Which of the substance is purified by sublimation?
A. Naphthalene
B. Benzoic acid
c. camphor
D. All of these


How many leap years are there in set of
any consecutive 400 years?


A charged particle initially at rest is kept
in an electric field (choose the most
appropriate option)
A. will always move perpendicular to the line of force.
B. will always move along the line of force in the direction of the field.
C. will always move along the line of force opposite to the direction of the field.
D. will always move along the line of force in the direction of the field or opposite to the direction of the field depending on the nature of the charge.


The weakest forces of interaction
among all classified forces are
A. electrostatic forces
B. gravitational forces
c. weak nuclear forces
D. electromagnetic forces


A stone is tied to the middle of a string
and suspended from one end as shown
in the given figure. Here \( S \) is the stone
and 0 is the point of suspension. If we
increase the pull at \( \mathrm{P} \) gradually, the
string will break
A. below the stone
B. at the point P itself
c. above the stone
D. nothing can be decided


State Kirchhoff's voltage law.


\( \operatorname{Let} f(x)=\frac{\sqrt{\operatorname{sgn}\left(\alpha x^{2}+\alpha x+1\right)}}{\cot ^{-1}\left(x^{2}-\alpha\right)} \)
\( f(x) \) is continuous for all \( x \in R, \) then
number of integer in the range of \( \alpha \), is [Note : sgn k denotes signum function of k.
\( \mathbf{A} \cdot \mathbf{0} \)
B. 4
c. 5
D. 6


Most copper \( (I) \) compounds are found to be colourless. This is due to
A. presence of low oxidation state of copper
B. completely filled d-level in \( C u(I) \)
c. diamagnetic nature of the compound
D. high polarizability of \( C u(I) \) ion


A series combination of two Carnots
engines operate between the
temperatures of \( 180^{0} C \) and \( 20^{0} C . \) If the
engines produce equal amount of work,then what is the intermediate
temperature(ln \( ^{0} C \) )?
\( A \cdot 80 \)
B. 90
\( c \cdot 100 \)
D. 110


Assertion
Some farmers feel that lightning helps
produce better crop.
Reason
Lighting forms No which is converted to
\( N o_{2}, H N O_{2} \) and \( H N O_{3} \) under
atomospheric condition. Thus, \( N O_{3}^{-} \) is a source of nutrients (fertilisers) to the
plant. Thus there are chances of better
crops when lightning occurs.

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


How is silver extracted from argentite
ore?


Using binomial theorem evaluate the
following:
\( (98)^{5} \)


State True or False:
Statement : The polar end in soap is called hydrophilic end.
A. True
B. False


Find the number of \( S-S \) linkage in
\( \boldsymbol{H}_{2} \boldsymbol{S}_{2} \boldsymbol{O}_{3} \)


An ideal gas occupying a volume of 2
\( d m^{3} \) and pressure of 5 bar undergoes isothermal and irreversible expansion
against an external pressure of 1 bar
Find the work done in the process?


f \( a, b, c \) are positive real numbers such
that \( a b^{2} c^{3}=64 \) then minimum value of \( \left(\frac{1}{a}+\frac{2}{b}+\frac{3}{c}\right) \) is equal to
\( A \cdot 6 \)
B. 3
\( c \cdot 2 \)
D. None of these


In a regular octahedral molecule, \( M X_{6} \)
the number of \( X-M-X \) bonds at an angle of
\( 180^{\circ} \) is
A. Three
B. Two
\( c . \) six
D. Four


Among the isomeric alkanes of molecular formula \( C_{5} H_{12}, \) identify the one that on photochemical chlorination
yields:
(i) A single monochloride
(ii) Three isomeric monochlorides
(iii) Four isomeric monochlorides.


The set values of \( x \) for which function
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x} \ln \boldsymbol{x}-\boldsymbol{x}+\mathbf{1} \)
\( A \cdot(1, \infty) \)
B. \( \left(\frac{1}{e}, \infty\right) \)
c. \( [e, \infty) \)
( \( ) \)
D \( \cdot(0,1) \cup(1, \infty) \)


If the diagonal BD of a quadrilateral
ABCD bisects both \( \angle B \) and \( \angle D \) then
\( A B=A D \)
A . True
B. False


A coil having an area \( A_{0} \) is placed in a
magnetic field which changes from \( \boldsymbol{B}_{\mathbf{0}} \)
to \( 4 B_{0} \) in time interval t. The e.m.f.
induced in the coil will be
A \( \cdot 3 A_{0} B_{0} / t \)
в. \( 4 A_{0} B_{0} / t \)
c. \( 3 B_{0} / A_{0} t \)
D \( \cdot 4 A_{0} / B_{0} t \)


Name the body part which have division-less cells.
A. Brain
B. Lungs
c. Kidney
D. Stomach


A man leaves a town at 8 a.m. on his
bicycle moving at \( 10 \mathrm{km} / \mathrm{hr} \). Another
man leaves the same town at 9 a.m. on
his scooter moving at \( 30 \mathrm{km} / \mathrm{hr} . \) At what time does he overtake the man on the
bicycle?
A. 8.30 a.m.
B. 9 a.m.
c. 9.30 a.m.
D. 10 am


Find the arithmetic mean of 4 and 6


A beam of light passes from the air
through a thick piece of glass as shown
in the figure. Identify which of the
following angles best describe the angle
of refraction?
\( A \)
\( B .2 \)
\( c \cdot 3 \)
D. 4
\( E .5 \)


Name the material transported by the following tissue/blood vessel.
a) Xylem
b) Pulmonary artery
c) Pulmonary vein
d) Phloem


An atomic nucleus \( A \) is composed of 84
protons and 128 neutrons. The nucleus
\( A \) emits an \( \alpha \) -particle and is
transformed into a nucleus \( B \). What is
the composition of \( \boldsymbol{B} \) ?
A. 80 protons and 126 neutrons
B. 82 protons and 126 neutrons
c. 82 protons and 124 neutrons
D. 80 protons and 124 neutrons


During heavy rains in a village, the rainwater carried away an excess of nitrogenous compound present in the soil to a pond. The growth of algae and phytoplankton in the pond
A. Decreases
B. Decreases but attain normal level after sometime
c. Increases causing bloom
D. Remains unchanged


Find the number of whole numbers in
the solution set of following
\( x-5<-2 \)


The most common oxidation state of
Lanthanoids is:
\( A \cdot+4 \)
\( B \cdot+3 \)
\( c \cdot+6 \)
\( D \cdot+2 \)


The osmotic pressure of an aqueous solution of sucrose is 2.47 atm at \( 303 \mathrm{K} \)
and the molar volume of the water
present is \( 18.10 \mathrm{cm}^{3} . \) Given \( \Delta H_{v a p}= \) \( \mathbf{5 4 0} \) cal / g. Assume the volume of
solvent equal to the volume of the
solution. The elevation in the boiling point of the solution is :
A \( .5 .145 \times 10^{-2} \)
B. \( 7.565 \times 10^{-2} \)
c. \( 6.355 \times 10^{-2} \)
D. None of these


Two cells of emf \( E_{1} \) and \( E_{2}\left(E_{1},>E_{2}\right) \)
are connected as shown in figure. When
a potentiometer is connected between \( \mathbf{A} \) and \( \mathrm{B} \), the balancing length of the potentiometer wire is \( 300 \mathrm{cm} \). When the
same potentiometer is connected between \( A \) and \( C, \) the balancing length
is \( 100 \mathrm{cm} . \) The ratio of \( E_{1} \) and \( E_{2} \) is
\( A \cdot 3: 2 \)
B. 4: 3
\( c \cdot 5: 4 \)
D. 2: 1


If \( \frac{\cos ^{4} \theta}{x}+\frac{\sin ^{4} \theta}{y}=\frac{1}{x+y} \) then \( \frac{d y}{d x}= \)
A . \( x y \)
B. \( \tan ^{2} \theta \)
\( c \cdot 0 \)
D. \( \left(x^{2}+y^{2}\right) \sec ^{2} \theta \)


Consider a rod of length of \( l \) resting on a wall and the floor. Its lower end pulled towards left with a constant velocity \( V \)
As a result the end \( B \) starts moving
down along the wall. Let us find the velocity of the end \( B \) downward when
the rod makes an angle \( \theta \) with the
horizontal.


Which of the following will be decomposed into hydrogen by metals like \( \boldsymbol{F e}, \boldsymbol{S n}, \boldsymbol{N} \boldsymbol{i} ? \)
A. Cold water
B. Boiling water
c. Steam
D. All of these


Waste water from industries should not
be used for irrigation without eliminating toxic chemicals from the
effluent. This is a measure to control
A. air pollution
B. water pollution
c. soil pollution
D. none of above


Complete the following:
\( \boldsymbol{F} \boldsymbol{e}^{\boldsymbol{3}+}+\boldsymbol{3} \boldsymbol{N} \boldsymbol{a} \boldsymbol{C} \boldsymbol{S} \longrightarrow----+ \)


Prove that: \( \left|\begin{array}{ccc}\mathbf{1} & \boldsymbol{x} & \boldsymbol{y}+\boldsymbol{z} \\ \mathbf{1} & \boldsymbol{y} & \boldsymbol{z}+\boldsymbol{x} \\ \mathbf{1} & \boldsymbol{z} & \boldsymbol{x}+\boldsymbol{y}\end{array}\right|=\mathbf{0} \)


Choose the correct statement(s):
(1) Sewage can be used with gobar and agricultural waste to produce bio gas in biogas plant.
(2) The largest composition in biofuel is of methane.
A. (1) only
B. (2) only
C. Both (1) and (2)
D. None of the above


Choose the appropriate terms for the following definitions.
Phloem, Vascular cambium, Mesophyll, Schizogenous, Dendrochronology, Aerenchyma, Velamen, Tylosis, Parenchyma, Collenchyma, Lysogenous, transfer cell
lateral meristem that produces
secondary phloem and secondary xylem.


Dalton's atomic theory is based on:
A. Law of conservation of mass
B. Law of definite proportion
C. Both A and B
D. None of these


The vapour pressure of water at \( 20^{\circ} \mathrm{C} \) is
17.54 \( m m H g \). Then the vapour pressure
of the water in the apparatus is lowered, decreasing the volume of the gas above the liquid to one half of its initia
volume (temp. constant) is:
A. \( 5.77 \mathrm{mmHg} \)
в. \( 16 \mathrm{mmHg} \)
c. 35.08 mmHg
D. between 8.77 and \( 15.54 \mathrm{mmHg} \)


Assertion \( (A): \) Both \( H_{2} S_{2} O_{2} \) and
\( H_{2} S_{2} O_{3} \) contain \( S=S \) bonds
Reason (R): 'ic' acids are more acidic
than 'ous' acids
The correct answer is
A. Both Assertion and Reason are correct and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are correct and Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true


A ball of weight \( W \) supported on a
vertical jet of water. If the stream of
water flowing from the nozzle has a
diameter \( D \) and velocity \( u \), determine
the value of \( H . \) Assume that no loss of
energy takes place.
Fig. 4.160


How are moist deciduous forests
different from dry deciduous forests?


A frog can jump higher than normal in a magnetic field because the tissues of a
frog are
A. paramagnetic
B. diamagnetic
c. ferromagnetic
D. antiferro magneticc


Which one of the following will have largest number of atoms?
A. \( 1 g A u \)
B. \( 1 g \) Na
c. \( 1 g L i \)
D. \( 1 g C l_{2} \)


State Coulomb's law in electrostatics.


The equivalent capacitance in the given
circuit is
\( A \cdot 3 \mu F \)
B. \( 1.5 \mu F \)
\( c \cdot 2 \mu F \)
D. \( 1 \mu F \)


Find the mean of the binomial distribution \( B\left(4, \frac{1}{3}\right) \)


n the figure, if \( A B=A C \) prove that \( B Q= \)
\( \mathrm{QC} \)


The sum of the series \( ^{20} C_{0}+^{20} C_{1}+ \)
\( ^{20} C_{2}+\ldots+^{20} C_{10} \) is
A \( 2^{20} \)
0
B . \( 2^{19} \)
C \( \cdot 2^{19}+\frac{1}{2} \cdot 20 C_{10} \)
D - \( 2^{19}-\frac{1}{2} \cdot 2^{0} C_{10} \)


Two sound speakers are driven in phase by an audio amplifier at frequency \( 600 H z . \) The speed of sound is \( 340 m / s \) The speakers are on the \( y \) -axis, one at
\( \boldsymbol{y}=+1.0 \boldsymbol{m} \) and the other at \( \boldsymbol{y}= \)
\( -1.0 m . \) A listener begins at \( y=0 \) and
walks along a line parallel to the \( y \) -axis at a very large distance \( x \) away. At \( \frac{\theta}{2} \) angle she will first hear a maximum
\( \left(\operatorname{after} 0^{\circ}\right) \) sound intensity. Find \( \theta: \)


The limiting value of static friction
between two contact surfaces is:
A. Proportional to normal force between the surfaces in contact.
B. Independent of area of contact
C. Depends on the microscopic area of constant magnitude.
D. All of the above


The slope of tangent to the curve \( x= \) \( \boldsymbol{t}^{2}+\mathbf{3} \boldsymbol{t}-\mathbf{8}, \boldsymbol{y}=\mathbf{2} \boldsymbol{t}^{2}-\boldsymbol{2} \boldsymbol{t}-\mathbf{5} \) at the
point (2,-1) is :
A \( \cdot \frac{22}{7} \)
B. \( \frac{6}{7} \)
c. -6
D. None of these


Find the modulus and argument of the following complex numbers and hence express each of them in the polar form:
\( \frac{-\mathbf{1 6}}{\mathbf{1 + i \sqrt { 3 }}} \)


The equation of the curve through \( \left(0, \frac{\pi}{4}\right) \) satisfying the differential
equation. \( e^{x} \tan y d x+(1+ \)
\( \left.e^{x}\right) \sec ^{2} y d y=0 \) is given by
A \( \cdot\left(1+e^{x}\right) \tan y=2 \)
B . \( 1+e^{x}=2 \tan y \)
C \( \cdot 1+e^{x}=2 \sec y \)
D・ \( \left(1+e^{x}\right) \tan y=1 \)


A cell of emf 'E' and internal resistance
is connected across a variable resistor
R'. Plot a graph showing variation of terminal voltage 'V' of the cell versus the current 'I'. Using the plot, show how the emf of the cell and its internal
resistance can be determined.


