Statement I: Ground state electronic
configuration of chromium atom is \( (A r) 4 s^{1} 3 d^{5} \)
Statement II: Exchange energy is more wtih \( (\boldsymbol{A} \boldsymbol{r}) \boldsymbol{4} \boldsymbol{s}^{1} \boldsymbol{3} \boldsymbol{d}^{5} \) then \( (\boldsymbol{A} \boldsymbol{r}) \boldsymbol{4} \boldsymbol{s}^{2} \boldsymbol{3} \boldsymbol{d}^{4} \)
A. Statement I is true, Statement II is also true Statement is the correct explanation of Statement
B. Statementl is true, statement II is also true:
Statement II is not the correct explanation of Statement
c. statement l is true, Statement II is false
D. Statement I is false, Statement II is true


Allanite wanted to prepare (R) 2-
Methoxy butane using Williamson ether synthesis. He remembered that
Williamson synthesis involves a \( \boldsymbol{S}_{N} \mathbf{2} \)
displacement, which takes place with inversion of configuration. He ordered a
bottle of (S) 2-Butanol for his chiral
starting material. He also
remembered that the \( S_{N} 2 \) goes best on
primary halides so he made methyl
halide and sodium
(S) 2 -butoxide after
warming these reagents together he obtained an excellent yield of 2 -Methoxy
butane.
2-Methoxy butane \( \frac{\text {anhydrous} \boldsymbol{H} \boldsymbol{I}}{\rightarrow} \)
products
Products formed are:
\( \mathbf{A} \cdot H_{3} C-I+C H_{3}-(O H) C H-C H_{2}-C H_{3} \)
B. \( C H_{3}-I+C H_{3}-C H_{2}-C H_{2}-C H_{3} \)
\( \mathbf{c} \cdot C H_{3}-O H+C H_{3}-C H(I)-C H_{2}-C H_{3} \)
D. \( C H_{3}-C H_{2}-I+C H_{3}-(O H) C H-C H_{3} \)


Two molecules of chlorine react with
ethyne to produce -
A . \( 1,1,2, \) 2-tetrachlorethane
B. \( 1,1, \) 2, 2-tetrachlormethane
c. vinyl chloride
D. None of these


Alkynes having four or more carbon atoms are functional isomers of trienes.
A. True
B. False


Acceleration of the particle when its
velocity becomes half of the initial
velocity


If \( \quad x \in\left(\frac{3 \pi}{2}, 2 \pi\right), \) then the value of the expression
\( \sin ^{-1}\left[\cos \left\{\cos ^{-1}(\cos x)+\sin ^{-1}(\sin x)\right\}\right. \)
\( ^{A} \cdot-\frac{\pi}{2} \)
в.
c. 0
D.


Markovnikov's rule for the addition of
hydrogen halides to alkenes states that the incoming hydrogen bonds to the :
A \( \cdot s p^{2} \) carbon with the most hydrogens already
B. \( s p^{2} \) carbon with the fewest hydrogens already
c. \( s p^{3} \) carbon with the most hydrogens already
D. \( s p^{3} \) carbon with the few hydrogens already


Assertion:When \( Q_{c}=K_{c}, \) reaction is
at equilibrium
Reason : At equilibrium, \( \Delta G \) is 0
A. Both assertion and reason are true and reason is the correct explanation of assertion.
B. Both assertion and reason are true but reason is not the correct explanation of assertion
c. Assertion is true but reason is false
D. Both assertion and reason are false


Pithecanthropus was discovered in
A. China
B. Germany
c. Java
D. Africa


Two identical conducting rings \( A \) and \( B \)
of radius \( R \) are rolling over a horizontal
conducting plane with same speed \( v \) but in opposite direction. A constant magnetic field \( B \) is present pointing
into the plane of the paper. Then the
potential difference between the highest points of the two rings is
\( A \)
в. \( 2 B v R \)
c. \( 4 B v R \)
D. none of these
E. answer require


Differentiate w.r.t \( x \)
\( \boldsymbol{y}=\boldsymbol{x}^{2} \sin 2 \boldsymbol{x} \)


Explain the magnetic separation
method.


process is used for the removal
of hardness of water.
A. Calgon
B. Baeyer
c. serpeck
D. Hoope


f \( 3 x-2 y=11 \) and \( x y=12, \) find the
value of \( 27 x^{3}-8 y^{3} \)


A true solution does not show Tyndal
effect, because of the


Vapour pressure of water is \( 360 \mathrm{mm} \mathrm{Hg} \) how much urea should be added to 200
mL water to reduce its vapour pressure by \( 0.5 \% ?(\text { Molecular wt. of urea }=60) \)
A . \( 2.52 g \)
в. 3.33 g
c. \( 3.96 g \)
D. None of these


When two capacitors are connected in parallel the resulting combination has capacitance \( 10 u F . \) The same
capacitors when connected in series results in a capacitance \( 0.5 u F . \) The respective values of individual
capacitors are
A . \( 1.9 u F \) and \( 0.2 u F \)
B . \( (8+2 \sqrt{5}) u F \) and \( (2-2 \sqrt{5}) u F \)
c. \( (5+2 \sqrt{5}) u F \) and \( (5-2 \sqrt{5}) u F \)
D. \( 12 u F \) and \( 17 u F \)
E . \( 5 u F \) and \( 2 u F \)


For an electron with \( n=3 \) has only one
radial node. The orbital angular momentum of the electron will be :
A. 0
B. \( \sqrt{6} \frac{h}{2 \pi} \)
c. \( \sqrt{2} \frac{h}{2 \pi} \)
D \( \cdot 3\left(\frac{h}{2 \pi}\right) \)


In which of the following Lanthanoids oxidation state +2 is most stable?
A . \( \mathrm{c} \)
B. Eu
\( c \cdot T b \)
D. Dy


If \( A \) is a square matrix then \( A-A^{\prime} \) is a
A. diagonal matrix
B. skew symmetric matrix
c. symmetric matrix
D. None of these


Solve:
\( \left(x \frac{d y}{d x}-y\right) \tan ^{-1} \frac{y}{x}=x \)


The equation to the normal to the hyperbola \( \frac{x^{2}}{16}-\frac{y^{2}}{9}=1 \) at (-4,0) is
A \( .2 x-3 y=1 \)
B. \( x=0 \)
\( \mathbf{c} \cdot x=1 \)
D. \( y=0 \)


The change in the entropy of a mole of ideal gas which went through an isothermal process from an initial state
\( \left(P_{1}, V_{1}, T\right) \) to the final state \( \left(P_{2}, V_{2}, T\right) \)
is equal to
A . zero
в. \( R \ln T \)
\( ^{c} \cdot \ln \frac{V_{1}}{V_{2}} \)
D. \( \ln \frac{V_{2}}{V_{1}} \)


During the preparation of phenol from benzene sulfonic acid for the
preparation of sodium benzo sulfonate
from benzene sulfonic acid which of
the following reaction takes place:
A. hydration
B. dehydration
c. chlorination
D. nitratration


Two cylinders \( A \) and \( B \) fitted with pistons contain equal number of moles
of an ideal monoatomic gas at \( 400 K \) The piston of \( A \) is free to move while that of B is held fixed Same amount of heat
energy is given to the gas in each cylinder. If the rise in temperature of the gas in \( A \) is \( 42 K \), the rise in temperature of the gas in \( \mathrm{B} \) is: \( \left(\gamma=\frac{5}{3}\right) \)
A . 21
в. 35 к
\( c \cdot 42 k \)
D. 7ок


A sulphate of a metal (M) on healing evolves two gases \( (\mathrm{B}) \) and \( (\mathrm{C}) \) and an oxide (D). Gas (B) turns acidified
dichromate paper green while gas \( (\mathrm{C}) \) forms a trimer. Compound (D) forms a Lewis acid (E) with HCI (g).
If, the number of \( S \) -S bonds in trimer of
gas
(C) be 'n' and the number of
equivalent M-Cl bonds in one molecule of anhydrous (E) be 'm', Then, \( (m+n) \) is:


When a little sulfuric acid is added to
water in a beaker, the water becomes
hot.


Evidence of eutrophication of water indicates
A. Reduced oxygen demand
B. Rapid decomposition of organic matter
c. Algal bloom
D. Red tide


If there are many forces acting on an
object, it must have a non-zero net (unbalanced) force acting on it.
A. True
B. False


In which group all the elements do not have same number of valence
electrons?
A. zero
B. first
c. second
D. seventh


Potato tuber is a modified
or
Edible part of potato is
A. Stem
B. Bulb
c. Stolon
D. Root


A projectile is fired horizontally with a speed of \( 98 m s^{-1} \) from the top of a hill
\( 490 m \) high. Find the magnitude of
vertical velocity with which the projectile hits the ground. (Take \( \boldsymbol{g}= \)
\( \left.9.8 m / s^{2}\right) \)
A \( \cdot 98 m s^{-1} \)
B. \( 40 \mathrm{ms}^{-1} \)
c. \( 116 \mathrm{ms}^{-1} \)
D. \( 196 \mathrm{ms}^{-1} \)


In which of the above species, starred \( C \)
has \( s p^{2} \) hybridisation?
\( A \cdot p, q \)
B. p, q, r
\( c \cdot p, q, s, t \)
\( \mathbf{D} \cdot \mathbf{q}, \mathbf{s}, \mathbf{t} \)


In the circuit shown in figure in
adjoining figure \( \boldsymbol{E}=\mathbf{1 0} \boldsymbol{V}, \boldsymbol{R}_{1}= \)
\( \mathbf{1} \mathbf{\Omega}, \boldsymbol{R}_{2}=\mathbf{2} \mathbf{\Omega}, \boldsymbol{R}_{3}=\mathbf{3} \mathbf{\Omega} \) and \( \boldsymbol{L}=\mathbf{2} \boldsymbol{H} \)
Calculate value of current \( i_{1}, i_{2} \) and \( i_{3} \)
immediately after key \( S \) is closed.
\( A .3 .3 \) amp \( , 3.3 \) amp \( , 3.3 \) amp
B. 3.3 amp, 3.3 amp, 0 amp
c. 3.3 amp, 0 amp, 0 amp
D. 3.3 amp, 3.3 amp, 1.1 amp


When a current of \( 2 \mathrm{A} \) flows in a battery
from negative to positive terminal, the potential difference across it is 12 V. If a
current of 3 A flowing in the opposite direction produces a potential difference of \( 15 V \), the emf of the battery is?
A . \( 54 v \)
B. \( 13.2 \mathrm{V} \)
c. \( 65 v \)
D. \( 50 v \)


A charge \( Q \) is uniformly distributed over a rod of length \( l \). Consider a hypothetical
cube of edge \( l \) with the centre of the cube at one end of the rod. Find the
minimum possible flux of the electric field through the entire surface of the
cube.


Which coal is the generally the primary source of coke production?
A. Leguminous coal
B. Bituminous coal
c. Black coal
D. All of these


Draw the pressure-temperature and volume-temperature diagrams for an isobaric process of expansion,
corresponding to \( n \) moles of an ideal
gas at a pressure \( P_{0}, \) from \( V_{0} \) to \( 2 V_{0} \)


Explain the working and applications of
SONAR.


Four ten litre flasks are separately filled
with the gases hydrogen, helium, oxygen and ozone at the same
temperature and pressure. The ratio of
the total number of atoms of these
gases present in different flasks would
be?
A .1: 2: 3: 2
B. 2: 1: 2: 3
\( \mathbf{c} \cdot 1: 3: 2: 2 \)


Assertion
The catalytic converter in the car's exhaust system converts polluting exhaust gases into non-toxic gases.
Reason
Catalytic converter contains a mixture of transition metals and their oxides
embedded in the inner support.
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


Represent the molecule \( H_{2} O \) using
Lewis notation.


The probability of an even happens in one trial of an experiment is \( 0.3 . \) Three independent trials of the experiments are performed. Find the probability that the event A happens at least once.
A .0 .657
B. 0.965
c. 0.796
D. 0.509


For which material the poisson's ratio is greater than 1
A. steel
B. Copper
c. Aluminium
D. None of the above


Derive the expression for motional EMF induced in a conductor moving in a uniform magnetic field.


The wave number of electromagnetic radiation emitted during the transition of electron in between the two levels of
\( \mathrm{Li}^{2+} \) ion whose principal quantum numbers sum is 4 and difference is 2
is:
A . \( 3.5 R \)
в. \( 4 R \)
\( c .8 R \)
D. \( 8 / 9 R \)


The velocity time graph of a body
moving in a straight line is shown in the figure. The displacement and distance traveled by the body in 8 s are
A. \( 12 \mathrm{m}, 20 \mathrm{m} \)
B. \( 14 \mathrm{m}, 12 \mathrm{m} \)
\( c \cdot 16 m, 20 m \)
D. \( 12 \mathrm{m} .16 \mathrm{m} \)


The offspring grow out of the parent's body in
A. Hydra
B. Amoeba
c. Paramecium
D. Human


Zinc granules are added in excess to \( \mathbf{5 0 0} \boldsymbol{m L} \) of \( \mathbf{1 . 0} \boldsymbol{M} \) nickel nitrate solution
at \( 25^{\circ} C \) until the equilibrium is reached. If the standard reduction
potentials of \( Z n^{2+} / Z n \) and \( N i^{2+} / N i \)
are -0.75 and -0.24 volt respectively
find out the concentration of \( N i^{2+} \) ions
in solution at equilibrium.


Define Displacement.


