The sum of the first 9 terms of an \( A . P \) is
81 and the sum of it's first 20 terms is
400. Find the first term, the common
difference and the sum upto 15 th term
A \( \cdot a=1, d=2, S_{15}=235 \)
В . \( a=3, d=4, S_{15}=215 \)
c. \( a=5, d=3, S_{15}=205 \)
D. None of these


The value of \( \left(1+i x+i^{2} x^{2}+i^{3} x^{3}+\right. \)
\( \ldots \text { to } \infty) \times \)
\( \left(1-i x+i^{2} x^{2}-i^{3} x^{3}+\ldots . t o \infty\right) \) is
A. Imaginary
B. a positive real
c. a negative real
D. equal to zero


If \( f(x)=\sin ^{-1} x+\sec ^{-1} x \) is defined
then which of the following value/values is/are in its range?
A \( \cdot \frac{-\pi}{2} \)
в. \( \frac{\pi}{2} \)
\( c . \pi \)
D. \( \frac{3 \pi}{2} \)


If \( \boldsymbol{y}=\boldsymbol{a} e^{-k t} \cos (\boldsymbol{p} \boldsymbol{t}+\boldsymbol{c}), \) then prove
that \( \frac{d^{2} y}{d t^{2}}+2 k \frac{d y}{d t}+n^{2} y=0, \) where \( n^{2}= \)
\( \boldsymbol{p}^{2}+\boldsymbol{k}^{2} \)


When there is a decrease of \( 5 k m / h r \) in the usual uniform speed of a good train repair work going on it takes 4 hours more than the usual time for travelling
the \( 400 \mathrm{km} \). Find the usual speed of the
train.


Main source of lead is galena \( (P b S) . \) It
is converted to \( P b \) by:
\( (A) P b S \frac{a i r}{\Delta} P b O+S O_{2} \stackrel{C}{\longrightarrow} P b+ \)
\( \boldsymbol{C O}_{2} \)
\( (B) P b S \frac{a i r}{\Delta} P b O+P b S \rightarrow P b+S O_{2} \)
Identify the self-reduction process.
A \( .(A) \)
в. \( (B) \)
c. Both \( (A) \) and \( (B) \)
D. None of the above


What are the causes of Peptization?


What is meant by sexual reproduction? Name its two main processes.


How many degrees of freedom are
associated with 2grams of He at NTP?
A. 3
B. \( 3.01 \times 10^{23} \)
c. \( 9.03 \times 10^{23} \)
D. 6


Choose the wrong statement:
A. the accelerated motion may be due to change in magnitude of velocity or direction of velocity or both.
B. the velocity and acceleration ofa body may not necessarily be in the same direction
C. the velocity and acceleration of body may not be zero simultaneously
D. when a body falls freely under the action of gravity, its acceleration is zero


State True or False.
A single photon excites only a single electron.
A. True
B. False


An automobile engine develops \( 100 \mathrm{kW} \) when rotating at a speed of 1800 rev/min. What torque does it deliver?
A. 350 Nm
B. 440 Nm
\( c .531 \mathrm{Nm} \)
D. \( 628 \mathrm{Nm} \)


Find the 1000 th term of the sequence
\( 3,4,5,6, \dots \)


When a ceiling fan is switched off, its angular velocity reduces to half its initial value after it completes 36
rotations. The number of rotations it will
make further before coming to rest is Assuming angular retardation to be
uniform
A . 10
B . 20
\( c .18 \)
D. 12


Two concentric spheres kept in air have radii 'R' and 'r'. They have similar charge
and equal surface charge density' \( \sigma^{\prime} \) The electric potential at their common
centre is. \( \left(\epsilon_{0}= \) permittivity of free \right. space \( ) \)
A \( \cdot \frac{\sigma(R+r)}{\epsilon_{0}} \)
в. \( \frac{\sigma(R-r)}{\epsilon_{0}} \)
c. \( \frac{\sigma(R+r)}{2 \epsilon_{0}} \)
D. \( \frac{\sigma(R+r)}{4 \epsilon_{0}} \)


Find at what height \( x_{m}, \) the ball will experience the maximum attraction.
A \( \cdot x_{m}=\frac{1}{\sqrt{a}} \)
B. \( x_{m}=\frac{1}{\sqrt{4 a}} \)
c. \( _{x_{m}}=\frac{1}{\sqrt{2 a}} \)
D. \( x_{m}=\frac{2}{\sqrt{a}} \)


Exhaustive set of values of parameter \( \boldsymbol{a} \)
so that \( \sin ^{-1} x-\tan ^{-1} x=a \quad \) has a
solution is
A. \( \left[-\frac{\pi}{6}, \frac{\pi}{6}\right] \)
B. \( \left[-\frac{\pi}{4}, \frac{\pi}{4}\right] \)
\( \mathbf{c} \cdot\left[-\frac{\pi}{2}, \frac{\pi}{2}\right] \)
D. none of these


Find the plane of the reflection experimentally for the incident ray which passes through the heads of the pins pierced in front of the mirror.


\( X e O_{3} \) has
\( \mathbf{A} \cdot \) one \( p \pi-p \pi \) and two \( p \pi-d \pi \)
B. three \( p \pi-p \pi \) bonds
\( \mathbf{C} \cdot \) four \( p \pi-d \pi \) bonds
D. three \( p \pi-d \pi \) bonds


Evaluate: \( \int e^{x}\left(x^{2}+2 x\right) d x \)


Radioactivity is generally does not
found in:
This question has multiple correct options
A. light nuclei
B. stable nuclei
C . heavy nuclie
D. nuclei of intermediate mass


What will be the value of van't Hoff
factor
(i) of benzoic acid if it demerises
in aqueous solution? How will the
experimental molecular weight vary as compared to the normal molecular
weight?


How is 0.0120 written as a scientific
notation?
A. \( 120 \times 10^{-4} \)
B . \( 1.2 \times 10^{-2} \)
c. \( 12 \times 10^{-3} \)
D. \( 12.0 \times 10^{-3} \)


Prove that \( \left|\begin{array}{lll}\boldsymbol{a} & \boldsymbol{a} & \boldsymbol{a} \\ \boldsymbol{a} & \boldsymbol{b} & \boldsymbol{b} \\ \boldsymbol{a} & \boldsymbol{b} & \boldsymbol{c}\end{array}\right|=\boldsymbol{a}(\boldsymbol{b}-\boldsymbol{c})(\boldsymbol{a}-\boldsymbol{b}) \)
Hence find the value of \( \left|\begin{array}{lll}\mathbf{3} & \mathbf{3} & \mathbf{3} \\ \mathbf{3} & \mathbf{5} & \mathbf{5} \\ \mathbf{3} & \mathbf{5} & \mathbf{7}\end{array}\right| \)


Find the principal value of:
\( \tan ^{-1}\left(2 \cos \frac{2 \pi}{3}\right) \)


Differentiate \( \tan ^{-1}\left(\frac{a \cos x-b \sin x}{b \cos x+a \sin x}\right) \)


Write the definition of acid and base
based on Arrhenius principle also write the limitations of this principle.


Evaluate \( \int_{1}^{2} \frac{x}{(x+1)(x+2)} d x \)


This famous scientist worked with a
mould called Neurospora crassa and came to the conclusion that the
characteristics function of the gene was to supervise the formation of a
particular enzyme. Who was he?
A. John Joseph Bittner
B. William Clouser Boyd
c. George Wells Beadle
D. wended Meredith Stanley


What is the multiplicative inverse of \( -1 \times \frac{-2}{5} \)


If same amount of milk and water are
kept in two beakers and heated on the
two burners of a gas by supplying equal amount of heat. Despite this, why is the rise in temperature of milk more than that of water?


Diazo coupling is useful to prepare
some:
A . pesticides
B. dyes
c. proteins
D. vitamins


\( A+B \rightleftharpoons C+D, K_{c} \) for this reaction is
10. If 1,2,3,4 mole/litre of \( A, B, C \) and
\( D \) respectively are present in a
container at \( 25^{\circ} C, \) the direction of
reaction will be:
A. from left to right
B. from right to left
c. reaction is at equilibrium
D. unpredictable


Muehlenbeckia is a good example of
A. Phyllode
B. Phylloclade
c. winged fruit
D. Parachute mechanism


Three convex lenses are available
having focal lengths of \( 4 \mathrm{cm}, 40 \mathrm{cm} \) and
\( 4 m \) respectively. Which one could be used as magnifying glass?
A. \( 4 c m \)
в. \( 40 \mathrm{cm} \)
\( c .4 m \)
D. All


If \( A \) and \( B \) are two events such that
\( \boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B})=\mathbf{0 . 6 5} \) and \( \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B})= \)
\( \mathbf{0 . 1 5}, \operatorname{then} \boldsymbol{P}(\overline{\boldsymbol{A}})+\boldsymbol{P}(\overline{\boldsymbol{B}})= \)
A . 0.6
B. 0.8
c. 1.2
D. 1.


Find the sum of the geometric series \( 4+2+1+\ldots+\frac{1}{16} \)
A \( \cdot \frac{17}{16} \)
в. \( \frac{107}{16} \)
c. \( \frac{117}{16} \)
D. \( \frac{12}{16} \)


A particle executes a simple harmonic motion of time period \( T . \) Find the time taken by the particle to go directly from its mean position to half the amplitude.
A \( \cdot \frac{T}{2} \)
в. \( \frac{T}{4} \)
c. \( \frac{T}{8} \)
D. \( \frac{T}{12} \)


The angle of dip at the location in
southern India is about \( 18^{\circ} . \) Would you
expect a greater or a smaller dip angle in Britain (Closer to the north pole.)


A step-up transformer operates on a \( 230 \mathrm{V} \) line and a load current of \( 2 \mathrm{A} \). The ratio of primary and secondary
windings is \( 1: 25 . \) Then the current in
the primary is?
A . 25 A
B. 50 A
c. 15 A
D. 12.5 A


Solve:
\( \frac{x}{2}-\frac{x}{3}-1=4 \)


Sodium, magnesium can be obtained from their oxides by:
A. calcination
B. roasting
c. electrolytic reduction
D. None of the above


Rogue element in the periodic table
is
A. oxygen
B. hydrogen
c. astatine
D. rhenium


Assertion
Emphysema is the permanent abnormal inflation of air space of
terminal bronchioles or alveolar sacs.
Reason
Destruction of pulmonary tissues specially alveolar septa and flattening of alveolar ducts occur in emphysema.
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


Find the equation to the ellipses, whose centres are the origin, whose axes are the axes of coordinates, and which pass through \( (\alpha) \) the points \( (2,2), \) and (3,1) and \( (\beta) \) the points (1,4) and (-6,1)


An LC circuit contains a \( 20 \mathrm{mH} \)
inductor and a \( 25 \mu \) F capacitor with an initial charge of 5 mC. The total energy stored in the circuit initially is
A . 5 J
в. 0.5
c. 50
D. 500 J


Which of the following is diamagnetic?
\( A \cdot O_{2} \)
в. \( C O \)
c. \( B_{2} \)
D. \( N O \)


A microscope is used with sodium light and its resolving power is not sufficiently large.Higher resolution will
be obtained by using wavelength of
A. 20 micron
B. 2 micron
c. 1 micron
D. \( 400 \mathrm{A}^{\circ} \)


The principal nitrogenous excretory compound in humans is synthesised
A. In kidneys as well as eliminated by kidneys
B. In liver and also eliminated by the same through bile
C. In the liver but eliminated mostly through kidneys
D. In kidneys but eliminated mostly through liver


Find the values of \( x, \) if \( \left|\begin{array}{cc}\mathbf{3 x} & \mathbf{7} \\ \mathbf{2} & \mathbf{4}\end{array}\right|=\mathbf{1 0} \)


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


The arithmetic mean of numbers
\( a, b, c, d, e \) is \( M . \) What is the value of \( (\boldsymbol{a}-\boldsymbol{M})+(\boldsymbol{b}-\boldsymbol{M})+(\boldsymbol{c}-\boldsymbol{M})+(\boldsymbol{d}- \)
\( M)+(e-M) ? \)
\( \mathbf{A} \cdot M \)
B. \( a+b+c+d+e \)
\( c \cdot 0 \)
\( D .5 M \)


The larger area bounded between the
curve \( |\boldsymbol{x}|^{2}+|\boldsymbol{y}|^{2}=\mathbf{1} \) and the line \( \boldsymbol{x}+ \)
\( y=1 \) is
\( ^{\mathrm{A}} \cdot\left(\frac{\pi}{4}-\frac{1}{2}\right) \) sq. unit
B. \( \left(\frac{\pi}{4}+1\right) \) sq. unit
c. \( \left(\frac{3 \pi}{4}+\frac{1}{2}\right) \) sq. unit
D \( \cdot\left(\frac{3 \pi}{4}-\frac{1}{2}\right) \) sq. unit


If the ratio of the cost price and sale
price is \( 25: 26 . \) Then find the profit in
percentage.


Solve for \( \boldsymbol{x} \)
\( 2 \tan ^{-1}(\cos x)=\tan ^{-1}(2 \operatorname{cosec} x) \)


For germanium diode, the junction voltage is about
A . \( 0.7 V \)
в. \( 0.3 V \)
\( c .0 .6 V \)
D. \( 3 V \)


Area of a sector of central angle \( 200^{0} \) of
a circle is \( 770 \mathrm{cm}^{2} \). The length of the corresponding arc of this sector is
A \( \cdot 73 \frac{1}{3} c m \)
B \( \cdot 156 \frac{1}{3} c m \)
\( \mathbf{c} \cdot 7 \frac{1}{3} c m \)
D. \( 22 \frac{1}{3} \) cm


Find the equation of the line passing through (1,2,-4) and perpendicular to both the lines \( \frac{x-1}{2}=\frac{y+2}{-3}=\frac{z-4}{4} \)
and \( \frac{\boldsymbol{x}-\mathbf{3}}{\mathbf{5}}=\frac{\boldsymbol{y}+\mathbf{6}}{\mathbf{1}}=\frac{\boldsymbol{z}+\mathbf{1 0}}{\mathbf{2}} \)


Which of these plants contains nitrogen-fixing bacteria?
\( A \cdot \) Gram
B. Wheat
c. Mustard
D. cotton


Water hyacinth is termed as 'terror of
Bengal'. It causes death of fish because
it
A. Covers water surface and inhibits sunlight to pass through
B. Drains oxygen from water that causes oxygen deficiency
c. Absorbs nutrients from water that causes malnutrition
D. Releases \( C O_{2} \) in huge amount which is lethal to fish


A toroid having average diameter \( 2.5 \mathrm{m} \) number A turns \( 400, \) current \( =2 A \) and
magnetic field has 10 T what will be induced magnetic field (in amp/m).
A \( \cdot \frac{10^{5}}{4 \pi} \)
в. \( \frac{10^{8}}{4 \pi} \)
c. \( \frac{10^{8}}{2 \pi} \)
D. \( \frac{10^{2}}{2 \pi} \)


The motion of a particle is described by
\( \boldsymbol{x}=\mathbf{3 0} \sin (\boldsymbol{\pi} \boldsymbol{t}+\boldsymbol{\pi} / \mathbf{6}), \) where \( \boldsymbol{x} \) is in \( \boldsymbol{c m} \)
and \( t \) in sec. Potential energy of the
particel is twice of kinetic energy for the first time after \( t=0 \) when the particle
is at position after
time.


