The element that does not show
catenation is:
\( A \cdot S n \)
в. \( G e \)
\( c \cdot s i \)
D. \( P b \)


Which of the following is an elastomer?
A. Vulcanized rubber
B. Dacron
c. Polystyrene
D. Melamine


In CAM the R.Q will be
A. zero
B. 1
c. More than one
D. Less than one


lonisation energy in the alkali metals
group:
A. increases from Li to cs
B. decreases from Li to cs
c. remains the same
D. first increases then decreases


Explain why rusting of iron objects is faster in coastal area than in deserts.


Evaluate: \( \int\left(\sqrt{\boldsymbol{x}}+\frac{\mathbf{1}}{\sqrt{\boldsymbol{x}}}\right) \boldsymbol{d} \boldsymbol{x} \)


An \( L C \) circuit contains a 20 m \( H \)
inductor and a \( 50 \mu F \) capacitor with an
initial charge of 10 mC.The resistance
of the circuit is negligible. Let the instant circuit is closed be at \( t=0 \)
What is the total energy stored initial? Is it conserved during the \( L C \) oscillations?
A. \( 0.01 \mathrm{J} \), yes
B. \( 0.1 \mathrm{J} \), yes
c. 1 J, yes
D. 2 J, yes


Find the area of a rhombus if its
vertices are (3,0),(4,5),(-1,4) and (-2,-1) taken in order


Oxidation of ammonia yields:
A \( . N O_{2} \)
в. \( N_{2} \),
c. \( N_{2} O_{5} \)
D. \( N O \)


Evaluate the following:
\( \int(3 x+1) \sqrt{2 x-1} d x \)


Let \( x \) be a real number \( [x] \) denotes the
greatest integer function, and \( \{x\} \)
denotes the fractional part and \( (x) \)
denotes the least integer function,then
solve the following. \( [x]^{2}+2[x]= \)
\( 3 x, 0 \leq x \leq 2 \)
\( \mathbf{A} \cdot\{0,1\} \)
B . \{-1,1\}
c. \{0,-1\}
D \( \cdot\{2,1\} \)


Which of the following are the ores of
zinc?
A. Calamine and zinc blend
B. Zinc blend and cerussite
c. calomine and siderite
D. zinc blend and carnallite


Food reserve of phaeophyceae is
A. Laminarin and floridean starch
B. Laminarin and mannitol
c. Fat
D. starch


The heart sound "DUP" is produced when
A. Mitral valve opens
B. Mitral valve closes
c. semilunar valve at the base of aorta closes
D. Tricuspid valve opens


An electron is moving round the nucleus of a hydrogen atom in a circular orbit of radius r. The coulomb
force \( \vec{F} \) between the two is -
\( ^{A} \cdot_{K} \frac{e^{2}}{r^{2}} \)
в. \( -K \frac{e^{2}}{r^{3}} \)
c. \( _{K} \frac{e^{2}}{r^{3}} \vec{r} \)
D. \( -K \frac{e^{2}}{r^{2}} \)


You are given a rod of length \( L \). The
linear mass density is \( \lambda \) such that \( \lambda= \) \( a+b x . \) Here \( a \) and \( b \) are constant and
the mass of the rod increases as \( x \)
decreases. Find the mass of the rod.


The half-life of \( ^{215} A t \) is \( 100 \mu \) s. The time
taken for the radioactivity of a sample of \( ^{215} A t \) to decay to \( 1 / 16 \) th of its initial value is
A. \( 400 \mu s \)
B. \( 6.3 \mu s \)
c. \( 40 \mu s \)
D. 300\mus


Simplify: \( (-\sqrt{3}+\sqrt{-2})(2 \sqrt{3}-i)=(a+ \)
ib) \( (-\sqrt{3}+\sqrt{-2}) . \) Find value of a and \( b \)


Find the approximate change in the
volume \( V \) of a cube of side \( x \) meters
caused by increasing the side by \( 2 \% \)


If \( \sin \theta=-\frac{4}{5}, \pi<\theta<\frac{3 \pi}{2}, \) then find
i) \( \sin 2 \theta \)
ii) \( \cos 2 \theta \)
iii) \( \tan 2 \theta \)


Draw labelled graphs to show how
electrical resistance varies with
temperature for:
(a) A metallic wire.


Assertion
Nitrogen does not form \( \boldsymbol{N} \boldsymbol{C} \boldsymbol{I}_{\mathbf{5}} \) or \( \boldsymbol{N} \boldsymbol{F}_{\mathbf{5}} \)
but phosphorus can.
Reason
Nitrogen \( \left(1 s^{2} 2 s^{2} 2 p^{3}\right) \) lacks \( 2 d \) -orbitals
in which electrons of 2 s can be excited
to make five orbitals unpaired. Only
three electrons remain unpaired hence
only \( N X_{3} \) is formed. In case of
\( P\left(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{3}\right), 3 s \) electron can be
excited into \( 3 d \) vacant orbitals thus
making five unpaired electrons, thus
\( P X_{5} \) is possible.
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


One mole of an ideal diatomic gas
undergoes a transition from \( A \) to \( B \)
along a path \( A B \) as shown in the figure
The change in internal energy of the gas during the transition is:
A. 20 .
B. \( -12 k J \)
\( c \cdot 20 k J \)
D. \( -20 k J \)


The electric field for \( r<R_{1} \) is given by \( \boldsymbol{E}=\frac{\boldsymbol{X} \boldsymbol{Q}}{\boldsymbol{\pi} \varepsilon_{0} \boldsymbol{r}^{2}}\left[\frac{r^{3}-\boldsymbol{R}_{1}^{3}}{\boldsymbol{R}_{2}^{3}-\boldsymbol{R}_{1}^{3}}\right] . \) Find \( \boldsymbol{X} \)


\( f(x)=x+2 \cos x \) is increasing in
A \( \cdot\left(0, \frac{\pi}{2}\right) \)
В \( \cdot\left(\frac{-\pi}{2}, \frac{\pi}{6}\right) \)
c. \( \left(\frac{\pi}{2}, \pi\right) \)
D. \( \left(\frac{-\pi}{2} \frac{\pi}{2}\right) \)


How many images of a candle will be formed if it is placed between two
parallel plane mirrors separated by 40 \( \mathrm{cm} ? \)


Study the bar graph and answer the
questions. The graph shows the quantities of different crop production
in different states of India.

The difference in value of production of
wheat and rice in Uttar Pradesh is
A. 60 tonnes
B. 80 tonnes
c. 20 tonnes
D. 40 tonnes


The \( p H \) of lemonjuice is:
A. 4.2 to 4.4
B. 10.2 to 11.4
\( c \cdot 6.2 \) to 6.8
D. 2.2 to 2.4


When \( \left(x^{3}-2 x+p x-q\right) \) is divided by
\( \left(x^{2}-2 x-3\right), \) the remainder is \( (x-6) \)
What are the values of \( p, q \) respectively.
A . -2,-6
в. 2,-6
c. -4,12
D. 2,6


if \( \lim _{x \rightarrow 0} \frac{a \sin x-b x+c x^{2}+x^{3}}{2 x^{2} \log (1+x)-2 x^{3}+x^{4}} \)
exists and is finite, then
A \( \cdot a=-6, L=-\frac{3}{40} \)
B. \( a=-6, L=\frac{3}{40} \)
c. \( b=6, c=0 \)
D. \( a=-6, b=-6, L=\frac{3}{40} \)


Write characteristics of an ideal fuel.


If \( \boldsymbol{f}:\left[\mathbf{0}, \frac{\boldsymbol{\pi}}{\mathbf{2}}\right] \rightarrow[\mathbf{0}, \infty] \) be a function
defined by \( y=\sin \left(\frac{x}{2}\right), \) then \( f \) is
A . Injective
B. Surjective
c. Bijective
D. None of these


Moment of inertia of a solid about its geometrical axis is given by \( l=\frac{2}{5} M R^{2} \)
where \( M \) is mass \( \& R \) is radius. Find
out the rate by which its moment of inertia is changing keeping density constant at the moment \( \boldsymbol{R}= \)
\( \mathbf{1} \boldsymbol{m}, \boldsymbol{M}=\mathbf{1} \boldsymbol{k} \boldsymbol{g} \) \& rate of change of
radius w.r.t. time \( 2 m s^{-1} \)
A. \( 4 \mathrm{kg} \mathrm{ms}^{-1} \)
B. 2 \( k g m^{2} s^{-1} \)
c. \( 4 \mathrm{kg} \mathrm{m}^{2} \mathrm{s}^{-1} \)
D. None of these


Find a value of \( \boldsymbol{x} \) if \( \left|\begin{array}{cc}\boldsymbol{x} & \boldsymbol{2} \\ \boldsymbol{1} \boldsymbol{8} & \boldsymbol{x}\end{array}\right|=\left|\begin{array}{cc}\boldsymbol{6} & \boldsymbol{2} \\ \boldsymbol{1} \boldsymbol{8} & \boldsymbol{6}\end{array}\right| \)


If \( i=\sqrt{-1}, \) then \( 1+i^{2}+i^{3}-i^{6}+i^{8} \) is
equal to -
A. 2-
в.
\( c \cdot-3 \)
D. -


Two bodies of equal weight are kept at heights of \( h \) and \( 1.5 h \) respectively. The ratio of their P.E. is
\( A \cdot 3: 2 \)
B. 2:3
\( c \cdot 1: 1 \)
D. None of these


Between any two points in a circuit, the sum of all \( \ldots \ldots . . . . . . . \) is the same through
any pathway.
A . charge
B. current
c. potential difference
D. resistance


If mass-energy equvalence is taken into account, when water is cooled to form
ice, the mass of ater should
A. Increase
B. Remain unchanged
c. decrease
D. First increase and then decrease


\( 0.73 g \) of organic compound gave \( 1.32 g \)
\( C O_{2} \). The \( \% \) of carbon in the organic
compound is:
\( A \cdot 55.24 \)
B. 49.32
c. 48.64
D. 45.24


Derive the expression for torque acting on a dipole \( \boldsymbol{\tau}=\boldsymbol{P} . \boldsymbol{E} \sin \boldsymbol{\theta} \)


State True or False.
Estimation of oxygen in an organic compound can be made by Aluise
method.
A. True
B. False


Which temperature is hottest?
A \( \cdot 17^{\circ} \mathrm{C} \)
\( \mathbf{B} \cdot 58^{\circ} F \)
\( \mathbf{c} \cdot 290 K \)
D. \( 16^{\circ} \mathrm{C} \)


sinusoidal waves \( 5.00 \mathrm{cm} \) in amplitude are to be transmitted along a string having a linear mass density equal to
\( 4.00 \times 10^{-2} k g / m . \) If the source can
deliver an average power of \( 90 W \) and the string is under a tension of \( 100 N \)
then find the frequency at which the source can operate. (take \( \left.\pi^{2}=10\right) \)


A Science teacher wrote 3 statements
about rancidity:
(i) When fats and oils are reduced, they become rancid
(ii) In chips packet, rancidity is
prevented by oxygen
(iii) Rancidity is prevented by adding antioxidants.
Selects the correct option.
A. (i)
B. (ii) and (iii)
c. (iii)
D. (i), (ii) and (iii)


If \( \boldsymbol{y}=\boldsymbol{e}^{\boldsymbol{x}^{3}}, \) find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \)


Give the uses of ultraviolet radiation


On hydrolysis, \( P C I_{3} \) gives:
A \( \cdot H_{3} P O_{3} \)
в. \( H_{3} P O_{4} \)
c. \( P O C I_{3} \)
D. \( H P O_{3} \)


Q Type your question
chamber of volume \( V / 4 \) in the cube as
shown. The chamber is completely filled
by \( \mathrm{m} \) kg of water. Water leaks through a hole \( \mathrm{H} \) and spreads in the whole cube.
Then then work done by gravity in this
process assuming that the complete
water finally lies at the bottom of the
cube is
\( A \)
B. \( \frac{3}{8} m g \)
\( c \)
\( D \)
\( m g \)


A uniform magnetic field of induction \( \mathrm{B} \)
is confined to a cylindrical region of
radius R. The magnetic field is
increasing at a constant rate of \( \frac{d B}{d t} T s^{-1} . \) An electron of charge \( e \) placed at the point \( P \) on the periphery of the field experiences an acceleration
A \( \cdot \frac{1}{2} \frac{e R}{m} \frac{d B}{d t} \) toward left
B. \( \frac{1}{2} \frac{e R}{m} \frac{d B}{d t} \) toward right
c. \( \frac{e R}{m} \frac{d B}{d t} \) toward left
D. zero


Which of the following is/are correct
about critical conditions of real gas
following van der Waal's equation of
state?
This question has multiple correct options
A \( \cdot \) At \( T_{C}, \) there is no distinction between liquid and
vapour state, hence the density of liquid becomes equal to the density of vapour
B. \( A t \)
\( T_{C}, \) both \( \left[\frac{\partial P}{\partial V}\right]_{T} \) and \( \left[\frac{\partial^{2} P}{\partial V^{2}}\right]_{T} \) are equal to zero
\( \mathbf{C} \cdot Z=3 / 8 \) for every gas at \( T_{C}, \) and gases are more compressible than ideal gas
D. For temperature less than \( T_{C} \), the volume has three imaginary roots


The method to purify colloids is:
A . peptisation
B. coagulation
c. dialysis
D. bredig's arc method


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


You have studied in Class IX, that a
median of a triangle divides it into two triangles of equal areas. Verify this result for \( \triangle A B C \) whose vertices are
\( \boldsymbol{A}(\mathbf{4},-\mathbf{6}), \boldsymbol{B}(\mathbf{3},-\mathbf{2}) \) and \( \boldsymbol{C}(\mathbf{5}, \mathbf{2}) \)


Find the square root of the following numbers by the factorisation numbers:
82944


Statement \( 1: A \) salt dissolved in an
organic solvent will be a good electrical conductor.
Statement 2: Salts will not dissolve
appreciably in an organic solvent.
A. Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation of Statement 1
B. Both the Statement 1 and Statement 2 are correct, but Statement 2 is not the correct explanation of Statement 1.
c. statement 1 is correct, but statement 2 is not correct
D. Statement 1 is not correct, but Statement 2 is correct


\( \operatorname{Let} f(x)=\left(2-\frac{x}{a}\right)^{\tan \left(\frac{\pi x}{2 a}\right)}, x \neq a \)
The value which should be assigned to \( f \) at \( x=a \) so that it is continuous
everywhere is
A \( -\frac{2}{\pi} \)
B . \( e^{-2 / \pi} \)
\( c \cdot 2 \)
\( \mathbf{D} \cdot e^{2 / \pi} \)


In stationary wave, antinodes are the
points where there is
A. Minimum displacement and minimum pressure change
B. Minimum displacement and maximum pressure change
C. Maximum displacement and maximum pressure change
D. Maximum displacement and minimum pressure change


Suppose you want to dry your school uniform quickly. Would spreading it near an anghiti or heater help you? If yes, how?