If a particle moves according to the law, \( s=6 t^{2}-\frac{t^{3}}{2}, \) then the time at which it
is momentarily at rest
A. \( t=0 \) only
B. \( t=8 \) only
c. \( t=0,8 \)
D. none of these


Compressed air in the tube of a wheel of a cycle at normal temperature suddenly starts coming out from a puncture.The
air inside:
A. starts becoming hotter
B. remains at the same temperature
c. starts becoming cooler
D. may become hotter or cooler depending upon the amount of water vapour present


In which quadrant does the terminal
side of the angle \( 250^{0} \) lie?
A. Quadrant III
B. Quadrant I
c. Quadrant
D. Quadrant IV


Assertion \( \operatorname{Let} a, b \in R, \) and \( I=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right] \) and \( J= \)
\( \left[\begin{array}{cc}\mathbf{0} & \mathbf{1} \\ -\mathbf{1} & \mathbf{0}\end{array}\right] \)
Inverse of \( a I+b J \) is \( c I+d J \) if and only
if
\( \boldsymbol{a c}-\boldsymbol{b d} \neq \mathbf{0} \) and \( \boldsymbol{a} \boldsymbol{d}+\boldsymbol{b} \boldsymbol{c}=\mathbf{0} \)
Reason
\( (\boldsymbol{a} \boldsymbol{I}+\boldsymbol{b} \boldsymbol{J})(\boldsymbol{c} \boldsymbol{I}+\boldsymbol{d} \boldsymbol{J})=(\boldsymbol{a} \boldsymbol{c}-\boldsymbol{b} \boldsymbol{d}) \boldsymbol{I}+ \)
\( (a d+b c) J \)
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 sum of the squares of three distinct
real numbers, which are in \( G . P . \) is \( S^{2} . \) If
their sum is \( \alpha S, \) show that \( \alpha^{2} \in \) \( \left(\frac{1}{3}, 1\right) \cup(1,3) \)


In the Wheatstone's network given, \( \boldsymbol{P}= \)
\( \mathbf{1 0 \Omega}, \boldsymbol{Q}=\mathbf{2 0 \Omega}, \boldsymbol{R}=\mathbf{1 5 \Omega}, \boldsymbol{S}=\mathbf{3 0 \Omega}, \) the
current passing through the battery (of
negligible internal resistance) is :
A . \( 0.36 A \)
3. zero
c. \( 0.18 A \)
D. 0.72 A


A heat engine produces \( 100 \mathrm{J} \) of heat, does 30 Jof work, and emits 70 Jinto a
cold reservoir. What is the efficiency of the heat engine?
A. \( 100 \% \)
в. 70\%
c. 42\%
D. 40\%
E . 30\%


Gas, which in cold(liquid form) expands on further cooling is:
A. Liquid Heliumm
B. Liquid Hydrogen
c. Liquid Ammonia
D. Liquid Oxygen


The velocity of rain with respect to the
man when he is moving down is
\( \mathbf{A} \cdot 3 m / s \)
В. \( 3 \sqrt{3} \mathrm{m} / \mathrm{s} \)
c. \( 4 m / s \)
D. None of these


If the \( H C F \) of 210 and 55 is expressible
in the form \( 210 \times 5+55 y, \) find \( y \)


Given below the phase diagram of
carbon, answer the following questions:
(a) How many triple points are there and
what are the phases that can co-exist at
each triple point?
(b) Which has a higher density, diamond?
A \( . \) (a) \( 1,(b) \) Diamond \( d \)
B. (a) 2, (b) Diamond
c. (a) \( 2, \) (b) Graphite
D. (a) \( 1, \) (b) Graphite


An element \( X(2,8,2) \) combines
separately with \( N O_{3} \) and \( \left(S O_{4}\right)_{2} \)
\( \left(P O_{4}\right)_{3} \) radicals. Write the formulae of
the three compounds so formed. To which group of the periodic tables does the element 'X' belong? Will it form
covalent or ionic compound? Why?


A bullet fired into a trunk of a tree loses
\( 1 / 4 \) of its kinetic energy in traveling a distance of \( 5 \mathrm{cm} . \) Assuming constant
retardation before stopping, it travels a further distance of
A. \( 150 \mathrm{cm} \)
B. \( 1.5 \mathrm{cm} \)
c. \( 1.25 \mathrm{cm} \)
D. \( 15 \mathrm{cm} \)


Root pressure is measured by
A. Manometer
B. Potometer
c. Auxanometer
D. osmometer


The density of \( C O \) at \( 273 K \) and 1 atm
is \( 1.2504 \mathrm{kg} \mathrm{m}^{-3} \). Calculate
(a) root mean square speed (b) the average speed and (c) most probable speed.


Using Trigonometric functions of \( \frac{\boldsymbol{\pi}}{\boldsymbol{4}} \)
Find the value of \( \sin \frac{\pi}{8}=? \)


Write the simplest form of :
\( \tan ^{-1} \frac{\sqrt{1+x^{2}}-1}{x}, x \neq 0 \)


Compound which is added to soap to impart antiseptic properties is
A. sodium laurylsulphate
B. sodium dodecylbenzenesulphonate
\( c \cdot \operatorname{rosin} \)
D. bithional


A clock fixed on a wall shows time 04:
\( 25: 37 . \) What time will its image in a
plane mirror show?
A .07: 43: 32
B. 07: 43: 32
c. 07: 35: 23
D. 43: 27: 36


Why are exothermic reactions said to
have a negative enthalpy?
A. Because energy is flowing from the system to the environment
B. Because energy is flowing from the environment into a closed system.
C. Because endergonic reactions like \( A T P \rightarrow A D P \) have
a negative change in free energy.
D. Because the movement of energy is based on the direction it is flowing.


In which of the following cases, \( \boldsymbol{p} \Leftrightarrow \boldsymbol{q} \) is
true?
A . p is true, q is true
B. p is false, q is true
c. p is true, q is false.
D. None of these.


Differentiate between mass and weight.


In medium wave broadcast a radio can
be tuned in the frequency range 800 \( \mathrm{kHz} \) to \( 1200 \mathrm{kHz} \). In L-C circuit of this
radio effective inductance is \( 200 \mu H \)
what should be the range of the variable capacitor?
\( A \cdot 88 \) pF to 198 pF
B. 98 pF to 198 pF
C. 78 pF to 146 pF
D. 20 pF to 112 pF


Number of atoms in 558.5 gram Fe is:
[At.wt. of \( \left.F e=55.85 g m o l^{-1}\right] \)
A. twice that 60 g carbon
B. \( 6.023 \times 10^{2} \)
c. half that in \( 8 \mathrm{g} \) He
D. \( 558.5 \times 6.023 \times 10^{23} \)


In which of these states water can
exist?
A. Solid
B. Liquid
c. Gas
D. All of the above


Which of the following genes is not transcribed from the promoter for \( \boldsymbol{\beta} \)
galactosidase?
A . Lac- \( z \)
B. Lac-i
c. \( \operatorname{Lac}-\gamma \)
D. Lac-A


\( f(x)=\left\{\begin{array}{ll}\cos x ; & x \geq 0 \\ x+k & ; x<0\end{array} \) find the \right.
value of \( k \) if \( f(x) \) is continuous at \( x=0 \)


Which features make reptiles successful on land?


\( \boldsymbol{P C} \)
\( \mathbf{A} \cdot \overrightarrow{P C}=2 b-a \)
B \( \cdot \overrightarrow{P C}=2 a+b \)
\( \mathbf{c} \cdot \overrightarrow{P C}=2 a-b \)
D. none of these


The largest muscle in human body is
A. Masseter
B. Sartorius
c. stapedius
D. Gluteus


"The exact path of an electron in \( 2 p \) orbital cannot be determined", This statement is based upon:
A. Hund's rule
B. Bohr's's rule
c. Uncertainty principle
D. Aufbau principal


If it is possible to make \( f(x) \) continuous \( \operatorname{at} x=2 \) then \( f(2) \) is equal to
A. 0
B. 2
\( c \cdot 3 \)
\( D \)


Which of the following is not correctly matched?
A. Sodium (ethylenediaminetetraacetato) chromate(II) \( N a_{2}\left[C r\left(C H_{3} C O O\right)_{4}(e n)\right] \)
B. Dichloridobis(ethane-1, 2-diamine) cobalt(III) ion \( \left[\mathrm{Co}(\mathrm{Cl})_{2}(\mathrm{en})_{2}\right]^{+} \)
C. Tris(bipyridyl)iron(II)ion - \( \left[F e\left(N H_{4} C_{5} C_{5} H_{4} N\right)_{3}\right]^{2} \)
D. Ammineaquadibromidocopper(II) \( \left[C u\left(N H_{3}\right)\left(H_{2} O\right) B r_{2}\right] \)
E. Potassium hexacyanoferrate(II) - \( K_{4} \operatorname{Fe}(C N)_{6} \) ]


Consider the statements.
A. 'Oral Rehydration Solution' (ORS)
should be given to cholera or diarrhoea patients at regular intervals.
B. Poliovirus is transmitted through
food or water and ultimately affect
central nervous system.
C. E.coli and Shigella bacteria are responsible for diarrhoea disease.
D. Rhinoviruses are responsible for
common cold.
The correct statements are
A. A and D
B. A and B
\( c \cdot A, C \) and \( D \)
D. All of the above


\( f\left(\mu_{0}=\sqrt{2} \) and the rayjust fail to \right.
emerge from the prism, refractive index
\( \mu \) of the solid will be
\( A \cdot 1.2 \)
B. \( \sqrt{2} \)
\( c \)
D. \( \sqrt{3} / 2 \)


Which of the following is not a quadratic equation
A \( \cdot x-\frac{3}{2 x}=5 \)
в. \( 4 x-\frac{5}{8}=x^{2} \)
c. \( _{x+\frac{1}{x}=9} \)
D. \( 4 x-\frac{2}{3 x}=4 x^{2} \)


Find the volume of a hemisphere whose radius is \( \frac{\mathbf{3}}{\mathbf{2}} \boldsymbol{c m} \)


Which of the following statements are
correct?
A. A meso compound has chiral centres but exhibits no optical activity
B. A racemic mixture is optically inactive because of two equal and opposite rotation of same isomers of the molecules in the mixture.
C. A meso compound has molecules which are superimpossible on their mirror images even though they contain chiral centres
D. a meso compound is optically inactive because the rotation caused by any molecule is cancelled by equal and opposite rotation caused by another molecules that is the mirror image of the first.


The pressure exerted by a liquid of height 'h' is given by :
\( ^{A} \cdot \frac{h}{\rho g} \)
в. \( h \rho g \)
\( c \cdot \frac{h}{\rho} \)
D. hg


The acceleration due to gravity g is determined by dropping an object through a distance of exactly 10 m. The time is to be measured so that the
result is to be good to \( 0.1 \% \). If the
absolute error is \( n \times 10^{-4} \mathrm{S} \), find \( n \)
(Take \( g=10 \mathrm{m} / \mathrm{s}^{2} \) in calculation)
\( A \cdot 7 \)
B. 3
c. 14
D. 6


\( \left|\begin{array}{ccc}-\mathbf{2} \boldsymbol{a} & \boldsymbol{a}+\boldsymbol{b} & \boldsymbol{a}+\boldsymbol{c} \\ \boldsymbol{b}+\boldsymbol{a} & -\boldsymbol{2 b} & \boldsymbol{b}+\boldsymbol{c} \\ \boldsymbol{c}+\boldsymbol{a} & \boldsymbol{c}+\boldsymbol{b} & -\boldsymbol{2 c}\end{array}\right|=\boldsymbol{4}(\boldsymbol{b}+\boldsymbol{c})(\boldsymbol{c}+ \)
\( \boldsymbol{a})(\boldsymbol{a}+\boldsymbol{b}) \)


Which of the following are natura
fibres?
A. wool, cotton, nylon, jute
B. jute, silk, rayon, wool
c. silk, cotton, wool, jute
D. silk,jute, cotton, polyester


Two \( n \times n \) square matrices \( A \) and \( B \) are
said to be similar if there exists a non-
singular matrix \( \boldsymbol{P} \) such that
\( \boldsymbol{P}^{-1} \boldsymbol{A} \boldsymbol{P}=\boldsymbol{B} \)
If \( A \) and \( B \) are similar and \( B \) and \( C \) are
similar, then
A. \( A B \) and \( B C \) are similar
B. \( A \) and \( C \) are similar
c. \( A+C \) and \( B \) are similar
D. none of these


Cells which help in stopping the flow of blood are
A. RBC
в. wвс
c. Thrombocytes/Blood platelets
D. None of the above


\( \int_{-1}^{1} e^{x} d x= \)


Which one of the following statements is CORRECT?
A. Lightning rods are made of insulators
B. A conductor holds charge
c. The earth is an insulator
D. An insulator prevents charge from flowing


In above que. find the condition when
bobbin moves to right-
A. \( R \sin \alpha=r \)
B. Rsin\alpha\( >r \)
c. Rsin\alpha\( <r \)
D. None of these


Differentiate the following functions
with respect to \( x \) :
\( \tan ^{-1}\left(\frac{a+b \tan x}{b-a \tan x}\right) \)


What is malleability?


An electron in \( H \) -atom in ground state
absorbs 1.5 times as much energy as the minimum required for its escape (i.e., \( 13.6 e V) \) from the atom. Calculate
the wavelength of emitted electron.
A . \( \lambda=4.70 \times 10^{-10} \mathrm{m} \)
В. \( \lambda=61 \times 10^{-9} m \)
c. \( \lambda=4.70 \times 10^{-14} \mathrm{m} \)
D. \( \lambda=2.7 \times 10^{-10} \mathrm{m} \)


Calcium chloride is used as a
dehydration agent because:
A. it has a strong affinity for water
B. it has water of crystalline attached to it
c. it loses water when exposed to air
D. it has a high melting point.


What is the value of \( -4 v\left(w^{2}+3 v w\right) \)
given that \( v=1 \) and \( w=4 \)
A . -84
B. 92
\( c .-98 \)
D. -104
E. -112


Generally metals react with acids to give salt and hydrogen gas. Which of the following acids does not give hydrogen gas on reacting with metals (except Mn and Mg)?
A. \( H_{2} S O_{4} \)
в. \( H C l \)
c. \( H N O_{3} \)
D. All of the above


Shyam's monthly income is \( R s .12,000 \)
He saves \( R s .1,200 . \) Find the present of
his saving and his expenditure.


A wire is bent in the form of a square of
side \( 16.5 \mathrm{cm} . \) It is straightened and then bent into a circle. What is the
radius of the circle so formed? \( \left(\text { Taken } \pi=\frac{22}{7}\right) \)


State whether true or false.
Natural magnets are more powerful than artificial magnets.
A. True
B. False


The compound interest on a certain
sum in 3 years at the rate of \( 8 \% \) per annum is how much percentage more
than its simple interest?