Calculate the amount and compound interest on
(a) \( R s \cdot 10,800 \) for 3 years at \( 12 \frac{1}{2} \% \) per annum compounded annually.
(b) \( R s .18,000 \) for \( 2 \frac{1}{2} \) years at \( 10 \% \) per annum compounded annually.
(c) \( R s .62,500 \) for \( 1 \frac{1}{2} \) years at \( 8 \% \) per annum compounded half yearly.
(d) \( R s .8,000 \) for 1 year at \( 9 \% \) per annum
compounded half yearly. (You could use the year by year calculating using SI formula to verify).
(e) \( R s .10,000 \) for 1 year at \( 8 \% \) per
annum compounded half yearly.


The ratio of change in dimension at right angles to applied force to the initial dimension is defined as
A. \( Y \)
B. \( \eta \)
\( c \cdot \beta \)
D. \( K \)


"Plant growth substances act together
or against each other". Give suitable examples in support of the statement


A narrow tube is bent in the form of a
circle of radius \( R, \) as shown in the
figure. Two small holes \( S \) and \( D \) are made in the tube at the positions right
angle to each other. A source placed at
S generated a wave of intensity \( l_{0} \) which is equally divided into two parts : One part travels along the longer path, while the other travels along the shorter path. Both the part waves meet at the point D where a detector is placed. If a maxima is formed at the detector then, the
magnitude of wavelength \( \lambda \) of the wave
produced is given by :
This question has multiple correct options
A . \( \pi R \)
в. \( \frac{\pi R}{2} \)
c. \( \frac{\pi R}{4} \)
D. \( \frac{2 \pi R}{3} \)


It is observed that the voltage of a galvanic cell using the reaction
\( M(s)+x H^{+} \rightarrow M^{x+}+\frac{x}{2} H_{2} \) varies
linearly with the log of the square root of the hydrogen pressure and the cube
root of the \( \mathrm{M}^{x+} \) concentration. The value
of \( x \) is :
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. 5


Draw the graph of the linear equation \( 4 x+y=6 . \) At what points the graph of the equation cuts the \( x \) -axis and the \( y \) -axis
? Find area bounded by this line and coordinate axes.


From the stability constants
(hypothetical value) given below,
predict the strongest ligand.
\( \mathbf{A} \)
\[
C u^{2+}+4 N H_{3} \rightarrow\left[C u\left(N H_{3}\right)_{4}\right]^{2+}, K=4.5 \times 10^{11}
\]
\( B \)
\[
C u^{2+}+4 C N^{-} \rightarrow\left[C u(C N)_{4}\right]^{2-}, K=2.0 \times 10^{27}
\]
\( \mathbf{c} \)
\[
C u^{2+}+2 e n \rightarrow\left[C u(e n)_{2}\right]^{2+}, K=3.0 \times 10^{15}
\]
D.
\[
C u^{2+}+4 H_{2} O \rightarrow\left[C u\left(H_{2} O\right)_{4}\right]^{2+}, K=9.5 \times 10^{8}
\]


A phagotrophic euglenoid is
A. Euglena
B. Peranema
c. Rhabdomonas
D. Both B and C


The \( p H \) of a solution containing \( 0.1 N \)
NaOH solution is:
\( \mathbf{A} \cdot \mathbf{1} \)
B . \( 10^{-1} \)
c. 13
\( \mathbf{D} \cdot 10^{-13} \)


Which of the following pair of compound are functional isomers?
\( A \)
в.
\( c \)
\( D \)


If the non-parallel sides of a trapezium are equal, then it is cyclic.
A. True
B. False


Metals can be recovered from their ores
by chemical methods.
A. True
B. False


A biased com wih probatnity \( \mathrm{p}, 0<\mathrm{p}<1 \) of heads is tossed until a head appears
for the first time. If the probatory that the number of tosses required is even is \( 2 / 5 \) find the value of \( p \)


The line \( A x+B y+C=0 \) cuts the
circle \( \boldsymbol{x}^{2}+\boldsymbol{y}^{2}+\boldsymbol{a} \boldsymbol{x}+\boldsymbol{b} \boldsymbol{y}+\boldsymbol{c}=\boldsymbol{0} \) in \( \boldsymbol{P} \)
and \( Q \)
The line \( \boldsymbol{A}^{\prime} \boldsymbol{x}+\boldsymbol{B}^{\prime} \boldsymbol{y}+\boldsymbol{C}^{\prime}=\mathbf{0} \) cuts the
circle \( \boldsymbol{x}^{2}+\boldsymbol{y}^{2}+\boldsymbol{a}^{\prime} \boldsymbol{x}+\boldsymbol{b}^{\prime} \boldsymbol{y}+\boldsymbol{c}^{\prime}=\mathbf{0} \) in \( \boldsymbol{R} \)
and \( S \).
If \( P, Q, R, S \) are concyclic, then show
that
\( \left|\begin{array}{ccc}\boldsymbol{a}-\boldsymbol{a}^{\prime} & \boldsymbol{b}-\boldsymbol{b}^{\prime} & \boldsymbol{c}-\boldsymbol{c}^{\prime} \\ \boldsymbol{A} & \boldsymbol{B} & \boldsymbol{C} \\ \boldsymbol{A}^{\prime} & \boldsymbol{B}^{\prime} & \boldsymbol{C}^{\prime}\end{array}\right|=\mathbf{0} \)


If \( a, b \) and \( n \) are natural numbers then
\( a^{2 n-1}+b^{2 n-1} \) is divisible by
A \( \cdot a+b \)
в. \( a-b \)
\( \mathbf{c} \cdot a^{3}+b^{3} \)
D. \( a^{2}+b^{2} \)


MATHEMATICS
\begin{tabular}{lcccc}
Classes & \( 0- \) 10 & \( 10- \) 20 & \( 20- \) 30 & \( 30- \) 40 \\
Frequencies & 5 & 8 & 15 & 16 \\
\hline
\end{tabular}


If \( \cos x \) and \( \sin x \) are solutions of the
different equation \( \boldsymbol{a}_{\mathbf{0}} \frac{\boldsymbol{d}^{\mathbf{2}} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}}+\boldsymbol{a}_{1} \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}+ \)
\( \boldsymbol{a}_{2} \boldsymbol{y}=\mathbf{0}, \) where \( \boldsymbol{a}_{0}, \boldsymbol{a}_{1}, \boldsymbol{a}_{2} \) are real
constants, then which of the following
is/are always true?
This question has multiple correct options
\( \mathbf{A} \cdot A \cos x+B \sin x \) is a solution, where \( A \) and \( B \) are real
costants
B. \( A \cos \left(x+\frac{\pi}{4}\right) \) is a solution, where \( A \) is real constant
c. \( A \cos x \sin x \) is a solution, where \( A \) is real constant
D. \( A \cos \left(x+\frac{\pi}{4}\right)+B \sin \left(x-\frac{\pi}{4}\right) \) is a solution, where \( A \)
and \( B \) are real constants


Find the prime factorisation of the following numbers:
\( 85^{3}-68^{3}+5^{3}-22^{3} \)


Which pair of elements of atomic numbers given below will have similar chemical properties?
\( \mathbf{A} \cdot 13,22 \)
в. 3,11
\( c \cdot 4,24 \)
D. 2,4


Multiple Correct Answers Type Which of the following pairs have different dimensions?

This question has multiple correct options
A. Frequency and angular velocity
B. Tension and surface tension
c. Density and energy density
D. Linear momentum and angular momentum


The depression in freezing point for
\( 0.01 m \) aqueous solution of
\( \boldsymbol{K}_{\boldsymbol{x}}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{\boldsymbol{6}}\right] \) is \( \boldsymbol{0 . 0 7 4 4} \boldsymbol{K} . \) The motal
depression constant for solvent is
\( 1.86 K k g \) mol\( ^{-1} . \) If the solute
undergoes complete dissociation, what is the correct molecular formula for the
solute?
\( A \cdot_{K_{2}\left[F e(C N)_{6}\right]} \)
B \( \cdot_{K_{3}}\left[F e(C N)_{6}\right] \)
c. \( \left._{K\left[F e(C N)_{6}\right.}\right] \)
D \( \quad K_{4}\left[F e(C N)_{6}\right] \)


Which of the following is first formed inert gas compound?
\( \mathbf{A} \cdot X e\left[P t F_{6}\right] \)
В. \( \operatorname{Kr}\left[P t F_{6}\right] \)
c. \( X e F_{2} \)
D. \( X e O_{3} \)


Calculate the work done in stretching steel wire of length \( 2 \mathrm{m} \) and of cross sectional area \( 0.0225 m m^{2}, \) when a
load of \( 100 \mathrm{N} \) is applied slowly to its free end. (Young's modulus of steel = 20 x
\( \mathbf{1 0}^{\mathbf{1 0}} \mathbf{N} / \boldsymbol{m}^{\mathbf{2}} \mathbf{)} \)


Find five rational numbers between \( \frac{2}{3} \) and \( \frac{\mathbf{3}}{\mathbf{5}} \)


The energy \( E \) of an oscillating body in simple harmonic motion depends on its
mass \( m \), frequency \( n \) and amplitude \( a \)
Using the method of dimensional analysis find the relation between
\( \boldsymbol{E}, \boldsymbol{m}, \boldsymbol{n} \) and \( \boldsymbol{a} \)
A \( \cdot E=k m n^{2} a^{2}(k=a \text { dimensionless constant }) \)
B . \( E=k m^{2} n^{2} a^{3}(k=a \text { dimensionless constant }) \)
C . \( E=k m^{1} n^{1} a^{2}(k=a \text { dimensionless constant }) \)
D. \( E=k m^{2} n^{1} a^{2}(k=a \text { dimensionless constant }) \)


Assertion: The buffer HCOOH/HCOONa
will have pH lesser than 7 . Reason: Conjugate base of a weak acid is a strong base.
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
E. Both Assertion and Reason are false


Which of the following statements
is/are correct?
This question has multiple correct options
A. Increase of pressure increases the amount of adsorption.
B. Increase of temperature may decrease the amount of adsorption.
C. The adsorption may be monolayered or multilayered.
D. Particle size of the adsorbent will not affect the
amount of adsorption.


Points \( P, Q \) and \( R \) are in a vertical line such that \( \mathrm{PQ}=\mathrm{QR} \). A ball at \( \mathrm{P} \) is allowed to fall freely. The ratio of times of descent through \( \mathrm{PQ} \) and QR is
A . 1:
B. \( 1: \sqrt{2} \)
c. \( 1:(\sqrt{2}-1) \)
D. \( 1:(\sqrt{2}+1) \)


If the sum of four consecutive even
numbers is \( 532, \) find the numbers.


In the oxidation of \( N_{2} H_{4} \) to \( N_{2} \)
equivalent weight of \( N_{2} H_{4} \) would be


A fish is \( 10.0 \mathrm{cm} \) from the front surface
of a spherical fish bowl of radius
\( 20.0 \mathrm{cm}, \) as shown in the figure. The
walls of the bowl are thin,and their
effects can be neglected. As
observed from the point \( \boldsymbol{P}(\text { see figure }) \)
the fish is at a distance of:
A. \( 6.7 \mathrm{cm} \) from the surface and appears magnified in size
B. \( 8.6 \mathrm{cm} \) from the surface and appears magnified in size
c. \( 10.3 \mathrm{cm} \) from the surface and appears diminished in size
D. \( 11.4 \mathrm{cm} \) from the surface and appears diminished in size


If in an inflorescence two lateral
branches develop on either side of the terminal flower which again branch is
known as
A. Monochasial cyme
B. Scorpiold cyme
C. Helicoid cyme
D. Dichasial cyme


The minimum number of dimensions
needed to construct a rectangle is
A .2
B. 3
\( c \cdot 4 \)
D.


Which of the following are arranged from smallest unit to largest unit?
\( \mathbf{A} \cdot \mathrm{cm}, \mathrm{m}, \mathrm{mm}, \mathrm{km} \)
B. km, m, cm, mm
\( \mathbf{c} \cdot \mathrm{cm}, \mathrm{mm}, \mathrm{m}, \mathrm{km} \)
\( \mathbf{D} \cdot \mathbf{m m}, \mathbf{m}, \mathbf{c m}, \mathbf{k m} \)
E . \( m m, c m, m, k m \)


A source of sound having frequency 2000Hr \( \& \) a receiver are located at the
same point at the instant \( t=0, \) the source starts moving with const \( \boldsymbol{a c c}^{n}\left(\boldsymbol{a}=\mathbf{1 0 m} / \boldsymbol{s}^{2}\right) \)
Find the frequency registered by the receiver at the instant \( t=10 \) sr. Velocity of sound in air is \( 340 \mathrm{m} / \mathrm{s} \)


Statement I: The number 5,007 has three significant figures Because
Statement II: Zeros between non-zero
digits are significant
A. one is True, second is True and currect expilanation
B. one is true and second is true
c. one is true and second is False
D. one is False and second is True
E. False False


In the Venn diagram, \( \boldsymbol{\xi} \) F UG \cup \( \boldsymbol{H} \). The
shaded region represents:
\( \mathbf{A} \cdot G^{\prime} \cap F \)
\( \mathbf{B} \cdot(F \cap H) \cup G^{\prime} \)
\( \mathbf{c} \cdot(F \cap H) \cap G^{\prime} \)
\( \mathbf{D} \cdot(F \cap G)^{\prime} \cap H \)


How water gets polluted? How the
pollution can be minimised?