In the following reaction:
\( \boldsymbol{A}^{+}+\boldsymbol{B} \rightarrow \boldsymbol{A}+\boldsymbol{B}^{+} \)
oxidizing agent is:
A \( . A^{+} \)
в. \( B \)
c. Both of them
D. None of them


The diagram below shows the different
modes of vibration \( P, Q \) and \( R \) of the same string of a given length
(a) Which vibration will produce a louder sound and why?
(b) Which vibration will produce the sound of maximum shrillness (or pitch)
and why?
(c) What is the ratio of the wavelength of vibrations P and R?


In which of the following cases more friction is desirable?
A. Movement of piston in a cylinder
B. Braking of a vehicle
c. skating on a track
D. All of the above


Bile and pancreatic ducts open into
A. Large intestine
B. Stomach
c. colon
D. Small intestine


For \( 2 A+2 B \rightleftharpoons 2 C+2 D, K_{c}=1 / 6 \)
then \( \boldsymbol{K}_{\boldsymbol{c}} \) for \( \boldsymbol{C}+\boldsymbol{D} \rightleftharpoons \boldsymbol{A}+\boldsymbol{B} \)
is \( _{\text {十一一一一一一一一一 }} \) (write only integer part)


A concave mirror cannot be used as a:
A. torch reflector
B. dentist's mirror
c. rear view mirror
D. magnifying mirror


A particle moves along a parabolic path
\( \boldsymbol{y}=\mathbf{9} \boldsymbol{x}^{2} \) in such a way that the \( \boldsymbol{x} \)
component of velocity remains constant and has a value \( 0.333 m / s . \) The magnitude of acceleration of the particle is:
A . 1
B. 2
\( c \cdot 3 \)
D.


Why are some elements chemically
inert?
A. Because their outermost shell is completely empty
B. Because their outermost shell is completely filled
C. Because their innermost shell is completely empty
D. Because their innermost shell is completely filled


ff \( y=\tan ^{-1}\left(\frac{x \sin \alpha}{1-x \cos \alpha}\right) . \) Find \( \cot y \)


How many high energy bonds are
present in ADP?
A. one
B. Two
c. Three
D. Four


What are ellingham diagrams? Write
any two features of it.


Which of the following is the formula of Sorel's cement?
A. \( K C l \cdot M g C l_{2} \cdot 6 H_{2} O \)
в. \( M g C l_{2} \cdot 5 M g O \cdot x H_{2} O \)
\( \mathbf{c} \cdot \operatorname{CaSO}_{4} \cdot 2 H_{2} O \)
D. \( M g C O_{3} \cdot C a C O_{3} \)


A piece of copper having a rectangular
cross-section of \( 15.2 \mathrm{mm} \times 19.1 \mathrm{mm} \) is
pulled in tension with \( 44,500 \mathrm{N} \) force, producing only elastic deformation. Calculate the resulting strain?


fthe matrix \( \boldsymbol{A}=\left[\begin{array}{lll}2 & 0 & 0 \\ 0 & 2 & 0 \\ 2 & 0 & 2\end{array}\right], \) then
\( \boldsymbol{A}^{n}=\left[\begin{array}{lll}\boldsymbol{a} & \boldsymbol{0} & \boldsymbol{0} \\ \boldsymbol{0} & \boldsymbol{a} & \boldsymbol{0} \\ \boldsymbol{b} & \boldsymbol{0} & \boldsymbol{a}\end{array}\right] . \boldsymbol{n} \in \boldsymbol{N} \) where
A \( \cdot a=2 n, b=2^{n} \)
B . \( a=2^{n}, b=2 n \)
c. \( a=2^{n}, b=n 2^{n-1} \)
D. \( a=2^{n}, b=n 2^{n} \)


Let \( f(x)=x^{3}-6 x^{2}-10 x \) and let \( c \) be
the number that satisfies the Mean
value theorem for \( f \) on the interval
\( [-4,5] . \) What is \( c ? \)
A . -1
B. -2
c. 0
D.


Calculate the formula unit mass (u) of
NaCl:
\( [\boldsymbol{N} \boldsymbol{a}=\mathbf{2} \boldsymbol{3} \boldsymbol{u}, \boldsymbol{C l}=\mathbf{3 5 . 5 u}] \)
\( \mathbf{A} \cdot 54.5 u \)
B. \( 55.5 u \)
\( \mathbf{c} .56 .5 u \)
D. \( 58.5 u \)


The osmotic pressure of a solution of benzoic acid dissolved in benzene is
less than expected because
A. benzoic acid is an organic solute
B. benzene is a non-polar solvent
c. benzoic acid dissociates in benzene
D. benzoic acid gets associated in benzene


\( A 220 V, 50 H z A C \) generator is connected to an inductor and a \( 50 \Omega \) resistance in series. The current in the
circuit is \( 1.0 A . \) What is the Potential
difference across inductor?
A. \( 102.2 V \)
в. \( 186.4 \mathrm{V} \)
c. \( 214 V \)
D. \( 170 V \)


The function \( \boldsymbol{f}: \mathbb{R} \rightarrow \mathbb{R} \) be defined by
\( f(x)=\left(x^{2}+1\right)^{35} . \) Prove that the
function \( f(x) \) is not one-one.


Hydroelectric power plants are more ecofriendly than thermal power plants. Justify this statement.


Atomic mass number of an element is
232 and its atomic number of \( 90 . \) The
end product of this radioactive element is an isotopes of lead (atomic mass 208
and atomic number 82 ). The number of
\( \alpha \) and \( \beta- \) particles emitted are :
A. \( \alpha=3, \beta=3 \)
в. \( \alpha=6, \beta=4 \)
c. \( \alpha=6, \beta=0 \)
D. \( \alpha=4, \beta=6 \)


Three rings each of mass \( m \) kg and
radius \( a \) are arranged as shown in the
figure. The moment of inertia of the arrangement about \( x-x^{\prime} \) axis will be
A \( \cdot \frac{3}{2} m a^{2} \)
B.
\( c \)
D. \( \frac{2}{5} m a^{2} \)


Distinguish between uniform velocity
and variable velocity.
A. Uniform velocity changes with time, while variable velocity doesn't changes with respect to time.
B. Uniform velocity is scalar, while variable velocity is vector
C. Uniform velocity doesn't change with time, while variable velocity changes with respect to time.
D. Uniform velocity is vector, while variable velocity is scalar.


NaOCl reacts with \( N H_{3} \) to produce :
A. \( N H_{2} O H \)
В. \( N H_{2} N H_{2} \)
c. \( N_{2} \)
D. \( N O \)


On rubbing a glass rod with silk cloth,
\( 6.84 \times 10^{16} \) electrons are transferred
from glass rod to silk cloth. Find the total charge transferred.


Which of the following possess homogametic male?
A. Plant
B. Man
c. Insect
D. Birds


Consider the following three
statements:
\( P \quad: 5 \) is a prime number.
\( Q: 7 \) is a factor of 192
\( R \quad: L . C . M . \) of 5 and 7 is 35
Then the truth value of which one of the
following statements is true?


Define the capacity of a condenser
Derive an expression for the capacity of a parallel plate condenser. How can its capacity be increased?


Sl unit of \( G \) is \( N m^{2} k g^{-2} \) Which of the following can also be used as the Sl unit of G?
A \( \cdot m^{3} k g^{-1} s^{-2} \)
B . \( m^{2} k g^{-2} s^{-1} \)
c. \( m k g^{-1} s^{-1} \)
D. \( m^{3} k g^{-3} s^{-2} \)


The colour of Lanthanoids and Actinoids
is due to:
A. s-ftransitions
B. p-f transitions
c. d-f transitions
D. f-f transitions


If \( \lim _{x \rightarrow 1}\left(1+a x+b x^{2}\right)^{\frac{c}{x-1}}=e^{3}, \) then
find conditions on a, b and c.


Inside a neutral metallic spherical shell
a charge \( Q_{1} \) is placed, and outside the
shell, a charge \( Q_{2} \) is placed.


What is the refractive index of a
medium?
A. The ratio of the speed of light in air to the speed of light in the medium
B. The ratio of the speed of light in the medium to the speed of light in air
C. The ratio of the speed of light in the medium to the speed of light in vaccum
D. The ratio of the speed of light in vacuum to the speed of light in the medium


Predict the product of the reaction between benzene diazonium chloride
and cuprous bromide.
A. Phenol
B. chlorobenzene
c. bromobenzene
D. dichlorobenzene


Find the value of \( \boldsymbol{p}(\boldsymbol{x})=\boldsymbol{x}^{2}-\boldsymbol{x}+\mathbf{1} \) at
\( \boldsymbol{x}=\mathbf{2} \)
\( A \cdot 3 \)
B. - -
\( c \)
D. -


What is the name of the strings which vibrate in our voice box when we talk?
A. oesophagus
B. pharyngeal slits
c. vocal cords
D. all


Evaluate \( \int_{0}^{2 \pi} \frac{x \sin ^{2 n} x}{\sin ^{2 n} x+\cos ^{2 n} x} d x, \) for
\( \boldsymbol{n}>\mathbf{0} \)
\( A \)
B. \( 2 \pi \)
\( \mathbf{c} \cdot \pi^{2} \)
D. \( \frac{1}{2} \pi \)


Assertion
For any two events \( A \) and \( B \) \( \boldsymbol{P}(\overline{\boldsymbol{A}} \cap \boldsymbol{B})=\boldsymbol{P}(\boldsymbol{B})-\boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B}) \)
Reason
\( A \cap B \) and \( \bar{A} \cap B \) are mutually
exclusive events.
A. Both Assertion \& Reason are individually true \& Reason is correct explanation of Assertion
B. Both Assertion \& Reason are individually true but Reason is not the , correct (proper) explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true


f \( \boldsymbol{m}=\mathbf{2}, \) find the value of \( \boldsymbol{3} \boldsymbol{m}-\boldsymbol{2} \)


Both gravitational and electric forces
are
A. contact forces
B. central forces
c. attractive forces
D. repulsive forces


Simplify :
\( x y+\left(x y+4 x^{3}+3 x-5\right)-\left(-3 x^{2}-\right. \)
4) \( -\left(x y+x^{3}-4\right) \)


The unit of Newton's cooling constant is
A \( \cdot c a l / s \)
B \cdot \( \operatorname{cal} / s^{\circ} C \)
c. \( c a l /^{\circ} C \)
D. \( ^{o} C^{-1} \)


Show that the three lines with direction
\( \operatorname{cosines} \)
\( \frac{12}{13}, \frac{-3}{13}, \frac{-4}{13}: \frac{4}{13}, \frac{12}{13}, \frac{3}{13} ; \frac{-4}{13}, \frac{12}{13} \) are mutually
perpendicular


Groundwater table may go down if the water is not sufficiently replenished. This may happen due to which of the following reason/(s)?
A. Scanty rainfall
B. Deforestation
C. Decrease in the effective area for seepage of water
D. All of the above


Two parallel chords in a circle are \( 10 \mathrm{cm} \) and \( 24 \mathrm{cm} \) long. If the radius of the
circle is \( 13 \mathrm{cm} \), find the distance between the chords if thay lie on the opposite sides of the center


Match the right pairs.


How much copper in grams can be
obtained from \( 100 g \) of copper sulphate
\( \left(\mathbf{C u S O}_{4}\right) ? \)


Which statement is wrong among the following statement? Statement 1: Non metal possess the property of ductility and malleability Statement 2: Non metallic elements in
solid form are brittle

Statement 3: Metal can produce ringing sound by striking Statement 4: Melting points and boiling points of metals are low
A. Statement 1 and 3
B. Statement 2 and 3
c. statement 1 and 4
D. Statement 2 and 4


Two identical circular wires \( P \) and \( Q \)
each of radius \( \boldsymbol{R} \) and carrying current
\( I^{\prime} \) are kept in perpendicular planes
such that they have a common centre
as shown in the figure. Find the
magnitude and direction of the net magnetic field at the common centre of
the two coils.


A Null di culsianc vulume Is didacıled
to a manometer tube open at other end
as shown in the figure. The manometer
is filled with a liquid of density \( (1 / 3)^{r d} \)
that of mercury. Initially \( h \) was \( 228 \mathrm{cm} \)
Through a small hole in the bulb, gas
leaked. Assuming the pressure decreases as \( \frac{\boldsymbol{d P}}{\boldsymbol{d t}}=-\boldsymbol{k} \boldsymbol{P} \) and the value
of \( h \) is \( 114 \mathrm{cm} \) after 14 min. What is the
value of \( k\left(\text { in hour }^{-1}\right) ?(\ln (4 / 3)=0.28 \)
and density of \( \boldsymbol{H} \boldsymbol{g}=\mathbf{1 3 . 6} \boldsymbol{g} / \boldsymbol{m} \boldsymbol{L} \) )
\( A \cdot 0.6 \)
B. 1.2
c. 2.4
D. none of the above


Very short answer type.
Give the exact location and function of
grana


\( C O_{2} \) is a gas, while \( S i O_{2} \) is a solid but
both are:
A. covalent containing \( \pi \) -bond
B. molecules having \( p \pi-d \pi \) bonding
c. acidic
D. discrete molecules


Consider the following properties of the
noble gases:
I: they readily from compounds
which are colourless.
II : they generally do not form ionic
compounds. III : they have variable oxidation states
in their compounds. \( I V: \) they generally do not form covalent compounds.
Select the the correct properties.
A. \( I, I I \) and \( I I I \) only
B. II and III only
C. \( I \) and \( I I I \) only
D. I only


Consider the following statements:
1. The function \( f(x)=x^{2}+2 \cos x \) is
increasing in the interval \( (0, \pi) \)
2. The function \( f(x)=\ln (\sqrt{1+x^{2}}-x) \)
is decreasing in the interval \( (-\infty, \infty) \) Which of the above statements is lare
correct?
A. 1 only
B. 2 only
c. Both 1 and 2
D. Neither 1 nor 2


The perimeter of a rhombus is \( 40 \mathrm{cm} \) and the length of one of its diagonals is 12 cm then the area of the rhombus is
\( \mathbf{A} \cdot 95 \mathrm{cm}^{2} \)
B. \( 96 \mathrm{cm}^{2} \)
c. \( 97 \mathrm{cm}^{2} \)
D. \( 98 \mathrm{cm}^{2} \)


Find the area of the shaded region in
PQRSPQRS is an equilateral triangle
A \( \cdot(6 \pi-9 \sqrt{3}) \mathrm{cm}^{2} \)
в. \( (4 \pi-9 \sqrt{3}) \) ст \( ^{2} \)
c. \( (3 \pi-9 \sqrt{3}) c m^{2} \)
D・ \( (2 \pi-9 \sqrt{3}) \) с \( m^{2} \)
E. None of thes