A body of mass \( 0.2 \mathrm{kg} \) dropped from a height '6 m'. If \( e=\frac{1}{\sqrt{6}} \) then K.E. lost
during its first bounce from the ground
is
\( \mathbf{A} \cdot 1.96 J \)
B. \( 9.8 J \)
c. 19.6 .5
D. zero


If \( \boldsymbol{f}(\boldsymbol{x})=-\sqrt{25-\boldsymbol{x}^{2}}, \) then find
\( \lim _{x \rightarrow 1} \frac{f(x)-f(1)}{x-1} \)


\( A g N O_{3}(a q .) \) was added to an aqueous
\( K C l \) solution gradually and the
conductivity of the solution was
measured. The plot of conductance \( (\wedge) \)
versus the volume of \( \boldsymbol{A} \boldsymbol{g} \boldsymbol{N} \boldsymbol{O}_{3} \)
is
\( (\mathbf{R}) \)
\( (\mathbf{S}) \)
A \( \cdot(P) \)
B. \( (Q) \)
c. \( (R) \)
D. \( (S) \)


Who proposed the term Protista?


A short bar magnet placed in a horizontal plane has its axis aligned along the magnetic north-south direction. Null points are found on the
axis of the magnet at \( 14 \mathrm{cm} \) from the
centre of the magnet. The earth's
magnetic field at the place is \( 0.36 \mathrm{G} \) and the angle of dip is zero.What is the
total magnetic field on the normal
bisector of the magnet at the same distance as the null-point (i.e., \( 14 \mathrm{cm} \) )
from the centre of the magnet? (At null points, field due to a magnet is
equal and opposite to the horizontal component of earth's magnetic field.)


A minimum value of \( \sin x \cos 2 x \) is-
\( A \cdot 1 \)
B. - 1
c. \( -2 / 3 \sqrt{6} \)
D. None of these


Find the value of \( \left(x^{3} \times x^{7}\right) \div x^{12} \) for \( x= \)
(-2)


is a popular polyester.
A. Plastic
B. Polythene
C . Rayon
D. Terylene


Define adjacent angle.


In a statistical diagrammatic representation, rectangular bars drawn after a discontinuous series is called
graph.
A. bar
B. histogram
c. pie
D. frequency curve


Weak van der Waal forces are
responsible for Physisorption.
A. True
B. False


An ideal gas at a pressure of 1
atmosphere and temperature of \( 27^{\circ} \mathrm{C} \) is compressed adiabatically until its pressure becomes 8 times the initial
pressure, then the final temperature is
\( (\gamma=3 / 2) \)
\( \mathbf{A} \cdot 627^{0} C \)
В. \( 527^{\circ} \mathrm{C} \)
c. \( 427^{\circ} \mathrm{C} \)
D. \( 327^{\circ} \mathrm{C} \)


If \( \boldsymbol{f}(\boldsymbol{x})=\mathbf{1} \) for \( \boldsymbol{x}<\mathbf{0}=\mathbf{1}+\sin \boldsymbol{x} \) for
\( 0 \leq x<\pi / 2, \) then at \( x=0, \) then show
that the derivative \( f^{\prime}(x) \) does not exist.


If \( x+\frac{1}{x}=3, \) then \( x^{4}+\frac{1}{x^{4}}= \)
A. 81
B . 23
c. 25
D. 47


Prove that the relation \( R \) defined on set
\( Z \) as \( a R b \Leftrightarrow a-b \) is divisible by 3 , is
an equivalence relation


In an oscillating LC circuit the maximum charge on the capacitor is \( Q \) The charge on the capacitor when the energy is stored equally between the electric and magnetic field is:
A \( \cdot \frac{Q}{3} \)
в. \( \frac{Q}{\sqrt{3}} \)
c. \( \frac{Q}{\sqrt{2}} \)
D.


Derive an expression for the circuit
current


Although \( A u \) is soluble in aqua regia
but \( A g \) is not. Explain.


Four charges, all of the same magnitude, are placed at the four corners of a square. At the centre of the
square, the potential is \( \mathrm{V} \) and the field
is E. With suitable choices of the signs of the four charges, which of the following can be obtained? This question has multiple correct options
A. \( V=0, E=0 \)
B. \( V=0, E \neq 0 \)
c. \( V \neq 0, E=0 \)
D. \( V \neq 0, E \neq 0 \)


Coordinates of the focus of the parabola
\( x^{2}-4 x-8 y-4=0 \) are
A \( .(0.2) \)
B. (2,1)
c. (1,2)
D. (-2,-1)


Describe the energy transformation taking place in an oscillating pendulum.


The first term of an arithmetic
progression is 15 and the last term is
\( 85 . \) If the sum of all terms is \( 750, \) what is the 6th term?
A . 30
B. 40
\( c \cdot 45 \)
D. 55


What happens to energy when a charged particle moving in a magnetic field although a magnetic force is acting on it?
A . remains constant
B. increases
c. decreases
D. none of these


Distinguish between the following. Water pollution - Land pollution.


Boiling is a surface phenomenon.
A. True
B. False


The most acidic hydrogen atoms are
present in:
A. ethane
B. ethene
c. ethyne
D. benzene


Truncus arteriosus is divided into
pylangium and synangium in a frog, it was first reported by
A. Oliver
B. William Harvey
c. waller
D. Malpighi.


The vapour pressure of pure benzene is
\( 639.7 \mathrm{mm} \mathrm{Hg} \) and the vapour pressure of a solution of a solute in benzene at the
temperature is \( 631.9 \mathrm{mm} \) Hg. If the
molality of the solution is \( 156 \times 10^{-x} \)
then what is the value of \( x ? \)


Which set does clearly identify striated
muscles?
A. Cylindrical, syncytial and unbranched
B. Spindle, unbranched and uninucleated
C . Cylindrical, striped and nucleated
D. Cylindrical, striped and branched


The gravitational force with which the
earth attracts the moon:
A. is less than the force with which the moon attracts the earth
\( \mathbf{B} \). is equal to the force with which the moon attracts the earth
c. is greater than the force with which the moon attracts the earth
D. varies with the phases of the moon


When \( \log \left(\frac{x}{m}\right) \) is plotted against \( \log P \) we get a straight line with slope \( \frac{1}{n} \)
A . True
B. False


Check whether the following is a quadratic equation or not
\( (x+1)^{2}=2(x-3) \)


Q Type your question
(a) \( \mathbf{B r}_{\mathbf{2}} / \mathbf{r} \boldsymbol{e} \)
\( (b) B r_{2} / C C l_{4} \)
\( (c) \prod B B \)
(d) \( \boldsymbol{H} \boldsymbol{B} \boldsymbol{r} \)
This question has multiple correct options
\( \mathbf{A} \)
(a) and para
\( B \)
(b)
\( c \)
\( (c) \)
D. \( (1,2-\mathrm{H} \) shift gives more stable benzylic carbocation)
\( (d) \)


At what temperature will the hydrogen molecules escape from Earth's surface?
\( A \cdot 10^{4} K \)
B . \( 10^{3} \mathrm{K} \)
\( c \cdot 10^{2} k \)
D. \( 10^{1} \mathrm{k} \)


'The year 2016 will have February of \( \ldots \) days'.
A . 28
B. 29
c. 28.5
D. 30


Assertion
On cooling, the brown colour of nitrogen dioxide disappears.
Reason
On cooling, \( N O_{2} \) undergoes
dimerisation resulting in the pairing of
the odd electron in \( N O_{2} \)
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 greater polarizability of anion gives rise to character for the
bond.
A . covalent
B. ionic
c. coordinate
D. none of these


Minimize \( z=6 x+2 y, \) Subject to \( x+ \)
\( 2 y \geq 3, x+4 y \geq 4,3 x+y \geq 3, x \geq \)
\( \mathbf{0}, \boldsymbol{y} \geq \mathbf{0} \)


Sum of the series \( 1+2.2+3.2^{2}+ \)
\( 4.2^{3}+\ldots+100.2^{99} \) is
B. \( 99.2^{100}+1 \)
D. \( 100.2^{100}-1 \)


When ATP is hydrolyzed, which of the bond is cleaved?
A. P-O-P bond
B. Sugar phosphate
c. Phosphate nucleotide bond
D. Nucleotide sugar bond


An arrangement with a pair of quarter circular coils of radii \( r \) and \( R \) with a
common centre \( C \) and carrying a
current I is shown.
The permeability of free space is \( \mu_{0} . \) The
magnetic field at \( \mathrm{C} \) is :
A \( \cdot \mu_{0} I(1 / r-1 / R) / 8 \) into the page
B. \( \mu_{0} I(1 / r-1 / R) / 8 \) out the page
C. \( \mu_{0}(1 / r+1 / R) / 8 \) into the page
D・ \( \mu_{0}(1 / r+1 / R) / 8 \) out the page


Find the value of \( K \) if the point \( A(2,3), B \) \( (4, K) \) and \( C(6,-3) \) are collinear?


Assertion
When number of turns in a coil is
doubled, coefficient of self-inductance
of the coil becomes 4 times.
Reason
This is because \( L \alpha N^{2} \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The height of a room is 'a' and the areas of the two adjacent walls of a room are
b' and 'c'. The area of the roof will be
A \( \cdot \frac{b c}{a} \)
B. \( b c \)
c. \( \frac{a c}{b^{2}} \)
D. \( \frac{b c}{a^{2} c} \)


Prove that of all rectangles with given area, the square has the smallest perimeter.


An inert gas with more than one orbit,
has electrons in its outermost
shell.
\( A \cdot O \)
B. 2
\( c \cdot 4 \)
D. 8


Find the order of magnitude of length of rod having length \( \left(10^{6}+10^{3}\right) \mathrm{m} \)


A parallel-plate capacitor is charged from a cell and then disconnected from
the cell. The separation between the plates is now doubled. This question has multiple correct options
A. The potential difference between the plates will become double
B. The field between the plates will not change.
c. The energy of the capacitor doubles
D. Some work will have to be done by an external agent on the plates.


Construct triangle \( \boldsymbol{A B C} \) in which
\( B C=5 c m, A B-A C=2.8 c m \) and
\( \angle B=40^{\circ} \)


Anhydrous \( A l C l_{3} \) is covalent however
when it is dissolved in water hydrated ionic species are formed. This transformation is owing to:
A. the trivalent state of Al
B. the large hydration energy of \( A l^{3+} \)
C. the low hydration energy of \( A l^{3} \)
D. the polar nature of water


A square hole of cross - sectional area
\( 4 c m^{2} \) is drilled across a cube with its
length parallel to a side of the cube. If
edge of the cube measures \( 5 c m, \) what is the total surface area of the body so formed?
A \( \cdot 140 \mathrm{cm}^{2} \)
В. \( 142 \mathrm{cm}^{2} \)
\( \mathrm{c} \cdot 162 \mathrm{cm}^{2} \)
D. \( 182 \mathrm{cm}^{2} \)


A part of circuit with current is shown.
The value of \( I \) is :
A \( .1 A \)
в. \( 2 A \)
\( c .4 A \)
D. zero


The total charge induced in a conducting loop when it is moved in magnetic field depends on
A. The rate of change of magnetic flux
B. Initial magnetic flux only
c. The total change in magnetic flux
D. Final magnetic flux only


Plant movement in response to diffuse
stimulus of light is
A. Phototropism
B. Photolysis
c. Phototaxis
D. Photonasty


\( \boldsymbol{B}(\boldsymbol{O} \boldsymbol{H})_{3}+\boldsymbol{N} \boldsymbol{a} \boldsymbol{O} \boldsymbol{H} \rightleftharpoons \boldsymbol{N} \boldsymbol{a} \boldsymbol{B} \boldsymbol{O}_{2}+ \)
\( \boldsymbol{N} \boldsymbol{a}\left[\boldsymbol{B}(\boldsymbol{O} \boldsymbol{H})_{4}\right]+\boldsymbol{H}_{2} \boldsymbol{O} \)
How can this reaction is made to
proceed in forward direction?
A. Addition of cis 1,2 diol
B. Addition of borax
c. Addition of trans 1,2 dio
D. Addition of \( N a_{2} H P O_{4} \)


If \( \sin \left(40^{\circ}+\theta\right)=b, 0<\theta<45 . \) find
\( \cos \left(70^{\circ}+\theta\right) \)


For three events \( A, B \) and \( C, P \) (Exactly
one of \( \boldsymbol{A} \text { or } \boldsymbol{B} \text { occurs })=\boldsymbol{P}( \) Exactly one
of \( B \text { or } C \text { occurs })=P(\text { Exactly one of } C \) or \( A \text { occurs })=\frac{1}{4} \) and \( P( \) All the three
events occur simultaneously) \( =\frac{1}{16} \)
Then the probability that at least one of the events occurs, is.
A \( \cdot \frac{7}{32} \)
в. \( \frac{7}{16} \)
c. \( \frac{7}{64} \)
D. \( \frac{3}{16} \)


A point moves along a circle with a velocity \( \boldsymbol{v}=\boldsymbol{a} \boldsymbol{t}, \) where \( \boldsymbol{a}=\mathbf{0 . 5 0} \boldsymbol{m} / \boldsymbol{s}^{2} \)
The total acceleration of the point at the moment when it covered the \( n^{t h}(n= \)
0.10) fraction of the circle after the
beginning of motion in \( m / s^{2} \) is \( \frac{x}{10} . \) Find
\( \mathcal{L} \)


In a straight contest, the loser polled
\( 42 \% \) votes and lost by 14400 votes. Find the total number of votes polled. If the total number of eligible voters was 1 lakh, find what percentage of voters did
not vote.