Ferric sulphate is represented by which formula?
A. \( F e S O_{4} \)
в. \( F e S O_{3} \)
\( \mathrm{c} \cdot \mathrm{Fe}\left(\mathrm{SO}_{4}\right)_{2} \)
D. \( F e_{2}\left(S O_{4}\right)_{3} \)


The numbers of ways in whi


For a given reaction, energy of
activation for forward reaction \( \left(\boldsymbol{E}_{\boldsymbol{a f}}\right) \) is \( 80 k J . m o l^{-1} . \Delta H=-40 k J . m o l^{-1} \) for
the reaction. A catalyst lowers \( E_{a f} \) to
20k \( J . \) mol \( ^{-1} \). The ratio of energy of
activation for reverse reaction before
and after addition of catalyst is :
A . 1.0
B. 0.5
\( c \cdot 1.2 \)
D. 2.0


Find the angle between two diameters of the ellipse \( \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 \) Whose
extremities have eccentricity angle a and \( \beta=a+\frac{\pi}{2} \)


The efficiency of a fuel cell is \( 80 \% \) and the standard heat of reaction is
\( -300 k J . \) The reaction involves two
electrons in redox change. \( \boldsymbol{E}^{\ominus} \) for the
cell is:
A . \( 1.24 V \)
B . \( 2.48 V \)
c. \( 0 V \)
D. \( 0.62 V \)


Calculate the area of the plates of a one
farad parallel plate capacitor if separation between plates is \( 1 \mathrm{mm} \) and plates are in vacuum:
A \( \cdot 18 \times 10^{8} m^{2} \)
B . \( 0.3 \times 10^{8} m^{2} \)
c. \( 1.3 \times 10^{8} m^{2} \)
D. \( 1.13 \times 10^{8} m^{2} \)


In \( \triangle A B C, \) if \( m \angle B=90 \& A C=10 \)
then length of median \( \boldsymbol{B} \boldsymbol{M}= \)
\( A \cdot 6 \)
B. \( 5 \sqrt{2} \)
c.
D. 8


The steam point and the ice point of a mercury thermometer are marked as
\( 80^{\circ} \) and \( 20^{\circ} . \) What will be the
temperature in centigrade mercury
scale when this thermometer reads \( 32^{\circ} \)


All heterogeneous catalysts are based on the process of adsorption
A. True
B. False


\( p K_{a} \) values of four acids are given
below at \( 25^{\circ} \mathrm{C} \). The strongest acid is:
A . 2.0
в. 2.
c. 3.0
D. 4.0


Effect of dispersion of light among the following is:
A . Mirage
B. Blue colour of the sky
c. Rainbow
D. Twinkling of stars


Evaluate \( : \int e^{\sin ^{-1} x}\left(\frac{\ln x}{\sqrt{1-x^{2}}}+\frac{1}{x}\right) d x \)


A four-digit number is formed by using the digits 1,2,4,8 and 9 without repitition. If one number is selected from those numbers, then what is the
probability that it will be an odd number
?
A \( \frac{1}{5} \)
B. \( \frac{2}{5} \)
\( c \cdot \frac{3}{5} \)
D. \( \overline{5} \)


Who suggested the distribution of
electrons into different orbits of an
atom?
A. E. Goldstein
B. Ernest Rutherford
c. Bohr and Bury
D. Dalton


An oxyacid of phosphorus has the
following properties:
Complex neutralization of the acid with
sodium hydroxide solution given an aqueous solution of sodium ions and
oxy-acid anions in the ratio 2:1. When a solution of the acid is warmed with a
silver nitrate solution, metallic silver is deposited.

What is the structure of the oxy-acid?
\( A \)
B. 2
\( c \cdot 3 \)
\( D \cdot 4 \)


Plane passing through the points \( A(2,1 \)
3), \( \mathrm{B}(-1,2,4) \) and \( \mathrm{C}(0,2,1) \). Determine its
point of intersection with the line \( r= \)
\( \boldsymbol{j}+\boldsymbol{k}+\boldsymbol{t}(\boldsymbol{2} \boldsymbol{i}+\boldsymbol{k}) \)
A \( \cdot(7,+1,4) \)
B. (9,+1,-2)
c. (7,-1,4)
D. (9,-1,2)


Which type of ion is present in aluminium oxide?
A \( . x^{+} \)
B. \( X^{2+} \)
\( c \cdot X^{3+} \)
D. \( X O_{3}^{2} \)
E \( . X O_{4}^{2} \)


Among the following bonds, which has the most polar character?
A \( . C-O \)
в. \( C-B r \)
c. \( C-F \)
D. \( C-S \)


In the given figure, \( 2 A P=5 P B \) and
\( 2 C P=5 P D \)
Is : \( \boldsymbol{A C} \| \boldsymbol{D B} \) ?
If the above statement is true then
mention answer as 1 , else mention 0


Statement 1: After a period of time in a
closed container, the rate of evaporation
of a liquid will equal the rate of condensation.
Statement 2: An equilibrium will be
established between a liquid and its
vapor in a closed container held at constant temperature.
A. Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation of Statement 1
B. Both the Statement 1 and Statement 2 are correct and Statement 2 is NOT the correct explanation of Statement 1
c. Statement 1 is correct but Statement 2 is not correct.
D. Statement 1 is not correct but Statement 2 is correct
E. Both the Statement 1 and Statement 2 are not correct


List two ways of increasing the strength of an electromagnet if the material of the electromagnet is fixed.


Find the value of \( \sin \left(\frac{1}{2} \cot ^{-1}\left(-\frac{3}{4}\right)\right) \)


For any square matrix \( \boldsymbol{A} \) with real numbers,
\( A+A^{\prime} \) is a symmetric and
\( A-A^{\prime} \) is a skew-symmetric


Polarity of carbonyl group increase with increase of
A. electronegative groups
B. electropositive groups
C . neutral group
D. none of these


Mention two functions of the AUG.


Write down the values of:
\( (\sqrt{5}+\sqrt{6})^{2} \)
A. \( \sqrt{5}+\sqrt{6}+\sqrt{30} \)
B. \( 11+2 \sqrt{30} \)
c. \( 11+\sqrt{30} \)
D. \( \sqrt{11}+60 \)


In the following figure, the area of the
shaded region is \( 20 \% \) of the area of the
whole circle centered at P. The angle
shown measures d degrees. What is its
measurement in radians?
\( A \cdot 1 \)
\( B \cdot \frac{2}{5} \pi \)
\( c \cdot \frac{4}{5} \pi \)
\( D \cdot \frac{2}{15} \pi \)
E \( \cdot \frac{4}{15} \pi \)


The following one is example to physical equilibrium:
A. solid \rightleftharpoons liquid
В. \( N_{2}+3 H_{2} \rightleftharpoons N H_{3} \)
\( \mathrm{c} \cdot \mathrm{CaCO}_{3} \rightleftharpoons \mathrm{CaO}+\mathrm{CO}_{2} \)
\( \mathrm{D} \cdot 2 \mathrm{SO}_{2}+\mathrm{O}_{2} \rightleftharpoons 2 \mathrm{SO}_{3} \)


Which of the following can be oxidized
by \( \boldsymbol{S O}_{2} \)
\( \mathbf{A} \cdot M g \)
в. \( K_{2} C r_{2} O_{7} \)
\( \mathbf{c} \cdot K M n O_{4} \)
D. All


To which group, an element with atomic number 88 will belong?
A. Group 12
B. Group 17
c. Group 10
D. Group 2


(i) Name the method of refining to obtain silicon of high purity.
(ii) What is the role of \( S i O_{2} \) in the
extraction of copper?
(iii) What is the role of depressants in froth floatation process?


Assertion
A dipole \( P \) applies a force \( F \) on dipole \( Q \) and dipole \( Q \) applies a force \( F \) on dipole
\( \boldsymbol{P} \)
Reason
Action and reaction are equal and opposite.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


What is the oxidation number of \( \boldsymbol{H} \) and
\( C l \) in \( H C l O_{4} \) respectively?
\( A \cdot+1,+7 \)
B. +2,+6
\( \mathrm{c} \cdot+3,+7 \)
\( \mathrm{D} \cdot+2,+7 \)


Synaptonemal complex is characteristic of
A. Mitotic chromosomes
B. Leptotene chromosomes
c. Paired meiotic chromosomes
D. Metaphase


A retarding force is applied to stop a train. The train stops after 80 m. If the speed is doubled, then the distance
travelled when same retarding force is applied is
A. The same
B. Doubled
c. Halved
D. Four times


A long capillary glass tube of uniform diameter of \( 1 \mathrm{mm} \) is filled completely
with water and then held vertically in air. It is now opened at both ends. Find the length of the water column
remaining in the glass tube. Surface tension of water is \( 0.075 N / m .(g= \) \( 10 m / s^{2} \) and density of water is
\( \left.\mathbf{1 0}^{\mathbf{3}} \mathbf{k g} / \boldsymbol{m}^{\mathbf{3}}\right) \)
A. Zero
в. \( 1.5 \mathrm{cm} \)
\( c \cdot 3 \mathrm{cm} \)
D. \( 6 \mathrm{cm} \)


According to CIP Sequence rule, the correct arrangement in order of decreasing priority is :
A. \( -O H>C H_{2} O H>-C H O>-C O O H \)
в. \( -O H>C O O H>-C H O>-C H_{2} O H \)
с. \( -C O O H>O H>-C O H>-C H_{2} O H \)
D. \( -C O O H>C H O>-C H_{2} O H>-O H \)


An electric dipole of momentum \( \vec{p} \) is placed in a uniform electric field. The dipole is rotated through a very smal angle from equilibrium and is released. Prove that it executes simple harmonic motion with frequency \( f=\frac{1}{2 \pi} \sqrt{\frac{p E}{1}} \)
Where, \( I= \) moment of inertia of the
dipole.


If K.E. of a particle increases by \( 125 \% \) then what is the \( \% \) increase in its
momentum?


Peptization is a process of converting a freshly prepared precipitate into a colloidal form by the addition of a suitable electrolyte.
State whether the statement is True or
False.


Fill in the blank.
In circular motion, force is always
to the displacement.
A. Perpendicular
B. Parallel
c. opposite
D. None


The binding energy of a nucleus is equivalent to
A. the mass of nucleus
B. the mass of proton
c. the mass of neutron
D. the mass defect of nucleus


The off springs produced by ........... detach from the parent body after they mature completely.
A. Budding
B. Binary fission
c. Fragmentation
D. Spore formers


According to the Nernst equation, the potential of an electrode changes by
\( \mathbf{5 9 . 2} \boldsymbol{m} \boldsymbol{V} \) whenever the ratio of the
oxidized and the reduced species
changes by a factor of 10 at \( 25^{\circ} \mathrm{C} \). What would be the corresponding change in the electrode potential if the
experiment is carried out at \( 30^{\circ} \mathrm{C} \) ?
A. \( 59.2 \mathrm{mV} \)
в. \( 71.0 \mathrm{mV} \)
c. \( 60.2 \mathrm{mV} \)
D. None of above


What do we call the gravitational force between the earth and an object?


Evaluate the given limit:
\( \lim _{x \rightarrow 0} \frac{a x+x \cos x}{b \sin x} \)


A metal plate can be heated by
A. passing either a direct or alternating current through the plate.
B. placing in a time varying magnetic field.
c. placing in a space varying magnetic field, but does not vary with time.
D. both
(a) and
(b) are correct


If by radiation, all nitrogenase enzymes are inactivated, then there will be no
A. Fixation of nitrogen in legumes
B. Conversion from ammonia to nitrate in soil
c. conversion from nitrate to nitrite in legumes
D. None of the above


Which of the following is metabolic waste of protein metabolism?
\( A \cdot N H_{3}, \) urea and \( C O_{2} \)
B. Urea, oxygen and \( \mathrm{N}_{2} \)
c. Urea, ammonia and alanine
D. Urea, ammonia and creatinine


In the table properties of some
specimens are given.
\( \begin{array}{llll}\text { Specimen } & \begin{array}{l}\text { Melting } \\ \text { Point }\end{array} & \text { Shining } & \text { Malleabi } \\ \mathrm{P} & \text { High } & \text { more } & \text { No } \\ \mathrm{Q} & \text { High } & \text { less } & \text { No } \\ \mathrm{R} & \text { High } & \text { more } & \text { Yes } \\ \mathrm{S} & \text { Low } & \text { less } & \text { Yes }\end{array} \) Which specimen is precisely a metal?
\( \mathbf{A} \cdot \mathbf{R} \)
\( B . \quad \) О
\( c \cdot F \)
\( D \cdot S \)


Prophase is longer in
A. Mitosiss
B. Meiosis
c. Equal in both
D. Amitosis


A small steel ball falls through a syrup
with a speed of \( 10 \mathrm{cm} \mathrm{s}^{-1} . \) If the steel ball is given an upward force equal to its effective weight, it would move upward with a speed of
A \( \cdot 10 \mathrm{cm} \mathrm{s}^{-1} \)
B . \( 20 \mathrm{cm} \mathrm{s}^{-1} \)
\( \mathrm{c} \cdot 5 \mathrm{cm} \mathrm{s}^{-1} \)
D. \( 10 \sqrt{3} \mathrm{cms}^{-1} \)


In a triangle, the sum of two angles is
\( 118^{\circ} \) and their difference is \( 32^{\circ} ; \) find
each angle of the triangle.
A \( \cdot 75^{\circ}, 43^{\circ} \) and \( 62^{\circ} \)
B . \( 70^{\circ}, 48^{8} \) and \( 62^{\circ} \)
c. \( 85^{\circ}, 43^{\circ} \) and \( 52^{\circ} \)
D. \( 75^{\circ}, 53^{\circ} \) and \( 52^{\circ} \)


Match the items in column I with the
item in column II.
Select the correct alternative.
\( \mathbf{A} \cdot|-A,| I-C,|I|-D, \mid V-B \)
B. I-B, II-D, III-C, IV-A
c. \( \mid-\mathrm{C}, \) । \( -\mathrm{A}, \) III-B, \( 1 \mathrm{V}-\mathrm{D} \)
D. I-D, II-B, III-A, IV-C


Find the maximum number of identical
angles in \( C H_{2} F_{2} \) molecule.
\( A \cdot 4 \)
B. 3
\( c \cdot 5 \)
D.