Which of the following statements about the isotopes of an element is NOT
correct?
A. Isotopes have the same proton number
B. Isotopes have the same chemical properties
C. Isotopes have the same nucleon number
D. Atoms of the isotopes of the element have the same number of electrons


The value of
\( \left(\cos 60^{\circ} \cos 30^{\circ}-\sin 60^{\circ} \sin 30^{\circ}\right) \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( \frac{\sqrt{3}}{2} \)
\( c \cdot \frac{1}{2} \)
\( D \)


\( \frac{5}{13}+-=\frac{5}{13} \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
c. \( \frac{5}{13} \)
D. \( \frac{2}{13} \)


The inhibition of glutamic dehydrogenase by ATP during cellular respiration is an example of
A. Feed back inhibition
B. Competitive inhibition
c. Allosteric inhibition
D. Both A and B


Find the coordinate of the point \( \boldsymbol{P} \) where the line through \( A(3,-4,-5) \) and \( B(2,-3,1) \) crosses the plane passing through three points \( \boldsymbol{L}(\mathbf{2}, \mathbf{2}, \mathbf{1}), \boldsymbol{M}(\mathbf{3}, \mathbf{0}, \mathbf{1}) \) and \( \boldsymbol{N}(\mathbf{4},-\mathbf{1}, \mathbf{0}) \)
Also, find the ratio in which \( P \) divides
the line segment \( \boldsymbol{A B} \)


We number both the rows and the
columns of an \( 8 \times 8 \) chess-board with
the numbers 1 to \( 8 . A \) number of grains are placed onto each square, in such a way that the number of grains on a certain square equals the product of its row and column numbers. How many
grains are there on the entire chessboard?
A . 1296
B. 1096
\( c .2490 \)
D. 1156


Two resistances \( R_{1} \) and \( R_{2} \) are made of
different materials. The temperature
coefficient of the material of \( \boldsymbol{R}_{1} \) is \( \boldsymbol{\alpha} \)
and that of material of \( \boldsymbol{R}_{2} \) is \( -\boldsymbol{\beta} \). The
material of \( \boldsymbol{R}_{1} \) and \( \boldsymbol{R}_{2} \) will not change with temperature if \( \frac{\boldsymbol{R}_{1}}{\boldsymbol{R}_{2}} \) equal to
\( \mathbf{A} \cdot \frac{\alpha}{\beta} \)
В. \( \frac{\alpha+\beta}{\alpha-\beta} \)
c. \( \frac{\alpha^{2}+\beta^{2}}{2 \alpha \beta} \)
D. \( \frac{\beta}{\alpha} \)


If all of a sudden the radius of the earth
decreases, then which one of the
following statements will be true?
A. The angular momentum of the earth will become greater than that of the sun
B. The periodic time of the earth will increase
C. The energy and angular momentum will remain constant
D. The angular velocity of the earth will increase


Which of the following layers you will find in the body wall of earthworm (from outside to inside)?
A. Non-cellular cuticle, epidermis, circular muscles longitudinal muscles, coelomic epithelium
B. Cuticle, epidermis, longitudinal muscles, circular muscles, coelomic epithelium
c. Non-cellular cuticle, epidermis, coelomic epithelium, circular muscles, longitudinal muscles
D. Cuticle, epidermis, peritoneal muscles


The gland which is related to the maturation of Iymphocytes is
A. Thymus
B. Thyroid
c. Adrenal
D. Pituitary


Of the students in a school, it is known
that \( 30 \% \) have \( 100 \% \) attendance and
70\% students are irregular. Previous year results report that \( 70 \% \) of all students who have \( 100 \% \) attendance
attain A grade and \( 10 \% \) irregular students attain A grade in their annual examination. At the end of the year, one
student is chosen at random from the
school and he was found to have an \( A \)
grade. What is the probability that the student has \( 100 \% \) attendance? Is regularity required only in school? Justify your answer.


If \( y=\sqrt{x}^{\sqrt{x} \sqrt{x}^{\sqrt{x}} \ldots \infty} \) then show that
\( x \frac{d y}{d x}=\frac{y^{2}}{2-y \log x} \)


Two wires of equal length and cross-
sectional area are suspended as shown
in figure. Their Young's modulii are \( Y_{1} \)
and \( Y_{2} \) respectively. The equivalent
Young's modulii will be:
A \( \cdot Y_{1}+Y_{2} \)
B.
c. \( \frac{Y_{1}+Y_{2}}{2} \)
D. \( \sqrt{Y_{1} Y_{2}} \)


The maximum number of persons in a
country in which no two persons have an identical set of teeth assuming that there is no person without a tooth is
\( \mathbf{A} \cdot 2^{3} \)
B. \( 2^{32}-1 \)
\( c .32 ! \)
D. 32! - 1


Form the differential equation from the following primitives where constant is arbitrary.
\( \boldsymbol{y}=\boldsymbol{a} \boldsymbol{x}^{2}+\boldsymbol{b} \boldsymbol{x}+\boldsymbol{c} \)


Conversion of acetyl Co-A to fatty acid is a/an
A. Anabolic reaction
B. Catabolic reaction
c. Anabolic and catabolic reaction
D. None of the above


Find the volume of the sphere whose
curved surface area is \( 616 \mathrm{cm}^{2} \)


Moment of inertia of a uniform circular
disc about a diameter is \( I \). Its moment
of in axis perpendicular to its plane and passing through a point on its rim will be:
A . \( 5 I \)
B. \( 6 I \)
\( c .3 I \)
D. \( 4 I \)


Which statement is incorrect related to
induced electric field due to changing magnetic flux?
A. It varies with time
B. It is non-conservative
c. It forms closed loop
D. Both (1) \& (3)


\( f(a>0,|z|=a, \) then find the real part of \( \left(\frac{\boldsymbol{z}-\boldsymbol{a}}{\boldsymbol{z}+\boldsymbol{a}}\right) \)


Which of the following will not undergo diazotisation?
A. m-toluidine
B. Aniline
c. p-aminophenol
D. Benzyl amine


Increasing order of density: \( N a<A l< \)
\( \boldsymbol{F} \boldsymbol{e}<\boldsymbol{P} \boldsymbol{b} \)
if true enter 1 , else enter 0 .
\( A \cdot 1 \)


If \( x \) is amount of adsorbate and \( m \) is
amount of adsorbent, which of the
following relations is not related to adsorption process?
A \( \cdot \frac{x}{m}=f(T) \) at constant \( P \)
B \( \cdot P=f(T) \) at constant \( \left(\frac{x}{m}\right) \)
c. \( \frac{x}{m}=P \times T \)
D. \( \frac{x}{m}=f(P) \) at constant \( T \)


Fishes which are parasite as well as
scavanger are
A. ostracoderm
B. cyclostomata
c. Tetrapoda
D. All of the above


Epiphytes like Vanda, develop special layer of absorptive tissue velamen consisting of 4 or 5 layers of long polygonal cells. Velamen is formed by
A. Prop roots
B. Stem
c. clinging roots
D. Hanging roots


What is transformation?


Identify the equation of a straight line passing through the point of intersection of \( \boldsymbol{x}-\boldsymbol{y}+\mathbf{1}=\mathbf{0} \) and \( \mathbf{3} \boldsymbol{x}+ \)
\( \boldsymbol{y}-\mathbf{5}=\mathbf{0} \) and perpendicular to one of
them.
A. \( x+y+3=0 \)
в. \( x+y-3=0 \)
c. \( x-3 y-5=0 \)
D. \( x-3 y+5=0 \)


The value of \( \boldsymbol{K}_{s p} \) is \( \boldsymbol{H} \boldsymbol{g} \boldsymbol{C l}_{2} \) at room
temperture is \( 4.0 \times 10^{-15} \). The
concentration of \( C l^{\ominus} \) ion in its
aqueous solution at saturation point is:
A \( \cdot 1 \times 10^{-5} \)
В. \( 2 \times 10^{-5} \)
c. \( 2 \times 10^{-15} \)
D. \( 8 \times 10^{-15} \)


The term ecosystem was used by
A. Tansley
B. Odum
c. Lamarck
D. Haeckel


In the adjoining graph, possible paths
\( A B C \) and \( A C \) for changing a gas from
the thermodynamic state \( A \) to the state
\( C: \) (i) Along which path greater amount
of work will have to be done? (ii) If the
internal energy of the gas at the state \( \boldsymbol{A} \)
be 5 joule, and 100 then calculate the
internal energy of the gas at the state \( C \)


Which of the following oxide is expected to react readily with NaOH?
A. \( N a_{2} O \)
в. \( C a O \)
c. \( N O \)
D. \( C l_{2} O_{7} \)


The area of the triangle whose vertices \( \operatorname{are}(3,8),(-4,2) \) and (5,-1) is :
A. 75 sq.units
в. 37.5 sq.units
c. 45 sq.units
D. 22.5 sq.units


If true then enter 1 and if false then
enter 0

Can two obtuse angles form a linear pair?


Figure shows a semicircle that is the graph of the equation \( y=\sqrt{6 x-x^{2}} \).
the semicircle is rotated \( 360^{\circ} \) about the
\( x \) -axis, calculate the volume of the
sphere that is created
\( A \cdot 6 \pi \)
В. \( 12 \pi \)
\( c .18 \pi \)
D. \( 24 \pi \)
E. \( 36 \pi \)


An uncharged parallel plate capacitor filled with a dielectric of dielectric
constant \( K \) is connected to an air filled
identical parallel capacitor charged to
potential \( V_{1} . \) If the common potential is
\( V_{2}, \) the value of \( K \) is
A. \( \frac{V_{1}-V_{2}}{V_{1}} \)
B. \( \frac{V_{1}}{V_{1}-V_{2}} \)
c. \( \frac{V_{2}}{V_{1}-V_{2}} \)
D. \( \frac{V_{1}-V_{2}}{V_{2}} \)
E \( \cdot \frac{V_{1}-V_{2}}{V_{1}+V_{2}} \)


ff \( p \) th \( , q \) th \( , r \) th and \( s \) th terms of a
G.p,prove that; \( (p-q),(q-r) \) and \( (r-s) \) are also in
G.P.


When white light passes through a dispersive medium, it breaks up into various colours. Which of the following
is true?
A. Velocity of light for violet is greater than the velocity of light for red colour
B. Velocity of light for violet is less than the velocity of light for red
c. velocity of light is the same for all colours
D. velocity of light for different colours


The IUPAC name of the compound is:
A. 3 -keto- 2 -methylhex- 5 -en-al
B. 3-keto-2-methylhex-4-en-al
C. 5 -formylhex- 2 -en-3-one
D. 5-methyl-4-oxohex-2-en-5-al


A small conduction loop is in a magnetic field pointing out of the screen.Which of the following would produce a counter-clockwise current in the loop?
I. Moving the coil out of the field.
II. Increasing the strength of the field.
III. Rotating the coil on its center axis.
A. I only
B. I and III only
c. Il only
D. I, II, and III


A gas thermometer measure the temperature from, the variation of
pressure of a sample of gas. If the pressure measured at the melting point of lead is 2.20 times the pressure
measured at the triple point of water find the melting point of lead.
\( A \cdot 601 K \)
B. 420 K
c. 790 к
D. 510 K


The product formed at anode and
cathode, when dilute \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) is electrolyzed are
A \( . S O_{2}, H \)
в. \( S O_{3}, H_{2} \)
c. \( H_{2} S_{2} O_{8}, H_{2} \)
D. \( O_{2}, H_{2} \)


If \( \cot ^{-1}\left(\frac{1}{a}\right)+\cot ^{-1}\left(\frac{1}{b}\right)+ \)
\( \cot ^{-1}\left(\frac{1}{c}\right)=\frac{\pi}{2}, \) then
\( \mathbf{A} \cdot a+b+c=a b c \)
B. \( a b+b c+c a=1 \)
c. \( a b+b c+c a=a b c \)
D. none of these


Shepherd's purse plant belong to family of
A. Cruciferae
B. Malvaceae
c. Solanaceae
D. Leguminosae


For the reaction, \( \boldsymbol{C O}_{(\boldsymbol{g})}+\boldsymbol{C l}_{2(\boldsymbol{g})} \leftrightharpoons \)
\( C O C l_{2(g)}, \) the value of \( K_{p} / K_{c} \) is equal
to:
A . 1.0
в. \( R T \)
c. \( \sqrt{R T} \)
D. \( \frac{1}{R T} \)


The ligaments connect two bones at the joints.
A. True
B. False


Murein does not occur in the wall of
A. Diatoms
B. Nostoç
c. Eubacteria
D. Blue green algae


A plant uses ........... means to transfer
information from one cell to another as
there is no specialized tissue present
for the conduction of information.
A. Thermal
B. Electrical
c. Chemical
D. Electrochemical


gas turns colourless nitrogen monoxide into brown fumes of nitrogen dioxide.
A. Chlorine
B. Oxygen
c. Methane
D. Fluorine


Complete the refracted ray in the
flowing ray diagram


n Fig, \( P Q \) and \( P R \) are the two light rays
emerging from an object \( \boldsymbol{P} \). The ray \( \boldsymbol{P Q} \)
is refracted as \( Q S \). Name the
phenomenon that occurs if the angle of
incidence \( \angle P Q N \) is increased :
A. Refraction
B. Total internal reflection
c. Minimum deviation
D. None of these


Solve: \( 2^{2 x+1}=8 \)


\( \boldsymbol{S} \boldsymbol{i} \boldsymbol{F}_{4}+\boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \boldsymbol{A} \stackrel{1000^{\circ} \boldsymbol{C}}{\longrightarrow} \boldsymbol{B} \stackrel{N a_{2} C O_{3}}{\longrightarrow} \boldsymbol{C} \)
In the above reaction, identify \( B \) and \( C \) respectively:
A. \( H_{4} \) Si \( O_{4} \) and \( N a_{2} \) SiO \( _{3} \)
B. \( \operatorname{SiO}_{2} \) and \( N a_{2} S \)
\( c \cdot \operatorname{si0}_{2} \) and \( N a_{2} C O_{2} \)
D. \( \operatorname{si} 0_{2} \) and \( N a_{2} \) Si \( O_{3} \)


A machine delivers power to a body which is proportional to velocity of the body. If the body starts with a velocity which is almost negligible, then the distance covered by the body is proportional to:
A \( \cdot \sqrt{v} \)
B. \( 3 \sqrt{\frac{v}{2}} \)
\( \mathbf{c} \cdot v^{5 / 3} \)
\( D \cdot v^{2} \)


A bomb is dropped from an aeroplane flying horizontally with a velocity of \( \mathbf{7} 20 k m / h \) at an altitude of \( 980 m . \) Time taken by the bomb to hit the ground is
\( \mathbf{A} \cdot 1 s \)
B. \( 7.2 s \)
c. \( 14.14 s \)
D. \( 0.15 s \)


