Select correct statement regarding waves on a string [all symbols have their usual meanings]
This question has multiple correct options
A. Power transfer through any point in standing wave is \( \mu v_{p}^{2} \)
B. Energy is not conserved between consecutive node and antinode.
C. Two travelling waves of same frequency which are moving in opposite direction must form standing wave
D. Speed of particle is maximum where slope is maximum


Which of the following compounds are formed by the reaction of ammonia with
acids?
This question has multiple correct options
A. Calcium ammonium nitrate
B. Ammonium chloride
c. Ammonium phosphate
D. Ammonium sulphate


\( \pi \) -Bonding occurs in each of the
following except:
A. \( C O_{2} \)
в. \( C_{2} H_{4} \)
c. \( C N^{-} \)
D. \( C H_{4} \)


If \( \cos ^{-1}\left(\frac{x^{2}-y^{2}}{x^{2}+y^{2}}\right)=k \) (a constant)
then \( \frac{d y}{d x}= \)
A. \( \frac{y}{x} \)
в. \( \frac{x}{y} \)
c. \( \frac{x^{2}}{y^{2}} \)
D. \( \frac{y^{2}}{x^{2}} \)


Starch digestion begins in
A. Small intestine
B. Large intestine
c. Stomach
D. Esophagus
E. Mouth


Assertion(A): \( f(x)= \) \( \left\{\begin{array}{ll}x^{2} \sin \left(\frac{1}{x}\right), & x \neq 0 \\ 0, & x=0\end{array} \) is continuous at \right.
\( \boldsymbol{x}=\mathbf{0} \)
Reason(R): Both \( h(x)=x^{2}, g(x)= \)
\( \left\{\begin{array}{ll}\sin \left(\frac{1}{x}\right), & x \neq 0 \\ 0, & x=0\end{array} \) are continuous at \right.
\( \boldsymbol{x}=\mathbf{0} \)
A. Both A and R are true and R is the correct explanation of
B. Both A and R are true and R is not the correct explanation of
c. \( A \) is true but \( R \) is false
D. R is true but A is false


If \( f(x)=\left\{\begin{array}{ll}\frac{1-\cos x}{x^{2}}, & x<0 \\ \frac{1}{2} e^{x}, \quad x \geq 0\end{array} \) then at \right.
\( \boldsymbol{x}=\mathbf{0}, \boldsymbol{f} \) is
A. continuous
B. not continuous
\( c . \) differentiable
D. none of these


Vinegar is present in acetic acid. Curd contains \( _{\text {the acid. }} \)
A . lactic acid
B. tartaric acid
c. citric acid
D. none of these


How can you synthesize Ethanol from
Ethene?


In Mac-Arthur Forrest method, silver is extracted from solution of
\( N a\left[A g(C N)_{2}\right] \) by the use of
A . \( F e \)
в. \( M g \)
c. \( C u \)
D. \( Z n \)


Forces measuring 5,3 and 1 unit act in the directions (6,2,3),(3,-2,6) and \( (5,-1,1) . \) Find the resultant force.


Find the median of the following:
2,3,5,7,9


A sinusoidal voltage of peak value \( 283 V \) and angular frequency \( 320 / s \) is applied to a series LCR circuit. Given
that \( \boldsymbol{R}=\mathbf{5} \boldsymbol{\Omega}, \boldsymbol{L}=\mathbf{2 5} \boldsymbol{m} \boldsymbol{H} \) and \( \boldsymbol{C}= \)
1000 \( \mu F \). The total impedance, and
phase difference between the voltage
across the source and the current will
respectively be:
\( \mathbf{A} \cdot 7 \Omega \) and \( 45^{\circ} \)
B. \( 10 \Omega \) and \( \tan ^{-1}\left(\frac{5}{3}\right) \)
c. \( 10 \Omega \) and \( \tan ^{-1}\left(\frac{8}{3}\right) \)
D. \( 7 \Omega \) and \( \tan ^{-1}\left(\frac{5}{3}\right) \)


A box contains 5 red marbles, 8 white
marbles and 4 green marbles. One marble is taken out of the box at
random. What is the probability that the
marble taken out will be
(i) red,
(ii) white,
(iii) not green?


n the circuit shown \( E, F, G \) and \( H \) are cells of e.m.f. \( 2 V, 1 V, 3 V \) and \( 1 V \) respectively and their resistances are \( 2 \Omega, 1 \Omega, 3 \Omega \) and \( 1 \Omega \) respectively. Then
choose the correct alternative
A \( \cdot V_{D}-V_{B}=-2 / 13 \mathrm{V} \)
B . \( V_{D}-V_{B}=2 / 13 \mathrm{V} \)
c. \( V_{G}=21 / 13 \) V


If circular race track is banked at angle
\( \theta(\theta>\text { angle of repose }), \) radius of track
is \( r \) and \( \mu \) is coefficient of friction
between car and road. Calculate
minimum speed on car on inclined plane to avoid slipping?
\( A \)
\[
v=\left[r g\left(\frac{\tan \theta-\mu}{1+\mu \tan \theta}\right)\right]
\]
B.
\[
v=\left[r g\left(\frac{\tan \theta+\mu}{1-\mu \tan \theta}\right)\right]
\]
\( c \)
\[
v=\left[r g\left(\frac{\tan \theta-\mu}{1+\mu \tan \theta}\right)\right]^{1 / 2}
\]
D.
\[
v=\left[r g\left(\frac{\tan \theta+\mu}{1+\mu \tan \theta}\right)\right]^{1 / 2}
\]


\( \operatorname{Given} \boldsymbol{A}(\mathbf{1},-\mathbf{1}, \mathbf{0}) ; \boldsymbol{B}(\mathbf{3}, \mathbf{1}, \mathbf{2}) ; \boldsymbol{C}(\mathbf{2},-\mathbf{2}, \mathbf{4}) \)
and \( D(-1,1,-1) \) which of the following
points neither lie on \( A B \) nor on \( C D \)
A \( .(2,2,4) \)
В. (2,-2,4)
c. (2,0,1)
D. (0,-2,-1)


Among \( K O_{2}, A l O_{2}^{-}, B a O_{2} \) and \( N O_{2}^{+} \)
unpaired electron is present in :
A. \( N O_{2}^{+} \) and \( B a O_{2} \)
B. \( K O_{2} \) and \( A l O_{2}^{-} \)
c. \( K O_{2} \) only
D. \( B a O_{2} \) only


The potential of a hydrogen electrode at \( \boldsymbol{p} \boldsymbol{H}=\mathbf{1} \) is
A. 0.059 volt
B. 0 volt
c. -0.059 volt
D. 0.59 volt


Find out incorrect statement:-
A. Brain box is formed of 8 bones
B. In skull the frontal bone is single
C. A single U-shaped bone present at the base of the buccal carity is quadrate
D. Hyoid bone is the part of skull


State True or False.
Bleaching action of \( S O_{2} \) is due to
reduction and it is temporary.
A. True
B. False


Solve \( \sin ^{-1}\left(\cos \frac{2 \pi}{3}\right) \)


Metals can resist strain without
breaking because of their high:
A. tensile strength
B. stress
c. strain
D. all of the above


\( y=2 x \)
\( y= \)


\( 40 \mathrm{mL} \) of \( 0.1 \mathrm{M} \) ammonia solution is
mixed with \( 20 \mathrm{mL} \) of \( 0.1 \mathrm{M} \) HCl
What is the \( p H \) of the mixture?
A . 5.74
B. 9.26
c. 4.56
D. 7.06


Assertion
Ferrous ion is a divalent ion.
Reason
Iron atom loses two electrons to carry
two positive charges.
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 wavelengths involved in the
spectrum of deuterium \( \left(_{1}^{2} D\right) \) are
slightly different from the hydrogen
spectrum, because:
A. Sizes of the two nuclei are different
B. Nuclear forces are different in the two cases
c. Masses of the two nuclei are different
D. Attraction between the electron and the nucleus in different in the two cases


What is used in manufacturing of steel?
A. coal
B. Coal tar
c. coke
D. Glass


A machine gun fires 10 bullets/s, each
of mass \( 10 g \), the speed of each bullet is
\( 20 c m / s, \) then force of recoil is
A. 200 dyne
B. 2000 dyne
c. 20 dyne
D. None


What is the focal length of a double convex lens \( (\mu=3 / 2) \) if radius of
curvature of its sides is \( 15 \mathrm{cm} \) ?
\( \mathbf{A} \cdot 30 \mathrm{cm} \)
в. \( 7.5 \mathrm{cm} \)
\( \mathbf{c} \cdot 15 c m \)
D. \( 45 \mathrm{cm} \)


Assertion: Fluorine exists only in -1
oxidation state.
Reason: Fluorine has \( 2 s^{2} 2 p^{5} \)
configuration
A. If both assertion and reason are true and the reason is a correct explanation of the assertion
B. If both assertion and reason are true but reason is not a correct explanation of the assertion
C. If the assertion is true but reason is false
D. If both the assertion and reason are false
E. If the assertion is false but the reason is true


Find the values of \( x \) and \( y \) in the
following triangle.


If enthalpies of formation for
\( C_{2} H_{4}(g), C O_{2}(g) \) and \( H_{2} O(I) \) at \( 25^{0} C \)
and 1 atm pressure are \( 52 ;-394 \) and \( -286 k J / m o l \) respectively, then
enthalpy of combustion of \( C_{2} H_{4}(g) \) will
be?


The temperature of a metal coin is
increased ny \( 100^{\circ} \mathrm{C} \) and its diameter by \( 0.15 \% \). Its area increases by nearly
A . 0.15\%
B . 0.60\%
c. \( 0.30 \% \)
D. 0.0225\%


In an adiabatic process.
A. Temperature remains constant
B. Pressure remains constant
c. Volume remains constant
D. There is no transfer of heat


If \( z=(i)^{(i)}^{(i)} \) where \( i=\sqrt{-1}, \) then \( |z| \)
is equal to
A . 1
B . \( e^{-\pi / 2} \)
\( \mathbf{c} \cdot e^{-\pi} \)
D. none of these


A spiral spring is stretched to \( 20.5 \mathrm{cm} \) gradation on a metre scale when loaded with a 100 g load and to the \( 23.3 \mathrm{cm} \) gradation by 200 g load. The spring is used to support a lump of metal in air and the reading now is \( 24.0 \mathrm{cm} . \) The mass of metal lump is :
A. 250gm
в. 225 gm
c. \( 145 \mathrm{gm} \)
D. 750 gm


A telephone cable at a place has four long straight horizontal wires carrying a current of \( 1.0 \mathrm{A} \) in the same direction
east to west. The earth's magnetic field at the place is \( 0.39 \mathrm{G}, \) and the angle of
dip is \( 35^{\circ} \).The magnetic declination is
nearly zero. What are the resultant magnetic fields at points \( 4.0 \mathrm{cm} \) below the cable?


Differentiate the following functions
with respect to \( \boldsymbol{x} \)
\( \boldsymbol{x} \sin 2 \boldsymbol{x}+\mathbf{5}^{\boldsymbol{x}}+\boldsymbol{k}^{\boldsymbol{k}}+\left(\tan ^{2} \boldsymbol{x}\right)^{2} \)


Find odd man out:
Give reason for your answer.


Two waves having equation \( x_{1}= \)
\( \boldsymbol{a} \sin \left(\omega t+\mathbf{\Phi}_{1}\right) \) and \( \boldsymbol{x}_{2}=\boldsymbol{a} \sin (\boldsymbol{\omega} \boldsymbol{t}+ \)
\( \mathbf{\Phi}_{2} \) ) If in the resultant wave the
frequency and amplitude remains equals to amplitude of superimposing waves. Then phase difference between
them :
A. \( \frac{\pi}{6} \)
в. \( \frac{2 \pi}{3} \)
c. \( \frac{\pi}{4} \)
D. \( \frac{\pi}{9} \)


Blood enters the heart because muscles
of the
A. Atrium contracts
B. Atrium relaxes
c. ventricle relaxes
D. ventricle contracts


Underwater divers wear , w. to move
easily in water.
A. A head torch
B. Oxygen cylinder
c. Flippers
D. A watch


A boy contains 100 bolts and 50 nuts. It
is given that \( 50 \% \) bolts and \( 50 \% \) nuts
are rusted. Two objects are selected from the box at random. Find the
probability that both are bolts or both are rusted.


The inventor of the chess board
suggested a reward of one gram of wheat for the first square, 2 grains for the second, 4 grains for the third and so on, doubling the number of the grains subsequent squares. How many grins would to be given to inventor? ( There are 64 squares in the chess board)


Write any two difference between aerobic and anaerobic muscles.


If angles \( P, Q, R \) and \( S \) of the quadrilateral PQRS, taken in order, are in the ratio 3: 7: 6: 4 then PQRS is a
A. rhombus
B. parallelogram
c. trapezium
D. kite


If two triangles are symmetric, then
they are
A . Equilateral
B. congruent
c. Equal
D. Isosceles


If two bodies do not interact
A. still a force can be applied
B. no force can be applied
C . contact force can be applied
D. non-contact force can be applied


Random movement of particles was discovered by:
A. Robert Brown
B. E. Goldstein
c. James chadwick
D. Wilheln Weins


The height at which the value of acceleration due to gravity becomes \( 50 \% \) of that at the surface of the earth.
(radius of the earth \( =\mathbf{6 4 0 0 k m} \) ) is
A . 2650
в. 2430
c. 2250
D. 2350


If \( x=2 R \), then the value of \( \mu \) is
4.1 .5
B.
\( c \)
D. none of thes


Prove that the sum of an odd number of
terms in A.P. is equal to the middle term multiplied by the number of terms.


Which of the following is an animal
fiber?
A . silk
B. Avian
c. Alpaca
D. All of the above


The IUPAC name of the compound is:
A. 3,3 -dimethyl-1-hydroxy cyclohexane
B. 1,1 -dimethyl-3-hydroxy cyclohexane
C. 3,3-dimethyl-1-cyclohexanol
D. none of the above


The activated complex is:
A. the point of equilibrium
B. the triple point
C. the freezing point
D. the point where reactants first form products
E . the boiling point


Anabolic reactions are always
endergonic reactions. Justify this statement with an example.