Two wires having different densities are joined at \( x=0 . \) An incident wave \( y= \)
\( A_{0} \sin \left(\omega t-k_{1} x\right) \) travelling to the right
in the wire \( \boldsymbol{x} \leq \mathbf{0} . \) If \( \boldsymbol{K}_{\mathbf{2}} \) is the wave
vector of the transmitted wave, then the
ratio of the amplitude of the reflected wave to that of the incident wave is:
\( \mathbf{A} \cdot \frac{A_{r}}{A_{0}}=\frac{k_{1}-k_{2}}{k_{1}+k_{2}} \)
В. \( \frac{A_{r}}{A_{0}}=\frac{k_{1}+k_{2}}{k_{1}-k_{2}} \)
C. \( \frac{A_{r}}{A_{0}}=\frac{2 k_{1} k_{2}}{k_{1}+k_{2}} \)
D. \( \frac{A_{r}}{A_{0}}=\frac{2 k_{1}}{k_{1}+k_{2}} \)


Number of periods in the long form of periodic table is:
A . 17
B. 6
c. 7
D. 13


The line \( 2 x-3 y=4 \)
A . passes through origin and \( m=-\frac{2}{3} \)
B. passes through (2,0) and \( m=\frac{2}{3} \)
c. passes through (0,2) and \( m=\frac{2}{3} \)
D. passes through (0,-2) and \( m=-\frac{2}{3} \)


What will be the number of waves
formed by a Bohr electron in one complete revolution in its second orbit?
A. Three
B. Two
c. one
D. zero


Assertion
When a current flows in the coil of a
transformer then its core becomes hot.
Reason

The core of transformer is made of soft-
iron.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


In the figure, PQ and PR are the tangents to a circle with centre 0. If \( \angle P=\frac{4}{5} \angle O . \) Find \( \angle O \) and \( \angle P \)


Evaluate: \( \int_{0}^{\pi} \frac{x}{a^{2} \cos ^{2} x+b^{2} \sin ^{2} x} d x \)
\( \mathbf{A} \cdot \frac{\pi^{2}}{a b} \)
B. \( \frac{\pi^{2}}{2 a b} \)
\( \mathbf{C} \cdot \frac{2 \pi^{2}}{a b} \)
D. \( \frac{\pi^{2}}{4 a b} \)


lonization potential values of an element \( X \) are 104 kJ, 200 kJ, 420 kJ
2825 kJ per mole. Identify the group to which the element belongs?
A. \( I A \)
в. \( I I A \)
c. \( I I I A \)
D. \( I V A \)


S.I unit of Heat Capacity is


Which of the following elements can not
exhibit \( s p^{3} d \) hybridisation state:
A .
B.
\( c \cdot c \)
D. B


The pH value of saliva before meal is
and after meal is
A. 5,7.4
B. 7,10
c. 7.4,5.8
D. 2, 5


Two frames, one stationary and the
other moving, are initially coincident. Two observers in the two frames
observe a body initially at rest in the coincident frame. A constant force \( \boldsymbol{F} \)
starts acting on the body along horizontal axis, when moving frame starts to separate from the fixed frame.
Work done \( W \) as observed by the
stationary frame and \( W^{\prime} \) as observed
from the moving frame are compared to the each other as:
A \( \cdot W=W^{\prime} \)
в. \( W \neq W^{\prime} \)
c. \( w=\frac{1}{2} W^{\prime} \)
D. \( W=2 W^{\prime} \)


The increase in the length of a wire on stretching is \( 0.025 \% \). If its Poisson's
ratio is \( 0.4, \) then the percentage decrease in the diameter is :
A . 0.01
B. 0.02
c. 0.03
D. 0.04


Which of the following statement is
true?
\( \mathbf{A} \cdot g \) is same at all places on the surface of earth.
B. g has its maximum value at the equator.
C. \( g \) is less at the earth's surface than at a height above it or a depth below it.
D. \( g \) is greater at the poles than at the equator.


A metallic wire is stretched by
suspending a weight to it. If \( \alpha^{2} \) is the longitudinal strain and Y is its Young's modulus of elasticity, then show that the elastic potential energy per unit volume is given by \( 1 / 2 Y^{2} \)


The compound interest of the second year on Rs 3000 at \( 10 \% \) is Rs


The value of \( \tan ^{-1} x+\cot ^{-1} x \) is.
A . \( \pi \)
B. zero
\( c \cdot \frac{\pi}{2} \)
D.


Freezing of water and evaporation of water are both physical changes.


Vapour density of \( N_{2} O_{4} \) which
dissciates according to teh equilibrium
\( N_{2} O_{4}(g) \rightleftharpoons 2 N O_{2}(g) \) is 25.67 at \( 100^{\circ} C \)
and a pressure of 1 atm. Calculate the degree dissociatrion for the reaction.


Sun glasses are made of polaroids and
not of coloured glasses, why? Give examples for two commonly used devices which make use of polarised light.


If \( \boldsymbol{I}=\int \log (\sqrt{1-\boldsymbol{x}}+\sqrt{1+\boldsymbol{x}}) \boldsymbol{d} \boldsymbol{x} \)
then I is equal to
A \( \cdot x \log (\sqrt{1-x}+\sqrt{1+x})+\frac{1}{2} x+C \)
B・ \( _{x \log (\sqrt{1-x}+\sqrt{1+x})}+\frac{1}{2} \sin ^{-1} x+C \)
c. \( _{x \log (\sqrt{1-x}+\sqrt{1+x})}+\frac{1}{2} \sin ^{-1} x-\frac{1}{2} x+C \)
D. \( x \log (\sqrt{1-x}+\sqrt{1+x})+\frac{1}{2} \sin ^{-1} x+\frac{1}{2} x+C \)


The sum \( ^{20} C_{0}+^{20} C_{1}+^{20} C_{2}+\ldots . .+^{20} \)
\( C_{10} \) is equal to
A \( \cdot 2^{20}+\frac{20 !}{(10 !)^{2}} \)
В. \( 2^{19}+\frac{1}{2} \cdot \frac{20 !}{(10 !)^{2}} \)
C \( \cdot 2^{19}+^{20} C_{10} \)
D. none of these


\( H_{2} S O_{4} \) solution attached to a bulb in a
beaker:
A. cannot light the bulb
B. can light the bulb
c. diffuses the bulb
D. none of above


A car moves at a speed of \( 20 \mathrm{ms}^{-1} \) on a banked track and describes an arc of a circle of radius \( 40 \sqrt{3} . \) The angle of
banking is (take, \( \left.g=10 m s^{-2}\right) \)
A \( .25^{\circ} \)
B. 60
\( c \cdot 45 \)
D. 30
E \( .40^{\circ} \)


Differentiate w.r.t. \( \boldsymbol{x} \)
\( \boldsymbol{y}=\boldsymbol{e}^{\boldsymbol{3} \boldsymbol{x}} \sin \boldsymbol{4} \boldsymbol{x} \)


Prove that \( \boldsymbol{I}=\int \frac{\boldsymbol{t}+\mathbf{1}}{\left(-\boldsymbol{t}^{2}+\boldsymbol{t}+\mathbf{3}\right)} \)


In experiment of convection heat transfer water inside the pipe, completely gets heated (with the application of heat source) can be explained best by which of the following statements,
A. Differences in densities produced between the bottom and the top of water, in turn produce the driving buoyant force which continuously circulates the water,
B. A continuous conductive channel is produced between the different layers of water in the pipe which circulates the heat
c. both the above explains correctly
D. all of the above


In the given figure, \( D E \| B C \), if \( A D= \)
\( 1.5 \mathrm{cm}, B D=2 A D \) then
\( \frac{a r(\Delta A D E)}{a r(t r a p e z i u m B C E D)} \)


In the reaction, the product \( (X) \) is:
\( \mathbf{A} \)
\( B \)
\( \mathbf{C} \)
\( D \)


In an achromatic combination of two
prisms, the ratio of the deviations produced by the two prisms is \( 2: 3, \) the ratio of their dispersive powers is
A .2: 3
B. 3:2
\( c \cdot 1: 1 \)
D. 4: 9


\( \operatorname{et} z=\left|\begin{array}{ccc}1 & 1+2 i & -5 i \\ 1-2 i & -3 & 5+3 i \\ 5 i & 5-3 i & 7\end{array}\right| \) then
A. z is purely real
B. z is purely imaginary
C \( \cdot(z-\bar{z}) \) i is real and imaginary both
D \( \cdot(z+\bar{z})=0 \)


Masses of \( 1 g, 2 g, 3 g \ldots .100 g \)
are suspended from the \( 1 \mathrm{cm}, 2 \mathrm{cm}, 3 \mathrm{cm} \) \( \ldots .100 \mathrm{cm} \) marks of a light metre scale. The system will be supported in equilibrium at :
\( \mathbf{A} \cdot 60 \mathrm{cm} \)
в. \( 67 \mathrm{cm} \)
\( \mathrm{c} .55 \mathrm{cm} \)
D. \( 72 \mathrm{cm} \)


Prove cos is continuous on R.


Which statement describes human
cells formed by meiosis?
A. They are genetically identical and they become gametes.
B. They are genetically identical and they become tissues.
C. They are not genetically identical and they become gametes.
D. They are not genetically identical and they become tissues.


Which of these is an accelerated form of
dialysis?
A. Electro dialysis
B. Ultra filtration
c. Ultra centrifugation
D. None of these


Magnetic moment \( 2.84 B M \) is given by
(Atomic numbers : \( \boldsymbol{N} \boldsymbol{i}=\mathbf{2 8}, \boldsymbol{T} \boldsymbol{i}= \)
\( \mathbf{2 2}, \mathbf{C r}=\mathbf{2 4}, \mathbf{C o}=\mathbf{2 7}) \)
A \( \cdot C r^{2} \)
в. \( C o^{2} \)
c. \( N i^{2} \)
D. \( T i^{3} \)


The adjoining figures represent three cases of a ray passing through a prism of an angle \( A \). Which of the following figure represents the minimum deviation condition
A.
B. 2
\( c .3 \)
D. None of these


\( \ln \) a fuel cell \( H_{2} \) and \( O_{2} \) react to
produce electricity. In the process \( \boldsymbol{H}_{2} \)
gas is oxidized at anode and \( O_{2} \) at
cathode. If 67.2 litre of \( H_{2} \) at STP reacts
in 15 minutes. The average current
produced is:
\( A \cdot 643.33 \mathrm{A} \)
B. 642.33 А
c. \( 682.33 \mathrm{A} \)
D. None of the above


Work done by all forces in ring in 0 to
\( \left(\frac{n}{\omega}\right) \) time interval is
\( A \)
в. \( \frac{1}{8} \frac{\left(B_{0} Q R\right)^{2}}{m} \)
c. \( \frac{1}{4} \frac{\left(B_{0} Q R\right)^{2}}{m} \)
D. \( \frac{1}{2} \frac{\left(B_{0} Q R\right)^{2}}{m} \)


Assertion
True solutions do not exhibit Tyndal effect.
Reason
In true solutions, size of solute particles is much smaller than the wavelength of light used.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


The percentage of marks obtained by the students in a class of 50 are given
below. Find the mean for the following
data.
Marks \( \begin{array}{lll}\mathbf{4 0}- & \mathbf{5 0}- & \mathbf{6 0}- \\ \mathbf{5 0} & \mathbf{6 0} & \mathbf{7 0}\end{array} \)
\( (\%) \)
Number
of
12
14
students
A . \( 64.6 \% \)
B . \( 65.6 \% \)
c. \( 66.6 \% \)
D. \( 67.6 \% \)


The condition for a uniform spherical mass \( m \) of radius \( r \) to be a black hole is
\( :[G=\text { gravitational constant and } g= \)
acceleration due to gravity].
\( ^{\mathrm{A}}\left(\frac{2 G m}{r}\right)^{1 / 2} \leq c \)
\( ^{\mathrm{B}}\left(\frac{2 g m}{r}\right)^{1 / 2}=c \)
\( \left(\frac{2 G m}{r}\right)^{1 / 2} \geq c \)
\( ^{\mathrm{D}}\left(\frac{g m}{r}\right)^{1 / 2} \geq c \)


If one body collides with another body of same mass at rest inelastically, the ratio of their speeds after collision shall
be-
\( A \)
в. \( \frac{1-e}{1+e} \)
c. \( \frac{1+e}{1-e} \)
\( D \cdot 1 \)


State whether true or false.
Newton's first law of motion gives the concept of momentum.
A. True
B. False


The mean of all the factors of 12 is
A \( \cdot 3 \frac{2}{3} \)
в. \( 4 \frac{3}{2} \)
\( c \cdot \frac{2}{3} \)
D. 12


The reaction is of first order in each
diagram, with an equilibrium constant of \( 10^{4} . \) For the conversion of chair form
to boat form \( e^{-E a / R T}=4.35 \times 10^{-8} \mathrm{at} \)
\( 298 K \) with pre-exponential factor of
\( 10^{12} s^{-1} . \) Apparent rate constant \( \left(=k_{A}\right) \)
at \( 298 K \) is:
A. \( 4.35 \times 10^{4} s^{-1} \)
в. \( 4.35 \times 10^{8} s^{-1} \)
c. \( 4.35 \times 10^{-8} s^{-1} \)
D. \( 4.35 \times 10^{12} s^{-1} \)


The relationship between A.C voltage and time in Sl unit is \( V= \)
\( 120 \sin (100 \pi T) \cos (100 \pi t) \) volt value
of peak voltage and frequency will be :
A. 120 volt and 100 \( \mathrm{Hz} \)
B . \( \frac{120}{\sqrt{2}} \) volt and \( 100 \mathrm{Hz} \)
c. 60 volt and 200 Hz
D. 60 volt and 100 нz


Usually refractory metals are used in
construction of furances because:
This question has multiple correct options
A. they are chemically inert
B. their melting point is high
C. they can withstand high temperature
D. none of the above


A circular table has a radius of \( 1 \mathrm{m} \) and
mass 20 kg. It has 4 legs of 1 m each
fixed symmetrically on its circumference. The maximum weight which can be placed anywhere on this
table without toppling it is :
A \( .84 .3 \mathrm{kg} \)
в. \( 34.8 \mathrm{kg} \)
c. \( 48.3 \mathrm{kg} \)
D. \( 43.8 \mathrm{kg} \)


The relation, between current density
and drift velocity \( v_{d} \) is?
A \( . j=n e v_{d} \)
B. \( j=\frac{n e}{v_{d}} \)
C. \( j=\frac{v_{d} e}{n} \)
D. \( j=n e v_{d}^{2} \)


Nucleosome core is intimately associated with
A . 160 bp DNA
B. 210 bp DNA
c. 250 bp DNA
D. 100 pp DNA


Maximum value of \( 1+ \)
\( 8 \sin ^{2}\left(x^{2}\right) \cos ^{2}\left(x^{2}\right) \) is
A. 3
B. -
\( c \cdot-8 \)
D.


Find the four numbers in A.P, whose
sum is 50 and in which the greatest
number is four times the least.


The movement of plant towards the direction of light is known as
A. Ciliary movement
B. Autotropic movement
c. Phototropic movement
D. Heterotropic movement


The kinetic energy for 14 grams of nitrogen gas at \( 127^{0} C \) is nearly (mol.
mass of nitrogen \( =28 \) and gas constant \( \left.=8.31 J K^{-1} m o l^{-1}\right) \)
\begin{tabular}{l}
A \( .1230 \mathrm{J} \) \\
\hline
\end{tabular}
B. 4015 J
c. 2493 J
D. \( 990 J \)


Give a brief account on Expiratory
capacity (EC)


In oxidative phosphorylation, oxidation and phosphorylation take place simultaneously and forms:
\( A \). NADP
B. DPN
c. Pyruvic acid
D. ATP
E. Both B and


Light travels at maximum speed in
A. Air
B. Water
c. vacuum
D. None of these


What advantage does an
electromagnet have over a permanent
magnet?
A. An electromagnet can be used for picking up more metals
B. An electromagnet can be switched off.
c. An electromagnet is lighter
D. All of these


Show that \( f(x)=\sin x \) is an increasing
function on \( (-\pi / 2, \pi / 2) ? \)


At present, electricity production is not taking place using
A. nuclear fission
B. nuclear fusion
c. burning of coil
D. it is being produced using all the above methods


Select the species which are isoelectronic.
A \( \cdot F^{-}, M g^{2+} \)
в. \( A r, K \)
c. \( M g^{2+}, O^{-} \)
D. \( R b^{+}, A r \)


The total cost \( C(x) \) associated with the
production of x units of an item is given
by \( C(x)=0.05 x^{3}-0.02 x^{2}+30 x+ \)
5000. Find the marginal cost when 3 units are produced, where by marginal
cost we mean the instantaneous rate of
change of total cost at any level of
output.