Which of the following statements, about the advantage of roasitng of sulphide ore before reduction is not
true?
A. Roasting of the sulphide to the oxide is thermodynamically feasible
B. Carbon and hydrogen are suitable reducing agents for metal sulphides
C. The \( \Delta_{f} G^{0} \) of the sulphide is greater than those for \( C S_{2} \) and \( H_{2} S \)
D. The \( \Delta_{f} G^{0} \) is negative for roasting of sulphide ore to oxide


In a parallel plate condenser if the distance between the plates is made half and the dielectric constant is doubled,
then the capacity increases by a factor:
A. 2 times
B. 4 times
\( c .8 \) times
D. 16 times


Discuss the commutativity and associativity of binary operation \( * \)
defined on \( A=Q-\{1\} \) by the rule \( a * \)
\( \boldsymbol{b}=\boldsymbol{a}-\boldsymbol{b}+\boldsymbol{a} \boldsymbol{b} \) fo all \( \boldsymbol{a}, \boldsymbol{b} \in \boldsymbol{A} . \) Also find
the identity element of \( * \) in \( A \) and hence
find the invertible elements of \( \boldsymbol{A} \)


A heat engine carries one mole of an
ideal mono-atomic gas around the cycle
as shown in figure, the amount of heat
added in the process \( A B \) and heat
removed in the process \( C A \) are:
A \( \cdot q_{A B}=450 R \) and \( q_{C A}=-450 R \)
B . \( q_{A B}=450 R \) and \( q_{C A}=-225 R \)
\( \mathbf{c} \cdot q_{A B}=450 R \) and \( q_{C A}=-375 R \)
\( \mathbf{D} \cdot q_{A B}=375 R \) and \( q_{C A}=-450 R \)


Why is electrical wiring usually made from copper and not silver?
A. Copper is a better conductor
B. Copper is a better insulator
c. copper is less expensive
D. copper is non magnetic


Which one of the following pairs represents the intensive properties?
A. Specific heat and temperature
B. Entropy and density
c. Enthalpy and mole fraction
D. Heat and temperature


Let \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{ll}x^{2}+k, & \text { when } x \geq 0 \\ -x^{2}-k, & \text { when } x<0\end{array} . \) If the \right.
function \( f(x) \) be continous at \( x=0 \)
then \( \boldsymbol{k}= \)
\( \mathbf{A} \cdot \mathbf{0} \)
B. 1
c. 2
D. -


\( \int_{0}^{16} \frac{x^{1 / 4} d x}{1+\sqrt{x}} \) is equal to
\( \mathbf{A} \cdot 4 / 3+\tan ^{-1} 2 \)
B. \( 8 / 3+4 \tan ^{-1} 2 \)
\( c \cdot 2 / 3+\tan ^{-1} 2 \)
D. None


Which of the following process is responsible for the smoke-like vapour which comes out of the mouth in
winter?
A. Precipitation
B. Evaporation
c. condensation
D. None of the above


The interior angles of a convex polygon
are in AP. The smallest angle is \( 120^{\circ} \& \)
the common difference is \( 5^{\circ} \). Find the
number of sides of the polygon.
\( \mathbf{A} \cdot \mathbf{9} \)
B . 16
c. 12
D. None of these


When \( 10 V, D C \) is applies across a coil
current through it is \( 2.5 \mathrm{A}, \) if \( 10 \mathrm{V}, 50 \mathrm{Hz} \mathrm{A} \)
C. is applied current reduces to 2 A. Calculate reluctance of the coil.


Which of the following is used in relieving pain?
A. Acetyl salicylic acid
B. Methyl salicylate
c. Methylacetate
D. Phenylacrylate


Rs. 20,000 is lent for 2 years at \( 5 \% \) compound interest. Calculate the compound interest and the amount
after 2 years if the interest is
compounded annually. What would have been the interest earned if the same
amount was lent for simple interest at the same rate for the same duration?


Calculate the force per unit length a
long sraight wire carring of 4.0 A due to a parallel wire carrying current of 6.0 a. This distance between the wire is 3.0
\( \mathrm{cm} \)


Oxygen is a non combustible gas.
A. True
B. False


The frequency of a man's voice is 300 \( \mathrm{Hz} \) and its wavelength is 1 meter. If the wavelength of a child's voice is \( 1.5 \mathrm{m} \) then the frequency of the child's voice is
A. 200 \( \mathrm{Hz} \)
в. 150 нz
\( c \cdot 100 \) нz
D. 350 нz


VAT is imposed -
A. Directly on consumer
B. On final stage of production
C. On first stage of production
D. On all stages between production and final sale


Copy and complete the following ray
\( \operatorname{diagram} .\left(i_{c}=42^{\circ}\right) \)


If the tangent at any point of an ellipse \( \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 \) makes an angle \( \alpha \) with
the major axis and an angle \( \beta \) with the
focal radius of the point of contact then show that the eccentricity'e' of the ellipse is given by the absolute value of \( \frac{\cos \beta}{\cos \alpha} \)


Acetyl CoA is produced from pyruvate by
A. oxidative decarboxylation
B. oxidative photophosphorylation
c. oxidative hydrogenation
D. oxidative photorespiration.


A stone is thrown with an initial speed
of \( 4.9 \mathrm{m} s^{-1} \) from a bridge in the vertically upward direction. It falls down in water after 2 s. The height of the bridge is :
A . 24.7 \( \mathrm{m} \)
B. 19.8 \( m \)
c. \( 9.8 \mathrm{m} \)
D. 4.9 \( m \)


State whether true or false:
During constructive interference, the crest of one wave meets the crest of the
other wave or the trough of one wave
meets the trough of the other wave.
A. True
B. False


Which metallurgy involves leaching?
A . \( A u \)
в. \( A g \)
c. Both (a) and (b)
D. None of these


The correct statement among the
following is:
\( \mathbf{A} \cdot\left(S i H_{3}\right)_{3} N \) is pyramidal and more basic than \( \left(C H_{3}\right)_{3} N \)
B. \( \left(\operatorname{Si} H_{3}\right)_{3} N \) is planar and more basic than \( \left(C H_{3}\right)_{3} N \)
C \( \cdot\left(S i H_{3}\right)_{3} N \) is pyramidal and less basic than \( \left(C H_{3}\right)_{3} N \)
D. \( \left(S i H_{3}\right)_{3} N \) is planar and less basic than \( \left(C H_{3}\right)_{3} N \)


If \( f(x)=\frac{1+\tan x}{1-\tan x} \) then \( f\left(\frac{\pi}{6}\right) \)


Find the value of \( x \) such that \( 1+4+ \)
\( \mathbf{7}+\mathbf{1 0}+\ldots \ldots+\boldsymbol{x}=\mathbf{7 1 5} \)


Kerosene is a mixture of:
A. aromatic hydrocarbons
B. aliphatic hydrocarbons
C. unsaturated hydrocarbons
D. saturated hydrocarbons


A long solenoid of radius \( 2 \mathrm{cm} \) has 100 turns/cm and carries a current of \( 5 A \). A
coil of radius \( 1 c m \) having 100 turns and a total resistance of \( 20 \Omega \) is placed inside the solenoid coaxially. The coil is connected to a galvanometer. If the current in the solenoid is reversed in direction, find the charge flown through the galvanometer
A \( \cdot 2 \times 10^{-4} C \)
B. \( 1 \times 10^{-4} C \)
c. \( 4 \times 10^{-4} C \)
D. \( 8 \times 10^{-4} C \)


\( \boldsymbol{C a O C l}_{2}+\boldsymbol{H}_{2} \boldsymbol{O}+\boldsymbol{C O}_{2} \longrightarrow \boldsymbol{C a} \boldsymbol{C O}_{3}+ \)
\( \boldsymbol{C a C l}_{2}+\boldsymbol{H O C l} \)
This reaction is simply:
A. oxidation
B. reduction
c. redox
D. hydrolysis in presence of \( C O_{2} \)


The vectors \( \vec{a}, \vec{b}, \vec{a} \times \vec{b} \) form
A. A right handed system
B. A left handed system
c. A set of coplanar vectors
D. A set of mutually perpendicular vectors


\( \operatorname{Let} \boldsymbol{A}=\left(\begin{array}{cc}\boldsymbol{x}+\mathbf{2} & \mathbf{3} \boldsymbol{x} \\ \boldsymbol{3} & \boldsymbol{x}+\mathbf{2}\end{array}\right), \boldsymbol{B}= \)
\( \left(\begin{array}{cc}\boldsymbol{x} & \mathbf{0} \\ \mathbf{5} & \boldsymbol{x}+\mathbf{2}\end{array}\right) . \) Then all solutions of the
equation \( \operatorname{det}(A B)=0 \) is
A. 1,-1,0,2
B. 1,4,0,-2
c. 1,-1,4,3
D. -1,4,0,3


At a certain point on a screen the path difference for the two interfering rays is
\( (1 / 8)^{t h} \) of a wavelength. Find the ratio of
the intensity at this point to that at the centre of a bright fringe.


How many moles of hydrogen are present in one \( g m \) of hydrogen?


Ozone hole is maximum over:
A . europe
B. antarctica
\( c . \) india
D. africa


An electron of mass m with an initial velocity \( \vec{V}=V_{0} \hat{i}\left(V_{0}>0\right) \) enters an electric field \( \overrightarrow{\boldsymbol{E}}=-\boldsymbol{E}_{0} \hat{\boldsymbol{i}}\left(\boldsymbol{E}_{0}= \) constant \right.
\( >0) \) at \( t=0 . \) If \( \lambda_{0} \) is its de-Broglie
wavelength initially, then its de-Broglie wavelength at time t is?
A \( \cdot \lambda_{0}\left(1+\frac{e E_{0}}{m V_{0}} t\right) \)
в. \( \lambda_{0} \)
\( ^{c} \cdot \frac{\lambda_{0}}{\left(1+\frac{e E_{0}}{m V_{0}} t\right)} \)
D. \( \lambda_{0} \)


The stage of meiosis where centromere
separate is
A. Metaphase I
B. Telophase II
c. Prophase
D. Anaphase II


Choose the correct statement from the
following.
A. The greater positive value of \( E_{o p}^{o} \) indicates greater reactivity of metal
B. \( F^{-} \) is strong oxidant while \( C u^{2+} \) is weak reductant
C. The metals placed above \( M g \) in the electrochemical series do not decompose water at ordinary temperature
D. Oxides of \( H g \) do not decompose on heating


Find the principal value of the following
\( \cos ^{-1}\left(\cos \frac{13 \pi}{6}\right) \)


Assertion
Lower parts of the ship or bridge is
coated with tar.
Reason
It is to increase rusting.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is
not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


The value of \( \beta \) of a transistor is \( 19 . \) The
value of \( \alpha \) will be
A . 0.93
B. 0.98
\( c .0 .99 \)
D. 0.95


8
\( d \)
\( d \)
\( d \)


The ratio of momenta of an electron and a
\( \alpha \) -particle which is accelerated from rest
by a potential difference of \( 100 \mathrm{V} \) is:
\( A \)
в. \( \sqrt{\frac{2 m_{e}}{m_{\alpha}}} \)
c. \( \sqrt{\frac{m_{e}}{m_{\alpha}}} \)
D. \( \sqrt{\frac{m_{e}}{2 m_{\alpha}}} \)


Find from first principles the
differential coefficient of \( 2 x^{2}+3 x \)


Consider the satellites revolving round the earth at different heights.The ratio of their orbital speed is 3: 2 . If one of them is at a height of \( 200 \mathrm{Km} \), the height of the other satellite is (Radius of the earth is \( R=6400 \mathrm{Km} \)
A. \( 8450 K m \)
в. 845 Кт
c. \( 84.5 K m \)
D. \( 84500 K m \)


A SONAR (sound navigation and ranging) uses ultrasonic waves to
detect and locate objects under water In a submarine equipped with a SONAR the time delay between generation of a probe wave and the reception of its echo after reflection from an enemy
submarine is found to be 77.0 s. What is
the distance of the enemy submarine?
(Speed of sound in water \( =1450 m s^{-1} \) ).


Aldol condensation will not be observed
in?
A. Chloral
B. Phenyl acetaldehyde
c. Hexanal
D. Ethanal


A tank containing water has an orifice on one vertical wall. If the centre of the
orifice is \( 4.9 \mathrm{m} \) below the surface of
water in the tank, the velocity of discharge is:
A. \( 0.98 \mathrm{m} / \mathrm{s} \)
в. \( 9.8 \mathrm{m} / \mathrm{s} \)
\( c \cdot 98 m / s \)
D. \( 9.8 \mathrm{cm} / \mathrm{s} \)


Mention any four electronic gadgets.


A uniform flexible chain of mass \( \mathrm{m} \) and
length \( 2 \ell \) hangs in equilibrium over a smooth horizontal pin of negligible diameter. One end of the chain slips over the pin. The speed of
chain when it leaves pin is
в. \( \sqrt{g \ell} \)
c. \( \sqrt{4 g \ell} \)
D. \( \sqrt{3 g \ell} \)


Two identical geostationary satellites are moving with equal speeds in the
same orbit but their sense of rotation
brings them on a collision course. The
debris will
A. Fall down
B. Move up
C. Begin to move from east to west in the same orbit
D. Begin to move from west to east in the same orbit


Why do young people get acne and pimples on face?


A ball of mass \( 1 k g \) is at rest in position
P by means of two light stings OP and
RP. The string RP is now cut and the ball
swings to position Q. Find the tensions in the strings in positions OP (when RP
was not cut ) and OQ(when RP was cut)
(Take \( \left.g=10 m / s^{2}\right) \)


Balance the following equation in basic medium by ion-electron method and oxidation number method and identify
the oxidising agent and the reducing
agent
\( N_{2} H_{4}(l)+C l O_{3}^{-}(a q) \rightarrow N O(g)+ \)
\( \boldsymbol{C l}^{-}(\boldsymbol{g}) \)


During winter, clothes tend to stick to our body as an action of force.
A. electrostatic
B. muscular
c. magnetic
D. contact


If \( \frac{p+q}{p-q}, x \quad \) and \( \quad p^{2}-q^{2} \) are in
continued proportion the find \( x \)


The shape of \( I F_{5} \) molecule is:
A. pentagonal bipyramidal
B. tetrahedral
c. square pyramidal
D. square planar


Beautiful, lake colours are formed by dyes with mordants, which paste the dye to the cloth or fabric. Which of the
following is a mordar used in dying?
A . Calcium carbonate
B. Aluminium sulphate
c. Calcium hydroxide
D. zinc phosphate


Yeast complete cell cycle in
A. 30 minutes
B. 60 minutes
c. 90 minutes
D. 120 minutes


Assertion
Latent heat of fusion of ice is 336000 J
\( k g^{-1} \)
Reason
Latent heat refers to change of state without any change in temperature.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is
not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Find the solution of following inequality,
also show it graphically:
\( \boldsymbol{x}<\mathbf{4}, \boldsymbol{x} \in \boldsymbol{R} \)
\( A \)
в.
c.
D.