Amount of usable energy available for
work at uniform temperature and
pressure is
A. Gravitational energy
B. Free energy
c. Activation energy
D. Spontaneous energy


The coordinates of centre of mass of
particles of mass \( 10,20,30 g m \) are \( (1,1,1) c m . \) The position of coordinates
of mass \( 40 g m \) which when added to the
system, the position of combined centre
of mass be at (0,0,0) are
A \( \cdot(3 / 2,3 / 2,3 / 2) \)
B . \( (-3 / 2,-3 / 2,-3 / 2) \)
c. \( (3 / 4,3 / 4,3 / 4) \)
D. \( (-3 / 4,-3 / 4,-3 / 4) \)


The ripening fruits soften due to
A. Conversion of starch into sugars.
B. Solubilisation of pectates in middle lamella.
C. Formation of organic acids
D. Conversion of fats into carbohydrates.


What will be the product of the
reaction?


Three positive charge each of magnitude \( Q \) are placed at the corner of the equilateral tringle. The value of charges placed at the centroid of the triangle such that system must be in equilibrium is
\( ^{A} \cdot \frac{+Q}{\sqrt{3}} \)
в. \( \frac{-Q}{\sqrt{3}} \)
c. \( \frac{-2 Q}{\sqrt{3}} \)
D. \( \frac{+2 Q}{\sqrt{3}} \)


The angle of dip at equator is :
A \( \cdot 0^{\circ} \)
B . \( 45^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 90^{\circ} \)


Number of electrons present in the last orbit generally is:
\( A \cdot 2 \)
B. 6
\( c \cdot 8 \)
D. 18


A circuit consists of a resistor,an
inductor and a capacitor connected in series. If the resistance of a resistor is
\( 25 \Omega \) and the value of inductive
reactance is equal to capacitive
reactance, then the net impedance of the circuit will be :
A . \( 5 \Omega \)
B. 25\Omega
c. \( 125 \Omega \)
D. \( 625 \Omega \)


The incenter of \( \Delta A B C \) with vertices
\( A(0,0,4), B(3,0,4), C(0,4,4) \) is
A \( .(1,1,1) \)
в. (1,1,2)
c. (1,1,3)
D. (1,1,4)


Which of the following halide does not hydrolyse?
A. \( \mathrm{NF}_{3} \)
в. PCls
c. \( \mathrm{AsCl}_{3} \)
D. \( \mathrm{SbCl}_{3} \)


\( \mathbf{7}^{\mathbf{N}^{\mathbf{1 4}}}+_{\mathbf{2}} \mathbf{H} e^{\mathbf{4}} \rightarrow \mathbf{X}+_{\mathbf{1}} \boldsymbol{H}^{\mathbf{1}} ; \mathbf{X} \) is
\( \mathbf{A} \cdot_{9} F^{18} \)
В. \( _{10} N e^{18} \)
\( \mathbf{c} \cdot_{8} O^{17} \)
\( \mathrm{D} \cdot_{6} C^{15} \)


The value of the expression \( \frac{2\left(\sin 1^{\circ}+\sin 2^{\circ}+\sin 3^{\circ}+\ldots+\sin 89^{\circ}\right)}{2\left(\cos 1^{\circ}+\cos 2^{\circ}+\ldots+\cos 44^{\circ}\right)+1} \)
is
A \( \cdot \sqrt{2} \)
в. \( \frac{1}{\sqrt{2}} \)
\( c \cdot \frac{1}{2} \)
\( D \)


The image of the point (-1,3,4) in the
plane \( \boldsymbol{x}-\mathbf{2} \boldsymbol{y}=\mathbf{0} \) is
\( ^{\mathbf{A}} \cdot\left(-\frac{17}{3},-\frac{19}{3}, 4\right) \)
В. (15,11,4)
\( ^{\mathbf{C}} \cdot\left(-\frac{17}{3},-\frac{19}{3}, 1\right) \)
D. \( \left(\frac{9}{5},-\frac{13}{5}, 4\right) \)


Two bodies of masses \( 0.1 k g \) and \( 0.4 k g \) move towards each other with velocities
\( 1 m / s \) and \( 0.1 m / s \) respectively. After
collision they stick together. In \( 10 s \) the combined mass travels
\( \mathbf{A} \cdot 120 m \)
B. \( 0.12 m \)
\( c .12 m \)
D. \( 1.2 m \)


Two elements \( A(A t . \text { wt } 75) \) and \( B(A t . \) wt
16) combine to yield a compound. The percentage by weight of 'A' in the compound was found to be 75.08 . The formula of the compound is:
A \( \cdot A_{2} B \)
в. \( A_{2} B_{3} \)
c. \( A B \)
D. \( A B_{2} \)


Disaccharide which gives two
molecules of glucose is
A. Lactose
B. Sucrose
c. Maltose
D. Galactose


Two coins are tossed simultaneously. Find the probability that either both
heads or both tails occur


The area of the parallelogram formed by
the lines \( 3 x-4 y+1=0,3 x-4 y+ \)
\( \mathbf{3}=\mathbf{0}, \mathbf{4} \boldsymbol{x}-\mathbf{3} \boldsymbol{y}-\mathbf{1}=\mathbf{0} \) and \( \mathbf{4} \boldsymbol{x}-\mathbf{3} \boldsymbol{y}- \)
\( \mathbf{2}=\mathbf{0}, \) is
A \( \cdot \frac{1}{6} \) sq.units
B. \( \frac{2}{7} \) sq.units
c. \( \frac{3}{8} \) sq.units
D. none of the above


Out of (ref. image), which is an example
of a benzylic halide?


What is the order of rotational
symmetry and angle of rotation symmetry for this design?
A \( \cdot 4 ; 90^{\circ} \)
B. \( 6 ; 120^{\circ} \)
c. \( 8: 60^{\circ} \)
D . \( 8 ; 45^{\circ} \)


Which peak is second highest?
\( A \cdot B \)
\( \mathbf{B} \cdot A \)
\( c \cdot C \)
\( D . E \)


Which of the following would not have a dipole moment?
(i) \( \boldsymbol{C C l}_{\mathbf{4}} \)
\( (i i i) 1,2- \)
dichloroacetylene
(ii) trans-1, 2-dichloroethene
\( \boldsymbol{C H}_{2} \boldsymbol{C l}_{2} \)
\( A \cdot \) (i) and (iv)
B. (i), (ii) and (iv)
C . (i), (ii) and (iii)
D. (ii) and (iii)


In the circuit shown in Figure. What
must the emf \( \epsilon \) of the battery be in
order for a current of \( 2.00 A \) to flow
through the \( 5.00 V \) battery? Is the
polarity of the battery correct as shown?


Among identical spheres \( A \) and \( B \) having charges as \( -5 C \) and -16 C
A. - -5C is at higher potential
B. -16C is at higher potential
c. Both are at equal potential
D. It cannot be said


Prove that \( \frac{\sin A-2 \sin ^{3} A}{2 \cos ^{3} A-\cos A}=\tan A \)


ff \( y=e^{a x}, \) then show that \( x \frac{d y}{d x}=y \log y \)


Name the two modes of reproduction.


The point \( F \) has the co-ordinates (0,-8)
IF the distance EF is 10 units, then the
co-ordinates of E will be
A. (-6,0)
B. (6,0)
c. (6,8)
(年. \( 6,8,8) \)
D. Either 1 or 2


\( \lim _{x \rightarrow 0}\left\{(1+x)^{\frac{2}{x}}\right\} \) (where \{\} denotes the
fractional part of \( x \) ) is equal to:
A \( \cdot e^{2}-7 \)
B \( \cdot e^{2} \)
c. \( e^{7}-7 \)
D. limit does not exist


A bag contains 8 black and 5 white
balls. 2 balls are drawn. Find the
probability that both the balls are white.


Secondary growth in dicots and
gymnosperms occurs by
A. Formation of vascular rays
B. Thickening of tracheary elements
C. Formation of meristematic cells in vascular region
D. Development of meristematic cells in vascular and cortical regions


A particular gene has 600 DNA nucleotides ignoring introns, stop and start signals. How many tRNA molecules are required to synthesize polypeptide coded for by this gene?
A . 200
B. 600
c. 900
D. 400


Divide the first expression by the
second. Write the quotient and the
remainder.
\( a^{2}-b^{2} ; a-b \)
A. Quotient \( =b \), Remainder \( =0 \)
B. Quotient \( =a+b \), Remainder \( =0 \)
c. Quotient \( =a b \), Remainder \( =a \)
D. Quotient \( =a-b \), Remainder \( =a \)


Explain the term 'doping'


Three 2 resistors, \( A, B, \) and \( C, \) are connected as shown below.Each of them
dissipates and can stand a maximum
power of \( 18 \mathrm{W} \) without melting. Find the maximum current that can
flow through the three resistors.


\( \boldsymbol{C a}+\boldsymbol{C}_{2} \rightarrow \boldsymbol{C a} \boldsymbol{C}_{2}+\boldsymbol{N}_{2} \rightarrow \boldsymbol{A} \)
Compound \( (A) \) is used as a/an:
A. fertillizer
B. dehydrating agent
c. oxidising agent
D. reducing agent


If helium effuses through a porous barrier at a rate of 4.0 moles per
minute, at what rate (in moles per
minute) would oxygen gas diffuse?
A . 0.20
B. 0.50
\( c \cdot 2.0 \)
D. 1.4


A 200 turn closely wound circular coil of
radius \( 15 \mathrm{cm} \) carries a current of \( 4 \mathrm{A} \)
The magnetic moment of this coil is:
\( \mathbf{A} \cdot 36.5 A m^{2} \)
B . \( 56.5 A m^{2} \)
\( \mathbf{c} \cdot 66.5 A m^{2} \)
D. \( 108 A m^{2} \)


Two cards are drawn simultaneously
from a well shuffled pack of 52 cards.
The expected number of aces is?
\( ^{A} \cdot \frac{1}{221} \)
в. \( \frac{3}{131} \)
c. \( \frac{2}{113} \)
D. \( \frac{1}{131} \)


The mutual force of repulsion between two point charges kept a fixed distance
apart is \( 9 \times 10^{-5} N \) when in vacuum
and \( 4 \times 10^{-5} N \) when placed in a
dielectric medium. What is the value of
dielectric constant of the medium?


Which of the following represents the SI unit of force?
A. Dyne
B. Gram-weight
c. Newton
D. Kilogram-weight


Draw a diagram to describe the life cycle of the moss, pointing out significant features


Express the following in the scientific notation:
(i) 0.0048
(ii) 234,000
(iii) 8008
(iv) 500.0
(v) 6.0012


In autumn, cambium is
A. Inactive
B. Less active
c. Mroe active
D. Killedd


Which statement is wrong from the
following?
A. The earthing wire is green coloured.
B. In India, current flowing through wire is \( A C \) and its frequency is \( 50 \mathrm{Hz} \)
C. In India, voltage between two wires is \( 110 V \)
D. T.V., Tublight, bulbs are connected with \( 5 A \) line.


There are 60 students in a class. Every student learns at least one of the
subjects Kannada or English. 45
students offer Kannada and 30 English.
How many students offer both the
subjects? Draw Venn diagram.


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


An electron in a hydrogen atom makes a
transition from \( n=n_{1} \) to \( n=n_{2} . \) The
time period of the electron in the initial state is eight times that in the final
state. The possible values of \( n_{1} \) and \( n_{2} \)
are
This question has multiple correct options
\( \mathbf{A} \cdot n_{1}=4, n_{2}=2 \)
B \( . n_{1}=8, n_{2}=2 \)
c. \( n_{1}=8, n_{2}=1 \)
D \( \cdot n_{1}=6, n_{2}=3 \)


In pseudo unimolecule reactions:
A. both the reactants are present in low concentration
B. Both the reactants are present in same concentration
C. One of the reactant is present in excess
D. One of the reactant is non-reactive


If \( n(\xi)=30, n(A)=22, n(B)=15 \) and
\( n(A \cup B)=25, \) then find \( : n\left(A \cap B^{\prime}\right) \)


Which of the following option is a water pollutant as well as a detrimental/toxic to marine flora and fauna to a large
extent?
A. Oil spillage during oil drilling
B. Sewage waste
c. Biological waste
D. None of the above


The time taken to assemble a car in a
certain plant is a random variable having a normal distribution of 20
hours and a standard deviation of 2
hours. What is the probability that a car can be assembled at this plant in a
period of time between 20 and 22
hours?
A . 0.3513
B. 0.3216
c. 0.3413
D. 0.3613


What is the main component in CNG?


Faraday has developed a plating process to make high-performance chrome coatings from trivalent chromium instead of highly toxic hexavalent chromium. This is an
application of:
A. Green revolution
B. Green chemistry
c. waste management
D. revolution resource recovery


For the matrix \( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{1} & \mathbf{5} \\ \mathbf{6} & \mathbf{7}\end{array}\right], \) verify that
(i) \( \left(A+A^{\prime}\right) \) is a symmetric matrix
(ii) \( \left(A-A^{\prime}\right) \) is a skew symmetric
matrix.


