There are two particles of same mass. If one of the particles is at rest always and the other has an acceleration \( \bar{a} \).
Acceleration of center of mass is :
A . zero
в. \( \frac{1}{2} \bar{a} \)
\( c \cdot \bar{a} \)
D. centre of mass for such a system can not be defined


\( \sigma^{2} \) is known as
\( A \cdot \) mean
B. variance
C. Standard deviation
D. quartile deviation


Define the term 'enthalpy'
What will happen to the internal energy if work is done by the system?


Which quantum number will determine the shape of the subshell?
A. Principal quantum number
B. Azimuthal quantum number
c. Magnetic quantum number
D. Spin quantum number


Homologue of \( \boldsymbol{C}_{3} \boldsymbol{H}_{4} \) is :
A \( \cdot C_{4} H_{6} \)
в. \( C_{2} H_{6} \)
\( \mathbf{c} \cdot C H_{3} O H \)
D. \( H C H O \)


If a battery is used to charge a capacitor, work done by the battery is \( W \) and energy stored in the capacitor is
E. How these two are related?


Auxin synthesis occurs in
A. Root/shoot tips
B. Cortex
C . Xylem
D. Phloem cells


\( N \) is the set of positive integers. The
relation \( R \) is defined on \( \mathrm{N} \times \mathrm{N} \) as follows:
\( (a, b) R(c, d) \Longleftrightarrow a d=b c \) Prove that
This question has multiple correct options
A. \( R \) is an equivalence relation
B. \( R \) is symmetric relation
c. \( R \) is transitive relation
D. \( R \) is not an equivalence relation.


An electric dipole is placed at an angle
of \( 30^{\circ} \) with an electric field of intensity
\( 2 \times 10^{5} N C^{-1} . \) It experiences a torque
of \( 4 N m . \) Calculate the charge on the
dipole if the dipole length is \( 2 \mathrm{cm} \) :
\( A \cdot 8 m C \)
в. \( 4 m C \)
\( c \cdot 8 \mu C \)
D. \( 2 m C \)


If due to air drag, the orbital radius of the earth decreases from \( \boldsymbol{R} \) to \( \boldsymbol{R}-\boldsymbol{\Delta} \boldsymbol{R} \)
\( \Delta R<<R, \) the work done by air friction
force \( W \) is
\( ^{\mathbf{A}} \cdot_{-} \frac{G M m}{R^{2}} \times \Delta R \)
\( ^{\text {в } \cdot \frac{G M m}{R^{2}} \times \Delta R} \)
\( ^{\mathrm{c}} \cdot \frac{G M m}{2 R^{2}} \times \Delta R \)
\( ^{\mathrm{D}} \cdot \frac{G M m}{2 R^{2}} \times \Delta R \)


A block released from rest from the top
of a smooth inclined plane of angle \( \boldsymbol{\theta}_{\mathbf{1}} \)
reaches the bottom in time \( t_{1} . \) The same
block released from rest from the top of
another smooth inclined plane of angle
\( \theta_{2}, \) reaches the bottom in time \( t_{2} . \) If the
two inclined planes have the same
height, the relation between \( t_{1} \) and \( t_{2} \) is
\( \mathbf{A} \cdot \frac{t_{2}}{t_{1}}=\left(\frac{\sin \theta_{1}}{\sin \theta_{2}}\right)^{1 / 2} \)
B. \( \frac{t_{2}}{t_{1}}=1 \)
\( \mathbf{C} \cdot \frac{t_{2}}{t_{1}}=\frac{\sin n_{1}}{\sin \theta_{2}} \)
\( \mathbf{D} \cdot \frac{t_{2}}{t_{1}}=\frac{\sin ^{2} \theta_{1}}{\sin ^{2} \theta_{2}} \)


The final product of the given reaction is, \( \boldsymbol{P h}-\boldsymbol{N}_{2} \boldsymbol{C l} \frac{\boldsymbol{C u}_{2} \boldsymbol{C l}_{2}}{\boldsymbol{P} \boldsymbol{h}-\boldsymbol{C l}+\boldsymbol{N}_{2} \uparrow} \)
A \( \cdot P h-N_{2} C l \stackrel{C u_{2} C l_{2}}{\longrightarrow} P h-C l+N_{2} \uparrow \)
B . \( P h-N_{2} C l \stackrel{C u_{2} C l_{2}}{\longrightarrow} P h-C l+N_{3} \uparrow \)
c. \( P h-N_{2} C l \stackrel{C u_{2} C l_{2}}{\longrightarrow} P h-C l_{2}+N_{2} \uparrow \)
D. \( P h-N_{2} C l \frac{C u_{2} C l_{2}}{\longrightarrow} P h_{2}-C l+N_{2} \uparrow \)


Work out the answers to the following
calculate the number line.
\( (-5)+(-4) \)


State Coulomb's law and express it in
vector form.


A plane electromagnetic wave of frequency 20 MHz travels through a space along \( x \) direction. If the electric field vector at a certain point in space is
\( 6 \mathrm{V} \boldsymbol{m}^{-1}, \) what is the magnetic field
vector at that point?
A \( \cdot 2 \times 10^{-8} T \)
B \( \cdot \frac{1}{2} \times 10^{-8} T \)
c. \( 2 T \)
D. \( \frac{1}{2} T \)


The minimum value of the function
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x} \log \boldsymbol{x} \) is
A. \( -\frac{1}{e} \)
B. \( -e \)
\( c \cdot \frac{1}{e} \)
D.


\( P C l_{5} \) in soild state dissociates into
\( \boldsymbol{P C l}_{4}^{+} \) and \( \boldsymbol{P C l}_{\mathbf{6}}^{-} \)
A. True
B. False


What is the smallest positive number
greater than 1 which is a cube as well
as a square?
A . 8
B. 64
\( c \cdot 72 \)
D. 144


A \( 1.2 \mathrm{m} \) wide railway track is parallel to magnetic meridian. The vertical component of earth's magnetic field is 0.5 Gauss. When a train runs on the
rails at a speed of \( 60 \mathrm{Km} / \mathrm{hr} \), then the
induced potential difference the ends of its axle will be
\( A \cdot 10^{-4} v \)
B . \( 2 \times 10^{-4} \mathrm{V} \)
c. \( 10^{-3} \mathrm{v} \)
D. zero


Define Newton's laws of motion.


What change would you observe in the
calcium hydroxide solution taken
in tube \( B ? \)
A. It will turn milky
B. It will turn yellow
c. It will turn blue
D. None of these


The criteria for spontaneity of a process is/are
This question has multiple correct options
A \( \cdot(d G)_{T P}<0 \)
B . \( (d E)_{S V}<0 \)
c. \( (d H)_{S P}<0 \)
D . \( (d S)_{E V}<0 \)


The position of a particle moving in the \( X \) -Y plane from origin at any time \( t \)
is given by \( \boldsymbol{x}=\left(\mathbf{3} \boldsymbol{t}^{2}-\mathbf{6} \boldsymbol{t}\right) \mathbf{m} ; \boldsymbol{y}=\left(\boldsymbol{t}^{2}-\right. \)
\( 2 t) \mathrm{m}, \) where \( t \) is in seconds. Select the
correct statement(s) about the moving particle from the following.
A. The acceleration of the particle is zero at \( t=0 \) second
B. The velocity of the particle is zero at \( t=0 \) second
c. The velocity of the particle is zero at \( t=1 \) second
D. The velocity and acceleration of the particle are never zero


If \( z(\neq-1) \) is complex number such that \( \frac{z-1}{z+1} \) is purely imaginary, then \( |z| \) is equal to
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c .3 \)
D.


Find Integrals of given function:
\( \int \tan \theta \tan ^{2} \theta \sec ^{2} \theta d \theta \)
\( ^{A} \cdot \frac{2 \tan ^{4} \theta}{4}+c \)
\( ^{\text {В }} \cdot \frac{\tan ^{4} \theta}{4}+c \)
c. \( \frac{\tan ^{4} \theta}{8}+c \)
D. None of these


Due to increasing air-borne allergens and pollutants, many people in urban areas are suffering from respiratory disorder causing wheezing due to
A. Benign growth on mucous lining of nasal cavity
B. Inflammation of bronchi and bronchioles
c. Proliferation of fibrous tissues and damage of the alveolar walls
D. Reduction in the secretion of surfactants by pneumocytes


Identify the monomers in the following polymers:


Show that any positive even integer is of the form \( 4 q \) or \( 4 q+2, \) where \( q \) is a whole
number.


(A) Estimate the speed with which electrons emitted from a heated emitter
of an evacuated tube impinge on the collector maintained at a potential difference of \( 500 \mathrm{V} \) with respect to the emitter. Ignore the small initial speeds of the electrons. The specific charge of the electron, i.e., its e/m is given to be \( 1.76 \times 10^{11} C k g^{-1} \)
(B) Use the same formula you employ in
(a) to obtain electron speed for a collector potential of \( 10 \mathrm{MV} \). Do you see what is wrong? In what way is the formula to be modified?


Complete the structures of following hydrocarbons by placing hydrogens only
(i) \( \mathrm{C}-\mathrm{C}=\mathrm{C}-\mathrm{C} \quad \) (ii) \( \mathrm{C}=\mathrm{C}-\mathrm{C}_{\mathrm{I}} \)
co
(iv) \( C=C-C \)
(v) \( c-c-c-c-c \)


A bullet of mass \( 50 g \) is moving with a
velocity of \( 500 \mathrm{ms}^{-1} \). it penetrates
\( 10 \mathrm{cm} \) into a still target and comes to rest.Calculate
(a) The kinetic energy possessed by the bullet,
(b) The average retarding force offered by the target.


Find the change in internal energy in joulewhen \( 10 g \) of air is heated from
\( 30^{\circ} \mathrm{C} \) to \( 40^{\circ} \mathrm{C} \)
A . 62.24J
B. 72.24J
c. 52.24J
D. 82.24J


Differentiate \( \boldsymbol{x}^{3} \) w.r.t \( \boldsymbol{x} \)


Find the area of a parallelogram with a base of 34 meters and a height of 8
meters.
A \( \cdot 262 m^{2} \)
B . 272 \( m^{2} \)
c. \( 282 \mathrm{m}^{2} \)
D. 292 \( m^{2} \)


In order to manage energy resources within the cell, the potential energy of an electrochemical gradient must be coupled with endergonic (less favorable) processes. If the membrane that sustains the
concentration gradient is disrupted, what happens to the cell?
A. The energetics of the cell will not be affected and will continue functioning normally.
B. The gradient will be reversed but still able to support cellular activity
C. The loss of a concentration gradient reduces the potential energy of the cell and diminishes the ability to do work
D. The endergonic nature of the reduced gradient can be coupled to endergonic reactions such as the synthesis of ATP


The plot represents the flow of current
through a wire at three different times.
The ratio of charges flowing through the wire at different times is (second
figure
\( \mathbf{A} \cdot 2: 1: 2 \)
B. 1: 3: 3
\( \mathbf{c} \cdot 1: 1: 1 \)
\( \mathbf{D} \cdot 2: 3: 4 \)


Ethyl alcohol and phenol both contain OH group. Why phenol is acidic and alcohol is neutral in nature? Give
reason.


Which of the following hydrides is electron-precise hydride?
A. \( B_{2} H_{6} \)
в. \( N H_{3} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{O} \)
D. \( C H_{4} \)


When magnesium ammonium phosphate is heated, it is converted to:
A. magnesium pyrophosphate
B. magnesium oxide
c. magnesium phosphate
D. magnesium nitride


\( \int_{-3 \pi / 2}^{-\pi / 2}\left[(x+\pi)^{3}+\cos ^{2}(x+3 \pi)\right] d x \) is
equal to
\( \mathbf{A} \cdot\left(\pi^{4} / 32\right)+(\pi / 2) \)
B. \( \pi / 2 \)
\( \mathbf{c} \cdot(\pi / 4)-1 \)
\( \mathbf{D} \cdot\left(\pi^{4} / 32\right) \)


The third term of an A.P is 7 and the
seventh term exceeds three times the
third term by 2. Find the first term, the
common difference and the sum of first
20 terms.


The incident ray,reflected ray and the normal ray, all lie on the plane.
A. different
B. same
c. mutually perpendicular
D. orthogonal


If \( A \) is a non zero square matrix of order
\( \boldsymbol{n} \) with \( \operatorname{det}(\boldsymbol{I}+\boldsymbol{A}) \neq \mathbf{0}, \) and \( \boldsymbol{A}^{3}=\mathbf{0} \)
where \( I, O \) are unit and null matrices of
order \( n \times n \) respectively, then
\( (\boldsymbol{I}+\boldsymbol{A})^{-1}= \)
A \( \cdot I-A+A^{2} \)
B . \( I+A+A^{2} \)
c. \( I+A^{2} \)
\( \mathbf{D} \cdot I+A \)


\( \left|\begin{array}{ccc}\boldsymbol{x}+\mathbf{2} & \mathbf{2} \boldsymbol{x}+\mathbf{3} & \mathbf{3} \boldsymbol{x}+\mathbf{4} \\ \mathbf{2} \boldsymbol{x}+\mathbf{3} & \mathbf{3} \boldsymbol{x}+\mathbf{4} & \mathbf{4} \boldsymbol{x}+\mathbf{5} \\ \mathbf{3} \boldsymbol{x}+\mathbf{5} & \mathbf{5} \boldsymbol{x}+\mathbf{8} & \mathbf{1 0} \boldsymbol{x}+\mathbf{1 7}\end{array}\right|=\mathbf{0} \) then
\( x \) is equal to
A \( .-1,-2 \)
в. 1,2
\( c \cdot 1,-2 \)
D. -1,2


An atom of an element has one electron
in the valence shell and the two inner
shells have 8 electrons each. Find the
atomic number of that element.


When the system shown in the adjoining fig. is in equilibrium and the
areas of cross sec. of the small and big
piston are \( ^{\prime} a^{\prime} \) and \( ^{\prime} 10 a^{\prime}, \) then what is
the value of \( \boldsymbol{m} / \boldsymbol{M} \) ?


Two halves of pelvic girdle are joined
together by
A. Pubic symphysis
B. Ischiac symphysis
c. Ischibpubic symphysis
D. By fusion


What other children's genotypes and
phenotypes there can be in the given family?