What is the oxidation state of \( K \) in \( K O_{2} \)
\( ? \)
A . -1
B. -2
\( c \cdot+1 \)
D. 0


Find the absolute maximum and the
absolute minimum value of the
following function in the given
intervals.
\( f(x)=3 x^{4}-8 x^{3}+12 x^{2}-48 x+25 \)
in \( [\mathbf{0}, \mathbf{3}] \)


shows a rod of length I resting on a wall and the floor. Its lower end A is pulled
towards left with a constant velocity \( v \) Find the velocity of the other end \( B \) downward when the rod makes an angle
\( \theta \) with horizontal.


Find the area of the triangle formed by joining the mid-points of the sides of the triangle whose vertices are (0,-1),(2,1) and \( (0,3) . \) Find the ratio of this area to the area of the given triangle.


Osteoporosis, an age-related disease of
skeletal system, may occur due to the.
A. Immune disorder affecting neuromuscular junction leading to fatigue
B. High concentration of \( C a^{++} \) and \( N a^{+} \)
C . Decreased level of oestrogen
D. Accumulation of uric acid leading to inflammation of joints


In Dryopteris, the opening mechanism of sporangium is effectively operated by
A. Stalk
B. Stomium
c. Annulus
D. Peristome


During which of the following process the diaphragm moves down?
A. Inspiration
B. Expiration
c. coughing
D. None of the above


Give the correct IUPAC names of the
following:
Isoprene


Two balls are drawn at random with
replacement from a box containing 10
black and 8 red balls. Find the
probability that the first ball is black and the second is red.


Match the following:
\( \begin{array}{ll}\text { List - I } & \text { List - II } \\ \text { A. } P_{c} & \text { (i) } 3 b \\ \text { B. } V_{c} & \text { (ii) } 8 a / 27 b R \\ \text { C. } T_{c} & \text { (iii) } a / 27 b^{2}\end{array} \)
\( \mathbf{A} \cdot A-(i), B-(i i), C-(i i i) \)
B . \( A-(i i i), B-(i i), C-(i) \)
c. \( A-(i i), B-(i i i), C-(i) \)
D. \( A-(i i i), B-(i), C-(i i) \)


A sample of a gas at STP contains \( 3.01 \times 10^{23} \) molecules and has a mass
of 22.0 grams. This gas is most likely:
A. \( C O_{2} \)
в. \( O_{2} \)
\( c \cdot N_{2} \)
D. co
E. NO


How does the metallic character vary
across the period? Explain.


How much does \( -5 a^{2}+3 a-5 b^{2} \)
\( \operatorname{exceed} 7 a^{2}+4 a-9 b^{2} ? \)


If \( \sin ^{-1} \frac{x}{5}+\operatorname{cosec}^{-1} \frac{5}{4}=\frac{\pi}{2}, \) then \( x \) is
equal to:
\( A \)
B. 4
\( c \cdot 3 \)
D. 5


The coefficient of the term independent of \( x \) in the expansion of
\( \left(\frac{x+1}{x^{\frac{2}{3}}-x^{\frac{1}{3}}+1}-\frac{x-1}{x-x^{\frac{1}{2}}}\right)^{10} \)
\( A \cdot 70 \)
в. 112
c. 105
D. 210


A manufacturer has three machine
operators \( A, B \) and \( C . \) The first operator \( A \) produces \( 1 \% \) defective items,
whereas the other two operators \( B \) and
\( C \) produce \( 5 \% \) and \( 7 \% \) defective items
respectively. \( A \) is on the job for \( 50 \% \) of
the time, \( B \) is on the job for \( 30 \% \) of the
time and \( C \) is on the job for \( 20 \% \) of the
time. A defective item is produced, what is the probability that it was produced
by \( \boldsymbol{A} \) ?


Which among the following is a feature of India's population?
A. High birth rate
B. High death rate
c. High female literacy ratio
D. Low life expectancy


Use Euclid division Lemma to show that
the cube of any positive integer Is either of the form \( 9 m, 9 m+1 \) or, \( 9 m+8 \) for
some integer \( \boldsymbol{m} \)


Consider the following statements \( A \) and \( \mathrm{B} \) and identify the correct answer:
\( A: \ln \) an elastic collision, if a body
suffers a head on collision with another
of same mass at rest, the first body
comes to rest while the other starts
moving with the velocity of the first one.
\( B: \) Two bodies of equal masses suffering a head-on elastic collision merely exchanges their velocities.
A. A and B are true
B. A and B are false
c. A is true but B is false
D. A is false but B is true


Out of \( C \) and \( C O, \) which is a better
reducing agent for \( Z n O ? \)


Assertion
Sandy areas have a wide range of daily
temperature.
Reason
Sand soil particles are good conductors
of heat.
\( A . \) If \( A \) and \( R \) both are true and \( R \) is correct explanation of
\( A \)
B. If \( A \) and \( R \) both are true but \( R \) is not correct explanation of \( \mathrm{A} \)
C. If \( A \) is correct and \( R \) is wrong.
D. If A is wrong and R is true.


Explain the postulates of Molecular Orbital Theory.


Two points of a rod move with velocities \( 3 v \) and \( v \) perpendicular to the rod and in the same direction,
separated by a distance 'r'. at Then the angular velocity of rod is :
A \( \cdot \frac{4 v}{r} \)
в. \( \frac{3 v}{r} \)
c. \( \frac{2 v}{r} \)
D. \( \frac{v}{r} \)


Minimum photocurrent which must be passed through the circuit
A . 2.88
B. 1.44
\( c \cdot 2.08 \)
D. 0.64


If \( \boldsymbol{A}=\left|\begin{array}{c}-\mathbf{2} \\ \mathbf{4} \\ \mathbf{5}\end{array}\right|, \boldsymbol{B}=|\mathbf{1} \quad \mathbf{3}-\mathbf{6}|, \) State
whether ist is true or false \( (A B)^{1}= \)
\( \boldsymbol{B}^{1} \boldsymbol{A}^{1} \)
A. True
B. False


Which of the following is not a natural
polymer?
A. wool
B. Silk
c. cotton
D. Teflon


A force-time graph for a linear motion is
shown in the figure where the segments
are circular. The linear momentum
gained between zero and 8 second is :
A . \( -2 \pi \) Newton seconds
B. 0 Newton seconds
c. \( 4 \pi \) Newton seconds
D. \( -6 \pi \) Newton seconds


Which of following is the fundamental cause of electron donor effect of alky
radicals?
A . tleffect
B. \( + \) R effect
c. hyperconjugation
D. electrometric effect


\( \int \frac{x}{\left(x^{2}-a^{2}\right)\left(x^{2}-b^{2}\right)} d x \) is equal to
\( \frac{1}{k\left(b^{2}-a^{2}\right)} \ln \frac{\left(x^{2}-b^{2}\right)}{\left(x^{2}-a^{2}\right)} \cdot \) Find \( k \)


Acetic acid dissolved in benzene shows
a molecular weight of
A . 60
B. 120
c. 180
D. 240


Photo-diode is operated in reverse bias
because
A. When the diode is reversed biased, no ordinary current flows and the detection of the photo-current is much easier
B. When the diode is reversed biased, ordinary current flows and the detection of the photo-current is much easier
C. In reverse biased it will conduct a lot of current and can't detect the small amount of excess current produced by the photoelectric effect
D. All of the above


Students \( A, B \) and \( C \) measure the
diameter of a wire using three different screw gauges of least count 0.01
\( \mathrm{cm}, 0.05 \mathrm{cm} \) and \( 0.001 \mathrm{cm} \) respectively. Each one makes 10 measurements.The
measurements will be more precise for
\( A \cdot A \)
B. B
\( c \cdot c \)
D. all


A novel species with double stranded genetic material consists of 5 bases
namely P.Q. R. S. T. with percentages
given below.
Percentage 22
\( 28 \quad 22 \)
Based on the above information, which
ONE of the following infrences is NOT supported by the observation?
A. S- base pairs with T, and Q base pairs with R
B. S base pairs with \( Q \),and T base pairs with \( Q \)
C. P base pairs with \( R \), and \( S \) base pairs with \( Q \)
D. P base pairs with \( \mathrm{R} \), and T base pairs with \( \mathrm{Q} \)


Haemodialysis is a treatment option for patients with malfunctions of
A. Kidney
B. Heart
c. Liver
D. Lungs


Compound \( A \) should be:
A. \( D- \) glucose
B. \( D \) - fructose
c. \( L- \) glucose
D. \( L \) -fructose


Solve: \( 5-\frac{2 d+7}{9}=0 \)
A . 19
B. 14
\( c .9 \)
D.


\( \tan ^{-1} x+\cot ^{-1} x=\frac{\pi}{2}, x \in \dot{R} \)
A. True
B. False


Calculate the range and coefficient of range from the following data:
Number of trees planted in 6 months:
\( \mathbf{1 8 6}, \mathbf{2 3 4}, \mathbf{4 6 5}, \mathbf{3 6 1}, \mathbf{2 9 0}, \mathbf{1 4 2} \)


Give balanced equation for each of the following:
Oxidation of carbon with concentrated
nitric acid:


The variance and \( S D \) of the following is
\( \begin{array}{cccccc}\boldsymbol{x} & \mathbf{4 . 5} & \mathbf{1 4 . 5} & \mathbf{2 4 . 5} & \mathbf{3 4 . 5} & \mathbf{4 4 . 5} \\ f & 1 & 5 & 12 & 22 & 17\end{array} \)
\( \mathbf{A} \cdot 176,13 \)
B. 175.9,13.26
\( \mathbf{c} .8 .56,13 \)
D. 4.1,12.13


If the vertices \( A, B, C \) of a triangle \( A B C \) are the points with position vectors
\( \boldsymbol{a}_{1} \hat{\boldsymbol{i}}+\boldsymbol{a}_{2} \hat{\boldsymbol{j}}+\boldsymbol{a}_{3} \hat{\boldsymbol{k}}, \boldsymbol{b}_{1} \hat{\boldsymbol{i}}+\boldsymbol{b}_{2} \hat{\boldsymbol{j}}+\boldsymbol{b}_{3} \hat{\boldsymbol{k}}, \boldsymbol{c}_{1} \hat{\boldsymbol{i}}+ \)
\( c_{2} \hat{j}+c_{3} \hat{k} \) respectively, what are the
vectors determined
by its sides? Find the length of these
vectors.


A transverse sinusoidal wave of
amplitude a, wavelength \( \lambda \) and frequency \( \boldsymbol{f} \) is travelling on a stretched string. The maximum speed of any point on the string is \( \frac{v}{10}, \) where \( v \) is the
speed of propagation of the wave. If \( \boldsymbol{a}= \)
\( 10^{-3} m \) and \( v=10 \mathrm{m} / \mathrm{s}, \) then \( \lambda \) is given
by This question has multiple correct options
\( \mathbf{A} \cdot \lambda=2 \pi \times 10^{-2} m \)
B. \( \lambda=10^{-3} m \)
C \( . \lambda=\pi \times 10^{-2} \)
D. \( \lambda=2 \pi \times 10^{-3} \)


Find the value of determinant \( \left|\begin{array}{cc}\mathbf{5} & -\mathbf{3} \\ -\mathbf{7} & -\mathbf{4}\end{array}\right| \)


Which has highest \( p H ? \)
A. \( C H_{3} \) СООК
в. \( N a_{2} C O_{3} \)
c. \( N H_{4} C l \)
D. \( N a N O_{3} \)


A potentiometer wire of length \( 10 m \)
and resistance \( 10 \Omega \) per metre is
connected in series with a
resistance box and a 2 volt battery. If a potential difference of \( 100 m V \) is balanced across the whole length of potentiometer wire, then the resistance introduced in the resistance box will be:
A . \( 1900 \Omega \)
в. \( 900 \Omega \)
\( \mathbf{c} \cdot 190 \Omega \)
D. \( 90 \Omega \)


A vertical ring of radius \( r \) and
resistance \( \boldsymbol{R} \) falls vertically. lt is in
contact with two vertical rails which are
joined at the top. The rails are without friction and resistance. There is a
horizontal uniform magnetic field of
magnitude \( B \) perpendicular to the
plane of the ring and the rails. When the
speed of the ring is \( v, \) the current in the top horizontal of the rail section is
A . 0
B. \( \frac{2 B r v}{R} \)
\( ^{\mathrm{c}} \cdot \frac{4 B r v}{R} \)
D. \( \frac{8 B r v}{R} \)


Suppose \( \boldsymbol{A}=\left[\begin{array}{ccc}\mathbf{1} & \mathbf{- 1} & \mathbf{5} \\ \mathbf{4} & \mathbf{3} & \mathbf{7}\end{array}\right] \) find \( \mathbf{4} \boldsymbol{A} \)


A DC circuit contains \( 10 \Omega \) of resistance
in series with \( 10 H \) coil. The impedance
of the circuit is
A . \( 10 \Omega \)
B. 20\Omega
c. \( 1 \Omega \)
D. zero


Assertion
The matrix \( \left(\begin{array}{cccc}.1 & 0 & 0 & 0 \\ 0 & 2 & 0 & 0 \\ 0 & 0 & 3 & 0\end{array}\right) \) is a
diagonal matrix
Reason
\( A=\left(a_{i j}\right)_{m \times m} \) is a square matrix such
that entry \( a_{i j}=0 \forall i \neq j, \) then \( A \) is
called diagonal matrix.
A. Both (A) \& (R) are individually true \& (R) is correct explanation of (A),
B. Both (A) \& (R) are individually true but (R) is not the correct (proper) explanation of (A).
C. (A) is true but (R)is false,
D. (A) is false but (R ) is true.


Correct statement about products \( x \) and
y is :
A. Both gives Tollen's test.
B. Both gives Fehling test.
C. Both gives 2, 4-DNP test.
D. Oxygen atom present in both the products.