The number of isomers of the
compound with molecular formula
\( \boldsymbol{C}_{2} \boldsymbol{H}_{3} \boldsymbol{C l}_{3} \) is:
A . two
B. three
c. four
D. five


Equation of current flowing towards left in the inductor


In which compound synergic effect is present?
\( \mathbf{A} \cdot\left[N i(C O)_{4}\right] \)
B・ \( \left[N i C l_{4}\right]^{2-} \)
c. \( \left[C u C l_{4}\right]^{2-} \)
D. \( \left[M n\left(H_{2} O\right)_{6}\right]^{2+} \)


Find the \( 7^{t h} \) term of the G.P. \( 2,-6,18, \dots \)
A. 1458
B. 2458 8
\( c .3458 \)
D. 4458


The total possible coordination isomers
for the following compounds respectively are:
\( \left.\left[\boldsymbol{C o}(\boldsymbol{e n})_{3}\right][\boldsymbol{C r}) \boldsymbol{C}_{2} \boldsymbol{O}_{4}\right)_{3} \)
\( \left[\boldsymbol{C u}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4}\right]\left[\boldsymbol{C u} \boldsymbol{C l}_{4}\right] \)
\( \left[\boldsymbol{N} \boldsymbol{i}(\boldsymbol{e n})_{3}\right]\left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{O}_{2}\right)_{6}\right] \)
\( A \cdot 4,4,4 \)
B. 2, 2, 2
\( c \cdot 2,2,4 \)
D. 4, 2, 3


The number of open chain isomers
possible for \( \boldsymbol{C}_{\boldsymbol{4}} \boldsymbol{H}_{\boldsymbol{6}} \)
\( A \cdot 6 \)
B. 5
\( c \cdot 4 \)
D. 2


Air expands from 5 litres to 10 litres at
2 atom pressure. External workdone is
A . \( 10 J \)
в. \( 1000 J \)
c. \( 3000 J \)
D. 300J


Evaluate the following limits. \( \lim _{x \rightarrow 0} \frac{\sqrt{a+x}-\sqrt{a}}{x \sqrt{a^{2}+a x}} \)
A \( \cdot \frac{1}{2 \sqrt{a}} \)
B. \( \frac{1}{2 a \sqrt{a}} \)
c. \( \frac{1}{2 a} \)
D. None of these


Which of the following is the wrong statement?
A. \( O N F \) and \( O N O^{\circ} \) are isoelectronic
B. \( C_{2} \) molecules is expected to exhibit diamagnetic behavior if \( s-p \) mixing is not operative
c. Ozone is diamagnetic gas


For any two real numbers \( \theta \phi, \) we define \( \theta R \phi \) if and only if \( \sec ^{2} \theta-\tan ^{2} \phi=1 \)
The relation \( \boldsymbol{R} \) is
A. Reflexive but not transitive
B. Symmetric but not reflexive
c. Both reflexive and symmetric but not transitive
D. An equivalence relation


In which of the following case/s, it is legal to terminate a pregnancy after 12 weeks of maternal age?
A. The continuation of the pregnancy would involve a risk to the life of the pregnant woman
B. There is a substantial risk that if the child was born he/she would suffer from such physical or mental abnormalities as to be seriously handicapped
c. To avoid possible pregnancy due to rape
D. All of the above


Find the derivative of the following functions from first principle \( \frac{x+1}{x-1} \)


If the first term of a geometric series is
\( 2, \) and its third term is \( 8, \) how many
digits are there in the \( 40^{t h} \) term of the
series, if the common ratio of the sequence is positive?
A . 10
B. 11
c. 12
D. 13
E. 14


Which of the following ore is best concentrated by froth flotation method? This question has multiple correct options
A. Galena
B. Cassiterite
c. Magnetite
D. zinc blende


Find the general solution of the differential equation \( \frac{d y}{d x}+y . c o t x= \)
\( 2 x+x^{2} \cdot \cot x \)


When the sound waves reach the
it starts vibrating:
A. pinna
B. stir rup
C . tympanic membrane
D. none of these


An ammeter has a resistance of \( G \)
ohms and range of \( I \) amperes. The value of resistance required in parallel to
convert it into an ammeter of range \( \boldsymbol{n} \boldsymbol{I} \)
is
A \( . n G \)
в. \( (n-1) G \)
c. \( G /(n-1) \)
D. \( G / n \)


The conditional probability that \( X \geq 6 \)
given the \( X>3 \) equals
A \( \cdot \frac{125}{216} \)
в. \( \frac{25}{216} \)
c. \( \frac{5}{36} \)
D. \( \frac{25}{36} \)


The method used to remove temporary
hardness of water is :
A. Calgon's method
B. Clark's method
c. lon-exchange method
D. synthetic resins method


The value of \( \int(x-1) e^{-x} d x \) is equal to
This question has multiple correct options
\( \mathbf{A} \cdot-x e^{x}+C \)
B . \( x e^{x}+C \)
c. \( -x e^{-x}+C \)
D. \( x e^{-x}+C \)


Explain the following with suitable
example:
(a) Rosenmund reduction
(b) Gatterman-Koch reaction


Describe the process of synthesis of fully functional \( m R N A \) in a eukaryotic
cell.


The existence of the states of matter is
due to
A. necessity of defining the three states
B. variation in the characteristics particles of matter
C. All of the above
D. None of the above


In a cell that utilizes the reaction \( Z n(s) \)
\( +2 H^{+}(a q) \rightarrow Z n^{2+}(a q)+H_{2}(g) \)
addition of \( \mathbf{H}_{2} \mathbf{S} \mathbf{O}_{4} \) to cathode
compartment, will:
A. lower the E and shift equilibrium to the left
B. lower the E and shift the equilibrium to the right
c. increase the \( \mathrm{E} \) and shift the equilibrium to the right
D. increase the E and shift the equilibrium to the left


Construct a quadrilateral \( A B C D \) in
which \( \boldsymbol{A B}=\mathbf{6} \mathrm{cm}, \boldsymbol{B C}=\mathbf{8} \mathrm{cm}, \boldsymbol{C D}= \)
\( \mathbf{5} \mathrm{cm}, \boldsymbol{A} \boldsymbol{D}=\mathbf{4} \mathrm{cm} \) and diagonal \( \boldsymbol{A} \boldsymbol{C}= \)
\( 4.5 \mathrm{cm} \)


lce at \( 0^{\circ} C \) is added to \( 500 g \) of water at
\( 100^{\circ} \mathrm{C} \) degree. Ice is continually added to the system until it has all melted and no more ice will melt. What will be the
temperature of the water in the system?
A . 50
B . 25
c. 4.184
D.
E .


Give reasons for the following:
It is dangerous to get down from a moving bus even if the bus is moving slowly.


Assertion
When an electric current is passed through an aqueous solution of sodium chloride, sodium ions move towards cathode and chloride ions move towards
anode.
Reason
Cathode is a negatively charged electrode and therefore attracts \( \boldsymbol{N} \boldsymbol{A}+ \)
ions. Anode is a positively charged
electrode and therefore attracts \( C l- \)
ions
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


Stability of the species \( L i_{2}, L i_{2}^{-} \) and
\( L i_{2}^{+} \) increases in the order of :
A \( \cdot L i_{2}<L i_{2}^{+}<L i_{2} \)
B . \( L i_{2}^{-}<L i_{2}<L i_{2}^{+} \)
C \( \cdot L i_{2}<L i_{2}^{-}<L i_{2}^{+} \)
D. \( L i_{2}^{-}<L i_{2}^{+}<L i_{2} \)


lonisation energies(IE) and electron affinities (EA) of F and Cl are given below: Compound formed between F and Cl is predominantly:
Element \( \quad \) IE \( \quad \) EA
\( F \)
\( 17.4 \mathrm{eV} \quad 3.45 \mathrm{eV} \)
\( \mathrm{c} \)
\( 13.0 \mathrm{eV} \quad 3.61 \mathrm{eV} \)
A \( \cdot F^{+} C l^{-} \)
B. \( C l^{+} F^{-} \)
c. F-cl
D.


The complex number \( \frac{1+2 i}{1-i} \) lies in the
quadrant :
\( A \)
B. I
c. ॥॥
D. IV


The above laboratory setup can be used to prepare which of the following?
I. \( C O_{2}(g) \)
Il. \( \boldsymbol{H}_{2}(\boldsymbol{g}) \)
III. \( O_{2}(g) \)
A . I only
B. III only
c. I and III only
D. II and III only
E . I, II, and III


A uniform rod of mass \( m=0.5 k g \) and
length \( 90 \mathrm{cm} \) rests on a smooth
horizontal surface. One of the ends of
the rod is stuck with impulse \( J= \)
\( 3.0 N s \) in a horizontal direction
perpendicular to the rod as shown in fig.
As a result the rod obtains momentum
\( \boldsymbol{p}=\mathbf{3 . 0} \boldsymbol{N} \boldsymbol{s} . \) Find


\( \sigma \)
\( \sigma \)
0


What is the \( 25^{t h} \) term of \( A P \)
\( -5, \frac{-5}{2}, 0, \frac{5}{2} \dots \dots \dots \)


A cycle pump becomes hot near the
nozzle after a few quick strokes even if they are smooth because
A. the volume of air decreases
B. the number of air molecules increase
c. the compression is adiabatic
D. collision between air particles increases


How many unpaired electrons are present in \( N i^{2+} \) ion?
A. 0
B. 2
\( c \cdot 4 \)
D. 8


A measured mass of an unreactive
metal was dropped into a small
graduated cylinder half filled with water. The following measurement were
made:
Mass of metal \( =25.200 g \)
Volume of water before addition of
metal \( =12.5 m L \)
Volume of water after addition of metal
\( =15.0 m L \)
The density of the metal should be reported as:
A. \( 10.0800 g / m L \)
\( L \)
в. \( 10.080 g / m L \)
c. \( 10.08 g / m L \)
D. \( 10.1 g / m L \)


Maximum prescribed limit of \( Z n \) in
drinking water is:
\( A \cdot 1 \) ppm
B. 10 ppm
c. 4 ppm
D. 5 ppm


The coefficient of mutual inductance
between two coils depends on
A. medium between the coils
B. separation between the two coils
c. orientation of the two coils
D. all of the above


For some constants \( a \) and \( b \) find the
derivative of
\( \frac{x-a}{x-b} \)


Assertion
o-Nitrophenol is more acidic than meta m-Nitrophenol
Reason
o-Nitrophenol has more I effect than \( m- \)
Nitrophenol
Read the above assertion and reason
and choose the correct statement
regarding it.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


If \( O \) is origin \( O P=3 \) with direction
ratios proportional to -1,2,-2 then what are the coordinates of \( P ? \)


Which of the following may exhibit
biradial symmetry
A. Ctenophora
B. Man
c. Radiolatian
D. sponge


For what value of \( n \), are the \( n^{t h} \) terms of
two \( A . P^{\prime} S 63,65,67, \dots \) and
\( \mathbf{3}, \mathbf{1 0}, \mathbf{1 7} \ldots . \) are equal


Magnetic field can be defined as the:
A. space surrounding the magnet in which magnetic force acts
B. space surrounding the magnet in which electric force acts
C. space surrounding the magnet in which no force acts
D. none


Show the solution of the problem of linear programming under the following restrictions by graphical method: \( \boldsymbol{x}+ \) \( \boldsymbol{y} \leq \mathbf{4}, \boldsymbol{x} \geq \mathbf{0}, \boldsymbol{y} \geq \mathbf{0} \)


\( 250 \% \) of \( x \) is increased by \( 250 \% \) to become \( 30 . \) what is the value of \( x ? \)
A . 3.42
в. 4.8
\( c .3 .81 \)
D. None of these


A p-n photodiode is fabricated from a
semiconductor with band gap of \( 2.8 e V \)
Can it detect a wavelength of 6000 nm?


Which of the following can be considered as an ideal fuel?
A. Kerosene
B. Petrol
c. Biogas
D. woodd


Hydrogen can be prepared on commercial scale by different methods. In its preparation by the action of steam
on hydrocarbons, a mixture of \( C O \) and
\( \boldsymbol{H}_{2} \) gas is formed called:
This question has multiple correct options
A. water gas
B. syngas
c. producer gas
D. industrial gas


Which of the following conditions correctly describes the manner of determining the sex in the given example?
A. \( X O \) type of sex determines male sex in grasshopper
B. \( X O \) condition in humans as found in Klinefelter's syndrome determines female sex
c. Homozygous sex chromosome \( X X \) produce male in Drosophila
D. Homozygous sex chromosome \( Z Z \) determine female \( \operatorname{sex} \) in birds


In which of the following electrolysis,
electrodes act as active electrodes.
Electrolysis of:
A. fused NaCl between graphite electrodes
B. fused AgNO between platinum electrodes
C . aqueous AgNO solution between Ag electrodes
D. aqueous AgNO solution between pt electrodes


Sl units of thermal conductivity are
\( A \cdot W / m-K \)
B. W/m
\( c \cdot w / k \)
D. None


Estradiol is responsible for the development of
A. Primary male characters
B. Secondary female characters
c. Primary female characters
D. Secondary male characters


Which of the following is correct sequence of layers in typical monocot root from outside to inside?
A. Pericycle, cortex, endodermis, epiblema
B. Epiblema, endodermis, cortex, pericycle
c. Epiblema, cortex, endodermis, pericycle
D. Epiblema, pericycle, cortex, endodermis


Root pressure is maximum when
A. Transpiration is high and absorption low
B. Transpiration is very low and absorption is high
C. Transpiration is very high and absorption is high
D. Transpiration and absorption both are slow


A wire of resistance \( R \) is stretched to
twice of its original length. Its new resistance will be:
\( A \cdot 4 R \)
в. \( R / 4 \)
\( c \cdot 2 R \)
D. \( R / 2 \)


In figure if \( D E \| B C \), then find the ratio
of \( a r .(\triangle A D E) \) and \( a r .(\triangle D E C B) . \) Also \( D E=6 \mathrm{cm}, B C=12 \mathrm{cm} \)


The compound with formula \( C_{6} H_{10} O \) is:
Yellow ppt.
\( A \)
B.
\( c \)
4-methoxypent-2-yne Chemical Formula: \( C_{6} H_{10} O \)
D. none of the above


Find the \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \) by implicit differentiation
\( \boldsymbol{x}^{2}-\mathbf{8} \boldsymbol{x} \boldsymbol{y}+\boldsymbol{y}^{2}=\boldsymbol{8} \)


Prove that, if \( x \) and \( y \) are odd positive integers, then \( x^{2}+y^{2} \) is even but not
divisible by 4.