Form the differential equation from the following primitive, where constant is
arbitrary.
\( \boldsymbol{y}=\boldsymbol{a} \boldsymbol{x}^{2}+\boldsymbol{b} \boldsymbol{x}+\boldsymbol{c} \)
A \( \cdot \frac{d y}{d x}=0 \)
B. \( \frac{d^{2} y}{d x^{2}}=0 \)
c. \( \frac{d^{3} y}{d x^{3}}=0 \)
D. None of these


The system of giving one name to the individual is
A. Quasibinomial system
B. Semibinomial system
c. Mononomial system
D. Uninomial system


Steroid hormones
A. Work via second messenger
B. Trigger rapid, short term response in cells
C. Alter the activity of genes
D. Initiate open channels in plasma membrane


In a division sum, the divisor is 10
times the quotient and five times the remainder. What is the dividend, if the
remainder is \( 46 ? \)
A .5636
в. 5536
\( c .5336 \)
D. 5436


The phenomenon of light coming back after hitting a smooth plane surface is called:
A . Reflection
B. Refraction
c. Dispersion
D. Total internal reflection


What percentage of amino acids is absorbed in the small intestine?
A . 15\%
B. 30\%
\( c \cdot 100 \% \)
D. 90-95\%


A soap bubble has a thickness of
\( 100 n m \) and a refractive Index of 1.35
Given that the wavelength of red light is about \( 700 n m \) and that of blue light is
\( 400 n m, \) what colour does the bubble appear to be at the point on its surface closest to an observer when it is
illuminated by white light?
A. White
B. Black
c. Red
D. Green


Write the direction cosines of the line
whose cartesian equations are \( 2 x= \)
\( \mathbf{3} \boldsymbol{y}=-\boldsymbol{z} \)


\( \int \frac{\cos x}{\cos (x-a)} d x \)


Phloem of gymnosperms differs from that of angiosperms in having
A. Parenchyma
B. No companion cells
c. No sieve cells
D. No sclerenchyma fibres


You are provided with a negatively charged gold leaf electroscope. What is the effect on the gold leaves when a glass rod rubbed with silk is brought near the disc of electroscope?
A. Divergence increases
B. Divergence decreases
c. Divergence remains same
D. Can not be determined


Balance the following equation by ion electron method.
\( \boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{O} \boldsymbol{H}+\boldsymbol{I}_{2}+\boldsymbol{O} \boldsymbol{H}^{-} \rightarrow \boldsymbol{C} \boldsymbol{H} \boldsymbol{I}_{3}+ \)
\( \boldsymbol{H} \boldsymbol{C O}_{2}^{-}+\boldsymbol{I}^{-}+\boldsymbol{H}_{2} \boldsymbol{O} \)


The axes being inclined at an angle of
\( 30^{\circ}, \) find the equation to the straight line which passes through the point
(-2,3) and is perpendicular to the
straight line \( \boldsymbol{y}+\mathbf{3} \boldsymbol{x}=\mathbf{6} \)


A pure germanium crystal at absolute zero is :
A. an insulator
B. a good conductor
c. a semiconductor
D. none of the above


Assertion
During anaphase, centromere of each chromosome splits to the chromatids
separate.
Reason
During anaphase, chromatids move to opposite poles.
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


Arrange the following in the decreasing order of solubility in water:
¡) \( \boldsymbol{C}_{\boldsymbol{6}} \boldsymbol{H}_{\boldsymbol{5}} \boldsymbol{N} \boldsymbol{H}_{\boldsymbol{2}} \)
ii) \( \left(C_{2} H_{5}\right)_{2} N H \)
iii) \( \boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{N} \boldsymbol{H}_{2} \)
A. i > ii > ii
\( \mathbf{c} . \) iii \( >\mathbf{i}>\mathrm{i} \mathrm{i} \)
D. iii >ii >


How does the resistance of a wire vary
with its cross sectional area.


The structure producing basidium in
Basidiomycetes is formed by the fusion of
A. Two vegetative cells
B. Two male gametes
C. Two female gametes
D. Male and female gametes


Fill in the blanks.
is used as a refrigerant.


The compounds \( \left[\boldsymbol{P t C l}_{2}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4}\right] \boldsymbol{B r}_{2} \)
and \( \left[\boldsymbol{P t B r}_{2}\left(\boldsymbol{N H}_{3}\right)_{4}\right] \boldsymbol{C l}_{2} \) constitute a
pair of:
A. coordination isomers
B. linkage isomers
c. ionisation isomers
D. optical isomers


A diatomic molecule has moment of
inertia \( I . \) By Bohrs quantization
condition its rotational energy in the \( n^{t h} \) level \( (n=0 \) is not allowed) is
A \( \cdot \frac{1}{n^{2}}\left(\frac{\mathrm{h}^{2}}{8 \pi^{2} \mathrm{I}}\right) \)
B. \( \frac{1}{\mathrm{n}}\left(\frac{\mathrm{h}^{2}}{8 \pi^{2} \mathrm{I}}\right) \)
\( ^{c} \cdot\left(\frac{h^{2}}{8 \pi^{2} I}\right) \)
D. \( _{\mathrm{n}^{2}}\left(\frac{\mathrm{h}^{2}}{8 \pi^{2} \mathrm{I}}\right) \)


The ionisation potential of hydrogen
atom is \( -13.6 \mathrm{eV} \). An electron in the
ground state of a hydrogen atoms absorb a photon of energy \( 12.75 \mathrm{eV} . \) How many different spectral line can one
expect when the electron make a
downward transition?
\( A \)
B. 4
\( c \cdot 2 \)
D. 6


A gold leaf electroscope is used
A. Detect the presence of charge on a body
B. Know the nature of charge on a charged body
C. Find the amount of charge present on a charged body
D. Both 1 and 2


How many moles of \( N O_{2} \) will be formed
by oxidation of 1 mole \( I_{2} \) by
concentrated \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} ? \)
A .4
B. 6
c. 8
D. 10


A shop-keeper increases the price of
commodity by \( \boldsymbol{x} \% \). Some time later, he
reduces the new price by \( y \% \) and
notices that the price is now the same as it was originally. The value of \( \frac{1}{y}-\frac{1}{x} \)
İS
A \( \cdot-\frac{1}{100} \)
B. 0
c. \( \frac{1}{100} \)
D. not uniquely determinable


Two balls of same mass are dropped from the same height \( h, \) on to the floor. The first ball bounces to a height \( h / 4 \) after the collision and the second ball to a height \( h / 16 . \) The impulse applied by the first and second ball on the floor are
\( I_{1} \) and \( I_{2} \) respectively. Find the ratio \( \frac{I_{1}}{I_{2}} \)


Weakest reducing agent is:
A. atomic hydrogen
B. nascent hydrogen
C . molecular hydrogen
D. occluded hydrogen


The figure given shows the variation of
an alternating emf with time. What is the average value of the emf for the
shaded part of the graph?
A . 100
B. 200
\( c .300 \)
D. 400


If \( \Delta \) DEF \( \equiv \Delta B C A, \) write the part(s) of \( \Delta \)
BCA that correspond to \( \angle \mathrm{E} \)


Its population after 6 years.
\( \mathbf{A} \cdot 85,846 \)
в. 86,846
\( c .87,846 \)
D. None of these


Trace the following central conics. \( \boldsymbol{x} \boldsymbol{y}-\boldsymbol{y}^{2}=\boldsymbol{a}^{2} \)


State True or False.
Numerically calorie is bigger than joule.


The secretion of adrenal gland is known
as
A. Thyroxin
B. Adrenalin
c. Calcitonin
D. None of these


Name the body structure concerned
with the given functional activity.
Protects the lungs from mechanical injuries.


Differential coefficient of \( \log (\sin x) \) with
respect to \( x \) is:
A . \( \cot x \)
B. \( \operatorname{cosec} x \)
\( c \cdot \tan x \)
D. sec \( x \)


Balance the given below reaction
\( \boldsymbol{x} \boldsymbol{A} \boldsymbol{s}_{2} \boldsymbol{S}_{3}+\boldsymbol{y} \boldsymbol{N} \boldsymbol{a} \boldsymbol{O} \boldsymbol{H}+\boldsymbol{z} \boldsymbol{N} \boldsymbol{a} \boldsymbol{C l} \boldsymbol{O}_{3} \rightarrow \)
\( \boldsymbol{a} \boldsymbol{N} \boldsymbol{a}_{3} \boldsymbol{A} \boldsymbol{s} \boldsymbol{O}_{4}+\boldsymbol{b} \boldsymbol{N} \boldsymbol{a}_{2} \boldsymbol{S} \boldsymbol{O}_{4}+\boldsymbol{c} \boldsymbol{N} \boldsymbol{a} \boldsymbol{C l O}+ \)
\( d H_{2} O \) Calculate the value of \( (x-y+z+a) \)
b+c), when the molar coefficient are in simplest whole number ratio.


SONAR is based on the principle of
This question has multiple correct options
A. echo
B. reverberation
c. resonance
D. Ultra sounds


The electric field within the nucleus is
generally observed to be linearly dependent on \( r . \) This implies.
A \( . a=0 \)
B. \( a=\frac{R}{2} \)
\( \mathbf{c} \cdot a=R \)
D \( a=\frac{2 R}{3} \)


Which of the following material take the Iongest to degenerate?
A. Paper
B. cotton cloth
c. Tin can
D. Plastic bags


Who unified celestial and terrestrial
mechanics?
A. sir Issac Newton
B. James Clerk Maxwell
c. Michael Faraday
D. None of the above


A ball is projected vertically up with a
velocity of \( 20 m s^{-1} . \) Its velocity, when
the displacement is \( 15 m, \) is......... \( m s^{-1} \)
(Take \( \boldsymbol{g}=\mathbf{1 0 m} \boldsymbol{s}^{-2} \mathbf{)} \)
A . 10
B. 15
\( c \cdot-10 \)
D. Both (A) and (C)


Functional group in saturated carboxylic acid is:
A. \( -C O O H \)
в. \( -C H O \)
\( \mathrm{c} \cdot-O H \)
D. \( -S O_{3} H \)


Which of the following solutions will
have blue colour?
\( A \cdot A 0.01- \) molar solution of \( H N O_{3} \)
B. A 0.01-molar solution of \( C H_{3} C O O H \)
C. A 0.01-molar solution of \( C u\left(N O_{3}\right)_{2} \)
D. A 0.01-molar solution of \( N a N O_{3} \)
E. A 0.01-molar solution of \( N a O H \)


\( \frac{\boldsymbol{b}+\boldsymbol{c}-\boldsymbol{a}}{\boldsymbol{a}}, \frac{\boldsymbol{c}+\boldsymbol{a}-\boldsymbol{b}}{\boldsymbol{b}}, \frac{\boldsymbol{a}+\boldsymbol{b}-\boldsymbol{c}}{\boldsymbol{c}} \) are in
A.P., then \( \frac{1}{a}, \frac{1}{b}, \frac{1}{c} \) are in
A. A.P.
в. н.Р
c. G.
D. A.G.P


Enthalpy is an extensive property.
A. True
B. False


In the sequences \( 2,5,8, \ldots \) upto 50
terms and \( 3,5,7, \dots \) upto 60 terms, find
the number of identical terms.


Show that:
\( (a-b)(a+b)+(b-c)(b+c)+(c- \)
\( \boldsymbol{a})(\boldsymbol{c}+\boldsymbol{a})=\mathbf{0} \)


Soil erosion can be prevented by
A. Raising forests
B. Deforestation
C. Excessive use of fertilizer
D. Overgrazing by animals


The electron in a hydrogen atom first jumps from the third excited state to the second excited state and
subsequently to the first excited state. The ratio of the respective wavelengths,
\( \lambda_{1} / \lambda_{2} \) of the photons emitted in this
process is:
A \( \cdot \frac{9}{7} \)
B. \( \frac{7}{5} \)
c. \( \frac{27}{5} \)
D. \( \frac{20}{7} \)


How orbital and escape velocities are
related?
A \( \cdot v_{e}=2 v_{0} \)
B \( \cdot v_{e}=\sqrt{3} v_{0} \)
c. \( v_{e}=1.31 v_{0} \)
D. \( v_{e}=1.41 v_{0} \)


\( \boldsymbol{P}(\mathbf{0}, \mathbf{5}, \mathbf{6}), \boldsymbol{Q}(\mathbf{1}, \mathbf{4}, \mathbf{7}), \boldsymbol{R}(\mathbf{2}, \mathbf{3}, \mathbf{7}) \) and
\( S(3,5,16) \) are four points in the space.
The point nearest to the origin \( \boldsymbol{O}(\mathbf{0}, \mathbf{0}, \mathbf{0}) \)
is
A. \( P \)
B. \( Q \)
\( c . R \)
D. \( S \)


Expand \( \left(x^{2}+y^{2}\right)\left(x^{2}-y^{2}\right) \)


Given \( \boldsymbol{a}=\boldsymbol{i}+\boldsymbol{j}-\boldsymbol{k}, \boldsymbol{b}=-\boldsymbol{i}+\boldsymbol{2} \boldsymbol{j}+\boldsymbol{k} \)
and \( c=-i+2 j-k \) a unit vector
perpendicular to both \( a+b \) and \( b+c \) is
\( \mathbf{A} \cdot i \)
B.
c. \( k \)
D. \( (i+j+k) / \sqrt{3} \)


The total number of benzene derivatives
having the molecular formula \( C_{7} H_{7} C l \)
is:
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. 5


R.Q. is more than one in the case of
A. Fat
B. Fructose
c. Glucose
D. organic acid


Arrange the following substances in increasing order of forces of attraction.
A. Oxygen, water, sugar
B. Sugar, water, oxygen
c. water, sugar, oxygen
D. Sugar, oxygen, water


What is released when di
nitrogen trioxide is reacted with a base
like \( N a O H ? \)
\( A \cdot O_{2} \)
в. \( N_{2} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{O} \)
D. no gas is released


The high boiling point of ethanol \( 78.2^{\circ} \)
compared to dimethyl ether \( -23.6^{\circ} \)
though they have the same molecular
formula \( \left[\boldsymbol{C}_{2} \boldsymbol{H}_{6} \boldsymbol{O}\right], \) is due to:
A. Hydrogen bonding
B. lonic bonding
c. co-ordinate covalent bonding
D. Resonance


If we plot a graph between \( \log _{10} k \) and \( \frac{1}{T} \) by Arrhenius equation, the slope is:
A \( .-E_{a} / R \)
в. \( +E_{a} / R \)
c. \( -\frac{E_{a}}{2.303 R} \)
D. \( +\frac{E_{a}}{2.303 R} \)


\( \mathbf{f}_{\boldsymbol{f}(\boldsymbol{x})}=\left\{\begin{array}{ll}\frac{\boldsymbol{x}^{2}-\boldsymbol{9}}{\boldsymbol{x}-\mathbf{3}}+\boldsymbol{\alpha} & , \text { for } \boldsymbol{x}>\mathbf{3} \\ \mathbf{5} & , \text { for } \boldsymbol{x}=\mathbf{3} \\ \mathbf{2} \boldsymbol{x}^{2}+\mathbf{3} \boldsymbol{x}+\boldsymbol{\beta} & , \text { for } \boldsymbol{x}<\mathbf{3}\end{array}\right. \)
is continuous at \( x=3, \) find \( \alpha \) and \( \beta \)


Find the multiplicative inverse of each of the complex numbers given in the Exercises 11 to 13
\( 4-3 i \)


Slow neutrons can bring about the
fission of :
A \( \cdot 92\left[U^{235}\right. \)
В. \( s_{2} U^{238} \)
c. \( _{82} P b^{207} \)
D・ \( 88 U^{226} \)


Assertion
Inverse of an orthogonal matrix is
orthogonal.
Reason
The inverse of an identity matrix is the
matrix itself.
\( \mathbf{A} \cdot \) Both \( (\mathrm{A}) \&(\mathrm{R}) \) are individually true \( \&(\mathrm{R}) \) 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.