A gas is filled in a cylinder, its
temperature is increased by \( 20 \% \) on kelvin scale and volume is reduced by 10\%. How much percentage of the gas will leak out:
A . \( 40 \% \)
B. 30\%
c. \( 15 \% \)
D. \( 25 \% \)


A ladder is more apt to slip when you
are high up on its rung than when you are just begin to climb. Why?
A. When you are high up, the moment of force tending to rotate the ladder about its base increases, while in the latter case, the moment of the force is insufficient to cause slipping
B. When you are high up, the ladder is in unstable, equilibrium
C. As you climb up, your potential energy increases
D. When you are high up, the centre of gravity of the system shifts upwards so the ladder is unstable, while in the latter case the system is more stable


Of the following statements:
\( (\boldsymbol{P}) \boldsymbol{C}_{6} \boldsymbol{H}_{5} \boldsymbol{N}=\boldsymbol{C} \boldsymbol{H}-\boldsymbol{C}_{6} \boldsymbol{H}_{5} \) is a
Schiff's base.
( \( Q \) ) A dye is obtained by the reaction of
aniline and \( C_{6} H_{5} N^{+} \equiv N C l \)
\( (R) C_{6} H_{5} C H_{2} N H_{2} \) on treatment with \( \left[N a N O_{2}+H C l\right] \) gives diazonium salt
\( (S) p- \) Toluidine on treatment with
\( \left[H N O_{2}+H C l\right] \) gives diazonium salt
A . only \( (P) \) and \( (Q) \) are correct
B. only (P) and (R) are correct
c. only \( (R) \) and \( (S) \) are correct
D. \( (P),(Q) \) and \( (S) \) are correct


What are food preservatives? Name two such substances.


Find the distance between the points
(0,0) and \( (36,15) . \) Can you now find the
distance between the two towns \( A \) and
\( \boldsymbol{B} \)


The theoretical limits of poisson's ratio lies between -1 to 0.5 because
A. Shear modulus and bulk's modulus should be positive
B. Bulk's modulus is negative during compression
c. Shear modulus is negative during compression
D. Young's modulus should be always positive


Light of frequency \( 7.21 \times 10^{14} H z \) is
incident on a metal surface. Electrons
with a maximum speed of \( 6.0 \times \)
\( 10^{5} m / s \) are ejected from the surface.
What is the threshold frequency for photoemission of electrons?


Factorise \( a^{2}(b+c)-(b+c)^{3} \)
A \( \cdot(b+c)\left(a^{2}-(b+c)^{2}\right. \)
В \( \cdot(b-c)\left(a^{2}-(b+c)^{2}\right. \)
c. \( (b+c)\left(a^{2}+(b+c)^{2}\right) \)
D. None of these


The type of glass used in making lenses and prisms is :
A. A flint glass
B. Jena glass
c. Pyrex glass
D. Quartz glass


Which of the following nuclear reactions
is not possible?
A \( \cdot \frac{12}{6} C+_{6}^{12} C \longrightarrow_{10}^{20} N e+_{2}^{4} H e \)
B . \( _{4}^{9} B e+_{1}^{1} H \rightarrow_{3}^{6} L i+_{2}^{4} H e \)
C \( \cdot \frac{11}{5} B e+_{1}^{1} H \rightarrow_{4}^{9} B e+_{2}^{4} H e \)
D. \( _{3}^{7} L i+_{2}^{4} H e \longrightarrow_{1}^{1} H+_{4}^{10} B \)


Flower of Hibiscus is
A. Actinomorphic and epigynous
B. Actinomorphic and hypogynous
c. zygomorphic and hypogynous
D. Zygomorphic and epigynous


For the isotope \( _{6} C^{13}, \) the number of neutrons is:
\( A \cdot 6 \)
B. 7
c. 19
D. 13


Find the value of \( x, y, z \) if \( \left[\begin{array}{ll}\mathbf{4} & \mathbf{3} \\ \boldsymbol{x} & \mathbf{5}\end{array}\right]=\left[\begin{array}{ll}\boldsymbol{y} & \boldsymbol{z} \\ \mathbf{1} & \mathbf{5}\end{array}\right] \)


\( \frac{\sqrt{4}}{\frac{4}{4}} \)


Complex number \( z \) satisfy the equation
\( |z-(4 / z)|=2 . \) Locus of \( z \) if \( \left|z-z_{1}\right|= \)
\( \left|z-z_{2}\right|, \) where \( z_{1} \) and \( z_{2} \) are complex
numbers with the greatest and the least moduli, is
A. line parallel to the real axis
B. line parallel to the imaginary axis
c. line having a positive slope
D. line having a negative slope


Evaluate the following limits. \( \lim _{x \rightarrow 1} \frac{x^{2}+1}{x+1} \)


The \( \ldots \ldots . . . \) are root - like structures which
help in anchorage and absorption of water in the bryophytes.


What is the energy of electron in second
Bohr's orbit of \( L i^{2+} ? \)


A particle covers equal distances around a circular path in equal
intervals of time. It is said to be
A . at rest
B. move with uniform speed
c. move with constant speed
D. position of particle


The rate law for the single-step reaction \( \mathbf{2} \boldsymbol{A}+\boldsymbol{B} \rightarrow \mathbf{2} \boldsymbol{C}, \) is given by
A \( \cdot \) rate \( =k[A][B \)
B . rate \( =k[A]^{2}[B] \)
c. rate \( =k[2 A][B] \)
D. rate \( =k[A]^{2}[B]^{0} \)


Let \( z_{1} \) and \( z_{2} \) be two roots of the
equation \( z^{2}+a z+b=0, z \) being
complex, Further, assume that the
origin \( z_{1} \) and \( z_{2} \) form an equilateral
triangle. Then,
A \( \cdot a^{2}=b \)
в. \( a^{2}=2 b \)
\( \mathbf{c} \cdot a^{2}=3 b \)
D. \( a^{2}=4 b \)


Between two plates charged to \( 10 q \) there is an electric field \( E, \) what acceleration
will a positively charged particle, with a charge of \( q \) and a mass of \( m \)
experience in this region, due only the electric field?
\( ^{\text {A } \cdot \frac{21 q E}{m}} \)
в. \( \frac{11 q E}{m} \)
\( ^{\mathbf{c}} \cdot \frac{10 q E}{m} \)
D. \( \frac{q E}{m} \)


a bar magnet is made to fall through a
long vertical copper tube .The speed (v) of the magnet as a function of time (t)
is best represented by
\( A \)
B.
\( c \)
\( D \)


Fraction for 0.012 is:
A \( \frac{12}{100} \)
в. \( \frac{12}{10} \)
c. \( \frac{2}{1000} \)
D. \( \frac{12}{1000} \)


Which hormone has an anti-insulin
effect?
A. cortisol
B. Oxytocin
c. Aldosterone
D. Glucagon


The length of minute hand of a clock is
14 \( m . \) Calculate the speed at which the
tip of minute hand moves.


List various types of isomerism possible for coordination compounds, giving an example of each.


To measure high temperatures \( > \)
\( 2500^{\circ} \mathrm{C}, \) we use
A. constant volume gas thermometer
B. thermocouple
c. resistance thermometer
D. pyrometer


Assertion
lonic bonds are directional in nature
whereas covalent bonds are non-
directional.
Reason
According to orbital overlap concept,
the formation of a covalent bond
between two atoms results by pairing of electrons present in the valence shell
having same spins.
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


How many gm of solid KOH must be added to \( 100 \mathrm{ml} \) of a buffer solution,
which is 0.1 each with respect to acid \( \mathrm{H} \)
\( A \) and salt \( K A \) to make the pH of the
solution 6.0?
\( \left[\text { Given: } \mathrm{pK}_{-} \mathrm{a}(\mathrm{HA})=5\right] \)


Which of the following match is correct?
A. Hormone-Oxytocin, Effect-Milk ejection hormone
B. Hormone-Glucagon, Effect-Decreases blood sugar level
C. Hormone-Adrenaline, Effect-Decreases heart rate
D. Hormone-Thyroxine, Effect-Decreases BMR


\( \int \frac{e^{x}}{x}(1+x \cdot \ln x) d x \)


Rauvolfia serpentina belongs to family
A . Rubiaceae
B. Solanaceae
C. Malvaceae
D. Apocyanaceae


Pollution from the burning of fossil fuels can be reduced by:
I. using an incinerator
Il. using renewable energy
III. fixing catalytic converters in vehicles
A. I only
B. Il and III only
c. I and II only
D. I, II and III


The balanced equations for : "Carbon dioxide is passed through a concentrated aqueous solution of sodium chloride saturated with
ammonia"
A \( \cdot \) NaCl \( +N H_{4} O H+C O_{2} \rightarrow N H_{4} C l+N a H C O_{3} \)
B . \( 2 \mathrm{NaCl}+\mathrm{NH}_{4} \mathrm{OH}+\mathrm{CO}_{2} \rightarrow \mathrm{NH}_{4} \mathrm{Cl}+2 \mathrm{NaH} \mathrm{CO}_{3} \)
c. \( N a C l+N H_{4} O H+C O_{2} \rightarrow N H_{4} C O+N a H C l_{3} \)
D. \( N a C l+N H_{4} O H+C O_{2} \rightarrow N H_{3}+N a C l+H_{2} C O_{3} \)


In a Wheatstone's bridge, three resistances \( P, Q \) and \( R \) are connected in
three arms and the fourth arm is
formed by two resistances \( S_{1} \) and \( S_{2} \) connected in parallel. The condition for the bridge to be balanced will be :
\( ^{\mathrm{A}} \cdot \frac{P}{Q}=\frac{2 R}{S_{1}+S_{2}} \)
в. \( \frac{P}{Q}=\frac{R\left(S_{1}+S_{2}\right)}{S_{1} S_{2}} \)
c. \( \frac{P}{\bar{Q}}=\frac{R\left(S_{1}+S_{2}\right)}{2 S_{1} S_{2}} \)
D. \( \frac{P}{Q}=\frac{R}{S_{1}+S_{2}} \)


The acceleration of a moving body can be found from
A. Slope of velocity time graph
B. Area under velocity time graph
c. slope of distance time graph
D. Area under distance time graph


Pure phosphine is not combustible while impure phosphine is combustible. This combustibility is due to the
presence of :
A \( \cdot P_{2} H_{4} \)
в. \( N_{2} \)
c. \( P H_{5} \)
D. \( P_{2} O_{5} \)


Is the image formed by the plane mirror exactly of the same size as the object?


Which of the following is doesn't come under the barrier method of
contraception?
A. Condoms
B. Diaphragms
c. cervical caps
D. copper-releasing IUDs


The length of a rectangle is \( 4 \mathrm{cm} \) more than the breadth, and the perimeter is
\( 11 \mathrm{cm} \) more than the breadth. Find the
length and breadth of the rectangle.
A. \( l=1, b=7 \mathrm{cm} \)
В. \( l=6, b=3 \mathrm{cm} \)
c. \( l=7, b=8 \mathrm{cm} \)


One metal wire is kept in east-
west direction. \( I \) is the current flow
due west. Then, due to magnetic field \( \vec{B} \) of the earth on the wire is in the
Direction.
A. downward
B. Upwarddardpwardd
c. north
D. south


Write the equations involved in the
following reaction.
Williamson ether synthesis.


A conducting rod of length I and mass \( \mathrm{m} \) is moving down a smooth inclined plane of inclination \( \boldsymbol{\theta} \) with constant
velocity \( v . \) A current \( i \) is flowing in the
conductor in a direction perpendicular to paper inward. A vertically upward magnetic field \( \vec{B} \) exists in space. Then,
magnitude of magnetic field \( \vec{B} \) is:
A \( \cdot \frac{m g}{i l} \sin \theta \)
B. \( \frac{m g}{i l} \tan \theta \)
c. \( \frac{m g \cos \theta}{i l} \tan \theta \)
D. \( \frac{m g}{\text {ilsint}} \)


The number of sori on the sporophyll in Nephrolepis are
A . 20
B. 30
\( c \cdot 40 \)
D. 50


Chlorine is prepared by heating a
mixture of \( M n O_{2} \) and \( \mathrm{NaCl} \) with conc.
\( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \)
A . True
B. False


The volume of a perfect gas at NTP is
A. 22.4 litres
B. 2.24 litres
c. 100 litres
D. None of these


Phenol \( \frac{(i) N a O H}{(i i) C O_{2} / 140^{\circ} C} A \frac{H^{+} / H_{2} O}{\longrightarrow} \)
\( \boldsymbol{B} \frac{\boldsymbol{A} \boldsymbol{l}_{2} \boldsymbol{O}_{3}}{\boldsymbol{C H}_{3} \operatorname{COOH}, \boldsymbol{\Delta}} \boldsymbol{C} \)
In this reaction, the end product \( C \) is:
A. salicylaldehyde
B. salicylic acid
c. phenyl acetate
D. aspirin


Solve the following inequalities. \( C_{m-2}^{13}>C_{m}^{18}, m \epsilon N \)


A wire in the form of a circular loop of one turn carrying a current produces a magnetic field \( B \) at the centre. If the
same wire is looped into a coil of two turns and carries the same current, the
new value of magnetic induction at the
centre is:
\( A .3 B \)
в. \( 5 B \)
\( c .4 B \)
D. 2 \( B \)


From the diagram, relation between \( A \) and B.......