Equivalent resistance between point \( \mathbf{A} \)
and \( \mathrm{B} \) in the combination of resistance
shown is
\( \mathbf{A} \cdot 7 / 5 \Omega \)
B . \( 13 / 5 \Omega \)
c. \( 9 / 8 \Omega \)
D. \( 7 / 13 \Omega \)


Figure given below shows uniformly
positively charged, thin rod of length \( L \)
and four points \( A, B, C \) and \( D \) at the
same distance \( d \) from the rod, with
position as marked. If \( V_{A}, V_{B}, V_{C} \) and
\( V_{D} \) are their respective potentials then.
A \( \cdot V_{B}>V_{A}>V_{C}>V_{D} \)
в. \( V_{B}>V_{A}>V_{C}=V_{D} \)
\( \mathbf{c} \cdot V_{A}=V_{B}>V_{C}=V_{D} \)
D. \( V_{D}>V_{B}>V_{A}>V_{C} \)


\( \boldsymbol{C O}, \boldsymbol{C O}_{2}, \boldsymbol{C}_{2} \boldsymbol{O}_{3} \) follows :
A. law of definite proportion
B. law of multiple proportion
c. law of conservation of mass
D. all of the above


A block of mass \( 100 g \) slides on a rough horizontal surface. If the speed of the
block decreases from \( 10 \mathrm{m} / \mathrm{s}^{-1} \) to
\( 5 m / s^{-1}, \) the thermal energy developed
in the process is:
A . \( 3.75 J \)
B. 37.5 \( J \)
c. 0.375 J
D. \( 0.75 J \)


Assertion
Stomata are generally open in light and
close in dark
Reason
Transpiration is enhanced by heating
effect of light
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 soil which is transported by wind is known as
A . Colluvial
B. Eolian
c. Alluvial
D. Glacial soil


Identify whether the following pairs of angles are complementary or
supplementary:
\( 63^{\circ}, 27^{\circ} \)


If the ratio of sum of \( n \) terms of two A.P.'s
is \( (3 n+8):(7 n+15), \) then the ratio of
\( 12^{t h} \) terms is
\( \mathbf{A} \cdot 16: 7 \)
B. 7: 16
c. 7: 12
D. 12: 5


A flywheel is making \( \frac{3000}{\pi} \) revolution per minute about its axis. If the
moment of inertia of the flywheel about that axis is \( 400 \mathrm{kgm}^{2} \), its rotational
kinetic energy is
A \( .2 \times 10^{6} J \)
B. \( 3 \times 10^{3} J \)
D. \( 12 \times 10^{3} J \)


If \( \boldsymbol{A}=\left\{4^{n}-3 n-1: n \in N\right\} \) and \( B= \)
\( \{9(n-1): n \in N\}, \) then?
\( \mathbf{A} \cdot B \subset A \)
B. \( A \cup B=N \)
c. \( A \subset B \)
D. None of these


A chlorine atom whose nucleus
contains 17 protons and 20 neutrons. Find out the composition of the nucleus of an isotope of chlorine?
A. 20 protons, 17 neutrons
B. 19 protons, 18 neutrons
c. 18 protons, 18 neutrons
D. 17 protons, 19 neutrons
E. 16 protons, 20 neutrons


The distance between (5,1,3) and the
line \( x=3, y=7+t, z=1+t \) is
A . 4
B. 2
\( c \cdot 6 \)
D. 8


The prefix 'milli' denotes the factor \( 10^{-x} \)
\( m \)
find \( \times ? \)


Two bodies of unequal masses are dropped from the top of building. Which of the following is equal for both bodies at any instance?
A. Speed
B. Force of gravity
c. Potential energy
D. Kinetic energy


German silver alloy contains:
A. Zinc, silver and copper
B. Nickel, silver and copper
C. Germanium, silver and copper
D. Zinc, nickel and copper


Choose the correct answer from the
alternatives given. Which of the following processes requires the greatest expenditure of energy by the cell?
A . Facilitated diffusion
B. Diffusion
c. Active transport
D. Osmosis


fsum \( =-12, \) product \( =-28 . \) Then find the 2 numbers.


In a hydrogen atom, the energy of an electron in an orbit is -3.4 eV. When it is
excited to the next higher energy level and comes back to ground state, calculate the wave length of emitted
radiation.
\( \mathbf{A} \cdot 9 \times 10^{-7} m \)
В. \( 9 \times 10^{-9} m \)
\( \mathbf{c} \cdot 9 A^{\circ} \)
D. none of these


\( \operatorname{can} \frac{2}{\sqrt{3}}, \frac{-2}{\sqrt{3}}, \frac{-1}{\sqrt{3}} \) be the direction ratios
of any directed line? Justify your
answer


Solve:
\( \int \log \left(1+x^{2}\right) d x \)
A \( \cdot x \log \left(1+x^{2}\right)-2 x+2 \tan ^{-1} x+c \)
B \( \cdot x \log \left(1+x^{2}\right)-2 x-2 \tan ^{-1} x+c \)
C \( \cdot \log \left(1+x^{2}\right)-2 x+2 \tan ^{-1} x+c \)
D. \( \log \left(1+x^{2}\right)+2 x-2 \tan ^{-1} x+c \)


Choose the correct statement(s).
This question has multiple correct options
A. Chlorine has two complete electron shells before its valence shell.
B. Bromine is solid at room temperature.
C. Chlorine has the third highest electro-negativity value in the periodic table.
D. lodine has the lowest ionisation energy among the halogens (consider \( F, C I, B r, 1) \)


Number of pi bonds in \( X e O_{4} \) is:


Which of the following steps is not
correct in the mechanism of
electrophilic substitution of benzene?
A. Generation of electrophile like \( X^{+}, R^{+}, R C^{+} O, N O_{2}^{+} \) etc.
B. Attack of electrophile resulting in the formation of arenium ion in which one of the carbon is \( s p^{3} \) hybridised.
C. Addition of proton on benzene ring to give carbocation.
D. Removal of proton from \( s p^{3} \) carbon atom to restore aromatic character.


Over which period of time did the student move the fastest ? can you
explain how you know this?
Distance \( / m \)
Time \( / s \)


Solve: \( \int \sin ^{3} 2 x \cdot d x \)


State True or False :
Convection currents are set up giving rise to sea breezes.
A. True
B. False


Moment of inertia of a thin circular
plate is minimum about the
A. axis perpendicular to plane of plate passing through its centre.
B. axis passing through any diameter of plate.
C. axis passing through any tangent of plate in its plane.
D. axis passing through any tangent perpendicular to its plane.


If the length of the diagonal of a square is increasing at the rate of \( 0.2 \mathrm{cm} / \mathrm{sec} \) then rate of increase of its area when its
side is \( 30 / \sqrt{2} \mathrm{cm}, \) is
\( \mathbf{A} \cdot 3 \mathrm{cm}^{2} / \mathrm{sec} \)
в. \( \frac{6}{\sqrt{2}} \mathrm{cm}^{2} / \mathrm{sec} \)
\( c \cdot \sqrt[3]{2} \mathrm{cm}^{2} / \mathrm{sec} \)
D. \( 6 \mathrm{cm}^{2} / \mathrm{sec} \)


If the \( n=16 \) in plant cell than what is possible in metaphase I of meiosis?
A. 32 bivalents
B. 16 tetravalents
c. 16 bivalents
D. 32 tetravalents


Select the correct I.U.P.A.C. name for
\( \left[\boldsymbol{P t} \boldsymbol{C l}_{2}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4}\right]\left[\boldsymbol{P t} \boldsymbol{C l}_{4}\right] \)
A. Tetraamminedichloridoplatinate(IV) tetrachloridoplatinate(II)
B. Tetraamminedichloridoplatinate(II) tetrachloridoplatinate(IV)
c. Tetraamminedichloridoplatinum(IV) tetrachloridoplatinate(II)
D. All are correct


The bulk modulus of a spherical objects is ' \( B \) '. If it is subjected to uniform
pressure 'P', the fractional decrease in
radius is:
A \( \cdot \frac{P}{3 B} \)
в. \( \frac{P}{B} \)
c. \( \frac{B}{3 P} \)
D. \( \frac{3 P}{B} \)


What is decarboxylation?


Which among the following is an example of heterogeneous equilibrium?
A \( \cdot 2 S O_{2}(g)+O_{2}(g) \rightleftharpoons 2 S O_{3}(g) \)
в. \( _{N_{2}} O_{4}(g) \stackrel{人}{\rightleftharpoons} 2 N O_{2}(g) \)
c. \( \operatorname{CaCO}_{3}(s) \triangleq \) 垃 \( a O(s)+C O_{2}(g) \)
D \( \cdot \operatorname{PCl}_{5}(g) \triangleq \operatorname{PCl}_{3}(g)+C l_{2}(g) \)


A regular polygon has 20 sides. How many triangles can be drawn by using the vertices but not using the sides?


Method of separation by sublimation is limited.
A . True
B. False


In which of the following species the
interatomic bond angle is \( 109^{\circ} 28^{\prime} ? \)
A \( \cdot N H_{3},\left(B F_{4}\right)^{-1} \)
B . \( \left(N H_{4}\right)^{+}, B F_{3} \)
c. \( N H_{3}, B F_{3} \)
D. \( \left(N H_{2}\right)^{-1}, B F_{3} \)


Sulphide ore is concentrated by the method:
1. Froth flotation process
2. Magnetic separation
3. Gravity method
4. Calcination method


Evaluate: \( \int \sqrt{\frac{\boldsymbol{x}-\mathbf{5}}{\boldsymbol{x}-\mathbf{9}}} \boldsymbol{d} \boldsymbol{x} \)


The correct IUPAC name of the given
compound is:
A. N-dimethyl 1-methyl-1-ethyl propane
B. 3-methyl-3(N, N-dimethyl amino) pentane
c. N-dimethyl amino-3-methyl pentane
D. 3, N, N - trimethyl-3-pentanamine


A chain of length \( l \) and mass \( m \) lies on
the surface of a smooth sphere of
radius \( R>l \) with one end tied to the
top of the sphere. Suppose the chain is released and slides down the sphere.
Find the kinetic energy of the chain,
when it has slid through an angle \( \theta \)
\( ^{\mathbf{A}} \cdot \frac{m R^{2} g}{l}\left[\sin \left(\frac{l}{R}\right)+\sin \theta-\sin \left(\theta+\frac{l}{R}\right)\right] \)
\( ^{\mathbf{B}} \cdot \frac{m R^{2} g}{l}\left[\sin \left(\frac{l}{R}\right)+\sin \theta+\sin \left(\theta+\frac{l}{R}\right)\right] \)
\( ^{\mathbf{C}} \cdot \frac{m R^{2} g}{l}\left[\sin \left(\frac{l}{R}\right)+\sin \theta+\sin \left(\theta-\frac{l}{R}\right)\right] \)
\( D \)
\[
\frac{m R^{2} g}{l}\left[\sin \left(\frac{l}{R}\right)+\sin \theta-\sin \left(\theta-\frac{l}{R}\right)\right]
\]


The equilibrium of the reaction
\( \boldsymbol{S O}_{2}(\boldsymbol{g})+\frac{1}{2} \boldsymbol{O}_{2}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{S} \boldsymbol{O}_{3}(\boldsymbol{g}) \) is \( \boldsymbol{4} \times \)
\( 10^{-3} a t m^{-1 / 3} . \) The equilibrium constant
of the reaction \( 2 S O_{3}(g) \rightleftharpoons 2 S O_{2}(g)+ \)
\( O_{2}(g) \) would be:
A. \( 250 a t m \)
B . \( 4 \times 10^{3} a t m \)
\( \mathbf{c} \cdot 0.25 \times 10^{4} a t m \)
D. \( 6.25 \times 10^{4} \) atm


Riya and Priya were sitting around a round table. They noticed that they could see their own and each other's
image onto the table top. Then table top
is made of
A. Unpolished wood, covered with white cloth
B. Polished glass of red colour
C. Glass covered with cellophane paper
D. Smoked glass covered with green colour cloth.


Characteristics which delimit a family are more general than those which delimit a
A. cohort
B. Phylum
c. class
D. Genus


A Zener diode, having breakdown
voltage equal to \( 15 V \), is used in a
voltage regulator circuit shown in
figure. The current through the diode is
A . \( 10 \mathrm{mA} \)
в. \( 15 \mathrm{mA} \)
\( c .20 m A \)
D. \( 5 m A \)


Prepare an acid salt from dil. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \)
A \( \cdot 2 H_{2} S O_{4}+2 C H_{3} C O O N a \rightarrow 2 N a H S O_{4}+ \)
\( C H_{3} C O O H \)
в. \( 2 H_{2} S O_{4}+C H_{3} C O O N a \rightarrow 2 N a H S O_{4}+C H_{3} C O O H \)
c. \( H_{2} S O_{4}+C H_{3} C O O N a \rightarrow N a H S O_{4}+C H_{3} C O O H \)
D. \( H_{2} S O_{4}+2 C H_{3} C O O N a \rightarrow N a H S O_{4}+2 C H_{3} C O O H \)


Which one of the following is an amphoteric oxide?
A. \( N a_{2} O \)
в. \( S O_{2} \)
\( \mathrm{c} \cdot B_{2} \mathrm{O}_{3} \)
D. \( Z n O \)


Peptization of silver iodide can take place on addition of This question has multiple correct options
A. silver nitrate
B. potassium iodide
c. potassium nitrate
D. potassium chloride


The slope of the normal to the curve \( x=1-a \sin \theta, y=b \cos ^{2} \theta \) at \( \theta=\frac{\pi}{2} \) is
A \( \cdot \frac{a}{2 b b} \)
в. \( \frac{2 a}{b} \)
c. \( \frac{a}{b} \)
D. \( \frac{-a}{2 b} \)


The observed dipole moment of \( H C l \) is 1.3 \( D \). If the bond length of \( H C l \) is \( 1.3 \dot{A} \)
then percentage ionic character of \( \boldsymbol{H}- \)
\( C l \) bond is nearly :
(Charge on electron \( =4.8 \times 10^{-10} \) esu)
A . \( 50 \% \)
B . \( 40 \% \)
\( c .30 \% \)
D. \( 17 \% \)


Show that the points
(2,-2),(8,4),(5,7) and (-1,1) taken
in order constitute the vertices of a
Rectangle.


The tension in a string is an example of electromagnetic force
True=1; False=0


The vapour pressure of three liquids
\( P, Q \) and \( R, \) of nearly equal molecular
masses is shown as a function of
temperature
The correct statement is:
A. The normal boiling points follow the order \( P>Q>R \)
B. The variation of pressure with respect to temperature for each liquid is given by \( \frac{d P}{d T}=\frac{K}{T^{2}}, \) where \( K \) is a
constant
c. The strength of intermolecular interactions follows the order \( P>Q>R \)
D. The normal boiling point of \( Q \) is close to \( 65^{\circ} \mathrm{C} \)


Silica dissolves in NaOH solution to
form:
A. quartz
B. sodium silicate
c. carborundum
D. jaspar


At a place horizontal component of Earth's magnetic field is \( \sqrt{3} \) times the vertical component, then the angle of dip at the given place is :
A \( \cdot 45^{\circ} \)
B. 30 \( ^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 15^{\circ} \)


State True or False.
\( H^{-} \) is unstable in water
A. True
B. False


The star-like objects at the edge of the universe are
A. comets
B. Black holes
c. Galaxies
D. Quasars


\( \sigma_{\infty}^{\text {and }} \)
0
0
0


Figure shows two blocks in contact
sliding down an inclined surface of
inclination \( 30^{0} . \) The friction coefficient
between the block of mass \( 2.0 \mathrm{kg} \) and
the incline is \( \mu_{1}=0.20 \) and that
between the block of mass \( 4.0 \mathrm{kg} \) and
the incline is \( \mu_{2}=0.30 . \) Find the
acceleration of \( 2.0 \mathrm{kg} \) block. \( g= \)
\( 10 m / s^{2} \)
\( \mathbf{A} \cdot 3.8 m / s^{2} \)
\( \mathbf{B} \cdot 5.1 \mathrm{m} / \mathrm{s}^{2} \)
\( \mathbf{c} \cdot 1.2 \mathrm{m} / \mathrm{s}^{2} \)
D. \( 2.7 \mathrm{m} / \mathrm{s}^{2} \)


Gallium at room temperature is in:
A. plasma state
B. liquid state
c. solid state
D. gaseous state


Prove that:
\( \int \frac{x^{2}}{1+x^{3}} d x \)


If the unit of power is 1 million erg per minute, the unit of force is 1000 dyne and that of time is \( \frac{1}{10} s, \) the unit of mass in the new system is :
\( A \cdot 6 g \)
B. 60 g
c. \( 106 g \)
D. 18


Why is tritium called as beta-emitter?