\( \boldsymbol{f}(\boldsymbol{x}+\mathbf{1})=(-1)^{x+1} \boldsymbol{x}-\boldsymbol{2} \boldsymbol{f}(\boldsymbol{x}) \) for \( \boldsymbol{x} \in \mathbb{N} \)
and \( f(1)=f(1986) . \) Then sum of digits
of \( (\boldsymbol{f}(\mathbf{1})+\boldsymbol{f}(\mathbf{2})+\ldots .+\boldsymbol{f}(\mathbf{1 9 8 5}))= \)
\( \mathbf{A} \cdot \mathbf{4} \)
B. 3
\( c \cdot 7 \)
D. 1


gas in an enclosure as shown in Fig (a). When a pump removes some of the gas, the manometer reads as in Fig (b). The
liquid used in the manometers is
mercury and the atmospheric pressure
is \( 76 \mathrm{cm} \) of mercury.
(a) Give the absolute and gauge
pressure of the gas in the enclosure for
cases
(a) and (b), in units of \( c m \) of
mercury.
(b) How would the levels change in case
(b) if \( 13.6 \mathrm{cm} \) of water (immiscible with
mercury) are poured into the right limb of the manometer? (Ignore the small change in the volume of the gas).
\( (a) \)


Integrate \( \int \frac{1}{\sqrt{3-x^{2}}} d x \)


Which one is not lyophobic in nature? This question has multiple correct options
A. Gelatin
B. Sulphur in water
c. starch
D. Protein


When temperature of a gas is \( 20^{\circ} \mathrm{C} \) and
pressure is changed from \( p_{1}=1.01 \times \)
\( 10^{5} P a \) to \( p_{2}=1.165 \times 10^{5} P a, \) the
volume changes by \( 10 \% . \) The bulk modulus is
\( \mathbf{A} \cdot 1.55 \times 10^{5} \)
B. \( 0.155 \times 10^{5} \)
C \( .1 .4 \times 10^{5} \)
D. \( 1.01 \times 10^{5} \)


The number of ways in which 5
Mathematics, 4 Physics, 2 Chemistry books can be arranged in a shelf if the books on the same subject are kept together.
A . 34,560
в. 34,500
c. 31,540
D. 32,850


The electrical conductivity of materials bounded by ionic bonding is:
A. very low
B. very high
c. infinity
D. zero


Very fine particles mainly scatter light.
A. Blue
B. White
c. Red
D. Violet


Write down the degree of the following polynomial:
\( 7 x^{3}-5 x^{3} y^{2}+4 y^{4}-9 \)
\( A \cdot 3 \)
B. 4
\( c \cdot 5 \)
\( D \)


Which of the following statements
about primary amines is false?
A. Alkyl amines are stronger bases than aryl amines
B. Alkyl amines react with nitrous acid to produce alcohols
C. Aryl amines react with nitrous acid to produce phenols
D. Alkyl amines are stronger bases than ammonia


Find the distance between the following pair of points. (-2,-3) and (3,2)


White, gray,brown and gold are the color bands on resistors.Find its resistance?
\( \mathbf{A} \cdot 98 \Omega \)
в. \( 950 \Omega \)
\( c .9 .8 \Omega \)
D. \( 9800 \Omega \)


If the DNA content in the sperm is \( 30 p g \) the what was the DNA content in its
mother cell at the end of meiosis \( \boldsymbol{I} \)
A . 30 p
в. 60 ря
c. \( 120 p g \)
D. 90 pg


Which statement is incorrect about
peptide bond?
\[
-C-\ddot{N} H-(\text { peptide bond })
\]
A. \( C N \) bond length in patients is longer than the usual bond length of N-bond
в. о
spectroscopic analysis show planar structure
c. \( C N \) bond length in proteins is smaller than usual bond length of \( C N \) bond
D. None of above


NAND gate in the following is
\( A \)
в.
\( c \)
D.


Which of the following statements is
not true about meso compounds?
A. They have an internal mirror plane.
B. They are optically active
c. They are optically inactive.
D. They are achiral.


The following velocity-time graph shows
the motion of a cyclist. Find (i) its acceleration, (ii) its velocity and (iii) the distance covered by the cyclist in 15
seconds.


The molecular formula of the
hydrocarbon (A) is:
\( (\mathrm{A}) \)
\( \mathbf{A} \cdot C_{2} H_{6} \)
\( \mathbf{B} \cdot C_{2} H_{4} \)
\( \mathbf{c} \cdot C_{3} H_{6} \)
D. \( C_{3} H_{8} \)


Why does carbon form number of
compounds?


Magnetic field inside a long solenoid carrying current is:
A. same at all points (uniform)
B. different at poles and at the centre
c. zero
D. different at all points


The variation in potential energy of a
harmonic oscillator is as shown in the
figure. The spring constant is
A \( \cdot 1 \times 10^{2} \mathrm{Nm}^{-1} \)
B. \( 1.5 \times 10^{2} N m^{-1} \)
c. \( 0.0667 \times 10^{2} N m^{-1} \)
D. \( 3 \times 10^{2} \mathrm{Nm}^{-} \)


In the group \( Q-\{-1\} \) under the binary
operation \( + \) defined by \( a * b=a+b+ \)
\( a b \) the inverse of 10 is
A \( \cdot \frac{1}{10} \)
в. \( \frac{11}{10} \)
c. \( \frac{-11}{10} \)
D. \( \frac{-10}{11} \)


No energy is required in the absorption
of water through
A. Passive absorption
B. Active absorption
c. Both passive and active absorption
D. None of the above


The sum of the series \( 1-\frac{3}{2}+\frac{5}{4}-\frac{7}{8}+ \)
\( \ldots \infty \) is
\( ^{A} \cdot \frac{2}{9} \)
B. \( \frac{-4}{9} \)
c. \( \frac{4}{9} \)
D. \( \frac{-2}{9} \)


Let \( A \) and \( B \) be sets. Show that \( f: A \times \)
\( B \longrightarrow B \times A \) such that \( f(a, b)=(b, a) \)
is bijective function


If the bar magnet is turned around by
\( 180^{\circ}, \) where will the new null points be located?


If enthalpies of formation for \( \boldsymbol{C}_{2} \boldsymbol{H}_{4}(\boldsymbol{g}) \)
\( C O_{2}(g) \) and \( H_{2} O(l) \) at \( 25^{\circ} \mathrm{C} \) and 1 atm pressure be 52,-394 and -286
\( k J \) mol\( ^{-1} \) respectively, then the
enthalpy of combustion of \( C_{2} H_{4}(g) \) will be:
A. \( -141.2 \mathrm{kJ} \mathrm{mol}^{-1} \)
B. - 1412 k J mol \( ^{-1} \) ?
c. \( +141.2 \mathrm{kJ} \mathrm{mol}^{-1} \)
D. +1412 k \( \mathrm{mol}^{-1} \)


is the most complicated and longest phase of meiotic division.
A. Prophase I
B. Prophase I
c. Metaphase I
D. Metaphase II


A metal \( X \) when burnt in air, \( X \) -forms
oxide and nitride both. \( X \) can be:
\( \mathbf{A} \cdot R b \)
в. \( M g \)
\( c . N a \)
D. \( K \)


Solve for \( \mathbf{y}:\left|\begin{array}{ccc}\boldsymbol{x}+\boldsymbol{y} & \boldsymbol{x} & \boldsymbol{x} \\ \boldsymbol{x} & \boldsymbol{x}+\boldsymbol{y} & \boldsymbol{x} \\ \boldsymbol{x} & \boldsymbol{x} & \boldsymbol{x}+\boldsymbol{y}\end{array}\right|= \)
\( \mathbf{1 6}(\boldsymbol{3} \boldsymbol{x}+\boldsymbol{4}) \)


n \( \Delta P Q R S \) is a point on \( P Q \) such that
\( \mathrm{SR}=\mathrm{QR}=\mathrm{SP} . \) and \( \angle P S R=120^{\circ} . \) Find
\( \angle P \)


Nephridia of Pheretima are
A. Protonephridia
B. Solenocytes
c. Micrometanephridia
D. Meganephridia


If \( f(x)=x^{2} e^{-x^{2} / a^{2}} \) is an increasing
function then (for \( a>0 \) ), x lies in the
interval
\( \mathbf{A} \cdot[a, 2 a] \)
в. \( (-\infty,-a) \cup(0, a) \)
c \( .(-a, 0) \)
D. None of these


Evaluate the given definite integrals as
limit of sums:
\( \int_{0}^{5}(x+1) d x \)


The oxidation state of \( \mathrm{Mn} \) in \( \boldsymbol{K}_{\mathbf{2}} \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{\boldsymbol{4}} \)
is:
\( A \cdot+5 \)
\( B \cdot+4 \)
\( c \cdot+7 \)
\( D \cdot+6 \)


An electron moves a distance of \( 6 \mathrm{cm} \)
when accelerated from rest by an electric field of strength \( 2 \times 10^{4} N C^{-1} \)
Calculate the time of travel. (mass of
electron \( \left.=9.1 \times 10^{-31} k g\right) \)


Area of a long solenoid is doubled.So how many times we have to increase its
length to keep its self inductance
constant-
A.
B. 2
\( c \cdot 3 \)
\( D \)


Find the middle term in the expansion of \( \left(\frac{x}{a}-\frac{a}{x}\right)^{21} \)
A \( \cdot 20_{110} \frac{x}{a},^{21} C_{10} \frac{a}{x} \)
В. \( _{20} C_{9} \frac{x}{a},^{2} 16_{10} \frac{a}{x} \)
\( ^{\mathrm{C}} \cdot_{21} C_{10} \frac{x}{a^{2}},-^{21} 1_{10} \frac{a}{x} \)
D. \( _{21} C_{9} \frac{x}{a},^{21} C_{10} \frac{a}{x} \)


Solve: \( 2 x-\frac{1}{3}=\frac{1}{5}-x \)


Following Reaction \( N H_{4}^{+}(a q)+C N^{-}(a q) \rightleftharpoons \)
\( \boldsymbol{H} \boldsymbol{C N}(\boldsymbol{a q})+\boldsymbol{N H}_{3}(\boldsymbol{a q}) \)
proceeds in:
A. forward direction
B. backward direction
C. in both sides equally
D. can't be predicted


Given a body has a heat capacity of
1.6 \( c a l /^{o} C . \) What is the amount of heat
required to raise its temperature by
\( \mathbf{1 0}^{\circ} \boldsymbol{C} ? \)
\( \mathbf{A} \cdot 16 \mathrm{cal} \)
B. 1.6 call
\( c .8 \) са\( a l \)
D. 4 call \( l \)


The mass of a metal scale of uniform
thickness is \( 1.6 k g \) and its length is \( 2 m \) This scale is placed on the horizontal surface of the table such that \( \frac{1}{4}^{t h} \) of its length is beyond the edge of the table. The maximum mass that can be
suspended to this scale at a distance of 10cm from the free end of the scale so
that scale does not turn down is:
A . \( 1 k g \)
в. \( 2 k g \)
\( c \cdot 2 \cdot 4 k g \)
D. 3.2 2 k


The term dephlogisticated air was given by
A. Von Mayer
B. Van Helmont
c. warburg
D. Priestely


Wave front means:
A. all particles in it have same phase
B. few particles are in same phase, rest are in opposite phase
C . all particles have opposite phase of vibrations
D. all particles have random vibrations


Draw the electron dot structure for
oxygen molecule.
\( A \)
B.
\( c \)
D.


Which one is common among nucleus, chloroplast and mitochondria?
A. Cristae
B. Nucleic acids
c. Thylakoids
D. Carbohydrate metabolism


Which of the following metal cannot occur in native state?
A. \( C u \)
в. \( A l \)
\( c . A g \)
D. None of the above


Point \( D \) has coordinates as (3,4,5)
Find the coordinates of point \( G \)
\( \mathbf{A} \cdot(0,3,5) \)
B. (3,0,4)
\( \mathbf{C} \cdot(3,5,4) \)
\( \mathbf{D} \cdot(3,0,5) \)


Phosphoric acid is highly soluble in :
A . oil
B. Ammonia solution
c. water
D. Benzene


Two straight wires \( A \) and \( B \) of lengths 10m and 12m carrying currents of 4.0 A and 6.0 A respectively in opposite direction, lie parallel to each other at a distance of \( 3.0 \mathrm{cm} . \) The force on a \( 15 \mathrm{cm} \)
section of the wire \( \mathrm{B} \) near its centre is
A. 2.4 \( \times 10^{-5} N \), attractive
B. 2.4 \( \times 10^{-5} N \), repulsive
C. \( 1.2 \times 10^{-5} N \), attractive
D \( \cdot 1.2 \times 10^{-5} N, \) repulsive


Q Type your question-
\( (A) \)
4
\( B \)
\( c \)
\( D \)
\( \& \)


At the uppermost point of a projectile its velocity and acceleration are at an angle of :-
A \( \cdot 180^{\circ} \)
B. \( 90^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 45^{\circ} \)


State Rolle's theorem.


What are the main constituents of
dettol?


A piece of elastic was stretched by \( 24 \% \)
to a length of \( 31 \mathrm{cm} \). Find its unstretched original length.
\( A \cdot 24 \mathrm{cm} \)
B . \( 26 \mathrm{cm} \)
c. \( 25 \mathrm{cm} \)
D. \( 20 \mathrm{cm} \)


Find the projection of the vector \( \hat{\mathbf{i}}-\widehat{\boldsymbol{j}} \) on the vector \( \hat{\mathbf{i}}+\widehat{\boldsymbol{j}} \)


Find three rational numbers between 5
and -2


What will be the molarity of \( 30 m L \) of
\( 0.5 M H_{2} S O_{4} \) solution diluted to
\( 500 m L ? \)
\( \mathbf{A} \cdot 0.3 M \)
в. \( 0.03 M \)
\( c .3 M \)
D. \( 0.103 M \)


Three years ago, the population of a town was \( 50000 . \) If the annual increase
during three successive years be at the rate of \( 5 \%, 4 \% \) and \( 3 \% \) respectively. What is the present population?


