:
(।) \( \boldsymbol{C} \boldsymbol{H}_{3}-\boldsymbol{C} \boldsymbol{H}_{2}-\boldsymbol{N} \boldsymbol{H}_{2} \)
(II) \( \boldsymbol{C H}_{3}-\boldsymbol{N} \boldsymbol{H}-\boldsymbol{C H}_{3} \)
(III) \( \boldsymbol{C H}_{3}-\boldsymbol{N} \boldsymbol{H}-\boldsymbol{P h} \)
\( (\mathrm{IV}) \boldsymbol{C} \boldsymbol{H}_{3}-\boldsymbol{N} \boldsymbol{H}-\boldsymbol{C} \boldsymbol{H} \boldsymbol{O} \)
A. \( I V<I I I<I>I I \)
в. \( I I I<I V<I>I I \)
c. \( I V<I I I<I I>I \)
D. \( I I<I<I I I>I V \)


A dentist uses a mirror to view
the inner parts of a patient's mouth.
A. Concave
B. Convex
c. Plain mirror
D. All of the above


Locus of a point that is equidistant from the lines \( x+y-2 \sqrt{2}=0 \) and
\( \boldsymbol{x}+\boldsymbol{y}-\sqrt{\mathbf{2}}=\mathbf{0} \) is
A \( . x+y-5 \sqrt{2}=0 \)
B . \( x+y-3 \sqrt{2}=0 \)
c. \( 2 x+2 y-3 \sqrt{2}=0 \)
D. \( 2 x+2 y-5 \sqrt{2}=0 \)


Let a function be defined as \( \boldsymbol{f}(\boldsymbol{x})= \) \( \frac{\boldsymbol{x}-|\boldsymbol{x}|}{\boldsymbol{x}} . \) Then \( \boldsymbol{f}(\boldsymbol{x}) \) is
A. continuous nowhere
B. continuous everywhere
c. continuous for all \( x \) except \( x=1 \)
D. continuous for all \( x \) except \( x=0 \)


Mannitol is stored food of
A. Rhodophyceae
B. xanthophyceae
c. Chlorophyceae
D. Phaeophyceae


If 10 g of a sample of water contains 16.2 gof \( \boldsymbol{C a}\left(\boldsymbol{H} \boldsymbol{C O}_{3}\right)_{2}, \) then the hardness of
water is:
A. 200 ppm
B. 300 ppm
c. 60 ppm
D. 100 ppm


Find the oxidation number of
Magnesium in Magnesium chloride.
\( A \cdot+1 \)
B. -
\( c \cdot+2 \)
\( D \cdot-2 \)


Define the term electric potential. State
its S.I. unit.


Find the slope of tangent to the curve \( y=3 x^{2}-6 \) at the point on it whose \( x \)
coordinate is 2


Schneiderian and tympanic membranes respectively belongs to
A. Ear and Nose
B. Ear and Eye
c. Ear and Ear
D. Nose and Ear


In a medium in which a transverse
progressive wave is travelling the phase difference between two points with a distance of separation \( 1.25 \mathrm{cm} \) is \( \frac{\pi}{4} . \)
the frequency of the wave is \( 1000 H z \)
its velocity will be
A \( \cdot 10^{4} m / s \)
в. \( 125 \mathrm{m} / \mathrm{s} \)
c. \( 100 m / s \)
D. \( 10 \mathrm{m} / \mathrm{s} \)


Find the distance between each of the
following pairs of points. \( \boldsymbol{L}(\mathbf{5},-\mathbf{8}), \boldsymbol{M}(-\mathbf{7},-\mathbf{3}) \)


Which of the following structure polynuclear aromatic
hydrocarbons possess?
A. Linear
B. Angular
c. Both \( A \) and \( B \)
D. None of the above


The value of the integral \( \int_{-\pi / 4}^{\pi / 4} \frac{d x}{a^{2} \cos ^{2} x+b^{2} \sin ^{2} x} \)
This question has multiple correct options
A \( \cdot \frac{2}{a b} \tan ^{-1} \frac{b}{a}(a>0, b>0) \)
B \( \cdot \frac{2}{a b} \tan ^{-1} \frac{b}{a}(a<0, b<0) \)
C \( \cdot \frac{\pi}{2}(a=1, b=1) \)
D. \( \frac{2}{a b} \tan ^{-1} \frac{a}{b}+\frac{1}{a b} \)


Imagine a light planet revolving around a very massive star in a circular orbit of
radius r with a period of revolution T. If the gravitational force of attraction between the planet and the star is
proportional to \( r^{5 / 2}, \) then the square of the time period will be proportional to.
A \( \cdot r^{3} \)
в. \( r^{2} \)
\( c \cdot r^{2.5} \)
D. \( r^{3.5} \)


Circle represent most acidic hydrogens
in these molecules. Which of the
following is correct representation?
\( A \)
\( B \)
\( c \)
All of these


\( \lim _{x \rightarrow 0} \frac{\sqrt{1+\sin x}-\sqrt{1-\sin x}}{x} \)


The interval a for which the local
minimum value of the function \( \boldsymbol{f}(\boldsymbol{x})= \) \( 2 x^{3}-21 x^{2}+60 x+a \) is positive. is
в. \( (-\infty,-25) \)
c. \( (25, \infty) \)
D. \( (-25, \infty) \)


The volume occupied by 11 grams of
\( C O_{2} \) gas at STP is:
A . \( 5.6 l \)
B. \( 11.2 l \)
c. \( 22.4 l \)
D. \( 44.8 l \)


Points \( P \) and \( Q \) have been taken on
opposite sides \( A B \) and \( C D \)
respectively of a parallelogram \( A B C D \) such that \( A P=C Q . \) Show that \( A C \) and
\( P Q \) disect each other.


Atomic radii of Flourine and Neon in
Angstorm units are given by?
A. 0.72,1.60
в. 1.60,1.60
c. 0.72,0.72
D. None of these


At \( 527^{\circ} \mathrm{C}, \) the reaction given below has
\( \boldsymbol{K}_{c}=\mathbf{4} \)
\( N H_{3}(g) \rightleftharpoons \frac{1}{2} N_{2}(g)+\frac{3}{2} H_{2}(g) \)
What is the \( K_{P} \) for the reaction?
\( N_{2}(g)+3 H_{2}(g) \rightleftharpoons 2 N H_{3}(g) \)
A. \( 16 \times(800 R)^{2} \)
\( ^{\text {В } \cdot}\left(\frac{800 R}{4}\right)^{-2} \)
\( \left(\frac{1}{4 \times 800 R}\right)^{2} \)
D. None of these


Which of the following compounds will
react with two moles of \( \boldsymbol{C H}_{3} \boldsymbol{M} \boldsymbol{g} \boldsymbol{B r} \) ?
A \( \cdot C_{2} H_{5} \) COOH
в. \( C H_{3} \) СООН
\( \mathbf{c} \cdot C H_{3} C \equiv C C H_{3} \)
D. \( H C \equiv C-C H_{2} O H \)


If \( n, e, \tau, m \) are representing electron density, charge, relaxation time and mass of an electron respectively then
the resistance of wire of length \( l \) and
cross sectional area \( \boldsymbol{A} \) is given by:
A \( \cdot \frac{m l}{n e^{2} \tau A} \)
в. \( \frac{2 m a}{n^{2} \tau} \)
\( \mathbf{c} \cdot n e^{2} \tau A \)
D. \( \frac{n e^{2} \tau A}{2 m} \)


In an atom, electrons revolve around the
nucleus. This gives rise to
A. only electric field
B. only magnetic field
c. both electric and magnetic fields
D. none of the above


What is meant by lightning?
A. It is sudden electrostatic discharge during an electrical storm between electrically charged regions of cloud.
B. It is sudden electrostatic discharge during an electrical storm between non-electrically charged regions of cloud
C. It is unsudden electrostatic discharge during an electrical storm between electrically charged regions of cloud.
D. None of the above


Which of the following will result when the temperature is increased as the chemical reaction proceeds?
I. Increased molecular collision
frequency
II. Increased numbers of molecules
possess energy greater than the activation energy
III. Decreased randomness of the
system
A . I only
B. Il only
c. I and II only
D. I and III only


When proving that a triangle is a right triangle using coordinate geometry
methods you must
A. show that the slopes of two of the sides are negative reciprocals creating perpendicular lines and right angles
B. show that the lengths of the sides satisfy the Pythagorean Theorem thus creating a right angle
C. both choices 1 and 2 may be used
D. neither choice 1 nor 2 may be used
E. none of these


The potential energy of a particle is directly proportional to its linear displacement from its mean position. Then, the particle performs a
A. Retarding straight line motion
B. Damped SHM
c. Linear SHM
D. Angular SHM


Water (Prevention and Control of
Pollution) Act was enacted during
A . 1952
в. 1972
\( c .1974 \)
D. 1969


In black and white photography, the developed film is fixed by washing with hypo solution which dissolves the under
composed \( A g B r \) to form a complex ion formed is:
\( A \cdot\left[A g\left(S_{2} O_{3}\right)_{2}\right]^{2} \)
B . \( \left[A g\left(S_{2} O_{3}\right)_{2}\right]^{3} \)
c. \( \left[A g\left(S_{2} O_{3}\right)_{2}\right] \)
D. none of these


Find the vertex of the median \( \boldsymbol{M}_{\mathbf{1}} \)
\( \mathbf{A} \cdot A \)
B. \( B \)
\( c \cdot C \)
\( D . D \)


Soaps are salts of :
A. Fatty Acids
B. Proteins
c. oils
D. None of these


The ratio of the energy required to set up in cube of side \( 10 \mathrm{cm} \) uniform magnetic field of \( 4 W b / m^{2} \) and a
uniform electric field of \( 10^{6} V / m \) is:
A \( \cdot 1.4 x 10^{7} \)
B. \( 1.4 x 10^{5} \)
c. \( 1.4 x 10^{6} \)
D. \( 1.4 x 10^{3} \)


TCA cycle is named after
\( A \). Embden
B. Emerson
c. Krebs
D. Calvin


A hole in a metal plate
heating.


Evaluate \( \cos ^{-1}(\cos 3) \)


Three fair coins are tossed
simultaneously. If X denotes the number of heads, find the probability distribution of \( X \)


Is zero a rational number? Can you write it in the form \( \frac{p}{q}, \) where \( p \) and \( q \) are integers and \( \boldsymbol{q} \neq \mathbf{0} ? \)


Zero of the polynomial \( p(x)=2-5 x \) is


Which of the following is not
hydrolysed?
This question has multiple correct options
A. \( A s C l_{3} \)
в. \( P F_{3} \)
\( \mathbf{c} \cdot \operatorname{Sb} C l_{3} \)
D. \( N F_{3} \)


Which of the following statements regarding the protozoans is correct?
A. They are unicellular.
B. They are eukaryotic
c. They are heterotrophic.
D. All of the above.


Given that \( \lim _{x \rightarrow \infty}\left(\frac{2+x^{2}}{1+x}-A x-B\right)= \)
3
What is the value of A?
A . -1
B. 1
\( c \cdot 2 \)
\( D \)


The frequency of the spectral line
obtained when the electron in \( n=3 \) of
Hydrogen atom drops to the fround
state is:
A \( \cdot 2.925 \times 10^{15} \) Hertz
B . \( 2.925 \times 10^{13} \) Hertz
C . \( 2.925 \times 10^{14} \) Hertz
D. \( 36559 \times 10^{10} \) Hertz


Find the values of \( c \) that satisfy the
Rolle's theorem for integrals on [-1,3]
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2}-\boldsymbol{2} \boldsymbol{x}-\boldsymbol{8} \)
\( \mathbf{A} \cdot c=3 \)
в. \( c=1 \)
\( \mathbf{c} \cdot c=0 \)
\( \mathbf{D} \cdot c=2 \)


Oxygen can be prepared from hydrogen peroxide and manganese dioxide in the laboratory.
A. True
B. False


A long coil containing a large number of close turns of insulated copper wire.
A. Toroid
B. Solenoid
c. Both
D. None


If the polynomials \( 2 x^{3}+m x^{2}+3 x-5 \)
and \( x^{3}+x^{2}-4 x+m \) leaves the same
remainder when divided by \( x-2, \) then
the value of \( m \) is
A \( \cdot-\frac{3}{13} \)
B. \( -\frac{13}{3} \)
\( c \cdot \frac{3}{13} \)
D. \( \frac{13}{3} \)


f \( y=m x \) be the equation of a chord of
a circle whose radius is \( a \), the origin of
coordinates being one extremity of the
chord and the axis of \( x \) being a diameter of the circle, prove that the equations of a circle of which this chord is the diameter is \( \left(1+m^{2}\right)\left(x^{2}+y^{2}\right)- \)
\( \mathbf{2} \boldsymbol{a}(\boldsymbol{x}+\boldsymbol{m} \boldsymbol{y})=\mathbf{0} \)


The balancing length for a cell is \( 560 \mathrm{cm} \)
in a potentiometer experiment. When an external resistance of \( 10 \Omega \) is connected
in parallel to the cell, the balancing length changes by \( 41 c m \). The internal resistance of the cell in ohms is
A . 1.6
B. 1.
\( c \cdot 12 \)
D. 0.8


Titration curves for \( 0.1 \mathrm{M} \) solutions of
three weak acids \( H A_{1}, H A_{2} \) ans \( H A_{3} \)
with ionization constants \( \boldsymbol{K}_{1}, \boldsymbol{K}_{2} \) and
\( K_{3} \) respectively are plotted in the figure.which of the following is/are
true?
\( \mathbf{A} \cdot K_{2}=\left(K_{1}+K_{3}\right) / 2 \)
B . \( K_{1}<K_{3} \)
\( \mathbf{c} \cdot K_{1}>K_{2} \)
D. \( K_{2}>K_{3} \)


An instructor has a question bank
consisting of 300 easy True / False questions, 200 difficult True / False
questions, 500 easy multiple choice questions and 400 difficult multiple choice questions. If a question is selected at random from the question
bank, what is the probability that it will
be an easy question given that it is a multiple choice question?