A bullet of mass \( 5 g \) travels with a speed
of \( 500 m s^{-1} . \) if it penetrates a fixed target which offers a constant resistive
force of \( 1000 \mathrm{N} \) to the motion of the
bullet, find :
(a) the initial kinetic energy of the bullet,
(b) the distance through which the bullet has penetrated.
\( \mathbf{A} \cdot s=0.625 m \)
B. \( s=0.725 \mathrm{m} \)
\( \mathbf{c} \cdot s=0.225 m \)
D. \( s=0.65 m \)


The thermometric liquid used to
measure up to \( -100^{\circ} \mathrm{C} \) is :
A. alcohol
B. mercury
c. water
D. benzene


Show that the statement
\( p: \) "If \( x \) is a real number such that \( x^{3}+ \)
\( 4 x=0 \) then \( x \) is \( 0^{\prime \prime} \) is true by
(i) direct method
(ii) method of contradiction
(iii) method of contrapositive


Radian measure of \( 175^{\circ} 45^{\prime} \) is
A \( \cdot \frac{700}{720} \pi \)
в. \( \frac{703}{720} \pi \)
c. \( \frac{705}{720} \pi \)
D. \( \frac{710}{720} \pi \)


Solve the differential equation \( y d x+ \)
\( \left(\boldsymbol{x}-\boldsymbol{y} \boldsymbol{e}^{\boldsymbol{y}}\right) \boldsymbol{d} \boldsymbol{y}=\mathbf{0} \)


The most resistant organic substance
which can withstand environmental
extremes and cannot be degraded by any enzyme is
A . Lignin
B. Suberin
c. cutin
D. sporopollenin


\( \boldsymbol{P h}-\underset{\boldsymbol{O} \boldsymbol{H}}{\boldsymbol{C} \boldsymbol{H}}-\stackrel{\boldsymbol{O}}{\boldsymbol{C}}-\boldsymbol{O H} \)
Correct IUPAC naming of given acid is:
A. 1-hydroxy-1-phenylethanoic acid
B. 2-hydroxy-2-phenylethanoic acid
c. 2-phenyl hydroxy ethanoic acid
D. none of these


The product of the digits of a two-digit number is one-third that number. If we
add 18 to the required number, we get a number consisting of the same digits written in the reverse order. Find
the number


Assertion
When a rod is pulled by a force acting on one end (longitudinally) then there will be no longitudinal stress in the rod. (Assume surface is friction-less)
Reason
Longitudinal stress is internal normal
force per unit area.
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


Let \( A \) and \( B \) be two independent events such that \( \boldsymbol{P}(\boldsymbol{A})=\frac{1}{5}, \boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B})=\frac{\mathbf{7}}{\mathbf{1 0}} \)
Then \( P(\bar{B}) \) is equal to
A \( \cdot \frac{3}{8} \)
B. \( \frac{2}{7} \)
\( c \cdot \frac{7}{9} \)
D. none of these


Match the following:


Write the following as a single matrix \( \left[\begin{array}{cc}-1 & 2 \\ 1 & -2 \\ 3 & -1\end{array}\right]+\left[\begin{array}{cc}0 & 1 \\ -1 & 0 \\ -2 & 1\end{array}\right] \)


A box measuring \( 51 c m \times 36 c m \times \)
18cm. In this box, how many compass-
boxes measuring \( 17 \mathrm{cm} \) in length, \( 9 \mathrm{cm} \) in width and \( 2 \mathrm{cm} \) in height can be
arranged?


Define biomass.
A. Fossil fuels are also called biomass.
B. The wastes and dead parts of living beings are called biomass.
C. The wastes from industrial applications are called biomass.
D. The wastes and dead parts of living beings buried deep inside the earth are called biomass.


2
\( g(x) \)
\( 11 \quad 19 \quad 27 \)
The table above defines several values
of the linear function \( g \). Calculate the
value of \( \boldsymbol{a} \)
\( A .31 \)
B. 33
c. 35
D. 37
E . 41


Alloy formation gives rise to:
A. decrease in corrosion
B. increase in hardness
C . decrease in conductivity
D. All are correct


The difference between the ages of a
woman and her son is 19 years and the
sum of their ages is 37 years. Find the age of the son.


A thin rod length L is bent to form a circle. Its mass is M. What force will act
on the mass \( \mathrm{m} \) placed at the center of the circle?
A \( \cdot \frac{4 \pi^{2} G M m}{L^{2}} \)
B. \( \frac{G M m}{4 \pi^{2} L^{2}} \)
c. \( \frac{2 \pi G M m}{L^{2}} \)
D. zero


\( P, Q, R \) are three collinear points. The coordinates of \( \mathrm{P} \) and \( \mathrm{R} \) are (3,4) and (11
10) respectively and PQ is equal to 2.5 units. Coordinates of \( Q \) are-
A \( \cdot(5,11 / 2) \)
B. (11,5/2)
c. \( (5,-11 / 2) \)
D. \( (-5,11 / 2) \)


Q Type your question
\( \mathbf{A} \)
\( B \)
\( \mathbf{c} \)
D.


The maximum value of \( \frac{\ln x}{x} \) is
A \( . e \)
B. \( \frac{1}{e} \)
\( c \cdot \frac{2}{e} \)
D.


Differentiate the follwoing w.r.t \( x \) :
\( \cos \left(\log x+e^{x}\right) \)


An object swinging on the end of a string forms a simple pendulum. Some students (and some texts) often cite the
simple pendulum's motion as an example of SHM. That is not quite accurate because the motion is really
A. approximately SHM only for small amplitudes
B. exactly SHM only for amplitudes that are smaller than a certain value
c. approximately SHM for all amplitudes.
D. None of the above


Alida runs her toy car on dry marble floor, wet marble floor, newspaper and towel spread on the floor. The force of friction acting on the car on different surfaces in increasing order will be
A. wet marble floor, dry marble floor, newspaper, towel.
B. newspaper,towel, dry marble floor, wet marble floor.
c. towel,newspaper, dry marble floor, wet marble floor.
D. wet marble floor, dry marble floor, towel, newspaper.


If \( \boldsymbol{A}=\left[\begin{array}{ll}2 & 5 \\ 4 & 4\end{array}\right], \quad B=\left[\begin{array}{ll}0 & 5 \\ 1 & 6\end{array}\right], \) find
\( 5 \boldsymbol{A}^{\prime}+3 B^{\prime} \)


Two parallel plates \( 5 \mathrm{cm} \) apart are connected to a 500 V D.C supply. Assuming that an electron starts from rest, its velocity after a nano second is
A \( \cdot 1.56 \times 10^{6} m / s \)
В . \( 1.66 \times 10^{6} \mathrm{m} / \mathrm{s} \)
c. \( 1.76 \times 10^{6} m / s \)
D. \( 1.86 \times 10^{6} \mathrm{m} / \mathrm{s} \)


Which of the following is responsible for the depletion of the ozone layer in the upper strata of the atmosphere?
A. Ferrocene
B. Fullerenes
c. Freons
D. Polyhalogens


Froth floatation process for the concentration of ores is an illustration
of physical phenomenon of
A. adsorption
B. absorption
c. conagulation
D. sedimentation


What do you understand by isoelectronic species? Name a species that will be isoelectronic with each of
the following atoms or ions:
¡) \( \boldsymbol{F}^{-} \)
ii) \( \boldsymbol{A} \boldsymbol{r} \)
iii) \( M g^{2+} \)
iv) \( \boldsymbol{R} \boldsymbol{b}^{+} \)


Why does synthesis of DNA proceed only
in the \( 5^{\prime} \) to \( 3^{\prime} \) direction?
A. DNA polymerases can only add nucleotides to the \( 3^{\prime} \) end of a polynucleotide strand.
B. The \( 3^{\prime} \) end of the polynucleotide molecule is more electronegative than the \( 5^{\prime} \) end.
c. This is the direction in which the two strands of DNA unzip
D. The chromosomes are always aligned in the \( 5^{\prime} \) to \( 3^{\prime} \) direction in the nucleus


What are stomata? Give two functions
of stomata.


The substance used for coagulating rubber from latex is :
A. Ethanol
B. Ethanoic acid
c. Both
D. None of these


A wave equation which gives the displacement along Y-direction is given \( \boldsymbol{y}=\mathbf{1 0}^{4} \sin (\mathbf{6 0} \boldsymbol{t}+\mathbf{2} \boldsymbol{x}) \) where \( \boldsymbol{x} \) and \( \boldsymbol{y} \)
are in meter and \( t \) in sec. Among the
following choose the correct statement:
This question has multiple correct options
A. It represents a wave propagating along positive x-axis with a velocity of \( 30 \mathrm{m} / \mathrm{s} \)
B. It represents a wave propagating along negative x-axis with a velocity of \( 120 \mathrm{m} / \mathrm{s} \)
c. It represents a wave propagating along negative x-axis with a velocity of \( 30 \mathrm{m} / \mathrm{s} \).
D. It represents a wave propagating along negative xaxis with a velocity of \( 10^{4} \mathrm{m} / \mathrm{s} \)


If an earthed plate is brought near a positively charged plate, the potential and capacity of charged plate respectively:
A. increases, decreases
B. decreases, increases
c. decreases, decreases
D. increases, increases


Consider the function
\( \frac{\sqrt{(1+x)}-\sqrt{(1-x)}}{x} \) Find the limit
as \( \boldsymbol{x} \rightarrow \mathbf{0} \)


Which group represent micronutrients?
A. Mn, Zn, Fe, B, CI, Ni
B. \( c, \mathrm{S}, \mathrm{O}, \mathrm{N}, \mathrm{K}, \mathrm{Ca} \)
\( c \cdot \) са, Мg, к, ऽ,
D. C, H, Fe, Mn, Си, Мо


Two points of a rigid body are moving as shown. Then determine the angular
velocity of the body is :
A \( \cdot \frac{v}{2 R} \)
B. \( \frac{v}{R} \)
c. \( \frac{2 v}{R} \)
D. \( \frac{2 v}{3 R} \)


The degree of ionisation of an acid HA is
0.00001 at 0.1 M concentration. Its
dissociation constant will be ?
A \( \cdot 10^{-9} \)
В. \( 10^{-11} \)
\( c \cdot 10^{-8} \)
D. \( 10^{-7} \)


Arrange the below molecules in order of
increasing ionic character
\( L i F, K_{2} O, N_{2}, S O_{2} \) and \( C l F_{3} \)


Write the degree of the differentia
quation \( :\left(\frac{d y}{d x}\right)^{4}+3 y\left(\frac{d^{2} y}{d x^{2}}\right)=0 \)


Minimum value of \( \lambda \) for which the
equation \( 9 a^{2 x}-(\lambda+2) a^{x}+4=0 \)
\( a>1 \) has atleast one real solution is:
A .4
B. 6
c. 8
D. 10


I torr is equal to the pressure exerted by
A. \( 1 \mathrm{mm} \) of a mercury column
B. \( \frac{1}{10} \mathrm{mm} \) of a mercury column
C. \( 10 \mathrm{mm} \) of a mercury column
D \( \cdot \frac{1}{5} \mathrm{mm} \) of a mercury column


The resultant of two forces, one double
then other in magnitude, is perpendicular to the smaller of the two
forces. The angle between the two forces
is
\( A \cdot 120^{\circ} \)
B. 60
\( c \cdot 90 \)
D. 150


Solve the following system of inequalities graphically \( x+2 y \leq 8 \)
\( 2 x+y \leq 8 \)
\( x \geq 0 \)
\( \boldsymbol{y} \geq \mathbf{0} \)


Assertion
Ohm's law is not valid if current
depends on voltage non-linearly.
Reason
Ohm's law is a fundamental law of
nature.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Assertion
\( O_{2} \) molecule is diamagnetic while \( C_{2} \)
molecule is paramagnetic in nature
Reason

Bond order of \( O_{2} \) molecule is 1.5 and
that of \( C_{2} \) molecule is 2.5
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A hole is drilled in a copper sheet. The
diameter of the hole is \( 4.24 \mathrm{cm} \) at
\( 27.0^{\circ} \mathrm{C} . \) what is the change in the
diameter of the hole when the sheet is
heated to \( 227^{\circ} \mathrm{C} \) ?
\( \alpha \) for copper \( =1.70 \times 10^{-5} K^{-1} \)
A \( \cdot 1.44 \times 10^{-2} \mathrm{cm} \)
B . \( 14.4 \times 10^{-2} \mathrm{cm} \)
\( \mathrm{c} \cdot 144 \times 10^{-2} \mathrm{cm} \)
D. \( 0.144 \times 10^{-2} \mathrm{cm} \)


Meristematic tissue in vascular bundle
is
A. Phellem
B. Procambium
c. Interfascicular cambium
D. Fascicular cambium


If the sum of \( n \) terms of an A.P.is \( n P+ \) \( \frac{1}{2} n(n-1) Q, \) where \( P \) and \( Q \) are
constants, find the common difference.