Which one of the following is not dependent on the intensity of incident photon in a photoelectric experiment?
A. work function of the surface
B. kinetic energy of photo-electron
c. stopping potential
D. amount of photo-electric current


Which of the following options is a major water pollutant nowadays?
A. Industrial effluents and waste
B. Agricultural waste
c. Domestic waste
D. None of the above


Which of the following water pollutants encourage the formation of algae?
A . Insecticides
B. Heavy metals
c. Plant nutrients
D. Sediments


A \( 10.0 \mathrm{W} \) electrical heater is used to
heat a container filled with \( 0.5 \mathrm{kg} \) of water. It is found that the temperature
of the water and the container rose by 3 K in 15 minutes. The container is then
emptied, dried, and filled with \( 2 \mathrm{kg} \) of an oil. It is now observed that the same
heater raises the temperature of the container-oil system by 2 Kin 20 minutes. Assuming no other heat losses in any of the processes, the specific
heat capacity of the oil is??
A \( .2 .5 \times 10^{3} J K^{-1} k g^{-1} \)
B. \( 5.1 \times 10^{3} J K^{-1} k g^{-1} \)
c. \( 3.0 \times 10^{3} J K^{-1} k g^{-1} \)
D. \( 1.5 \times 10^{3} J K^{-1} k g^{-1} \)


(i) Why are interhalogen compounds more reactive than halogens?
(ii) All the five bonds in \( P C l_{5} \) are not
equivalent. Justify.


Consider the following statements in respect of lanthanoids.
1. The basic strength of hydroxides of
lanthanoids increases from \( \mathrm{La}(O H)_{3} \) to
\( \boldsymbol{L} \boldsymbol{u}(\boldsymbol{O} \boldsymbol{H})_{4} \)
2. The lanthanoid ions \( \boldsymbol{L} \boldsymbol{u}^{3+}, \boldsymbol{Y} \boldsymbol{b} \boldsymbol{6} \boldsymbol{2}+, \boldsymbol{C} \boldsymbol{e}^{4+} \) are diamagnetic.
Which of the statement(s) given above is are correct?
A. Only 1
B. Only 2
c. Both 1 and 2
D. Neither 1 nor 2


\( \mathbf{n} \Delta \boldsymbol{P} \boldsymbol{Q} \boldsymbol{R}, \angle \boldsymbol{P}=\mathbf{2} \boldsymbol{x}+\mathbf{1}^{\circ}, \angle \boldsymbol{Q}=\mathbf{3} \boldsymbol{x}+ \)
\( \mathbf{3}^{\circ} \boldsymbol{a} \boldsymbol{n} \boldsymbol{d} \angle \boldsymbol{R}=\boldsymbol{x}+\boldsymbol{2}^{\circ} . \) What is the value
of x?


Find the total cost of white washing the
4 walls of a cuboidal room at the rate
Rs.15 per \( m^{2} . \) The internal measures of the cuboidal room are length \( 10 \mathrm{m} \) breadth \( 4 \mathrm{m} \) and height \( 4 \mathrm{m} \)


Perform the division.
\( (10 x-25) \div 5 \)


is a transparent liquid that is highly flammable.
A. Uranium
B. Methane
c. Ethane
D. Acetone


A plant is exposed to an optimum amount of carbon dioxide, with a limited light intensity. As the intensity of light increases, the rate of photosynthesis increases.Which of the following act as limiting factor in above-given case?
A. Light
B. Carbon dioxide
c. Temperature
D. All of the above


Which of the following reagents will give white precipitate with the aqueous solution of sulphurous acid?
\( \mathbf{A} \cdot B a C l_{2} \)
в. \( H C l \)
c. \( N a C l \)
D. KCl


Assertion
The bob of a simple pendulum is a ball full of water. If a fine hole is made in the
bottom of the ball, the time period first increases and then decreases.
Reason
As water flows out of the bob the weight of bob decreases.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Which of the following catalyst is used in the Haber process for the manufacture of ammonia?
A. Platinized asbestos
B. Iron with a suitable promoter
c. copper oxide
D. Alumina


A satellite of mass \( m \) moves along
an elliptical path around the earth. The areal velocity of the satellite is proportional to
A . \( m \)
B. \( m^{-1} \)
\( c \cdot m^{0} \)
\( D \cdot m^{\frac{1}{2}} \)


Which of the following is true for
spontaneous adsorption of \( \boldsymbol{H}_{2} \) gas
without dissociation on the solid
surface?
A. Process is exothermic and \( \Delta \mathrm{S}<0 \)
B. Process is endothermic and \( \Delta S>0 \)
c. Process is exothermic and \( \Delta S>0 \)
D. Process is endothermic and \( \Delta S<0 \)


The range of the function \( y= \) \( \frac{1}{(2-\sin 3 x)} \) is
\( ^{\mathrm{A}} \cdot\left(\frac{1}{3}, 1\right) \)
в. \( \left[\frac{1}{3}, 1\right) \)
c. \( \left[\frac{1}{3}, 1\right] \)
D. None of these


A chain of length \( L \) and mass \( m \) is placed upon a smooth surface. The length of BA is \( (\boldsymbol{L}-\boldsymbol{b}) \). Calculate the
velocity of the chain when its end
reaches B.
B. \( 2 \sqrt{\frac{g \sin \theta}{L}}\left(L^{2}-b^{2}\right) \)
c. \( \sqrt{\frac{g \sin \theta}{L}\left(L^{2}-b^{2}\right)} \)
D. \( \sqrt{\frac{g \sin \theta}{2 L}}\left(L^{2}-b^{2}\right) \)


The cube of two digit number may have seven or more digits
A. True
B. False
c. Ambiguous
D. Data insufficient


Assertion
For the function \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2}+\boldsymbol{3} \boldsymbol{x}+\boldsymbol{2} \)
\( \boldsymbol{L} M \boldsymbol{V} \boldsymbol{T} \) is applicable in \( [\mathbf{1}, \boldsymbol{2}] \) and the
value of \( c \) is \( \frac{3}{2} \)
Reason
If \( L M V T \) is known to be applicable for
any quadratic polynomial in \( [a, b], \) then \( c \) of \( L M V T \) is \( \frac{(a+b)}{2} \)
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


Is it right to say that \( \sin (A+B)= \)
\( \sin A+\sin A . \) Justify your answer?


In which of the following, use of non metals is more as compared to
metals?
A. human body
B. fertilisers
c. crackers
D. all of the above


\( \boldsymbol{x}=\mathbf{0}, \boldsymbol{y}=-\mathbf{0 . 5 0 0 m}, \boldsymbol{z}=+\mathbf{0 . 5 0 0 m} \)


Which of the following statement
concerning Lanthanoid is incorrect?
A. All Lanthanoids are highly dense metals.
B. Most characteristic oxidation state of Lanthanide
elements is +3.
C. The ionic radii of trivalent Lanthanides steadily increase with increase in the atomic number
D. Lanthanoids are separated from one another by ion exchange methods


Outer ear is called
A. Tympanic Membrane
B. Cochlea
C. Pinna
D. Auditory canal


In the series \( (k b j s s a f e e n o p q f j \) i o \( \mathrm{m} \mathrm{p} \), the number of consonant present
are :
A . 11
B . 13
c. 14
D. 12


Which of the following is Iyophobic colloid?
A. starch in water
B. Gum in water
c. soap in water
D. Gold solution


8
box and covered it with a black paper
from all sides. They fixed a source of light (a torch) at one end of the box by making a hole in it and made another
hole on the other side to view the light.
They placed a milk sample contained in a beaker/tumbler in the box as shown
in the Fig.2.4. They were amazed to see
that milk taken in the tumbler was
¡IIluminated. They tried the same
activity by taking a salt solution but
found that light simply passed through
it?
Explain why the milk sample was illuminated. Name the phenomenon
involved.


Solve: \( 2.25 x-125=3 x+3.75 \)


For the equilibrium
\( N_{2}(g)+3 H_{2}(g) \Leftrightarrow 2 N H_{3}(g) \) at \( 1000^{\circ} \)
\( C \)
the equilibrium constant is very low, then which of the following is correct at
equilibrium?


Change in the state of rest or of uniform motion is brought about by:
A. Acceleration
B. Force
c. Energy
D. None


Calculate the probability that a number selected at random from the set \{ \( \mathbf{2}, \mathbf{3}, \mathbf{7}, \mathbf{1 2}, \mathbf{1 5}, \mathbf{2 2}, \mathbf{7 2}, \mathbf{1 0 8}\} \) will be
divisible by both 2 and 3
A
в. \( \frac{3}{8} \)
\( c \cdot \frac{3}{5} \)
D.
\( E \cdot 7 \)
8


Write IUPAC names of the given compounds.
\( \boldsymbol{C H}_{2}=\boldsymbol{C H C l} \)


If \( a+b+c=0 \) then prove that \( a^{3}+ \)
\( b^{3}+c^{3}=3 a b c \)


Which if the following is a common reducing agent for extracting metals from ore?
A. \( C O \)
B. Carbon
c. Hydrogen
D. All of the above


Which of the following is capable of self replication?
A. A protein molecule
B. A carbohydrate molecule
c. A water molecule
D. A nucleic acid


Identify \( Z \) in the following sequence.
\[
\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{Br} \stackrel{\mathrm{KCN}}{\longrightarrow}(\mathrm{Q}) \frac{\mathrm{dil.HCl}}{\Delta}>\widehat{\mathrm{Z}}
\]
A \( \cdot \mathrm{CH}_{3} \mathrm{COCl} \)
в. \( \mathrm{CH}_{3} \mathrm{CONH}_{2} \)
c. \( \mathrm{CH}_{3} \mathrm{COOH} \)
D. \( \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{COOH} \)


Explain the extraction of zinc from its
chief ore.


Find the mean deviation about the
median for the following data. \( \mathbf{1 3}, \mathbf{1 7}, \mathbf{1 6}, \mathbf{1 1}, \mathbf{1 3}, \mathbf{1 0}, \mathbf{1 6}, \mathbf{1 1}, \mathbf{1 8}, \mathbf{1 2}, \mathbf{1 7} \)


A projectile is projected at a speed u at an angle with the horizontal. At the highest point projectile split into two fragments comming to rest Then.


The displacement of a particle is given by \( \vec{r}=A(\vec{i} \cos \omega t+\vec{\jmath} \sin \omega t) . \) The
motion of the particle is:
A. simple harmonic
B. On a straight line
c. on a circle
D. With constant acceleration


Which of the following on thermal decomposition yields a basic as well as an acidic oxide?
A. \( N a N O_{3} \)
в. \( K C l O_{3} \)
\( \mathrm{c} \cdot \mathrm{CaCO}_{3} \)
D. \( N H_{4} N O_{3} \)


Which of the following statements is
correct?
rhis question has multiple correct options
A. Dipole moment
B. Stability of free radical
c. Basic strength: \( C H_{3} O^{\ominus}>\stackrel{\delta}{O} H>R \) S
D. Basic and nucleophilic strength: \( I^{\ominus}>B r^{\ominus}>C l^{\ominus} \) >
\( F^{c} \)


\( \operatorname{Let} \overrightarrow{\boldsymbol{a}}=2 \hat{\hat{\boldsymbol{i}}}+\boldsymbol{\lambda}_{1} \hat{\boldsymbol{j}}+\boldsymbol{3} \hat{\boldsymbol{k}}, \overrightarrow{\boldsymbol{b}}=\boldsymbol{4} \hat{\boldsymbol{i}}+(\boldsymbol{3}- \)
\( \left.\lambda_{2}\right) \hat{j}+6 \hat{k} \) and \( \vec{c}=3 \hat{i}+6 \hat{j}+\left(\lambda_{3}-1\right) \hat{k} \)
be three vectors such that \( \vec{b}=2 \vec{a} \) and \( \vec{a} \)
is perpendicular to \( \vec{c} \). Then a possible
value of \( \left(\lambda_{1}, \lambda_{2}, \lambda_{3}\right) \) is?
\( ^{\mathbf{A}} \cdot\left(\frac{1}{2}, 4,-2\right) \)
в. \( \left(-\frac{1}{2}, 4,0\right) \)
c. (1,3,1)
D. (1,5,1)


A nucleus of lead \( P b_{82}^{314} \) emits two electrons'followed by an alpha particle. The resulting nucleus will have
A. 82 protons and 128 neutrons
B. 80 protons and 130 neutrons
c. 82 protons and 130 neutrons
D. 78 protons and 134 neutrons


In human beings, sex is determined
A. Before fertilization of ovum
B. During 6th week of foetal life when androgens are produced
C. At the time of fertilization of ovum
D. During 7th and 8th weeks of foetal life when gonads differentiate into testis and ovary


From the mast head of a ship the angle of depression of a boat is \( \tan ^{-1}\left(\frac{5}{12}\right) \) If the mast head is 100 metres. The
distance of the boat from the ship is
\( \mathbf{A} \cdot 120 m \)
B. \( 180 m \)
c. \( 240 m \)
D. None of these


In the Newton's gravitational law, \( \boldsymbol{F}= \) \( \frac{G M m}{d^{2}}, \) the quantity \( G \)
A. depends on the value of \( g \) at the place of observation
B. is used only when the earth is one of the two masses
c. is greatest at the surface of the earth
D. is universal constant in nature


\( 3000 J \) of heat is given to a gas at a
constant pressure of \( 2 \times 10^{5} N / m^{2} . \) If
its volume increases by 10 litres during the process find the change in the
internal energy of the gas.