A disc of mass \( \mathrm{M} \) and radius \( \mathrm{R} \) is
reshaped in the form of ring of same
R. The radius of mass but radius 2
gyration increased by a factor:


Animals that feed on organic matter through mud are
A. Myrmacophagous
B. Detritivorous
c. saprophytic
D. coprophagous


If \( \alpha, \beta \) are the roots of the equation
\( \left(\tan ^{-1}(x / 5)\right)^{2}+(\sqrt{3}- \)
1) \( \tan ^{-1}(x / 5)-\sqrt{3}=0,|\alpha|>|\beta| \) then
This question has multiple correct options
A \( \cdot \alpha+\beta=-5 \pi / 12 \)
в. \( |\alpha-\beta|=35 \pi / 12 \)
\( \mathbf{c} \cdot \alpha \beta=-25 \pi^{2} / 12 \)
D. \( 3 \alpha+4 \beta=0 \)


Consider the following structures. Which of the following pairs represent
D- and L-fructose respectively?
A. II and I
B. I and III
c. III and IV
D. II and IV


Number of water molecules attached on
\( C u^{2+} \) ion in \( C u S O_{4} \cdot 5 H_{2} O \) is :


If a unit vector is represented by \( \mathbf{0 . 5} \overline{\mathbf{i}}+\mathbf{0 . 8} \overline{\mathbf{j}}+\mathbf{c \overline { k }} \)
then the value of 'c' is
\( A \)
B. \( \sqrt{0.8} \)
c. \( \sqrt{0.11} \)
D. \( \sqrt{0.01} \)


Match the physical quantities given in
Column I with suitable dimensions
expressed in Column II.
Column Column I II
a) Angular momentum
g) \( M L^{2} T^{-2} \)
Latent heat
h) \( M L^{2} Q^{-2} \)
b)
Torque \( M L^{2} T^{-1} \)
c)
i)
d) Capacitane
j) \( M L^{3} T^{-1} Q^{-2} \)
Inductance
k)
e) \( M^{-1} L^{-2} T^{2} Q^{2} \) \( L^{-2} T^{2} Q^{2} \)
\( f) \)
Resistivity ।) \( L^{2} T^{-2} \) \( T \)
A. a-i, b-l, c-g, d-k, e-h, f-j
B. a-l, b-i, c-k, d-g, e-j, f-h
c. a-i, b-l, c-h, d-j, e-g, f-k
D. a-h, b-j, c-g, d-k, e-i \( f- \)


In the figure given \( L_{1} \) and \( L_{2} \) are
parallel. The sum of the angles \( \boldsymbol{\alpha}, \boldsymbol{\beta}, \boldsymbol{\gamma} \)
marked in the diagram is:
\( A \cdot 180^{\circ} \)
В. \( 270^{\circ} \)
\( c \cdot 360^{\circ} \)
D. \( \leq 270^{\circ} \)


A box contain 10 red balls, 20 yellow balls and 50 blue balls. If a ball is drwan
at random from the box, find the probability that it will be
(i) a blue ball
(ii) neither yellow nor
blue


What are the size of \( X \) and \( X^{\prime} \) in the
interhalogen compounds?


Find an equation of the line through the points (-3,5) and (9,10) and write it in standard form \( A x+B y=C, \) with \( A> \)
0
A \( .6 x-10 y=-75 \)
B. \( 5 x-12 y=-75 \)
c. \( 4 x-11 y=-65 \)
D. \( x-6 y=-15 \)


Given point are \( \boldsymbol{P}=(\mathbf{1},-\mathbf{2}), \boldsymbol{Q}=(\mathbf{7}, \mathbf{6}) \)
is the origin. The length of the common chord of the circles with \( \mathrm{OP} \) and \( \mathrm{OQ} \) as diameters is
A . 1
B. 2
\( c \cdot 4 \)
D. 6


Quinhydrone half cell is not reversible
to:
This question has multiple correct options
\( \mathbf{A} \cdot \mathbf{H}^{+} \)
B. quinone
c. quinol
D. он


Which of the following order of acidity is
correct?
(I) \( \quad \mathbf{C H}_{3}-\mathbf{N H}_{2} \)
(II) \( \mathbf{H}-\mathbf{C} \equiv \mathbf{C}-\mathbf{H} \)
(III)
(IV)
A. \( I I I>I V>I>I I \)
В. \( I I I>I V>I I>I \)
c. \( I V>I I I>I>I I \)
D. \( I V>I I I>I I>I \)


In right angle \( \triangle A B C, \angle B=90^{\circ}, \angle A= \)
\( 45^{\circ}=\angle C, \) then \( \operatorname{cosec} 45^{\circ}= \)
\( \mathbf{A} \cdot \mathbf{1} \)
B. \( \sqrt{2} \)
c. \( \frac{1}{\sqrt{2}} \)
D. None of above


A ball with momentum \( 0.5 k g m s^{-1} \) coming towards a batsman is hit by him such that it goes on the same path in opposite direction with momentum \( 0.3 k g m s^{-1} . \) If the time of contact of
the ball with the bat is \( 0.02 s \), find the
force on the ball by the bat.
A . \( 10 N \)
в. \( 40 N \)
\( c .75 N \)
D. 30 N


Which of the following is a polysaccharide?
A. Cellulose
B. Sucrose
c. Galactose
D. Maltose


Find the square root of 841
A . 2
B. 28
\( c \cdot 29 \)
D. 25


A steel wire with cross section \( 3 \mathrm{cm}^{2} \)
has elastic limit \( 2.4 \times 10^{8} \) Pa. Find the
maximum upward acceleration that can be given to a \( 1200 k g \) elevator supported by this cable if the stress is not to exceed \( 1 / 3 r d \) of the elastic limit
\( \mathbf{A} \cdot 9 m s^{-2} \)
B. \( 10 \mathrm{ms}^{-2} \)
\( \mathrm{c} \cdot 11 \mathrm{ms}^{-2} \)
D. \( 12 \mathrm{ms}^{-2} \)


Sanitation at public places can be maintained by
A. Proper drainage.
B. Garbage management.
c. Sufficient public toilet facilities.
D. All of the above.


Molar conductivities of oxalate, \( \boldsymbol{K}^{+} \) and
\( N a^{+} \) ions at infinite dilution are 148.2 \( \mathbf{5 0 . 1 , 7 3 . 5} S \mathrm{cm}^{2} \) mol \( ^{-1} \) respectively.
Then, equivalent conductivity at infinite dilution for sodium-potassium oxalate \( \left[\left(\boldsymbol{C O O}^{-}\right)_{2} \boldsymbol{N} \boldsymbol{a}^{+} \boldsymbol{K}^{+}\right] \) will be:
A. \( 271.8 \mathrm{S} \mathrm{cm}^{2} \) eq \( ^{-1} \)
В. \( 67.95 \mathrm{S} \mathrm{cm}^{2} \mathrm{eq}^{-1} \)
c. \( 543.6 S \mathrm{cm}^{2} e q^{-1} \)
D. \( 135.9 S \mathrm{cm}^{2} e q^{-1} \)


At what height in km over the earth's pole the free fall acceleration decreases
by one percent? (Assume the radius of
the earth to be \( 6400 \mathrm{km} \) )
A .32
B. 64
c. 80
D. 1.253


The angle between any two diagonals of
cube are:
A \( \cdot \cos ^{-1}\left(\frac{1}{2}\right) \)
B. \( \cos ^{-1}\left(\frac{1}{3}\right) \)
\( ^{\mathbf{C}} \cdot \cos ^{-1}\left(\frac{1}{\sqrt{3}}\right) \)
\( \mathrm{D} \cdot \cos ^{-1}\left(\frac{1}{\sqrt{2}}\right) \)


In a series \( L, R, C \) circuit which is
connected to ac source, when resonance
is obtained then net impedance Z will
be:
A \( . Z=R \)
B. \( \quad Z=\omega L-\frac{1}{\omega C} \)
\( \mathbf{c} \cdot Z=\omega L \)
D. \( z=\frac{1}{w C} \)


Two cylindrical vessels of equal cross-
sectional area \( A \) contain water upto
heights \( h_{1} \) and \( h_{2} \). The vessels are interconnected so that the levels in
them become equal. Calculate the work done by the force of gravity during the process. The density of water is \( \rho \)


A metal rod of uniform thickness and of
length \( 1 m \) is suspended at its \( 25 c m \)
division with the help of a string. The rod remains horizontally straight when a block of mass \( 2 k g \) is suspended to
the rod at its \( 10 \mathrm{cm} \) division from same
end. The mass of the rod is:
A. \( 0.4 \mathrm{kg} \)
B. \( 0.8 \mathrm{kg} \)
c. \( 1.2 \mathrm{kg} \)
D. \( 1.6 \mathrm{kg} \)


Presence of CFCs in the atmosphere is responsible for
A. Formation of ozone
B. Production of healthy plants
c. Depletion of ozone layer
D. None of these


A ladder of length I and mass m is placed against a smooth vertical wall, but the ground is not smooth. Coefficient of friction between the
ground and the ladder is \( \mu . \) The angle \( \theta \)
at which the ladder will stay in equilibrium is:
A \( \cdot \theta=\tan ^{-1}(\mu) \)
B . \( \theta=\tan ^{-1}(2 \mu) \)
c. \( \theta=\tan ^{-1}\left(\frac{\mu}{2}\right) \)
D. none of these


Which of the following oxide is thermally least stable?
A. \( C a O \)
в. \( A l_{2} O_{3} \)
\( \mathrm{c} \cdot \mathrm{Fe}_{2} \mathrm{O}_{3} \)
D. \( A g_{2} O \)


A conductivity cell filled with \( 0.01 M \)
KCl gives at \( 25^{\circ} \mathrm{C} \) the resistance of
604 ohms. The conductivity of \( K C l \) at
\( 25^{\circ} C \) is \( 0.00141 \Omega^{-1} c m^{-1} . \) The same
cell filled with \( 0.001 M A g N O_{3} \) gives a
resistance of 6529 ohms. Calculate the
molar conductivity of \( 0.001 M A g N O_{3} \)
solution at \( 25^{\circ} \mathrm{C} \)


Rate constant \( k=2 \times \)
\( 10^{3} \operatorname{mol}^{-1} L s^{-1} \) and \( E_{a}=2.0 \times \)
\( 10^{2} k J m o l^{-1} . \) What is the value of \( A \)
when \( \boldsymbol{T} \rightarrow \infty ? \)
A \( .2 .0 \times 10^{2} \mathrm{mol}^{-1} \)
В. \( 2.0 \times 10^{3} \) mol\( ^{-1} L s^{-1} \)
c. \( 2.0 \times 10^{3} \) mol \( L^{-1} s^{-1} \)
D. 2.0 \( \times 10^{3} \) mol \( ^{-1} s^{-1} \)


In the projectile motion shown is figure,
\( \operatorname{given} t_{A B}=2 s \) then which of the
folowing is correct \( :\left(g=10 m s^{-2}\right) \)
his question has multiple correct options
A. particle is at point B at 3 s
B. maximum height of projectile is 20 m
c. initial vertical component of velocity is \( 20 \mathrm{ms} \)
D. horizontal component of velocity is \( 20 \mathrm{ms} \)


Which of the following statements is incorrect?
A. Generally the radius trend and the ionization energy trend across a period are opposites.
B. Metallic and covalent radii of potassium are \( 2.3 A^{\circ} \) and
\( 2.03 A^{\circ} \) respectively.
C. Amongst \( L i^{-}, B e^{-}, B^{-} \) and \( C^{-}, L i^{-} \) is least stable ion.
D. Atomic and ionic radii of Niobium and Tantalum are
almost same.


0.75 g of an organic compound on complete combustion gave 1.6 g of carbon dioxide and 0.47 g of water. \( A \) given weight of the compound when heated with nitric acid and silver
nitrate gave an equal weight of silver chloride. 0.75 g of the compound gave \( 58.57 \mathrm{ml} \) of nitrogen at 1 atm and \( 273 \mathrm{K} \) The empirical formula of the compound
is :
A \( \cdot C_{7} H_{10} N C l \)
B . \( C_{6} H_{12} N C l \)
c. \( C_{7} H_{12} N C l \)
D. \( C_{7} H_{14} N C l \)


If water be used to construct a
barometer, what would be the height of water column at standard atmospheric pressure (76 cm of mercury)?