Fungi and bacteria grow mostly in
A. subsoil
B. Top soil
c. Bedrock
D. All of the above


\( P \) and \( Q \) are two elements which form
\( P_{2} Q_{3} \) and \( P Q_{2} \) compounds. If 0.15
moles of \( \boldsymbol{P}_{2} \boldsymbol{Q}_{3} \)
\& \( P Q_{2} \) weigh 15.9 g and \( 9.3 \mathrm{g} \) respectively, then the atomic mass of \( 6 Q \) is \( Y \). Then \( Q \) is:


A person throws balls into air vertically upward in regular intervals of time of one second. The next ball is thrown
when the velocity of the ball thrown earlier becomes zero. The height to which the balls rise is
(Assume, \( \left.g=10 m s^{-2}\right) \)
A. \( 5 m \)
B. \( 10 m \)
c. \( 7.5 m \)
D. \( 20 m \)


A stone is dropped from the top of a tower and travels \( 24.5 ~ m \) in the last
second of its journey. The height of the tower is :
A . \( 44.1 m \)
в. \( 49 m \)
c. \( 78.4 m \)
D. \( 72 m \)


\( \angle A D E \)


Q Type your question
\( m_{1} \) and \( m_{2}, \) the coetticient of triction
between the body \( m_{1} \) and the horizontal
plane is equal to \( k, \) and a pulley of mass
\( m \) is assumed to be a uniform disc. The
thread does not slip over the pulley. At
the moment \( t=0 \) the body \( m_{2} \) starts
descending. Assuming the mass of the thread and the friction in the axle of the
pulley to be negligible, find the work performed by the friction forces
acting on the body \( m_{1} \) over the first \( t \) seconds after the beginning of motion.
\( ^{\mathbf{A}} \cdot_{A}=-\frac{k m_{1}\left(m_{1}-k m_{1}\right) g^{2} t^{2}}{m+2\left(m_{1}+m_{2}\right)} \)
B. \( A=-\frac{k m_{1}\left(m_{1}+k m_{1}\right) g^{2} t^{2}}{m+2\left(m_{1}-m_{2}\right)} \)
c. \( A=\frac{k m_{1}\left(m_{1}+k m_{1}\right) g^{2} t^{2}}{m+2\left(m_{1}+m_{2}\right)} \)
D. None of these


Which statement about microwaves is
correct?
A. Microwaves are longitudinal waves
B. The frequencies of microwaves are greater than the frequencies of visible light
C. The speed of microwaves in a vacuum is equal to the speed of visible light in a vacuum
D. The wavelengths of microwaves are smaller than the wavelengths of infra-red


The variance of \( 10,10,10,10,10, \) is
A . 10
B. \( \sqrt{10} \)
\( c .0 \)
D. 5


f \( 18, a, b,-3 \) are in \( A P \) then find \( a+b \)


Total number of cars of models \( P, Q \) and
T manufactured in 2000 is?
A. 2,45,000
B. 2,27,500
c. 2,10,000
D. 1,92,500


Which of the following reaction is not
feasible?
\( (P) \)
\( (Q) \)
(R)
(S)
A. Only P, Q are not feasible reactions
B. Only P, S are not feasible reactions
c. only \( Q, R \) are not feasible reactions
D. Only Q, S are not feasible reactions


On doping germanium with donor atoms of density \( 10^{17} \mathrm{cm}^{-3} \) its conductivity in \( m h o / c m \) will be
\( \left[\text { Given: } \mu_{e}=3800 \mathrm{cm}^{2} / V-s \text { and } n_{i}=\right. \)
\( \left.2.5 \times 10^{13} c m^{-3}\right] \)
A . 30.4
B. 60.8
c. 91.2
D. 121.6


Find the half life of a radioactive
element, if its activity decreases for 1 month by \( 10 \% \)
A. 193.3 days
B. 197.3 days
c. 198.5 days
D. 199.7 days


Peroxy acids of sulphur are:
This question has multiple correct options
\( \mathbf{A} \cdot H_{2} S_{2} O_{8} \)
\( \mathbf{B} \cdot H_{2} S O_{5} \)
\( \mathbf{c} \cdot H_{2} S_{2} O_{7} \)
D. \( H_{2} S_{2} O_{3} \)


Positive electric flux indicates that
electric lines of force are directed
A. outwards
B. inwards
c. either (a) or (b)
D. none of these


Two conducting spheres of radii \( r_{1} \) and
\( r_{2} \) are charged such that they have the same electric field on their surfaces.
The ratio of the electric potential at
their centres is :
A. \( \sqrt{\frac{r_{1}}{r_{2}}} \)
в. \( \frac{r_{1}}{r_{2}} \)
c. \( \frac{r_{1}^{2}}{r_{2}^{2}} \)
D. none of the above


Which of the following shows acidic character?
\( \mathbf{A} \cdot C H_{3}-C H_{3} \)
в. \( C H_{3}-C \equiv C H \)
c. \( C H_{3}-C=C-H_{3} \)
D. None of these


\( f\left(\begin{array}{lll}1 & 0 & 1 \\ 0 & 1 & 2 \\ 0 & 0 & 4\end{array}\right], \) then show that
\[
|\mathbf{3} \boldsymbol{A}|=\mathbf{2 7}|\boldsymbol{A}|
\]


If the function \( f(x)=2 x^{2}+3 x+5 \)
satisfies LMVT at \( x=2 \) on the
closed interval \( [1, a] \) then the value of ' \( a^{\prime} \)
is equal to
A . 3
B. 4
\( c \cdot 6 \)
D.


If the current population of Chennai city
is 3888180 and the average rate of population growth in Bangalore city is \( 10 \% \) p.a., what can city planners expect the population of Chennai city to be in
10 years?


is the disadvantage of asexual reproduction
A. Repid reproduction
B. Lack of genetic variation
c. Both a and \( b \)
D. None of above


The velocity of a particle increases from \( u \) to \( v \) in a time \( t \) during which it covers a distances \( S \). If the particle has a uniform acceleration, which one of the following equations does not apply to the motion?
\( \mathbf{A} \cdot 2 S=(v+u) t \)
B. \( a=\frac{v-u}{t} \)
c. \( v^{2}=u^{2}-2 a S \)
D. \( s=\left(u+\frac{1}{2} a t\right) t \)


The solution which has the highest boiling point temperature is:
\( \begin{array}{lll}\text { A. } 0.1 & M & M g C l_{2}\end{array} \)
\( \begin{array}{lll}\text { В. } 0.1 & M & H C l O_{4}\end{array} \)
\( \begin{array}{llll}\text { c. } 0.1 & M & N H_{4} O H\end{array} \)
\( \begin{array}{lll}\text { D. } 0.1 & M & \text { KOH }\end{array} \)
\( \begin{array}{lll}\text { E. } 0.1 & M & L i N O_{3}\end{array} \)


Name the device used to make a circuit
function, only when needed?


Nature of valves in the heart is
A. Membranous
B. Ligamentous
c. Tendinous
D. None of the above


What determines the size of
isoelectronic species?
A. Valence
B. Nuclear charge
c. lonization potential
D. None of these


When the number of turns per unit length in a solenoid is doubled then its
coefficient of self induction will become
A . half
B. double
c. four times
D. unchanged


Choose the correct option:
Dalton's atomic theory suffered from
A. Atoms of the same or different types have a strong tendency to combine together to form a new group of atom
B. The atom can no longer be considered indivisible
C. Discovery of isotopes indicated that all atoms of the same element are not perfectly identical
D. All of the above


An object is kept at a distance of \( 20 \mathrm{cm} \)
from a converging lens of focal length 10cm. What will be the magnification?
A \( \cdot \frac{1}{2} \)
B.
c. 2
D.


Air column of \( 20 \mathrm{cm} \) length in a resonance tube resonates with a
certain tuning fork when sounded at its upper open end. The lower end of the tube is closed and adjustable by
changing the quantity of mercury filled inside the tube. The temperature of the
air is \( 27^{\circ} \mathrm{C} \). The change in length of the
air column required, if the temperature
falls to \( 7^{\circ} \mathrm{C} \) and the same tuning fork is again sounded at the upper open end is
\( \mathbf{A} \cdot 1 \mathrm{mm} \)
B. 7 mm
\( c \cdot 5 m m \)
D. \( 13 \mathrm{mm} \)


A die is thrown thrice. A success is 1 or 6
in a throw. If the sum of the mean and variance of the number of successes is \( \frac{a}{3}, \) the value of a is


Which of the following is a vessel less angiosperm?
A. Tetracentron
B. Trochodendron
c. wintera
D. All of these


Consider the function \( y=|x-1|+ \)
\( |x-2| \) in the interval [0,3] and discuss
the continuity and differentiability of
the function in this interval.
This question has multiple correct options
A. continuous everywhere
B. differentiable everywhere except at \( x=1 \) and \( x=2 \)
c. differentiable everywhere
D. continuous everywhere except at \( x=1 \) and \( x=2 \)


Name two catalysts that can be used in
the hydrogenation of unsaturated compounds.


What is the action of carbon on the
following metal oxide ZnO in vertical retort furnace.


Change in concentration of product is 0.05 mole \( l^{-1} \) in 20 seconds. Average
rate of reaction is
A .0 .0025 moles \( s^{-1} \)
B. 1 moles \( s^{-1} \)
c. 0.05 moles \( s^{-1} \)
D. none of these


Very Short Answer Types:
Name three steps of aerobic respiration


How will you show that air and moisture both are required for rusting of iron?


Choose the correct answer form the
alternatives given. Which of the following compounds are not arranged in correct order as indicated?
A \( \cdot \operatorname{Sr} C l_{2}<C a C l_{2}<M g C l_{2}<B e C l_{2} \) (increasing extent
of hydrolysis)
B. \( S r C l_{2}<C a C l_{2}<M g C l_{2}<B e C l_{2} \) (increasing lattice energy）
\( \mathrm{c} \cdot \mathrm{CaSO}_{4}<\mathrm{MgSO}_{4}<\mathrm{BeSO}_{4} \) (increasing stability)
D. \( B e(O H)_{2}<M g(O H)_{2}<C a(O H)_{2} \) (increasing solubility)


lodoform is used as:
A. anaesthetic
B. antiseptic
C . analgesic
D. anti febrin


Let \( A \) and \( B \) be two symmetic matrices
of order 3
Statement \( -1: \boldsymbol{A}(\boldsymbol{B} \boldsymbol{A}) \) and \( (\boldsymbol{A B}) \boldsymbol{A} \) are
symmetric matrices.
Statement - \( 2: A B \) is symmetric matrix if matrix multiplication of \( \boldsymbol{A} \) and \( \boldsymbol{B} \) is
commutative.
A. Statement-1 is True, Statement-2 is True, Statementis a correct explanation for Statement-
B. Statement-1 is True, Statement-2 is True, Statementis NOT a correct explanation for Statement-
c. Statement-1 is True, Statement-2 is False
D. Statement-1 is False, Statement-2 is True


You may have noticed that chicken-egg is very strong along its long axis so much so that it does not break even
when pressed very hard. Which of the following is the main constituent of egg-shell?
A. \( \operatorname{CaSO}_{4} \cdot 2 \mathrm{H}_{2} \mathrm{O} \)
B. \( C a S O_{4} \cdot \frac{1}{2} H_{2} O \)
\( \mathrm{c} \cdot \operatorname{casio}_{3} \)
\( \mathrm{D} \cdot \mathrm{CaCO}_{3} \)


The number of rational numbers
between two given rational numbers is
A . Infinite
B. Finite
c. Two
D. one


If an \( A . P . \) has 21 terms, and the sum of \( 10^{t h}, 11^{t h} \& 12^{t h} \) terms is 129 and sum
of last three terms is 237 . Find first
term.


Assume that two deuteron nuclei in the
core of fusion reactor at temperature \( T \) are moving toward each other, each with kinetic energy \( 1.5 \mathrm{kT} \), when the separation between them is large enough to neglect Coulomb potential energy. Also, neglect any interaction from other particles in the core. The minimum temperature T required for
them to reach a separation of \( 4 x \)
\( 10^{-15} m \) is in the range
A . \( 1.0 \times 10^{9} K<T<2.0 \times 10^{9} K \)
B . \( 2.0 \times 10^{9} K<T<3.0 \times 10^{9} K \)
c. \( 3.0 \times 10^{9} K<T<4.0 \times 10^{9} K \)
D. \( 4.0 \times 10^{9} K<T<5.0 \times 10^{9} K \)


Which of the following solution is used as washing solution for eyes to free them from microorganisms?
A. \( 1 \% \) Phenol solution
B. \( 2-3 \% \) lodine solution
c. \( 0.2 \% \) Phenol solution
D. Dilute aqueous solution of Boric acid


\( 6 g \) urea and \( 11.8 g \) glucose are dissolved
in \( 100 m l H_{2} O . \) What is the osmotic
pressure at \( 300 K \)
A. 27.06 atm
B. 30 atm
c. 45 atm
D. 13.07 atm


The value of \( \left(n_{2}+n_{1}\right) \) and \( \left(n_{2}^{2}-n_{1}^{2}\right) \) for
\( H e^{+} \) ion in atomic spectrum are 4 and 8 respectively. The wavelength of emitted photon when electron jump
from \( n_{2} \) to \( n_{1} \) is:
\( ^{\mathbf{A}} \cdot \frac{32}{9} R_{H} \)
в. \( \frac{9}{32} R_{H} \)
c. \( \frac{9}{32 R_{H}} \)
D. \( \frac{32}{9 R_{H}} \)


If pitqj is a unit vector perpendicular to \( 4 i+3 j, \) then
A. P= \( -3 / 5 \) and \( q=-4 / 5 \)
B. P=4/5 and q=3/5
c. \( P=2 / 5 \) and \( q=1 / 5 \)
D. None


Evaluate the following definite integral:
\( \int_{0}^{\pi / 2} \cos ^{2} x d x \)


If the resistance of the upper half of a
rigid loop is twice of that of the lower
half, the magnitude of magnetic
induction at the centre is equal to:
A. zero
B. \( \frac{\mu_{0} I}{4 a} \)
c. \( \frac{\mu_{0} I}{12} \)
D. None of these


What is a leap year?
A . 366
в. 365
\( c .364 \)
D. 363


Find all points of local maxima and local minima of the function f given by
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{3}-\boldsymbol{3} \boldsymbol{x}+\boldsymbol{3} \)


Positively charged colloid is coagulated
by positive ion. Enter 1 if true else enter
0


Which of the following gas is used in vehicles?
A. L.P.G.
B. C.N.G
c. Nitrogen
D. Nitrogen dioxide


Fill in the blanks with the appropriate
words.
The net result of glycolysis of one glucose molecule is the. formation
of \( \ldots \ldots \ldots . \) NADH and \( \ldots \ldots . . . . \) ATP


If \( I=\int \frac{d x}{\sqrt{(1-x)(x-2)}}, \) then \( I \) is
equal to
\( A \cdot \sin ^{-1}(2 x-3)+C \)
B. \( \sin ^{-1}(2 x+5)+C \)
\( c \cdot \sin ^{-1}(3-2 x)+C \)
D \( \cdot \sin ^{-1}(5-2 x)+C \)


The number of gas molecules striking per second per square meter of the top surface of a table placed in a room at
\( 20^{\circ} \mathrm{C} \) and 1 atmospheric pressure is of
the order of \( \left(k_{B}=1.4 \times 10^{-23} J / K, \) and \right.
the average mass of an air molecule is
\( \left.\mathbf{5} \times \mathbf{1 0}^{-\mathbf{2 7}} \mathbf{k g}\right) \)
\( A \cdot 10^{27} \)
B. \( 10^{23} \)
\( c \cdot 10^{25} \)
D. \( 10^{2} \)


A solid sphere, solid cylinder, hollow sphere, hollow cylinder of same mass and same radii are rolling down freely on an inclined plane. The body with maximum acceleration is:
A. Solid sphere
B. Solid cylinder
c. Hollow sphere
D. Hollow cylinder


Name a substance which, on heating, leaves behind no residue.
A. Methane gas
B. Ammonium nitrate
c. Camphor
D. All of the above


What are undefined objects in Euclids
geometry?