Name in IUPAC System:
(a) \( \boldsymbol{K}_{2}\left[\boldsymbol{P t C l}_{6}\right] \)
(b) \( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{6}\right] \boldsymbol{C l}_{3} \)


Q Type your question
from a solid surface is represented by which of the graphs shown in the
figure?
\( A \)
B.
\( c \)
\( D \)


Sap ascends in woody stem, because of
A. Transpiration pull
B. Capillarity
c. Molecular adhesion
D. Photosynthesis


Five forces \( \vec{F}_{1}, \vec{F}_{2}, \vec{F}_{3}, \vec{F}_{4} \) and \( \vec{F}_{5} \) are
acting on a particle of mass \( 2.0 \mathrm{kg} \) so that it is moving with \( 4 m / s^{2} \) in east direction. If \( \vec{F}_{1} \) force is removed, then
the acceleration becomes \( 7 \mathrm{m} / \mathrm{s}^{2} \) in north, then the acceleration of the block if only \( \vec{F}_{1} \) is acting will be :
A \( \cdot 16 m / s^{2} \)
B . \( \sqrt{65} \mathrm{ms}^{2} \)
c. \( \sqrt{260} \mathrm{ms}^{2} \)
D. \( \sqrt{3} 3 m s^{2} \)


Assertion
Two different reactions can never have
same rate of reaction.
Reason
Rate of reaction always depends only on
frequency of collision and Arrhenius
factor.
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 energy required for the excitation of
carbon atom is
A. 6584 KJ/ mol
в. 827.0 KJ/ mol
c. 341.0 KJ/ mo
D. 610.0 KJ/ mol


If the slope of P-T graph for a given mass
of a gas increases, then the volume of the
gas
A. Increases
B. Decreases
C. Does not change
D. May increase or decrease


The slope of any line which is parallel to the \( x \) -axis is
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot-1 \)
\( D \)


The number of such numbers which are
divisible by two and five (all digits are not different) is
A . 125
B. 76
\( c \cdot 65 \)
D. 100


The compound \( X \) is:
\( \mathbf{A} \cdot B_{2} H_{6} \)
B. \( B_{2} O_{3} \)
\( \mathbf{C} \cdot\left[B(O H)_{4}\right] \)
D. none of these


The greatest number of antimicrobic allergies is reported for which drug?
A. Sulfonamides
B. Quinolones
c. Tetracycline
D. Penicillin


State whether True or False.
Divide: \( x^{6}-8 \) by \( x^{2}-2, \) then the
answer is \( x^{4}+2 x^{2}+4 \)
A. True
B. False


Which of the following configurations represent the metallic element?
A .2,8,8
B. 2, 8, 7
c. 2,8,2
D. 2, 8,4


At Jammu temperature was \( -5^{\circ} \mathrm{C} \) on
Monday and then it dropped by \( 2^{\circ} \mathrm{C} \) on
Tuesday. What was the temperature of Jammu on Tuesday


\( \Delta A B C \sim \)
4. \( \Delta Q P R \)
8. \( \Delta P Q R \)
c. \( \Delta R P Q \)
D. \( \Delta P R Q \)


The structures of \( \boldsymbol{O}_{3} \) and \( \boldsymbol{N}_{3}^{-} \) are :
A. linear and bent, respectively
B. both linear
c. both bent
D. bent and linear, respectively


The volume of sphere with radius \( 3 c m \)
is \( c m^{3} \)
A . \( 14 \pi \)
B. \( 18 \pi \)
\( c \cdot 2 \pi \)
D. \( 36 \pi \)


Given that:
\( \boldsymbol{A}(s) \longrightarrow \boldsymbol{A}(l) ; \boldsymbol{\Delta} \boldsymbol{H}=\boldsymbol{x} \)
\( \boldsymbol{A}(l) \longrightarrow \boldsymbol{A}(\boldsymbol{g}) ; \boldsymbol{\Delta} \boldsymbol{H}=\boldsymbol{y} \)
The heat of sublimation of A will be:
A. \( x-y \)
в. \( x+y \)
\( \begin{array}{llll}\mathbf{c} \cdot x & \text { or } & y\end{array} \)
D. \( -(x+y) \)


Sulfide ion in alkaline solution reacts
with solid sulfux to form polysulfide ions having formules \( S_{2}^{-2}, S_{3}^{2-}, S_{4}^{2-} \) and so on. The equilibrium constant for the formation of \( S_{2}^{2-} \) is \( 12\left(K_{5}\right) \& \) for the formulation of \( S_{3}^{2-} \) is \( 132\left(K_{2}\right), \) both
from \( \mathrm{S} \) and \( S^{2-} . \) What is the equilibrium content for the formation of \( S_{3}^{2-} \) from \( S_{2}^{2-} \) and \( s ? \)
A. 11
в. 12
\( c \cdot 132 \)
D. None of these


In the figure given, \( A B \) is a mirror, \( P Q \) is
the incident ray and \( Q R \), the reflected
ray. If \( \angle \mathrm{PQR}=112^{\circ}, \) find \( \angle \mathrm{PQA} \)


symmetry exists when the figure can be rotated and the image is identical to the original.
A. Rotational
B. Linear
c. Reflection
D. Non-linear


Which of the following is a synthetic indicator?
A. Methyl violetttet thet
B. Alizarin yellow R
c. Methyl red
D. All of above


The radius of a sphere is \( 3.5 \mathrm{cm} \). Find
the surface area and volume.


An irreversible process can be described as a thermodynamic process
that:
A. maintains equilibrium
B. leaves equilibrium
\( c . \) is slow
D. None of these


Mixotrophic (dual mode) nutrition is a characteristic of
A. Paramoecium
B. Amoeba
c. Plasmodium
D. Euglena


A car of mass \( \mathrm{m} \) is moving on a level
circular track of radius R. If \( \mu_{s} \)
represents the static friction between
the road and tyres of the car, the maximum speed of the car in circular motion is given by:
A \( \cdot \sqrt{R g / \mu_{s}} \)
B . \( \sqrt{m R g / \mu_{s}} \)
\( \mathrm{c} \cdot \sqrt{\mu_{s} R g} \)
D. \( \sqrt{\mu_{s} m R g} \)


Find the mean of the following First eight even natural numbers.


The horizontal component of earth's magnetic field at a place is \( 3 \times 10^{-4} T \) and the dip is \( \tan ^{-1}\left(\frac{4}{3}\right) \cdot A \) metal rod of length \( 0.25 m \) is placed in \( N-S \)
direction and is moved at a constant
speed of \( 10 \mathrm{cm} s^{-1} \) towards the east
The emf induced in the rod will be
A \( .1 \mu V \)
B. \( 5 \mu V \)
c. \( 7 \mu V \)
D. \( 10 \mu V \)


Among the electrolytes
\( N a_{2} S O_{4}, C a C l_{2}, A l_{2}\left(S O_{4}\right)_{3} \) and
\( N H_{4} C l, \) the most effective coagulating
agent for \( S b_{2} S_{3} \) solution is:
A \( \cdot N a_{2} S O_{4} \)
в. \( C a C l_{2} \)
\( \mathbf{c} \cdot A l_{2}\left(S O_{4}\right) \)
D. \( N H_{4} C l \)


State true or false:
\( A B C D \) is a parallelogram. \( P \) and \( Q \) are the mid-points of sides \( A B \) and \( A D \) respectively. Hence, area of triangle \( A P Q=\frac{1}{8} \) of
the area of parallelogram \( A B C D \)
A. True
B. False


The number of atoms present in 52
moles of \( H e \) are \( x N_{o}, \) then \( x \) is :


The body temperature of a patient in
\( 104^{\circ} F . \) Calculate his body temperature in celsius scale.


In experiment of convection heat transfer, water inside the pipe is heated by which of the following principles,
A. free convection+conduction
B. free convection
c. forced convection
D. mixed convection


Find the axis of symmetry of the
parabola shown
A \( . x=1 \)
в. \( x=2.5 \)
\( \mathbf{c} \cdot x=3 \)
D. None of these


Which is called stranger gas?
A. \( K r \)
в. \( X e \)
\( \mathrm{c} . \) Не
D. Ne


Find the principal value of the following
\( \tan ^{-1}\left(\tan \frac{7 \pi}{6}\right) \)


Peroxide ion
(i) has five completely filled antibonding molecular orbitals
(ii) is diamagnetic
(iii) has bond order one
(iv) is isoelectronic with neon
Which one of these is correct?
A. (ii) and (iii)
B. (i), (ii) and (iv)
c. (i), (ii) and (iii)
D. (ii) and (iv)


Ratio of the greatest and least focal distances of a point on the ellipse \( 4 x^{2}+9 y^{2}=36 \) is:
A. \( 4+\sqrt{5}: 4-\sqrt{5} \)
B. \( 5+\sqrt{5}: 4-\sqrt{3} \)
c. \( 3+\sqrt{5}: 3-\sqrt{5} \)
D. \( \sqrt{7}: 2 \)


Find the total surface area of a cube
with side \( 5 \mathrm{cm} \)


Find two numbers whose arithmetic
mean is 34 and the geometric mean is
16


The cambium which produces cork is called as
A. Phelloderm
B. Phellogen
c. Periblem
D. Plerome


What is \( \operatorname{cis} 0 ? \)


The radius of \( \boldsymbol{H}- \) atom in its ground
state is \( 0.53 A^{\circ} . \) The radius of \( L i^{2+} \) in
the similar is:
\( \mathbf{A} \cdot 0.058 A^{\circ} \)
B. \( 0.171 A^{\circ} \)
c. \( 0.706 A^{\circ} \)
D. \( 1.06 A^{\circ} \)


Solve the following pair of simultaneous equations:
\( \frac{\boldsymbol{x}}{\mathbf{3}}+\boldsymbol{y}=\mathbf{1 . 7} \) and \( \frac{\mathbf{1 1}}{\boldsymbol{x}+\underline{\boldsymbol{y}}}=\mathbf{1 0} \) for all
\( \left[\boldsymbol{x}+\frac{\boldsymbol{y}}{\mathbf{3}} \neq \mathbf{0}\right] \)
A \( . x=2 \) and \( y=7 \)
В. \( x=0.9 \) and \( y=-2.5 \)
c. \( x=0 \) and \( y=-4 \)
D. \( x=0.6 \) and \( y=1.5 \)


Electrons accelerated from rest by an electrostatic potential are collimated and sent through a Young's double slit setup. The figure width is w. If the accelerating potential is doubled then the width is now close to.
\( \mathbf{A} \cdot 0.5 \mathrm{w} \)
в. 0.7 w
c. \( 1.0 \mathrm{w} \)
D. 2.0 w


A photon and electron have got the same de Broglie wavelength. Explain
which has greater total energy.


Nature of \( C O \) when it reacts with
NaOH is acidic. State True or False:
A . true
B. false
c. neither true nor false
D. none of the above


Which of the following are peroxoacids
of sulphur?
\( \mathbf{A} \cdot H_{2} S O_{5} \) and \( H_{2} S_{2} O_{8} \)
\( \mathbf{B} \cdot H_{2} S O_{5} \) and \( H_{2} S_{2} O_{7} \)
\( \mathbf{c} \cdot H_{2} S_{2} O_{7} \) and \( H_{2} S_{2} O_{8} \)
D. \( H_{2} S_{2} O_{6} \) and \( H_{2} S O_{5} \)


In context of the lanthanoids, which of
the following statements is not correct?
A. There is a gradual decrease in the radii of the members with increasing atomic number in the series
B. All the members exhibit + 3 oxidation state
c. Because of similar properties the separation of lanthanoids is not easy
D. Availability of 4f electrons results in the formation of compounds in +4 state for all the members of the series


toppr
Q Type your question
B.
\( \mathbf{C} \)
\( D \)


Man dies in an atmosphere of carbon
monoxide because it :
A \( \cdot \) combines with the \( O_{2} \) present in the body to form \( C O_{2} \)
B. reduces the organic matter of tissues.
c. combines with hemoglobin of blood, making it incapable of absorbing \( O_{2} \)
D. dries up the blood


State Ohm's Law using a suitable experiment,explain the terms involved and draw its graphical representation.


Transition metals and their compounds
catalyse reactions because:
A. they have completely filled \( s \) - subshell.
B. they have a comparable size due to poor shielding of d-subshell.
C. they introduce an entirely new reaction mechanism with lower activation energy.
D. they have variable oxidation states.


A wheel makes 240 revolutions in one
minute The measure of the angle it
describes at the centre in 15 seconds is
\( \mathbf{A} \cdot 60 \pi \)
в. \( 120 \pi \)
\( c \cdot 8 \pi \)
D. \( \pi \)


Which characteristic property of the
fungi made them be placed in a separate kingdom?
A. Cell wall composition
B. Cell wall structure
C. Nutrition
D. None of these


A cricket ball of mass 500 gm strikes a bat normally with a velocity \( 30 \mathrm{m} / \mathrm{s} \) and rebounds with a velocity \( 20 \mathrm{m} / \mathrm{s} \) in the opposite direction. The impulse of the force exerted by the ball on the bat is:
A. \( 0.5 \mathrm{N} . \)
B. 1.0 N.s
c. 25 N.
D. 50 N.s


Temperature for both sample and reference vary from industry to industry. Is the statement True or False


Which is last step?
4. \( (a) \)
3. \( (b) \)
\( (c) \)
2


Solubility product of a salt \( A B \) is \( 1 \times \) \( 10^{-8} \) in a solution in which
concentration of \( A \) is \( 10^{-3} \) M. The salt
will precipitate when the concentration of B becomes more than:
A \( \cdot 10^{-4} \)
B. \( 10^{-7} \)
\( \mathrm{c} \cdot 10^{-6} \)
D. \( 10^{-5} \)


Solve:- \( \sin ^{-1}(\cos x) \)


Structure of \( X e F_{6} \) is octahedron with
\( s p^{3} d^{3} \) hybridization of Xe.
A. True
B. False


Two moles of \( N_{2} \) and two moles of \( H_{2} \)
are taken in a closed vessel of 5 liters
capacity and suitable conditions are provided for the reaction. When the equilibrium is reached, it is found that
a half mole of \( N_{2} \) is used up. The
equilibrium concentration of \( \boldsymbol{N} \boldsymbol{H}_{3} \) is:
A . 0.3
B. 0.4
\( c .0 .2 \)
D. 0.1


We can see a non-luminous object when
light:
A. emitted by the object falls on the eye
B. is reflected from the object towards our eye
C . completely passes through the object
D. gets completely absorbed by the object


Count the total number of \( X-O \) bonds
having equal length in \( \boldsymbol{H} \boldsymbol{S} \boldsymbol{O}_{4}^{-} \) and
\( \boldsymbol{S}_{3} \boldsymbol{O}_{6}^{2-} \) respectively. (If the answer is 5 and 3 then represent as 53 )
A . 36
B. 40
\( c \cdot 42 \)
D. 44


\( \mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}(\mathrm{s}) \leftrightharpoons 3 \mathrm{Ca}^{2+}(\mathrm{aq})+2 \mathrm{PO}_{4}^{3-}(\mathrm{aq}) \)
Find the equilibrium expression for the
dissolution of \( \boldsymbol{C a}_{3}\left(\boldsymbol{P} \boldsymbol{O}_{4}\right)_{2} ? \)
\( \mathbf{A} \cdot \mathbf{K}_{s p}=\left[\mathbf{C} \mathbf{a}^{2+}\right]^{3}\left[\mathbf{P} \mathbf{O}_{4}^{3-}\right]^{2} \)
B. \( \kappa_{s p}=\left[\mathrm{Ca}^{2+}\right]^{2}\left[\mathrm{PO}_{4}^{3-}\right]^{3} \)
C. \( \kappa_{s p}=\left[\mathrm{Ca}^{2+}\right]\left[\mathrm{PO}_{4}^{3-}\right] /\left[\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}\right] \)
D. \( \kappa_{s p}=\left[\mathrm{Ca}^{2+}\right]^{3}\left[\mathrm{PO}_{4}^{3-}\right]^{2} /\left[\mathrm{C} \mathrm{ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}\right] \)
E \( \cdot K_{s p}=\left[\mathrm{Ca}^{2+}\right]^{2}\left[\mathrm{PO}_{4}^{3-]}\right]^{3} /\left[\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}\right] \)


Which protein is found in maximum
amount
A. Catalase
B. Zinc carbonic anhydrase
c. Transferase
D. RUBISCO


What percentage of \( C O_{2} \) is transported
as \( H b C O_{2} ? \)
A . 42 \%
B . 10 \%
c. 70 \%
D. 50\%


Two thin wire rings each having a
radius \( R \) are placed at a distance
d apart with their axes coinciding. The
charges on the two rings are \( +q \) and \( -q \) The potential difference between the
centres of the two rings is
A \( \cdot \frac{Q \cdot R}{4 \pi \varepsilon d^{2}} \)
B \( \cdot \frac{Q}{2 \pi \varepsilon_{0}}\left[\frac{1}{R}-\frac{1}{\sqrt{R^{2}+d^{2}}}\right] \)
c. \( \frac{Q}{4 \pi \varepsilon_{0}}\left[\frac{1}{R}-\frac{1}{\sqrt{R^{2}+\bar{d}^{2}}}\right] \)
D.