\( 1 k g \) of water at \( 20^{\circ} C \) is, mixed with
\( 800 g \) of water at \( 80^{\circ} \mathrm{C} \). Assuming that no heat is lost to the
surroundings, calculate the final temperature of the mixture:
A \( \cdot 24.44^{\circ} \mathrm{C} \)
B . \( 46.67^{\circ} \mathrm{C} \)
c. \( 44.44^{\circ} \mathrm{C} \)
D. \( 54.44^{\circ} \mathrm{C} \)


A \( 200 g \) cricket ball is thrown with a
speed of \( 3.0 \times 10^{3} \mathrm{cm} \) sec \( ^{-1} \). What will
be its de Broglie's wavelength? \( \left(h=6.6 \times 10^{-27} g c m^{2} s e c^{-1}\right) \)
\( \mathbf{A} \cdot 1.1 \times 10^{-32} c m \)
B . \( 2.2 \times 10^{-32} \mathrm{cm} \)
C \( .0 .55 \times 10^{-32} \mathrm{cm} \)
D. \( 11.0 \times 10^{-32} \mathrm{cm} \)


Light travels as a
A. parallel beam in each medium
B. convergent beam in each medium
C. divergent beam in each medium
D. divergent beam in one medium and convergent beam in the other medium


One mole of 1,2-dibromopropane on
treatment with \( \boldsymbol{X} \) moles of \( \boldsymbol{N} \boldsymbol{a} \boldsymbol{N} \boldsymbol{H}_{2} \)
followed by treatment with ethyl
bromide gave a 2 -pentyne. The value of \( \boldsymbol{X} \) is:
A. one
B. two
c. three
D. four


A convex lens of focal length \( 15 \mathrm{cm} \) is placed infront of a plane mirror at a distance \( 25 \mathrm{cm} \) from the mirror. Where
on the optical axis and from the centre of the lens should a small object
be placed such that the final image coincides with the object?
A. \( 15 \mathrm{cm} \) and on the opposite side of the mirror
B. \( 15 \mathrm{cm} \) and between the mirror and the lens
c. \( 7.5 \mathrm{cm} \) and on the opposite side of the mirror
D. \( 7.5 \mathrm{cm} \) and between the mirror and the lens


Hydrolysis of sucrose is called
A. mutarotation
B. saponification
c. inversion
D. de-esterification


An object is moving with uniform deceleration.
Which statement describes its motion?
A. Its rate of change of speed of decreasing
B. Its speed is constant
c. Its speed is decreasing
D. Its speed in increasing


What are the steps in photosynthesis?


If two supplementary angles are in the ratio \( 4: 5, \) then the angles are
A. \( 80^{\circ}, 100^{\circ} \)
в. \( 85^{\circ}, 95^{\circ} \)
c. \( 40^{\circ}, 50^{\circ} \)
D. \( 60^{\circ}, 120^{\circ} \)


What would happen if fangs of
venomous snake are pulled out? They
will
A. Get replaced
B. Become double
c. Be safe to handle
D. Never get replaced


I. If the curve \( y=x^{2}+b x+c \) touches
the straight line \( y=x \) at the point
(1,1) then \( b \) and \( c \) are given by 1,1
Il. If the line \( \boldsymbol{P x}+\boldsymbol{m} \boldsymbol{y}+\boldsymbol{n}=\boldsymbol{0} \) is a
normal to the curve \( x y=1, \) then \( P> \)
\( \mathbf{0}, \boldsymbol{m}<\mathbf{0} \)
Which of the above statements is
correct
A. onlyı
B. only II
c. both I and II
D. Neither I nor II


Find the 5 th term of the sequence \( 1, \sqrt{2}, 2 \ldots \)
A.
B. 2
\( c \cdot 3 \)
\( D \)


Match items in column A with one or
more items in column
\( \begin{array}{ll}\text { Column } A & \text { Column } B \\ \text { (i) Inner planet } & \text { (a) Saturn } \\ \text { (ii) Outer planet } & \text { (i) }\end{array} \) er planet (k Outer p er plane I (b) Pole star (iii) Constellation
(iv) Satellite of the earth
(d) Moon
(e) Earth
(f) Orion
(g) Mars
\( A \)
\( (i)-g, e(i i)-a(i i i)-c, f(i v)-d \)
B \( \cdot(i)-g, e(i i)-c, f(i i i)-a(i v)-d \)
C \( .(i)-a(i i)-b(i i i)-c, f(i v)-d \)
D. None of these


\( \boldsymbol{B e}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\boldsymbol{B r} \rightarrow \boldsymbol{H}-\boldsymbol{C} \equiv \)
\( C-H \)
The reagents for the following conversion, is/are:
A. Alcoholic \( K O H \)
B. Alcoholic KOH followed by \( \operatorname{NaNH}_{2} \)
C. Aqueous KOH followed by NaNH
D. \( Z n / C H_{3} O H \)


If \( (x-1)\left(x^{2}+1\right)>0, \) then find the
value of \( \sin \left(\frac{1}{2} \tan ^{-1} \frac{2 x}{1-x^{2}}-\tan ^{-1} x\right) \)
A . \( -1 / 2 \)
B. -
\( c \cdot 1 / 2 \)
D.


Find minimum value \( 4 x+\frac{9}{x} \quad x>0 \)


The position \( x \) of a particle with respect
to time \( t \) along \( x- \) axis is given by \( x= \)
\( 9 t^{2}-t^{3} \) where \( x \) is in metres and \( t \) in
seconds. What will be the position of this particle when it achieves
maximum speed along the \( +x \)
direction?
A . \( 24 m \)
в. 32 т
\( \mathrm{c} .54 \mathrm{m} \)
D. \( 81 m \)


How many times does the electron go
round the first Bohr orbit of hydrogen atoms in 1 s? (in peta Hz)


\( A 2000 \mathrm{kg} \) automobile is travelling at \( 54 \mathrm{kmph} . \) Find the average force to stop it in \( 25 \mathrm{m} \)
A. 8000 N
B. 9000 N
c. 7000 N
D. 6000 N


Calculate the rate of flow of glycerin of
density \( 1.25 \times 10^{3} k g / m^{3} \) through the
conical section of a pipe, if the radii of its ends are \( 0.1 m \) and 0.04 m and the
pressure drop across its length is
\( \mathbf{1 0} N / \boldsymbol{m}^{2} \)
A \( \cdot 6.43 \times 10^{-4} m^{3} / s \)
B. \( 5.43 \times 10^{-4} \mathrm{m}^{3} / \mathrm{s} \)
c. \( 5.44 \times 10^{-3} \mathrm{m}^{3} / \mathrm{s} \)
D. \( 6.43 \times 10^{-3} \mathrm{m}^{3} / \mathrm{s} \)


State for what purpose is bleaching
powder is used in water treatment plant.


Cooking oil can be converted into
vegetable ghee by the process of:
A. hydrogenation
B. distillation
c. crystallisation
D. oxidation
E . ionisation


Two men ' \( A \) ' and ' \( B \) ' are standing on a
plank.' \( B^{\prime} \) is at the middle of the plank
and ' \( A \) ' is at the left end of the plank. Surface of the plank is smooth. System
is initially at rest and masses are as
shown in figure. ' \( \boldsymbol{A}^{\prime} \) and \( ^{\prime} \boldsymbol{B}^{\prime} \) start moving
such that the position of ' \( B \) ' remains
fixed with respect to ground and ' \( \boldsymbol{A}^{\prime} \)
meets ' \( B \) '. Then the point where \( A \)
meets \( B \) is located at
A. the middleof the plank
B. 30cm from the left end of the. plank
c. the right end of the plank
D. None of these


When \( C O_{2} \) is passed through sodium metaborate, which is found as a product?
A. Sodium borate
B. Borax
c. Boric oxide
D. None of these


Assertion
During covalent bonding the electronegativity difference between
two atoms is greater than 1.7
Reason
Covalent bond is formed by sharing of electrons between atoms that have
same size
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 point which divides the line joining the points (1,3,4) and (4,3,1) internally in the ratio \( 2: 1, \) is
A. (2,-3,3)
в. (2,3,3)
c. \( \left(\frac{5}{2}, 3, \frac{5}{2}\right) \)
D. (-3,3,2)
E \( .(3,3,2) \)


Compound \( (\boldsymbol{F}) \) is:
\( \mathbf{A} \)
\( B \)
\( \mathbf{C} \)
D.


Fluorine is the best oxidising agent
because it has:
A. highest electron affinity
B. highest reduction potential
c. highest oxidation potential
D. lowest electron affinity


frue Enter \( ^{\prime} 1^{\prime} \) else \( ^{\prime} 0^{\prime} \)
\( \left|\begin{array}{ccc}\boldsymbol{x} & \boldsymbol{y} & \boldsymbol{x}+\boldsymbol{y} \\ \boldsymbol{y} & \boldsymbol{x}+\boldsymbol{y} & \boldsymbol{x} \\ \boldsymbol{x}+\boldsymbol{y} & \boldsymbol{x} & \boldsymbol{y}\end{array}\right|=-\boldsymbol{2}(\boldsymbol{x}+ \)
\( \boldsymbol{y})\left(\boldsymbol{x}^{2}+\boldsymbol{y}^{2}-\boldsymbol{x} \boldsymbol{y}\right) \)


Sugar is bought at Rs. 16.20 per \( \mathrm{kg} \) and sold at Rs. 17.28 per kg. The gain
percent is
A \( \cdot 6 \frac{2}{3} \% \)
в. \( 3 \frac{1}{3} \% \)
\( c \cdot 10 \% \)
D. \( _{10} \frac{2}{3} \% \)


\( 2 S O_{2}+O_{2} \rightleftharpoons 2 S O_{3} \) starting with 2
mol of \( S O_{2} \) and 1 mol of \( O_{2} \) in 1 litre
flask, mixture required 0.4 mol of
\( M n O_{4}^{-} \) in acid medium. Hence \( K_{c} \) is:
\( \mathbf{A} \cdot 80 \)
B. 2
\( c \cdot ! 6 \)
D. 2.6


Two reactions
(i) \( \boldsymbol{A} \rightarrow \) products
\( B \rightarrow \) products, follow first order
kinetics. The rate of the reaction (i) is
doubled when the temperature is raised from \( 300 \mathrm{K} \) to \( 310 \mathrm{K} \). The half life for this
reaction at \( 310 \mathrm{K} \) is 30 minutes. At the
same temperature B decomposes twice as fast as A. If the energy of activation for the reaction (ii) is half that of
reaction (i), calculate the rate constant
of the reaction (ii) at \( 300 \mathrm{K} \)
A. \( k=0.0327 \min ^{-1} \)
В. \( k=0.327 \mathrm{min}^{-1} \)
c. \( k=3.27 \mathrm{min}^{-1} \)
D. \( k=32.7 \) min \( ^{-1} \)


To obtain maximum EMF from a
number of cells, they must be
connected in
A. Series
B. Parallel
c. Both (a) and (b) above
D. None of these


Verify Rolle's Theorem for the function
\( f(x)=x(x-1)^{2} \) in the interval [0,1]


The relation between \( T \) and \( g \) by
\( \mathbf{A} \cdot T \propto g \)
в. \( T \propto g^{2} \)
c \( \cdot T^{2} \propto g^{-1} \)
D \( T \propto \frac{1}{g} \)


Phenobarbitone is a sleep-inducing drug. It is also used in making:
A . acetylene
B. soap
c. alcohol
D. urea


The cathode in outer compartments of Castner-Kellner process is made of:
A . iron
B. copper
c. graphite
D. mercury


Determine the binomial distribution
whose mean is 4 and variance 3


A cart \( A \) of mass \( 50 k g \) moving at a
speed of \( 20 k m / h \) hits a lighter cart \( B \)
of mass \( 20 \mathrm{kg} \) moving towards it at a speed of \( 10 \mathrm{km} / \mathrm{h} \). The two carts cling to
each other. Find the change of
momentum of cart A.


If the surface area of a sphere is
\( 144 \pi \mathrm{cm}^{2}, \) then its radius is:
\( A \cdot 6 c m \)
B. \( 8 \mathrm{cm} \)
\( \mathrm{c} \cdot 12 \mathrm{cm} \)
D. \( 10 \mathrm{cm} \)


What is the electrode potential in (in \( V \) ) of the following electrode at
\( \mathbf{2 5}^{o} \boldsymbol{C}>\boldsymbol{N} \boldsymbol{i}^{2+}(\mathbf{0 . 1} \boldsymbol{M}) \mid \boldsymbol{N} \boldsymbol{i}(\boldsymbol{s}) \)
(standard reaction potential of
\( \left.N i^{2+} / N i \text { is }-0.25 V\right) \)
A . \( -0.28 v \)
B. -0.34 V
c. \( -0.82 v \)
D. -0.22V


In the thermal expansion of an ideal gas
This question has multiple correct options
\( \mathbf{A} \cdot \Delta U=0 \)
B \( . \Delta T=0 \)
C. work done by the gas is equal to the heat supplied to the gas
D. work done by the gas is equal to the change in internal energy


Then the maximum height attained by the ball is
A . \( 11.25 \mathrm{m} \)
B. 48.2 m
c. \( 23.5 \mathrm{m} \)
D. 68 m


Chemically, matter can be classified as
A. pure and impure substances
B. elements, compounds and mixtures
c. solids, liquids and gases
D. metals and non-metals


Evaluate \( \int \frac{d x}{a^{2}-x^{2}}, \) where \( a>x \)


Which one is correct for \( \boldsymbol{H}_{2} \boldsymbol{O} \) at \( \boldsymbol{2} \boldsymbol{5}^{\boldsymbol{o}} \boldsymbol{C} \)
This question has multiple correct options
\( \mathbf{A} \cdot \) Ionic product of water, \( K_{w}=10^{-14} \)
B. Equilibrium constant for dissociation of water \( K_{c}= \) \( 1.8 \times 10^{-16} \)
C. Aotoprotolysis constant of water, \( K_{A P}=3.2 \times 10^{-18} \)
D. On heating \( K_{w} \) increases with temperature


If the velocity v of a particle moving
along a straight line decreases linearly
with its displacements from \( 20 m s^{-1} \) to
a value approaching zero at \( s=30 \mathrm{m} \)
then acceleration of the particle at \( s=15 \)
\( m \) is:
A \( \cdot \frac{2}{3} m s^{-2} \)
B. \( -\frac{2}{3} m s^{-2} \)
c. \( \frac{20}{3} m s^{-2} \)
D. \( -\frac{20}{3} m s^{-2} \)


The third term of an A.P. is \( 18, \) and the
seventh term is \( 30 ; \) find the sum of 17
terms.