The potential difference between any two points is measured in:
A. volts
B. joules
c. coulombs
D. none of these


A hair dresser stands with her nose 20
\( \mathrm{cm} \) infront of a plane mirror for what distance must she focus her eyes in
order to see her nose in the mirror?
A . \( 40 \mathrm{cm} \)
B. \( 50 \mathrm{cm} \)
c. \( 30 \mathrm{cm} \)
D. \( 60 \mathrm{cm} \)


Find \( x, y \) and \( z \)


Find the complement of the angles
represented in given figure.


Force exerted by a truck is \( 500000 N \)
and the pressure on the ground is
\( 2500000 P a . \) Calculate the area of
contact of tyres with ground?


Photorespiration occurs in
A . Green photosynthetic parts
B. All living cells
c. Mitochondria
D. Root


According to Bohr's theory of hydrogen-
atom, for the electron in the \( n^{t h} \)
permissible orbit This question has multiple correct options
A \( \cdot \) Linear Momentum \( \propto \frac{1}{n} \)
B. Radius of orbit \( \propto n \)
c. Kinetic Energy \( \propto \frac{1}{n^{2}} \)
D. Angular Momentum \( \propto n \)


The negation of the statement \( \boldsymbol{q} \vee \) \( (p \wedge \sim r) \) is equivalent to
\( \mathbf{A} \cdot \sim q \wedge(p \rightarrow r) \)
в. \( q \vee \sim(p \rightarrow r) \)
c \( \cdot q \wedge(\sim p \wedge r) \)
D. None of these.


Express \( 1 . \overline{32}+0 . \overline{35} \) in the form of \( \frac{p}{q} \) where \( p \) and \( q \) are integers and \( q \neq 0 \)
Find \( p+q \)


The structure of silicon(IV) oxide
belongs to the type:
A . ionic lattice
B. macromolecular, with a layer structure
C. molecular lattice, with van der Waals forces among the molecules
D. macromolecular, with a non-layer structure


Is the following sequence an A.P.? If yes,
then find the common difference.
\( \mathbf{2}, \mathbf{4}, \mathbf{6}, \mathbf{8}, \dots \)


Molar conductance of a \( 0.2 \mathrm{M} \) solution
of a weak acid, \( \boldsymbol{H} \boldsymbol{A} \) is \( 2.8 \times 10^{-2} \boldsymbol{S m}^{2} \)
mol \( ^{-1} \). If the limiting molar conductance of \( \boldsymbol{H} \boldsymbol{A} \) is \( \mathbf{5 6 0} \mathbf{~} \mathbf{S} \boldsymbol{m}^{2} \boldsymbol{m o l}^{-1} \)
the dissociation constant of the acid is:
\( \mathbf{A} \cdot 5 \times 10^{-10} \)
B . \( 10^{-10} \)
C \( .5 \times 10^{-5} \)
D. \( 2 \times 10^{-15} \)


Where was the first museum built in
India?
A. Delhi
B. Mumbai
c. Kolkata
D. Hyderabadd


Presence of sharp claws and powerful
feet in the fishing eagle is an adaptation to
A. Available food
B. Self protection
c. Climate
D. changing environment


Find the local maxima and local
minima of the function \( f(x)=\sin x- \)
\( \cos x, 0<x<2 \pi . \) Also find the local
maximum and local minimum values.


Given \( a_{n}=4, d=2, S_{n}=-14, \) then
find the \( n \) and \( a_{n} \)


If \( (x+i y)(2-3 i)=4+i\left(\frac{1}{2}\right) \) then
\( \boldsymbol{x}+\boldsymbol{y}= \)
\( A \cdot \frac{3}{2} \)
B.
c.
D.


Which from the given options is not correctly matched?
A . \( X e O_{3} \) -Trigonal bipyramidal
B . \( C l F_{3}- \) bent T-shape
c. \( X e O F_{4} \) -Square pyramidal
D. \( X e F_{2} \) -Linear shape


What is the surface area of a cube
whose volume is \( 64 \mathrm{cm}^{3} \) ?
\( \mathbf{A} \cdot 16 \mathrm{cm}^{2} \)
B. \( 64 \mathrm{cm}^{2} \)
c. \( 96 \mathrm{cm}^{2} \)
D. \( 128 \mathrm{cm}^{2} \)


Light is incident at an angle \( \phi \) with the
normal to a plane containing two slits of
separation \( d . \) Select the expression that
correctly describes the positions of the
interference maxima in terms of the
incoming angle \( \phi \) and outgoing angle \( \theta \)
\( ^{\mathbf{A}} \cdot \sin \phi+\sin \theta=\left(m+\frac{1}{2}\right) \frac{\lambda}{d} \)
\( \mathbf{B} \cdot d \sin \theta=m \lambda \)
\( \mathrm{c} \cdot \sin \phi-\sin \theta=(m+1) \frac{\lambda}{d} \)
" \( \sin \phi+\sin \theta=m \frac{\lambda}{d} \)


An \( A C \) rms voltage of \( 2 V \) having a frequency of \( 50 \mathrm{KHz} \) is applied to a
condenser of the capacity of \( 10 \mu F . \) The maximum value of the magnetic field between the plates of the condenser if
the radius of a plate is \( 10 \mathrm{cm} \) is


A series LCR-circuit with \( \boldsymbol{R}=\mathbf{2 0} \boldsymbol{\Omega} \)
\( \boldsymbol{L}=\mathbf{1 . 5} \boldsymbol{H} \) and \( \boldsymbol{C}=\mathbf{3 5} \boldsymbol{\mu} \mathrm{F} \) is connected
to a variable frequency \( 200 V \) ac supply When the frequency of the supply equals the natural frequency of the circuit, the average power transferred to the circuit in one complete cycle is?
\( \mathbf{A} \cdot 200 W \)
в. \( 2000 \mathrm{W} \)
\( c .100 W \)
D. \( 4000 \mathrm{W} \)


Write the degree of the differential
equation \( \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}}+\boldsymbol{x}\left(\frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}\right)^{2}= \)
\( 2 x^{2} \log \left(\frac{d^{2} y}{d x^{2}}\right) \)


Assertion
A positively charged particle always moves along the electric lines of forces.
Reason
Force on a charged particle is tangential to the electric lines of force.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


Find the value of other five
trigonometric ratios:
\( \sec x=\frac{13}{5}, x \) lies in fourth quadrant


How many turns of Calvin cycle would
generate one molecule of glucose/hexose?
A. One cycle
B. Three cycles
c. six cycles
D. Twelve cycles


Why do soaps not work in hard water?


How many structural isomers of pentyl
alcohol on oxidation will produce ketones only?


By which mechanism water is absorbed
under low transpiring conditions?
A. Osmosis
B. Active absorption
c. Both of the above
D. Passive absoprtion


The magnetic moment is associated with its spin angular momentum and
orbital angular momentum. Spin only
magnetic moment value of \( \boldsymbol{C r}^{3+} \) ion is :
\( \mathbf{A} \cdot 2.87 \mathrm{B} . \mathrm{M} \)
B. 3.87 В.М.
c. 3.47 В.M.
D. 3.57 В.М.


Show that the points \( \boldsymbol{A}(-\mathbf{3} \hat{\boldsymbol{i}}+\boldsymbol{3} \hat{\boldsymbol{j}}+\mathbf{5} \hat{\boldsymbol{k}}), \boldsymbol{B}(\hat{\boldsymbol{i}}+\mathbf{2} \hat{\boldsymbol{j}}+\mathbf{3} \hat{\boldsymbol{k}}), \boldsymbol{C} \)
are collinear.


The mass of a molecule of the
compound \( \boldsymbol{C}_{\mathbf{6 0}} \boldsymbol{H}_{\mathbf{1 2 2}} \) is
A \( \cdot 1.4 \times 10^{-21} \mathrm{g} \)
В. \( 1.09 \times 10^{-21} \mathrm{g} \)
\( \mathbf{c} \cdot 5.025 \times 10^{23} \mathrm{g} \)
D. \( 16.023 \times 10^{23} \mathrm{g} \)


State two ways to prevent the rusting of iron:


A body \( P \) moving with a velocity of 20
\( \mathrm{ms}^{-1} \) collides with another body \( Q \) of
same mass at rest. After collision \( \boldsymbol{P} \)
comes to rest. What is the velocity of the
body \( Q ? \)
A \( \cdot 10 \mathrm{ms}^{-1} \)
B. \( 20 \mathrm{ms}^{-1} \)
\( \mathrm{c} \cdot 30 \mathrm{ms}^{-1} \)
D. \( 5 \mathrm{ms}^{-1} \)


Calculate the velocity constant.


The edge formed by the two refracting surfaces is the refracting edge in glass prism. Is this statement True or False?
A. True
B. False


If \( S=\tan ^{-1}\left(\frac{1}{n^{2}+n+1}\right)+ \)
\( \tan ^{-1}\left(\frac{1}{n^{2}+3 n+3}\right)+\ldots+ \)
\( \tan ^{-1}\left(\frac{1}{1+(n+19)(n+20)}\right) \) then \( \tan S \) is
equal to
\( \mathbf{A} \cdot \frac{20}{401+20 n} \)
B. \( \frac{n}{n^{2}+20 n+1} \)
\( \mathbf{C} \cdot \frac{20}{n^{2}+20 n+1} \)
\( D \cdot \frac{n}{401+20 n} \)


Sugarcane and corn are one of the most
efficient plants in trapping light energy because
A. They have \( C_{4} \) acid cycle
B. They do not involve photorespiration
c. They perform calvin cycle
D. All of the above


Which tissue are removed when a plant
is girdled?
A. Xylem and pith
B. Xylem and phloem
c. Phloem to epidermis
D. Phloem to pith


In the figure, if \( \boldsymbol{A B}=\boldsymbol{C D} \) and
\( \angle A O B=90^{\circ} \) find \( \angle C O D \)


Formation of real image using a biconvex lens is shown below:
f the whole set up is immersed in water
without disturbing the object and the screen position, what will one observe
on the screen?
A. Image disappears
B. No change
C. Erect real image
D. Magnified image


How many ATP's are produced by
consumption of \( 1- \) glucose molecule in
RBC?


Tassar silk is secreted by
A. Antheraea assamensis
B. Bombyx mori
C. Philosamia recini
D. Antheraea paphia


A steel wire is \( 1 \mathrm{m} \) long and \( 1 \mathrm{mm}^{2} \) in the
area of cross-section. If it takes \( 200 N \)
to stretch the wire by 1 m \( m \), the force that will be required to stretch the wire of the same material and cross-
sectional area from a length of \( 10 m \) to
\( 1002 \mathrm{cm} \)
A. \( 100 N \)
B. \( 200 N \)
c. \( 400 N \)
D. 2000N


toppr OGIN No
Q Type your question_
evenly at the same steady rate to both
substances.
Which table best describes the
properties of these substances?
\( A \)
\begin{tabular}{|l|l|}
\hline \multicolumn{1}{|c|} { Quantity } & Greater for Which Substance? \\
\hline Solid Specific Heat & \( \mathrm{P} \) \\
Liquid Specific Heat & \( \mathrm{G} \) \\
Latent Heat of Vaporization & \( \mathrm{P} \) \\
\hline
\end{tabular}
\( B \)
\begin{tabular}{|l|l|}
\hline \multicolumn{1}{|c|} { Quantity } & Greater for Which Substance? \\
\hline Solid Specific Heat & \( \mathrm{P} \) \\
Liquid Specific Heat & \( \mathrm{P} \) \\
Latent Heat of Vaporization & \( \mathrm{G} \) \\
\hline
\end{tabular}
\( c \)
\begin{tabular}{|l|l|}
\hline \multicolumn{1}{|c|} { Quantity } & Greater for Which Substance? \\
\hline Solid Specific Heat & \( \mathrm{P} \) \\
Liquid Specific Heat & \( \mathrm{P} \) \\
Latent Heat of Vaporization & \( \mathrm{G} \) \\
\hline
\end{tabular}
\( D \)
\begin{tabular}{|l|l|}
\hline \multicolumn{1}{|c|} { Quantity } & Greater for Which Substance? \\
\hline Solid Specific Heat & \( \mathrm{G} \) \\
Liquid Specific Heat & \( \mathrm{G} \) \\
Latent Heat of Vaporization & \( \mathrm{G} \) \\
\hline
\end{tabular}
\( E \)
\begin{tabular}{|l|l|}
\hline \multicolumn{1}{|c|} { Quantity } & Greater for Which Substance? \\
\hline Solid Specific Heat & \( \mathrm{P} \) \\
Liquid Specific Heat & \( \mathrm{G} \) \\
Latent Heat of Vaporization & \( \mathrm{G} \) \\
\hline
\end{tabular}


The inward force required to keep a satellite moving a circular orbit is?
A. Gravitational field
B. Centripetal force
c. centrifugal force
D. Aerodynamic forç


If \( m \) arithmetic means are inserted
between 1 and \( 31, \) so that the ratio of
the \( 7^{t h} \) and \( (m-1)^{t h} \) means is 5: 9
then the value of \( m \) is
\( \mathbf{A} \cdot \mathbf{9} \)
B. 11
c. 13
D. 14


Gangue have:
\( A \). sand and soil
B. silt
C . gravel
D. all of these


Which of the following fossil general stand midway between pteridophytes and gymnosperms?
A. Lycopodites
B. Selaginella
c. Matonidium
D. callixylon


Portland cement does not contain:
A. \( C a_{3} A l_{2} O_{6} \)
в. \( C a_{2} \) Si \( O_{3} \)
\( \mathbf{c} \cdot C a_{2} S i O_{4} \)
D. \( C a_{3}\left(P O_{4}\right)_{2} \)


Hormones produced by the anterior pituitary that have a direct effect on the
body, rather than trigger another gland,
are :
A. TSH, ACTH, and gonadotropic hormones
B. FH, LSH and progesterone
c. GH, prolactin, and MSH
D. testosterone and estrogen


A source \( x \) of unknown frequency produces 8 beats with a source of 250 \( \mathrm{Hz} \) and 12 beats with a source of \( 270 \mathrm{Hz} \)
The frequency of source x is
A. 258 Hz
B. 242 нz
c. 262 н
D. 282 нz