What is the angle between the incident and reflected rays when a ray of light is incident normally on a plane mirror?
A \( \cdot 90^{\circ} \)
B . \( 45^{\circ} \)
\( c \cdot 180^{\circ} \)
D. \( 0^{\circ} \)


\( M X_{2} \) dissociates in \( M^{2+} \) and \( X^{-} \) ions
in an aqueous solution with a degree of dissociation \( 0.5(\alpha) . \) The ratio of the observed depression of the freezing point of the aqueous solution to the value of the depression of freezing point in the absence of ionic dissociation
is


The initial phase of a pulse travelling on a string is \( \pi / 3 . \) The reflected pulse has
a phase of
A . \( 4 \pi / 3 \)
в. \( 2 \pi / 3 \)
c. \( \pi / 3 \)
D. \( 5 \pi / 3 \)


A solution is prepared by dissolving \( 5.64 \mathrm{g} \) of glucose in \( 60 \mathrm{g} \) of water. Calculate the mole fraction of
each of glucose and water respectively.
B. 0.01,0.99
c. 0.92,0.08
D. 0.789, 0.211


The solvent used in Etard reaction
during the formation of benzaldehyde from toluene is :
A. \( C H_{3} \) СООН
в. \( H_{2} \) О
c. La. \( N H_{3} \)
D. \( C S_{2} \)


The equation \( \sin ^{2} \theta=\frac{x^{2}+y^{2}}{2 x y} \) is
possible if
A. \( x=y \)
в. \( x=-y \)
c. \( 2 x=y \)
D. none of these


A soap bubble of radius \( r \) is blown up to
form a bubble of radius 2r under
isothermal conditions. If \( T \) is the surface
tension of soap solution, the energy
spent in the blowing
\( \mathbf{A} \cdot 3 \pi T r^{2} \)
в. \( 6 \pi T r^{2} \)
\( \mathrm{c} \cdot 12 \pi T r^{2} \)
D. \( 24 \pi T r^{2} \)


During the formation of \( N a C l, \) which of
the enthalpies are negative?
A. Lattice enthalpy
B. Electron affinity
c. Both \( A \) and \( B \)
D. None of these


Select the numbers with same
significant figures:
This question has multiple correct options
A \( \cdot 6.02 \times 10^{23} \)
B. 0.25
c. \( 6.60 \times 10^{-34} \)
D. 1.50


Find the inverse of the following matrix using elementary row transformation. \( \left[\begin{array}{cc}\mathbf{1} & \mathbf{2} \\ \mathbf{2} & -\mathbf{1}\end{array}\right] \)


Assertion
Lateral-line organs are important in connection with aquatic mode of life.
Reason

They are highly supplied with branches of cranial nerves and they are entirely disappeared in terrestrial forms.
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 Reason is correct


\( \lim _{x \rightarrow \infty} \frac{(3 x-1)(2 x+5)}{(x-3)(3 x+7)} \) is equal to
\( A \cdot \frac{1}{2} \)
B. 2
\( c \cdot 0 \)
D. none of these


Calcium floats over water during its reaction with water. Give reason.


Molten sodium is used in nuclear
reactors to:
A. absorb neutrons in order to control the chain reaction
B. slow down the fast neutrons
C. absorb the heat generated by nuclear fission
D. extract radio -isotopes produced in the reactor


Dfferentiate w.r.t \( x \) :
\( \tan ^{2} 7 x \)


Statement A: For a particular character in an individual, each gamete gets only one allele.
Statement B: Chromatids of a
chromosome split (separate) and move towards opposite poles during anaphase of mitosis.
A. Both the statements are correct and \( B \) is the reason fo
\( A \)
B. Both the statements are correct and B is not the reason for \( A \)
c. statement A is correct and statement B is wrong.
D. statement B is correct and statement A is wrong


If \( x \) and \( y \) are arbitrary intensive
variables, then:

This question has multiple correct options
A. \( x y \) is an intensive variable
B. \( x / y \) is an intensive variable
c. \( x+y \) is an extensive property
D. \( d x / d y \) is an intensive property


Give the IUPAC name for \( \boldsymbol{H}_{3} \boldsymbol{C}-\boldsymbol{C} \boldsymbol{H}_{2}- \)
\( \boldsymbol{C H}_{2}-\boldsymbol{O H} \)
A. Propanal
B. Propanol
c. Propionic acid
D. Propane


Pyrolysis of wood occurs in
A. Presence of air
B. Absence of air
C . limited supply of air
D. Both B and C


Arrange the following compounds in an increasing order of their reactivity in nucleophilic addition reactions:
ethanol, propanal, propanone, butanone


Infinite long wire having linear charge density \( 0.2 \mathrm{C} / \mathrm{m} \). find electric intensity at a distance \( 2 \mathrm{m} \) from wire?
A \( \cdot 1.8 \times 10^{9} \mathrm{V} / \mathrm{m} \)
B. \( 0.9 \times 10^{9} \mathrm{V} / \mathrm{m} \)
c. \( 2.7 \times 10^{9} \vee / \) m
D. 0.3x10^ \( v / m \)


Thomson's model could not explain the :
A. stability of an atom
B. position of nucleus in an atom
c. scattering of alpha particles
D. all of above


Which of the following is called as club
moss?
A. Pteris
B. Lycopodium
c. Equisetum
D. Marsilea


Which of the following hydrocarbons has the lowest dipole moment?
A. cis-2-butene
B. 2-butyne
c. I=butyne
D. \( H_{2} C=C H-C \equiv C H \)


Let \( \boldsymbol{A}=\{1,2,3,4,5,6\} \) and \( B= \)
\( \{6,7,8\} . \) Find \( A \triangle B \) and draw Venn
diagram


A boat takes 2 hours to travel \( 8 k m \) and
back in still water lake. With water
velocity of \( 4 k m / h, \) the time taken for going upstream of \( 8 k m \) and coming back is
A. 160 minutes
B. 80 minutes
c. 100 minutes
D. 120 minutes


Find \( 4^{t h} \) term from the end of the G.P.
\( \mathbf{3}, \mathbf{6}, \mathbf{1 2}, \mathbf{2 4}, \dots, \mathbf{3 0 7 2} \)


A completely inelastic is one in which the two colliding particles
A. split into small fragments flying in all directions
B. remain together after the collision.
c. are separated after the collision.
D. none of the above


Assertion
Molecular formula shows the exact
number of different types of atoms
present in a molecule of a compound.
Reason
Molecular formula can be obtained
directly from empirical formula which represents the simplest whole number ratio of various atoms present in a
compound.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


What is the product formed when gold
is dissolved in aqua regia?
A. \( H_{3} A u C l_{2} O_{2} \)
в. \( H A u C l_{4} \)
c. \( H_{2} A u C l_{4} \)
D. \( H_{2} A u C l O_{2} \)


Add the following:
\( (-100)+(-92)+(-84)+\ldots . .+92 \)


Determine the coefficient of dynamic viscosity of the liquid.
A \( .0 .45 \mathrm{N} / \mathrm{m}^{2} \)
В. \( 0.85 \mathrm{N} / \mathrm{m}^{2} \)
c. \( 0.56 N / m^{2} \)
D. \( 0.77 \mathrm{N} / \mathrm{m}^{2} \)


The sum of the probabilities of each
outcome in an experiment is


The most stable fullerene is :
A . \( C_{6} \)
в. \( C_{7} \)
c. \( C_{100} \)
D. \( C_{9} \)


The first term of an \( A . P . \) is \( 5, \) the
common difference is 3 and the last
term is \( 80, \) find the number of terms.


Offspring formed by asexual method of reproduction have greater similarity among themselves, because
A. Asexual reproduction involves only one parent
B. Asexual reproduction involves gametes
c. Asexual reproduction occurs before sexual reproduction
D. Asexual reproduction occurs after sexual reproduction


The curve \( y=a x^{2}+b x+c \) passes
through the point (1,2) and its tangent
at origin is the line \( y=x \). The area
bounded by the curve, the ordinate of the curve at minima an the tangent line
is
A \( \cdot \frac{1}{24} \)
B. \( \frac{1}{12} \)
\( c \cdot \frac{1}{8} \)
D. \( \frac{1}{6} \)


A beaker contains a solution of
substance 'A'. On dissolving substance \( A^{\prime} \) in small amount in this solution,
precipitation of substance ' \( \boldsymbol{A}^{\prime} \) takes place. The solution is
A. concentrated
B. Saturated
c. Unsaturated
D. super saturated


For a chemical change to occur the particles should be in:
A . equilibrium
B. same temperature
c. close contact
D. high pressure


What is the hybridization state of
cation part of solid \( \boldsymbol{P} \boldsymbol{C l}_{5} \) ?
A \( \cdot s p^{3} d^{2} \)
B \( \cdot s p^{2} \)
\( c \cdot s p^{3} \)
\( \mathrm{D} \cdot s p^{3} d \)


The fraction of the total current carried
by an ion is known as:
A. transport number of that ion
B. conductance of that ion
c. both (A) and (B)
D. none of the above


Which is the accepted structure of
\( H_{2} O_{2} \) in gas phase?
\( A \)
в.
c. both
D. none


The wrong statements about \( N H_{3} \) is :
A. it is oxidised with oxygen at \( 700^{\circ} \mathrm{C} \) in the presence of platinum
B. it gives black precipitate with calomel
\( \mathbf{C} \cdot \) it can be dried by \( P_{2} O_{5}, H_{2} S O_{4} \) and \( C a C l_{2} \)
D. it gives white fumes with HCI


Which of the following is Heisenberg uncertainty principle?
A \( \cdot \Delta x \cdot \Delta p \geq \frac{h}{4 \pi} \)
в. \( \Delta x . \Delta p=\frac{h}{4 \pi} \)
c. \( \Delta x . \Delta p \leq \frac{h}{4 \pi} \)
D. \( \Delta x . \Delta p<\frac{h}{4 \pi} \)


Fill in the blank.
Electromagnetic induction occurs in a
wire when a change occurs in
in wire.
A . current
B. intensity of the electric field
C . voltage applied
D. magnetic field intensity applied
E. resistance added to the wire


Inequality \( a+i b>c+i d \) can be
explained only when :
A. \( b=0, c=0 \)
В. \( b=0, d=0 \)
c. \( a=0, c=0 \)
D. \( a=0, d=0 \)


A parallel plate air capacitor has a
capacitance \( C . \) When it is half filled with a dielectric of dielectric constant 5
the percentage increase in the capacitance will be
A . \( 400 \% \)
B . \( 66.6 \% \)
c. \( 33.3 \% \)
D. 200\%


Quadrilaterals ABCD and PQRS are
similar.What is the length of PQ?
A . 2.67
B. 3.75
\( c \)
\( D .5 \)


The fixed resistance is called
A. rheostat
B. resistor
\( c \cdot k e y \)
D. switch


If
\( D \) and \( E \) are the midpoint of the sides
\( A B \) of a triangle \( A B C, \) Prove that \( \boldsymbol{B E}+\overline{\boldsymbol{D C}}=\frac{\mathbf{3}}{\mathbf{2}} \overline{\boldsymbol{B} \boldsymbol{C}} \)


\( P, Q \) and \( R \) are three points in a uniform
electric field. The electric potential is
A. minimum at R
B. minimum at
\( c . \) minimum at
D. Same at all three points


What do you mean by coherent source.


Why oxygen was initially considered as a reference for atomic mass?
A. It has lower mass
B. It reacted with large number of elements and formed compounds
c. This atomic mass unit gave masses of most of the elements as whole numbers
D. Both B and C


The corrosive action of \( H_{2} S O_{4} \) on the
skin is due to its
(dehydrating/hydrating) action.


The set representing the correct order of first ionization potential is :
\( A \cdot K>N a>L i \)
в. \( \mathrm{Mg}>\mathrm{Be}>\mathrm{Ca} \)
C. \( B>C>N \)
D. \( S c>Y>L a \)


In how many steps, \( C O_{2} \) is released in aerobic respiration of pyruvic acid?
A. one
B. Six
c. Three
D. Twelve


An optician, while testing the eyes of a patient, keeps a chart of letters \( 3 \mathrm{m} \)
behind the patient and asks her to see the letters on the image of chart formed
in a plane mirror kept at distance \( 2 \mathrm{m} \) in front of her. How far away is the chart seen by the patient?
A. 3 m
B. 2 m
\( c \cdot 6 m \)
D. \( 7 \mathrm{m} \)


Study the following lists.
ListList-II
(A) A piece of underground
(I) Mentha food branches store
(B) Underground branches grow obliquely upward from
(II) Hydrocotyl the axillary buds of nodes of the stem below the soil.
(III) Agave and produce
(C) Aerial branches grow adventitious yownwards. \( \quad \) roots after obliquely o touching the soil
(V) Stachys and
(D) Weak stemmed plants \( \quad \) roots at every have a cluster of leaves.
(V) Jasminum
\( A \cdot A-(111), B-(1 V), C-(11), D-(1) \)
B. A- (IV), B- (V), C- (III), D- (II)
C. \( A-(1 V), B-(1), C-(V), D-(11) \)
D. \( A-(11), B-(V), C-(1), D-(1) \)


If \( \int \frac{1}{5+4 \cos 2 \theta} d \theta=A \tan ^{-1}(B \tan \theta)+c \)
then \( (A, B)= \)


Allium cepa is example of
A . Cruciferae
B. Liliaceae
c. Solanaceae
D. compositae


Polyuronic acid and polysulphate esters are characteristic in cell wall of
A. Brown algae
B. Red algae
c. Dinoflagellates
D. Diatoms


If \( \boldsymbol{a}=\lim _{x \rightarrow \infty}(\sqrt{x+\sqrt{x}-} \sqrt{x}) \) and \( b= \)
\( \lim _{x \rightarrow \infty}(x-\sqrt{x+x^{2}}) \) then
\( \mathbf{A} \cdot a+b=1 \)
B . \( a+b=0 \)
\( \mathbf{c} \cdot a=b \)
D. \( a+b=2 \)


Ozone is not:
This question has multiple correct options
A . paramagnetic
B. a bleaching agent
C . an oxidising agent
D. a reducing agent


Boyle's law states that:
A. \( V \propto T \) at constant pressure.
B. \( P \propto T \) at constant volume.
\( ^{\mathrm{C}} P \propto \frac{1}{V} \) at constant temperature
D. None of these.