When an ac source of voltage \( \boldsymbol{V}= \)
\( V_{0} \sin 100 t \) is connected across a
circuit, the phase difference between
the voltage \( V \) and current lin the circuit
is observed to be \( \pi / 4, \) as shown in
figure. If the circuit consists
possibly only of RC or RL or LC in series,
find possible values of two elements.
A \( . R=1 k \Omega, C=10 \mu F \)
B. \( R=1 k \Omega, C=1 \mu F \)
c. \( R=1 k \Omega, L=10 m H \)
D. \( R=10 k \Omega, L=10 m H \)


On igniting \( F e_{2} O_{3} \) at \( 1400^{\circ} C \)
the product obtained is
A. \( F e_{2} O_{3} \) melt
B. FeO
\( \mathrm{c} \cdot F e_{3} O_{4} \)
D. metallic iron


\( \operatorname{Let} \vec{A}=\hat{i} A \cos \theta+\hat{j} A \sin \theta, \) be any
vector. Another vector \( \vec{B} \) which is normal to \( \vec{A} \) is :
A \( . \hat{i} B \cos \theta+\hat{j} B \sin \theta \)
B. i \( B \) sin \( \theta+\hat{j} B \cos \theta \)
c. \( \hat{i} B \sin \theta-\hat{j} B \cos \theta \)
D. \( \hat{i} B \cos \theta-\hat{j} B \sin \theta \)


\( \sum_{r=1}^{n} \tan ^{-1}\left(\frac{2^{r-1}}{1+2^{2 r-1}}\right) \) is equal to:
\( \mathbf{A} \cdot \tan ^{-1}\left(2^{n}\right) \)
B \cdot \( \tan ^{-1}\left(2^{n}\right)-\frac{\pi}{4} \)
c. \( \tan ^{-1}\left(2^{n+1}\right) \)
\( \mathbf{D} \cdot \tan ^{-1}\left(2^{n+1}\right)-\frac{\pi}{4} \)


\( \int x \cos ^{-1} x d x \)


Boyle's law is valid for real gases at :
a) low pressure
b) high pressure
c) low temperature
d) high temperature
\( A \cdot a, c \)
в. а,
\( c \cdot b, c \)
D. b,


By examine the chest the chest \( X- \) ray probability that \( T . B \) is detected when a
person is actually suffering is \( 0.99 . \) The probability that the doctor diagnoses incorrectly that a person has \( T . B \) on the bases of \( X- \) ray is \( 0.001 . \) In a certain city 1 in 1000 person suffers from \( T . B \) A person is selected at random is
diagnoses to have \( T . B \). What is the
chance that the actually has \( T . B ? \)


The values of \( X_{L}, X_{C} \) and \( R \) in series
with an A.C. circuit are \( 8 \Omega, 6 \Omega \) and \( 10 \Omega \)
respectively. The total impedance of the circuit will be
\( \Omega \)
A . 10.2
B. 12.2
c. 10
D. 24.4


Identify what happens to a stream of \( \alpha \)
particles that is shoot at a thin sheet of gold foil in a rutherford experiment?
A. All of the particles pass straight through
B. A few of the particles bounce back at \( 180^{\circ} \)
C. All of the particles bounce back at \( 180^{\circ} \)
D. Most of the particles are absorbed by the foil
E. None of the particles are deflected by more than \( 45^{\circ} \)


Solid PCls exists as:
A \( . \) PCls molecule
в. \( \mathrm{P}_{2} \mathrm{Cl}_{10} \)
\( \mathbf{c} \cdot\left[\mathbf{P} \mathrm{Cl}_{4}\right]^{+} \) and \( \left[\mathrm{PCl}_{6}\right] \)
D. None of these


The function of tracheal hair is to
A. Pass mucus out
B. Pass mucus in
c. Pass air out
D. Pass air in


The osmotic pressure of a decimolar
solution of glucose at \( 30^{\circ} \mathrm{C} \) is :
\( \mathbf{A} \cdot 24.88 \mathrm{atm} \)
B. 2.488 atm
\( \mathbf{c} .0 .248 \mathrm{atm} \)
D. \( 189.09 \mathrm{cm} \)


For what \( a<0 \) does the inequality \( \int_{a}^{0}\left(3^{-2 x} 2.3^{-x}\right) d x \geqslant 0 \) hold true?


The graph of the equation \( y=a \) is a
straight line parallel to
A . \( x \) -axis
B. \( y \) -axis
c. cannot be determined
D. Not Paralle


Checking of reradiating heat by
atmospheric dust, \( O_{3}, C O_{2} \) and water vapours is
A. Ozone layer effect
B. Radioactive effect
c. Greenhouse effect
D. Solar effect


The resistance of a conductor at \( 20^{\circ} \mathrm{C} \) is
3.15 ohm and at \( 100^{\circ} \mathrm{C} \) is 3.75 ohm.
Determine the temperature co-efficient of resistance of the conductor. What will
be the resistance of the conductor at 0
\( ^{o} C ? \)


The slope and \( y \) -intercept of the
following line are respectively
\( \mathbf{5} \boldsymbol{x}-\mathbf{8} \boldsymbol{y}=-\mathbf{2} \)
A \( \cdot \) slope \( =m=-\frac{5}{8} \) and \( y \) -intercept \( =\frac{1}{4} \)
B. slope \( =m=\frac{5}{8} \) and \( y \) -intercept \( =-\frac{1}{4} \)
c. slope \( =m=-\frac{5}{8} \) and \( y \) -intercept \( =-\frac{1}{4} \)
D. slope \( =m=\frac{5}{8} \) and \( y \) -intercept \( =\frac{1}{4} \)


The standard Gibbs energy change at \( 300 K \) for the reaction \( 2 A \rightleftharpoons B+C \) is
\( 2494.2 J . \) At a given time, the composition of the reaction mixture is
\( [\boldsymbol{A}]=\frac{1}{2},[\boldsymbol{B}]=\mathbf{2},[\boldsymbol{C}]=\frac{1}{2} . \) The reaction
proceeds in the:
\( [\boldsymbol{R}=\mathbf{8 . 3 1 4} \boldsymbol{J} / \boldsymbol{K} / \boldsymbol{m o l}, \boldsymbol{e}=\mathbf{2 . 7 1 8}] \)
A. Reverse direction because \( Q<K_{c} \)
B. Forward direction because \( Q>K_{c} \)
c. Reverse direction because \( Q>K_{c} \)
D. Forward direction because \( Q<K_{c} \)


The diagram below shows a lever of uniform mass, supported at the middle point. Four coins of equal masses are placed at mark 4 on the left hand side. Where should be 5 coins of same mass,
as that of previous coins be located to balance the lever?


If \( \boldsymbol{A}=[\boldsymbol{a} \boldsymbol{i} \boldsymbol{j}] \) is a matrix of order \( 2 x \boldsymbol{2} \)
such that \( |A|=15 \) and cij represents
the co factor of aij then find \( a_{21} c_{21}+ \)
\( \boldsymbol{a}_{22} \boldsymbol{c}_{22} \)


In Lloyd's single mirror method we have
A. Both sources virtual
B. One source virtual and one real
c. Both sources real
D. None of these


Formula unit mass of \( C a C O_{3} \) is :
A. \( 104 u \)
B. \( 106 u \)
c. \( 100 u \)
D. \( 1144 u \)


Prove that \( : \frac{1}{\sin 10^{\circ}}-\frac{\sqrt{3}}{\cos 10^{\circ}}=4 \)


There are 44 students in class \( X \) of \( a \)
school of whom 32 are boys and 12 are girls. The class teacher has to select one student as a class representative. He writes the name of each student on a
separate card, the cards being identical. Then he puts cards in a bag
and stir them thoroughly. He then draws one card from the bag. What is the probability that the name written on the card is the name of a girl?
A \( \cdot \frac{1}{11} \)
B. \( \frac{5}{11} \)
\( c \cdot \frac{7}{11} \)
D. None of these


Roots of the equations \( x^{2}-3 x+2=0 \)
are
A. 1,-2
B . -1,2
c. -1,-2
D. 1,2


Define the term aestivation


The Sl unit for mass is kg.
A. True
B. False


Which of the following statements is
true concerning ethene?
A. Both carbon atoms are \( s p^{2} \) hybridized and the molecule is planar
B. Both carbon atoms are \( s p^{2} \) hybridized and all bond
angles are approximately \( 109.5^{\circ} \)
C. One carbon atom is \( s p \) hybridized while the other is \( s p^{2} \)
D. Both carbon atoms are \( s p^{3} \) hybridized and all bond angles are approximately \( 109.5^{\circ} \)
E. Both carbon atoms are \( s p \) hybridized and the molecule
is planar


Give three properties of electric charge.


Which sugar is present in nucleic acid
A. Pentose
B. Hexose
c. Fructose
D. Glucose


A bullet of mass \( 20 \mathrm{g} \) travelling horizontally with a speed of \( 500 \mathrm{m} / \mathrm{s} \)
passes through a wooden block of mass
10.0kg initially at rest on a surface. The bullet emerges with a speed of \( 100 \mathrm{m} / \mathrm{s} \)
and the block slides \( 20 \mathrm{cm} \) on the
surface before coming to rest, the coefficient of friction between the block
and the surface. \( \left(\boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{2}\right) \)
A . 0.16
B. 0.8
c. 0.32
D. 0.24


Thermal electricity is generated from:
A . oil
B. coal
c. gas
D. all of the above


Which polymers occur naturally?
A. Starch and nylon
B. Cellulose and nylon
c. starch and cellulose
D. Protiens and PVC


Rutherford's experiment, which established the nuclear model of the
atom, used a beam of:
A. \( \beta \) -particles, which impinged on a metal foil and got absorbed
B. \( \gamma \) -rays, which impinged on a metal foil and ejected electrons
c. helium atoms, which impinged on a metal foil and got scattered
D. helium nuclei, which impinged on a metal foil and got scattered


In an equilateral triangle \( A B C, D \) is a point on side \( B C \) such that \( B D=\frac{1}{3} \)
Prove that \( 9 A D^{2}=7 A B^{2} \)


From among the elements, choose the
following:
\( \mathrm{Cl}, \mathrm{Br}, \mathrm{F}, \mathrm{O}, \mathrm{Al}, \mathrm{C}, \mathrm{Li}, \mathrm{Cs} \) and \( \mathrm{Xe} \)
The element which belongs to zero
group.


Evaluate \( \lim _{x \rightarrow 2} \frac{7 x^{2}-11 x-6}{3 x^{2}-x-10} \)
A \( \cdot \frac{17}{11} \)
в. \( \frac{11}{17} \)
c. \( \frac{17}{14} \)
D. \( -\frac{17}{11} \)


Evaluate:
\( \lim _{x \rightarrow 0} \frac{\sin x}{\sqrt{x^{2}}}= \)
\( \mathbf{A} \cdot \mathbf{1} \)
B. -
\( c \cdot 0 \)
D. doesn't exist


What are the objectives of petroleum conservation research association:
A. To create awareness among masses about the importance, benefits and methods of conserving petroleum products \& clean environment by enhancing information and capacity building.
B. To provide training and technical advisory services, designed to achieve economy \& efficiency in use of petroleum products for cleaner environment.
c. To function as a Think Tank to the Govt. of India for proposing policies and strategies on petroleum conservation and environment protection aimed at reducing excessive dependence on oil
D. all of these.


Which of the following order of root
mean square speed of different gases
at the same temperature is true?
A \( \cdot\left(U_{r m s}\right)_{H_{2}}>\left(U_{r m s}\right)_{C H_{4}}>\left(U_{r m s}\right)_{N H_{3}}>\left(U_{r m s}\right)_{C O} \)
B . \( \left(U_{r m s}\right)_{H_{2}}<\left(U_{r m s}\right)_{C H_{4}}<\left(U_{r m s}\right)_{N H_{3}}<\left(U_{r m s}\right)_{C O} \)
C. \( \left(U_{r m s}\right)_{H_{2}}<\left(U_{r m s}\right)_{C H_{4}}>\left(U_{r m s}\right)_{N H_{3}}>\left(U_{r m s}\right) \) Co \( _{2} \)
D. \( \left(U_{r m s}\right)_{H_{2}}>\left(U_{r m s}\right)_{C H_{4}}<\left(U_{r m s}\right)_{N H_{3}}<\left(U_{r m s}\right)_{C O} \)


Give reason: Carbonate and sulphide ores are usually converted into oxides
during the process of extraction.


Edaphology is the relationship between
A. Plant and biosphere
B. Animal and ecosystem
c. Soil and living organisms
D. Soil and biosphere


Which of the following compounds gives
chlorine dioxide when it reacts with
\( \boldsymbol{S} \boldsymbol{O}_{2} \) in the presence of acid?
A. Sodium chloride
B. Sodium chlorate
C. Sodium perchlorate
D. Sodium chlorite


represents the graph of the function \( f(x)=\lim _{n \rightarrow \infty} \frac{2}{\pi} \tan ^{-1}(n x) ? \)
\( A \)
B.
\( c \)
\( D \)


A car travels a distance \( 100 \mathrm{m} \) with a constant acceleration and average
velocity of \( 20 m s^{-1} . \) The final velocity
acquired by the car is \( 25 m s^{-1} \). Find the
acceleration of the car.
A \( \cdot 1 m s^{-2} \)
B. \( 2 m s^{-2} \)
\( \mathbf{c} \cdot 0 m s^{-2} \)
D. \( 4 m s^{-2} \)


A lower \( p H \) means:
A. higher basicity.
B. lower acidity
c. higher acidity.
D. both \( A \) and \( C \).