In a circle if a chord \( A B \) is nearer to the
centre \( \boldsymbol{O} \) than the chord \( \boldsymbol{C} \boldsymbol{D} \) then:
\( \mathbf{A} \cdot A B>C D \)
B. \( A B=C D \)
c. \( A B<C D \)
D. none of these


Two spring of force constant \( 300 \mathrm{N} / \mathrm{m} \) (spring \( A \) ) and \( 400 \mathrm{N} / \mathrm{m} \) (spring \( \mathrm{B} \) ) are joined together in series. The combination is compressed by \( 8.75 \mathrm{cm} \) The ratio of energy stored in \( A \) and \( B \) is
\( \underline{E}_{\boldsymbol{B}_{\boldsymbol{B}}} \)
A \( \cdot \frac{4}{3} \)
в. \( \frac{16}{9} \)
\( c \cdot \frac{3}{4} \)
D. \( \frac{9}{16} \)


A long horizontal wire \( \boldsymbol{P} \) carries a
current \( 50 A \). It is rigidly fixed. Another
line wire \( Q \) is placed directly above and
parallel to \( P . \) The weight of wire \( Q \) is
\( 0.075 N m^{-1} \) and caries a current of
\( 25 A . \) Find the position of wire \( Q \) from \( P \) so that wire to remains suspended due to the magnetic repulsion-
A. \( 3.33 \mathrm{mm} \)
B. \( 33.3 \mathrm{mm} \)
c. 334 mm
D. 333 mm


\( X e F_{4} \) reacts with water \( a t-80^{\circ} C \) to
give:
A \( . \quad X e O F_{2} \)
в. \( X e O F_{4} \)
\( \mathbf{c} \cdot X e O_{3} \)
D. \( X e O_{2} F_{2} \)


Write two examples of ferromagnetic
substance.


wire/is/are connected
directly to the electric meter.
A. line wire
B. earth wire
c. neutral wire
D. all


\( \int \frac{1-\cos x}{\cos x(1+\cos x)} d x \)
A. \( \log (\sec x-\tan x)-2 \tan \frac{x}{2} \)
B. \( \log (\sec x+\tan x)-\tan \frac{x}{2} \)
C \( \cdot \log (\sec x+\tan x)+2 \tan \frac{x}{2} \)
D \( \cdot \log (\sec x+\tan x)-2 \tan \frac{x}{2} \)


f \( x=3 t, y=1 / 2(t+1), \) then the value
of \( t \) for which \( x=2 y \) is
\( A \cdot 1 \)
B. \( 1 / 2 \)
\( c .-1 \)
D. \( 2 / 3 \)


A body cools from \( 60^{\circ} \mathrm{C} \) to \( 50^{\circ} \mathrm{C} \) in
2 min when it is placed in a room
maintained at \( 30^{\circ} \mathrm{C} \). The time taken by the same body in the same room to cool
further from \( 50^{\circ} \mathrm{C} \) to \( 40^{\circ} \mathrm{C} \) will be
A. Less than 2 min
B. Approximately 2 min
c. Greater than 2 min
D. 2 min


Name any two defects vision which can
be corrected by any of spectacles.


Calculate the enthalpy change when
\( 50 m L \) of \( 0.01 M C a(O H)_{2} \) reacts with
\( 25 m L \) of \( 0.01 M H C l . \) Given that \( \Delta H^{o} \)
neutralisation of a strong acid and a
strong base is \( 140 k \) cal \( m o l^{-1} \)
A . 14 kcall \( l \)
B. 35 kcall
c. \( 10 \mathrm{kcal} \)
D. 7.5k call


Endospores develop in
A. Mucor and Bacillus
B. Saccharomyces and Clostridium
C. Monococcus and Clostridium
D. Bacillus and Clostridium


Find the area of the region bounded by
the following curves, the \( X \) -axis and
the given lines.
\( \boldsymbol{y}=\boldsymbol{x}^{4}, \boldsymbol{x}=\mathbf{1}, \boldsymbol{x}=\mathbf{5} \)


'Rat-ki-Rani' and tomato belongs to
family
A. Mimosoideae
B. Oleaceae
c. Solanaceae
D. Malvaceae


The correct order of increasing bond
order is :
\( \mathbf{A} \cdot C O<C O_{2}<C O_{3}^{2-}(\mathrm{CO} \text { bond }) \)
B. \( C N^{-}<N C N^{2-}<R-C(N H)-N H_{2}(C-N \text { Bond}) \)
c. \( C l O<C l O_{2}<C l O_{3}<C l O_{4} \) (Cl-O bond)
D. \( S O_{2}<S O_{4}^{2-}<S O_{3}^{2-}(\text { SO bond }) \)


The oxide of a metal contains \( 52.91 \% \) of
the metal. If the formula of the metal
oxide is \( M_{2} O_{3}, \) what is the atomic
mass of the metal?
\( \mathbf{A} .8 .99 \)
B. 26.96
c. 17.97
D. 53.93


In RNA thymine is replaced by which nucleotide?
A. Adenine
B. Uraci
c. cytosine
D. Guanine


A body is projected up along a rough
inclined plane of inclination \( 45^{\circ} . \) The
coefficient of friction is \( 0.5 . \) Then the
retardation of the block is:
A \( \cdot \frac{g}{2 \sqrt{2}} \)
в. \( \frac{g}{2} \)
c. \( \frac{3 g}{2 \sqrt{2}} \)
D. \( \frac{g}{\sqrt{2}} \)


Four equipotential curves in an electric
field are shown in the figure. A,B,C are
three points in the field. If electric
intensity at \( A, B, C \) are \( E_{A}, E_{B}, \) and \( E_{C} \)
then:
\( \mathbf{A} \cdot E_{A}=E_{B}=E_{C} \)
в. \( E_{A}>E_{B}>E_{C} \)
c. \( E_{A}<E_{B}<E_{C} \)
D. \( E_{A}>E_{B}<E_{C} \)


Assertion
The capacitive reactance limits the amplitude of the current in a purely capacitive circuit
Reason
Capacitive reactance is proportional to
the frequency and the capacitance
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


Use the given figure to find :
Given, \( n(\xi)=52, n(A)=43 \) and
\( \boldsymbol{n}(\boldsymbol{B})=\mathbf{2 7} \)
\( n\left(B^{\prime}\right) \)


A high concentration of synthetic auxins is generally used for
A. Weed control
B. Enhancing root initiation
c. controlling of cell enlargement
D. Preventing the growth of the lateral buds


The cube of an odd natural number is
always
A. Even
B. Odd
c. Even or odd
D. Can't say


The equation of motion for a particle executing SHM is given by \( \boldsymbol{x}= \)Atan\omegat
A. True
B. False


Mosses and ferns are found in moist
and shady places because both
A. Require presence of water for fertilization
B. Do not need sunlight for photosynthesis.
c. Depend for their nutrition on micro-organisms which can survive only at low temperature.
D. Cannot compete with sun-loving plants


Seema's uncle was advised by his doctor to have an MRI
(Magnetic Resonance Imaging) scan of his brain. Her uncle felt it to be
expensive and wanted to postpone it. When Seema learnt about this, she took
the help of her family and
also approached the doctor, who also offered a substantial discount. She
then convinced her uncle to undergo the
test to enable the doctor to know
the condition of his brain. The
information thus obtained greatly helped the doctor to treat him properly. Based on the above paragraph, answer the question. Assuming that MRI test was performed using a magnetic field of \( 0.1 \mathrm{T} \), find the minimum and maximum values of
the force that the magnetic field could exert on a proton moving with a speed of
\( \mathbf{1 0}^{4} \mathbf{m} / \mathbf{s} \)

Given charge of proton \( =1.6 \times 10^{-19} \mathrm{C} \)


chlorine. If the atomic mass of chlorine
is \( 35.5, \) then molar mass ratio of these
isotopes is \( x: 1, \) where \( x \) is:


The escape velocity of a body depends upon its mass as
\( \mathbf{A} \cdot m^{0} \)
B . \( m^{\text {। }} \)
\( \mathrm{c} \cdot m^{3} \)
D. \( m^{2} \)


The function \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \frac{\log (1+a x)-\log (1-b x)}{x} \) is not
defined at \( x=0 . \) The value which
should be assigned to \( f \) at \( x=0 \) so that
it is continuous there, is
A \( . a-b \)
B. \( a+b \)
\( \mathbf{c} \cdot \log a+\log b \)
D. none of these


What is cardiac output? What is the
value of it in healthy man?


Which of the following subjects is not included in the union list?
A. Defence
B. Income tax
c. Railway
D. Sales tax


is the force of attraction
between any two bodies in the universe.
A. Gravitation
B. Polarityyy
c. Induction
D. Joule


At sea level, the vertical height of
mercury supported in the tube of simple barometer is
above the mercury level in the bowl
A . 36
B. 76
c. 100
D.


When the number of nucleons in nuclei
increases, 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


Collect information about sea weeds,
sea kelp from your school library and write a note with examples.


The difference in number of angular nodes and the number of radial nodes in
the orbital to which the last electron of
chromium present is


\( \mathbf{1} \boldsymbol{A}= \)
\( \mathbf{A} \cdot 10^{2} \)
B. \( 10^{3} \)
\( \mathbf{c} \cdot 10^{-3} \)
D. \( 10^{-6} \)


The acceleration - time graph for a particle in rectilinear motion is as
shown in the figure. Find the average
acceleration in first twenty seconds.
\( A \cdot 10 m s^{-2} \)
B. \( 15 \mathrm{ms}^{-2} \)
\( \mathrm{c} \cdot 20 \mathrm{ms}^{-2} \)
D. \( 25 \mathrm{ms}^{-2} \)


The type of soil which can hold water for more time have
A. Lower percolation rate
B. Higher percolation rate
c. Intermediate percolation rate
D. None of the above


A bimetallic strip of steel and brass of length \( 10 \mathrm{cm}, \) initially at \( 15^{\circ} \mathrm{C}, \) is heated to \( 45^{\circ} \mathrm{C} \). What is the difference in length
between the two substances after they have been heated? The coefficient of
linear expansion for steel is \( 1.2 \times \) \( 10^{5} / C^{o}, \) and the coefficient of linear
expansion for brass is \( 1.9 \times 10^{5} / C^{o} \)


In a uniform electric field, equipotential
surfaces must:
This question has multiple correct options
A. be plane surfaces
B. be normal to the direction of the field
C. be spaced such that surfaces having equal differences in potential are separated by equal distances
D. have decreasing potentials in the direction of the field


' toppr 5
\( Q \) туре
Provide the structure form as it exists
in the intestine
\( x \)
\( x \)
\( c \)


For any two events \( A \) and \( B \) in a sample
space:
This question has multiple correct options
\( ^{\mathbf{A}} \cdot p(A \mid B) \geq \frac{P(A)+P(B)-1}{P(B)}, P(B) \neq 0, \) is always true
B \( . P(A \cap \bar{B})=P(A)-P(A \cap B) \), does not hold
C \( . P(A \cup B)=1-P(\bar{A}) P(\bar{B}) \), if \( A \) and \( B \) are independent
D \( . P(A \cup B)=1-P(\bar{A}) P(\bar{B}) \), if \( A \) and \( B \) are disjoint


A parallel plate capacitor has capacitance \( C . \) If it is equally filled the parallel of materials of dielectric
constant \( K_{1} \) and \( K_{2} \) its capacity
becomes \( C_{1} . \) The ratio of \( C_{1} \) and \( C \) is
A. \( K_{1}+K_{2} \)
в. \( \frac{K_{1} K_{2}}{K_{1}+K_{2}} \)
c. \( \frac{K_{1}+K_{2}}{K_{1} K_{2}} \)
D. \( \frac{2 K_{1} K_{2}}{K_{1}+K_{2}} \)


Find the time period of a wave whose frequency is \( 400 \mathrm{Hz} ? \)
A. 0.0012 s
B. 0.0025 s
c. 0.0015 s
D. 0.0010 s


The length and breadth and height of a cuboid are \( (x+3),(x-2) \) and \( (x-1) \)
respectively. Find its volume.


If an electron is travelling at \( 200 m / s \) within 1 m/ \( s \) uncertainty, what is the theoretical uncertainty in its position in \( \mu m(\text { micrometer }) ? \)
A . 14.5
B . 29
c. 58
D. 114


Name a material which is used in
making control rods in a nuclear
reactor


A generator or dynamo works on the principle:
A. Heating effect of electric current
B. Electromagnetic induction
c. chemical effect of electric current
D. All of the above


Remainder when \( p(x)=x^{4}-5 x+6 \) is
divided by \( g(x)=2-x^{2} \) is \( -m x+2 m \)
Find \( \boldsymbol{m} \)


A boy sitting firmly over a rotating stool (constant angular velocity) has his arms folded. If he stretches his arms,
his angular momentum about the axis of rotation.
A. increases
B. decreases
c. remains unchanged
D. None of the above


A metal rod \( A \) of \( 25 \mathrm{cm} \) length expands by \( 0.050 \mathrm{cm} \) when its temperature is raised from \( 0^{\circ} \mathrm{C} \) to \( 100^{\circ} \mathrm{C} \). Another rod
B of a different metal of length \( 40 \mathrm{cm} \) expands by \( 0.040 \mathrm{cm} \) for the same rise in temperature. A third rod C of 50 cm
length is made up of pieces of rods \( A \) and B placed end to end expands by
\( 0.03 \mathrm{cm} \) on heating from \( 0^{\circ} \mathrm{C} \) to \( 50^{\circ} \mathrm{C} \)
Find the lengths of each portion of the composite rod.


If \( s \) and \( t \) respectively the sum and the sum of the squares of n successive positive integers beginning with a, then
show that \( n t-s^{2} \) is independent of a.


Four charges \( \boldsymbol{q}_{1}=\mathbf{1} \mu \boldsymbol{C}, \boldsymbol{q}_{2}=\boldsymbol{2} \boldsymbol{\mu} \boldsymbol{C} \)
\( \boldsymbol{q}_{3}=\boldsymbol{3} \boldsymbol{\mu} \boldsymbol{C} \) and \( \boldsymbol{q}_{4}=\boldsymbol{4} \boldsymbol{\mu} \boldsymbol{C} \) are placed at
\( (0,0,0),(1 m, 0,0),(0,1 m, 0),(0,0,1 m) \)
respectively. Let \( \vec{F}_{i} \) be the net force
acting on ith charge of the given charges then \( \sum \overrightarrow{\boldsymbol{F}}_{\boldsymbol{i}}=\ldots \)
A. 0.018
B. \( 0.02 N \)
\( c .0 .036 N \)
D. zero


Which of the following postulates of
kinetic theory of gases is not correct?
A. Gases consist of particles which are in continuous, random motion
B. The particles are infinitely small and very close to each other
C. The collisions of the particles with each other are elastic
D. The pressure of a gas is caused by the collisions of gas particles with the wall of the container


IUPAC name of valeric acid is:
A. Propanoic acid
B. Butanoic acid
c. Ethanoic acid
D. Pentanoic acid


Prove that 7 is a factor of \( 2^{3 n}-1 \) for all
natural numbers n.


Which soil is red in colour?
A. Multani soil
B. Shadu soil
c. Terracotta soil
D. Kaolin (china clay)


A Standard unit does not change with respect to space and time.
A . True
B. False


If the formula weight of \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) is 98 then the amount of acid present in 400 \( \mathrm{ml} \) of 0.1 molar solution of acid will be:
A. \( 2.45 g \)
B . \( 3.92 g \)
c. \( 4.90 g \)
D. \( 9.80 g \)


Find the radian measures
corresponding to the following degree
measures:
\( 25^{\circ} \)
\( -47^{\circ} 30 \)
\( 240^{\circ} \)
\( 520^{\circ} \)


The diameter of a metallic ball is 4.2
cm. What is the mass of the ball, if the
density of the metal is 8.9 g per \( \mathrm{cm}^{3} \) ?