Find the magnetic moment vector of the
loop
A \( \cdot(0.1 \hat{i}+0.05 \hat{j}-0.05 \hat{k}) A m^{2} \)
B . \( (0.1 \hat{i}+0.05 \hat{j}+0.05 \hat{k}) A m^{2} \)
C \( \cdot(0.1 \hat{i}-0.05 \hat{j}+0.05 \hat{k}) A m^{2} \)
D. \( (0.1 \hat{i}-0.05 \hat{j}-0.05 \hat{k}) A m^{2} \)


A long straight wire along the Z-axis
carries a current \( ^{\prime} \boldsymbol{I}^{\prime} \) in the negative \( \mathbf{Z}^{-} \)
direction. The induced magnetic field \( B \)
at a point having coordinates \( (x, y) \) is:
\( ^{\mathrm{A}} \cdot_{\frac{\mu_{0} I}{2 \pi}} \frac{(x \hat{\imath}-y \hat{\jmath})}{\left(x^{2}+y^{2}\right)} \)
в. \( \frac{\mu_{0} I}{2 \pi} \frac{(x \hat{\jmath}-y \hat{\imath})}{\left(x^{2}+y^{2}\right)} \)
c. \( \frac{\mu_{0} I}{2 \pi} \frac{(x \hat{i}+y \hat{j})}{\left(x^{2}+y^{2}\right)} \)
D \( \frac{\mu_{0} I}{2 \pi} \frac{(y \hat{i}-x \hat{j})}{\left(x^{2}+y^{2}\right)} \)


The diameter of iron wheel is \( 1 \mathrm{cm} \). If its
temperature is increased by \( 700^{\circ} \mathrm{C} \)
What is the increase in circumference
of the wheel?
\( \left(\alpha=12 \times 10^{-6} /^{\circ} \mathrm{C}\right) \)
A . \( 0.0264 \mathrm{cm} \)
B. \( 0.264 \mathrm{cm} \)
c. \( 2.64 \mathrm{cm} \)
D. \( 26.4 \mathrm{cm} \)


The placenta is swollen and fleshy in
A. Solanaceae
B. Cucurbitaceae
c. compositae
D. Liliaceae


Which of the following is a basic carbonate mineral?
¡) Malachite
ii) Dolomite
iii) Azurite
iv) Magnesite
A . i, iii and iv
B. ii, iii and iv
c. i and iv
D. iii and iv


Find the median of the following data:
2,7,3,15,12,17 and 5


A value of \( x \) satisfying the equation
\( \sin \left[\cot ^{-1}(1+x)\right]=\cos \left[\tan ^{-1} x\right], \) is.
A. \( -\frac{1}{2} \)
B. \( \frac{1}{2} \)
c. -1
\( D \)


In the given figure a Plane concave lens
is placed on paper on which a flower is
drawn. How far above its actual position
does the flower appear to be?
Radius of
\( A \cdot 10 c m \)
B. \( 15 \mathrm{cm} \)
\( c \cdot 50 c m \)
D. none of these


The energy required to remove a body of mass 'm' from earths surface is/are
equal to:
\( \mathbf{A} \cdot-\mathbf{G M m} / \mathrm{R} \)
в. \( \mathrm{mgR} \)
c. -mgR
D. none of these.


The maximum value of \( \left(\frac{1}{x}\right)^{x} \) is \( e^{1 / e} \)
A. True
B. False


If the position vector \( \vec{a} \) of a point \( (12, n) \) is such that \( |\vec{a}|=13 \), find the value of
\( \mathbf{n} \)


List three characteristics properties of electric lines of forces?


Which of the following equations does not represent the kinematic equations
of motion?
\( \mathbf{A} \cdot v=u+a t \)
B. \( S=u t+\frac{1}{2} a t^{2} \)
c. \( S=a t+\frac{1}{2} a t^{2} \)
D. \( v^{2}-u^{2}=2 a S \)


If \( I=\int_{\alpha}^{\beta}\left[\log \log x+\frac{1}{(\log x)^{2}}\right] d x \)
then \( \boldsymbol{I} \)
equals
A. \( \alpha \log \log \alpha-\beta \log \log \beta \)
B. \( \frac{1}{\alpha}-\frac{1}{\beta}+\log \log \alpha-\log \log \beta \)
c. \( \frac{\beta-\alpha}{\alpha \beta}+\alpha \log \log \alpha-\beta \log \log \beta \)
D. none of these


Q Type your question
det u lu
maximum flow of 10 litres/min at the
bottom of the tank, but the output is
proportional to the water present in the tank at any given time. How will the \( v \)
volume of water content in the tank,
change with time?
\( A \)
B.
\( c \)
D.


The value of \( \int_{-\pi}^{\pi} \frac{\cos ^{2} x}{1+a^{x}} d x, a>0, \) is
A \( \cdot \frac{\pi}{2} \)
в. \( a \pi \)
c. \( 2 \pi \)
D.


Evaluate:
\( \int\left(\frac{x \cos x+\sin x}{x \sin x}\right) d x \)


Diosgenin is
A. Saccharide
B. Steroid
C. Amino acids
D. Peptide


Identify the linear molecule with lone
pairs?
B. \( \mathrm{cO}_{2} \)
\( c \cdot c_{2} H_{2} \)
\( D \cdot X e F_{2} \)


Construct a histogram for the following
data:
Monthly
\( \begin{array}{llll}\text { 30- } & \text { 60- } & \text { 90- } & \text { 120 }\end{array} \) School fee(inRs) 60
90 120
No.of
12
14
School


DNA separated from one cell,when
introduced into another cell is able to
bestow some of the properties of former to the latter.What is this change called
in technical terms? Describe the
experimental evidences which led to the
discovery of the above phenomenon.


Refer the above figure and find the
value of \( \sec n \)
A \( \cdot \sqrt{5} \)
B. \( 2 \sqrt{5} \)
c. \( \frac{\sqrt{5}}{2} \)
D. \( \frac{\sqrt{5}}{5} \)
E. \( \frac{2 \sqrt{5}}{5} \)


Two force, with equal magnitude \( F, \) at on a body and the magnitude of the resultant force is \( \frac{F}{3} . \) The angle between
the two force is
\( ^{\mathrm{A}} \cdot \cos ^{-1}\left(-\frac{17}{18}\right) \)
в. \( \cos ^{-1}\left(-\frac{1}{3}\right) \)
c. \( \cos ^{-1}\left(-\frac{2}{3}\right) \)
D. \( \cos ^{-1}\left(-\frac{8}{9}\right) \)


In the adjoining figure, \( A B \| C D \) and \( E F \)
is transversal. the value of \( x-y \) is
A \( \cdot 75^{\circ} \)
B . \( 40^{\circ} \)
\( c \cdot 35^{\circ} \)
Don


In a nuclear fusion reaction hydrogen
atoms combine to create a helium
atom. But in a hydrogen atom there are no neutrons, then where does the
neutrons in helium nucleus come from
\( ? \)


If the diagonals of a parallelogram are \( \bar{i}+5 \bar{j}-2 \bar{k} \) and \( -2 \bar{i}+\bar{j}+3 \bar{k}, \) then the
lengths of its sides are
A \( \cdot \frac{\sqrt{38}}{2}, \frac{\sqrt{50}}{2} \)
B. \( \frac{\sqrt{35}}{2}, \frac{\sqrt{45}}{2} \)
c. \( \sqrt{38}, \sqrt{50} \)
D. \( \sqrt{35}, \sqrt{45} \)


We can burn a piece of paper by focusing the sun rays by using a particular type of lens. Name the type of lens used for the above purpose.


Electric flux is \( \quad \) if the field lines
come out of the surface and is if
they go into it.
A. positive, positive
B. negative, positive
c. negative, negative
D. positive, negative


A compound \( C_{6} H_{14} O_{2} \) has two tertiary
alcoholic groups. The IUPAC name of compound is:
A. 2,3 - dimethyl - 1,2 - butanediol
B. 3,3 - dimethyl- 1,2 - butanediol
c. 2,3 - dimethyl- 2,3 - butanediol
D. 2 - methyl - 2,3 - pentanediol


The IUPAC name for the compound:
A. 3,4 -Dimethyl-2-butene- -4-ol
B. 1, 2-Dimethyl-2-butenol
c. 3-Methyl pent-3-en-2-ol
D. 2, 3-Dimethyl-3-pentenol


A square loop of uniform conducting
wire is as shown in figure.A current \( \boldsymbol{I} \) (in
ampere) enters the loop from one end
and exits the loop from opposite end as
shown in figure.

The length of one side of square loop is \( l \)
meter.The wire has uniform cross-
section area and uniform linear mass
density. The magnetic field is in Tesla and force is in newton.


Determine whether the argument used to check the validity of the following statement is correct.
\( p: \) If \( x^{2} \) is irrational, then \( x \) is rational
The statement is true because the
number \( x^{2}=\pi^{2} \) is irrational, therefore
\( x=\pi \) irrational.
A. True
B. False


Haemodialysis is carried out in case of
severe defect in
A. Kidney
B. Liver
c. Lung
D. Stomach


Two bodies of mass m and \( 4 \mathrm{m} \) are
attached with string as shown in the figure. The body of mass m hanging
from a string of length I is executing
oscillations of angular amplitude \( \boldsymbol{\theta}_{\mathbf{0}} \)
while the other body is at rest. The
minimum coefficient of friction
between the mass \( 4 \mathrm{m} \) and the
horizontal surface should be
\( \mathbf{A} \)
B \( \cdot 2 \cos ^{2}\left(\frac{\theta_{0}}{2}\right) \)
c. \( \left(\frac{1-\cos \theta_{0}}{3}\right) \)
D.


A wave has a wavelength of \( 0.01 A^{\circ} \) Name the wave:
A. \( x \) rays
B. Micro waves
c. Gamma waves
D. Radio waves


A wire has resistance of \( 12 \Omega \). It is cut
into two parts and both halve are connected in parallel. The new resistance is
A . \( 3 \Omega \)
в. \( 1.5 \Omega \)
c. \( 12 \Omega \)
D. \( 6 \Omega \)


If each edge of a cube is tripled, then find how many times will its volume become?


\( \sinh \left(\cosh ^{-1} x\right)= \)
A \( \cdot \sqrt{x^{2}+1} \)
B. \( \frac{1}{\sqrt{x^{2}+1}} \)
c. \( \sqrt{x^{2}-1} \)
D. \( \frac{1}{\sqrt{x^{2}-1}} \)


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


Two blocks of masses 5 kg and 2 kg are placed on a frictionless surface and connected by a spring. An external kick gives a velocity of \( 14 \mathrm{m} / \mathrm{s} \) to the heavier block in the direction of lighter one. The magnitudes of velocities of two blocks
in the centre of mass frame after the
kick are, respectively:
A. \( 4 \mathrm{m} / \mathrm{s}, 4 \mathrm{m} / \mathrm{s} \)
B. \( 10 \mathrm{m} / \mathrm{s}, 4 \mathrm{m} / \mathrm{s} \)
\( c \cdot 4 m / s, 10 m / s \)
D. \( 10 \mathrm{m} / \mathrm{s}, 10 \mathrm{m} / \mathrm{s} \)


Name an artificial sweetener whose use
is limited to cold drinks.


n-Butane and isobutane are a pair of:
A. chain isomers
B. position isomers
c. metamers
D. functional isomers


According to Newton, the viscous force
acting between liquid layers of area \( \boldsymbol{A} \)
and velocity gradient \( \frac{\Delta v}{\Delta z} \) is given by \( F=-\eta a \frac{d v}{d z}, \) where \( \eta \) is constant called
\( \mathbf{A} \cdot\left[M L^{-2} T^{-2}\right] \)
В \( \cdot\left[M^{0} L^{0} T^{0}\right] \)
\( \mathbf{c} \cdot\left[M L^{2} T^{-2}\right] \)
D. \( \left[M L^{-1} T^{-1}\right] \)


A particle of ass \( \mathrm{m} \) and charge \( \mathrm{Q} \) is placed in an electric field E which varies
with time \( t \) ass \( E=E_{0} \) sin \( \omega t . \) It will undergo simple harmonic motion of amplitude
A \( \cdot \frac{Q E_{0}^{2}}{m \omega^{2}} \)
в. \( \frac{Q E_{0}}{m \omega^{2}} \)
c. \( \sqrt{\frac{Q E_{0}}{m \omega_{2}}} \)
D. \( \frac{Q E_{0}}{m \omega} \)


Name and draw the cell that is without
membrane bound nucleus.