Identify the compounds among the following:
(a) Milk
(b) Sodium
(c) Calcium
Carbonate
(d) Methane
A. Milk, Calcium carbonate
B. Sodium
c. Calcium carbonate, Methane
D. None of the above


Simplify: \( (3.5 e-4.5 f)(1.5 e+4 f+ \)
\( e f)-4.5 e+10 f \)


A bike accelerates uniformly from rest to a speed of \( 7.10 \mathrm{m} / \mathrm{s} \) over a distance of
\( 35.4 m . \) Determine the acceleration of
the bike. \( \left(\operatorname{in} m / s^{2}\right) \)
\( \mathbf{A} \cdot 0.712 \)
в. 0.71
\( c .0 .7 \)
D. 7.71


State True or False.
\( X e F_{4} \) molecule is square planar in shape.
A. True
B. False


Assertion(A): \( \cos ^{-1} x \) and \( \tan ^{-1} x \) are
positive for all positive real values of \( x \)
in their domain.
Reason(R): The domain of \( f(x)= \)
\( \cos ^{-1} x+\tan ^{-1} x \) is [-1,1]
A. Both A and R are true and R is the correct explanation of A
B. Both A and R are true but R is not correct explanation of
c. A is true but R is false
D. A is false but R is true


If (1,-2,-2) and (0,2,1) are direction ratios of two lines, then the direction
cosines of a perpendicular to both the
lines are
\( ^{\mathrm{A}} \cdot\left(\frac{1}{3},-\frac{1}{3}, \frac{2}{3}\right) \)
в. \( \left(\frac{2}{3},-\frac{1}{3}, \frac{2}{3}\right) \)
\( ^{c} \cdot\left(-\frac{2}{3},-\frac{1}{3}, \frac{2}{3}\right) \)
D. \( \left(\frac{2}{\sqrt{14}},-\frac{1}{\sqrt{14}}, \frac{3}{\sqrt{14}}\right) \)


If \( \mathrm{M} \) is the mass of the earth and \( \mathrm{R} \) its
radius, the ratio of the gravitational acceleration and the gravitational constant is given by:
A \( \cdot \frac{R^{2}}{M} \)
в. \( \frac{M}{R^{2}} \)
c. \( M R^{2} \)
D. \( \frac{M}{R} \)


A transition metal 'X' has a
configuration \( [\mathrm{Ar}] 3 d^{4} \) in its +3
oxidation state, its atomic number is:
A . 25
B . 26
\( c \cdot 22 \)
D. 19


When a beam of light from an object
appears to meet at a point after reflection from a mirror then the image formed is known as:
A. Real image
B. Virtual image
c. Incident image
D. All


The enzyme involved in transcription is
A. RNA polymerase
B. DNA polymerase I
c. DNA polymerase II


Which among the following reaction is
an example of a zero order reaction?
B \( \cdot 2 N H_{3(g)} \stackrel{P t}{\rightarrow} N_{2(g)}+3 H_{2} \)
\( \mathrm{c} \cdot 2 \mathrm{H}_{2} \mathrm{O}_{2(l)} \rightarrow 2 \mathrm{H}_{2} \mathrm{O}_{(l)}+O_{2(g)} \)
D. \( H_{2(g)}+I_{2(g)} \rightarrow 2 H I_{(g)} \)


Which of the following is not a hormone secreted by the ovaries?
A. Estrogen
B. Progesterone
c. oxytocin
D. None of the above


In the phase diagram shown, the point
corresponds to the triple point of water
The regions I, II and III respectively
correspond to phases:
A . liquid, solid, vapour
B. solid, liquid, vapour
c. liquid, vapour, solid
D. solid, vapour, liquid


Coal gas mainly consists of high molecular mass aromatic
hydrocarbons.
A. True
B. False


The value of \( p \) for which the roots are
real and equal of the following equation \( p x(x-3)+9=0 \) is


The tertiary alkyl halide is called as tertiary because:
A. the functional group attached primary carbon atom
B. the functional group attached to secondary carbon atom
C. the functional group attached to tertiary carbon atom
D. none of these


The name for ethers is
alkoxy-alkanes.
A. IUAPC
c. IUPAC


The points with co-ordinates \( (2 a, 3 a) \) (3b, 2b) and (c,c) are collonear?
A. For no value of \( a, b, c \)
B. For all values of \( a, b, c \)
c. If a \( , c / 5 \) b are in \( \mathrm{H.P} \)
D. \( 5 a=c \)


Given \( (1+x)^{n} \geq(1+n x), \) for all
natural number \( n, \) where \( x>-n . \) What
will be the value of \( n \)


The number of growth rings (sum of the rings of spring wood and autumn wood) in the year 2000 is found to be \( 20 . \) What
will be the number of annual rings in
\( 2018 ? \)
A . 38
B. 8
\( c \cdot 28 \)
D. 18


\( \frac{A}{S} \)


The atomic and ionic radii \( \left(\mathrm{M}^{3+} \) ions) of \right.
Lanthanide elements decrease with
increase in atomic number. This effect is
called:
A. Lanthanoid contraction
B. f-fransition
c. Actinoid contraction
D. shielding effect


If \( \boldsymbol{A}=\{\mathbf{2}, \mathbf{3}, \mathbf{4}, \mathbf{5}, \mathbf{7}, \mathbf{9}\}, \boldsymbol{B}= \)
\( \{\mathbf{2}, \mathbf{3}, \mathbf{4}, \mathbf{5}, \mathbf{6}\} \) then \( \boldsymbol{B}-\boldsymbol{A}= \)


Which of the following forms a basic oxide?
\( A \cdot B \)
в. T
\( c \cdot A \)
D. Ga
E. None of the above


Mention the post fertilisation changes
that occur in a flower.


Two point charges \( Q \) and \( -Q / 4 \) are
separated by a distance \( x . \) Then:
This question has multiple correct options
A. potential is zero at a point on the axis which is \( x / 3 \) on the right side of the charge \( -Q / 4 \)
B. potential is zero at a point on the axis which is \( x / 5 \) on the left side of the charge \( -Q / 4 \)
C. electric field is zero at a point on the axis which is at a distance \( x \) on the right side of the charge \( -Q / 4 \)
D. there exist two points on the axis where electric field is zero


\( \boldsymbol{H}_{2} S \) acts only as reducing agent while
\( S O_{2} \) can act both as reducing agent
and oxidising agent. Explain.


A and \( \mathrm{B} \) are the centres of two circles
that just touch each other at \( P \) If \( A \) is
\( (4,1), B \) is (2,2) and the radii of the
circles are 2 and 3 respectively then \( P \)
has coordinates
\( A \cdot(4,3) \)
B. (3,3)
\( c \cdot(16 / 5,7 / 5) \)
D. \( (4 / 5,4 / 5) \)


An atomic hydrogen is:
A. Electrically neutral
B. positively charged
C . negatively charged
D. a free radical with one odd electron


Why must electrostatic field at the
surface of a charged conductor be
perpendicular to every point on it?


Simple epithelium is a tissue in which
the cells are
A. Hardened and provide support to the organ
B. Cemented directly to one another to form a single layer
C. Continuously dividing to provide form to an organ
D. Loosely connected to one another to form an irregular organ


Construct a triangle \( A B C, \) given: \( B C=7 \)
\( \mathrm{cm}, \mathrm{AB}-\mathrm{AC}=1 \mathrm{cm} \) and \( \angle A B C=45^{\circ} \)
Measure the lengths of \( A B \) and \( A C \).
\( A \cdot A B=8.6 \mathrm{cm}: A C=7.6 \mathrm{cm} \)
B. AB = 2.7 cm: AC = 1.7 cm
\( \mathrm{C} \cdot \mathrm{AB}=6.1 \mathrm{cm}: \mathrm{AC}=5.1 \mathrm{cm} \)
D. Data insufficient


t is given that rate of heat transfer in convection is directly proportional to area of plate across which fluid flows \( \boldsymbol{A} \) , density of fluid \( (\rho), \) velocity of flow \( (V \) ,temperature difference
\( (t) \) with
proportionality constant of 2 units.Also fluid is flowing across edge to edge on a square plate of side length of 0.1 unit with density of fluid is 10 units and
velocity of 2 units. Then what will be the rate of heat conducted through the plate if temperature difference between plate and fluid is unity?(assume that all \( u n i t s \) are in international standards


Among the following, in how many cases equilibrium \( C a C O_{3}(s) \rightleftharpoons \) \( \boldsymbol{C a O}(s)+\boldsymbol{C O}_{2}(\boldsymbol{g}) \) will shift in forward
direction?
(i) addition of \( C a C O_{3}(s) \)
(ii) addition of \( \operatorname{CaO}(s) \)
(iii) addition of \( C O_{2}(g) \)
(iv) addition of \( N_{2} \) at constant volume
(v) addition of \( N_{2} \) at constant pressure
(vi) increase in temperature
(vii) increase in pressure
(vii) addition of \( \boldsymbol{H} \boldsymbol{C l} \)
(ix) addition of \( N a O H \)


Find the principal value of:
\( \sin ^{-1}\left(-\frac{\sqrt{3}}{2}\right)+\operatorname{cosec}^{-1}\left(-\frac{2}{\sqrt{3}}\right) \)


If \( \frac{z+1}{z+i} \) is purely imaginary, then z lies
on a
A. straight lone
B. circle
c. circle with radius 1
D. circle passing through (1,1)


An organic compound on analysis gave \( \boldsymbol{C}=\mathbf{4 2 . 8 \%}, \boldsymbol{H}=\mathbf{7 . 2 0 \%}, \) and \( \boldsymbol{N}=\mathbf{5 0 \%} \)
Volume of 1 g of the compound was found to be \( 200 \mathrm{mL} \) at STP. Molecular
formula of the compound is :
A \( \cdot C_{4} H_{8} N_{4} \)
B. \( C_{16} H_{32} N_{16} \)
c. \( C_{12} H_{24} N_{12} \)
D. \( C_{2} H_{4} N_{2} \)


A wet cotton handkerchief soaked in
alcohol will not each fire even it is set
fire to? Why?


Compute \( : \lim _{x \rightarrow \infty} \frac{(\sqrt{x^{2}}+x-x)}{x} \)


The power of a progressive wave of wave
speed \( \mathbf{v} \) is the energy supplied to a medium of length \( v \) in one second :
A. True
B. False


The radius of curvature of the convex
surface of a plano-convex lens is \( 10 \mathrm{cm} \)
What is the focal length of the plano-
convex lens? (Here \( \mu=1.5) \)
\( \mathbf{A} \cdot 10 \mathrm{cm} \)
B. \( 20 \mathrm{cm} \)
\( \mathbf{c} \cdot 15 \mathrm{cm} \)
D. \( 5 \mathrm{cm} \)


Prove that: \( \cos ^{2} \boldsymbol{\alpha}+\cos ^{2}(\boldsymbol{\alpha}+\boldsymbol{\beta})- \)
\( \boldsymbol{2} \cos \boldsymbol{\alpha} \cos \boldsymbol{\beta} \cos (\boldsymbol{\alpha}+\boldsymbol{\beta})=\sin ^{2} \boldsymbol{\beta} \)


Two trains, each \( 50 \mathrm{m} \) long are travelling in opposite direction with velocity 10 \( \mathrm{m} / \mathrm{s} \) and \( 15 \mathrm{m} / \mathrm{s} \) The time of crossing is:
A \( .2 s \)
B. \( 4 s \)
c. \( 2 \sqrt{3} s \)
D. \( 4 \sqrt{3} s \)


Select the correct order of bond angle.
This question has multiple correct options
\( \mathbf{A} \cdot O s F_{2}<O s C l_{2}<O s B r_{2} \)
B \( \cdot S b C l_{3}<S b B r_{3}<S b I_{3} \)
\( \mathbf{C} \cdot P I_{3}>A s I_{3}>S b I_{3} \)
\( \mathbf{D} \cdot P I_{3}<A s I_{3}<S b I_{3} \)


If the mass of the single atom is \( 1.794 \times 10^{-22} \mathrm{g} \) what is the atomic
mass of silver?
\( A \cdot 108.95 u \)
B. 108.0
c. 106.05 u
D. 0.110


Check whether the values given in the
brackets are the solutions of the
corresponding equation:
\( \boldsymbol{x}+\mathbf{5}=\mathbf{1 9} ;(\boldsymbol{x}=\mathbf{4}) \)


\( \operatorname{Let} \boldsymbol{\alpha}=\frac{-\mathbf{1}+\boldsymbol{i} \sqrt{\mathbf{3}}}{\mathbf{2}} . \) If \( \boldsymbol{a}= \)
\( (1+\alpha) \sum_{k=0}^{100} \alpha^{2 k} ; b=\sum_{k=0}^{100} \alpha^{3 k}, \) then \( a \)
and \( b \) are the roots of the quadratic equation:
A \( \cdot x^{2}-102 x+101=0 \)
B. \( x^{2}-101 x+100=0 \)
c. \( x^{2}+102 x+101=0 \)
D. \( x^{2}+101 x+100=0 \)


Rewrite the following scientific names correctly. Ficus religiousa(peepal), zea Mays(maize) and Bombyx Mori(silk moth)


Both avian and mammalian hearts are
four chambered. The anatomy and physiology of heart is described by
A. Blood always enters into an atrium and then is pumped into a ventricle
B. Blood pressure alternates between systolic pressure and diastolic pressure
C. The atria provide one pump and the ventricles provide a second pump
D. The heart sends blood out through arteries and retrieves blood through veins
E. The heart pumps blood simultaneously through a pulmonary circuit and a systemic circuitt


The compressions and rarefactions are
transmitted across the middle ear
through
A. auditory tube
B. ear ossicles
c. cochlea
D. all of these


A rectangular solid has a square base,
with each side of the base measuring 4
meters. If the volume of the solid is 112
cubic meters, what is the surface area
of the solid?
A. \( \$ 1,500 \)
B. \( \$ 1,700 \)
\( c . \$ 2,200 \)
D. \( \$ 3,000 \)


Which of the following is/are contributing to the irreversibility of
processes?
This question has multiple correct options
A. Flow of electric current through a resistance
B. Unrestrained expansion of fluids
c. A quasi-static isothermal expansion of ideal gas
D. Spontaneous chemical reactions


The compound whose 0.1M solution is more basic is:
A. Ammonium acetate
B. Calcium carbonate
c. Ammonium sulphate
D. Sodium acetate


An illustration of the associative law for
multiplication is given by
A \( \cdot\left(\frac{1}{3} \times 5\right) \times 8=\frac{1}{3} \times(5 \times 8) \)
В \( \cdot \frac{1}{3} \times 5 \times 8=\frac{1}{3} \times 8 \times 5 \)
c. \( \frac{1}{3} \times 5+\frac{1}{3} \times 8=\frac{1}{3} \times 13 \)
D \( \cdot \frac{1}{3} \times 5 \times 8=\left(\frac{1}{3} \times 5\right) \times\left(\frac{1}{3} \times 8\right) \)
E. none of these


What is meant by ferrimagnetism? Give any two examples.


Oxidation of one molecule of glucose yields 38 mols of ATP in the proportion
of
A. 8 in cytosol and 30 in mitochondrion
B. 30 in cytosol and 8 in mitochondrion
\( c .38 \) in cytosol
D. 38 in mitochondrion


If \( \boldsymbol{x}+\mathbf{1}<\mathbf{0} \) then \( |\boldsymbol{x}| \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( x+1 \)
\( c .-x \)
D. \( -x-1 \)
\( E \)


Construct an equilateral triangle, given its side \( =3 \) and justify the
construction.