A rod of length L lies along the \( x \) -axis with its left end at the origin. It has a nonuniform charge density \( \boldsymbol{\lambda}=\boldsymbol{\alpha} \boldsymbol{x} \)
where \( \alpha \) is a positive constant. What are
the units of \( \boldsymbol{\alpha} \) ?
A \( \cdot \frac{C}{m^{2}} \)
в. \( \frac{c}{m^{1}} \)
\( \mathrm{c} \cdot \mathrm{Cm} \)
D. \( C m^{2} \)


Which of the following group of elements has the same size?
A. \( S e, V, M n \)
в. \( M n, \) Fe, Со
c. \( T i, V, C r \)
D. \( L i, B e, B \)


The color of \( K M n O_{4} \) is due to:
A . L-> M charge transfer transition
B . \( \sigma-\sigma^{*} \) transition
c. M-> L charge transfer transition
D. d-d transition


Constituent of gasohol is:
\( \mathbf{A} \cdot 90 \% \) petrol \( +10 \% \) alcohol
B. 80\% petrol + 20\% ethanol
C . \( 60 \% \) petrol \( +40 \% \) ethanol
D. 50\% petrol + 50\% ethanol


\( \boldsymbol{K}_{2} \boldsymbol{C r}_{2} \boldsymbol{O}_{7}+\boldsymbol{H} \boldsymbol{C l} \rightarrow \boldsymbol{C r} \boldsymbol{C l}_{3}+\boldsymbol{H}_{2} \boldsymbol{O}+ \)
\( \boldsymbol{C l}_{2}+\boldsymbol{K} \boldsymbol{C l} \)
Balance in basic medium by ionelectron identity spectator ion.


Solve: \( 4 x+\frac{6}{y}=15 \) and \( 6 x-\frac{8}{y}=14 \)
Hence, find \( \boldsymbol{a} \) if \( \boldsymbol{y}=\boldsymbol{a} \boldsymbol{x}-\boldsymbol{2} \)
A \( \cdot x=2 ; y=26 \) and \( a=2 \frac{5}{3} \frac{5}{3} \)
B・ \( x=3 ; y=2 \) and \( a=1 \frac{1}{3} \)
c. \( _{x}=1 ; y=5 \) and \( a=2 \frac{7}{3} \)
D. \( x=5 ; y=1 \) and \( a=5 \frac{1}{8} \)


Three masses are placed on the x-axis:
\( 300 g \) at origin, \( 500 g \) at \( x=40 c m \) and
\( 400 g \) at \( x=70 c m . \) The distance of the
centre of mass from the origin is-
\( \mathbf{A} \cdot 45 \mathrm{cm} \)
в. \( 50 \mathrm{cm} \)
\( \mathbf{c} .30 \mathrm{cm} \)
D. \( 40 \mathrm{cm} \)


\( f(\alpha, \beta, \gamma \) are three real numbers and
\( \boldsymbol{A}= \)
\( \left[\begin{array}{ccc}\mathbf{1} & \cos (\boldsymbol{\alpha}-\boldsymbol{\beta}) & \cos (\boldsymbol{\alpha}-\gamma) \\ \cos (\boldsymbol{\beta}-\boldsymbol{\alpha}) & \mathbf{1} & \cos (\boldsymbol{\beta}-\gamma) \\ \cos (\gamma-\boldsymbol{\alpha}) & \cos (\gamma-\boldsymbol{\beta}) & \mathbf{1}\end{array}\right] \)
then
This question has multiple correct options
A. \( A \) is symmetric
B. \( A \) is orthogona
c. \( A \) is singular
D. \( A \) is not invertible


A diode having potential difference \( 0.5 V \) across its junction which does not depend on current, is connected in
series with resistance of \( 20 \Omega \) across
source. If \( 0.1 A \) current passes through
resistance then what is the voltage of the source?
A. \( 1.5 V \)
в. \( 2.0 V \)
\( \mathrm{c} .2 .5 \mathrm{V} \)
D. \( 5 V \)


If \( A \) is a skew-symmetric matrix of
order \( n \) and \( C \) is a column matrix of
order \( n \times 1 \) then \( C^{T} A C \) is
A. a identity matrix of order \( n \).
B. a unit matrix of order
c. a zero matrix of order 1
D. none of these


A reflecting telescope utilises:
A. a convex mirror
B. a concave mirror
\( c . \) a prism
D. a plano-concave lens


Assertion
Fat digestion in stomach is an emulsification process.
Reason
Emulsion of fat in water is stabilized by
the bile juice.
Read the above assertion and reason
and choose the correct option regarding
¡t.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


Variation of \( \log _{10} K \) with \( \frac{1}{T} \) is shown by the graph in which straight line is at
\( 45^{\circ} \mathrm{C}, \) hence \( \Delta H^{o} \) is:
\( \mathbf{A} \cdot-4.606 k J / m o l \)
B. \( -19.147 k J / \) mol
c. \( 8.314 k J / m o l \)
D. \( 10 k J / m o l \)


Which element out of He, Ar, Kr and Xe forms least number of compounds?
\( \mathbf{A} \cdot \mathbf{K} \)
B. xe
c. Ar
D. не


The diagonal of a rectangle whose length is \( 20 \mathrm{cm} \) and breadth in \( 15 \mathrm{cm} \) is
\( \mathbf{A} \cdot 35 \mathrm{cm} \)
B. \( 30 \mathrm{cm} \)
c. \( 25 \mathrm{cm} \)
D. \( 40 \mathrm{cm} \)


\( \lim _{\boldsymbol{x} \rightarrow \mathbf{0}} \frac{(\mathbf{1}+\boldsymbol{x})^{\mathbf{1} / \mathbf{6}}-(\mathbf{1}-\boldsymbol{x})^{\mathbf{1} / \mathbf{6}}}{\boldsymbol{x}} \)


Essential elements are
A. Only macronutrients
B. Only micronutrients
C. Both macro and micronutrients
D. \( \mathrm{C}, \mathrm{H}, \mathrm{O} \) and \( \mathrm{N} \) only


To measure the field \( B \) between the
poles of an electromagnet, a small test loop of area \( 1 \mathrm{cm}^{2} \), resistance \( 10 \Omega \) and 20 turns is pulled out of it. A galvanometer shows that a total charge of \( 2 \mu C \) passed through the loop. The
value of \( B \) is
A . \( 0.001 T \)
в. \( 0.01 T \)
\( c .0 .17 \)
D. \( 1.0 T \)


Two particles \( A \) and \( B \) each of mass \( m \)
are attached by a light inextensible string of length \( 2 l . \) The whole system
lies on a smooth horizontal table with \( \boldsymbol{B} \)
initially at a distance \( l \) from \( A \). The
particle at end \( B \) is projected across the table with speed \( u=4 \sqrt{3} m / s \)
perpendicular to \( A B \). Find velocity of
ball \( A \) just after the jerk?


For the reaction \( N_{2}(g)+3 H_{2}(g) \rightarrow \)
\( 2 N H_{3}(g), \) under certain conditions of
temperature and partial pressure of the
reactants, the rate of formation of \( \boldsymbol{N} \boldsymbol{H}_{3} \)
is \( 1.0 \times 10^{-4} \) mollit \( ^{-1} h^{-1} \). The rate of
conversion of \( \boldsymbol{H}_{2} \) under the same
conditions is:
A \( \cdot 6.7 \times 10^{-4} \) mollit \( ^{-1} h^{-1} \)
B. \( 3.3 \times 10^{-3} \) mollit \( ^{-1} h^{-1} \)
c. \( 1.5 \times 10^{-4} \) mollit \( ^{-1} h^{-1} \)
D. \( 0.5 \times 10^{-4} \) mollit \( ^{-1} h^{-1} \)


On a two lane road a car A is travelling
with a speed of \( v=10 m s^{-1} . \) Two cars \( B \)
and \( C \) approach car \( A \) in opposite
directions with a speed \( u=15 m s^{-1} . \) At a certain instant when the \( \mathrm{B} \) and \( \mathrm{C} \) are
equidistant from A each being I =1000
\( \mathrm{m}, \mathrm{B} \) decides to overtake \( \mathrm{A} \) before \( \mathrm{C} \)
does. What minimum acceleration of
car \( \mathrm{B} \) is required to avoid an accident
with c:


A person met with an accident and died instantaneously without any injury to heart, brain, stomach or kidney, which
one of the following must be the reason?
A. Diaphragm got punctured
B. Stomach stopped digestion
c. Intestine got twisted
D. RBC's got coagulated


Two glass prisms \( P_{1} \) and \( P_{2} \) are to be combined together to produce dispersion without deviation. The
angles of the prisms \( P_{1} \) and \( P_{2} \) are
selected as \( 4^{\circ} \) and \( 3^{\circ} \) respectively. If the refractive index of prism \( P_{1} \) is 1.54 , then
that of \( P_{2} \) will be
A . 1.48
B. 1.58
\( c \cdot 1.62 \)
D. 1.72


Which of the following body part has more number of bone that others?
A. Skull
B. Chest
c. Forelimb
D. Pelvis


At some temperature and under a
pressure of 4 atm, \( P C l_{5} \) is \( 10 \% \) dissociated. Calculate the pressure
at which \( P C l_{5} \) will be \( 20 \% \) dissociated,
temperature remaining same.
A. 1.84 atm
B. 0.97 atm
c. 2.87 atm
D. None of these


If the coefficient of variation and
standard deviation are \( 60 \% \) and 21
respectively, the arithmetic mean of
distribution is.
A . 30
B. 21
\( c \cdot 60 \)
D. 35


Armature is pulled towards the spring when it strikes the gong because
A. The electromagnet gets demagnetized
B. The current flow breaks
c. spring effect
D. All of the above


If a vector is multiplied by a real number, then which of the following statements is incorrect?
A. only magnitude of the vector may change
B. Only direction of the vector may change
c. Both magnitude and direction of the vector may change
D. Its direction will never change


Decreasing the temperature makes metal:
A . brittle
B. ductile
c. malleable
D. sonorous


Three elements \( A, B \) and \( C \) belong to
the same group of the modern periodic table such that the difference in atomic
weight of \( A \) and \( B \) is equal to the
difference in atomic weight of \( B \) and \( C \) The sum of atomic weights of elements \( A \) and \( C \) is 46 and that of \( A \) and \( B \) is 30
Identify elements \( A, B \) and \( C . \)


The rays of light, which are not paralle to each other and spread out from a point, are called and
a bundle of rays, which are parallel to
one another, is called
A. parallel beam of light, convergent rays
B. divergent rays, convergent rays
c. convergent rays, parallel beam of light
D. divergent rays, parallel beam of light


A convex lens of focal length \( 20 \mathrm{cm} \) is placed coaxially with a convex mirror of radius of curvature \( 20 \mathrm{cm} . \) The two are
kept at \( 15 \mathrm{cm} \) apart from each other. \( \mathrm{A} \) point object lies \( 60 \mathrm{cm} \) in front of the convex lens. Draw a ray diagram to show the formation of the image by the combination. Determine the nature and
position of the image formed.


Detailed study of pigment systems was carried out by
A. Robert Hill
B. H. P. Nanda
c. Govindjee
D. Emmerson


In circular motion, the
A. Direction of motion is fixed
B. Direction of motion changes continuously
C. Acceleration is zero
D. Velocity is constant


The figure shown a triangular pulse on rope at \( t=0 . \) It is approaching a fixed end at \( 2 \mathrm{cm} / \mathrm{s} \) Draw the pulse at \( t=2 \)
\( \sec \)


Speed of the current.


A metallic sphere of radius \( 18 \mathrm{cm} \) has
been given a charge of \( 5 \times 10^{-6} \) C. The
energy of the charged conductor is:
A. 0.25
J \( J \)
в. 0.6 .5
c. \( 1.2 J \)
D. 2.4J


Which of the following can be used as plasticisers?
This question has multiple correct options
A. Sodium hexametaphosphate
B. n-dibutyıphthalate
c. Tricresyl phosphate
D. Diethyl phthaalate


The limit of the following is \( \lim _{x \rightarrow 3} \frac{\sqrt{1-\cos \left(x^{2}-10+21\right)}}{x-3} \)
\( A \cdot_{-}(2)^{\frac{3}{2}} \)
B・(2)
c. \( (2)^{-\frac{3}{2}} \)
D.


8
\( H=30 \mathrm{cm} \) and same refractive index
\( \boldsymbol{n}=1.5 \) are placed on a horizontal
surface as shown in figure. Cylinder
has a flat top, cylinder II has a convex
top and cylinder III has a concave top.
The radii of curvature of the two curved
tops are same \( (R=3 m) . \) If \( H_{1}, H_{2} \) and
\( H_{3} \) are the apparent depths of a point \( X \)
on the bottom of the three cylinders,
respectively, the correct statement (s)
is/are:
This question has multiple correct options
\( \mathbf{A} \cdot H_{2}>H_{1} \)
В \( \cdot H_{3}>H_{1} \)
C. \( 0.8 \mathrm{cm}<\left(\mathrm{H}_{2}-\mathrm{H}_{1}\right)<0.9 \mathrm{cm} \)
D. \( H_{2}>H_{3} \)


The value of integral \( \int_{-1}^{3}\left(\tan ^{-1}\left(\frac{x}{1+x^{2}}\right)+\tan ^{-1}\left(\frac{x^{2}+1}{x}\right)\right. \)


What is light emitting diode (LED)? Explain its working principle and state factors on which the colour of light emitted by it depends.


What does not occur in
photorespiration?
A. Utilization of \( O_{2} \)
B. Production of \( C O_{2} \)
c. synthesis of ATP
D. All of the above


Molecularity of a reaction can be known
from:
A. the stoichiometric equation
B. the mechanism of the reaction
C. the order of the reaction
D. the energy of activation of the reaction


Two identical bodies are made of a
material for which the heat
capacity increases with temperature.
One of these is at \( 100^{\circ} \mathrm{C}, \) while the
other one is at \( 0^{0} \mathrm{C} \). If the two bodies
are brought into contact, then
assuming no heat loss, the find common temperature is
\( \mathbf{A} \cdot 0^{\circ} C \)
B. \( 550^{\circ} \mathrm{C} \)
c. more than \( 50^{\circ} \mathrm{C} \)
D. Less than \( 50^{\circ} \mathrm{C} \) but greater than \( 0^{\circ} \mathrm{C} \)


The electron is present in the -1.51 eV
energy state. Find the angular momentum of the electron.
A. \( \frac{h}{\pi} \)
в. \( \frac{h}{2 \pi} \)
c. \( \frac{3 h}{2 \pi} \)
D. \( \frac{2 h}{\pi} \)
E. none of these


Fizzy drinks are
A. basic
B. acidic
c. neutral
D. none of these


Place of 3 in 30,25,69,214
A. Ten crores
B. Millions
\( c \cdot 3,00,00,000 \)
D. 30,00,00,000


A ray of light is incident on the interface
between water and glass at an angle
and refracted parallel to the water
surface, then value of \( \mu_{g}, \) refractive
index of glass will be:
A \( \cdot(4 / 3) \sin i \)
B. \( \frac{1}{\sin i} \)
\( c \cdot \frac{4}{3} \)
\( D \)


If the radius of first Bohr orbit is \( x p m \)
then the radius of the third orbit would
be:
в. \( (6 \times x) \) рт
C \( \cdot\left(\frac{1}{2} \times x\right) p m \)
D. \( (9 \times x) p m \)


In which of the following situations, does the list of numbers involved make
an arithmetic progression, and why?
(i) The taxi fare after each \( \mathrm{km} \) when the
fare is Rs.15 for the first \( \mathrm{km} \) and Rs. 8
for each additional km.
(ii) The amount of air present in a cylinder when a vacuum pump removes
\( \frac{1}{4} \) of the air remaining in the cylinder at a time.
(iii) The cost of digging a well after every metre of digging, when it costs Rs.
150 for the first metre and rises by Rs.
50 for each subsequent metre.
(iv) The amount of money in the
account every year, when Rs. 10000 is deposited at compound interest at \( 8 \% \)
per annum.