toppr
Q Type your question
Fill in the blanks by choosing an appropriate option.
At a particular spot of an object made of
iron, \( (i) \) of iron to ferrous ion takes
place and that spot behaves as \( (i i) \)
Electrons released at \( (i) \) spot move through the metal and \( \$ 0 \) to another
spot on the metal and reduce oxygen in
presence of \( \boldsymbol{H}^{+} . \) This spot behave as
(iiii). The ferrous ions are further
oxidised by atmospheric oxygen to ferric ions which come out as rust, \( (i v) \) and with further production of \( (v) \) ions.
\( A \cdot(i)- \) Oxidation
(ii)- Anode, (iii)-Cathode, (iv)\( F e_{2} O_{3} \cdot x H_{2} O,(v)-H y d r o g e n \)
B. (i)- Reduction, (ii)-Cathode, (iii)-Anode, (iv)- \( F e_{3} O_{4},(v) \)
Hydrogen
C . (i)-Oxidation, (ii)-Cathode, (iii)-Anode, (iv)\( F e_{2} O_{3} x H_{2} O,(v)-H y d r o g e n \)
D. (i)-Oxidation, (ii)-Anode, (iii)-Cathode, (iv)- \( F e_{2} O_{3} \) \( H_{2} O,(v) \) -Ferrous


The average of \( 1 \frac{1}{6}, 2 \frac{1}{3}, 6 \frac{2}{3} \) and \( 8 \frac{5}{6} \) is
A \( \cdot 6 \frac{3}{4} \)
в. \( _{5} \frac{3}{4} \)
c. \( _{4} \frac{3}{4} \)
D. \( _{3} \frac{3}{4} \)


Match the following.
List-I \( \quad \) List-II (Monomer)
A) Sucrose
i) \( \beta \) -D-Galactose and \( \beta \) -D-Glucose
B) Cellulose
ii) \( \alpha \) -D-Glucose and \( \beta \) -D-Fructose
c) Starch
iii) \( \beta \) -D-Glucose
D) Lactose
iv) \( \alpha \) -D-Glucose
A. A-i; B-ii; C-iii; D-iv
B. A-ii; B-i; C-iii; D-iv
c. A-ii; B-iii; C-iv; D-i
D. A-iv; B-iii; C-i; D-ii


Which of the following \( N^{3-}, O^{2-}, F^{-} \) is
largest in size?
A \( \cdot N^{3} \)
B. \( O^{2} \)
\( c \cdot F^{-} \)
D. All of these


Identify the wrong statement in the following. Coulomb's law correctly describes the electric force that
A. binds the electrons of an atom to its nucleus
B. binds the protons and neutrons in the nucleus of an atom
c. binds atoms together to form molecules
D. binds atoms and molecules together to form solids


The \( p H \) of \( 0.01 M \) solution of sodium salt of a substituted benzoic acid at
\( 25^{\circ} C \) is: \( \left(K_{a}=1.0 \times 10^{-4} \text {at } 25^{\circ} C\right) \)
A. 6
B. 4
\( c \cdot 8 \)
D. 10


An acid is a substance that produces
ions in a water solution
A. oxygen
B. nitrogen
c. carbon
D. hydrogen


A transformer steps up an \( A C \) supply from \( 220 V \) to \( 2200 V . \) If the secondary
coil of the transformer has 2000 turns, the number of turns in its primary coil will be:
A . 200
в. 100
c. 50
D. 20


Colligative molality \( = \) molality \( \times \)
Van't Hoff factor
If true enter \( 1, \) if false enter 0


The angle of incidence at which reflected light is totally polarised for reflection from air to glass (refractive index \( n \) ) is
A \( \cdot \sin ^{-1}(n) \)
B. \( \sin ^{-1}\left(\frac{1}{n}\right) \)
\( ^{\mathbf{c}} \cdot \tan ^{-1}\left(\frac{1}{n}\right) \)
\( \mathbf{D} \cdot \tan ^{-1}(n) \)


The sun appears red at the time of sun-
rise and sun-set. This is because:
A. red colour is least scattered
B. red colour is most scattered
c. the sun is red in colour
D. our eyes can sense only red colou


If \( \cos \left(\log i^{4 i}\right)=a+i b, \) then
B . \( a=-1, b=1 \)
c. \( a=1, b=0 \)
D. \( a=1, b=2 \)


In the detection test of carbon and
hydrogen with cupric oxide, carbon is oxidized to:
A. carbon monoxide
B. carbon dioxide
c. carbonic acid
D. copper sulphate


In the following reaction.
\( \left[\boldsymbol{C u}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{3} \boldsymbol{O} \boldsymbol{H}\right]^{+}+ \)
\( \left[\boldsymbol{A l}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{6}\right]^{3+} \longrightarrow\left[\boldsymbol{C u}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{4}\right]^{2+}+ \)
\( \left[\boldsymbol{A l}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{5}(\boldsymbol{O} \boldsymbol{H})\right]^{2+} \)
\( (\boldsymbol{A}) \)
\( (B) \)
\( (C) \)
\( (D) \)
This question has multiple correct options
A \( .(A) \) is an acid and \( (B) \) is a base
B. \( (A) \) is a base and \( (B) \) is an acid
C. \( (C) \) is the conjugate acid of \( (A) \) and \( (D) \) is the conjugate base of \( (B) \)
D. \( (C) \) is the conjugate base of \( (A) \) and \( (D) \) is the conjugate acid of \( (B) \)


Which of the following is not proposition?
A. 3 is prime.
B. \( \sqrt{2} \) is irrational.
c. Mathematics is interesting
D. 5 is an even integer


The value of \( k \) for which the lines \( 2 x+ \)
\( \mathbf{3} \boldsymbol{y}+\boldsymbol{a}=\mathbf{0} \) and \( \mathbf{5} \boldsymbol{x}+\boldsymbol{k} \boldsymbol{y}+\boldsymbol{a}=\mathbf{0} \)
represent family of parallel lines is
\( A \cdot 3 \)
в. 4.5
\( c .7 .5 \)
D. 15


A circular disc of mass \( 10 \mathrm{kg} \) and radius
\( 0.2 \mathrm{m} \) is set into rotation about an axis
passing through its centre and perpendicular to its plane by applying torque \( 10 \mathrm{Nm} \). Calculate angular velocity of the disc that it will attain at the end
of 6 s from the rest.


Take the mean distance of the moon
and the sun from the earth to be \( 0.4 \times \)
\( 10^{6} k m \) and \( 150 \times 10^{6} k m \) respectively.
Their masses are \( 8 \times 10^{22} k g \) and \( 2 \times \)
\( 10^{30} k g \) respectively. The radius of the
earth is \( 6400 \mathrm{km} \). Let \( \Delta F_{1} \) be the difference in the forces exerted by the
moon at the nearest and farthest points
on the earth and \( \Delta F_{2} \) be the difference
in the force exerted by the sun at the nearest and farthest points o the earth. Then, the number closest to \( \frac{\Delta F_{1}}{\Delta F_{2}} \) is :
A .2
B. \( 10^{-2} \)
\( c .0 .6 \)
D.


Find the \( 13^{t h} \) terms in the expansion of
\( \left(9 x-\frac{1}{3 \sqrt{x}}\right)^{18}, x \neq 0 \)
A . 18564
B. 87328
c. 17374
D. 35546


Mark the correct statement(s) based on
the phase diagram of \( C O_{2} \) shown in the graph.
rhis question has multiple correct options
A \( \cdot 298 \mathrm{K} \) is the normal boiling point of liquid \( C O_{2} \)
B. At 1 atm \& 190 K \( C O_{2} \) will exist as gas.
\( \mathrm{c} \cdot \mathrm{CO}_{2}(s) \) will sublime above \( 195 \mathrm{K} \) under norma atmospheric pressure
D. Melting point \& boiling point of \( C O_{2} \) will increase on increasing pressure.


\( \boldsymbol{R}_{1}, \boldsymbol{R}_{2}, \boldsymbol{R}_{3} \) are different values of \( \boldsymbol{R} \)
\( \mathbf{A}, \mathbf{B}, \mathbf{C} \) are the null points obtained
corresponding to \( \boldsymbol{R}_{1}, \boldsymbol{R}_{2} \) and \( \boldsymbol{R}_{3} \)
respectively. For which resistor, the value of \( X \) will be the most accurate and
why?
\( A \cdot R_{1} \)
B. \( R_{2} \)
\( c \cdot R_{3} \)
D. All same


Which of the following could be the value of \( A C-B C \) in the construction
of a triangle \( A B C \) in which base \( A B= \)
\( \mathbf{5} c m, \angle A=30^{\circ} ? \)
A . 5.5
B. 5
c. 2.5
D. None of these


Vulcanised rubber resists:
This question has multiple correct options
A. wear and tear due to friction
B. cryogenic temperature
C . high temperature
D. action of acids


The hybridization of atomic orbitals of
nitrogen in \( N O_{2}^{+}, N O_{3}^{-} \) and \( N H_{4}^{+} \) are:
A \( . s p, s p^{3} \) and \( s p^{2} \) respectively
B. \( s p, s p^{2} \) and \( s p^{3} \) respectively
\( \mathrm{c} \cdot s p^{2}, \mathrm{sp} \) and \( s p^{3} \) respectively
D. \( s p^{2}, s p^{3} \) and sp respectively


Which of the following is not an aliphatic hydrocarbon?
A. ethene
B. ethane
c. propyne
D. benzene


A cylinder of radius \( R \) is to roll without
slipping between two planks as shown in the figure, Then
This question has multiple correct options
A. angular velocity of the cylinder is \( \frac{v}{R} \) counter clockwise
B. angular velocity of the cylinder is \( \frac{2 v}{R} \) clockwise
c. velocity of centre of mass of the cylinder is v towards left
D. velocity of centre of mass of the cylinder is \( 2 v \) towards right


A particle starts with angular
acceleration 2 rad/sec\( ^{2} \). It moves
100 rad in a random interval of 5 sec.
Find out the time at which random
interval starts.
A. 7.5 sec
B. 4.5 sec
\( \mathrm{c} .5 \mathrm{sec} \)
D. 6 sec


An equipotential surface is that surface
A. on which each and every point has the same potential
B. which has negative potential
C . which has positive potential
D. which has zero potential


The act of breathing out air from the lungs is called as
A. Absorption
B. Exhalation
c. Excretion
D. Inhalation


Sucrose molecule is made up of:
A \( . \alpha-D- \) gluco pyranose and \( \beta-D- \) fructo pyranose
B. \( \alpha-D- \) gluco pyranose and \( \beta-D- \) fructo furanose
C \( . \alpha-D- \) gluco furanose and \( \beta-D- \) fructo pyranose
D. \( \alpha-D- \) gluco furanose and \( \beta-D- \) fructo furanose


The sun subtends an angle of half a
degree at the pole of a concave mirror which has a radius of cutvature of \( 15 m \)
Then the size(diameter) of the image of
the sun formed by the concave mirror is
A \( .7 .5 \mathrm{cm} \)
B. \( 6.55 \mathrm{cm} \)
\( \mathrm{c} .3 .7 \mathrm{cm} \)
D. 13.1cm


Excretory product of spider is
A. Ammonia
B. Uric acid
C. Guanine
D. All the above


Find the mean deviation about the
median for the following continuous distribution:
\( \begin{array}{lllll}\text { Marks } & 0- & 10- & 20- & 30- \\ \text { obtained } & 10 & 20 & 30 & 40\end{array} \)
No. of
body 6
\( 8 \quad 14 \)


A radioactive element \( X \) distintegrates
successively \( \boldsymbol{X} \stackrel{\boldsymbol{\beta}^{-}}{\longrightarrow} \boldsymbol{X}_{\mathbf{1}} \stackrel{\boldsymbol{\alpha}}{\longrightarrow} \boldsymbol{X}_{2} \stackrel{\boldsymbol{\beta}^{-}}{\longrightarrow} \boldsymbol{X}_{\mathbf{3}} \stackrel{\boldsymbol{\alpha}}{\longrightarrow} \boldsymbol{X}_{\mathbf{4}} \)
If atomic number and atomic mass
number of \( X \) are respectively 72 and \( 180, \) what are the corresponding values
for \( \boldsymbol{X}_{4} ? \)
A .69,172
B. 69,176
c. 71,176
D. 70,172


What would be the pH of an aqueous
solution of \( 1 N \) tribasic acid?
A. 3
B.
\( c \cdot 0 \)
D. 1.5


Value based questions. What would be expected to happen if:
you forget to add cytokinin to the culture medium.


A spherical capacitor consists of two
concentric spherical conductors, held in
position by suitable insulating
supports (Fig.). Show that the
capacitance of a spherical capacitor is
given by \( c=\frac{4 \pi \epsilon_{0} r_{1} r_{2}}{r_{1}-r_{2}} \)
where \( r_{1} \) and \( r_{2} \) are the radii of outer
and inner spheres, respectively.


According to Einstein's theory of relativity, mass can be converted into energy and vice-versa. The lightest elementary particles, taken to be the electron, has a mass equivalent to
\( 0.51 M e V \) of energy. Then we can say
that
This question has multiple correct options
A. The minimum amount of energy available through conversion of mass into energy is \( 1.02 \mathrm{MeV} \)
B. The least energy of a \( \gamma- \)ray photon that can be converted into mass is \( 1.02 \mathrm{MeV} \)
c. Whereas the minimum energy released by conversion of mass into energy is \( 1.02 \mathrm{MeV} \), it is only a \( \gamma-\mathrm{ray} \) photon of energy \( 0.51 \mathrm{MeV} \) and above that can be converted into mass
D. Whereas the minimum energy released by conversion of mass into energy is \( 0.51 \mathrm{MeV} \), it is only a \( \gamma-\mathrm{ray} \) photon of energy \( 1.02 \mathrm{MeV} \) and above that can be converted into mass


In ancient India, the shapes of altars used for house hold rituals were
A. squares and circles
B. triangles and rectangles
c. trapeziums and pyramids
D. rectangles and squares


Which one of the following statements
is correct?
A. At present it is not possible to grow maize without chemical fertilizers.
B. Extensive use of chemical fertilizer may lead to eutrophication of nearby water bodies.
C. Both Azotobacter and Rhizobium fix atmospheric nitrogen in root nodules of plants.
D. Cyanobacteria such as Anabaena and Nostoc are important mobilizers of phosphates and potassium for plant nutrition in the soil.