In which of the following cases forces are not required. To keep the:
A. particle going in a circle
B. particle going along a straight line
c. momentum of the particle is constant
D. acceleration of the particle is constant


The exothermic formation of \( C l F_{3} \) is
represented by the equation: \( C l_{2}(g)+ \)
\( \mathbf{3} F_{2}(\boldsymbol{g}) \rightleftharpoons 2 \boldsymbol{C l} \boldsymbol{F}_{3}(\boldsymbol{g}), \boldsymbol{\Delta} \boldsymbol{H}=-\mathbf{3 2 9} \mathbf{k J} \)
Which of the following will increase the
quantity of \( C l F_{3} \) in an equilibrium
mixture of \( C l_{2}, F_{2} \) and \( C l F_{3} ? \)
A. Increasing the temperature
B. Removing \( C l_{2} \)
c. Increasing the volume of container
D. Adding \( F_{2} \)


Prove \( : 1^{2}+\left(1^{2}+2^{2}\right)+ \)
\( \left(1^{2}+2^{2}+3^{2}\right)+\ldots \) upto \( n \) terms \( = \)
\( \frac{n(n+1)^{2}(n+2)}{12} \)


If \( \sqrt{3} \tan 2 \theta+\sqrt{3} \tan 3 \theta+ \)
\( \tan 2 \theta \tan 3 \theta=1, \) then the general
value of \( \theta \) is
A \( . \quad n \pi+\frac{\pi}{5} \)
B \( \cdot\left(n+\frac{1}{6}\right) \frac{\pi}{5} \)
\( ^{c} \cdot\left(2 n \pm \frac{1}{6}\right) \frac{\pi}{5} \)
D. \( \left(n+\frac{1}{3}\right) \frac{\pi}{5} \)


\( \int \sqrt{e^{x}+1} d x \)


From a disc of radius \( R \) and mass \( M, \) a
circular hole of diameter \( R \), whose rim
passes through the centre is cut. What is the moment of inertia of the
remaining part of the disc about a perpendicular axis, passing through the centre?
\( ^{A} \cdot \frac{9 M R^{2}}{32} \)
в. \( \frac{15 M R^{2}}{32} \)
c. \( \frac{13 M R^{2}}{32} \)
D. \( \frac{11 M R^{2}}{32} \)


The branch of biology dealing with classification is known as
A. Physiology
B. Taxonomy
c. Paleontology
D. Mycology


The cost of an article is Rs.6,000 to a
distributor. He sells it to a trader for Rs.
7,500 and the trader sells it to a customer for Rs. \( 8,000 . \) If the VAT rate is \( 12.5 \% ; \) find the VAT paid by the: (i) distributor
(ii) trader.
A . (i) Rs. 137.50
(ii) Rs. 71.22
B. (i) Rs. 187.50
(ii) Rs. 62.50
c. (i) Rs. 263.50
(ii) Rs. \$\$50.50\$
D. None of these


Find the following integrals:
i) \( \int \frac{x^{3}-1}{x^{2}} d x \)
ii) \( \int\left(x^{\frac{2}{3}}+1\right) d x \)
iii) \( \int\left(x^{\frac{3}{2}}+2 e^{x}-\frac{1}{x}\right) d x \)


The sum of 15 terms of an arithmetic
progression is 600 , and the common difference is \( 5, \) then the first term is
A . 3
B. 4
\( c .5 \)
D. none of these


If \( D, E \) are the mid-points of \( A B, A C \) of \( \triangle A B C \) and \( \overline{D E}=\lambda \overline{B C} \) then \( \lambda= \)
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c \cdot \frac{1}{2} \)
D. 3


If two vertices of an equilateral triangle \( \operatorname{are}(2,1,5) \) and \( (3,2,3), \) then its third vertex is:
A. (1,2,4)
в. (4,0,4)
c. (0,-4,4)
a 5
D. (4,4,1)


The variance of first 20 natural
numbers is
\( \mathbf{A} \cdot 133 / 4 \)
B. \( 279 / 2 \)
c. \( 133 / 2 \)
D. \( 399 / 4 \)


\( \mid \)
\( N \)
\( \mathrm{O} \)
\( \| \)
\( -\mathrm{C}-\mathrm{N}- \)
\( \mathrm{O} \)
\( \| \)
\( \mathrm{C} \)
\( \left(\begin{array}{cc}\mathrm{H} & \mathrm{H} \\ \mathrm{I} & \mathrm{I} \\ -\mathrm{C} & \mathrm{C}- \\ \mathrm{I} & \mid \\ \mathrm{H} & \mathrm{H}\end{array}\right) \)


Find the value of \( \cos ^{-1}\left(\cos \frac{5 \pi}{3}\right)+ \)
\( \sin ^{-1}\left(\sin \frac{5 \pi}{3}\right) \)


Which of the following is the unit of specific heat?
\( \mathbf{A} \cdot J k g^{o} C^{-1} \)
в. \( \frac{J}{k g^{o} C} \)
c. \( \frac{k g^{o} C}{J} \)
D. \( \frac{J}{k g^{o} C^{-2}} \)


Find the equation of the hyperbola satisfying the given conditions: Foci \( (\pm 3 \sqrt{5}, 0) \) the latus rectum is of length 8


Assertion
(A): Two metallic spheres of
same size, one of copper and other of aluminium heated to the same
temperatures, will cool at the same
rate when they are suspended in the
same enclosure.
Reason (R): The rate of cooling of a body is directly proportional to the excess of
temperature of the body over the surroundings.
A. both \( A \) and \( R \) are true and the \( R \) is correct explanation of the A
B. both A and R are true, but R is not correct explanation of the A
C. A is true, but the R is false.
D. A is false, but the R is true.


Which of the following is Snell's law?
A \( \cdot n_{1} \sin i=\frac{\sin r}{n_{2}} \)
B. \( \frac{n_{1}}{n_{2}}=\frac{\sin r}{\sin i} \)
c. \( \frac{n_{2}}{n_{1}}=\frac{\sin r}{\sin i} \)
D. \( n_{2} \sin i= \) constant


The reptile which glides in the air is
A. Draco
B. Phrynosoma
c. Anguis
D. calotes


If a man walks at a speed of \( 4 \mathrm{kmph} \) how long will it take him to walk \( 3 \mathrm{km} \) ?


The number of molecules of Grignard's
reagent consumed per mole of the
compound is :
\( A \)
B . 2
\( c \)
D


Echocardiography is used to diagnose
heart diseases which utilises infrasonic
waves.
A. True
B. False
c. Ambiguous
D. Data insufficient


The coefficient of \( x^{4} \) in the expansion of
\( \{\sqrt{1+x^{2}}-x\}^{-1} \) in ascending powers
of \( x, \) when \( |x|<1 \) is
\( \mathbf{A} \cdot \mathbf{0} \)
в. \( \frac{1}{2} \)
\( c \cdot-\frac{1}{2} \)
D. \( -\frac{1}{8} \)


A Line is of length 10 and one end is \( (2,-3) . \) If the abscissa of the other end is \( 10, \) then find its ordinate.


Fill in the blanks with the appropriate
words in each case
Element 'Z' in a sub-group 2[II A] is below element 'Y' in the same sub-
group.The element 'Z' will be expected to
have atomic size and metallic
character than \( y \)
A. lower, more
B. lower, less
c. higher, more
D. higher, less


A conductor of length \( I \) has a
nonuniform cross-section. The radius of
cros-ssection varies linearly from \( a \) to \( b \)
Find the resistance of the material is \( \boldsymbol{p} \)
Find the resistance of the conductor
across its ends.
A \( \cdot \frac{2 \rho l}{\pi a b} \)
в. \( \frac{\rho l}{\pi a b} \)
c. \( \frac{2 \rho l}{9 \pi a b} \)
D. \( \frac{4 \rho l}{5 \pi a b} \)


If the set \( A \) has 3 elements and the set
\( B=\{3,4,5\} \) then find the number of elements in \( (\boldsymbol{A} \times \boldsymbol{B}) \) ?


The structure meant for the
nourishment of developing embryo in case of plants is
A. Pollen tube
B. Endosperm
c. Both A and B
D. None of the above


An aeroplane moving horizontally at 20
\( \mathrm{ms}^{-1} \) drops a bag. What is the displacement of the bag after 5 seconds ? Give
\( \left(g=10 \mathrm{ms}^{-2}\right) \)


Biochemical Oxygen Demand (BOD) is a measure of organic material present in water. BOD value less than 5 ppm
indicates a water to be
A. rich in dissolved oxygen
B. poor in dissolved oxygen
c. highly polluted
D. not suitable for aquatic life


In a first order reaction, the
concentration of reactant is reduced to
\( 1 / 8 \) of the initial concentration in 75 minutes at \( 298 K . \) What is the half-life
period of the reaction in minutes?
A . 50 min
B. 15 min
\( c .30 \) min
D. 25 min


Solve \( \mathbf{5} \boldsymbol{x}+\frac{\mathbf{2 7}}{\mathbf{3}}=\mathbf{0} \)


If the phase difference between Alternating Voltage and Alternating
Current is \( \frac{\pi}{6} \) and the resistance in the circuit is \( \sqrt{300} \Omega, \) then the impedance of the circuit will be
A . 25\Omega
B. \( 50 \Omega \)
\( c \cdot 20 \Omega \)
D. \( 100 \Omega \)


Factorize:
\( 99 x^{2}-202 x y+99 y^{2} \)


Is the following equation a quadratic equation?
\( 16 x^{2}-3=(2 x+5)(5 x-3) \)
A. Yes
B. No
c. Ambiguous
D. Data insufficient


When one end of the capillary is dipped in water, the height of water column is
\( h^{\prime} . \) The upward force of 105 dyne due to surface tension balanced by the force due to the weight of water column. The inner circumference of the capillary is (Surface tension of water \( =\mathbf{7} \times \)
\( \mathbf{1 0}^{-\mathbf{2}} \mathbf{N} / \boldsymbol{m} \)
A \( .1 .5 \mathrm{cm} \)
B. 2 cm
\( c .2 .5 \mathrm{cm} \)
D. 3 ст


Which of the following processes requires the most energy input? Given below is the properties of the
water
Value Property
Specific Heat
Latent Heat of Fusion \( 80 \mathrm{cal} / \mathrm{g} \)
Latent Heat of Vaporization 540 cal/g 1
A. Melting \( 100 \mathrm{g} \) of ice at \( 0^{\circ} \mathrm{C} \)
B. Freezing 100 g of water at \( 0^{\circ} \mathrm{C} \)
c. Boiling \( 100 \mathrm{g} \) of water at \( 100^{\circ} \mathrm{C} \)
D. condensing 100 g of steam at 100 \( ^{\circ} \mathrm{C} \)
E. Heating \( 100 \mathrm{g} \) of water from \( 0 \mathrm{c} \) to \( 100^{\circ} \mathrm{C} \)


In the picture shown below, the man is
A. Applying no force on the stool
B. Applying pressure on the stool
C. Applying force on the stool
D. Both \( (B) \&(C) \)


Mean deviation of
\( \mathbf{3 9}, \mathbf{4 0}, \mathbf{4 0}, \mathbf{4 1}, \mathbf{4 1}, \mathbf{4 2}, \mathbf{4 2}, \mathbf{4 3}, \mathbf{4 3}, \mathbf{4 4}, \mathbf{4 4}, \mathbf{4} \)
from their median is?
A . 15
в. 1.5
c. 42
D. 35 5


Assertion:
A catalyst enhances the rate of a reaction.
Reason:
The energy of activation of the reaction is lowered in the presence of a catalyst.
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 is incorrect but Reason is correct


The resistance across \( \mathrm{M} \) and \( \mathrm{N} \) in the
given figure where each resistor shown
if of \( r \Omega \) is:
\( A \cdot \frac{r}{2} \)
B. \( \frac{r}{3} \)
\( c \cdot 6 r \)
D. 2r


Draw a ray diagram to show the refraction of a monochromatic ray
through a prism when it suffers minimum deviation


State True or False.
The mean free path of molecules in gas increases and the number of collisions
per unit volume decreases with the
lowering of pressure.
A. True
B. False


Give scientific term for adjustment of the eye in order to obtain a clear vision
of objects at different distances.


When the number of nucleons in nuclei
increase, the binding energy per
nucleon
A. increases continuously with mass number
B. decreases continuously with mass number
c. remains constant with mass number
D. first increases and then decreases with increase of mass number


If \( 4 x=\csc \theta \& \frac{4}{x}=\cot \theta, \) find the value
of \( 4\left[x^{2}-\frac{1}{x^{2}}\right] \)


In a certain gas, the ratio of the speed of sound and root mean square speed is \( \frac{\mathbf{5}}{\mathbf{g}} \) The molar heat capacity of the gas in a process given by \( \mathrm{PT}= \) constant is (Take \( R=2 \) cal/mole \( K \) ). Treat the gas as ¡deal.
\( A \cdot \frac{f+2}{f} \)
в. \( \frac{3 R}{2} \)
c. \( \frac{5 R}{2} \)
D. \( \frac{7 R}{2} \)


The following table shows the interest paid by a company (in lakhs):
1995- \( \quad 1996-\quad 1997- \)
Year \( \quad 96 \)
Interest
in lakes 20
25
of rupees)
Draw the bar graph to represent the above information.


Benzene bums in \( O_{2} \) according to the equation:
\( \boldsymbol{C}_{6} \boldsymbol{H}_{6}(l)+\frac{\mathbf{1 5}}{\mathbf{2}} \boldsymbol{O}_{2}(\boldsymbol{g}) \longrightarrow \mathbf{3} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g})+ \)
\( \mathbf{6} C O_{2}(\boldsymbol{g}) \)
If standard heat enthalpies of
\( \boldsymbol{C}_{6} \boldsymbol{H}_{6}(\boldsymbol{l}), \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \boldsymbol{a} \boldsymbol{n} \boldsymbol{d} \boldsymbol{\theta}_{2}(\boldsymbol{g}) \) are 11.7
-68.3 and -94.0 kcal respectively. The amount of heat liberated by burning 1 kg benzene in kcal is:
A. 10007.4
B. 1000
c. 500
D. None of these


A swimming pool is \( 18 \mathrm{m} \) long and \( 8 \mathrm{m} \) wide. Its deep and shallow ends are \( 2 \mathrm{m} \) and \( 1.2 \mathrm{m} \) respectively. Find the capacity of the pool, assuming that the bottom of the pool slopes uniformly.
A . 230.4 cu. \( \mathrm{m} \)
B. 420.4 cu. \( \mathrm{m} \)
c. 340.4 cu. \( \mathrm{m} \)
D. 190.4 cu. \( m \)


Assertion
Gypsum is added to powdered clinkers to get cement.
Reason
Addition of gypsum to clinker decreases its setting time and thus cement hardens readily on mixing with
water
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Chernobyl nuclear tragedy occurred in
A. April, 1986
B. August 6, 1945
c. August 9,1945
D. December 3, 1984


A man travelled \( 72 \mathrm{km} \) to the North of
Hubballi and then \( 121 \mathrm{km} \) to the south
of it. How far from Hubballi was he
finally.
\( \mathbf{A} \cdot 49 \mathrm{km} \)
B. 9 кт
c. \( 49 \mathrm{m} \)
D. \( 4 \mathrm{km} \)


Contraceptive pills does not
A. Engulf the sperm
B. After the quality of cervical mucus
C. Prevent the entry of sperm
D. Inhibits implantation


Select the correct statement from the
following.
A. Activated sludge-sediment in settlement tanks of sewage treatment plant is a rich source of aerobic bacteria
B. Biogas is produced by the activity of aerobic bacteria on animal waste
C. Methano bacterium is an aerobic bacterium found in
rumen of cattle
D. Biogas, commonly called as global gas, is pure methane


Fill in the blanks.
Nitrogen is not a supporter of


A simple telescope has
A. A convex lens and a concave lens
B. A concave mirror and a convex lens
C. Two convex lenses
D. Two concave lenses


Which of the following statements does
not apply to a given rate law corresponding to a specific reaction?
A. As the temperature changes, the rate of reaction changes.
B. As the reaction rate changes, the rate constant does not change
c. As the concentration of the reactants changes, the unit of the rate constant changes.
D. As the concentration of the reactants change, the rate of reaction changes