Solve:
\( 2-\frac{7 x}{29}<\frac{5}{3} \)


The image of our face in a plane mirror
is
A . real
B. magnified
c. diminished
D. Same as the size of the object


\( \frac{1}{2}=0.5 \)
It is a terminating decimal because the denominator has a factor as
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D. 6


The defect hypermmetropia of an eye can be corrected by using spectacles containing lens.


If the wheel of the bus is \( 90 \mathrm{cm} \)
diameter makes 210 revolutions per
minute, then find the speed of the bus
in \( k m / h r, \) to the nearest integer.


In an arithmetic series \( S_{20}=-850 \) and
\( t_{20}=-90, \) find \( t_{1} \)
A. 5
B. 4
\( c \cdot 3 \)
\( D \cdot 2 \)


Benzoyl chloride is prepared from benzoic acid by:
A. \( C l_{2} \) and \( h v \)
в. \( S O_{2} C l_{2} \)
c. \( \operatorname{sOCl}_{2} \)
D. \( C l_{2} \) and \( H_{2} O \)


The displacement of a particle undergoing \( S H M \) of time period \( T \) is
given by \( \boldsymbol{x}(\boldsymbol{t})=\boldsymbol{x}_{\boldsymbol{m}} \cos (\boldsymbol{\omega} \boldsymbol{t}-\boldsymbol{\phi}) . \) The
particle is at \( \boldsymbol{x}=-\boldsymbol{x}_{m} \) at time \( \boldsymbol{t}=\mathbf{0} \)
The particle is at \( \boldsymbol{x}=+\boldsymbol{x}_{\boldsymbol{m}} \) when
\( \mathbf{A} \cdot t=0.25 T \)
в. \( t=0.50 T \)
c. \( t=0.75 T \)
D. \( t=1.00 T \)


\( \int_{\pi / 6}^{\pi / 4} \frac{d x}{\sin 2 x} \) is equal to
A \( \cdot \frac{1}{2} \log (-1) \)
B \( \cdot \log (-1) \)
\( \mathbf{c} \cdot \log 3 \)
D \( \cdot \frac{1}{2} \log \sqrt{3} \)


a poin
is put through a cycle consisting of the following three reversible steps:
(CA): Isothermal compression from 2
atm and 10 litres to 20 atm and 1 litre.
(AB): Isobaric expansion to return the
gas to the original volume of 10 litres
with T going from \( \boldsymbol{T}_{\mathbf{1}} \) to \( \boldsymbol{T}_{\mathbf{2}} \).
(BC): Cooling at constant volume to bring the gas to the original pressure and temperature.

The steps are shown schematically in
the figure given above
(a) Calculate \( T_{1} \) to \( T_{2} \)
(b) Calculate \( \Delta U, q \) and \( w \) in calories,
for each step and for the cycle.


Check whether the vector \( 4 \hat{\mathbf{i}}+\mathbf{1 3} \hat{\mathbf{j}}- \)
\( 18 \hat{k} \) is a linear combination of the vectors \( \hat{i}-2 \hat{j}+3 \hat{k} \) and \( 2 \hat{i}+3 \hat{j}-4 \hat{k} \)


In the oxidation test of sulphur, organic compound is fused with a mixture of:
A. sodium nitrite \& potassium sulphide
B. potassium carbonate \& sodium nitrate
c. potassium nitrate \& sodium carbonate
D. none of the above


Consider the following groups \( A \) and B.A \( : 3,4,5, \dots \dots \dots \dots \) pto n terms
\( B: 15,19,23, \dots \dots \dots \) pto \( n \) terms
If means deviations of groups \( A \) and \( B \) about their means are \( \alpha \) and \( \beta \)
respectively then
A \( . \beta=5 \alpha \)
в. \( \beta=4 \alpha+3 \)
c. \( \beta=4 \alpha \)
D. None


Q Type your question-
to two ideal voltmeters \( V_{1} \& V_{2} \)
Assume that a voltmeter reads \( \Delta V= \)
\( -\int_{a}^{b} \vec{E} \cdot d \vec{\ell} \) between its terminals. A time varying magnetic field \( B(t) \) exists in a circular region of radius a and it is
directed into the plane of the figure
\( B(t)=B_{0} t \) where \( B_{0} \) is a positive
constant of proper dimensions and t is
the time. The emf induced in the circuit
is :
\( A \cdot 2 \pi a^{2} B_{0} \)
В \( \cdot \pi a^{2} B_{0} \)
c. \( \frac{a^{2} B_{0}}{2} \)
D・ \( \pi a^{2} B_{0} \)


toppr
Q Type your question
the liquid columns in the two tubes?
\( A \)
(1)
\( B \)
(2)
\( c \)
(3)
\( D \)
(4)


If the specific conductance and conductance of a solution are same, then
its cell constant is equal to:
\( A \)
B.
c. 10
D. 100


Assertion
\( C l_{2} \) or \( B r_{2} \) changes \( K I \) into \( I_{2} \) (violet in
\( C C l_{4} \) layer), \( C l_{2} \) changes \( K B r \) into \( B r_{2} \)
(orange-yellow in \( C C l_{4} \) layer). Thus, \( C l_{2} \) would change mixture of \( K I \) and \( K B r \) into violet layer in
\( \boldsymbol{C C l}_{4} \)
Reason
Oxidising power is in order \( \boldsymbol{I}_{2}<\boldsymbol{B} \boldsymbol{r}_{2}< \)
\( \boldsymbol{C l}_{2}<\boldsymbol{F}_{2} \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct.


The probability that a student selected at random from a class will pass in Mathematics is \( 4 / 5, \) and the probability that he/she passes in Mathematics and Computer Science is \( 1 / 2 . \) What is the probability that he/she will pass in Computer Science if it is known that he has passed in Mathematics?


With the one slit \( 25 \mathrm{mm} \) from the
biprism and the other \( 16 \mathrm{mm} \) and using light of wavelength \( 1200 \mathrm{nm} \), fringes were formed on a screen \( 0.5 \mathrm{m} \) from the single slit.The fringe width is
A. \( 0.03 \mathrm{cm} \)
B. \( 0.03 \mathrm{mm} \)
\( c \cdot 0.3 \mathrm{cm} \)
D. \( 0.3 \mathrm{m} \)


Which of the following enzyme converts maltose to glucose?
A. Invertase
B. Zymase
c. Maltase
D. Diastase


Choose the correct option. Sound can not travel in:
A. Iron
B. Water
c. Air
D. Vacuum


When water is heated from \( 0^{\circ} \mathrm{C} \), its
volume will
A. decrease till \( 4^{\circ} \mathrm{C} \) then increase
B. decrease till \( 4^{\circ} \mathrm{C} \)
c. remain the same
D. first increase then decrease


If the displacement of a particle varies with time as \( \sqrt{x}=t+7 \), then
(1) velocity of the particle is inversely porportional to
(2) velocity of the particle is directly porportional to
(3) velocity of the particle is porportional to \( \sqrt{\boldsymbol{t}} \)
(4) the particle moves with a constant acceleration


In a certain shop, which stocks four types of caps, there are \( 1 / 3 \) as many red caps as blue and \( 1 / 2 \) as many green caps as red caps. There are equal
numbers of green caps and yellow caps. If there are 42 blue caps, then what
percent of the total caps in the shop are
blue?
A . \( 70 \% \)
B. \( 28 \% \)
\( c \cdot 60 \% \)
D. \( 14 \% \)


Which of the following chalcogen does not make bonds with germanium?
A. Sulfur
B. Selenium
c. Tellurium
D. Polonium


One of the most known antiseptic, dettol is a mixture of terpineol and:
A. bithlonal
B. chloroxylenol
c. o-cresol
D. serotonin


Most abundant lipid in cell membrane
is
A. sphingolipid
B. Glycolipid
c. Phospholipid
D. cholesterol


Which of the following compound
cannot be oxidised by \( \boldsymbol{O}_{3} ? \)
A. \( K I \)
в. \( K M n O_{4} \)
c. \( K_{2} \) Мп \( O_{4} \)
D. \( F e S O_{4} \)


Which of the following substance is stored under water:
A. White phosphorus
B. red phosphorus
c. Sodium metal
D. Both white phosphorous and red phosphorus


At a certain place the horizontal component of the earth's magnetic field
is H and the angle of dip is \( 45^{\circ} . \) The total
intensity of the field at that place will
be:
A.
B. \( \sqrt{2} \) н
c. २म
D.


The motion of a bus going around a traffic roundabout is curvilinear
motion. True or false
A. True
B. False


A uniform rule is pivoted at its mid point. A weight of \( 50 g f \) is suspended at one end of it. Where should a weight of
\( 100 g f \) be suspended, to keep the rule horizontal?
A. \( 10 \mathrm{cm} \) from mid point
B. \( 25 \mathrm{cm} \) from mid point
c. \( 20 \mathrm{cm} \) from mid point
D. \( 15 \mathrm{cm} \) from mid point


The values of current I flowing in a given resistor for the corresponding values of potential difference V across the resistor are given below -
|(amperes) 2
\( V(v \text { olts }) \) 1. 6
. 6 3.4 6.7
Plot a graph between \( \mathrm{V} \) and \( \mathrm{I} \) and
calculate the resistance of that resistor.


Identify the direction of the angular velocity vector for the second hand of a
clock going from 0 to 60 seconds?
A. Outward from the clock face
B. Inward toward the clock face
D. Downward
E. To the right


The non zero vector \( \vec{a}, \vec{b}, \vec{c} \) related by \( \vec{a}=8 \vec{b} \) and \( \vec{c}=-7 \vec{b}, \) then angle
between \( \vec{a} \& \vec{c} \) is
A . \( \pi \)
в. \( \frac{\pi}{2} \)
c. 0
D. \( \frac{\pi}{4} \)


f \( p \) is a prime, show that the sum of the
\( (p-1)^{t h} \) powers of any \( p \) numbers in arithmetical progression, wherein the common difference is not divisible by \( \boldsymbol{p} \)
is less by 1 than a multiple of \( p \)


joule coulomb \( ^{-1} \) is same as


The addition compounds which retain their identity in a solution are called:
A. normal salts
B. double salts
c. complex compounds
D. co-ordination compounds


Six capacitors each of capacitance of
\( 2 \mu F \) are connected as shown in the
figure. The effective capacitance
between \( A \) and \( B \) is:
\( \mathbf{A} \cdot 12 \mu F \)
в. \( \frac{8}{3} \mu F \)
\( c .6 \mu F \)
D \( \frac{2}{3} \mu F \)


Prove that if the diagonals of a parallelogram are equal then it is a rectangle.


Which ore is concentrated by froth flotation method?
A. Horn silver
B. Bauxite
c. cinnabar
D. Haemattie


A semicircular piece of paper of radius \( 14 \mathrm{cm} \) is rolled to form a cone of the
largest possible size. Find the capacity
of the cone.
A \( \cdot 721.5 \mathrm{cm}^{3} \)
B. \( 645.10 \mathrm{cm}^{3} \)
c. \( 449.64 \mathrm{cm}^{3} \)
D. \( 622.37 \mathrm{cm}^{3} \)


Let, \( \boldsymbol{f}: \boldsymbol{A} \rightarrow \boldsymbol{B} \) be an invertible function
If \( f(x)=2 x^{3}+3 x^{2}+x-1, \) then
\( f^{\prime-1}(5)= \)
A \( \cdot \frac{1}{13} \)
B.
\( c \cdot 6 \)
D. can not be determined


toppr
Q Type your question
whicn grapn correctly represents \( \boldsymbol{E}_{\text {cell}} \) \( (Y-a x i s) \) as a function of \( \log \frac{\left[Z n^{2+}\right]}{\left[C u^{2+}\right]} \)
axis)?
\( A \)
B.
\( c \)
\( D \)


A train A which is 120 \( \mathrm{m} \) long is running with velocity \( 20 \mathrm{m} / \mathrm{s} \) while train \( \mathrm{B} \) which
is \( 130 \mathrm{m} \) long is running in opposite direction with velocity \( 30 \mathrm{m} / \mathrm{s} \). What is the time taken by train \( \mathrm{B} \) to cross the
\( \operatorname{train} A ? \)
A. 5 s
B. 25 s
\( c \cdot 10 s \)
D. 100 s


What is number of degrees of freedom
of an ideal diatomic molecule at
ordinary temperature?
A. 7
B. 6
\( c \cdot 5 \)
D.


\( x \cos (a+y)=\cos y \)
then prove that \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\frac{\cos ^{2}(\boldsymbol{a}+\boldsymbol{y})}{\sin _{\boldsymbol{a}}} \)


The value of \( k \) for which \( x-1 \) is a
factor of the polynomial \( 4 x^{3}+3 x^{2}- \)
\( 4 x+k \) is
\( A \cdot 3 \)
B.
\( c \cdot 1 \)
D. - 3


\( \operatorname{Prove} \sin \left(\mathbf{6 0}^{0}+\boldsymbol{\theta}\right)-\sin \left(\mathbf{6 0}^{\mathbf{0}}-\boldsymbol{\theta}\right)= \)
\( \sin \boldsymbol{\theta} \)


If \( L \equiv 2 x+y-6=0, \) then the locus of
circumcentre of \( \triangle P Q R \) is
A. \( 2 x-y=4 \)
в. \( 2 x+y=3 \)
c. \( x-2 y=4 \)
D. \( x+2 y=3 \)


\( A B C D \) is a trapezium with parallel
\( \operatorname{sides} A B=a c m \) and \( D C=b c m . E \)
and \( F \) are the mid-points of the non-
parallel sides. The ratio of \( a r(A B F E) \)
and \( a r(E F C D) \) is
\( A \cdot a: b \)
B. \( (3 a+b):(a+3 b \)
\( c \cdot\left(a+3 b_{\cdot}(3 a+b)\right. \)
D. \( (2 a+b):(3 a+b) \)


Find principal and general solution of the equation, \( \cot x=-\sqrt{3} \)


Isobars are:
A. the atoms of same element having the same atomic number but different mass numbers
B. the atoms of same element having different atomic numbers but same mass number
C. atoms of different elements with same atomic
number which have different mass numbers
D. atoms of different elements with different atomic numbers which have same mass number


For two events \( \boldsymbol{A} \) and \( \boldsymbol{B}, \) if \( \boldsymbol{p}(\boldsymbol{A})= \)
\( \boldsymbol{p}(\boldsymbol{A} \mid \boldsymbol{B})=\frac{1}{4} \) and \( \boldsymbol{p}(\boldsymbol{B} \mid \boldsymbol{A})=\frac{1}{2}, \) then
\( P\left(\frac{\bar{B}}{\bar{A}}\right)=\frac{m}{n} \) where \( m+n= \)


Leaves are modified into spines in
A. Nepenthes
B. Australian Acacia
c. opuntia
D. Utricularia
E. Tamarix


What are the characteristics of the
particles of matter?