One cyclic acetal form of D-galactose is
shown
Which atom is the anomeric carbon?
\( \mathbf{A} \cdot \) Atom \( A \)
B. Atom B
c. Atom \( c \)
D. Atom D
E. Atom E
\( F . \) Atom \( F \)


For \( \boldsymbol{x} \boldsymbol{\epsilon} \boldsymbol{R}, \boldsymbol{x} \neq \boldsymbol{0}, \) if \( \boldsymbol{y}(\boldsymbol{x}) \) is a
differentiable function such that
\( \boldsymbol{x} \int_{1}^{x} \boldsymbol{y}(\boldsymbol{t}) \boldsymbol{d} \boldsymbol{t}=(\boldsymbol{x}+\mathbf{1}) \int_{1}^{\boldsymbol{x}} \boldsymbol{t} \boldsymbol{y}(\boldsymbol{t}) \boldsymbol{d} \boldsymbol{t}, \) then
\( \boldsymbol{y}(\boldsymbol{x}) \) equals:
(Where \( C \) is a constant)
\( ^{A} \cdot_{C x^{3} e^{\frac{1}{x}}} \)
в. \( \frac{c}{x^{2}} e^{-\frac{1}{x}} \)
c. \( \frac{c}{x} e^{-\frac{1}{x}} \)
D. \( \frac{c}{x^{3}} e^{-\frac{1}{x}} \)


How does the atomic hydrogen or oxy-
hydrogen torch function for cutting and welding purposes? Explain.


Temperature of core of earth is equal to
\( 3727^{0} C . \) This temperature in Kelvins is
equal to:
A . \( 4000 K \)
в. \( 3727 K \)
c. \( 3454 K \)
D. none of the above


A particle of mass \( 4 m \) which is at rest
explodes into three fragments. Two of the fragments each of mass \( m \) are
found to move with a speed \( v \) each in
mutually perpendicular directions. The total energy released in the process of explosion is


\( A 26 \mathrm{ml} \) of \( N-N a_{2} C O_{3} \) solution is
neutralized by the solutions of acids \( A \) and \( \mathrm{B} \) in different experiments. The volumes of the acids \( A \) and \( B \) required
were \( 10 m l \) and \( 40 m l \), respectively. How
many volumes of \( A \) and \( B \) are to be mixed in order to prepare 1 litre of normal acid solution?
A \( .179 .4,820.6 \)
B. 820.6,179.4
c. 500,500
D. 474.3,525.7


What is the IUPAC name of \( \boldsymbol{C H}_{3}- \)
\( \boldsymbol{C H}_{2}-\boldsymbol{C H O} \)


Multiple Choice Questions Which statement is correct for pond
ecosystem
A. Pyramid of numbers is upright
B. Pyramid of mass is inverted
c. Pyramid of energy is upright
D. All the above


A bullet of mass \( m \) is fired from the
gun, the acceleration of the bullet is
A. greater than the acceleration of the gun
B. equal to the acceleration of the gun
C. equal but opposite to the acceleration of the gun
D. directly proportional to the mass of the bullet
E. inversely proportional to the force of the bullet


Consider a current carrying coil placed in a magnetic field. What are the requirements for induced current to
flow as per electromagnetic induction
A . Coil of wire carrying current
B. Change in magnetic field associated with the coil
c. Both A and B
D. None


How many minimum number of
coplanar vectors which represent same physical quantity having different magnitudes can be added to give zero
resultant.
A . (A) 2
в. (В) 3
\( c \cdot(c) 4 \)
D. (D) 5


If \( \boldsymbol{A}=\left[\begin{array}{l}\mathbf{1} \\ \mathbf{2} \\ \mathbf{3}\end{array}\right], \) then find \( \boldsymbol{A} \boldsymbol{A}^{\boldsymbol{T}} \)


\( B F_{3} \) has less lewis acidic property than
\( B B r_{3} . \) Why?
A. 0
в.
c. no idea
D. wron question


Mixed ether will not be formed in the
reaction?
A \( \cdot C H_{3} O C H_{2} C l+C_{2} H_{5} M g B r \)
в. \( C H_{2} N_{2}+C_{2} H_{5} O H \)
c. \( C_{2} H_{5} O N a+C H_{3} \)
D. \( C_{2} H_{5} O H+H_{2} S O_{4}\left(140^{0} C\right) \)


ff \( P=\{a, b\} \) and \( Q=\{x, y, z\}, \) show
that \( \boldsymbol{P} \times \boldsymbol{Q} \neq \boldsymbol{Q} \times \boldsymbol{P} \)


Typical battery used is the mercury cell, which is used in?
A . Electric watches
B. Television sets
c. Radio transistors
D. Electric torches


DNA synthesis occurs in
A. G-phase
B. S-phase
c. \( G_{2} \) phase
D. M phase


\( \begin{array}{ll}\text { Types of roots } & \text { Plants } \\ \text { A) Prop root } & \text { 1) Radish } \\ \text { B) Epiphytic root } & \text { 2) Turnip } \\ \text { C) Stilt root } & \text { 3) Cassava } \\ \text { D) Tuberous root } & \text { 4) Baniyan } \\ \text { E) Fusiform } & \text { 5) Maize } \\ \text { F) Napiform } & \text { 6) Orchid }\end{array} \)
\( \mathbf{A} \)
\( A-1, B-2, C-3, D-4, E-5, F-7 \)
7
B. A-2, B-4, C-6, D-1, E-2, F- 5
C. \( A-4, B-6, C-5, D-3, E-1, F-2 \)
D. A- 4, B-1, C- 2, D-3, E- 5, F- 6


A light bulb burns in front of the center
of a \( 40 \mathrm{cm} \) wide plane mirror that is hung vertically on a wall. A man walks
in front of the mirror along a line that is parallel to the mirror and twice as far from it as the bulb. The greatest
distance he can walk and still see the
image of the bulb.
\( \mathbf{A} \cdot 20 \mathrm{cm} \)
B. \( 40 \mathrm{cm} \)
c. \( 60 \mathrm{cm} \)
D. \( 120 \mathrm{cm} \)


A hollow cylinder with a very thin wall and a block are placed at rest at the top
of a plane with inclination \( \boldsymbol{\theta}=\mathbf{4 5}^{\circ} \)
above the horizontal. The cylinder rolls down the plane without slipping and the block slides down the plane; it is found
that both objects reach the bottom of the plane simultaneously. If the coefficient of kinetic friction between
the block and the plane is \( \mu, \) the value of
\( 18 \mu \) is


In the Born-Haber cycle for the
formation of solid common salt (Nacl)
the largest contribution comes from
A. the low ionization potential of \( N a \)
B. the high electron affinity of \( C l \)
C. the low \( \Delta H_{v a p} \) of \( N a(s) \)
D. the lattice energy


Evaluate the given integral \( \int x \cdot \operatorname{cosec}^{2} x d x \)


Choose the correct option
A. A clinical thermometer should be washed using water before and after use
B. A clinical thermometer should be washed using antiseptic solution before and after use
C. A clinical thermometer can be used after it is heated by fire
D. None of the above


For the dichromate dianion, which of the
following is true?
1) \( 4 C r-O \) bonds are equivalent
2) \( 6 C r-O \) bonds are equivalent


From the experimental data, the compositions are found as barium = \( 58.81 \% \), sulfur \( =13.73 \% \), and oxygen \( = \)
\( 27.46 \% . \) Predict the empirical formula of the compound.
A. \( B a S O_{4} \)
в. \( B a S_{2} O \)
c. \( B a_{2} S O_{3} \)
D. \( B a S_{2} O_{4} \)
E \( . B a_{2} \mathrm{SO}_{4} \)


Spin only magnetic moment value of \( C r^{3+} \) ion is:
A . 2.87 вм
в. 3.87 вм
\( \mathrm{c} .3 .47 \) вм
D. 3.67 ВМ


Which of the following phenomena can be demonstrated by light. But not with sound waves in an air column?
A . Reflection
B. Diffraction
c. Refraction
D. Polarization


The value of the integral \( \int_{-a}^{a} \frac{x e^{x^{2}}}{1+x^{2}} d x \)
is
A \( \cdot e^{a^{2}}^{2} \)
B.
\( \mathbf{c} \cdot e^{-a^{2}}^{2} \)
D. \( a \)


A house is fitted with ten lamps of each
\( 60 W . \) Each lamp burns for 5 hrs a day
on an average. The cost of consumption in a month of 30 days at 2.80 rupees
per unit is:
A . Rs.152
B. Rs.252
c. \( R s .352 \)
D. Rs.452


(5,0) is a point that lies on
A. \( y \) -axis
B. \( x \) -axis
\( \mathbf{c} \cdot y=x \)
D. \( y=5 x \)


Cohesion-tension theory regading ascent of sap was given by
A. Dixon and Jolly
B. J.C. Bose
c. christian Wolf
D. Godlewski


Two triangles having the same base (or
equal bases) and equal areas lie
between the same parallels


How many times a normal man respires per minute?
A. \( 10-15 \) times
B. \( 14-18 \) times
c. \( 20-25 \) times
D. \( 25-30 \) times


Specific heat of water is \( 4.2 J / g^{o} C . \) I
light of frequency \( 3 \times 10^{9} H z \) is used to
heat \( 400 g m \) of water from \( 20^{\circ} \mathrm{C} \) to
\( 40^{\circ} \mathrm{C}, \) the number of photons needed
will be?
A . \( 1.69 \times 10^{29} \)
B. \( 1.69 \times 10^{28} \)
C \( \cdot 2.80 \times 10^{4} \)
D. \( 2.80 \times 10^{5} \)


If egg of an organism has \( 10 p g \) of DNA in its nucleus. How much DNA would a
diploid cell of same organism have in
\( G_{2} \) phase of meiosis?
A . \( 10 p g \)
B. \( 5 p g \)
\( \mathrm{c} \cdot 2 p g \)
D. \( 40 p g \)


A light ray is incident normally on the
surface \( A B \) of a prism of refracting angle
\( 60^{\circ} . \) If the light ray does not emerge from
\( A C, \) then find the refractive index of the
prism.
\( ^{A} \cdot_{\mu} \geqslant \frac{\sqrt{3}}{2} \)
B. \( _{\mu} \leqslant \frac{\sqrt{3}}{2} \)
\( c \cdot_{\mu} \geqslant \frac{2}{\sqrt{3}} \)
D. \( _{\mu} \leqslant \frac{2}{\sqrt{3}} \)


The area bounded by the curves \( x+ \)
\( \mathbf{2}|\boldsymbol{y}|=\mathbf{1} \) and \( \boldsymbol{x}=\mathbf{0} \) is?
A \( \cdot \frac{1}{4} \)
в. \( \frac{1}{2} \)
\( c .1 \)
D. 2


Number of plants described by
Linnaeus is
A . 15000
B. 13291
\( c .5900 \)
D. 2781


State whether the statement is true or
false.

Statement: Generally non-metals react
with acids.
A. True
B. False


Assertion
Nitric oxide, though an odd electron molecule in diamagnetic in liquid state
Reason

There occurs only partial dimerisation
of \( N O \) to \( N_{2} O_{2} \)
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


Explain the formation of following compound:
CaO
\( \boldsymbol{C a}:[\boldsymbol{A r}] \boldsymbol{4 s}^{2} \longrightarrow \boldsymbol{C a}^{2+}[\boldsymbol{A r}] \quad \boldsymbol{O}: \)
\( 1 s^{2} 2 s^{2} 2 p^{4} \longrightarrow \)
\( \boldsymbol{O}^{2-} \mathbf{1} \boldsymbol{s}^{2} \mathbf{2} \boldsymbol{s}^{2} \mathbf{2} \boldsymbol{p}^{\boldsymbol{6}} \quad \boldsymbol{C} \boldsymbol{a}^{\mathbf{2}+}[\boldsymbol{:} \ddot{\boldsymbol{O}}:]^{2-} \)
If true enter 1 , else enter 0 .


Select the correct statement.
\( \mathbf{A} \cdot \) The \( S-F \) bond length is longer in \( S F_{6} \) compared to
that in \( S F_{2} \)
B. In \( P C l_{5} \) axial bonds are smaller than of equatorial bonds.
C \( \cdot \ln I F_{7} \) axial bonds are longer than that of equatorial bonds
D. All are correct.


A bus travelling along a straight highway covers one-third of the total distance between two places with a velocity \( 20 k m h^{-1} . \) The remaining part
of the distance was covered with a
velocity of \( 30 k m h^{-1} \) for the first half of
the remaining time and with velocity
\( 50 k m h^{-1} \) for the next half of the time.
Find the average velocity of the bus for its whole journey.


The particle of charge \( q \) and mass \( m \) starts moving from origin under the
action of an electric field \( \boldsymbol{E}=\boldsymbol{E}_{0} \boldsymbol{i} \) and
magnetic field \( V=V_{0} i . \) Its velocity at \( (x, 3,0) \) is \( (4 i+3 \hat{i}) . \) The value of \( x \) is :
A. \( \frac{\sqrt{3} m v_{0}}{q E} \)
в. \( \frac{25 m}{2 q E_{o}} \)
c. \( \frac{10 m}{q E_{o}} \)
D. \( \frac{25 E_{0} B_{0}}{m} \)


Water expands when it freezes. Determine amount of work in joules,
done when a system consisting of \( 1.0 L \) of liquid water freezes under a constant
pressure of \( 1.0 a t m \) and forms \( 1.1 L \) of
¡ce.