If \( \boldsymbol{A}=\left[\begin{array}{cc}\mathbf{1} & \mathbf{1} \\ -\mathbf{1} & \mathbf{1}\end{array}\right] \) and \( \quad \boldsymbol{n} \boldsymbol{\epsilon} \boldsymbol{N}, \) then \( \boldsymbol{A}^{n} \) is
equal to
\( \mathbf{A} \cdot 2^{n} A \)
B \( \cdot 2^{n-1} A \)
\( c \cdot n A \)
D. None of these


Let the equation of the plane through the points
(-2,-2,2),(1,1,1),(1,-1,2) be \( k x+ \)
\( \boldsymbol{m} \boldsymbol{y}+\boldsymbol{n} \boldsymbol{z}+\boldsymbol{p} . \) Find \( \boldsymbol{k}+\boldsymbol{m}+\boldsymbol{n}+\boldsymbol{p} \)
\( A \cdot 7 \)
B.
\( c \cdot 4 \)
D. 6


Pressure which a fluid exerts on the
sides of a container, below its free
surface is known as
A. Fluid pressure
B. Iateral pressure
c. Atmospheric pressure
D. None


Electric field due to a point charge \( \boldsymbol{q} \) at
distance \( r \) has magnitude:
A \( \cdot \frac{q}{4 \pi \varepsilon_{0} r^{3}} \)
в. \( \frac{q}{4 \pi \varepsilon_{0} r^{2}} \)
c. \( \frac{q}{4 \pi \varepsilon_{0} r} \)
D. \( \frac{q^{2}}{4 \pi \varepsilon_{0} r^{2}} \)


How much will the reduction potential of a hydrogen electrode change when its solution initially at \( \mathrm{pH}=0 \) is neutralised to \( \mathrm{pH}=7 ? \)
A. Increases by \( 0.059 \mathrm{V} \)
B. Decreases by \( 0.059 \mathrm{V} \)
c. Increases by \( 0.41 V \)
D. Decreases by \( 0.41 V \)


What is the bond-order of \( C N \) ?
[Note : Write the answer after
multiplying it with \( 4] \)


In YDSE ratio of width of slit is 4: 1
then ratio of maximum to minimum
intensity
\( \mathbf{A} \cdot \mathbf{9} \)
B . 27
\( c .3 \)
D. 81


Solve, and express the answer graphically. \( \frac{4 x+4}{x-4} \leq 0 \)


Which of the following is a greenhouse gas?
A. Nitrogen
B. Oxygen
c. Ozone
D. Helium


Artificial rubies and sapphires can be made by heating alumina in?
A. An oxy-hydrogen flame
B. An oxy-acetylene flame
c. Burning methane
D. An electric furnace


Check whether the function is
homogenous or not. If yes then find the degree of the function
\( g(x)=x^{2}-8 x^{3} \)
A. Not homogenous
B. Homogenous with degree 4
c. Homogenous with degree 2
D. None of these


\( \frac{a-b}{a}+\frac{1}{2}\left(\frac{a-b}{a}\right)^{2}+\frac{1}{3}\left(\frac{a-b}{a}\right)^{3}+= \)
A \( \cdot \log _{e}\left(\frac{a}{b}\right) \)
\( ^{\mathrm{B}} \cdot \log _{e}\left(\frac{b}{a}\right) \)
\( \mathbf{c} \cdot \log _{e}(a+b) \)
\( \mathbf{D} \cdot \log _{e}(a-b) \)


Which one of the following processes
will produce hard water?
This question has multiple correct options
A. saturation of water with \( C a C O_{3} \)
B. Addition of \( N a_{2} S O_{4} \) to water.
c. saturation of water with \( M g C O_{3} \)
D. saturation of water with \( C a S O_{4} \)


Colloidal solutions of metals like
\( \boldsymbol{C u}, \boldsymbol{A} \boldsymbol{g}, \boldsymbol{A u} \) and \( \boldsymbol{P t} \) are generally
prepared by using:
A. peptization
B. bredig's arc method
c. exchange of solvent
D. oxidation method


A zener diode voltage regulator
operated in the range \( 120-180 V \)
produces a constant supply of \( 110 V \)
and \( 250 m A \) to the load. If the
maximum current is to be equally
shared between the load and zener, then
the values of series resistance \( \left(R_{S}\right) \) and
load resistance \( \left(R_{L}\right) \) are:
\( \mathbf{A} \cdot R_{L}=70 \Omega ; R_{S}=280 \Omega \)
B . \( R_{L}=440 \Omega ; R_{S}=140 \Omega \)
C \( . R_{L}=140 \Omega ; R_{S}=440 \Omega \)
\( \mathbf{D} \cdot R_{L}=280 \Omega ; R_{S}=70 \Omega \)


Which
is the most important factor for the suc
cess of animal population?
A. Natality
B. Unlimited food
c. Adaptability
D. Interspecies activity


An organism which can reproduce by two asexual reproduction methods one similar to the reproduction in yeast and the other similar to the reproduction in planaria is?
A. Spirogyra
B. Bryophyllum
c. Hydra
D. Sea anemone


The position vector of a particle is \( \vec{r}= \) \( (a \cos \omega t) \hat{i}+(a \sin \omega t) \hat{j} . \) The velocity of
the particle is
A. Parallel to position vector
B. Perpendicular to position vector
c. Directed towards the origin
D. Directed from away from the origin


Who proposed the principle of "Induced fit"?
A. Jacob
B. Fischer
c. koshland
D. Laderberg


Find :
(a) the average emf developed in half a turn from a position where the coil is perpendicular to the magnetic field,
(b) the net charge displaced in part (a).


A conductor is made of an isotropic
material (resistivity \( \rho \) ) has rectangular
cross section. The horizontal
dimensions of the conductor decreases linearly from \( 2 x \) at one end to \( x \) at the
other end and vertical dimensions
increase from y to 2y as shown in the figure. The length of conductor along the axis is equal to I and a battery is connected across the conductor, then
A \cdot resistance of conductor is equal to \( \frac{4 \rho l}{9 x y} \)
B . resistance of conductor is equal to \( \frac{9 \rho l}{4 x y} y \)
c. drift velocity of conduction electrons is maximum at the middle section
D. drift velocity of conduction electrons is minimum at the middle section


\( \frac{2^{n+4}-2 \times 2^{n}}{2 \times 2^{n+3}}+2^{-3}=? \)
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot \frac{1}{2} \)
D.


Assertion
Boiling and melting points of amides are higher than corresponding acids.
Reason
It is due to strong intermolecular hydrogen bonding in their molecules
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 value of \( (3+2) \times(6-4) \) is equal
to
\( A \cdot 7 \)
B . 2
\( c \cdot 4 \)
D. 10


Let
\( \{x\} \&[x] \) denotes the fraction and integral part of a real number \( x \) respectively, then match the column


The cubical container ABCDEFGH which
is completely filled with an ideal (nonviscous and incompressible) fluid,
moves in a gravity free space with a acceleration of \( \boldsymbol{a}=\boldsymbol{a}_{0}(\hat{\boldsymbol{i}}-\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}}) \)
where \( a_{0} \) is a positive constant. Then,
the pressure will be minimum at point:
\( A \)
B.
\( c \)
2


Half litre each of three samples of \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) labelled 10 volume, 15 volume and 20
volume are mixed and then diluted with
equal volume of water. The relative strength of resultant \( H_{2} O_{2} \) solution is:
A . 2.5
B. 5.0
c. 7.5
D. 10


To a person, going eastward in a car with a velocity of \( 25 \mathrm{Km} / \mathrm{hr} \), a train
appears to move towards north with a velocity of \( 25 \sqrt{3} \mathrm{Km} / \mathrm{hr} \). The actual
velocity of train will be:
\( A \cdot 25 \mathrm{Km} / \mathrm{hr} \)
B. 50 Km/hr
c. \( 5 \mathrm{Km} / \mathrm{hr} \)
D. \( 5 \sqrt{3} \mathrm{Km} / \mathrm{hr} \)


A man goes 100 m North then 100 m
East and then 20 m North and then \( 100 \sqrt{2} \) m South West. Find the displacement
\( \mathbf{A} \cdot 20 m \) west
B. \( 20 \mathrm{m} \) East
c. \( 20 m \) North
D. \( 20 m \) south


Find \( A \triangle B \) and draw Venn diagram
when:
\( \boldsymbol{A}=\{1,4,7,8\} \) and \( \boldsymbol{B}=\{4,8,6,9\} \)


Assertion
Two cylinders, one hollow (metal) and the other solid (wood), with the same
mass and identical dimensions are
simultaneously allowed to roll without slipping down an inclined plane from the same height. The hollow cylinder will reach the bottom of the inclined plane
first.
Reason
By the principle of conversation of
energy the total kinetic energies of both the cylinders are identical when they
reach the bottom of the incline.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is
not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


Find the perimeter and area of semicircles(Half cut rings) whose diameters are
¡) \( 2.8 \mathrm{cm} \)
ii) \( 56 \mathrm{cm} \)
iii) \( 84 \mathrm{cm} \)
iv) \( 112 \mathrm{cm} \)


A parallel plate capacitor with circular plates of radius \( R \) is being charged as shown. At the instant shown, the
displacement current in the region between the plates enclosed between \( \frac{R}{2} \) and \( R \) is given by
A \( \cdot \frac{3}{4} \)
в. \( \frac{1}{4} \)
\( c \cdot 3 i \)
D. \( \frac{4}{3} i \)


Which of the following graphs represents the correct variations for De
Broglie wavelengths of electrons:
\( A \)
B.
\( c \)
D. none


Reaction \( \boldsymbol{H}-\boldsymbol{C} \equiv \boldsymbol{C}-\boldsymbol{H}+\boldsymbol{H} \boldsymbol{O C l} \rightarrow \)
product, here product will be:
A. \( C l C H_{2}-C H O \)
в. \( C H O-C H O \)
c. \( C H-C l=C H C l \)
D. \( C H C l_{2}-C H C l_{2} \)


Four capacitor are connected, as shown
Calculate the equivalent capacitance between the points \( \boldsymbol{P} \) and \( \boldsymbol{Q} \)
\begin{tabular}{c|cc|c|c}
\hline \( \mathbf{P} \) & & & & \\
\hline & & & & \\
\( 2 \mu \mathbf{F} \) & \( 3 \mu \mathbf{F} \) & \( \mathbf{5} \mu \mathbf{F} \) & \( \mathbf{1 0 \mu F} \) & \\
\hline
\end{tabular}


Why is argon used in lamps?
A. Argon forms molecules when electricity is passed through it
B. Argon is inert and so does not react with the hot filament
C. Argon is less dense than air
D. Argon produces light when it burns


The minimum orbital angular momentum of the electron in a
hydrogen atom is
\( A \cdot h \)
B. \( h / 2 \)
\( c \cdot h / 2 \pi \)
D. \( h / 2 \lambda \)


Conversion of glucose to glucose- 6 phosphate, the first irreversible reaction of glycolysis, is catalysed by?
A. Aldolase
B. Hexokinase
c. Enolase
D. Phosphofructokinase


Let \( a_{n} \) be an A.P. for which \( a_{2}=20 \) and
\( \boldsymbol{a}_{\mathbf{1 0}}=\mathbf{4 0 .} \) Find \( \boldsymbol{a}_{\mathbf{5}} \)
A. 0
B. 10
\( c \cdot 20 \)
D. 30


Which of the following statements are
correct?
(I) Monoclinic sulphur contains \( \boldsymbol{S}_{8} \)
molecules.
(II) Sulphur forms \( S F_{6}, S F_{4}, S F_{2} \) and
\( \boldsymbol{S}_{2} \boldsymbol{F}_{2} \)
(III) Peroxo group is present in \( \boldsymbol{H}_{2} \boldsymbol{S}_{2} \boldsymbol{O}_{6} \)
A . ॥, ॥ ॥
B. ।, ॥
\( c \cdot \) ।, ॥
D. I, II, III


Among the following orbitals which orbital will experience the larger
effective nuclear charge? \( 2 s, 3 s, 4 d, 4 f, 3 d, 3 p \)


What is a potential meter explain its principal
(a)Explain how it can be used to compare the emf of two cells
(b)Explain how it can be used to determine the internal resistance of a
cells.


Copper wire test of halogens in known
as:
A. Liebig's test
B. lassaigne's test
c. Fusion test
D. Beilstein's test


Which of the following can be beaten into sheets?
A. Sulphur
B. Aluminium
c. chlorine
D. Fluorine


The perimeter of a parallelogram is
\( 60 \mathrm{cm} \) and the ratio of its adjacent sides
is \( 3: 2 . \) If the altitude corresponding to
larger side of the parallelogram is \( 5 \mathrm{cm} \) Find the area of the parallelogram and
the altitude corresponding to the smaller side.


A bullet of mass \( m \) hits a target of mass \( M \) hanging by a string and gets embedded in it. If the block rises to a
height \( h \) as a result of this collision, the
velocity of the bullet before the collision
is:
A. \( v=\sqrt{2 g h} \)
B. \( v=\sqrt{2 g h}\left(1+\frac{m}{M}\right) \)
c. \( v=\sqrt{2 g h}\left(1+\frac{M}{m}\right) \)
D. \( v=\sqrt{2 g h}\left(1-\frac{m}{M}\right) \)


In a rhombus of side \( 10 \mathrm{cm} \), one of the
diagonals is \( 12 \mathrm{cm} \) long. Find the length of the second diagonal.
\( \mathbf{A} \cdot 15 \mathrm{cm} \)
B. \( 16 \mathrm{cm} \)
\( c .17 c m \)
D. none of the above


The dispersion medium in aerosol is
gas. If true enter 1 , else enter 0 .
\( A \)


Which of the following is not a function of transpiration?
A. Excretion of minerals
B. Cooling of leaves
c. Uptake of water
D. Uptake of minerals


The near point and far point of a person
are \( 40 \mathrm{cm} \) and \( 250 \mathrm{cm} \) respectively. Determine the power of the lens he/she
should use while reading a book kept at distance \( 25 \mathrm{cm} \) from the eye.
A .2 .5 D
в. 5.0 D
\( c .1 .5 \)
D. 3.5


Draw a circle with centre 0 and radius
\( 3.5 \mathrm{cm} . \) Draw two tangents PA and PB from an external point \( P \) such that \( < \)
\( A P B=45^{0} . \) What is the value of \( < \)
\( \boldsymbol{A O B}+<\boldsymbol{A P B} \)


Abhishek has Rs.7.45. He bought toffees
for Rs.5.30. Find the balance amount left
with him.