\( \sin 20^{0} \times \cos 40^{0} \times \tan 45^{0} \times \cos 90^{0}= \)


\( \frac{\tan ^{2} \theta}{1+\sec \theta}+1 \) equals to
\( A \cdot \tan \theta \)
B. \( \frac{1}{\cos \theta} \)
\( \mathbf{c} \cdot \sec \theta-1 \)
\( \mathbf{D} \cdot \sec \theta+\tan \theta \)


Write balanced chemical equations for the reaction which would be used in the
laboratory to obtain iron
(II) sulphate.


Sandmeyer reaction is better than
Gattermann reaction because:
A. sandmeyer reaction uses salt of copper while Gattermann reaction uses copper powder
B. only one salt is produced in Sandmeyer reaction while Gattermann reaction produces two salts.
C. sandmeyer reaction gives better yield than Gattermann reaction.
D. all of the above.


An open U-tube contains mercury. When \( 13.6 \mathrm{cm} \) of water is pourd into one of the
\( \operatorname{arms} \) of the tube then the mercury rise
in the other arm from its initial level is:
A . \( 1 c m \)
B. \( 0.5 \mathrm{cm} \)
\( \mathbf{c} \cdot 10 \mathrm{cm} \)
D. \( 5 \mathrm{cm} \)


Choose the correct answers from the
alternatives given Which of the following categories is at the top of the classification hierarchy?
A. Order
B. Class
c. Family
D. Phylum


A car A moves with velocity \( 15 m s^{-1} \) and B with velocity \( 20 m s^{-1} \) are moving in opposite directions as shown in the figure. Find the relative velocity of B
w.r.t. \( A \) and \( A \) w.r.t. \( B \).


A cell with two electrodes, one of grey
tin and the other white tin, both dipped
in solution of \( \left(N H_{4}\right)_{2} S n C l_{6} \) showed
zero e.m.f. at \( 18^{\circ} \mathrm{C} \). What conclusion may
be drawn from this?
A. The e.m.f. developed at the electrode-solution phase boundary cancels the normal e.m.f.
B. Grey tin being non-metallic ceases to provide a reversible electrode reaction
C. Electrode surface develops a protective layer and the cell develops a very large internal resistance
D. The Gibbs energy change of the cell becomes zero


The product obtained when ethyl alcoho is distilled with bleaching powder is? This question has multiple correct options
A. Chloroform
B. Ethyl chloride
c. Acetaldehyde
D. chloral


Find HCF of 45 and 72


A glider is oscillating in SHM on an air track with an amplitude A. You slow it so that its amplitude becomes half.
Find the total mechanical energy in terms of previous value.
A \( \cdot 1 / 2 \)
в. \( 1 / 3 \)
c. \( 1 / \sqrt{5} \)
D. \( 1 / 4 \)


Two electrolytic cells containing molten solutions of nickel chloride and
aluminium chloride are connected in
series. If same amount of electric
current is passed through them, what will be the weight of nickel obtained when 18 g of aluminium is obtained?
\( \left[A \mid=27 \mathrm{g} / \mathrm{mol}, \mathrm{Ni}=58.5 \mathrm{g} / \mathrm{mol}^{-1}\right] \)
A . 117 g
B. \( 58.5 \mathrm{g} \)
c. \( 29.25 \mathrm{g} \)
D. \( 5.85 \mathrm{g} \)


A random variable \( \boldsymbol{X} \) has the following probability distribution:
\[
\begin{array}{lcccc}
\begin{array}{l}
\text { Values } \\
\text { of } \mathbf{X}:
\end{array} & -2 & -1 & 0 & 1 \\
\hline P(x): & 0.1 & \mathrm{k} & 0.2 & 2 \mathrm{k} \\
& & & & \\
& P(x): & & &
\end{array}
\]
Find the value of \( a, \) if \( k=\frac{1}{a} \)


f \( a_{i j}=0(i \neq j) \) and \( a_{i j}=1(i=j) \)
then the matrix \( A=\left[a_{i j}\right]_{n \times n} \) is a
matrix
A. Null
B. Identity
c. Scalar
D. Triangular


Differentiate the following w.r.t \( x \)
\( \sin \left(x^{2}+5\right) \)


The wave function for an orbital is \( \boldsymbol{H}- \)
atom is given as:
\( \mathbf{\Psi}= \)
\( \left(\frac{\sqrt{2}}{81 \sqrt{\pi}}\right)\left(\frac{1}{a_{0}}\right)^{\frac{2}{3}}\left(6-\frac{r}{a_{0}}\right)\left(\frac{r}{a_{0}}\right)^{-\frac{r}{3 a}} \)
The orbital is:
\( A \cdot 2 s \)
в. \( 3 p \)
\( c \cdot 2 p \)
D. \( 3 d \)


Assertion
The number of significant figures in 507000 is three.
Reason
In \( 507000, \) all the zeros are significant.
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


Assertion
Chlorine gas disproportionates in hot and conc. NaOH solution
Reason
NaCl and NaOCl are formed in the above
reaction
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The weight in grams of \( O_{2} \) formed at \( P t \)
anode during the electrolysis of aq.
\( K_{2} S O_{4} \) solution during the passage of one coulomb of electricity is:
A \( \cdot \frac{16}{96800} \)
в. \( \frac{8}{96500} \)
c. \( \frac{32}{96500} \)
D. \( \frac{64}{96500} \)


A water tank is \( 1.4 \mathrm{m} \) long. Im wide and
0.7m deep. then the volume of the tank in litres
A. 780 litres
B. 860 litres
c. 980 litres
D. none of these


Use the Squeeze Theorem to determine the value of: \( \lim _{x \rightarrow 0} x^{4} \sin \frac{\pi}{x} \)


Consider the equation \( \frac{x^{2}}{a^{2}+\lambda}+ \) \( \frac{y^{2}}{b^{2}+\lambda}=1 \) where a and \( b \) are specified
constants and \( \lambda \) is an arbitrary
parameter. Find a differential equation satisfied by it.


For the reaction
\( \mathbf{2} \boldsymbol{N} \boldsymbol{O}_{2}(\boldsymbol{g}) \rightleftharpoons \mathbf{2} \boldsymbol{N} \boldsymbol{O}(\boldsymbol{g})+\boldsymbol{O}_{2}(\boldsymbol{g}) \)
\( \boldsymbol{K}_{c}=\mathbf{1 . 8} \times \mathbf{1 0}^{-\mathbf{6}} \mathbf{a t} \mathbf{1 8 4}^{\boldsymbol{o}} \boldsymbol{C} \)
\( \boldsymbol{R}=\mathbf{0 . 0 8 3 1 k J} \quad \boldsymbol{K}^{-1} \boldsymbol{m o l}^{-1} \)
when \( K_{p} \) and \( K_{c} \) are compared at
\( 184^{\circ} \mathrm{C} \) it is found that:
\( \mathbf{A} \cdot K_{p} \) is greater than \( K_{c} \)
B. \( K_{p} \) is less than \( K_{c} \)
\( \mathbf{c} \cdot K_{p}=K_{c} \)
D. Whether \( K_{p} \) is greater than, less than or equal to \( K_{c} \) depends upon the total gas pressure


Following is the distribution function
\( (x) \) of a discrete \( r . v . x \)
\( F(x) \) \begin{tabular}{l}
0.2 \\
\hline
\end{tabular} 0.37 \( \begin{array}{ll}\text { 0.48 } & \text { 0.62 }\end{array} \)
(i) Find the probability distribution of \( x \)
(ii) Find \( P(x \leq 3),(2<x<5) \)


Find the area \( \left(\text {in } c m^{2}\right) \) of a
parallelogram \( \boldsymbol{P Q R S}, \) if \( \boldsymbol{P R}=\mathbf{2 4} \boldsymbol{c m} \)
and \( Q U=S T=8 c m \)


Consider the situation shown in figure. Both the pulleys and the string are light and all the surfaces are frictionless.
Calculate the force exerted by the clamp on the pulley A in the figure.


An intrinsic semiconductor at the
absolute zero temperature
A. behaves like a metallic conductor
B. behaves like an insulator
c. has a large number of holes
D. has a large number of electrons


Methyl orange (an acid -base indicator) can be prepared by following sequence
of reactions

What would be the structure of methyl
orange?


What is the role of a moderator in a
nuclear reactor?


A concave mirror of radius of curvature
\( 40 \mathrm{cm} \) forms an image of an object placed on the principal axis at a distance \( 45 \mathrm{cm} \) in front of it. Now if the system (including object) is completely immersed in water \( (\mu=1.33), \) then:
A. the image will shift towards the mirror
B. the magnification will reduce.
c. the image will shift away from the mirror and magnification will increase.
D. the position of the image and magnification will not change.


If a line \( O P \) of length \( r \) (Where ' \( O \) ' is the origin) makes an angle \( \alpha \) with \( x \) -axis
and lies on the xz-plane, then what are the coordinates of \( P ? \)
A \( \cdot(r \cos \alpha, 0, r \sin \alpha) \)
B . \( (0,0, r \sin \alpha) \)
\( \mathbf{c} \cdot(r \cos \alpha, 0,0) \)
D \( \cdot(0,0, r \cos \alpha) \)


A stone falls from a balloon that is
descending at a uniform rate of \( 12 m s^{-1} \)
The displacement of the stone from the point of release after 10 sec is :
A. \( 490 \mathrm{m} \)
B. \( 510 \mathrm{m} \)
c. \( 610 \mathrm{m} \)
D. 725m


\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}\left(\sin ^{2} \boldsymbol{x}\right) \)
\( \mathbf{A} \cdot \sin 2 x \)
B. \( \cos 2 x \)
\( c \cdot \sin 4 x \)
D. \( \cos 4 x \)


If the replacement set \( = \) \{-6,-3,0,3,6,9\}\( ; \) find the truth set of
the following:
\( 2 x-1>9 \)
A \( \cdot\{6,9\} \)
в. \{2,6\}
c. \{7,3\}
D. \{5,8\}


In the given figure, \( O \) is the centre of the
circle, \( \angle A C B=54^{\circ} \) and \( B C E \) is a
straight line. Find \( \boldsymbol{x} \)
\( A \cdot 126 \)
B. 54
\( c \cdot 108 \)
D. 90


By passing \( H_{2} S \) gas in acidified
\( K M n O_{4} \) solution, we
get
\( A \cdot K_{2} S \)
B. s
\( \mathrm{c} \cdot \mathrm{K}_{2} \mathrm{SO}_{3} \)
D. \( M n O_{2} \)


Each half of pelvic girdle is made up of
A. Ischium
B. Illium
c. Pubis
D. All of the above


A metal piece of mass \( 160 g \) lies in equilibrium inside a glass of water. The pieces touch the glass at small number of point. If the density of the metal is \( 8000 \mathrm{kg} / \mathrm{m}^{3} \) then the normal force exerted by the bottom of the glass on the metal piece is
\( A \cdot 2 N \)
В. 8 N
c. \( 0.16 N \)
D. 1.4


\( P \) is the point (-5,3) and \( Q \) is the point \( (-5, m) . \) If the length of the straight line PQ is 8 units, the the possible value of "m"' is:
A \( .-5 \) and 5
B. - 5 or 11
c. -5 or -11
D. 5 or 11


Two objects \( A \) and \( B \) are moving towards
each other with velocities \( 10 \mathrm{m} / \mathrm{s} \) and
12 \( \mathrm{m} / \mathrm{s} \) respectively as shown. Find the velocity of B with respect to A.
\( \mathbf{A} \)
A. \( -22 \mathrm{m} / \mathrm{s} \)
в. \( 22 \mathrm{m} / \mathrm{s} \)
c. \( -40 m / s \)
D. \( 17 \mathrm{m} / \mathrm{s} \)


An electric dipole (dipole moment p) is placed in a uniform electric field in stable equilibrium position at rest. Now it is rotated by a small angle and released. The time after which it comes
to the equilibrium position again (for first time) is \( t . \) If the moment of inertia
of the dipole about the axis of rotation is \( x \frac{t^{2} p E}{\pi^{2}}, \) then \( x \) is:
\( A \)
B. 2
\( c \cdot 8 \)
\( D \)


The physical quantity having the same unit in all the systems of unit is :
A. length
B. mass
c. time
D. foot


Initial mass of a radioactive substance
is \( 3.2 \mathrm{mg} \). It has a half-life of \( 4 \mathrm{h} \). Find the mass of the substance left
undecayed after \( 8 \mathrm{h} \)


The covalency of central atom is
maximum in:
\( \mathbf{A} \cdot H C N \)
B. \( N H_{4}^{+} \)
c. \( P C l_{5} \)
D. \( H_{2} O \)


In Millikan oil drop experiment a charged drop falls with a terminal velocity V. If an electric field E is applied vertically upwards it moves with terminal velocity \( 2 V \) in upward
direction. If electric field reduces to \( \boldsymbol{E} / \mathbf{2} \)
then its terminal velocity will be-
A \( \cdot \frac{V}{2} \)
B.
c. \( \frac{3 V}{2} \)
D. \( 2 V \)


If \( H_{2} O \) is taken in large excess, the
order of the reaction will be:
\( \mathbf{A} \cdot \mathbf{1} \)
B.
\( c \cdot 3 \)
D. 2


Define linear magnification produced
by a mirror.


The differential equation for the family of curves \( x^{2}+y^{2}-2 a y=0, \) where \( a \) is
an arbitrary constant is
A \( \cdot 2\left(x^{2}-y^{2}\right) y^{\prime}=x y \)
B \( \cdot 2\left(x^{2}+y^{2}\right) y^{\prime}=x y \)
c. \( \left(x^{2}-y^{2}\right) y^{\prime}=2 x y \)
D. \( \left(x^{2}+y^{2}\right) y^{\prime}=2 x y \)


Let \( l \) be the length of each equal side of
an isosceles triangle. If the length of each equal side is doubled, keeping its height unchanged, then the difference of the squares of bases of the new triangle and the given triangle is
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( 4 l^{2} \)
\( \mathrm{c} \cdot 9 l^{2} \)
D. \( 12 l^{2} \)


A bottle completely filled with conc.
\( H_{2} S O_{4} \) is left unstoppered for several
days and we observe spontaneous overflow of acid. It is due to
A. change in temperature
B. hygroscopic nature of \( H_{2} S O_{4} \)
C. absorption of air by \( H_{2} S O_{4} \)
D. dehydration of \( H_{2} S O_{4} \)


Let I be the purchase value of an equipment and \( V(t) \) be the value after it has been used for t years. The value \( V(t) \) depreciates at a rate given by differential equation \( \frac{\boldsymbol{d} \boldsymbol{V}(\boldsymbol{t})}{\boldsymbol{d} \boldsymbol{t}}=-\boldsymbol{k}(\boldsymbol{T}- \)
\( t), \) where \( k>0 \) is a constant and T is
the total life in years of the equipment. Then the scrap value \( V(t) \) of the
equipment is?
A \( \cdot_{I-\frac{k(T-t)^{2}}{2}} \)
\( \frac{k(T-t)^{2}}{2}+I \)
\( c \cdot T^{2}-\frac{I}{k} \)
D. \( _{I-\frac{k T^{2}}{2}} \)


Calculate the pH of a buffer solution
prepared by dissolving 30 g of \( N a_{2} C O_{3} \)
in \( 500 \mathrm{mL} \) of an aqueous solution
containing \( 150 \mathrm{mL} \) of \( 1 \mathrm{M} \) HCl. \( K_{a} \) for:
\( \boldsymbol{H} \boldsymbol{C O}_{3}=\mathbf{5 . 6 3} \times \mathbf{1 0}^{-11}\left[\log \left(\frac{\mathbf{1 3 3}}{\mathbf{1 5 0}}\right)=\right. \)
\( -\mathbf{0 . 0 5} \)
A . 8.25
B. 9.19
c. 10.43
D. 11.56


Stomatal frequency indicates
A. Number of stomata per unit area
B. Rate of water loss
C . Rate of gaseous exchange
D. Width of stomatal aperture


What is rectification? Explain the working of a full wave rectifier.