What is gravitational potential energy?
Explain with the help of an example.


Seismic zones are also
called


Evaluate the following definite integrals
\( \int_{0}^{3} x^{2} d x \)


The relation among \( u, v \) and \( f \) for a
mirror is:
A . \( f=u v(u+v) \)
в. \( v=f u(u+f) \)
c. \( u=f v(f+v) \)
D. None of these


The vapor pressure of water is
\( 12.3 K P a \) at \( 300 K . \) Calculate the vapor
pressure of 1 molal solution of a non-
volatile solute in it.


toppr
Q Type your question
virtually all or the transıtion metals form dipositive \( (2+) \) cations, along with
one or more other forms. For example,
titanium forms \( \boldsymbol{T} \boldsymbol{i}^{2+} \) ad \( \boldsymbol{T} \boldsymbol{i}^{4+}, \) and
cobalt forms \( C o^{2+} \) and \( C o^{3+} \)
The principal exceptions to this
predominance of cations with a \( 2^{+} \)
charge are scandium and yttrium,
which form only tripositive cations.
\( S c^{3+} \) and \( Y^{3+}, \) and copper and silver
which form cations with a single
positive charge. \( C u^{+} \) and \( A g^{+} \)
[While copper also forms dipositive
\( C u^{2+}, \) silver exhibits the single positive
state essentially exclusively.]
Which of the following offers a
POSSIBLE explanation for the existence
of \( C u^{+} \) and \( A g^{+} ? \)
A. Mendeleev placed copper and silver in Group IB on his original periodic table because they formed compounds with the same combining ratios as elements in Group \( 1 A \)
B. Elemental copper and silver have a single valence electron, which is lost in cation formation
C. Copper and silver have higher ionization energies than the other transition metals in their respective periods, so are unable to lose more than one electron.
D. The loss of one electron gives copper and silver noble gas configurations.


The \( p H \) of neutral solution at \( 35^{\circ} C \) is:
A. 7
B. <7
\( c \cdot>7 \)
D. zero


Which of the following releases less amount of pollutants on combustion?
A . Diesel
B. Coal gas
c. c. N.G
D. water gas


Chlorine was discovered by:
A . Davy
B. Priestly
c. Rutherford
D. sheele


The pressure \( P \) and volume \( V \) of a gas
are connected by the relation \( \boldsymbol{P} \boldsymbol{V}^{1 / 4}= \)
constant. The percentage increase in
the pressure corresponding to a deminition of \( \frac{1}{2} \% \) in the volume is
A \( \cdot \frac{1}{2} \% \)
B. \( \frac{1}{4} \% \)
c. \( \frac{1}{8} \% \)
D. none of these


The work performed (in J) to make a
hoop out of a steel band of length \( l= \)
\( 2.0 m, \) width \( h=6.0 \mathrm{cm}, \) and thickness
\( \boldsymbol{\delta}=\mathbf{2 . 0} \boldsymbol{m m} \) is \( \boldsymbol{x} \times \mathbf{1 0}^{\mathbf{1}} \boldsymbol{J} . \) The process
is assumed to proceed within the elasticity range of the material. Find the
value of \( \boldsymbol{x} \)


Which of the following statements are incorrect?
(i) Average velocity is path length divided by time interval.
(ii) In general, speed is greater than the magnitude of the velocity.
(iii) A particle moving in a given direction with a non-zero velocity can have zero speed.
(iv) The magnitude of average velocity is the average speed.
A. (ii) and (iii)
B. (ii) and (iv)
c. (i), (iii) and (iv)
D. All four


Equation of a plane


The angle between two plane refracting surfaces of the prism is called the angle of
A . prism
B. emergence
c. deviation
D. incidence


The value of unknown resistance \( \boldsymbol{X} \) will
be
A \( .402 .49 \Omega \)
3. 403 .
\( c \cdot 404 \Omega \)
D. 210\Omega


Which of the following order is wrong?
\( \mathbf{A} \cdot N H_{3}<P H_{3}<A s H_{3}: \) Acidic strength
B . \( L i<B e<B<C: I E_{1} \)
c. \( A l_{2} O_{3}<M g O<N a_{2} O<K_{2} O: \) Basic strength
D \( \cdot L i^{+}<N a^{+}<K^{+}<C s^{+}: \) Ionic character


f the value of \( T \) is \( 4 s, \) then the times
after which A will meet B i
\( 4.12 \mathrm{s} \)
B. 6 s
\( c \cdot 8 s \)
D. data insufficient


Evaluate \( \int e^{x}\left(\frac{1+\sin x}{1+\cos x}\right) \)


Which of the following statement(s) is/are correct?
I. Natural starch contains \( 10-20 \% \)
amylopectin and \( 90-80 \% \) amylose.
II. Amylose is insoluble in water.
III. Amylopectin is soluble in water.
V. Starch is white amorphous powder found in roots and seeds of plants.
A. IV only
B. II only
c. II and III
D. I and IV


Cementation process involves
formation of:
A . gel
B. emulsion
\( c . \) sol
D. solid aerosol


Electrolytic reduction of alumina to
aluminium by Hall-Heroult process is carried out:
A. in the presence of Nacı
B. in the presence of fluoride
c. in the presence of cryolite which forms a melt with lower melting temperature.
D. in the presence of cryolite which forms a melt with higher melting temperature


Mark the correct alternative of the
following.
In figure, the value of \( x \) is?
\( A \cdot 84 \)
B. 74
\( c .94 \)
D. 57


Product \( (A) \) is:
Снз \( -c \equiv c- \) сн \( _{3} \) Соыа КМпо \( _{4}(t) \)
\( \mathbf{C H}_{3}-\mathbf{C H}_{2}-\mathbf{U}-\mathbf{C}-\mathbf{H} \)
\( \mathbf{C H}_{3}-\mathbf{U}-\| \)
\( \mathbf{O H} \mathbf{~ O H} \)
\( \mathbf{C H}_{3}-\mathbf{C H}-\mathbf{C H}-\mathbf{C H}_{3} \)
\( o=C H-C H \)
\( h \)


\( A B C D \) is a parallelogram of area
162 sq.cm. \( P \) is a point on \( A B \) such
that \( \boldsymbol{A P}: \boldsymbol{P B}=\mathbf{1}: \mathbf{2} \)
Calculate the ratio \( \boldsymbol{P} \boldsymbol{A}: \boldsymbol{D} \boldsymbol{C} \)
A . 1: 3
B. 3: 1
\( c .3: 2 \)
D. 2: 3


Cortisol is a
A. Mineralocorticoid
B. Glucocorticoid
c. catecholamines
D. Thymosins


If the wavelength of light used is 6000 A. The angular resolution of telescope of objective lens having diameter \( 10 \mathrm{cm} \) is rad
A \( \cdot 7.52 \times 10^{-6} \)
в. \( 6.10 \times 10^{-6} \)
c. \( 6.55 \times 10^{-6} \)
D. \( 7.32 \times 10^{-6} \)


Explain the given reactions with the examples. Oxidation reaction:
A \( \cdot C_{2} H_{5} O H \stackrel{A l k . K M n O_{4}}{\longrightarrow} C H_{2} O H C O O H \)
в. \( C_{2} H_{5} \) ОН \( \frac{\text {Аlк.КМп} O_{4}}{\longrightarrow} C H_{3} C H_{3} \)
c. \( C_{2} H_{5} O H \frac{A l k . K M n O_{4}}{\longrightarrow} C H_{3} C H_{2} O H \)
D. \( C_{2} H_{5} O H \frac{A l k . K M n O_{4}}{\longrightarrow} C H_{3} C O O H \)


The value of \( -3 \sqrt{-10} \) is equal to
A. \( -3 \sqrt{10} \)
00
B. \( 3 \sqrt{10} \)
c. \( -3 i \sqrt{10} \)
D. None of these


In E.coli, the chain initiating amino acid
in protein synthesis is
A. N-formyl methionine
B. Methionine
c. Glycine
D. serine


\( \boldsymbol{P}(\boldsymbol{x})=\mathbf{5} \boldsymbol{x}^{5}+\mathbf{3} \boldsymbol{x}^{3}-\boldsymbol{7} \boldsymbol{g}(\boldsymbol{x})=\boldsymbol{2} \boldsymbol{x}^{2}+\mathbf{1} \)
Find \( q(x) \) and \( r(x) \) by dividing \( p(x) \) by \( g(x) \)


For each natural number \( k \), let \( C_{k} \)
denote the circle with radius \( k \)
centimeters and centre at the origin \( O \)
on the circle \( C_{k} \) a particle moves \( k \) centimetres in the counter-clockwise
direction. After completing its motion
on \( C_{k}, \) the particle moves to \( C_{k+1} \) in the radial direction (away from centre). The motion of the particle continues in this manner. The particle starts at \( (1,0) . \) If the particle crosses the positive direction of \( x \) -axis for the first time on
the circle \( C_{n}, \) then \( n= \)
A. 4
B. 5
c. 6
D.


Which of the following is used as refrigerant? This question has multiple correct options
A. \( C H_{3} C O C H_{3} \)
в. \( C C l_{4} \)
\( \mathbf{c} \cdot C_{2} H_{5} C l \)
D. \( C F_{4} \)


A beam of electrons accelerated by a large potential difference \( V \) is made to
strike a metal target to produce \( \boldsymbol{X} \) rays. For which of the following values of \( V, \) the resulting \( X \) -rays have the
lowest minimum wave length:
A . \( 10 \mathrm{KV} \)
в. \( 20 \mathrm{KV} \)
c. \( 30 K V \)
D. \( 40 \mathrm{KV} \)


If \( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{3} & \mathbf{7} \\ \mathbf{2} & \mathbf{5}\end{array}\right] \) and \( \boldsymbol{B}=\left[\begin{array}{cc}-\mathbf{3} & \mathbf{2} \\ \mathbf{4} & -\mathbf{1}\end{array}\right] \) find
the matrix \( C \) if \( 2 C=A+B \)


Two radios were bought at the same
cost. One was sold at a profit of \( 12 \% \)
and the other at a profit of \( 17 \% \). If the difference in the selling price of the two radios was \( R s 125, \) what was the cost
price of each radio?


A cell of E.M.F. E and internal resistance
supplies currents for the same time through external resistance \( \boldsymbol{R}_{1} \) and \( \boldsymbol{R}_{2} \)
respectively. If the heat produced in both cases is the same then the internal
resistance is
A \( \cdot 1 / r=1 / R_{1}+1 / R_{2} \)
B. \( r=\left(R_{1}+R_{2}\right) / 2 \)
\( \mathbf{c} \cdot r=\left(R_{1} R_{2}\right) \)
D. \( r=R_{1}+R_{2} \)


A block of mass \( 0.1 k g \) is held against a wall by applying a horizontal force on
\( \mathbf{5} N \) on it. If \( \mu_{s} \) between the wall and the
block is 0.5 the magnitude of the frictional force acting on the block is :
A . \( 0.98 N \)
B. \( 0.49 N \)
c. \( 4.9 N \)
D. \( 2.5 N \)


Evaluate \( \int_{0}^{2} x \sqrt{x+2} d x \)


On a platform a man is watching two trains one leaving the station the other approaching the station, both with the same velocity \( 2 \mathrm{m} / \mathrm{s} \) and blowing their horn with a frequency 480 Hz. The number of beats heard by the man will
be (Velocity of sound in air is \( 320 \mathrm{m} / \mathrm{s} \) )
A . 6
B. 3
c. 2
D. 4


The most abundant element in the
earths crust by weight is:
A . \( S i \)
в. \( A l \)
\( c \cdot O \)
D. \( F e \)


(a) A mobile phone lies along the principal axis of a concave mirror. Show, with the help of a suitable
diagram, the formation of its image. Explain why magnification is not uniform.
(b) Suppose the lower half of the concave mirror's reflecting surface is
covered with an opaque material. What
effect this will have on the image of the object? Explain.


Oxygen can be prepared by heating
A. potassium permanganate
B. methane
c. carbon
D. none of these


Due to migration to cities, the population of a town decreases every year by \( 10 \% \). If the present population of
the town is \( 14600, \) find the population two years hence.


Which one of the following is not a photosynthetic diazotroph.
A. Nostoc
B. Frankie
c. Anabaena
D. Rhodospirillum


Which of the following has a weak
force?
This question has multiple correct options
A. covalent bonds
B. ionic bonds
C . Dipole-dipole interaction
D. London dispersion force


A transmitter transmits at a
wavelength of \( 300 m . \) A condenser of
capacitance \( 2.4 \mu F \) is being used. The
value of the inductance for the resonant
circuit is approximately
В . \( 10^{-6} \) Н
\( \mathrm{c} \cdot 10^{-8} \mathrm{H} \)
D. \( 10^{-10} H \)


Solve graphically the following pairs of
equations
\( 4 x-y-5=0 ; x+y-5=0 \)
\( \mathbf{A} \cdot(2,3) \)
B \( \cdot(3,3) \)
\( \mathbf{c} \cdot(4,3) \)
D. None of these


A magnetic needle lying parallel to a magnetic field requires W units of work
to turn it through \( 60^{0} \). The torque needed to maintain the needle in this
position will be:
A \( \cdot \sqrt{3} \mathrm{W} \)
B. \( W \)
c. \( \sqrt{3 / 2} \mathrm{W} \)
D. 2w


" \( X e F_{4} \) disproportionates to stable \( X e O \)
and \( X e O_{4} \)
Answer whether the above statement is
true or false.
If true enter 1 , else enter 0 .


Dry hydrogen chloride gas does not turn blue litmus to red whereas hydrochloric acid does. Why?


Suppose a gaseous mixture of \( H e, N e, A r, K r \) is irradiated with photons of frequency appropriate to
ionize \( A r . \) What ions will be present in the mixture?
\( \mathbf{A} \cdot A r^{+} \)
в. \( K r^{+} \)
\( \mathrm{c} \cdot \mathrm{He}^{+} \)
D. Both \( A \) and \( B \)


At a given place on earth's surface the horizontal component of earths magnetic field is \( 2 \times 10^{-5} \mathrm{T} \) and
resultant magnetic field is \( 4 \times 10^{-5} \mathrm{T} \)
The angle of dip at this place is?
A . \( 30^{\circ} \)
B. \( 60^{\circ} \)
\( c \cdot 90^{\circ} \)
D. \( 45^{\circ} \)


Match column I with item of column II.
\( \begin{array}{llll} & \text { Column I } & & \text { Column II } \\ \text { I. } & \text { Lohi } & \text { A. } & \text { Hosiery } \\ \text { II. } & \text { Nali } & \text { B. } & \text { Coarse wool } \\ \text { III. } & \text { Patanwadi } & \text { C. } & \text { Carpet wool } \\ \text { IV. } & \text { Marwari } & \text { D. } & \text { Good quality wool }\end{array} \)
Select the correct alternative.
A. \( |-D,||-C,|||-A, \mid V-B \)
B. I-D, II-B, III-A, IV-C
C. \( \mid-\mathrm{C}, \) ।I-В, \( , \) II \( -\mathrm{A}, \) IV-D
D. I-B, II-C, III-A, IV-D


Oxidation states of chlorine in the
products when chlorine reacts with hot
and conc. NaOH are:
A \( \cdot-1,+1 \)
B. -1,+3
\( c \cdot-1,+5 \)
D. -1,+7


i). State Raoult's Law.
ii). The vapour pressure of pure benzene at a certain temperature is 0.850 bar. \( A \) non-volatile non-electrolyte solid weighing 0.5 g when added to 39.0 gof benzene (molar mass 78 g \( m o l^{-1} \) ). Vapour pressure of the solution, then is
0.845 bar. What is the molar mass of
the solid substance?