Match the elements of table I and II.
\begin{tabular}{ll}
Table I & table II \\
a) Myopia & i) Bifocal len \\
b) Hypermetropia & ii) Cylindrical lens \\
c) Presbyopia & iii) Concave lens \\
d) Astigmation & iv) Convex lens \\
\hline
\end{tabular}
\( A \cdot a- \) iii, b - iv, c-i, d -ii
B. a - iv, b - iii, c-i, d- i i
\( c \cdot a-i, b-i i, c-i i i, d-i v \)
D. a - ii, b - iv, c-i, d- iii


Electrolysis of \( 50 \% H_{2} S O_{4} \) produces:
A. \( H_{2} S_{2} O_{8} \) at anode
B. \( H_{2} \) at anode
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{SO}_{5} \) at cathode
D. \( H_{2} O_{2} \) at anode


Solubility product expression of salt
\( M X_{4} \) which is sparingly soluble with a solubility \( s \) can be given as:
A . \( 256 s^{5} \)
B . \( 16 s^{3} \)
\( c \cdot 5 s \)
D. 25s


Solve the system of inequalities
graphically:
\( \mathbf{2} \boldsymbol{x}+\boldsymbol{y} \geq \mathbf{4}, \boldsymbol{x}+\boldsymbol{y} \leq \mathbf{3}, \mathbf{2} \boldsymbol{x}-\mathbf{3} \boldsymbol{y} \leq \mathbf{6} \)


An electric iron uses a power of \( 1320 W \) when set to higher temperature. If set to lower temperature one third of higher
temperature current is used. If iron is
connected to a potential of \( 220 V \), then power used to lower temperature is
\( \mathbf{A} \cdot 220 W \)
в. \( 440 \mathrm{W} \)
c. \( 660 W \)
D. \( 880 W \)


Name the smallest bone in the human
body.


The angles of the \( \Delta A B C \) and \( \Delta D E F \)
are given as follows; \( \boldsymbol{A}=\mathbf{9 0}^{\circ}, \quad \boldsymbol{B}=\mathbf{3 0}^{\circ}, \quad \boldsymbol{D}=\mathbf{9 0}^{\circ}, \) and \( \boldsymbol{E}= \)
\( \mathbf{3 0}^{\circ} \)
If the side \( B C \) is twice the side \( E F \)
which of the following statement is
true?
\( \mathbf{A} \cdot \sin B=2 \sin E \)
B. \( \sin E=2 \sin B \)
\( c \cdot \sin B=\sin E \)
\( \mathbf{D} \cdot \sin A=\sin B \)


What is a solenoid?


Find 'a', if \( x+1 \) is a factor of \( x^{3}+3 x^{2}- \)
\( 2 a x \)


The moment of inertia of a uniform
semi circular disc about an axis
passing through its centre of mass and perpendicular to its plane is (Mass of this disc is \( M \) and radius is \( R \) )
\( ^{\mathbf{A}} \cdot \frac{M R^{2}}{2}+M\left(\frac{4 R}{3 \pi}\right)^{2} \)
\( ^{\text {В }} \cdot \frac{M R^{2}}{2}-M\left(\frac{4 R}{3 \pi}\right)^{2} \)
\( ^{\mathrm{c}} \cdot \frac{M R^{2}}{2}-M\left(\frac{2 R}{\pi}\right)^{2} \)
\( ^{\mathrm{D}} \cdot \frac{M R^{2}}{2}+M\left(\frac{2 R}{\pi}\right)^{2} \)


When \( 0.4 \mathrm{kg} \) of brass at \( 100^{\circ} \mathrm{C} \) is
dropped into \( 1 \mathrm{kg} \) of water at \( 20^{\circ} \mathrm{C} \), the
final temperature is \( 23^{\circ} \mathrm{C} \). Find the
specific heat of brass.
\( \mathbf{A} \cdot 307 J k g^{-1}^{o} C^{-1} \)
В. 407 Jkg\( ^{-1} \) о \( C^{-1} \)
c. \( 507 J k g^{-1} \circ C^{-1} \)
D. 607 Jkg\( ^{-1} \) o \( C^{-1} \)


Suppose that spin quantum number did not exist, such that only one electron could each orbital of a many-
electron atom will have. Now the atomic
number of the noble gas atoms in this
case is:
\( A \cdot 2 \)
B. 10
\( c \cdot 9 \)
D. none


Find the value of \( 4 \cos 60^{\circ}+2 \sin 30^{\circ} \)
\( \mathbf{A} \cdot \mathbf{0} \)
B . 2
\( c .-3 \)
D. 3


n measuring the sides of a rectangle,
one side is increases by \( 30 \% \), and the other side is decreased by \( 15 \% . \) What is the change in its area as a percentage?


n figure a square \( O A B C \) is inscribed
in a quadrant \( O P B Q \) of a circle. If
\( O A=21 c m . \) find the area of the shaded
region


The ether that undergoes electrophilic
substitution reaction is :
A. \( C H_{3} O C_{2} H_{5} \)
в. \( C_{6} H_{5} O C H_{3} \)
\( \mathbf{c} \cdot C H_{3} O C H_{3} \)
D. \( C_{2} H_{5} O C_{2} H_{5} \)


An arrow shot vertically upwards loses its initial speed by \( 60 \% \) in 3 seconds. The maximum height reached by the
\( \operatorname{arrow} \) is \( \left(g=9.8 m s^{-2}\right) ? \)
A . \( 122.5 m \)
в. \( 44.1 \mathrm{m} \)
c. \( 100 m \)
D. \( 45 \mathrm{m} \)


A \( 5 k g \) ball is thrown upwards with a
speed of \( 10 \mathrm{m} / \mathrm{s} \). Then, the maximum
height attained by it is:
\( \mathbf{A} \cdot 5 m \)
в. 15 т
\( c .50 m \)
D. 25 \( m \)


"I is
smooth wall, as shown in the diagram,
making a variable angle \( \theta \) with the
horizontal floor. There is no friction with
the vertical wall.
At which angle \( \theta \) will the normal force
exerted by the floor upwards be at its
maximum?
Do not consider any motion by the plank (consider the forces exerted when the
plank is perfectly still for a given angle
\( \theta) \)
A. When \( \theta=0.00^{\circ} \) (the plank is horizontal)
B. When \( \theta=45.0^{\circ} \)
C. When \( \theta=90.0^{\circ} \) (the plank is vertical)
D. The angle \( \theta \) makes no difference
E. More information is needed


If \( \boldsymbol{A}=\{\mathbf{2}, \mathbf{3}\} \) and \( \boldsymbol{B}=\{1,2, \mathbf{3}, 4\}, \) then
which of the following is not a subset of \( \boldsymbol{A} \times \boldsymbol{B} \)
A \( \cdot\{(2,3),(2,4),(3,3),(3,4)\} \)
B - \{(2,2),(3,1),(3,4),(2,3)\}
c. \{(2,1),(3,2)\}
D \cdot \{(1,2),(2,3)\}


\( 10 \mathrm{ml} \) of a mixture of \( \boldsymbol{C H}_{4}, \boldsymbol{C}_{2} \boldsymbol{H}_{4} \) and
\( C O_{2} \) were exploded with excess of air. After explosion, there was contraction on cooling of \( 17 \mathrm{ml} \) and after treatment with KOH, there was further reduction of
\( 14 \mathrm{ml} . \) What is the composition of the mixture?
A \( \cdot C H_{4}=4.5 \mathrm{ml}, \mathrm{CO}_{2}=1.5 \mathrm{ml} \)
в. \( C H_{4}=3.6 \mathrm{ml}, \mathrm{CO}_{2}=2.5 \mathrm{ml} \)
c. \( C H_{4}=4.8 m l, C O_{2}=1.8 m l \)
D. \( C H_{4}=5.1 m l, C O_{2}=2.8 m l \)


let ABCD is trapezium such that \( \overrightarrow{A B}=3 \overrightarrow{D E}, \) E divides line segement
AB internally in the ratio 2: 1 and \( F \) is mid point of DC. if position vector of \( A, B \) and \( \mathrm{C} \) are \( \vec{a}, \vec{b} \) and \( \vec{c} \) respectively then find the vector \( \overrightarrow{\boldsymbol{F E}} \).


A block of ice at temperature \( -20^{\circ} \) is
slowly heated and converted to steam at
\( 100^{\circ} . \) Which of the following diagram is
most appropriate?
\( \mathbf{A} \)
B.
\( c \)
D.


Simplify: \( \left(8 m^{2}-9 m\right) \div 3 m \)
A \( \cdot \frac{1}{3}(8 m-9) \)
B. \( 8 m-9 \)
c. \( \frac{1}{3}(8 m-3) \)
D. \( 5 m-3 \)


In the series \( L C R \) circuit as shown in
figure, the voltmeter and ammeter
readings are:
A. \( V=100 \) volt, \( I=2 \) amp
B. \( V=100 \) volt, \( I=5 \) amp
c. \( V=1000 \) volt, \( I=2 \) amp
D. \( V=300 \) volt, \( I=1 \) amp


If \( a=107, b=13, \) using Euclid's
division algorithm find the values of \( ^{\prime} \boldsymbol{q}^{\prime} \)
and ' \( r^{\prime} \) such that \( a=b q+r \)


In moving coil galvanometer, strong horses shoe magnet of concave shaped
pole pieces is used to?
A. Increase space for rotation of coil
B. Reduce weight of galvanometer
c. Protect magnetic field which is parallel to plane of coil at any position
D. Make magnetic induction weak at the cnetre


Write the number of all possible matrices of order \( 2 \times 2 \) with each entry
1,2 or 3


The bond energy in \( k c a l m o l^{-1} \) of a \( C- \)
\( -C \) single bond is approximately:
\( A \)
B. 10
\( c \cdot 100 \)
D. 1000


Which of the following statement is not
applicable to the structure of cartilage?
A. Free surface of hyaline cartilage is covered by a fibrous cover called the perichondrium
B. Chondrocytes are metabolically more active than chondroblasts
C. The growth of cartilage always unidirectional
D. Hyaline cartilage forms the embryonic skeleton in bony vertebrates


What do we call to the process of transfer of characters from parents to
the progeny?


Glass or silica soluble in:
A \( . H C l O_{4} \)
в. \( H F \)
c. aqua-regia
D. \( H_{2} S O_{4} \)


A light is travelling from air into a medium. The velocity of light in a medium is reduced to 0.75 times the
velocity in air. Assume that angle of incidence \( i \) is very small, the deviation
of the ray is:
\( \mathbf{A} \cdot i \)
B. \( \frac{i}{3} \)
\( c \cdot \frac{i}{4} \)
D. \( \frac{3 i}{4} \)


When molten sulphur is suddenly cooled by pouring into water, it takes the form of :
A. Milk of sulphur.
B. Colloidal sulphur
C. Flower of sulphur.
D. Plastic sulphur.


X-rays are incident on a target metal atom having 30neutrons. The ratio of radii of nucleus to that of Helium
nucleus is \( 14^{1 / 3} \)
(a) Find the atomic number of target
atom.
(b) Find the frequency of \( \boldsymbol{K}_{\boldsymbol{\alpha}} \) line
emitted by this metal.
\( \boldsymbol{R}=\mathbf{1 . 1} \times \mathbf{1 0}^{\mathbf{7}} \mathbf{m}^{-1}, \boldsymbol{c}=\mathbf{3} \times \mathbf{1 0}^{\mathbf{8}} \mathbf{m} / \mathbf{s} \)
A \( .20,1.546 \times 10^{4} \mathrm{Hz} \)
В . 24. \( 1.546 \times 10^{1} 0 H z \)
\( \mathbf{c} \cdot 26,1.546 \times 10^{1} 8 H z \)
D. None of these


The relation between internal energy U, pressure \( P \) and volume \( V \) of a gas in an adiabatic process is \( U=a+b P V, \) where a and b are positive constants. What is the value of \( \gamma \) ?
A. \( \frac{a}{b} \)
B. \( \frac{b+1}{b} \)
c. \( \frac{a+1}{a} \)
D.


Starting from rest the fly wheel of a motor attains an angular velocity of \( 60 r a d / s \) in \( 5 s, \) the angular acceleration of the fly wheel is:
A \( \cdot 6 \) rad/s\( ^{2} \)
B. 12 rad / \( s^{2} \)
C \( .300 \mathrm{rad} / \mathrm{s}^{2} \)
D. 150 rad/s\( ^{2} \)


State the position of hydrogen in the
periodic table.


Which of the following is the hierarchy sequence?
A. Phylum, class, order, family
B. Phylum, division, family, class
c. Genus, species, order, family
D. Division, order, class, genus


A convex lens is given, for which the minimum distance between an object
and its rel image is \( 40 \mathrm{cm} . \) An object is
placed at a distance of \( 15 \mathrm{cm} \) from this lens. The liner magnification of adjustment will be
A \( \cdot \frac{5}{3} \)
B. - 2
\( c \cdot 2 \)
D.


Figure shows a qualitative plot of
current vs potential difference for a p-n
junction. Which of the following is true
regarding the above graph.
A. Junction offer a little resistance if we try to pass an electric current from p-side to the n-side
B. Junction offer a high resistance if we try to pass an electric current from n-side to p-side
c. The device which allows current in both the direction forward as well as backward) is called as Ideal junction or diode
D. Both A and B


Evaluate: \( \left(3 n^{2}-2 n+5 n^{4}+3\right)(-6) \)
A. \( -30 n^{4}+18 n^{2}-12 n-18 \)
B. \( -30 n^{4}-18 n^{2}-12 n-18 \)
c. \( 30 n^{4}-18 n^{2}-12 n-18 \)
D. \( 30 n^{4}+18 n^{2}-12 n-18 \)


The energy released in a modest size
atomic bomb (20 kiloton) is about \( 10^{14} \)
J. On a monsoon day in Mumbai, there was a heavy rainfall of about 100 \( \mathrm{cm} \) over an area of about \( 100 \mathrm{km}^{2} \). The
energy released in the atmosphere on that day is roughly equivalent to that released in:
(Assume average height of clouds to be \( 2000 \mathrm{m} \)
A. 20 atomic bombs
B. 100 atomic bombs
c. Atomic bomb
D. Negligible compared to an atomic bomb


Chemical reactions of the type \( \boldsymbol{X} \stackrel{\boldsymbol{k}_{1}}{\rightarrow} \)
\( \boldsymbol{Y} \stackrel{\boldsymbol{k}_{2}}{\rightarrow} \boldsymbol{Z} \) are called:
A. consecutive reactions
B. parallel reactions
c. reversible reactions
D. chain reactions


Which of the following sets is infinite?
A. \( \{x: x \text { is neither prime, nor composite }\}, x \in N \)
B. The set of all rivers in India
C. Set of concentric circles
D. \( A=\{x: x \text { is a letter of the English alphabet }\} \)


In Fig, initially the capacitor is charged
to a potential of \( 5 \mathrm{V} \) and then connected
to position across the inductor at
position 2. The maximum current
flowing in the LC circuit when the
capacitor is connected across the
inductor is :
\( \mathbf{A} \cdot 10 A \)
B. \( 20 A \)
c. \( 30 A \)
D. None of these


Write \( \frac{4}{25} \) as percentage.