Nuclei containing different number of protons but same number of neutrons
are called
A. Isoclines
B. isobars
c. isotones
D. isotopes


The inactivated enzymes present in
digestive tract like pepsinogen is an inactive form of pepsin. Such
substances are called
A. Zymogens
B. Catalyst
c. Holoenzyme
D. Activators


Increasing order of acidic strength among p=methoxy phenyl (I), p-methyl phenol (II) and p-nitrophenol (III) is:
A . III, ।, ॥
B. ॥, ।, ॥।
c. ॥॥, ॥।,
D. I, II, III


Expand
\( \left(2 x^{2}+3\right)^{4} \)


Calculate the number of
revolutions/sec around the nucleus of
an electron placed in III orbit of \( \boldsymbol{H} \) -atom
A \( \cdot 1.44 \times 10^{12} \)
B . \( 7.29 \times 10^{7} \)
c. \( 15.33 \times 10^{14} \)
D. \( 2.44 \times 10^{14} \)


In the valance band, the current is due
to
A. the presence of electrons
B. the presence of holes
c. the presence of both electrons and holes
D. none of the above


Find the value of \( k \) if \( f(x) \) is continuous
at \( \boldsymbol{x}=\boldsymbol{\pi} / 2, \) where \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{l}\frac{k \cos x}{\pi-2 x}, x \neq \pi / 2 \\ 3, \quad x=\pi / 2\end{array}\right. \)


For Uranium nucleus, how does its
mass vary with volume?
\( A \cdot m \propto V \)
в. \( m \propto 1 / V \)
\( \mathbf{c} \cdot m \propto \sqrt{V} \)
D \( \cdot m \propto V^{2} \)


One a.m.u. or one 'u' is equal to:
A \( \cdot 1.6605389210^{-27} \mathrm{kg} \)
B . \( 1.6605389210^{-29} \mathrm{kg} \)
c. \( 1.2345765610^{-27} \mathrm{kg} \)
D . \( 1.2345765610^{-29} \mathrm{kg} \)


What is the pH number of hydrochloric acid?
A. Below 7
B. Above 7
c. 7
D. Between 8 and 10


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


Opening on the leaf through which transpiration occurs is called


Give equations for the decomposition of a metallic
¡] chloride
ii] nitrate with conc. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \)


If the distance between the plates of a
parallel plate capacitor of capacity 10 \( \mu \) \( F \) is doubled. then new capacity will be :
\( \mathbf{A} \cdot 5 \mu F \)
в. \( 20 \mu F \)
c. \( 10 \mu F \)
\( \mathbf{D} \cdot 15 \mu F \)


The unit formerly used for measuring
heat capacity of a body was:
A. Calories/('C)
B. Joules/('C)
c. calories
D. Joules


Acids contain replaceable (oxygen/hydrogen)


Match the species with type of wood
(a) Tectona grandis
(b) Cedrus deodara
(c) Shorea robusta
(d) Dalbergia sisso
(e) Softwood
(f) Hardwood
A. a-e, b-f, c-f, d-e
B. a-e, b-e, c-f, d-f
c. a-f, b-e, c-f, d-f
D. a-f, b-e, c-e, d-f


Find the area of triangle formed by the points (8,-5),(-2,-7) and (5,1)


Find the derivative of \( x^{4}+4 \)


The internal energy of a gram-molecule of an ideal gas depends on
A. pressure alone
B. volume alone
c. temperature alone
D. both pressure as well as temperature


John and jivanti together have 45 marbles. Both of them lost 5 marbles
each , and the product of the number of
marbles they now have is \( 128 . \) Form the quadratic equation.


Match the following.
(1) Antibiotic
(a) Lysozyme blotic If
(2)
Antacid
(b) Bithionol
(3) Antipyretic
(c) Omeprazole gite ole
(4)
\( n \) Anti-microbial \( (d) \) Analgin
e) Penicillin \( (e) \)
A. \( 1-\mathrm{c}, 2-\mathrm{d}, 3-\mathrm{e}, 4-\mathrm{b} \)
B. \( 1-e, 2-c, 3-d, 4-a \)
C. \( 1-\mathrm{e}, 2-\mathrm{d}, 3-\mathrm{a}, 4-\mathrm{c} \)
D. \( 1-\mathrm{d}, 2-\mathrm{a}, 3-\mathrm{c}, 4-\mathrm{e} \)


Dehydration of alcohols can be done by using:
A . conc. \( H_{2} S O_{4} \)
в. \( A l_{2} O_{3} \)
c. \( C a O \)
D. both A and B


Calculate the following limits. \( \lim _{n \rightarrow \infty} \frac{3 n^{4}+2 n^{3}+3}{12 n^{4}-7 n^{2}+n}, n \epsilon N \)


Find the least number of children in the
interval \( 20-30 \) hours?
4.1
в. 15
\( c .25 \)
D. 45


A soap bubble of radius \( R \) with wall
thickness \( t \) is charged to a potential \( V_{0} \)
The bubble bursts and becomesa
spherical drop of soap solution of
radius \( r . \) Now, it has potential, \( V \)
Assume, the soap solution to be a
conductor.

Then the charge carried by the soap
bubble is :

Spherical drop
A \( \cdot 4 \pi \varepsilon_{0} R V_{0} \)
В \( \cdot 2 \pi \varepsilon_{0} R V_{0} \)
\( \mathbf{c} \cdot 4 \pi \varepsilon_{0} r V \)
D. Both (A) and (C)


\( \int|x+y| d x, \) where \( \frac{d y}{d x}=0 \) is given by
A . 0
в. \( \frac{(x+y)^{2}}{2}+c \)
c. \( -\frac{(x+y)^{2}}{2}+c \)
D. \( \frac{(x+y)|x+y|}{2}+c \)


For what value of \( \lambda \), the vector \( i-\lambda j+ \)
\( 2 k \) and \( 8 i+6 j-k \) are at right angles?


f \( \boldsymbol{A}=\left[\begin{array}{ll}\boldsymbol{x} & \mathbf{1} \\ \mathbf{1} & \mathbf{0}\end{array}\right], \boldsymbol{A}^{2}=\boldsymbol{I} \) then find ' \( \boldsymbol{x}^{\prime} \)


The main difference in the blood and
Iymph is
A. Absence of RBC
B. Absence of WBC
c. Number of WBC is less in blood
D. None of the above


Two charges of same magnitude move
in two circlesof radii \( \boldsymbol{R}_{1}=\boldsymbol{R} \) and \( \boldsymbol{R}_{2}= \)
\( 2 R \) in a region of constant uniform
magnetic field \( B_{0} . \) The work \( W_{1}, \) and \( W_{2} \)
done by the magnetic field in the Two cases, respectively are such that:
A \( . W_{1}=W_{2}=0 \)
В. \( W_{1}>W_{2} \)
c. \( W_{1}=W_{2} \neq 0 \)
D. \( W_{1}<W_{2} \)


Which of the following is a metal?
A. Selenium
B. Phosphorus
c. Chlorine
D. Mercury


Wall of internal organs (stomach, intestine, blood vessels) contains
muscles
A. Striped
B. Cardiac
c. smooth
D. None of the above


The estrogen derivative which is used in combination with progesterone derivative is
A. Novestrol
B. Dysidazirine
c. chloramphenicol
D. Amoxycillin


The additive identity for integers is
\( A \cdot 0 \)
B.
\( c .0 . \)
D. 2


Storage sprouting of potato can be
prevented by
A. Maleic hydrazide
B. Cytokinins
c. Gibberellins
\( D \cdot \) IAA


The ratio of the electric force between
two proton to that between two
electrons under similar conditions is
the order of:
\( \mathbf{A} \cdot 10^{4} \)
B. \( 10^{3} \)
\( c \cdot 10^{36} \)
D.


If \( \lim _{x \rightarrow 0}\left(x^{-3} \sin 3 x+a x^{-2}+b\right) \) exists
and is equal to \( 0, \) then
\( ^{\mathbf{A}} \cdot_{a}=-3 \) and \( b=\frac{9}{2} \)
в. \( _{a=3} \) and \( b=\frac{9}{2} \)
c. \( _{a=-3 \text { and } b=-\frac{9}{2}} \)
D. \( _{a=3} \) and \( b=-\frac{9}{2} \)


The resistance \( R \) of a conductor varies
with temperature as shown in the given figure. If the relation between \( R \) and \( t \) is
given as,
\( \boldsymbol{R}_{t}=\boldsymbol{R}_{0}\left(1+\boldsymbol{\alpha}+\boldsymbol{\beta} \boldsymbol{t}^{2}\right), \) then
A. \( \alpha \) and \( \beta \) are negative
B. \( \alpha \) is positive but \( \beta \) is negative
\( c \cdot \alpha \) and \( \beta \) are positive
D. \( \alpha \) is negative but \( \beta \) is positive


Find the cube root of each of the
following cube numbers through
estimation.
\( \mathbf{8 5 1 8 4} \)


Magnesium fluoride \( \left(M g F_{2}\right) \) is generally used as anti-reflection coating.
If refractive index of \( M g F_{2} \) is 1.25 and
if the minimum thickness of film is not
technologically possible to manufacture, then next thickness of film required is (approximately) (Take \( \boldsymbol{\lambda}=\mathbf{5 0 0 n m}) \)
A. 300 nm
в. \( 12 n m \)
c. \( 750 n m \)
D. \( 550 n m \)


\( \boldsymbol{f}(\boldsymbol{x})=([\boldsymbol{x}]-[-\boldsymbol{x}]) \boldsymbol{s i n}^{-1}|\boldsymbol{x}-\mathbf{1}| \)
Which of the following statements is/are correct?
(Note : [.] denotes the greatest integer function)
This question has multiple correct options
A. \( f(x) \) is continuous at \( x=1 \)
B. \( f(x) \) is differentiable at \( x=1 \)
c. \( f(x) \) is not differentiable at \( x=1 \)
D. \( f(x) \) is discontinuous at \( x=1 \)


A rigid massless rod of length \( \boldsymbol{L}=\mathbf{1} \boldsymbol{m} \)
joins two particles each of mass \( m= \)
1 kg. The rod lies on a frictionless table,
and is struck by a particle of equal
mass \( m=1 k g \) and velocity \( v_{0}=7 \sqrt{2} \)
moving as shown in the figure. After the collision the partcle moves straight back. Calculate the angular velocity of mass after collision, assuming that collision is perfectly elastic.


The digested food is absorbed by the of the small intestine.
A. Vill
B. Rugae
c. taenia coli
D. None of the above


The value of dissolved oxygen in polluted water is:
A \( .>4 \) ppm
В. \( <4 \) ppm
\( \mathbf{c} .=4 \mathrm{ppm} \)
\( \mathrm{D} .=6 \mathrm{ppm} \)


What is the function of distribution box
in domestic electrical circuit
A. It distributes voltage across appliances as per need
B. It provides isolation between set of appliances and improves reliability
C. It distributes Losses among all parts of circuit equally
D. It allows user to manually distribute power as per his need


Mac Arthur process is used for:
A \( . A g \)
в. \( F e \)
c. \( C l \)
D. \( O_{2} \)


Which compound is different from the others?
A. Methyl ethyl ketone
B. Pentan-2-one
c. 2-Pentanone
D. Methyl propyl ketone


Give the structures and IUPAC names of
monohydric phenols of
molecular formula, \( C_{7} H_{8} O \)


Draw lines of symmetry for the following figures. Identify which of them have point symmetry. Is there any implication between lines of symmetry and point symmetry?


In a prism a ray deviates towards:
A. base of prism
B. refracting edge of a prism
c. normal to the base
D. second phase of the prism


When two electrons are placed in two
degenerate orbitals of the atom, the energy is lower if their spin is parallel. The statement is based upon:
A. Pauli's exclusion
B. Bohr's's rule
c. Hund's rule
D. Aufbau principle


Rohit says to Ajay "Give me a hundred, I shall then become twice as rich as you." Ajay replies "If you give me ten, I shall be
six times as rich as you." How much does each have originally?
A. Rohit has Rs. 20 and Ajay has Rs. 90
B. Rohit has Rs. 50 and Ajay has Rs. 200
c. Rohit has Rs. 40 and Ajay has Rs. 170
D. Rohit has Rs. 56 and Ajay has Rs. 190


Consider a ring performing pure rolling when on a fixed rough surface. There is
a point 'A' marked on the circumference of it. If velocity of centre of ring is uniform, then this point will move in cycloidal path as shown. Now, if the ring is performing pure rolling with uniform acceleration what will be the
path followed by this point?
A. increasing size of cycloid
B. decreasing size of cycloid
c. It will depend on direction of acceleration whether it is in the direction of velocity of centre or opposite.
D. No change in path will occur


A point object is placed \( 33 \mathrm{cm} \) from a
convex mirror of curvature radius \( =40 \)
\( \mathrm{cm} . \) A glass plate of thickness \( 6 \mathrm{cm} \) and index 2.0 is placed between the object and mirror, close to the mirror. The distance of final image from the object is
\( \mathbf{A} \cdot 90 \mathrm{cm} \)
B. \( 35 \mathrm{cm} \)
\( \mathrm{c} .36 \mathrm{cm} \)
D. \( 45 \mathrm{cm} \)
E. None of these


Torque applied on a particle is zero,
then, its angular momentum will be
A . Equal in direction
B. Equal in magnitude
c. Both (a) and (b)
D. Data Insufficient


Show that if the diagonal of a quadrilateral bisect each other at right angles,then it is a rhombus


A table cover \( 6 m \times 3 m \) is spread on a
table top. If \( 25 \mathrm{cm} \) of the cover hangs all
around the table then the cost of
polishing the table @ Rs \( 12 m^{2} \) is
A . \( R s 165 \)
B. \( R s 175 \)
c. \( R s 180 \)
D. \( R s 195 \)


\( \boldsymbol{S} \boldsymbol{i} \boldsymbol{C l}_{4} \stackrel{\boldsymbol{H}_{2} \boldsymbol{O}}{\longrightarrow} \boldsymbol{X} \stackrel{\mathbf{1 0 0} \boldsymbol{0}}{\longrightarrow} \boldsymbol{Y} \)
In the above reaction, how many oxygen atom(s) is/are present in \( \mathrm{X} \) and \( \mathrm{Y} \) ? [f answer is \( 6 \text { and } 4, \text { represent as } 64] \)


Halo arenes undergo Wurtz-Fitting reaction.
(i) What is Wurtz-Fitting reaction?
(ii) ref. image Write the formulae of \( A \) and \( B \) in the
above reaction?