What is the function of refrigerants in
heat pumps?
A. Refrigerants supply heat to the atmosphere
B. Refrigerants evaporate heat and cool the room
C. Refrigerant carries heat from the atmosphere to the room, which is to be heated
D. None of these


\( \lim _{x \rightarrow \infty} \sin x \) is equal to:
\( \mathbf{A} \cdot 0 \)
\( B . \infty \)
C. Exists is finite and non-zone
D. Does not exist


The output \( Y \) of the logic circuit given
above is:
\( \mathbf{A} \cdot \bar{A}+B \)
в. \( \bar{A} \)
c. \( \overline{(\bar{A}+B)} \cdot \bar{A} \)
D. \( \overline{(\bar{A}+B)} \cdot \). \( A \)


\( \sin 3 x+\sin x+2 \cos x=\sin 2 x+ \)
\( 2 \cos ^{2} x \)


The resistances of a platinum resistance thermometer at the ice
point, the steam point and the boiling point of sulphur are 2.50,3.50 and 6.50 \( \Omega \) respectively. Find the boiling point
\( ^{o} C \) ) of sulphur on the platinum scale. The ice point and the steam point
measure \( 0^{\circ} \mathrm{C} \) and \( 100^{\circ} \mathrm{C} \) respectively


If the third term in the expansion of \( \left[x+x^{\log _{10} x}\right]^{5} \) is \( 10^{6}, \) then \( x \) can be
This question has multiple correct options
A \( \cdot 10^{-1 / 3} \)
B. 10
c. \( 10^{-5 / 2} \)
D. \( 10^{2} \)


Examine the applicability of Mean Value Theorem for the following function. \( f(x)=x^{2}-1 \) for \( x \epsilon[1,2] \)


The total energy of electron in the ground state of hydrogen atom is 13.6
eV. The kinetic energy of an electron in the first excited state is :
A \( .1 .7 e V \)
B. \( 3.4 e V \)
c. \( 6.8 e V \)
D. \( 13.6 e V \)


What is the unit of ratio \( \frac{E}{H} ? \)


Calculate \( \left[\boldsymbol{H}^{+}\right] \) in a \( \mathbf{0 . 2 0} \boldsymbol{M} \) solution of
dichloroacetic acid \( \left[\boldsymbol{K}=\mathbf{5} \times \mathbf{1 0}^{-\mathbf{2}}\right] \)
that also contains \( 0.1 ~ M \) sodium
dichloroacetate. Neglect hydrolysis of sodium salt.
A. \( 0.078 M \)
В. 0.05 М
c. \( 0.06 M \)
D. \( 0.04 M \)


Three coins are tossed. Describe
three events \( A, B \) and \( C \) which are
mutually exclusive and exhaustive


The donations given to an orphanage home by the students of different classes of a secondary school are given below.
\( \begin{array}{ll}\text { Class } & \text { Donation by each } \\ & \text { students }(\text { in } R s)\end{array} \) No. of
students
donated
\( _{5} \) vı vıl 7 vııl 10 Ix 15 \( x \) 20
Find the mean, median and mode of the
data
A. Rs.11.26, Median = Rs.10; Mode = Rs.10
B. \( R s .1 .26, \) Median \( =R s .10 ; \) Mode \( =R s .10 \)
c. \( R s .11 .26, \) Median \( =R s .20 ; \) Mode \( =R s .10 \)
D. None of these


Assertion
STATEMENT-1: If \( f(x) \) is continuous on
\( [a, b], \) then there exists a point \( c \in(a, b) \)
such that \( \int_{a}^{b} f(x) d x=f(c)(b-a) \)
Reason
STATEMENT-2: For \( a<b \), if \( m \) and \( M \) are,
respectively, the smallest and greatest
values of \( \boldsymbol{f}(\boldsymbol{x}) \) on \( [\boldsymbol{a}, \boldsymbol{b}] \)
\( \operatorname{then} m(b-a) \leq \int_{a}^{b} f(x) d x \leq(b- \)
\( \boldsymbol{a}) \boldsymbol{M} \)
A. STATEMENT-1 is True, STATEMENT-2 is True STATEMENT-2 is a correct explanation for STATEMENT-
1
B. STATEMENT-1 is True, STATEMENT-2 is True STATEMENT-2 is NOT a correct explanation for STATEMENT-1.
C . STATEMENT-1 is True, STATEMENT-2 is False
D. STATEMENT-1 is False, STATEMENT-2 is True


Which or tollowing Is an example of
Pinacol-Diazotization?
\( \mathbf{A} \)
\( B \)
\( c \)
D.


Van't Hoff's factor of aq. \( K_{2} S O_{4} \) at infinite dilution has value equal to:
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c .3 \)
D. Between 2 and 3


Let \( A \) and \( B \) be two sets such that \( A \times \)
\( B \) Consists of 6 elements. If three
elements of \( A \times B \) are
(1,4),(2,6),(3,6) then \( B \times A . \) is \( = \)
\( \{(a, 1),(6,1),(4, d),(c, 2),(4,3)(b, 3)\} \)
Find \( \boldsymbol{a}+\boldsymbol{b}+\boldsymbol{c}+\boldsymbol{d} \)


The natural phenomenon which we are not yet able to predict accurately is:
A. earthquake
B. flood
c. volcanic erruption
D. thunderstorm


Fruits falling from a tree is an example of random motion?
A. True
B. False


Which of the following is the infrared wavelength?
A \( \cdot 10^{-4} \mathrm{cm} \)
B \( \cdot 10^{-5} \mathrm{cm} \)
\( \mathbf{c} \cdot 10^{-6} c m \)
D. \( 10^{-7} \mathrm{cm} \)


Find all the values of \( \theta \) which satisfy the equation: \( \cos \theta \cdot \cos 2 \theta \cdot \cos 3 \theta=1 / 4 \)


Let \( \boldsymbol{f}(\boldsymbol{x}) \) be defined in the interval [-2,2] such that \( f(x)= \)
\( \left\{\begin{array}{ll}-1, & -2 \leq x \leq 0 \\ x-1, & 0<x \leq 2\end{array} \text { and } g(x)=\right. \)
\( \boldsymbol{f}(|\boldsymbol{x}|)+|\boldsymbol{f}(\boldsymbol{x})| \) Test the differentiablity
of \( g(x) \) in (-2,2)
A. not derivable at \( x=0 \) and \( x=1 \)
B. derivable at all points
c. not derivable at \( x=0 \)
D. not derivable at \( x=1 \)


The value of \( \lim _{n \rightarrow \infty} \Sigma_{1}^{n} \sin \left(\frac{\pi}{4}+\frac{\pi i}{2 n}\right) \frac{\pi}{2 n}=? \)
\( ^{\mathbf{A}} \cdot \int_{\frac{\pi}{2}}^{\frac{\pi}{4}} \sin x d x \)
B. \( \int_{\frac{\pi}{2}}^{\frac{3 \pi}{4}} \sin x d x \)
\( ^{\mathrm{c}} \cdot \int_{\frac{\pi}{7}}^{\frac{3 \pi}{4}} \sin x d x \)
D. \( \int_{\pi}^{3 \pi} \sin x d x \)


Which are the different types of
ecosystems?


Define a relation \( R \) on the set \( N \) of
natural numbers by \( \boldsymbol{R}=\{(\boldsymbol{x}, \boldsymbol{y}): \boldsymbol{y}= \)
\( x+5, x \) is a natural number less than
\( \mathbf{4} ; \boldsymbol{x}, \boldsymbol{y} \in \boldsymbol{N}\} . \) Depict this relationship
using roster form. Write down the domain and the range.


In an hydrogen atom, the electron
revolves around the nucleus in an orbit
of radius \( 0.53 \times 10^{-10} m . \) Then the
electrical potential produced by the nucleus at the position of the electron is


One mole of steam is condensed at
\( 100^{\circ} \mathrm{C} \) the water is cooled to \( 0^{\circ} \mathrm{C} \) and
frozen to ice. Which of the following statements are correct, given heat of vapourization and fusion are \( 540 c a l / g m \) and \( 80 c a l / g m \) (average
heat capacity of liquid water \( =1 \) cal
\( \boldsymbol{g} \boldsymbol{m}^{-1} \boldsymbol{d} \boldsymbol{e} \boldsymbol{g} \boldsymbol{r} \boldsymbol{e} e^{-1} \boldsymbol{\} \)
This question has multiple correct options
A. Entropy change during the condensation of steam is \( -26.06 c a l /^{o} C \)
B. Entropy change during cooling of water from \( 100^{\circ} \mathrm{C} \) to \( 0^{o} C \) is \( -5.62 c a l /^{o} C \)
C. Entropy change during freezing of water at \( 0^{\circ} \mathrm{C} \) is \( -5.27 c a l /^{o} C \)
D. Total entropy change is -36.95 cal\( /^{\circ} \mathrm{C} \)


Find the difference of the arithmetic
progression an if \( a_{1}=7 \) and \( a_{3}=16 \)
A . 4.5
B. 5
\( c .5 .5 \)
D. 6


The centre of mass of a rigid body always lies inside the body. Is this statement true or false?
A. True
B. False


Who proposed the 'Binomial
Nomenclature System'?
A. Whittaker
B. Mendel
c. carl Linnaeus
D. Tippo


If the distance between the earth and
the Sun were half its present value, the number of days in a year would have
been
A . 64.5
в. 129
c. 182.5
D. 730


On an average, for every \( C O_{2} \) molecule
fixed by photosynthesis, how many molecules of oxygen are released?
A
B. 2
\( c \cdot 3 \)
D. 6


Why doesn't sea water freeze so easily?


Which one of waves tans our skin and
causes some substances to become
fluorescent?
A. infrared waves
B. ultraviolet waves
c. gamma rays
D. infrared and ultraviolet waves both


Draw a labelled diagram of an alternating current Generator. Determine the induced electromotive
force by the rotation of coil in it.


Which of the following is incorrectly matched?

Complex compound and number of
unpaired electrons
\( \mathbf{A} \cdot\left[F e F_{6}\right]^{3-}, 5 \)
B \( \cdot\left[C r(e n)_{3}\right]^{2}+, 2 \)
c. \( \left[\operatorname{Co}\left(N H_{3}\right)_{6}\right]^{3+}, 4 \)
D \( \cdot\left[M n\left(H_{2} O\right)_{6}\right]^{2+}, 5 \)


Addition of iron or zinc to copper sulfate causes precipitation of copper owing to
the
A . reduction of \( C u^{2} \)
B. oxidation of \( C u^{2} \)
c. hydrolysis of \( C u S O_{4} \)
D. ionisation of \( C u S O_{4} \)


Compound \( A \) when reacted with \( P C l_{5} \)
and then with ammonia gave \( \boldsymbol{B} . \boldsymbol{B} \)
when treated with bromine and caustic
potash produced \( C . C \) on treatment
with \( H C l \) and \( N a N O_{2} \) at \( 0^{\circ} C \) and then
on boiling produced ortho-cresol. Compound \( \boldsymbol{A} \) is :
A . \( o \) -Toluic acid
B. \( o \) -Chlorotoluene
c. \( o \) -Bromotoluene
D. m-Toluic acid


What is the name of the process of heat transfer using electromagnetic waves?
A. Conduction
B. Convection
c. Evaporation
D. Radiation


Where should the object be placed if we
use convex lens to obtain real, inverted and diminished image?
A. object should be placed at focal point
B. object should be placed at finite distance from Focal point
c. object should be placed at infinity
D. object should be placed between F and 2F


What is the difference between
distillation,distillation under reduced
pressure and steam distillation?


In the periodic table, vertical columns of elements are called \( \ldots . . \) and horizontal
rows of elements are called
A. Groups, periods
B. Periods, groups
c. Periods, periods
D. Groups, groups


Two mirrors are placed at right angles to each other as shown in the figure.
Total number of images of an object 0 placed between them, that are seen are:
A. Two
B. Three
c. Four
D. Six


If \( \lim _{x \rightarrow 1} \frac{x^{4}-1}{x-1}=\lim _{x \rightarrow k} \frac{x^{3}-k^{3}}{x^{2}-k^{2}}, \) then find
the value of \( k \)
\( A \cdot \frac{5}{3} \)
B. \( -\frac{8}{3} \)
\( c \cdot \frac{8}{3} \)
D. None of these


Which of the following has the highest acidic strength?
\( A \cdot \| \)
B. IV
\( c \)
\( D \)


Pb is a very important element of carbon family. It forms a number of compounds which are very useful in
industries. The process of removal of base metals \( (\mathrm{Cu}, \mathrm{Sn}, \mathrm{Bi}, \mathrm{As}) \) from lead is called:
A. softening process
B. liquation
c. parke's process
D. cupellalion


Chloroquine, camoquin and primaquine
are :
A. Anti malarial drug
B. Anti dengue drug
c. Anti tuberculosis drug
D. Both A and B


Divide the polynomial \( p(x) \) by the
polynomial \( p(g) \) and find the quotient
an in each of the following:
\( \boldsymbol{p}(\boldsymbol{x})=\boldsymbol{x}^{3}-\boldsymbol{3} \boldsymbol{x}^{2}+\boldsymbol{5} \boldsymbol{x}-\boldsymbol{3}, \boldsymbol{g}(\boldsymbol{x})= \)
\( x^{2}-2 \)
\( \boldsymbol{p}(\boldsymbol{x})=\boldsymbol{x}^{4}-\boldsymbol{3} \boldsymbol{x}^{2}+\boldsymbol{4} \boldsymbol{x}+\mathbf{5}, \boldsymbol{g}(\boldsymbol{x})= \)
\( \boldsymbol{x}^{2}+\mathbf{1}-\boldsymbol{x} \)
\( \boldsymbol{p}(\boldsymbol{x})=\boldsymbol{x}^{4}-\boldsymbol{5} \boldsymbol{x}+\boldsymbol{6}, \boldsymbol{g}(\boldsymbol{x})=\boldsymbol{2}-\boldsymbol{x}^{2} \)


Which of the following is a measurement of water pollution?
A . PSC
в. РСВ
\( c . \) во
D. coo


Assertion: The element carbon forms
the basic structural framework of more
compounds than any other element Reason: The carbon-carbon bond is
ionic.
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
E. Both Assertion and Reason are incorrect


An electric heater consists of a
nichrome coil and runs under \( 220 V \)
consuming \( 1 k W \) power. Part of its coil
burned out and it was reconnected after
cutting off the burnt portion, The power
it will consume now is:
A. More than \( 1 k W \)
B. Less that \( 1 k W \), but not zero
\( \mathrm{c} .1 \mathrm{kW} \)
D. \( 0 k W \)


Buna-S is a copolymer of:
A. styrene and 1,3 - butadiene
B. styrene and ethylene
3 - butadiene and ethylene
\( \mathbf{C} \cdot 1,3 \)
D. 1,3 - butadiene and acrylonitrile


If \( A \) is \( n \) squared matrix then \( A A^{\prime} \) and
\( A^{\prime} A \) are symmetric.