The correct name of
\( \left[\boldsymbol{P t}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4} \boldsymbol{C l}_{2}\right]\left[\boldsymbol{P} \boldsymbol{t} \boldsymbol{C l}_{4}\right] \) is:
A. Tetraammine dichloro platinum (IV) tetrachloro platinate(II)
B. Dicholoro tetra mmine platinum (IV) tetrachloro platinate (II)
C . Tetrachloro platinum
(II) tetraammine platinate (IV)
D. Tetrachloro platinum (II) dichloro tetraamine platinate \( (1 V) \)


Let \( N \) denote the set of all natural
numbers and R a relation on \( N \times N \)
Which of the following is an equivalence
relation?
\( \mathbf{A} \cdot(a, b) R(c, d) \) if \( a d(b+c)=b c(a+d) \)
B. \( (a, b) R(c, d) \) if \( a+d=b+c \)
\( \mathbf{c} \cdot(a, b) R(c, d) \) if \( a d=b c \)
D. all the given


In the figure, \( \Delta P Q R \) is a right angled at
\( \mathrm{Q}, \bar{M} L \| \bar{R} Q \) and \( \angle L M R=130^{\circ} . \) Find
\( \angle L P M \) and \( \angle P M L \)


A group of interbreeding organisms is
A. Genus
B. Family
c. Order
D. species


\( A \) tank of size \( 10 m \times 10 m \times 10 m \) is ful
of water and built on the ground. If \( g= \)
\( 10 m s^{-2}, \) the potential energy of the
water in the tank is:
A \( .5 \times 10^{7} \) J
В. \( 1 \times 10^{8} \) у
\( c \cdot 10^{4} \)
D. \( 10^{5} \) J


How many terms of the AP \( 20,19 \frac{1}{3}, 18 \frac{2}{3}, \ldots \) must be taken to make
the sum \( 300 ? \) Explain the double
answer


In a vessel, as shown in fig, point \( P \) is
just visible when no liquid is filled in
vessel through a telescope in the air.
When liquid is filled in the vessel
completely, point \( Q \) is visible without
moving the vessel or telescope. Find the
refractive index of the liquid.
A \( \cdot \frac{\sqrt{14}}{3} \)
B. \( \frac{\sqrt{85}}{5} \)
\( c \cdot \sqrt{2} \)
\( D \)


Assertion
All pteridophytes have originated from
Rhynia.
Reason
It is a living fossil fern.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct.


is the anhydride of
\( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{3} \)


Simplify : 6324 \( \times 124 \)


The value of the integral \( \int_{0}^{\pi / 2} \frac{1}{1+(\tan x)^{101}} d x \) is equal to
A . 1
в.
c.
D.


A unit radian is approximately equal to
A \( \cdot 57^{\circ} 17^{\prime} 43^{\prime} \)
,
B . \( 57^{\circ} 17^{\prime} 45 " \)
c. \( 57^{\circ} \) 17' \( 47 " \)
D. \( 57^{\circ} 17^{\prime} 49^{\prime} \)


Assertion
Internal energy change in a cyclic
process is zero.
Reason
Internal energy is a state function.
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


\( \boldsymbol{f}(\boldsymbol{x})=\frac{\boldsymbol{a}+\boldsymbol{b}^{\frac{1}{x}}}{\boldsymbol{c}+\boldsymbol{d}^{\frac{1}{x}}}, \boldsymbol{b}>1, \boldsymbol{d}>1, \boldsymbol{c} \neq \mathbf{0} \)
\( \boldsymbol{f}(\mathbf{0})=\mathbf{1} \) is left continuous at \( \boldsymbol{x}=\mathbf{0} \)
then
\( \mathbf{A} \cdot a=0 \)
B . \( a=2 c \)
c. \( a=c \)
D. \( a \neq c \)


A molecule of a substance has a
permanent electric dipole moment of magnitude \( 10^{-30} \mathrm{cm} . \) A mole of this substance is polarised by applying a strong electrostatic field of magnitude \( 10^{7} V m^{-1} . \) The direction of field is
changed by an angle \( 60^{\circ} . \) The heat released by the substance in aligning its dipole along the new direction of the field is
A. -6.5
в. \( -3 . \)
\( c .3 J \)
D. 65


"Both Li and Mg forms Basic oxides."." Answer whether the above statement is
true or false.
If true enter 1 , else enter 0 .


Identify the correct statement(s) in
relation to \( C_{4} \) photosynthesis.
A. Kranz anatomy is an essential feature for \( C_{4} \) plants
B. \( C_{4} \) plants have higher water use efficiency than \( C_{3} \) plants
C. Photorespiration can be minimized when \( C_{4} \) pathway is in operation
D. All of the above


Two identical glass rods \( S_{1} \) and \( S_{2} \)
(refractive index \( =1.5 \) ) have one convex
end of radius of curvature \( 10 \mathrm{cm} . \) They are placed with the curved surfaces at a distance d as shown in the figure, with their axes (shown by the dashed line) aligned. When a point source of light \( P \)
is placed inside rod \( S_{1} \) on its axis at a
distance of \( 50 \mathrm{cm} \) from the curved face,
the light rays emanating from it are
found to be parallel to the axis inside \( S_{2} \)
The distance \( d \) is :
\( A \cdot 60 \mathrm{cm} \)
B. 70 cm
\( c .80 \mathrm{cm} \)
D. \( 90 \mathrm{cm} \)


Q Type your question-
gives acetone as one of the products.
The structure of the compound is
\( A \)
\( B \)
\( c \)
\( D \)


Which of the following are defects of
vision?
This question has multiple correct options
A. Myopia
B. Hypermetropia
c. colour blindness
D. Night blindness


Which of the following statements is wrong?
A. single N-N bond is stronger than the single P-P bond
B. \( P H_{3} \) can act as a ligand in the formation of coordination compound with transition elements
C. \( N O_{2} \) is paramagnetic in nature
D. covalency of nitrogen in \( N_{2} O_{5} \) is four


\( \int x e^{2 x}(1+x) d x \) equal to
A \( \cdot \frac{x e^{x}}{2}+c \)
B \( \cdot \frac{\left(e^{x}\right)^{2}}{2} r \)
c. \( \frac{(1+x)^{2}}{2}+c \)
D. \( \frac{\left(x e^{x}\right)^{2}}{2} \)


Find the surface area of sphere of
diameter \( 14 \mathrm{cm} \)
\( A \cdot 616 c m^{2} \)
В. \( 661 \mathrm{cm}^{2} \)
\( c \cdot 166 c m^{2} \)
D. None of these


\( \cos ^{-1}(44 / 125) \) is equal to
A \( .2 \alpha \)
в. \( 3 \alpha \)
c. \( \pi-3 \alpha \)
D. \( \pi-2 \alpha \)


Consider the following statements in the context of formulation of any law of Physics
l.explain the existing physical facts Il.no need of experimental verification III.predict future results Then, any formulated law of physics, should be true with respect to
A . I and II
B. Il and II
c. I and III
D. I, II and III


Find the transpose of matrix \( \left[\begin{array}{ll}2 & 5 \\ 1 & 3\end{array}\right] \)


The energy of a hydrogen atom in the ground state is \( 13.6 \mathrm{eV} \). The energy of a
\( \mathrm{He}^{+} \) ion in the first excited state will be:
A . -6.8 ev
B . -13.6 ev
c. - 27.2 ev
D. - 54.4 ev


In the figure \( A B C \) is the cross section of
a right angled prism and BCDE is the
cross section of a glass slab. The value
of \( \theta \) so that light incident normally on
the face \( A B \) does not cross the face \( B C \)
is \( \left(\text { given } \sin ^{-1}(3 / 5)=37^{\circ}\right) \)
A \( \cdot \theta \leq 37^{\circ} \)
В \( \cdot \theta>37^{\circ} \)
\( \mathbf{c} \cdot \theta \leq 53^{\circ} \)
D. \( \theta<53^{\circ} \)


Which of the following pairs contains isoelectronic species?
\( \mathbf{A} \cdot B e \) and \( L i^{+} \)
B . \( P^{+} \) and \( S^{-} \)
c. \( N^{2-} \) and \( N e \)
\( D \cdot O^{2-} \) and \( N a^{+} \)


A \( p \) -type semiconductor has acceptor levels 57 me \( V \) above the valance band.
The maximum wavelength of light required to create a hole is (Planck's
constant \( \left.h=6.6 \times 10^{-34} J-s\right) \)
A \( .57 \AA \)
В. \( 57 \times 10^{-3} \dot{A} \)
c. 217100 月
D . \( 11.61 \times 10^{-33} \dot{A} \)


Consider the following reaction
sequence,
\( \boldsymbol{C H}_{3} \boldsymbol{C H}(\boldsymbol{O H}) \boldsymbol{C H}_{3} \frac{\operatorname{Conc.H}_{2} \boldsymbol{S O}_{4}}{\boldsymbol{H e a t}} \)
\( \boldsymbol{X} \frac{d i l \cdot \boldsymbol{H}_{2} \boldsymbol{S O}_{4}}{\boldsymbol{H}_{2} \boldsymbol{O}} \boldsymbol{Y} \)
\( x \) and \( Y \) in the reaction respectively are :
A \( \cdot C H_{3} C H=C H_{2}, C H_{3} C H(O H) C H_{3} \)
в. \( C H_{3} C H=C H C H_{3}, C H_{3} C H_{2} C H_{2} O H \)
c. \( C H_{3} C H_{2} C H=C H_{2}, C H_{3} C H_{2} C H_{2} O H \)
D. \( C H_{3} C H_{2} C H_{2} C H_{3}, C H_{3} C H(O H) C H_{2} C H_{3} \)


An organic compound
(A) (molecular
formula \( C_{8} H_{16} O_{2} \) ) was hydrolysed with dilute sulphuric acid to give a carboxylic acid (B) and an alcohol (C). Oxidationof
(C) with chromic acid
produced (B).
(C) on dehydration gives but-1-ene.Write equations for the reactions involved.


A beam has intensity \( 2.5 \times 10^{14} W m^{-2} \)
The ratio of electric and magnetic fields in the beam is
A . \( 3.44 T \)
в. \( 3.14 T \)
c. \( 1.004 T \)
D. 1.447


Which of the following statement is
correct about alkyl halides?
A. They are associated with each other by H-bonds.
B. They dissolve in water quickly.
C. They dissolve easily in organic solvents.
D. They do not contain any polar bonds in their molecules.


f \( x=-3, \) find the value of:
\( 2 x-3 \)


In Krebs cycle the FAD participates as electron acceptor during the conversion of
A. Succinyl CoA to succinic acid
B . \( \alpha \) - ketoglutarate to succinyl COA
c. Fumaric acid to malic acid
D. Succinic acid to fumaric acid


Match the column:


An element forms two oxides \( \boldsymbol{X} \boldsymbol{O}, \boldsymbol{X} \boldsymbol{O}_{2} \)
The oxide \( X O \) is neutral, insoluble in water and burns with blue flame. It is
poisonous. \( X O_{2} \) is acidic in nature.
Soluble in water and extinguishes fire.
(i) Identify the \( x \)
(ii) write reaction of \( X O_{2} \) with water.
(iii) What happens when \( X O_{2} \) is passed in lime water


The radiant energy from the sun, incident normally at the surface of
earth, is \( 20 k c a l / m^{2}- \) min. What would have been the radiant energy incident normally on the earth, if the sun had
a temperature twice of the present one?
A \( .40 \mathrm{kcal} /\left(\mathrm{m}^{2}-\mathrm{min}\right) \)
B. 80 kcal/(m^-min)
c. \( 160 \mathrm{kcal} /\left(\mathrm{m}^{2}-\mathrm{min}\right) \)
D. 320 kcal/(m^-min)


How many \( ^{137} \) Cs need to be present in
each \( k g \) of body tissue if an equivalent does for one week is 3.55 Sv?
A \( \cdot 1.25 \times 10^{-9} \)
B . \( 1.25 \times 10^{11} \)
C. \( 1.25 \times 10^{13} \)
D. none


\( 20 \% \) of dolls produced in a factory were defective, \( 25 \% \) of the remaining were damaged. If 4800 dolls were left over
what was the original number of dolls?


Write the polynomial in standard form and also write down their degree. \( \left(x^{2}-\frac{2}{3}\right)\left(x^{2}+\frac{4}{3}\right) \)


Largest muscle is
A. Gluteus maximus
B. Sartorius
C . Stapedius
D. Biceps muscle


The value of \( \tan \alpha+2 \tan (2 \alpha)+ \)
\( 4 \tan (4 \alpha)+\ldots+2^{n-1} \tan \left(2^{n-1} \alpha\right)+ \)
\( 2^{n} \cot \left(2^{n} \alpha\right) \) is
A \( \cdot \cot \left(2^{n} \alpha\right) \)
B \( \cdot 2^{n} \tan \left(2^{n} \alpha\right) \)
\( c \)
D. \( \cot \alpha \)


What is electromagnetic induction?


\( C a C_{2} \stackrel{H_{2} O}{N H_{4} C l} \frac{C u_{2} C l_{2}}{(2) M g / \text { ether }} B \frac{(1) 1 \text { eqv. } H C l}{(3) C O_{2} / H_{2} O / H^{+}} C \)
In above reaction product \( (C) \) is?
\( \mathbf{A} \cdot C H_{2}=C H-C O O H \)
\( \mathbf{B} \cdot H C \equiv C-C O O H \)
c. \( H O O C-C \equiv C-C O O H \)
\( \mathbf{D} \cdot C H_{2}=C H-\underset{\cot }{C}=C H_{2} \)


A beam of light propagates through a
medium 1 and falls onto another
medium \( 2, \) at an angle \( \alpha_{1} \) as shown in
Fig. After that, it propagates in medium
2 at an angle \( \alpha_{2} \) as shown. The light's
wavelength in medium 1 is \( \lambda_{1} . \) What is
the wavelength of light in medium 2?
\( A \)
в.
\( c \cdot \frac{\cos \alpha_{1}}{\cos \alpha_{2}} \lambda_{1} \)
\( D \)