The area of a rectangular garden of length \( 40 m \), is 1000 sqm. Find the breadth of the garden and its perimeter. The garden is to be enclosed by 3 rounds of fencing, leaving an entrance of \( 4 m . \) Find the cost of fencing garden
at a rate of 250 rupees per meter


A point on the principal axis of a lens, to which light rays parallel to the principal axis converge after passing through the lens, is
A. Centre of curvature
B. Origin
c. Focus
D. optical centre


A particle is performing SHM of amplitude "A" and time period "T". Find the time taken by the particle to go from 0 to \( A / \sqrt{2} \)
A . T/12
B. \( T / \sqrt{2} \)
c. \( \pi / 6 \)
D. \( t / 4 \)


If \( \boldsymbol{x}=\operatorname{cost} \) and \( \boldsymbol{y}=\sin 4 \boldsymbol{t} \) then \( (1- \)
\( \left.\boldsymbol{x}^{2}\right) \boldsymbol{y}_{2}-\boldsymbol{x} \boldsymbol{y}_{1}= \)
A . \( 4 y \)
в. \( -4 y \)
c. \( 16 y \)
D. \( -16 y \)


A solid hemisphere of radius R is
mounted on a solid cylinder of same
radius and density as shown. The height of the cylinder is such that resulting center of mass is \( 0 . \) If the radius of the
sphere is \( 2 \sqrt{2} m \) and the height of the
cylinder is \( n \) meter. Find \( n \)


Find the smallest number by which the following number must be divided to obtain a perfect cube:
128


\( 0.8 \mathrm{J} \) work is done in rotating a magnet
by \( 60^{\circ}, \) placed parallel to a uniform
magnetic field. How much work is done
in rotating it \( 30^{\circ} \) further?
A \( \cdot 0.8 \times 10^{7} \) erg
B. \( 0.8 e r g \)
\( c .8 J \)
D. 0.45


Which antibiotic inhibits interaction
between tRNA and mRNA during bacterial protein synthesis?
A. Streptomycin
B. Tetracycline
c. Erythromycin
D. Neomycin


A patient was administered a chemical agent called Guanfacine hydrochloride after the patient showed the symptoms like shortness of breath and headache.
Guantacme hydrochloride is a known
stimulant of central \( \alpha-2 \) -adrenergic
receptors of the medulla regulating the sympathetic nervous system. The patient in this case must be suffering from
A. Hypertension
B. Hyperslimulation
c. Hyperpolarization
D. None of the above


The sum of two complex numbers \( a+ \)
ib and \( c+ \) id is a real number if
A \( \cdot a+c=0 \)
B. \( b+d=0 \)
\( \mathbf{c} \cdot a+b=0 \)
D. \( b+c=0 \)


The breakdown field strength for dry air
is \( 3 \times 10^{6} \mathrm{V} / \mathrm{m} \). Each of the plates of the
parallel plate capacitor has an area of
\( 0.2 m^{2} . \) The maximum charge that can be
collected is : (Given permittivity of air \( \left.\epsilon_{\circ}=8.85 \times 10^{-12} C^{2} / N m^{2}\right) \)
A. \( 5.3 \mu \) С
в. \( 0.6 \mu \mathrm{c} \)
c. \( 1.5 \mu \) С
D. \( 4.56 \mu \) С


How many moles are there in \( 200 g \) of
Na?


A body starts from rest with uniform acceleration. If its velocity after \( n \) second is \( v, \) then its displacement in
last two seconds is:
A \( \cdot \frac{2 v(n+1)}{n} \)
B. \( \frac{v(n+1)}{n} \)
c. \( \frac{v(n-1)}{n} \)
D. \( \frac{2 v(n-1)}{n} \)


Which of the following quantities remain constant in a planetary system when seen from the surface of the sun.
This question has multiple correct options
A . KE
B. angular speed
c. speed
D. angular momentum
E. binding energy


Name the Indian philosopher who proposed the theory matter.


A gardener waters a lawn with a hose ejecting \( 250 \mathrm{cc} \) of water per second through an orifice of area \( 2.5 \mathrm{sqcm} \)
Find the backward force on the
gardener.
A . \( 0.15 N \)
B. \( 1.25 N \)
c. \( 0.20 N \)
D. \( 0.25 N \)


Behaviour of \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) and \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4} \) is
different Nal because:
A \( \cdot H_{2} S O_{4} \) is stronger acid than \( H_{3} P O_{4} \)
B. \( H_{2} S O_{4} \) is a strong oxidising agent and oxidises colourless gas to coloured vapour
\( \mathrm{c} \cdot H_{3} P O_{4} \) is tribasic acid
D. \( H_{2} S O_{4} \) is a dibasic acid


A series LCR circuit is connected to an
a.c. source of variable frequency. Draw a suitable phasor diagram to deduce the expressions for the amplitude of the current and phase angle.


If \( \int \frac{\boldsymbol{f}(\boldsymbol{x})}{\log (\sin \boldsymbol{x})} \boldsymbol{d} \boldsymbol{x}=\log [\log \sin \boldsymbol{x}]+\boldsymbol{c} \)
\( \operatorname{then} f(x)=\dots \)
A . \( \cot x \)
B. \( \tan x \)
\( c . \sec x \)
D. \( \operatorname{cosec} x \)


At \( 1127 \mathrm{K} \) and 1 atm pressure,
gaseous mixture of \( C O \) and \( C O_{2} \) in
equilibrium with solid carbon has \( 90.55 \% C O \) by mass;
\( \boldsymbol{C}_{(s)}+\boldsymbol{C O}_{2(g)} \rightleftharpoons \mathbf{2} \boldsymbol{C O}_{(\boldsymbol{g})} \)
Calculate \( K_{c} \) for the reaction at the
above temperature


Solution of \( \frac{\boldsymbol{d} \boldsymbol{x}}{\boldsymbol{d} \boldsymbol{y}}+\boldsymbol{m} \boldsymbol{x}=\mathbf{0}, \) where \( \boldsymbol{m}<\mathbf{0} \)
is:
A \( . x=C e^{m y} \)
B . \( x=C e^{-m y} y \)
c. \( x=m y+C \)
D. \( x=C \)


If \( L, C \) and \( R \) denote the inductance, capacitance and resistance
respectively, the dimensional formula
for \( C^{2} \) LR is :
\( \mathbf{A} \cdot\left[M L^{-2} T^{-1} I^{0}\right] \)
B \cdot \( \left[M^{0} L^{0} T^{3} I^{0}\right] \)
\( \mathbf{c} \cdot\left[M^{-1} L^{-2} T^{6} I^{2}\right] \)
D \( \cdot\left[M^{0} L^{0} T^{2} I^{0}\right] \)


Two waves, each having a frequency of \( 100 H z \) and a wavelength of \( 2.0 \mathrm{cm} \) are travelling in the same direction on a string. What is the phase difference between the waves
\( (a) \) if the second wave was produced \( 0.015 s \) later than the first one at the same
place,
(b) if the two waves were produced at a same instant but the first one was produced a distance \( 4.0 \mathrm{cm} \) behind the second one?
\( (c) \) If each of
the waves has an amplitude of \( 2.0 m m \) what would be the amplitudes of the resultant waves in part
\( (a) \) and
\( (b) ? \)


Q Type your question
in it. On testing, at the time of packing, it was noted that there are some faulty pieces in the packets. The data is as
below :
No. of faulty packet Number of
packets
0
1
2
3
4
Total number of packets 500
If one packet is drawn from the box, what
is the probability that all the four devices in the packet are without any fault?
A . 0.5
B. 0.6
c. 0.8
D. 0.9


What should be added to \( x^{2}+x y+y^{2} \)
to obtain \( 2 x^{2}+3 x y \)


Metal nails weighing \( 100 g \) are heated
to \( 100^{\circ} C \) and dropped into a copper calorimeter of mass \( 100 g \) containing \( 40 g \) of water at \( 1^{\circ} C . \) If the resulting
temperature is \( 10^{\circ} \mathrm{C} \), the specific heat of metal is (Sp. heat of copper is
\( 0.1 \mathrm{calg}^{-1 o} C^{-1} \) ):
A . 0.01 calg \( ^{-1} \) o \( C^{-1} \)
B. 0.05 calg\( ^{-1} \) o \( C^{-1} \)
c. 0.03 calg \( ^{-1} \) o \( C^{-1} \)
D. 0.5 calg\( ^{-1} \) o \( C^{-1} \)


The balancing length for a cell is 560 \( \mathrm{cm} \) in a potentiometer experiment. When an external resistance of \( 10 \Omega \) is
connected in parallel to the cell, the balancing length changes by 60cm. The internal resistance of the cell in ohms is
A . 1.6
B. 1.4
c. 1.2
D. 0.12


A small circular ring is kept inside a
larger loop connected to a switch and a
battery as shown. The direction of
induced current when the switch is
made (i) ON (ii) OFF after it was ON for a
long time is:
A. clockwise, anti-clockwise
B. clockwise, clockwise
C. anti-clockwise, clockwise
D. anti-clockwise, anti-clockwise


In the adjoining figure, \( A B=A C \) and
\( A P \perp B C . \) Then:
\( \mathbf{A} \cdot A B=A P \)
B. \( A B<A P \)
c \( . A B>A P \)
D. \( A B \leq A P \)


Two plane mirrors are placed parallel to each other at a distance Lapart. A point
object 0 placed between them, at a distance L/3 from one mirror. Both
mirrors form multiple images. The distance between any two images
cannot be
A \( \cdot \frac{3 L}{2} \)
в. \( \frac{2 L}{3} \)
\( c \cdot 2 L \)
D. \( L \)


Using binomial theorem, prove that
\( 6^{n}-5 n \) always leaves remains 1 when
divided by 25


Find odd one w.r.t.ploidy in bryophytes
A. NCC
B. VcC
c. Spore
D. Foot


If \( \sec 2 A=\operatorname{cosec}\left(A-42^{\circ}\right) \) where \( 2 A \)
is acute angle, then value of \( A \) is
A \( \cdot 44 \)
B \( .22^{\circ} \)
\( c \cdot 21^{\circ} \)
D. \( 66^{\circ} \)


Write the value of \( \cos ^{-1}\left(\cos \frac{5 \pi}{4}\right) \)


The equation of a wave is given by \( \boldsymbol{Y}= \)
\( A \sin \omega\left(\frac{x}{v}-k\right), \) where \( \omega \) is the angular
velocity and \( v \) is the linear velocity. Find
the dimension of \( k ? \)


The dimensions of \( \frac{1}{\mu_{0} \in_{0}} \) is (where
symbols have their usual menaing)
A \( \cdot\left[L^{2} T^{-2}\right] \)
в. \( [A] \)
C \( \cdot\left[M L^{2} T^{-2}\right] \)
D. \( \left[M L^{-2} T^{-2}\right. \)


If \( \boldsymbol{m}\left[\begin{array}{ll}-\mathbf{3} & \mathbf{4}\end{array}\right]+\boldsymbol{n}\left[\begin{array}{ll}\mathbf{4} & -\mathbf{3}\end{array}\right]=\left[\begin{array}{ll}\mathbf{1 0} & -\mathbf{1 1}\end{array}\right] \)
then \( 3 m+7 n= \)
\( A \cdot 3 \)
B. 5
c. 10
\( D \)


\( \ln 2006, \) the IAU adopted a new
definition of a planet. IAU stands
for
A. Indian Astronomical Union
B. International Astronomy of Universe
c. International Astronomical Union
D. Indian Astronomy of Universe


A solid sphere of radius \( r \) and mass \( m \) is spinning about a diameter as axis with
a speed \( \omega_{0} . \) The temperature of the
sphere increases by \( 100^{\circ} \mathrm{C} \) without any
other disturbance. If the coefficient of
linear expansion of material of sphere
is \( 2 \times 10^{-4} /^{\circ} C, \) the ratio of angular
speed at \( 100^{\circ} \mathrm{C} \) and \( \omega_{0} \) is
A . 1:
B. 1: 1.04
\( c \cdot 1.04: \)
D. 1:1.02


When the determinant \( \left|\begin{array}{lll}\cos 2 x & \sin ^{2} x & \cos 4 x \\ \sin ^{2} x & \cos 2 x & \cos ^{2} x \\ \cos 4 x & \cos ^{2} x & \cos 2 x\end{array}\right| \) is expanded in
powers of \( \sin x, \) then the constant term in that expression is
\( A \)
B.
\( c \cdot-1 \)
D.


Numerous vascular bundles occur
scattered in the ground tissue of
A. Monocot stem
B. Monocot root
c. Dicot stem
D. Dicot root


When cobalt trifluoride is treated with
sulphur, the compound formed is :
A. \( S F_{6} \)
в. \( S F_{4} \)
\( c \cdot S_{2} F_{2} \)
D. \( S F_{2} \)


If volume of the cubical tank is
\( 2197000 m^{3} . \) Find the length of its side.