What is the S.I. unit of density?
A \( \cdot \) Kg \( m^{-3} \)
в. Ку \( m^{3} \)
c. \( K g m^{-2} \)
D. \( K g m^{2} \)


Three forces \( \vec{P}, \vec{Q} \) and \( \vec{R} \) acting along \( I A \)
IB and IC, where I is the incentre of a
\( \Delta \mathrm{ABC}, \) are in equilibrium. Then \( \overrightarrow{\mathbf{P}}: \overrightarrow{\mathbf{Q}}: \)
\( \overrightarrow{\mathbf{R}} \) is:
\( ^{A} \cdot \cos \frac{A}{2}: \cos \frac{B}{2}: \cos \frac{C}{2} \)
B \( \cdot \sin \frac{\mathrm{A}}{2}: \sin \frac{\mathrm{B}}{2}: \sin \frac{\mathrm{C}}{2} \)
c. \( \sec \frac{\mathrm{A}}{2}: \sec \frac{\mathrm{B}}{2}: \sec \frac{\mathrm{C}}{2} \)
D \( \operatorname{cosec} \frac{\mathrm{A}}{2}: \operatorname{cosec} \frac{\mathrm{B}}{2}: \operatorname{cosec} \frac{\mathrm{C}}{2} \)


What is a Thermostat?


A pressure of \( 100 k P a \) causes a decrease in volume of water by
\( 5 \times 10^{-3} \) percent. The speed of sound in water is
A \( \cdot \) १४१४ \( m s^{-1} \)
B. \( 1000 \mathrm{ms}^{-1} \)
c. \( 2000 \mathrm{ms}^{-1} \)
D. 3000 \( m s^{-1} \)


More than \( 70 \% \) of world's freshwater is
contained in
A. Antarctica
B. Glaciers and mountains
c. Greenland
D. Polarice


If \( A \) and \( B \) are two event such that, \( P(A)=\frac{6}{11}, P(B)=\frac{5}{11} \) and \( P(A \cup \)
\( B)=\frac{7}{11}, \) find \( P(A r \)
\( \boldsymbol{B}), \boldsymbol{P}(\boldsymbol{A} / \boldsymbol{B}), \boldsymbol{P}(\boldsymbol{B} / \boldsymbol{A}) \)


Consider a two-input AND gate of figure
below. Out of the four entries for the
Truth Table given here, the correct ones
are
\( -1-1 \) \begin{tabular}{|c|c|c|c|}
\hline \multirow{2}{*} {1} & A & B & C \\
\cline { 2 - 5 } & 0 & 1 & 0 \\
\cline { 2 - 4 } & 1 & 0 & 0 \\
\cline { 2 - 4 } 3 & 1 & 1 & 1 \\
\hline \multirow{2}{*} {4} & 0 & 0 & 1 \\
\hline
\end{tabular}
\( \mathbf{A} \cdot \) Al
B. 1 and 2 only
C. 1,2 and 3 only
D. 1,3 and 4 only


Which of following is unary operation?
A. Addition
B. Multiplication
c. Square root
D. None of these


\( \boldsymbol{A}-[\boldsymbol{B} \cup \boldsymbol{C} \cup \boldsymbol{D}]=(\boldsymbol{A}-\boldsymbol{B}) \cap \ldots \ldots \cap \)
A \( . A-C \) and \( A-D \)
B. \( C-A \) and \( A-D \)
c. \( C-A \) and \( D-A \)
D. \( A-C \) and \( D-A \)


Two radio frequency point sources
\( S_{1} \) and \( S_{2} \), separated by distance \( 2.5 \mathrm{m} \)
are emitting in phase waves of wavelength \( 1 \mathrm{m} . \) A detector moves in a large circular path around the two sources in a plane containing them. The number of maxima that will be detected
by it over the complete circular path,
are
A . 16
B. 12
\( c \cdot 10 \)
D. 8


A force \( \overrightarrow{\boldsymbol{F}}=\boldsymbol{\alpha} \hat{\boldsymbol{i}}+\boldsymbol{3} \hat{\boldsymbol{j}}+\boldsymbol{6} \hat{\boldsymbol{k}} \) is acting at \( \mathbf{a} \)
point \( \vec{r}=2 \hat{i}-6 \hat{j}-12 \hat{k} . \) The value of \( \alpha \) for which angular momentum about origine is conserved is
\( \mathbf{A} \cdot \mathbf{1} \)
B. -
\( c \cdot 2 \)
D. zero


When \( 100 \mathrm{ml} \) of \( O_{2}-O_{3} \) mixture was
passed through turpentine oil, there was reduction of volume by \( 20 \mathrm{ml} \). If 100
\( \mathrm{ml} \) of such a mixture is heated, what will be the increase in the volume (ml)? (Write the answer in the form of
volume/2)


(a) Draw the structures of the following
molecules:
(i) \( \boldsymbol{X} \boldsymbol{e} \boldsymbol{O} \boldsymbol{F}_{\boldsymbol{4}} \)
(ii) \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \)
(b) Write the structural difference
between white phosphorus and red
phosphorus.


Define magnetic 'declination' and 'dip'
at a place


Find the area of the shaded region


If \( g \) on the surface of the Earth is 9.8
\( m s^{-2}, \) then it's value at a depth of 3200
\( k m \) (Radius of the earth \( =6400 \mathrm{km} \) ) is
\( \mathbf{A} \cdot 9.8 m s^{-2} \)
в. zero
C \( .4 .9 \mathrm{ms}^{-2} \)
D. \( 2.45 \mathrm{ms}^{-2} \)


Which of the following have peroxy
linkages?
This question has multiple correct options
A. \( H_{2} T i O_{4} \)
в. \( O s O_{4} \)
c. \( K_{2} C r_{2} O_{7} \)
D. \( C r O_{5} \)


Very short answer type.
Where is the hormone vasopressin
(ADH) synthesized?


When the load applied to a suspended wire is increased from 3 kg-wt to 5 kgwt; the elongation increases from 0.6 \( \mathrm{mm} \) to \( 1 \mathrm{mm} . \) How much work is done
during the extention of the wire.


Drinking water may contain dissolved calcium hydrogen-carbonate,
\( \boldsymbol{C} \boldsymbol{a}\left(\boldsymbol{H} \boldsymbol{C} \boldsymbol{O}_{3}\right)_{2} . \) How many electrons are
present in a hydrogen-carbonate anion?
A . 30
B. 31
c. 32
D. 33


The equivalent capacitance between
points a and b in given arrangement of plates will be:(each plate has the area
'A' \( \& \) separation between two adjacent plates is 'd')
A \( \cdot \frac{2}{3} \frac{\varepsilon_{o} A}{d} \)
B \( \cdot \frac{3}{2} \frac{\varepsilon_{o} A}{d} \)
c. \( \frac{2 \varepsilon_{o} A}{d} \)
D. \( \frac{\varepsilon_{o} A}{3 d} \)


If a substance gains oxygen during a reaction, it is being oxidized. If it loses oxygen, it is being reduced. Oxidation and Reduction always take place together, so that if one substance is oxidized, another is reduced. Using this idea, say which substance is oxidised and which substance is reduced in each
reaction
¡) \( M g+O_{2} \rightarrow 2 M g O \)
\( (s) \)
\( (s) \)
ii) \( Z n O+C \rightarrow Z n+C O \)
iii) \( F e_{2} O_{3}+3 C O \rightarrow 2 F e+3 C O_{2} \)
iv) \( C r_{2} O_{3}+2 A l \rightarrow 2 C r+A l_{2} O_{3} \)


In a circle with centre \( O \) chord \( A B= \)
chord \( A C . \) Chord \( A D \) cuts \( B C \) in \( E . \) If
\( \overline{A C}=12 \) and \( \overline{A E}=8, \) then \( \overline{A D} \) equals:
A .27
B . 24
c. 21
D. 18


Five conducting parallel plates having
area \( A \) and separation between them \( d \)
are placed as shown in the figure. Plate number 2 and 4 are connected with wire
and between \( A \) and \( B, \) a cell of emf \( E \) is
connected. Find the charge flown
through the cell.


Above structure is of an auxin, that is
A . IAA
B. Auxin b
c. Auxin a
D. None of the above


Write a note on coagulation of blood.


Van't Hoff factor of \( 0.01 M B a C l_{2} \) is
1.98, percentage dissociation of \( B a C l_{2} \)
on this concentration will be:
\( \mathbf{A} \cdot 69 \)
в. 100
c. 49
D. 98


If the system of equations \( 3 x-2 y+ \)
\( z=0, \lambda x-14 y+15 z=0, x+2 y- \)
\( \mathbf{3} z=\mathbf{0} \) have non zero solution, then find
\( \lambda \)


Solve the differential equation \( \left[\frac{e^{-2 \sqrt{x}}}{\sqrt{x}}-\frac{y}{\sqrt{x}}\right] \frac{d x}{d y}=1 \quad \dots(x \neq 0) \)


The element in the second row and third
column of the matrix \( \left[\begin{array}{ccc}\mathbf{4} & \mathbf{5} & \mathbf{- 6} \\ \mathbf{3} & \mathbf{- 4} & \mathbf{3} \\ \mathbf{2} & \mathbf{1} & \mathbf{0}\end{array}\right] \) is
\( A \cdot 3 \)
B.
\( c \cdot 2 \)
D. -


Two elements \( X \) and \( Y \) contain only one
electron in the outer level. Element \( X \) is
reactive and loses electron easily while element \( Y \) is relatively unreactive and
non-corrosive. The elements \( \boldsymbol{X} \) and \( \boldsymbol{Y} \)
respectively are:
\( \mathbf{A} \cdot C s \) and \( L i \)
B. \( R b \) and \( N a \)
c. \( L i \) and \( C u \)
D. \( A g \) and \( A u \)


Four angles of a polygon are \( 120^{\circ} \) each
and the remaining angles are all equal
to \( 160^{\circ} \) each. Find the number of sides


The \( H F_{2}^{-} \) ion exists in the solid state and also in liquid HF solution, but not in dilute aqueous solution.
If true enter 1 , else enter 0
\( A \cdot 1 \)


A bullet of mass \( 10 g \) leaves a rifle at an
initial velocity of \( 1000 m / s \) and strikes the earth at the same level with a
velocity of \( 500 m / s \). the work done in
joules overcoming the resistance of air will be
A. 375
в. 3750
c. 500
D. 5000


The focal length of a convex lens is \( 25 \mathrm{cm} . \) Find its power with sign.
\( A \cdot+4 D \)
в. \( -4 D \)
\( c .+2.5 D \)
D. \( -2.5 D \)


A parabola has \( x \) - axis as its axis, \( y \) axis as its directrix and \( 4 a \) as its latus
rectum. If the focus lies to the left side
of the directrix then the equation of the parabola is
\( \mathbf{A} \cdot y^{2}=4 a(x+a) \)
B \( \cdot y^{2}=4 a(x-a) \)
C \( \cdot y^{2}=-4 a(x+a) \)
D \( \cdot y^{2}=4 a(x-2 a) \)


Amino acids can be identified by using
the staining agent:
A. ninhydrin
B. sulphuric acid
c. ethydium bromide
D. coomassie brilliant blue


The principle value of \( \cos ^{-1}\left(\frac{-1}{2}\right) \) is
A \( \cdot \frac{-\pi}{3} \)
в. \( \frac{2 \pi}{3} \)
c. \( \frac{4 \pi}{3} \)
D.


Check whether \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) be a function defined by \( f(x)=\frac{x^{2}+2 x+5}{x^{2}+x+1} \) is one
one or not.


Which of the following is not a physical change?
A. Dissolution of sugar or salt in water
B. Powdering of sugar
c. Mixing of iron particles and sand
D. Burning of paper


Which is correct about the reaction
between \( H_{2} O \) and \( O_{2} ? \)
\( \mathbf{A} \cdot \) It is a case of mutual reduction
B. \( O_{3} \) will oxidize \( H_{2} O_{2} \) into \( O_{2} \)
C. It is not a redox reaction
D. \( H_{2} O_{2} \) being a stronger oxidizing agent will decompose ozone into oxygen


Which is the following are true about
the chemical equilibrium?
A. The chemical equilibrium is a state in which the rate of the forward reaction is equal to the rate of the reverse reaction.
B. The chemical equilibrium takes at least 10 hours to be established.
C. The chemical equilibrium is a state in which the rate of the forward reaction is not equal to the rate of the reverse reaction.
D. The chemical equilibrium can only occur at temperatures above room temperature.
E. None of these answers are correct


Find the minimum value the function
\( f(x)=\frac{\pi^{2}}{16 \cot ^{-1}(-x)}-\cot ^{-1} x \)
\( ^{A} \cdot-\frac{\pi}{4} \)
B. \( -\frac{\pi}{2} \)
c.
D.