\{1,2,3\}\( \nsubseteq\{1,3,5\} \) as \( m \notin\{1,3,5\} \)
Then \( m \) is:


Which of the following statement is/are
correct for photorespiration?
A. Glycerate diffuses out of peroxisome and enters chloroplast, here it is phosphorylated
B. Glyoxylate is used in the synthesis of glycine in peroxisome
C. In mitochondria when glycine is converted into serin at that time glycine first oxidized and later reduced
D. Coordinated of chloroplast, peroxisome and mitochondrion is essential in photorespiration


gram sample of \( N H_{4} N O_{3} \) is decomposed in a bomb calorimeter. The temperature of the calorimeter increases by 6.12 K. The heat capacity of the system is 1.23 kJ/g-deg. What is the molar heat of decomposition for
\( N H_{4} N O_{3} ? \)
A . -7.53 kJ/mol
B. -398.1 kJ/mol
c. - -16.1 kJ/mol
D. 602 kJ/mol


The force of gravity with which a body is attracted towards the centre of the
earth is
A. weight
B. mass
c. position
D. ripple


The tro ends of a train moving with constant acceleration pass a certain
point with velocities \( u \) and \( 3 u \). The
velocity with which the middle point of the train passes the same point is
A \( .2 u \)
в. \( \frac{3}{2} u \)
c. \( \sqrt{5} u \)
D. \( \sqrt{10} u \)


The number of sulphur atoms present in
0.2 mole of sodium thiosuphate is:
\( (N=\text { avogadro number }) \)
A \( .4 N \)
В. \( 0.2 N \)
\( c \cdot 0.4 N \)
D. \( 0.1 N \)


Calculate the cell potential (in V) if \( \triangle G=-96.5 k J / m o l \) and \( n=1 \)
\( A \)
B. 5
c. 10
D. 4


\( \operatorname{Prove} \cos ^{2} \alpha-\sin ^{2} 2 \alpha= \)
\( \cos ^{2} \alpha \cos 2 \alpha-2 \sin ^{2} \alpha \cos ^{2} \alpha \)


A condenser of capacity \( 0.2 \mu F \) is
charged to a potential of 600 V. The battery is now disconnected and the
condenser of capacity \( 1 \mu F \) is connected across it. The potential of the condenser will reduce to
\( \mathbf{A} \cdot 600 V \)
B. \( 300 V \)
c. \( 100 V \)
D. \( 120 V \)


Consider the following feature of tissues.
A. They are similar and dissimilar cells.
B. They are performing a common function.
C. They have a common origin.
D. They are characterized by the distinct
cell wall.
The correct ones are grouped in
\( A \cdot A, B \) and \( D \)
B. B, C and D
c. \( A, B \) and \( c \)
D. \( A, C \) and \( D \)


If number of gas molecules in a cubical vessel is increased from \( \mathrm{N} \) to \( 3 \mathrm{N} \), then
its pressure and total energy will become
A. four times
B. three times
c. double
D. half


A radioactive sample has \( 2.0 \times 10^{20} \)
active nuclei at a certain instant of
time. Then the the number of samples
in the same active state after three half-
lives is
A \( .2 .5 \times 10^{15} \)
B. \( 2.5 \times 10^{21} \)
c. \( 2.5 \times 10^{19} \)
D. \( 2.5 \times 10^{16} \)


Two thin similar convex glass pieces
are joined together front to front with its rear portion silvered such that a sharp
image is formed \( 20 \mathrm{cm} \) from the mirror.
When the air between the glass pieces
is replaced by water \( \left(\mu_{W}=4 / 3\right), \) then the image formed from the mirror is at
a distance of
\( A \cdot 8 \mathrm{cm} \)
B. \( 10 \mathrm{cm} \)
\( c \cdot 6 \mathrm{cm} \)
D. \( 12 \mathrm{cm} \)


"Na and Mg are also called bridge
element since it links Group IA and Group IB".

State whether the above statement is
true or false.


The radius ratio of an ionic solid
\( \left.A^{+} B^{-}\right) \) is \( 0.69 . \) What is the
coordination number of \( \boldsymbol{B}^{-} \) ?
A. 6
B. 8
\( c \cdot 2 \)
D. 10


Source \( S \) emits microwaves with a
constant amplitude. The microwave hit a metal screen \( P \) and are reflected. stationary wave is formed between \( S \)
and \( P . \) The wavelength of the microwaves is much smaller than the
distance between \( S \) and \( P \)
A detector \( Q \) is moved at a slow,
constant speed from \( S \) to \( P \)
What happens to the amplitude of the signal detected by \( Q> \)
A. decreases steadily
B. increases and decreases steadily
c. increases steadily
D. remains constant


\( \mathbf{A} \)
\( 1.5 k W \) (kilo-watt) laser beam of wavelength \( 6400 \dot{A} \) is used to levitate a
thin aluminium disc of same area as
the cross section of the beam. The laser
light is reflected by the aluminium disk without any absorption. The mass of the
disc is close to:
A \( \cdot 10^{-9} k g \)
в. \( 10^{-3} \mathrm{kg} \)
\( \mathrm{c} \cdot 10^{-4} \mathrm{kg} \)
D. \( 10^{-6} \mathrm{kg} \)


Which of the following statements are
not true for hydrogen?
This question has multiple correct options
A. It exists as diatomic molecule
B. It has one electron in the outermost shell
C. It can lose an electron to form a carbon which can freely exist
D. It forms a large number of ionic compounds by losing an electron


In the given figure, the diagonals \( A C \)
and BD intersect at point \( 0 . \) If \( O B=0 D \)
and AB//DC, show that:
Area \( (\Delta D O C)=A r e a(\Delta A O B) \)
f the \( A(\triangle D O C)=21 \) sq. units, then
\( \boldsymbol{A}(\triangle \boldsymbol{D} \boldsymbol{O} \boldsymbol{C})+\boldsymbol{A}(\triangle \boldsymbol{A} \boldsymbol{O} \boldsymbol{B}) \) is :


Ideally a rigid body is-
A. which is solid at room temperature.
B. on applying force the distance between two point does not change.
c. both of them
D. none of them


Construct a right angled \( \triangle A B C \) with
\( \angle B=90^{\circ}, B C=5 c m \) and \( A C= \)
\( 10 \mathrm{cm} \) and find the the length of side
\( A B \)
\( \mathbf{A} \cdot 6.2 \mathrm{cm} \)
B. \( 5 \mathrm{cm} \)
\( c .8 .7 \mathrm{cm} \)
D. \( 7.2 \mathrm{cm} \)


If the axes are transformed from origin to the point \( (-2,1), \) then new coordinates of (4,-5) are
A. (2,6)
(年) (2,6)
в. (6,4)
c. (6,-6)
D. (2,-4)


Which is not aromatic?
\( A \)
(1)
в.
(2)
\( c \)
(3)
D.
(4)


\( f(x)=\sin x \) and \( g(x)=\sec x \) then
\( \frac{f(\pi)-f\left(\frac{3 \pi}{2}\right)+f(0)}{g(\pi)+g(0)+g\left(\frac{\pi}{3}\right)} \)
\( ^{\mathrm{A}} \cdot \frac{1}{2} \)
B.
\( c \)
\( D \)
:


Let the function \( f(x) \) be defined as
follows: \( f(x)= \)
\( \left\{\begin{array}{cc}x^{3}+x^{2}-10 x & -1 \leq x<0 \\ \cos x & 0 \leq x<\frac{\pi}{2} \\ 1+\sin x & \frac{\pi}{2} \leq x \leq \pi\end{array}, \) then \right.
which of the following statement(s) is/are correct
This question has multiple correct options
A. Local maximum at \( x=0 \)
B . Local maximum at \( x=\frac{\pi}{2} \)
c. Absolute maxima at \( x=-1 \)
D. Absolute minima at \( x=\pi \)


A convex lens of focal length \( 5 \mathrm{cm} \) is
placed at a distance of \( 6 \mathrm{cm} \) from a wall. How far from the lens should an object be placed so as to form its real image on the wall?
\( \mathbf{A} \cdot 30 \mathrm{cm} \)
B. \( -30 c m \)
\( \mathrm{c} \cdot 1.2 \mathrm{cm} \)
D. -1.2cm


Two glass bulbs \( A \) and \( B \) are connected by a very small tube having a stop cock.
Bulb A has a volume of \( 100 \mathrm{cm}^{3} \) and
contained the gas, while bulb B was empty. On opening the stop cock, the pressure fell down 40\%. The volume of
the bulb B must be ?
A \( .75 \mathrm{cm}^{3} \)
В. \( 125 \mathrm{cm}^{3} \)
\( c \cdot_{150} c m^{3} \)
D. \( 250 \mathrm{cm}^{3} \)


Carbocation having more stability is :
A . \( 1^{0} \) carbocation
B. \( 2^{0} \) carbocation
\( \mathrm{c} \cdot 3^{0} \) carbocation
D. none


\( \operatorname{Let} u=\int_{0}^{\infty} \frac{d x}{x^{4}+7 x^{2}+1} \& v= \)
\( \int_{0}^{\infty} \frac{x^{2} d x}{x^{4}+7 x^{2}+1} \) then:
This question has multiple correct options
\( A \cdot v>u \)
B. \( 6 v=\pi \)
c. \( 3 u+2 v=5 \pi / 6 \)
D. \( u+v=\pi / 3 \)


\( C a^{2+} \) is isoelectronic with?
\( \mathbf{A} \cdot M g^{2+} \)
в. \( K r \)
c. \( A r \)
D. \( N a^{+} \)


What must happen for an electromagnet to have a magnetic field?
A. It must be heated
B. It must be touching another magnett
c. It must be lined up with earth's magnetic field
D. It must be connected to an electrical source


A freshly prepared radioactive source of
half-life \( 2 h \) emits radiation of intensity which is 64 times the permissible safe level. The minimum time after which it
would be possible to work safely with this source is
\( \mathbf{A} \cdot 6 h \)
B. \( 12 h \)
\( c .24 h \)
D. \( 28 h \)


Sulphide ores of metals are usually concentrated by Froth Flotation process. Which one of the following sulphide ores offers and exception and is concentrated by chemical leaching?
A. Sphalerite
B. Argentite
c. Galena
D. copper pyritee


Which of the following describes
homeostasis?
A. An animal maintaining a home range.
B. A population maintaining a constant population size.
C. Females remaining in their parents territory.
D. Plants ceasing to grow at a maximum height.
E. Maintaining a steady state internal environment.


State Kohlrausch Law, and write
mathematical expression of molar conductivity of the given solution at infinite dilution.


Have you ever read this kind of news in
any newspaper? How did people solve their problem of water? Did they repair and reuse any old lake or stepwell?


If a Bismuth rod is introduced in the air
coil as shown then current in the coil
A. increases
B. remains unchanged
c. decrreases
D. none of these


Draw Fig.16.6 showing the position of
the plane mirror. What is correct?
A. \( x= \) angle of incidence and \( y= \) angle of reflection
B. \( y= \) angle of incidence and \( y= \) angle of reflection
c. \( x \) and \( y \) are both angle of incidence.
D. \( x \) and \( y \) are both angle of reflection.


When an inflated tyre bursts, the air escaping out
A. will get heated up
B. will be cooled
c. will not undergo any change in its temperature
D. will be liquefied


Sodium hydroxide reacts with \( S O_{2} \) in aqueous medium to give:
A. \( \operatorname{NaHSO}_{3} \)
в. \( N a_{2} S_{2} O_{3} \)
\( \mathbf{c} \cdot \operatorname{NaH} S O_{4} \)
D. \( N a_{2} S O_{3} \)


Which of the following is/has the
weakest attractive forces?
A. vander Waals
B. Coordinate covalent bonding
c. covalent bonding
D. Polar covalent bonding
E. lonic bonding


A circular thin disc of mass 5 kg has a diameter \( 1 \mathrm{m} . \) The moment of inertia
about an axis passing through the edge and perpendicular to the plane of the disc is
A \( \cdot(8 / 15) k g-m^{2} \)
В \( \cdot 8 k g-m^{2} \)
\( \mathbf{c} \cdot(15 / 8) k g-m^{2} \)
D. \( 1 k g-m^{2} \)


Choose the correct statement.
A. Biomass energy causes no pollution.
B. Biomass energy causes heavy pollution.
C. Biomass energy causes less pollution as compared to conventional sources of energy.
D. Biomass energy is costly.


What torque will increase angular velocity of a solid disc of mass \( 16 k g \)
and diameter \( 1 \mathrm{m} \) from zero to \( 2 \mathrm{rpm} \) in
\( \mathbf{8 s} ? \)
A \( \cdot \frac{\pi}{4} N-m \)
в. \( \frac{\pi}{2} N-m \)
\( ^{\mathbf{c}} \cdot \frac{\pi}{3} N-m \)
D. \( \pi N-m \)


In the cyanide process for extraction of
gold and silver from ores, the cyanide
solution acts as a:
A. Reducing agent to reduce the gold and silver compounds present in the ores into the metallic states
B. Leaching agent to bring the gold and silver into solution as cyanide complexes and thus separate these metals from the ores
C. Leaching agent to dissolve all the other constituents of the ores leaving the gold and silver as metals
D. Leaching agent to bring the ores into solution


The process by which impure metals are purified electrolytically is called as
A. electrorefining
B. electroplating
\( c \cdot \) both
D. none of these


The three elements \( A, B \) and \( C \) with
similar properties have atomic masses
\( x, Y \) and \( z \) respectively. The mass of \( Y \) is approximately equal to the average mass of \( X \) and \( Z . \) Such an
arrangement of elements called as:
A. Dobereiner triad
B. Mendeleev triad
c. Modern triad
D. none of the above