Braille system used for visually challenged person is a:
A. Visual aid
B. Auditory aid
c. Tactual aid
D. Electronic aid


Find \( \frac{d y}{d x} \) where \( \boldsymbol{y}=\sqrt{\frac{\boldsymbol{x}^{2}+\mathbf{1}}{\boldsymbol{x}^{2}+\mathbf{2}}} \)


The length of metallic wire is \( l_{1} \) when
the tension is \( T_{1} \) and \( l_{2} \) when the
tension is \( T_{1} . \) The original length of the wire is
A \( \cdot \frac{l_{1}+l_{2}}{2} \)
в. \( \frac{l_{1} T_{2}+l_{2} T_{1}}{T_{1}+T_{2}} \)
c. \( \frac{l_{1} T_{2}-l_{2} T_{1}}{T_{2}-T_{1}} \)
D. \( \sqrt{T_{1} T_{2} l_{1} l_{2}} \)


In a right angled \( \Delta B A C, \angle B A C=90^{\circ} \)
segment \( A D, B E \) and \( C F \) are the medians
Prove that \( 2\left(A D^{2}+B E^{2}+C F^{2}\right)= \)
\( 3 B C^{2} \)


Which of the following complexes exists as pair of enantiomers?
\( \mathbf{A} \cdot\left[\operatorname{Co}\left(N H_{3}\right)_{4} C l_{2}\right]^{+} \)
B. \( \left[C r(e n)_{3}\right]^{3+} \)
c. \( \left[\operatorname{Co}\left(P\left(C_{2} H_{5}\right)_{3}\right)_{2} C l B r\right. \)
D. \( \operatorname{trans}-\left[\operatorname{Co}(e n)_{2} C l_{2}\right]^{+} \)


An astronaut, inside an earth satellite,
experiences weightlessness because
This question has multiple correct options
A. no external force is acting on him
B. he is falling freely
C. no reaction is exerted by the floor of the satellite
D. he is far away from the earth's surface


A bulb is located on a wall. Its image is to be obtained on a parallel wall with the help of convex lens. If the distance
between parallel walls and lens is \( ^{\prime} d^{\prime} \) then, required focal length of lens placed in between the walls is:
A \( \cdot \) only \( \frac{d}{4} \)
B. only \( \frac{d}{2} \)
c. More than \( \frac{d}{4} \) but less than \( \frac{d}{2} \)
D. Less than or equal to \( \frac{d}{4} \)


What is tincture of iodine? Write its one
use.


Solve
\( \frac{1}{2} \int \frac{(-4+2 x)}{\sqrt{5-4 x+x^{2}}} \)


A current of \( 10 A \) passes through two
very long wires held parallel to each other and separated by a distance of
1 \( m \). What is the force per unit length
between them?


Gypsum is added to clinker during
cement manufacturing to:
A. Decrease the rate of setting of cement
B. Bind the particles of calcium silicate
C. Facilitate the formation of colloidal gel
D. All of the above


A streamlined body:
A. increases friction
B. reduces friction
C . decreases weight
D. increases weight


What type of bond exists between \( \boldsymbol{H} \boldsymbol{F} \)
\( N H_{3}, C_{2} H_{5} O H \) molecules?


Select incorrect reduction process:
\( \mathbf{A} \cdot 2\left[A g(C N)_{2}\right]^{-}+Z n \rightarrow\left[Z n(C N)_{4}\right]^{2-}+2 A g \)
в. \( C u O+H_{2} \rightarrow C u+H_{2} O \)
c. \( Z n O H_{2} \rightarrow Z n+H_{2} O \)
D. \( M g O+C \rightarrow M g+C O \)


Which of the following does not contain material particles?
A. \( \alpha \) -rays
B. \( \beta \) -rays
c. \( \gamma \) -rays
D. Anode rays


The palisade tissue occurs on the surface of the leaf.
A. Adaxial
B. Abaxial
c. Both A and B
D. None of the above


Which ionic hydride is stable upto its melting point?
\( \mathbf{A} \cdot N a H \)
в. \( C a H_{2} \)
c. \( L i H \)
D. \( B a H_{2} \)


In the Lac-operon of Escherichia coli, there are three adjacent structural genes viz., lac \( Z \), lac \( Y \), and lac \( A \). Lac \( A \)
gene codes for
A. Beta glactosidase
B. Beta galactoside transacetylase
c. Beta galactoside permease
D. Polymerase


Which of the following is capable of forming either a branch or a flower?
A. Intercalary meristem
B. Axillary budd
c. vegetative bud
D. None of these


Write a short note on shoulder bone.


If \( y=a \cos (\log x)-b \sin (\log x), \) then
the value of \( x^{2} \frac{d^{2} y}{d x^{2}}+x \frac{d y}{d x}+y \) is
\( A \cdot 0 \)
B.
\( c \cdot 2 \)
D.


A vector \( \vec{r} \) is inclined at equal angles to
\( \boldsymbol{O} \boldsymbol{X}, \boldsymbol{O} \boldsymbol{Y} \) and \( \boldsymbol{O} \boldsymbol{Z} . \) If the magnitude of \( \boldsymbol{r} \)
is 6 units, then \( \vec{r} \) is equal to This question has multiple correct options
A \( \cdot \sqrt{3}(\hat{i}+\widehat{j}+\widehat{k}) \)
B. \( -\sqrt{3}(\hat{i}+\hat{j}+\widehat{k}) \)
c \( \cdot 2 \sqrt{3}(\hat{i}+\hat{j}+\widehat{k}) \)
D. \( -2 \sqrt{3}(\hat{i}+\hat{j}+\widehat{k}) \)


If \( \Delta_{1}=\left|\begin{array}{lll}\boldsymbol{x} & \boldsymbol{b} & \boldsymbol{b} \\ \boldsymbol{a} & \boldsymbol{x} & \boldsymbol{b} \\ \boldsymbol{a} & \boldsymbol{a} & \boldsymbol{x}\end{array}\right| \) and \( \boldsymbol{\Delta}_{2}=\left|\begin{array}{ll}\boldsymbol{x} & \boldsymbol{b} \\ \boldsymbol{a} & \boldsymbol{x}\end{array}\right| \) are
the given determinants, then
A \( \cdot \Delta_{1}=3\left(\Delta_{2}\right)^{2} \)
в. \( \frac{d}{d x}\left(\Delta_{1}\right)=3 \Delta_{2} \)
c. \( \frac{d}{d x}\left(\Delta_{1}\right)=3\left(\Delta_{2}\right)^{2} \)
D. \( \Delta_{1}=3 \Delta_{2}^{3 / 2} / 2 \)


When a hot liquid is mixed with a cold
liquid, the temperature of the mixture
A. first decreases and then becomes constant
B. first increases and then becomes constant
C. continuosly increases
D. is undefined for some time and then becomes nearly constant


The planet Uranus rotates on its axis from
A. east to west
B. west to east
c. north to south
D. south to north


Across the surface of a charged
conductor, the electric:

This question has multiple correct options
A. field id continuous
B. potential is continuous
C. field is discontinuous
D. potential is discontinuous


A compound contains \( C=90 \% \) and
\( \boldsymbol{H}=\mathbf{1 0 \%} . \) Empirical formula of the
compound is :
A. \( C_{15} H_{30} \)
в. \( C_{15} \mathrm{H}_{20} \)
\( \mathbf{c} \cdot C_{3} H_{4} \)
D. \( C_{3} H_{10} \)


The rms value of current in an \( A C \)
circuit is \( 10 A . \) What is the peak
current?
A . \( 14.1 A \)
B. \( 35.2 A \)
\( \mathrm{c} .58 .9 A \)
D. \( 23.5 A \)


How much oxygen is delivered by 100 \( \mathrm{ml} \) of oxygenated blood to the tissues under normal physiological conditions?
\( \mathbf{A} \cdot 15 \mathrm{m} \)
B. \( 10 \mathrm{ml} \)
\( c .5 \mathrm{m} \)
D. 2.5 m


A boat at anchor is rocked by waves whose crests are 100 m apart and
velocity is 25 m/ sec. The boat bounces up once in every:
\( \mathbf{A} \cdot 2500 s \)
в. \( 75 s \)
c. \( 4 s \)
D. \( 0.25 s \)


State True or False.
The magnetic quantum number gives the orientation of electron clouds with
respect to external magnetic field.
A . True
B. False


A gas mixture consists of 2 moles of
oxygen and 4 moles of Argon at temperature T. Neglecting all vibrational modes, the total internal
energy of the system is?
A . \( 4 \mathrm{RT} \)
B. 9 RT
\( c .11 R T \)
D. 15RT


Prisms are used in binoculars. Collect
information why prisms are used in
binoculars.


A Proton of mass \( 1.6 \times 10^{-27} \) kg goes
round in a circular orbit of radius \( 0 . \)
metre under a centripetal force of \( 6 \times \)
\( 10^{-14} N \) then the frequency of revolution
of proton is about?
A . \( 1.25 \times 10^{6} \mathrm{rps} \)
в. \( 2.50 \times 10^{6} \)rps
c. \( 3.75 \times 10^{r} r p s \)
D. \( 5 \times 10^{6} r p s \)


If \( 7.25 \% \) of a number is 2.9 , find the
number.


What is the order of rotational
symmetry of a regular pentagon?
A . 2
B. 5
c. 10
D. 15


What work should be done in order to
squeeze all water from a horizontally located cylinder (figure shown above) during the time \( t \) by means of a constant force acting on the piston? The volume of water in the cylinder is equal
to \( V \), the cross-sectional area of the
orifice to \( s, \) with \( s \) being considerably less than the piston area. The friction
and viscosity are negligibly small
\( A=\frac{1}{2} \rho \frac{V^{3}}{(S t)^{2}} \)
B. \( A=\frac{3}{2} \rho \frac{V^{3}}{(S t)^{2}} \)
\( c \)
D. None of thes


Which of the following is not an inert gas?
A. Helium
B. Xenon
c. Hydrogen
D. Argon


Explain Adsorption theory of Heterogeneous Catalysis.


Evaluate the following:
\( [\mathbf{2} \hat{\mathbf{i}} \hat{\mathbf{j}} \hat{\mathbf{k}}]+[\hat{\mathbf{i}} \hat{\mathbf{k}} \hat{\mathbf{j}}]+[\hat{\boldsymbol{k}} \hat{\mathbf{j}} \mathbf{2} \hat{\mathbf{i}} \)


Find the second derivative of \( \sin 3 x \cos \)
\( 5 x \)


A planet whose mass and radius are
both half of that of earth. Acceleration
due to gravity(g) at its surface should
be:
A \( \cdot 29.4 m / s e c^{2} \)
в. \( 19.6 \mathrm{m} / \mathrm{sec}^{2} \)
\( \mathrm{c} \cdot 9.8 \mathrm{m} / \mathrm{sec}^{2} \)
D. \( 4.9 \mathrm{m} / \mathrm{sec}^{2} \)


Which principle provides that all matter may be considered a wave?
A. Bohr model
B. deBroglie's wave hypothesis
C . Heisenberg's uncertainly principle
D. Quantum theory
E. Atomic theory


If \( A \) and \( B \) are matrices of the same
order, then \( A B^{T}-B A^{T} \) is a
A. Skew-symmetric matrix
B. Null matrix
c. Unit matrix
D. symmetric matrix


Photochromic sunglasses, which darken when exposed to light, contain a
small amount of colourless \( \boldsymbol{A} \boldsymbol{g} \boldsymbol{C l}(\boldsymbol{s}) \)
embedded in the glass. When irradiated with light, metallic silver atoms are produced and the glass darkens.
\[
\boldsymbol{A} \boldsymbol{g} \boldsymbol{C l}(\boldsymbol{s}) \longrightarrow \boldsymbol{A} \boldsymbol{g}(\boldsymbol{s})+\boldsymbol{C l}
\]
Escape of chlorine atoms is prevented
by the rigid structure of the glass and the reaction therefore, reverses as soon
as the light is removed. If \( 310 k J / \) mol of
energy is required to make the reaction proceed, what wavelength of light is
necessary?


Which of the statements given is true for p-type semiconductors
(a) Electrons are majority carriers and trivalent atoms are the dopants.
(b) Electrons are minority carriers and pentavalent atoms are the dopants.
(c) Holes are minority carriers and pentavalent atoms are the dopants.
(d) Holes are majority carriers and trivalent atoms are the dopants.


Which of the oxide gives two oxyacid in
water?
A. \( N_{2} O_{3} \)
a
B. \( N O \)
\( c \cdot N O_{2} \)
D. \( P_{4} O_{10} \)


Which one of the following is \( \alpha \) -amino
acid?
A. \( N H_{2}-C_{6} H_{5}-C H-C H_{2}- \) COOH
В. \( N H_{2}-C H_{2}-C H_{2}-C H_{2}-C H_{2}-C O O H \)
с. \( N H_{2}-C H_{2}- \)СООН
D. \( N H_{2}-C_{6} H_{5}-C H-C H_{2}-C H_{2}-C O O H \)


If \( A \) and \( B \) are symmetric matrices, then \( (A B-B A) \) is skew-symmetric.
A. True
B. False


Gas obtained from animal dung and human excreta is called:
A. biogas
B. water gas
c. waste gas
D. all of these


If \( \boldsymbol{f}(\boldsymbol{x})+\mathbf{2} \boldsymbol{f}(\mathbf{1}-\boldsymbol{x})=\boldsymbol{x}^{2}+\boldsymbol{2} ; \forall \boldsymbol{x} \in \boldsymbol{R} \)
then \( f(x) \) is given by
A \( \cdot \frac{(x-1)^{2}}{3} \)
B. \( -\frac{(x-2)^{2}}{3} \)
c. \( x^{2}-1 \)
D. \( x^{2}-2 \)


The maximum possible number of hydrogen bonds formed by one water molecule is:
A. one
B. two
c. three
D. four


How much water, in liters, must be added to 0.5 L of 6 M HCl to make it 2 M?
A . 0.33
B. 0.5
\( c \cdot 1 \)
D. 1.5
\( E \cdot 2 \)


The increase in boiling point of a solution containing \( 0.6 g \) urea in \( 200 g \)
water is \( 0.50^{\circ} \mathrm{C} \). Find the molal
elevation constant.
A \( \cdot 10 K \) kg mol\( ^{-1} \)
в. \( 10 \mathrm{K} \) g \( \mathrm{mol}^{-1} \)
c. \( 10 K \) kg moll \( l \)
D. \( 1.0 K \) kg mol\( ^{-1} \)


Solved:
\( 65536=4^{n-1} \)


State when a function \( f(x) \) is said to be
increasing on an interval \( [a, b] . \) Test whether the function \( f(x)=x^{2}-6 x+ \)
3 is increasing on the interval [4,6]


A plane mirror is moving in a circle in front of a stationary point object 0 as shown in fig. Then path of image of object is:
A . circle
B. straight line.
c. ellipse
D. parabolic.


In which of the following brain is absent?
A. cyclostomata
B. Pisces
c. Amphibia
D. Protochordata


State whether the following statements
are true or false.

Photosynthesis is the most abundant form of anabolic metabolism in life.
A. True
B. False


The end product of Krebs cycle is
A. Pyruvic acid
B. Citric acid
c. Malic acid.
D. Lactic acid.