Ohm's law is used to determine
resistance of a conductor.
A. True
B. False


If the sides \( a, b, c \) of \( \triangle A B C \) are in \( A . P . \)
prove that \( a \cos ^{2} \frac{C}{2}+c \cos ^{2} \frac{A}{2}=\frac{3 b}{2} \)


In a series of observations, \( \mathrm{S.D.}=7 \) and
mean is 28 , the coefficient of variation
is
A .4
B . \( 1 / 4 \)
c. 25
D. 12.5


Average life span of RBCs is days.


Pulmonary vein carries
A. Deoxygenated bloodd
B. Oxygenated blood
c. Mixed blood
D. None of the above


If \( f o g=|\sin x| \) and \( g o f=\sin ^{2} \sqrt{x}, \) then
\( f(x) \) and \( g(x) \) are
A \( \cdot f(x)=\sqrt{\sin x}, g(x)=x^{2} \)
B. \( f(x)=|x|, g(x)=\sin x \)
c. \( f(x)=\sqrt{x}, g(x)=\sin ^{2} x \)
D. \( f(x)=\sin \sqrt{x}, g(x)=x^{2} \)


Based on the following thermochemical equations
\( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{C}(s) \longrightarrow \boldsymbol{C} \boldsymbol{O}(\boldsymbol{g})+\boldsymbol{H}_{2}(\boldsymbol{g}) \)
\( \Delta \boldsymbol{H}=\mathbf{1 3 3} \boldsymbol{k} \boldsymbol{J} \boldsymbol{m o l}^{-1} \)
\( \boldsymbol{C O}(\boldsymbol{g})+\frac{1}{2} \boldsymbol{O}_{2}(\boldsymbol{g}) \longrightarrow \boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g}) ; \boldsymbol{\Delta} \boldsymbol{H}= \)
\( -282 k J m o l^{-1} \)
\( \boldsymbol{H}_{2}(\boldsymbol{g})+\frac{\mathbf{1}}{\mathbf{2}} \boldsymbol{O}_{2}(\boldsymbol{g}) \longrightarrow \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) ; \boldsymbol{\Delta} \boldsymbol{H}= \)
\( -242 k J m o l^{-1} \)
\( \boldsymbol{C}(s)+\boldsymbol{O}_{2}(\boldsymbol{g}) \longrightarrow \boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g}) ; \boldsymbol{\Delta} \boldsymbol{H}= \)
\( \boldsymbol{x} \boldsymbol{k} \boldsymbol{J} \boldsymbol{m} \boldsymbol{o l}^{-1} \)
The value of \( x \) will be:
A. \( 393.0 \mathrm{KJ} \)
в. \( 655.0 \mathrm{KJ} \)
D. \( -655.0 K J \)


of the rod is \( M \) ad mass of bead is \( m \)
and \( M>m . \) The bead slides with some
friction. The mass of the pulley and friction in its axle are negligible. At the
initial moment the bead was located
opposite the lower end. If set free both the bodies move with constant
accelerations. The frictional force
between the bead and the thread so that
\( t \) second after release ball reaches the
upper end of the rod is given as \( \boldsymbol{F}_{\boldsymbol{f}}= \) \( \frac{\boldsymbol{x} \boldsymbol{m} \boldsymbol{M} \boldsymbol{l}}{(\boldsymbol{M}-\boldsymbol{m}) \boldsymbol{t}^{2}} . \) Find \( \boldsymbol{x}, \) Length of the rod is
\( l \)


Define peptization.


The characteristic type of placentation found in the members of
Caryophyllaceae is
A. Parietal
B. Marginal
c. Basal
D. Axile
E. Free central


An ellipse passing through the point \( (2 \sqrt{13}, 4) \) has its foci at (-4,1) and \( (4,1), \) then its eccentricity is
A \( \cdot \frac{2}{3} \)
B. \( \frac{1}{3} \)
\( c \cdot \frac{1}{4} \)
D.


Water acts as Bronsted acid as well as a
Bronsted base. Give one example each to illustrate this statement.


The bond formed between an enzyme
and an inhibitor:
A. can be broken easily
B. cannot be broken easily
c. is a weak bond
D. none of the above


The driver of a train \( A \) running at
\( 25 m s^{-1} \) sights a train \( B \) on the same
track with \( 15 m s^{-1} . \) The driver of train \( A \)
applies brakes to produce a
deceleration of \( 1.0 m s^{-2} . \) If the trains
are \( 200 m \) apart, will the trains collide?
A . yes
B. no
c. collision just avoided
D. none of these


For the reaction: \( C a C O_{3}(s) \rightleftharpoons \operatorname{CaO}(s)+ \)
\( C O_{2}(g) . K_{p}=1 \) atm at \( 927^{0} \mathrm{C} . \) If \( 20 \mathrm{g} \) of
\( \mathrm{CaCO}_{3} \) were kept in a 10 liter vessel at
\( 927^{0} \mathrm{C}, \) then calculate percentage of
\( C a C O_{3} \) remaining at equilibrium:


The standard potential of the reaction:
\( H_{2} O+e^{-} \rightarrow \frac{1}{2} H_{2}+O H^{-} \) at \( 298 \mathrm{K} \) by
using \( \boldsymbol{K}_{\boldsymbol{w}}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)=\mathbf{1 0}^{-14} \)
\( A .-0.828 V \)
в. 0.828 v
c. \( 2.0 v \)
D. -0.5


The speed of an electron having a
wavelength of \( 10^{-10} m \) is :
A \( \cdot 4.24 \times 10^{6} m / s \)
B . \( 5.25 \times 10^{6} \mathrm{m} / \mathrm{s} \)
c. \( 6.25 \times 10^{6} m / s \)
D. \( 7.25 \times 10^{6} \mathrm{m} / \mathrm{s} \)


During a natural radioactive decay:
This question has multiple correct options
A. mass number can increase only
B. atomic number can increase or decrease
C \( . p / n \) can increase or decrease
D. number of protons can increase or decrease


Two short magnets of magnetic moment \( 1000 A m^{2} \) are placed as
shown at the corners of a square of side
10 \( c m . \) The net magnetic induction at \( P \)
is
A \( .0 .1 T \)
B. \( 0.2 T \)
c. \( 0.3 T \)
D. \( 0.4 T \)


In a game called 'odd man out', \( m(m> \)
2) persons toss a coin to determine who
will buy refreshment for the entire
group. A person who gets an outcome
different from that of the rest of the
members of the group is called the odd man out. The probability that there is a
loser in any game is
A. \( 1 / 2 m \)
в. \( m / 2^{m-1} \)
c. \( 2 / m \)
D. none of these


or using fungus to metabolize contaminants and accumulate heavy
metals.
A. Bioremediation
B. Phytoremediation
c. Both A and B
D. Mycoremediation


A bullet of mass \( m \) moving with a horizontal velocity \( v \) strikes a stationary
block of mass \( M \) suspended by a string
of length \( L \). The bullet gets embedded in the block. What is the maximum angle made by the string after impact?
A \( \cdot \theta=\cos ^{-1}\left(\frac{M}{m}\right) \)
в. \( \theta=\cos ^{-1}\left(\frac{m}{M}\right) \)
c. \( _{\theta}=\cos ^{-1}\left(\frac{m V}{M+m}\right) \)
" \( \quad \theta=\cos ^{-1}\left(1-\frac{1}{2 g L}\left(\frac{m v}{m+M}\right)^{2}\right) \)


The 8: 8 type of packing is present
in \( _{\text {十一一一一一一一一一一 }}\left(M g F_{2}, C s C l\right) \)


Find the equation of straight lines passing through (1,1) and which are at a distance of 3 units from (-2,3)


In the given reaction, the product \( (B) \) is
\( \boldsymbol{C H}_{3} \boldsymbol{C H O} \frac{(i) N a C N / \boldsymbol{H} C l}{(i i) \boldsymbol{H}_{2} \boldsymbol{O} / \boldsymbol{H} \oplus / \boldsymbol{\Delta}}(\boldsymbol{A}) \frac{\boldsymbol{F e n t o n}}{\text {reagent}} \)
\( (B) \)
A . acetic acid
B. oxalic acid
c. pyruvic acid
D. citric acid


Conc. \( H N O_{3} \) can be stored in container
of :
A . \( A l \)
в. \( S n \)
c. \( C u \)
D. \( Z n \)
E. Answer required


f \( \boldsymbol{y}=\mathbf{1}+\boldsymbol{x} \cdot \boldsymbol{e}^{\boldsymbol{y}}, \) show that \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\frac{\boldsymbol{e}^{\boldsymbol{y}}}{\boldsymbol{2}-\boldsymbol{y}} \)


The estrous cycle occurs in
A. Mouse
B. Gorilla
c. Chimpanzee
D. Monkey


Obtain pair of linear equations in two variables: In a cricket match, rohit makes his score twice Dhawan's scored
Both of them together make a total score 150 runs.


Sulphuric acid reacts with \( P C l_{5} \) to give:
A. Thionyl chloride
B. Sulphur monochloride
c. sulphur chloride
D. Sulphur ultrachloride


The mobility of free electrons is greater
than that of free holes because
A. they carry negative charge
B. they are light
C. their mutual collisions are less
D. they require low energy to continue their motion


Two chemical reactions are given:
i. Sulphur dioxide combines with oxygen to form sulphur trioxide.
ii. Sodium reacts with water
(a) Write the balanced chemical
equation for any one of the above reactions.
(b) Which of the above reactions is a
reversible reaction?
(c) What is the effect of pressure and temperature on this reversible reaction? Give reason


A metal wire of resistance \( 3 \Omega \) is
elongated to make a uniform wire of
double its previous length. This new wire is now bent and the ends joined to make a circle. If two points on this circle
make an angle \( 60^{\circ} \) at the centre, the equivalent resistance between these
two points will be?
A \( \cdot \frac{12}{5} \Omega \)
в. \( \frac{5}{3} \Omega \)
c. \( \frac{5}{2} \Omega \)
D. \( \frac{7}{2} \Omega \)


The capacitance in an oscillatory LC circuit is increased by \( 1 \% \). The change in inductance required to restore its frequency of oscillation is to
A. decrease it by 0.5\%
B. increase it by 1\%
c. decrease it by 1\%
D. decrease it by \( 2 \% \)


A metal \( X \) on heating in nitrogen gas gives a compound \( Y . \) Compound \( Y \)
on treatment with \( H_{2} O \) gives a colourless gas which when passed
through \( C u S O_{4} \) solution gives a blue colour. Then, compound \( Y \) is:
A \( . M g\left(N O_{3}\right)_{2} \)
в. \( M g_{3} N_{2} \)
c. \( N H_{3} \)
D. \( M g O \)


Mohr salt, \( \boldsymbol{F} \boldsymbol{e} \boldsymbol{S} \boldsymbol{O}_{4} \cdot\left(\boldsymbol{N} \boldsymbol{H}_{4}\right)_{2} \cdot \boldsymbol{S} \boldsymbol{O}_{4} \)
\( 6 H_{2} O, \) is preferred over \( F e S O_{4} \cdot 7 H_{2} O \)
for standardization of \( K M n O_{4} \) solution
because:
A. Mohr's salt is a double salt wile ferrous sulphate
B. Mohr's salt is not hygroscopic but \( F e S O_{4} \cdot 7 \mathrm{H}_{2} \mathrm{O} \) is hygroscopic.
c. Moh'sr salt contains only ferrous ions whereas ferrous sulphate contains some ferric ions
D. Mohr's salt solution can be titrated even in the absence of \( H_{2} S O_{4} \)


A straight conductor carrying a current is split into identical semicircular
turns of radius \( r \) as shown in the figure.
The magnetic induction at the center \( C \)
of the circular loop is:
A \( \cdot \frac{\mu_{0}}{4 r_{n}} \)
в. \( \frac{\mu_{0} i}{8 r} \)
c. \( \frac{\mu_{0}}{2 r} \)
D. zero


A translucent white waxy solid \( (A) \) on
heating in an inert atmosphere is
converted to its allotropic form \( (\boldsymbol{B}) \)
Allotrope \( (A) \) on reaction with very
dilute aqueous \( K O H \) liberates a highly poisonous gas \( (C) \) having rotten fish smell. With excess of chlorine it forms
\( (D) \) which hydrolyses to compound \( (E) \) Identify compounds
\( (A) \) to \( (E) \)


On the set \( Z \), of all integers \( * \) is defined by \( a * b=a+b-5 . \) If \( 2 *(x * 3)=5 \)
then \( \boldsymbol{x}= \)
\( \mathbf{A} \cdot \mathbf{0} \)
B. 3
\( c .5 \)
D. 10


The rational number lying between the numbers \( \frac{1}{3} \) and \( \frac{3}{4} \) are
A. \( \frac{97}{300}, \frac{299}{500} \)
в. \( \frac{99}{300}, \frac{301}{400} \)
c. \( \frac{95}{300}, \frac{301}{400} \)
D. \( \frac{117}{300}, \frac{287}{400} \)


In the expansion of \( (\sqrt{2}+\sqrt[3]{5})^{20} \) the
number of rational terms will be:
\( A \cdot 3 \)
B. 10
\( c \cdot 4 \)
D.