The projection of \( \overrightarrow{\boldsymbol{a}}=\boldsymbol{2} \hat{\boldsymbol{i}}+\boldsymbol{3} \hat{\boldsymbol{j}}-\boldsymbol{2} \hat{\boldsymbol{k}} \) on
\( \overrightarrow{\boldsymbol{b}}=\hat{\boldsymbol{i}}+\boldsymbol{2} \hat{\boldsymbol{j}}+\boldsymbol{3} \hat{\boldsymbol{k}} \) is:
A \( \cdot \frac{1}{\sqrt{14}} \)
B. \( \frac{2}{\sqrt{14}} \)
c. \( \frac{-1}{\sqrt{14}} \)
D. \( \frac{-2}{\sqrt{14}} \)


A parallel beam of light is incident from
air at an angle \( \alpha \) on the side PQ of a
right-angled triangular prism of refractive index \( n=\sqrt{2} . \) Light
undergoes total internal reflection in
the prism at the face PR when \( \alpha \) has
minimum value of \( 45^{\circ} . \) The angle \( \theta \) of
the prism is:
A . \( 15^{\circ} \)
B . \( 22.5^{\circ} \)
\( c .30 \)
D. 45


When the displacement of a particle executing SHM is one - fourth of its amplitude, what fraction of the total
energy is the kinetic energy?
A \( \cdot \frac{16}{15} \)
в. \( \frac{15}{16} \)
\( c \cdot \frac{3}{4} \)
D. \( \frac{4}{3} \)


Very short answer type:
Mention the most significant function
of bundle sheath.


Which metal is protected by layer of its own oxide?
A . \( A l \)
в. \( A g \)
c. \( A u \)
D. \( F e \)


The limiting friction between two surfaces does not depend
A. on the nature of two surfaces.
B. on normal reaction
c. on the weight of the body
D. on height of the body


Sea water of density \( 1300 k g m^{-3} \) exerts a pressure of \( 104 \times 10^{5} P a \) on the floor.
Calculate the depth of the sea at that place \( \left(\boldsymbol{g}=\mathbf{1 0 m} \boldsymbol{s}^{-2}\right) \)


If \( A, B \) are complementary angles, then \( \cos ^{2} A+\cos ^{2} B \)


A ball is thrown vertically upward with speed \( 70 m / s . \) After \( 1 s, \) another ball is dropped from a height \( 185 \mathrm{m} \) in the same vertical line. At what height the balls collide?
\( \mathbf{A} \cdot 150 \mathrm{m} \)
B. \( 160 \mathrm{m} \)
c. \( 168 \mathrm{m} \)
D. 165m


Let \( \boldsymbol{A}=\left[\boldsymbol{a}_{i j}\right] \) and \( \boldsymbol{B}=\left[\boldsymbol{b}_{\boldsymbol{i} j}\right] \) be two \( \boldsymbol{3} \times \boldsymbol{3} \)
real matrices such that \( b_{i j}= \)
\( (3)^{(i+j-2)} a_{i j}, \) where \( i, j=1,2,3 . \) If the
determinant of \( B \) is 81 , then the
determinant of A is :
A. \( 1 / 3 \)
B. 3
c. \( 1 / 81 \)
D. \( 1 / 9 \)


Excess of Natt ions in human system
causes
A. Diabetes
B. Anemia
c. Low blood pressure
D. High blood pressure


A \( 5 k g \) rod of square cross section 5 cm
on a side and 1 m long is pulled along a
smooth horizontal surface by a force
applied at one end. The rod has a
constant acceleration of \( 2 m / s^{2} \) Determine the elongation in the rod.
(Young's modulus of the material of the
\( \left.\operatorname{rod} \text { is } 5 \times 10^{3} N / m^{9}\right) \)
A. Zero, as for elongation to be there, equal and opposite forces must act on the rod
B. Non-zero but cannot be determine from the given situation
\( \mathbf{c} .4 \mu m \)
D. \( 16 \mu m \)


A ball is thrown vertically upward from the \( 12 \mathrm{m} \) level with an initial velocity of \( 18 \mathrm{m} / \mathrm{s} . \) At the same instant an open
platform elevator passes the \( 5 \mathrm{m} \) level, moving upward with a constant velocity of \( 2 \mathrm{m} / \mathrm{s} \). Determine \( \left(\mathrm{g}=9.8 \mathrm{m} / \mathrm{s}^{2}\right) \)
(a) when and where the ball will meet
the elevator
(b) the relative velocity of the ball with respect to the elevator when the ball
hits the elevator.


Arrange the following compounds in increasing order of acidity:
\( \boldsymbol{C H} \equiv \boldsymbol{C H}, \boldsymbol{C H}_{2}= \)
\( \boldsymbol{C H}_{2}, \boldsymbol{C I C H}_{2} \boldsymbol{C H}_{3}, \boldsymbol{F C H}_{2} \boldsymbol{C H}_{3}, \boldsymbol{C H}_{3} \boldsymbol{C l} \)
A. \( C H \equiv C H<C H_{2}=C H_{2}<C H_{3} C H_{3}< \)
\( C I C H_{2} C H_{3}<F C H_{2} C H_{3} \)
в. \( C H_{3} C H_{3}<C H_{2}=C H_{2}<C H \equiv C H< \)
\( C I C H_{2} C H_{3}<F C H_{2} C H_{3} \)
c. \( C I C H_{2} C H_{3}<F C H_{2} C H_{3}<C H_{2}=C H_{2}<C H \equiv \)
\( C H<C H_{3} C H_{3} \)
D. \( C H_{3} C H_{3}<C I C H_{2} C H_{3}<F C H_{2} C H_{3}<C H_{2}= \)
\( C H_{2}<C H \equiv C H \)


What is the function of valves present in
the heart?


Hiccough (hiccup) is due to activity of
A. Intercostal muscle
B. Food in air tract
c. Diaphragm
D. Inadequate oxygen in environment


In Wheatstone's bridge, three resistors \( P, Q, R \) are connected in three arms in
order and \( 4^{t h} \) arm is formed by two
resistors \( s_{1} \) and \( s_{2} \) connected in
parallel. The condition for bridge to be balanced is \( \frac{P}{Q}= \)
A. \( \frac{R\left(s_{1}+s_{2}\right)}{s_{1} s_{2}} \)
в. \( \frac{s_{1} s_{2}}{R\left(s_{1}+s_{2}\right)} \)
c. \( \frac{R s_{1} s_{2}}{\left(s_{1}+s_{2}\right)} \)
D. \( \frac{\left(s_{1}+s_{2}\right)}{R s_{1} s_{2}} \)


Uricose glands are part of
A. Colleterial glands
B. Mushroom glands
c. conglobate glands
D. Vasa deferentia


\( \boldsymbol{H}_{2} \boldsymbol{O}_{2}+\boldsymbol{C l}_{2} \rightarrow \boldsymbol{2} \boldsymbol{H} \boldsymbol{O} \boldsymbol{l} \boldsymbol{l} \)
A. True
B. False


In the sexual mode of reproduction, greater diversities are generated.
A. True
B. False


Which of the following reactions can be used for the preparation of propane? This question has multiple correct options
\( \mathbf{A} \cdot C H_{3} C H=C H_{2} \underset{2 . C H_{3} C O O H}{1 . B_{2} D_{H}} \)
B. \( C H_{3} C H_{2} C H_{2} C l_{2 . H_{2} O}^{1 . M g / \text { (ther }} \)
C \( \cdot C H_{3} C H_{2} C H_{2} I^{R e d P / H I / 150^{\circ} C} \)
D. \( C H_{3} C H_{2} C H_{2} C O O N a \stackrel{N a O H / C a o}{\Delta} \)


Mustard gas is represented by formula:
A \( \cdot C H_{2} C l_{2} \)
в. \( C_{4} H_{8} C l_{2} S \)
c. \( C_{2} H_{2} \)
D. \( C C l_{3} N O_{3} \)


Find the term of the expansion of \( (\sqrt[3]{x^{-2}}+x)^{7} \) containing \( x \) in the
second power
\( \mathbf{A} \cdot T_{4} \)
в. \( T_{5} \)
c. \( T_{6} \)
\( \mathbf{D} \cdot T_{7} \)


\( S F_{2}, S F_{4} \) and \( S F_{6} \) have the
hybridisation of sulphur atom
respectively as:
A \( \cdot s p^{2}, s p^{3}, s p^{3} d^{2} \)
B \( \cdot s p^{3}, s p^{3}, s p^{3} d^{2} \)
\( \mathbf{c} \cdot s p^{3}, s p^{3} d, s p^{3} d^{2} \)
D \( \cdot s p^{3}, s p^{3} d^{2}, d^{2} s p^{3} \)


Solve the following inequalities graphically in two-dimensional plane:
\( x+y<5 \)


A long solenoid with 20 turns per \( c m \)
has a small loop of area \( 2.0 \mathrm{cm}^{2} \) placed inside the solenoid normal to its axis. If
the current carried by the solenoid changes steadily from \( 2.0 A \) to \( 4.0 A \) in
\( 0.1 \mathrm{sec}, \) calculate the induced emf in
the loop while the current is changing.


(o)
(d)


In the conversion of \( C_{2} H_{4} \) to \( C_{2} H_{6} \)
breakage of one \( \pi \) bond accounts for
formation of \( \sigma \) bond.
A .
B. 2
\( c \cdot 3 \)
D.


Find the limit \( \lim _{x \rightarrow 0} \frac{x}{\sqrt{1+x}-1} \)


A stone is dropped into a well and the report of the stone striking the bottom is heard 7.7 seconds after it is dropped.
Assume that the stone falls \( 16 t^{2} m \) in \( t \)
seconds and that the velocity of sound
is 1,120 per second. The depth of the well is:
\( \mathbf{A} \cdot 784 \mathrm{m} \)
в. \( 342 \mathrm{m} \)
\( c .1568 \mathrm{m} \)
D. \( 156.8 \mathrm{m} \)
E. none of these


Find the derivative of the following function at the indicated points. \( \sin 2 x \) at \( x=\frac{\pi}{2} \)


Codon degeneracy means that
A. Several of the amino acids are coded by more than one codon
B. One codon can code for many amino acids
C. One amino acid can be coded by only one codon.
D. The codons are triplet nucleotide sequences.


Deforestation causes climatic changes.
A. True
B. False


\( \ln \Delta A B C, A B=8 \mathrm{cm}, A C=5 \mathrm{cm} \) and
\( \boldsymbol{m} \angle \boldsymbol{A}=\mathbf{5 0}^{\circ} . \) Then
(a) What is the length of the perpendicular from \( C \) to \( A B ? \)
(b) Find the length of BC \( \left[\sin 50^{\circ}=0.7660, \cos 50^{\circ}=\right. \)
\( 0.6428, \) tan50 \( ^{\circ}=1.1918 \)


In polysaccharides, the linkage connecting monosaccharides is called:
A. Glycoside
B. Nucleoside
c. Glycogen
D. Peptide


Chlorine, bromine and iodine form a Dobereiner's triad. Chlorine has atomic
mass 35.5 and iodine has atomic mass
126.9. Predict the atomic mass of
bromine.


Find the value of the determinant \( \left|\begin{array}{ccc}1 & 0 & 0 \\ 2 & \cos x & \sin x \\ 3 & \sin x & \cos x\end{array}\right| \)
\( \mathbf{A} \cdot \cos 2 x \)
B.
\( c \cdot 0 \)
D. \( \sin 2 x \)


If the sum of 7 terms is \( 49, \) and the sum
of 17 terms is \( 289, \) find the sum of \( n \)
terms.


Choose the correct answer from the
alternatives given.
Directions for questions 71 to 75 : Study
the following bar-graph and answer the
questions What is the ratio of highest
consumption in the year 2012 and 2013
respectively?
A . 7: 6
B. 6: 7
\( c \cdot 7: 2 \)
D. 14: 1


If radius of \( 3^{r d} \) orbit of \( L i^{2+} \) ion is 'x' \( \mathrm{cm} \)
then de-broglie wavelength of electrons
in the \( 1^{s t} \) orbit is :
\( A \cdot \frac{2 \pi x}{3} \mathrm{cm} \)
в. \( 6 \pi x \) ст
c. \( 3 \pi x \) ст
D. \( \frac{2 \pi x}{6} \mathrm{cm} \)


At what angle will a ray of light be inclined on one face of an equilateral
prism, so that the emergen ray may graze
the second surface of the prism \( (\mu=2) \)
A \( \cdot 30^{\circ} \)
B . \( 90^{\circ} \)
c. \( 45^{\circ} \)
D. \( 60^{\circ} \)


Which of the following is an element?
A. sand
B. Diamond
c. Nacl
D. Glass


Solutions which strictly obey
law are called
solutions.


A bomber plane moves horizontally with a speed of \( 600 \mathrm{m} / \mathrm{s} \) and a bomb released from it, strikes the ground in 10 \( s \). The angle with horizontal at which it strikes the ground will be
\( A \cdot \tan ^{-1}(1 / 2) \)
B \cdot \( \tan ^{-1}(1 / 6) \)
C \( \cdot \tan ^{-1}(4 / 5) \)
\( \mathbf{D} \cdot \tan ^{-1}(3 / 4) \)


The radioactivity in any nucleus is measured in
A. Curie
B. Rutherford
c. Both
D. Newton


Area enclosed by curves \( y=2^{x} \) and
\( \boldsymbol{y}=|\boldsymbol{x}+\mathbf{1}| \) in the first quadrant is?
A \( \cdot \frac{1}{2}-\frac{1}{\log 2} \)
B. \( \frac{3}{2}-\frac{1}{2 \log 2} \)
c. \( \frac{3}{2}-\frac{1}{\log 2} \)
D. \( \frac{1}{2}+\frac{3}{\log 2} \)


Mineral nodules present in ocean which can meet shortage of important soil nutrient are
A. Manganese nodules
B. Phosphorite nodules
c. Magnesium nodules
D. All of the above


Benzene reacts with chlorine in
presence of light to yield:
A. chlorobenzene
B. trichlorobenzene
c. tetrachlorobenzene
D. benzenehexachloride