The ratio between the areas of two
circles is \( 16: 9 . \) Find the ratio between
their radii:
\( A \cdot 3: 4 \)
B. 16: 9
c. 4: 3
D. None of these


Assertion
Suppose some reaction takes place in a container which has a movable
side,then if it is known that for that
particular reaction its entropy change is negative then we can necessarily say that that reaction is not possible.
Reason
For any process to undergo,its entropy change must be positive.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


\( A \) and \( B \) are two wires. The radius of \( A \)
is twice that of \( B \). They are stretched by
the same load. Then the stress on \( B \) is
A. equal to that on \( A \)
B. four times that on \( A \)
c. two times that on \( A \)
D. half that on \( A \)


The number of ways in which 6 Boys and 5 Girls can sit in a row so that all the
girls may be together is
A . \( 6 ! \times 5 ! \)
B . \( 6 !^{7} P_{5} \)
c. \( (6 !)^{2} \)
D. \( 7 ! \times 5 ! \)


If \( \hat{\boldsymbol{i}}+\widehat{\boldsymbol{j}}, \widehat{\boldsymbol{j}}+\widehat{\boldsymbol{k}}, \hat{\boldsymbol{i}}+\widehat{\boldsymbol{k}} \) are the position
vectors of the vertices of a \( \Delta A B C \)
taken in order, then \( \angle A \) is equal to
A \( \cdot \frac{\pi}{2} \)
в.
c.
D.
E \( \cdot \frac{\pi}{3} \)


A circular coil of 300 turns and
diameter \( 14 \mathrm{cm} \) carries a current of 15
A. The magnitude of magnetic moment associated with the loop is?
A . 51.7 J \( T^{-1} \)
B . 69.2 J \( T^{-1} \)
c. 38.6 J \( T^{-1} \)
D. 19.5 J \( T^{-1} \)


The IUPAC name of given compound is:
A. Butene
B. Butadiene
c. But-1,2-diene
D. But-1, 3-diene


\( \boldsymbol{C}_{\boldsymbol{6}} \boldsymbol{H}_{\boldsymbol{6}}+\boldsymbol{C l}_{2}(\boldsymbol{e} \boldsymbol{x} \boldsymbol{c} \boldsymbol{e} \boldsymbol{s} \boldsymbol{s}) \frac{A \boldsymbol{n} \boldsymbol{h} \boldsymbol{y} \cdot \boldsymbol{A} \boldsymbol{c} \hat{d}_{3}}{d \boldsymbol{a r k}, c o l d} \boldsymbol{P} \)
Product, \( \boldsymbol{P} \) is:
\( \mathbf{A} \cdot C_{6} H_{5} C l \)
B \( . C_{6} H_{4} C l_{2} \)
c. \( C_{6} H_{6} C l_{6} \)
D. \( C_{6} C l_{6} \)


Identify (A) to (F) in the following:
\( F e S O_{4} \stackrel{\Delta}{\rightarrow} \underbrace{(A)}_{\text {solid }}+\underbrace{(B)+(C)}_{g a s} \)
\( (B) \stackrel{O_{2}}{\longrightarrow} \)
\( (C) \quad(A) \stackrel{H_{2} O}{\rightarrow} \)
\( (D) \) brown \( p p t \)
\( (D) \stackrel{\Delta}{\rightarrow}(A) \)
\( (A) \stackrel{H C l}{\rightarrow} \)
deep yellow solution \( (E) \)
\( (E)^{K_{4}\left[F e(C N)_{6}\right]} \)
blue ppt. \( (F) \)


Q Type your question
(i) and refraction \( (r) ? \)
\( A \)
B.
\( c \)
\( D \)


Sugar's colour turns
addition of conc. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \)
A . black
B. blue
c. brown
D. colour less


A wire is bent in the form of an
equilateral triangle of side \( 100 \mathrm{cm} \) and
carries a current of \( 2 A . \) It is placed in
the magnetic field of induction \( 2.0 T \)
directed perpendicular to the plane of the paper. The direction and magnitude
of the magnetic force acting on each side of the triangle will be.
A. \( 2 N \) normal to the side towards centre of the triangle
B. \( 2 N \) normal to the side away from the centre of the triangle
c. \( 4 N \) normal to the side towards centre of the triangle
D. None of these


Construct a \( \triangle A B C \) in which \( A B= \)
\( 5 \mathrm{cm}, B C=6 \mathrm{cm} \) and \( C A=7 \mathrm{m} \)


Is the binary operation \( * \) defined on the set of integer \( z \) by the rule \( a * b=a- \)
\( b+2 \) commutative?


What is the \( p H \) of dil.HCl solution
with concentration \( 10^{-8} \) mol \( / L \) ?
\( A \cdot 7 \)
B. 8
c. 6.98
D. 10


When disc \( B \) is brought in contact with
disc \( A, \) they acquire a common angular velocity in time \( t . \) The average frictional torque on one disc by the other during this period is
A \( \cdot \frac{2 I \omega}{3 t} \)
в. \( \frac{9 \text { Гс }}{2 t} \)
c. \( \frac{9 \text { ा }}{4 t} \)
D. \( \frac{3 I \omega}{2 t} \)


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


The plants excrete \( C O_{2} \) produced as a waste during process in night
time.
A. Photosynthesis
B. Translocation
c. Respiration
D. Transpiration


The important conclusion given by Millikan's experiment about the charge
is
A. Charge is never quantised
B. Charge has no definite value
c. Charge is quantised
D. Charge on an oil drop always increases


An oscillator is nothing but an amplifier
with
A. positive feedback
B. large gain
c. no feedback
D. negative feedback


Explain the relationship between sanitation and disease


Ether is less soluble in water than
alcohol.
A . True
B. False


Three numbers are chosen at random
from the first 20 natural numbers. Then
what is the probability that their product is odd?


The IUPAC name of
\( \left(\boldsymbol{C H}_{3}\right)_{2} \boldsymbol{C H C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{O H} \) is:
A. 3-Methyl butan-1-ol
B. 2-methyl pentan-1-ol
c. 3-ethyl pentan-1-o
D. 2-ethyl butan-1-ol


Draw the histogram of the following
frequency distribution:
\( \begin{array}{ll}\text { Class-Interval } & \text { Frequency } \\ 0-9 & 5 \\ 10-19 & 8 \\ 20-29 & 12 \\ 30-39 & 18 \\ 40-49 & 22 \\ 50-59 & 10\end{array} \)


The temperature at which a body does not radiate energy
\( \mathbf{A} \cdot 0^{0} \mathbf{C} \)
в. \( 0 K \)
c. \( 273 K \)
D. \( 4^{\circ} \) С


A square planar complex is formed by hybridisation of which atomic orbital?
A \( \cdot s, p_{x}, p_{y}, d_{y z} \)
B. \( s, p_{x}, p_{y}, d_{x^{2}-y^{2}} \)
\( \mathbf{c} \cdot s, p_{x}, p_{y}, d_{z} \)
D. \( s, p_{x}, p_{y}, d_{x y} \)


Let \( \boldsymbol{f}: \boldsymbol{N} \rightarrow \boldsymbol{R} \) be such that \( \boldsymbol{f}(\mathbf{1})=\mathbf{1} \)
and \( \boldsymbol{f}(\mathbf{1})+\mathbf{2} \boldsymbol{f}(\mathbf{2})+\mathbf{3} \boldsymbol{f}(\boldsymbol{3})+\ldots+ \)
\( \boldsymbol{n} \boldsymbol{f}(\boldsymbol{n})=\boldsymbol{n}(\boldsymbol{n}+1) \boldsymbol{f}(\boldsymbol{n}), \) for all \( \boldsymbol{n} \in \)
\( N, n \geq 2, \) where \( N \) is the set of natural
numbers and \( R \) is the set of real
numbers. Then, the value of \( f(500) \) is
A. 1000
B. 500
c. \( \frac{1}{500} \)
D. \( \frac{1}{1000} \)


\( A \) and \( B \) are two sets having 3 elements in common. If \( n(A)=5, n(B)=4, \) then
what is \( n(A \times B) \) equal to?
\( \mathbf{A} \cdot \mathbf{0} \)
B. 9
c. 15
D. 20


A point charge \( Q \) is located on the axis
of a disc of radius \( R \) at a distance \( b \)
from the plane of the disc (figure). Show that if one-fourth of the electric flux
from the charge passes through the
disc, then \( R=\sqrt{3} b \)


The length of the longest interval, in
which \( f(x)=3 \sin x-4 \sin ^{2} x \) is
increasing, is
A.
в.
\( c \cdot \frac{3 \pi}{2} \)
D.


From below expressions, by which heat capacity of a body can be measured?
A. Mass of body \( ^{*} \) Specific capacity of body
B. Mass of body + Specific capacity of body
c. Mass of body / Specific capacity of body
D. Mass of body - Specific capacity of body


A turn has a radius of 10 m. If a vehicle
goes round it at an average speed of 18 \( \mathrm{km} / \mathrm{h}, \) what should be the proper angle of banking?
A \( \cdot \tan ^{-1}(1 / 4) \)
B \( \cdot \tan ^{-1}(1 / 2) \)
\( c \cdot \tan ^{-1}(3 / 4) \)
D \( \cdot \tan ^{-1}(5 / 7) \)


Which of the following substances
adsorbs \( \boldsymbol{H}_{2} \) gas most strongly?
A. Platinum black
B. Nickel powder
c. Activated charcoal
D. silica gel


The range of \( f(x)=^{16-x} C_{2 x-1}+^{20-3 x} \)
\( C_{4 x-5} \) is
B . \{0,728\}
C \( \cdot\{728,1617\} \)
D. None of these


A point charge \( Q \) is placed at the centre
of a circular wire of radius \( \boldsymbol{R} \) having
charge q. The force of electrostatic
interaction between point charge and
the wire is:
\( A \)
в. \( \frac{q}{4 \pi \varepsilon_{R}} \)
c. zero
D. none of thes


The number of ordered pairs \( (x, y) \) of
real numbers that satisfy the simultaneous equations.
\( x+y^{2}=x^{2}+y=12 \) is.
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D. 4


Name different body division of
cockroach.


The range of the function \( \boldsymbol{f}(\boldsymbol{x})=\sin \left(\boldsymbol{x} e^{[x]}+\boldsymbol{x}^{2}-\boldsymbol{x}\right), \forall \boldsymbol{x} \epsilon(-1, \infty) \)
where \( [x] \) denotes the greatest integer function is :
\( A \cdot \phi \)
B. [0,1]
c. [-1,1]
D. \( R \)


If \( x=2+2^{\frac{1}{3}}+2^{\frac{2}{3}}, \) then the values of
\( \boldsymbol{x}^{3}-\mathbf{6} \boldsymbol{x}^{2}+\boldsymbol{6} \boldsymbol{x} \) is
\( \mathbf{A} \cdot \mathbf{3} \)
B. 4
\( c \cdot-2 \)
D.


If both roots of the equation \( a x^{2}+ \) \( 2 x a+1+a^{2}-16=0 \) are opposite in
\( \operatorname{sign}, \) then the range of \( a \) is
\( A \cdot(-\infty,-4) \cup(4, \infty) \)
B . (-4,4)
\( \mathbf{c} \cdot(-\infty,-4) \cup(0,4) \)
D \( \cdot(0,4) \)


A family has two children. What is the
probability that both the children are boys, given that atleast one of them is a boy?


Which of the following phenomenon has two angles that are equal to each other?
A. Reflection
B. Refraction
c. Diffraction
D. constructive interference
E. Destructive interference


A total reflecting equilateral prism can be used to deviate a ray of light through:
A \( .30^{\circ} \)
B. \( 60^{\circ} \)
\( c \cdot 75^{\circ} \)
D. \( 90^{\circ} \)


Two points such that each focus for the rays proceedings from the other, are called:
A. Centres of curvature
B. Conjugate foci
c. converging foci
D. None of these


Find the last digit of \( 1^{5}+2^{5}+\ldots . .+ \)
\( 99^{5} \)


A positive charge \( +Q \) is fixed at a point
A. Another positively charged particle of mass \( \mathrm{m} \) and charge \( +\mathrm{q} \) is projected from a point B with velocity u as shown in the figure. The point B is at a large distance from \( A \) and at a large distance d from the line AC. The initial velocity is parallel to the line AC. The point \( C \) is at very large distance from A. Find the minimum distance (in meter) of \( +q \)
from \( +Q \) during the motion. \( [\text { take } Q q= \)
\( \left.4 \pi \epsilon_{0} m u^{2} d\right] \)
A. \( d(1+\sqrt{2}) \)
B . \( d(\sqrt{2}-1) \)
c. \( \frac{d}{(1+\sqrt{2})} \)
D. \( \frac{d}{(\sqrt{2}-1)} \)


Use the identity \( (x+a)(x+b)=x^{2}+ \)
\( (a+b) x+a b \) to find the following
product.
\( \left(2 a^{2}+9\right)\left(2 a^{2}+5\right) \)


In which stage of meiosis the structures, number and shape of chromosomes can be observed?
A. Prophase I
B. Metaphase
c. Anaphase!
D. Telophase I


\( \int \frac{6 x^{2}+2 x+5}{2 x^{3}+x^{2}+5 x+6} d x \)


If expected value in n Bernoulli trials is 8 and variance is \( 4 . \) If \( P(x \leq 2)=\frac{k}{2^{16}} \)
then value of k is?
\( \mathbf{A} \cdot \mathbf{1} \)
B. 137
c. 136
D. 120


Most of the hydrolytic enzymes of lysosomes function at
A . Acidic pH
B. Basic pH
c. Neutral pH
D. None of the above


Suppose \( U= \)
\( \{3,4,5,6,7,8,9,10,11,12,13\}, A= \)
\( \{3,4,5,6,9\}, B=\{3,7,9,5\} \) and \( C= \)
\( \{6,8,10,12,7\} . \) Write down the
following set and draw Venn diagram
for:
\( \boldsymbol{A}^{\prime} \)


A player kicks a football of mass \( 0.5 \mathrm{kg} \) and the football begins to move with a
velocity of \( 10 \mathrm{m} / \mathrm{s} \). If the contact
between the leg and the football lasts for \( \frac{1}{50} \) sec, then the force acted on the football should be
A \( .2500 N \)
в. \( 1250 N \)
c. \( 250 N \)
D. \( 625 N \)


\( -50 \div 7 \) find the quotient and
remainder.


Element with electronic configuration \( 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} \) is a
A . metal
B. non-metal
c. metalloid
D. inert gas


Which of the following correctly represents symbol for silver in Berzelius
system?
\( A \cdot A g \)
B. Am
\( c \cdot s i \)
D. Au


A sealed tube containing phosphorus was weighed and heated carefully. After completion of the reaction, the tube was re-weighed under similar conditions. The weight of the tube will:
A. increases
B. decreases
c. remains same
D. None of the above


Consider the function \( \boldsymbol{f}:(-\infty, \infty) \rightarrow \)
\( (-\infty, \infty) \) defined by \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \frac{x^{2}-a x+1}{x^{2}+a x+1}, 0<a<2 \)
Which of the following is true?
A. \( f(x) \) is decreasing on (1,1) and has a local minimum at \( x=1 \)
B. \( f(x) \) is increasing on (1,1) and has a local maximum at \( x=1 \)
c. \( f(x) \) is increasing on (1,1) but has neither a local maximum nor a local minimum at \( x=1 \)
maximum nor a local minimum at \( x=1 \)