Which is not the unit of Force?
A. Pound
B. Dyne
c. Joule
D. Newton


In a box containing 15 bulbs, 5 are
defective. If 5 bulbs are selected at
random from the box, find the probability of the event, that None of them is defective


Two identical galvanometers are joined by connecting wires. One of them is placed on the table and the other is held in the hand. One in the hand is shaken
violently so that it shows a deflection of 10 division. The reading in the other
galvanometer (on the table) is
A . zero
B. 10 division
c. 5 division
D. insufficient data to reply


Study the following lists:
List-I
(A) Anucleate
(1) Spirogyra gamciangium
(B) Uninucleate
(2) Rhizopus chlamydospore
(C) Multinucleate
(3) Pteris
neck canal cell
(D) Binucleate
(4) Vitis
matured sieve element
(5) Akinite of
Spirogyra
\( A \cdot A-(1 V), B-(1), C-(11), D-(1) \)
B. A-(I), B-(III), C-(II),D-(IV)
\( c \cdot A-(1 V), B-(1), C-(11), D-(11) \)
D. A-(1), B-(IV), C-(V), D-(II)


The areas of two similar triangles are \( 100 \mathrm{cm}^{2} \) and \( 64 \mathrm{cm}^{2} \). If the median of
greater side of first triangle is \( 13 \mathrm{cm} \) find the corresponding median of the other triangle.
A . \( 20 \mathrm{cm} \)
B. \( 15 \mathrm{cm} \)
c. \( 10 \mathrm{cm} \)
D. \( 16 \mathrm{cm} \)


The hybridization of the central atoms of compounds \( A, B, C \) and \( D \) are
\( s p^{3} d, s p^{3}, s p^{2} \) and \( s p \) respectively. If the
compounds \( A \) and \( D \) have the same
shape like \( I_{3}^{-} \) and the compounds \( B \) and \( C \) have the same shape like water
molecule,
then the value of \( \boldsymbol{P}+\boldsymbol{Q}+\boldsymbol{R}+\boldsymbol{S} \) is:
(Given that \( P, Q, R \) and \( S \) are the
number of lone pairs of electrons on
central atoms of compounds \( \boldsymbol{A}, \boldsymbol{B}, \boldsymbol{C} \) and \( D \) respectively.


What is the force acting on the
connecting bar?
A . \( 150 \mathrm{N} \)
B. 100 N
\( c .75 \mathrm{N} \)
D. 125 N


Check the commutative property of multiplication for \( \frac{-\mathbf{7}}{\mathbf{1 3}}, \frac{\mathbf{2 5}}{\mathbf{2 7}} \)


Explain following terms.
(i) Hydrogen economy
(ii) Hydrogenation
(iii) Syngas
(iv) Water-gas shift reaction
(v) Fuel-cell


What is the effect of HCL on following?
(a) Mg ribbon
(b) \( \mathrm{NaOH} \)
(c) crushed eggshell


Find the value \( c \) in mean value theorem
for the function \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}+\frac{\mathbf{1}}{\boldsymbol{x}}, \boldsymbol{x} \boldsymbol{\epsilon}[\mathbf{1}, \boldsymbol{3}] \)


Which one of the following pairs of atomic numbers represents elements belonging to the same group?
A. 11 and 20
B. 13 and 30
c. 13 and 31
D. 14 and 31


How many electrons can fit in the orbital for which \( n=3 \) and \( l=1 ? \)
A . 10
B. 14
\( c \cdot 2 \)
D. 6


In a cyclotron, magnetic field of \( 1.4 W b / m^{2} \) is used. To accelerate
protons, how rapidly should the electric field between the Dees he reversed?
\( \left(\boldsymbol{\pi}=\mathbf{3 . 1 4 2}, \boldsymbol{M} \boldsymbol{p}=\mathbf{1 . 6 7} \times \mathbf{1 0}^{-\mathbf{2 7}} \mathbf{k g}, \boldsymbol{e}=\right. \)
\( \left.\mathbf{1 . 6} \times \mathbf{1 0}^{-\mathbf{1 9}} \mathbf{C}\right) \)


A moon of Saturn has a nearly circular orbit of radius \( R \) and an orbit period of \( T \). Which of the following expressions gives the mass of Saturn?
\( ^{A} \cdot \frac{2 \pi R}{T} \)
в. \( \frac{4 \pi^{2} R}{T} \)
\( ^{\mathbf{c}} \cdot \frac{2 \pi R^{3}}{\left(G T^{2}\right)} \)
D. \( \frac{4 \pi^{2} R^{2}}{\left(G T^{2}\right)} \)
E \( \cdot \frac{4 \pi^{2} R^{3}}{\left(G T^{2}\right)} \)


\( P \) is a point in the interior of a
parallelogram \( A B C D . \) Show that
\( \boldsymbol{a r}(\triangle \boldsymbol{A P D})+\boldsymbol{a r}(\triangle \boldsymbol{P B C})= \)
\( \boldsymbol{a r}(\triangle \boldsymbol{A} \boldsymbol{P B})+\boldsymbol{a r}(\triangle \boldsymbol{P} \boldsymbol{D}) \)


On which of the following continent, maximum fossils of prehistoric man have been found?
A . Africa
B. Europe
c. Asia
D. America


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


of elements combine
in the ratio of whole numbers to
produce a large number of a compound
called molecules.
\( A \). Atom
B. Ion
c. charges
D. None of the above


A quantity of heat 'Q' is supplied to a mono-atomic ideal gas which expands at constant pressure. The fraction of heat that goes into work done by the gas is:
A \( \cdot \frac{2}{5} \)
B. \( \frac{3}{5} \)
\( c \cdot \frac{2}{3} \)
D.


A ball is thrown at angle \( \theta \) and another
ball is thrown at an angle \( (90-\theta) \) with
the horizontal direction from the same
point with the same speed \( 40 m s^{-1} \). The
second ball reaches \( 50 m \) higher than the first ball. Find their individual
heights.
A. \( 20 m, 70 m \)
B . \( 25 m, 75 m \)
\( \mathbf{c} \cdot 15 m, 65 m \)
D. \( 10 m, 60 m \)


What is the torque of the force \( \overrightarrow{\boldsymbol{F}}= \) \( (2 \hat{i}-3 \hat{j}+4 \hat{k}) N, \) acting at the point \( \vec{r}=(3 \hat{i}+2 \hat{j}+3 \hat{k}) m \) about the origin
\( (\operatorname{in} N-m) \)
A . \( 6 \hat{i}-6 \hat{j}+12 \hat{k} \)
B . \( 17 \hat{i}-6 \hat{j}-13 \hat{k} \)
c. \( -6 \hat{i}+6 \hat{j}-12 \hat{k} \)
D. \( -17 \hat{i}+6 \hat{j}-13 \hat{k} \)


The density of \( N H_{3} \) at \( 30^{\circ} C \) and 5 atm
pressure is:
A \( \cdot 3.417 \mathrm{mg} \mathrm{L}^{-1} \)
в. \( 3.417 g^{-1} L \)
c. \( 3.417 g L^{-1} \)
D. 3.417 kg L \( ^{-1} \)


Kirchhoff's law of meshes is in
accordance with law of conservation of:
A. charge
B. current
c. energy
D. angular momentum


Which of the following statement is/are
not true?
A. Cyclic menstruation is an indication of normal reproductive phase
B. Progesterone is essential for maintenance of the fertilized ovum
C. High titre of progesterone is essential for implantation.
D. Release of LH is highest at the time of ovulation and is maintained throughout the luteal phase.


Oxyhaemoglobin dissociates into oxygen and deoxyhaemoglobin at
A \( \cdot \) low \( O_{2} \) pressure in tissue
B. high \( O_{2} \) pressure in tissue
c. equal \( O_{2} \) pressure inside and outside tissue
D. all times irrespective of \( O_{2} \) pressure


In a parallel L-C-R circuit spring constant \( K \) is analogous to:
A .
B.
\( c \cdot 1 / L \)
D. \( 1 / c \)


\( \sin ^{-1} \frac{2 a}{1+a^{2}}+\cos ^{-1} \frac{1-b^{2}}{1+b^{2}}= \)
\( 2 \tan ^{-1} x \)


The Lanthanoid contraction refers to
decrease in the:
A. valence electrons of the Lanthanide series
B. ionic radius of the series
c. the density of the series
D. nuclear mass of the series


A merchant buys \( 1260 \mathrm{kg} \) of corn \( \frac{1}{4} \) of which he sells at a gain of \( 5 \%, \frac{1}{3} \) at a gain of \( \% \) and the remainder at a gain of \( 12 \% \). If he had sold the whole at a gain
of \( 10 \% \) he would have gained \( \operatorname{Rs} 27.30 \)
more. Find the cost price per \( \mathbf{k g} \)
A . Rs 5
B. Rs 2
c. Rs 3
D. Rs 2.50


Standard free energies of formation (in kJ/mol) at \( 298 \mathrm{K} \) are -237.2,-394.4 and
-8.2 for \( \boldsymbol{H}_{2} \boldsymbol{O}(l), \boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g}) \) and pentane \( (g) \)
respectively The value of \( E_{c e l l}^{0} \) for the pentane-oxygen fuel cell is:
A \( .1 .0968 \mathrm{V} \)
в. \( 0.0968 V \)
c. \( 1.968 V \)
D. \( 2.0968 V \)


If \( \boldsymbol{A}=\left[\begin{array}{cc}-\mathbf{4} & -\mathbf{1} \\ \mathbf{3} & \mathbf{1}\end{array}\right], \) then the determinant
of the matrix \( \left(A^{2016}-2 A^{2015}-A^{2014}\right) \)
is:
A. -175
в. 2014
\( c .2016 \)
D. -25


Chloroplast and other specialized plastids are present in animal cells?
A. True
B. False


Velamen is a tissue found in
A. Parasites
B. All epiphytes
c. Aerial roots of some orchids/ vanda
D. Halophytes


\( \int \frac{1}{\sqrt{\sin ^{3} x \sin (x+a)}} d x \) is equal to
A \( \cdot 2 \cos e c \alpha \sqrt{\cos \alpha+\sin \alpha \tan x}+c \)
B. \( -2 \cos e c \alpha \sqrt{\cos \alpha+\sin \alpha \cot x}+c \)
\( \mathbf{c} \cdot \cos e c \alpha \sqrt{\cos \alpha+\sin \alpha \tan x}+c \)
D. \( -\cos e c \alpha \sqrt{\cos \alpha+\sin \alpha \tan x}+c \)


Verify the property \( \boldsymbol{a} \times(\boldsymbol{b}+\boldsymbol{c})=(\boldsymbol{a} \times \)
\( b)+(a \times c) \) When \( a=\frac{1}{2}, b= \)
\( \frac{3}{7} \quad \& \quad c=\frac{5}{14} \)


The Hooke's law defines
A. modulus of elasticity
B. stress
C. strain
D. elastic limit


Neptunium is radioactive and emits a beta particle and gives:
A. plutonium
B. uranium
c. californium
D. curium


In YDSE, find the missing wavelength at \( \boldsymbol{y}=\boldsymbol{d}, \) where symbols have their usual meaning (take \( D>>d \) ).
\( ^{\mathrm{A}} \cdot \frac{d^{2}}{D} \)
B. \( \frac{2 d^{2}}{7 D} \)
c. \( \frac{3 d^{2}}{D} \)
D. \( \frac{d^{2}}{3 D} \)


What is the recoil velocity of the gun of mass \( 8 \mathrm{kg} \) when a bullet of mass \( 10 \mathrm{g} \) is fired from it with a velocity of \( 400 \mathrm{m} / \mathrm{s} ? \)
\( \mathbf{A} \cdot 5 \mathrm{m} / \mathrm{s} \)
B. \( 2 \mathrm{m} / \mathrm{s} \)
c. \( 50 \mathrm{m} / \mathrm{s} \)
D. \( 0.5 \mathrm{m} / \mathrm{s} \)


Why is cardiac muscles controlled
involuntarily?
A. To pump blood through the heart
B. To reduce the flow of blood
c. For the function of lungs
D. All of the above


If the door of a refrigerator is kept open
in a dosed room then room:
A. heated
B. cooled
c. heated or cooled depending upon the initial temperature of the room
D. neither cooled nor heated


Which of the following expressions regarding entropy is not correct?
A \( \cdot \Delta S_{\text {system}}=\frac{q}{T} \)
B. \( \Delta S_{\text {system}}=\Delta S_{\text {total}}+\Delta S_{\text {surroundings}} \)
C \( . \Delta S=S_{\text {final}}-S_{\text {initial}} \)
D. \( \Delta S_{\text {total}}=\Delta S_{\text {system}}+\Delta S_{\text {surrounding}} \)


A sol has positively charged colloidal particles. Which of the following solutions is required in lowest concentration for coagulation?
A. \( \mathrm{NaCl} \)
B . \( \mathrm{K}_{4}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right] \)
\( c \cdot \mathrm{ZnCl}_{2} \)
D. \( \mathrm{Na}_{2} \mathrm{SO}_{4} \)


\begin{tabular}{ll|l}
& \( \mathbf{X} \) & \( \mathbf{Y} \) \\
& & \\
Normal & 2,8,7 & \\
Electronic & & 2,8,2 \\
Configuration & Dissolves in & Very low \\
Nature of & water and & solubility in \\
oxide & turns blue & water. \\
& litmus red & Dissolves in \\
& & hydrochloric \\
Tendency for & acid \\
oxidising & Tends to & Tends to act \\
and reducing & oxidise & as a \\
reactions & elements & reducing \\
Electrical and & and & agent \\
thermal & compounds & Good \\
conductivity & Very poor & Electrical \\
& electrical & conductor \\
& conductor & Good \\
& Poor thermal & Thermal \\
& conductivity & conductor \\
Tendency to & & \\
form & No tendency & \\
alloys and & to form & Forms alloys \\
amalgums & alloys &
\end{tabular} Using the information above, complete
the following

Non-metallic elements tend to be electricity


Methane gas has highest............ among all hydrocarbons
A . Ignition temperature
B. Ratio of hydrogen to carbon
c. calorific value
D. Both Band C are correct


Which of the following statements
about tautomerism is/are correct?
This question has multiple correct options
A. It is a type of functional isomerism.
B. It is shown by alcohols only.
C. Isomers exists in dynamic equilibrium with each other
D. Tautoisomers possess different functional group.


\( \Delta \mathrm{SOH} 2(g)=130.6 \mathrm{JK}-1 \mathrm{mol}-1 \Delta \mathrm{SH} 2(\mathrm{g}) 0=130 \)
6JK-1mol-1 is:
A . \( -163.2 \mathrm{Jmol}^{-1} \mathrm{K}^{-1} \)
B. +163.2Jmol-1K-1+163.2Jmol-1K-1
c. \( -303 J \) mol \( ^{-1} K^{-1} \)
D. \( +303 J \) mol \( ^{-1} \) K \( ^{-1} \)


A plank of mass \( M \) is suspended
horizontally by using two wires as shown in the figure.They have same length \( (L) \) and same cross sectional
\( \operatorname{area}(A) . \) Their Young's modulus are \( Y_{1} \)
and \( Y_{2} \) respectively. The elastic
potential energy of the system will be
\( A \)
\[
\frac{2 M^{2} g^{2} L}{A\left(Y_{1}+Y_{2}\right)}
\]
в.
\[
\frac{m^{2} g^{2} L}{A\left(Y_{1}+Y_{2}\right)}
\]
\( c \)
\[
\frac{m^{2} g^{2} L}{2 A\left(Y_{1}+Y_{2}\right)}
\]
D.
\[
\frac{M^{2} g^{2} L\left(Y_{1}+Y_{2}\right)}{2 A Y_{1} Y_{2}}
\]


A gland called 'Clock of ageing' that gradually reduces and degenerates in ageing is
A. Thyroid
B. Thymus
c. Parathyroid
D. Pituitary


Which of the following is an addition polymer?
A. Terylene
B. Bakelite
c. Polyesters
D. Teflon


Elements \( X \) and \( Y \) are from two different
compounds. In the first, 0.324 g of \( X \) is combined with 0.471 g of \( Y \). In second, 0.117 g of \( X \) is combined with 0.509 g of
Y. State the law illustrated by these chemical combinations.
A. Law of constant proportion
B. Law of multiple proportion
c. Law of reciprocal proportion
D. None of these


Which of the following statements is
not correct for \( \boldsymbol{S} \boldsymbol{i} \boldsymbol{F}_{\boldsymbol{6}}^{2-} \) and \( \boldsymbol{C l} \boldsymbol{F}_{\boldsymbol{6}}^{+} \boldsymbol{?} \)
This question has multiple correct options
A. They are isoelectronic.
B. They are isostructural
C. All possible \( \angle F S i F \) and \( \angle F C l F \) angles are identical.
D. \( d_{S i-F} \) and \( d_{C l-F} \) (bond lengths) are identical


Which year exhibited the highest
growth in FDI in India over the period
shown?
Trends of FDI in India
\( \mathbf{A} \cdot 1993 \)
B. 1994
\( c \cdot 1995 \)
D. 1996


Express as centimeter (cm) using
decimals:
\( 4 \mathrm{cm} 5 \mathrm{mm} \)


Express the given statements in the form linear equations in two variables. One is added to numerator and 4 is
subtracted from denominator, the
fraction becomes 1.


Bleaching powder is used for disinfecting drinking water.
A. True
B. False


Starch is converted into disaccharide in
presence of
A. Diastase
B. Maltose
c. zymose
D. Lactose


A ball kept in a closed container moves in it making collision with the walls. The container is kept on a smooth surface.
The velocity of the centre of mass of :
A. the ball remains fixed
B. the ball relative to container remains fixed
c. the container remains fixed
D. both container and ball remain fixed


Two bodies start falling freely from the rest from the same height at an interval of 1 s. How long after the first body begins to fall will the two bodies be \( 10 \mathrm{m} \)
apart? \( \left(g=10 m / s^{2}\right) \)
A . \( 0.5 \mathrm{s} \)
B. \( 1.0 \mathrm{s} \)
\( c \cdot 1.5 s \)
D. 2.0 s


Which of the following is the negation of the statement, For all odd primes \( \boldsymbol{p}<\boldsymbol{q} \)
there exists positive non-primes \( r<s \)
such that \( p^{2}+q^{2}=r^{2}+s^{2} \)
A. For all odd primes \( p<q \) there exists positive nonprimes \( r<s \) such that \( p^{2}+q^{2}=r^{2}+s^{2} \)
B. There exists odd primes \( p<q \) such that for all positive non-primes \( r<s, p^{2}+q^{2}=r^{2}+s^{2} \)
C. There exists odd primes \( p<q \) such that for all positive non-primes \( r<s, p^{2}+q^{2} \neq r^{2}+s^{2} \)
D. For all odd primes \( p<q \) and for all positive nonprimes \( r<s, p^{2}+q^{2} \neq r^{2}+s^{2} \)


Calculate Van't Hoff factor (i) for an
aqueous solution of \( \boldsymbol{K}_{\mathbf{3}}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{\boldsymbol{6}}\right] \)
having a degree of dissociation \( (\boldsymbol{\alpha}) \)
equal to 0.778
A .4 .334
B. 3.334
c. 0.222
D. 2.334


Evaluate the following integrals:
\( \int \frac{1}{\sqrt{7-3 x-2 x^{2}}} d x \)


Which one of the following is correct in
respect of the function \( \boldsymbol{f}(\boldsymbol{x})=\frac{\boldsymbol{x}^{2}}{|\boldsymbol{x}|} \) for
\( \boldsymbol{x} \neq \mathbf{0} \) and \( \boldsymbol{f}(\mathbf{0})=\mathbf{0} ? \)
A. \( f(x) \) is discontinuous everywhere
B. \( f(x) \) is continuous everywhere
c. \( f(x) \) is continues at \( x=0 \) only
D. \( f(x) \) is discontinuous at \( x=0 \) only


Choose the mirror image of the word above:
ANS43Q12
(1) AHZA EOT S
(2) \( \sin \varepsilon \) 오 2 ИА
(3) 2ИA£AOSI
(4) ド \( S O A \varepsilon \) АИ 2
\( A \)
B. 2
\( c \cdot 3 \)
\( D \)


Write the mathematical equation of
Ampere-Maxwell law'


\( \boldsymbol{F e}(\boldsymbol{O} \boldsymbol{H})_{3} \) sol contains positively
charged colloidal particles.
A. True
B. False


On multiplying 137592 by the smallest number \( _{--}-_{-}- \) the product is a perfect cube, the cube root of this perfect cube number is
A \( \cdot 7 \times 13^{2}, 546 \)
В. \( 7 \times 13^{3}, 546 \)
c. \( 5 \times 13,546 \)
D. \( 7 \times 13^{4}, 546 \)


Fill in the blanks with suitable words
The range of wavelength of visible light is


What is spitting of silver? How can it be
prevented?


NADP is
\( A \cdot \) A coenzyme
B. A part of tRNA
C. An enzyme
D. A part of rRNA


The area of an equilateral triangle of
side ' \( a^{\prime} \) feet is increasing at the rate of 4 sq. ft./ sec. The rate at which the perimeter is increasing is
A \( \cdot \frac{3 \sqrt{8}}{2} \)
B. \( \frac{8 \sqrt{3}}{a} \)
c. \( \frac{\sqrt{3}}{a} \)
D. \( \frac{2 \sqrt{3}}{a} \)


What will be the effect on the
divergence of the leaves of a uncharged gold leaf electroscope on bringing a negatively charged rod near electroscope?
A. Leaves diverge
B. Leaves converge
c. Leaves remains at same position
D. Can not be determined


A cylindrical tank stands on a frictionless surface.The seal over a
circular hole of radius \( 0.5 \mathrm{cm} \) in the wall
of the tank ruptures when the level of water above the hole is 1 metre. The
force that a person must apply on the cylinder to keep it from being set in motion is
A . \( 1.54 \times 10^{-3} N \) forward
B . \( 1.54 \times 10^{-3} N \) backward
c. \( 1.54 N \) forward
D. \( 1.54 N \) backward


Two bodies of mass \( m_{1} \) and \( m_{2}\left(<m_{1}\right) \)
are connected to the end of massless
cord and allowed to move as shown. The
pulley is mass less and friction less
determine the acceleration of the centre
of mass


Match the correct one
A. A: afferent arteriole, B: Proximal convoluted tubule, C
Henle's loop, D: Distal convoluted tubule, E: Peritubular
capillaries, F: collecting duct
B. F: efferent arteriole, B: PCT, C: Henle's loop, D: DCT, E:
peritubular capillaries, F: collecting duct
C. A: afferent arteriole, B: peritubular capillaries, C:
Henle's loop, D: DCT, E: PCT, F: collecting duct
D. A: afferent arteriole, B: Henle's loop, C: collecting ductt
D: PCT, E: DCT, F: peritubular capillaries


A plane progressive wave is given by \( \boldsymbol{y}=25 \cos (2 \pi t-\pi x) \) Then the
amplitude and frequency are respectively
A . 25,100
B. 25,
\( c .25 .2 \)
D. \( 50 \pi, 2 \)


Solve the following pair of linear equations:
\( \frac{10}{x+y}+\frac{2}{x-y}=4 ; \frac{15}{x+y}-\frac{5}{x-y}= \)
-2


Evaluate the definite integral:
\( \int_{-1}^{1} 5 x^{4} \sqrt{x^{5}+1} d x \)


A wire \( 88 \mathrm{cm} \) long bent into a circular loop is placed perpendicular to the magnetic field of flux density 2.5 Wb
\( m^{-2} . \) Within \( 0.5 \mathrm{s} \), the loop is changed
into a square and flux density is increased to \( 3.0 \mathrm{Wb} \mathrm{m}^{-2} \). The value of
e.m.f. induced is :
A . \( 0.018 v \)
B. 0.016v
c. \( 0.020 v \)
D. 0.012V


The moment of inertia of a metre stick
of mass \( 300 g \), about an axis at right
angles to the stick and located at \( 30 \mathrm{cm} \)
mark, is
\( \mathbf{A} \cdot 8.3 \times 10^{5} g \mathrm{cm}^{2} \)
в. \( 5.8 g \mathrm{cm}^{2} \)
C. \( 3.7 \times 10^{5} \mathrm{g} \mathrm{cm}^{2} \)
D. None of these


A chord of circle of radius \( 10 \mathrm{cm} \)
subtends a right angle at the centre. Find area of the minor sector


Which of the following is(are) Dobereiner's triads?
(a) \( P, A s, S b \)
(b) \( \mathrm{Cu}, \mathrm{Ag}, \mathrm{Au} \)
(c) \( \mathrm{Fe}, \mathrm{Co}, \mathrm{Ni} \)
\( (d) S, S e, T e \)
\( A \cdot \) a and \( b \)
B. b and c
\( c . \) a and d
D. all of the above


For the formation of \( C r_{2} O_{3} \) and \( A l_{2} O_{3} \)
values of \( \Delta_{f} G^{o} \) are \( 540 \mathrm{kJ} \mathrm{mol}^{-1} \) and
\( -827 \mathrm{kJ} \mathrm{mol}^{-1} \) respectively. What will be
the possibility for reaction of \( C r_{2} O_{3} \) by
Al?
A. Reduction of \( C r_{2} O_{3} \) by Al will take place
B. Oxidation of \( C r_{2} O_{3} \) by Al will take place
c. Neither oxidation nor reduction will take place
D. Reaction is not feasible


The most conspicuous visible change that occurs in boys during puberty is
A. Breast development
B. Increase in height
c. Production of sperms
D. None of the above


Show that \( y=\frac{1}{x} \) is a solution of the differential equation \( \frac{d y}{d x}=\log x \)


The value of \( \lim _{n \rightarrow \infty}\left(\frac{1}{\sqrt{4 n^{2}-1}}+\frac{1}{\sqrt{4 n^{2}-4}}+\dots+\frac{ }{\sqrt{3}}\right. \)
is.
A \( \cdot \frac{1}{4} \)
B. \( \frac{\pi}{12} \)
c.
D.


How is \( X e O F_{4} \) prepared ? Describe its
molecular shape.


In photorespiration the number of ATP and NADPH synthesised are respectively
A . 1 and 3
B. 2 and 3
\( c \cdot 3 \) and 4
D. o and 0


Paramecia are members of the Kingdom
A. Fungi
B. Animalia
c. Archaea
D. Protistata
E. Plantae