The relation among \( u, v \) and \( f \) for \( a \)
mirror is
\( \mathbf{A} \cdot f=u v /(u+v) \)
В \( . v=f u /(u+f) \)
\( \mathbf{c} . u=f v /(f+v) \)
D. All of these


toppr
Q Type your question
\( A \)
\( B \)
\( c \)
\( D \)


The first and second dissociation
constant of an acid \( \boldsymbol{H}_{2} \boldsymbol{A} \) are \( \mathbf{1 . 0} \times \)
\( \mathbf{1 0}^{-5} \) and \( \mathbf{5 . 0} \times \mathbf{1 0}^{-\mathbf{1 0}} \) respectively. The
over all dissociation constant of the
acid will be:
A. \( 5.0 \times 10^{-5} \)
В. \( 5.0 \times 10^{15} \)
c. \( 5.0 \times 10^{-15} \)
D. \( 0.2 \times 10^{5} \)


A cylindrical vessel of base radius \( \mathrm{R} \) and
height H has a narrow neck of height h and radius \( r \) at one end(see figure). The
vessel is filled with water(density \( \rho_{w} \) )
and its neck is filled with immiscible oil
(density \( \rho_{o} \) ). Then the pressure at:
A \( \cdot \) M is \( g\left(h \rho_{o}+H \rho_{w}\right) \)
B. \( \quad \) N is \( g\left(h \rho_{o}+H \rho_{w}\right) \frac{r^{2}}{R^{2}} \)
c. \( \mathrm{M} \) is \( g H \rho_{w} \)
D. \( \mathrm{N} \) is \( g \frac{\rho_{w} H R^{2}+\rho_{o} h r^{2}}{R^{2}+r^{2}} \)


The number \( \mathbf{P} \boldsymbol{\pi}-\mathbf{d} \boldsymbol{\pi} \) bondsin \( \mathbf{X} \mathbf{e} \mathbf{O}_{\mathbf{4}} \) is :
A. zero
B. Two
c. Three
D. Four


Lenz's law is a consequence of law of conservation of
A. momentum
в. energy
c. charge and mass
D. angular momentum


Define many-one function. Give an
example of function.


Which of the following is incorrect relation fot a perfect gas?
A. \( \quad\left(\frac{\delta U}{d V}\right)_{T}=0 \)
в. \( \quad\left(\frac{^{\frac{0}{0} H}{\delta P}}\right)_{T}=0 \)
\( \begin{array}{ll}\text { c. } & \left(\frac{\delta T}{\delta P}\right)_{H}=0\end{array} \)
D. \( \quad\left(\frac{\tilde{\sigma} U}{\delta T}\right)_{V}=0 \)


A rod of \( 10 \mathrm{cm} \) length is moving perpendicular to uniform magnetic field of intensity \( 5 \times 10^{-4} W b / m^{2} . \) If the
acceleration of the rod is \( 5 m / s^{2}, \) then the rate of increase of induced emf is
A \( .2 .5 \times 10^{-4} V s^{-1} \)
B . \( 25 \times 10^{-4} V s \)
c. \( 20 \times 10^{-4} V s \)
D. \( 20 \times 10^{-4} V s^{-1} \)


If \( \lim _{x \rightarrow \infty}\{(\sqrt{x^{4}+a x^{3}+3 x^{2}+b x+2}-\sqrt{a} \)
is finite, then the value of \( a \) is?
A . 3
B. 5
\( c \cdot 2 \)
D. Any real number


Match each coordination compound in List-I with an appropriate of characteristics from List-II. (en \( = \)
\( \boldsymbol{H}_{2} \boldsymbol{H} \boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{N} \boldsymbol{H}_{2} ; \) Atomic numbers:
\( \mathrm{Ti}=22, \mathrm{Cr}=24 ; \mathrm{Co}=27 ; \mathrm{Pt}=78) \)
List 1
Parama dexhil
\( A \)
4 \( \left[C r\left(N H_{3}\right)_{4} C l_{2}\right] C l \) and ionizatio
Diamag \( \operatorname{lex} \)
\( B \)
3 \( \left[T i\left(H_{2} O\right)_{3} C l\right]\left(N O_{3}\right)_{2} \)
2
and cis-trans
Parama \( \operatorname{exn} \)
\( c \)
\( \left[P t(e n)\left(N H_{3}\right) C l\right] N O_{3} \) 3 and cis-trans so ।
\( \left[C o\left(N H_{3}\right)_{4}\left(N O_{3}\right)_{2}\right] N O_{3} \) Diamagn
and exhib
ionizatior
isomerisr 4


The remainder when \( x^{3}-2 x^{2}+4 x \) is
divided by \( x^{2} \) is
A .
в. \( x-2+\frac{4}{x} \)
c. \( 4 x \)
D. \( 4 x-2 x^{2} \)


(a) Deduce an expression for the frequency of revolution of a charged particle in a magnetic field and show that it is independent of velocity or energy of the particle.
(b) Draw a schematic sketch of a
cylotron. Explain, giving the essential details of its construction, how it is used to accelerate the charged
particles.


What type of oxide would Ekaaluminium form?
A. \( E O_{3} \)
в. \( E_{3} O_{2} \)
\( \mathrm{c} \cdot E_{2} \mathrm{O}_{3} \)
D. \( E O \)


A car is traveling in plane curved road of radius 125 m. If the coefficient of
friction between the tyres and road is
0.5 and \( g=10 m / s^{2} . \) The maximum
speed to avoid skidding is:
A . \( 50 \mathrm{m} / \mathrm{s} \)
в. \( 25 \mathrm{m} / \mathrm{s} \)
c. \( 20 m / s \)
D. 10 \( m / s \)


Ocean thermal energy is due to
A. temperature difference at different levels in the ocean
B. tides in the ocean
C . energy stored by the water waves
D. pressure different at different levels in the ocean


In figure, if the current \( i \) decreases at a
rate \( \alpha, \) then \( V_{A}-V_{B} \) is
A. zero
в. \( -\alpha L \)
\( c \cdot \alpha L \)
D. No relation exists


A reaction in which there is a transfer of
electrons from one reactant to another
is called a (combustion/redox) reaction.


Find the value of \( x \) and \( y \). (Use
Pythagoras theorem)
A \( . x=12 \) and \( y=3 \)
3. \( x=10 \) and \( y=5 \)
c. \( x=12 \) and \( y=5 \)
\( x=11 \) and \( y=5 \)


Which type of hybridsation is present in carbon atom in fullerence?


Pressure depends on distance as, \( \mathbf{p}= \) \( \frac{\boldsymbol{\alpha}}{\boldsymbol{\beta}} \exp \left(-\frac{\boldsymbol{\alpha} \mathbf{z}}{\mathbf{k} \boldsymbol{\theta}}\right), \) where \( \boldsymbol{\alpha}, \boldsymbol{\beta} \) are constants
\( \mathbf{z} \) is distance, \( \mathbf{k} \) is Boltzman's constant
and \( \theta \) is temperature. The dimension of
\( \beta \) are
\( \mathbf{A} \cdot \mathbf{M}^{o} \mathrm{L}^{o} \mathrm{T}^{o} \)
B. \( \mathrm{M}^{-1} \mathrm{L}^{-1} \mathrm{T}^{-1} \)
c. \( \mathrm{M}^{\circ} \mathrm{L}^{2} \mathrm{T}^{\circ} \)
D. \( \mathrm{M}^{-1} \mathrm{L}^{1} \mathrm{T}^{2} \)


Choose the correct answers from the
alternatives given :
In alcoholic fermentation is the final
acceptor of the electrons stripped from glucose.
A. sulphate
B. pyruvate
c. acetaldehyde
D. oxygen


Let \( a, b, c, d \) and \( e \) be the observations
with mean \( m \) and standard deviation \( S \)
The standard deviation of
the observations \( a+k, b+k, c+k, d+ \)
\( k \) and \( e+k \) is


All halogenoalkanes contain a halogen
atom - fluorine, chlorine, bromine or
iodine - attached to a/an \( _{--}- \) group.
A . alky
B. aryl
c. benzyl
D. benzylic


Near and far points of healthy human eye respectively are:
A. \( 0,25 \mathrm{cm} \)
B. \( 0, \) infinity
\( \mathrm{c} .25 \mathrm{cm}, 100 \mathrm{cm} \)
D. \( 25 c m \), infinity


\( \mathbf{2} \boldsymbol{A} \boldsymbol{l}\left(\boldsymbol{N} \boldsymbol{O}_{3}\right)_{3} \stackrel{\boldsymbol{\Delta}}{\rightarrow} \boldsymbol{A} \boldsymbol{l}_{2} \boldsymbol{O}_{3}+\boldsymbol{6} \boldsymbol{N} \boldsymbol{O}_{3}+ \)
\( \mathbf{1 . 5 0}_{\mathbf{2}} \)
If reaction is correct enter 1 else 0


A card is thrown from a pack of 52 cards
so that each cards equally likely to be selected. In which of the following cases are the events \( A \) and \( B \) independent?


Which of the following charging methods work without ever touching the object to be charged to the object used to charge it?
A. charging by friction
B. charging by contact
c. charging by induction
D. all of these


Auto-reduction is employed in the
metallurgy of :
A. \( H g \)
в. \( A l \)
c. \( T i \)
D. \( Z n \)


The area of rectangle of size \( 1.23 \mathrm{cm} \times \)
\( 2.345 \mathrm{cm} \) is ?
A. \( 2.88 c m^{2} \)
2
B . \( 2.884 c m^{2} \)
\( \mathrm{c} \cdot 2.9 \mathrm{cm}^{2} \)
D . \( 2.88435 \mathrm{cm}^{2} \)


What does the slope of V-I graph for a conductor represent?
A. Capacitance
B. Power
c. Inductance
D. Resistance


What are the value of \( c \) for which Rolle's
theorem for the function \( f(x)=x^{3}- \)
\( 3 x^{2}+2 x \) in the interval [0,2] is
verified?
A \( . c=\pm 1 \)
B. \( _{c=1 \pm \frac{1}{\sqrt{3}}} \)
c. \( c=\pm 2 \)
D. None of these


A field is in the shape of a trapezium
whose parallel sides are \( 25 m \) and \( 13 m \) The non-parallel sides are \( 10 m \) and
10 \( m . \) Find the area of the field.


The potential energy (in Sl units) of a particle of mass \( 2 k g \) in a conservative
field is \( U=6 x-8 y . \) If the initial velocity of the particle is \( \vec{u}=-1.5 \hat{i}+ \) \( 2 \hat{j} \) then the total distance travelled by
the particle in first two seconds is:
A. \( 10 \mathrm{m} \)
B. 12m
\( c .15 \mathrm{m} \)
D. 18m


The range of the function \( f(x)= \)
\( \log _{e}\left(3 x^{2}-4 x+5\right) \)
\( ^{A} \cdot\left(-\infty, \log _{e} \frac{11}{3}\right] \)
B. \( \quad\left[\log _{e} \frac{11}{3}, \infty\right) \)
c. \( \left[-\log _{e} \frac{11}{3}, \log _{e} \frac{11}{3}\right. \)
D. None of these


A liquid boils at such a temperature at which the saturated vapour pressure, as compared to atmospheric pressure, is
A. one-third
B. equal
c. half
D. doubl


If an object is placed in a tunne running through the Earths centre, it does simple harmonic motion. Calculate the time period for this. If radius of Earth is \( 6.4 \times 10^{6} m \) and
\( \operatorname{mass} \) is \( 6 \times 10^{24} k g \)


Alka was making tea in a kettle. Suddenly she felt intense heat from the puff of steam gushing out of the spout of the kettle. She wondered whether the
temperature of the steam was higher than that of the water boiling in the
kettle. Comment.


Describe the role of the following in metallurgy:
lime Stone in blast furnace


If soldiers had the options to use guns of different weights but the bullets used are of a fixed weight, what would they
prefer and why?
A. Light guns, because handling them is easy
B. Heavy guns, because they can be held firmly
c. Heavy guns because they have less recoil
D. Light guns, because they can be carried easily


has an inductor of inductance \( L \) and a
resistor of resistance it connected in
series. Using the phasar diagram,
explain why the voltage in the circuit
will lead the current in phase.
(b) The potential difference across the
resistor is \( 160 \% \) and that across the
inductor is \( 120 V . \) Find the effective
value of the applied voltage. If the
effective current in the circuit be \( 1.0 A \)
calculate the total impedance of the circuit.
(c) What will be the potential difference
in the circuit when direct current is
passed through the circuit??


On passing \( 0.5 \mathrm{F} \) of electricity through molten sodium chloride, sodium deposited at cathode will be
A . \( 29.25 g \)
в. \( 11.50 g \)
c. \( 58.50 g \)
D. \( 0.00 g \)


A student conducted an experiment and obtained three values during three repetitive trials: \( 1.65,1.68,1.71 . \) Later, the student discovered that the true value
was \( 2.37 . \) In contrast to the real value,
the experimental results should be characterized as:
A. not accurate and not precise
B. accurate but not precise
c. not accurate but precise
D. accurate and precise
E. accurate, precise, but unrealiable


Pressure cannot be measured in:
\( \mathbf{A} \cdot \mathbf{N} m^{-2} \)
B. bar
c. Ра
D. kg wt tt


If a particle is thrown with velocity more than \( 10 m / s \) vertically upward, then the distance traveled by the particle in last second of its ascent is:
\( \mathbf{A} \cdot g \)
в. \( \frac{g}{2} \)
c. \( \frac{g}{4} \)
D. \( \frac{g}{8} \)


In a hypothetical H-atom the mass of
electron \( \& \) its charge is double of what we consider calculate the total energy
(in eV) of electron in the \( 1^{s t} \) orbit of such
a hypothetical H-atom?


Which family is represented by the largest number of species in Indian
flora?
A. Gramineae
B. Leguminosae
c. orchidaceae
D. Solanaceae


In which of the following pairs, hydrogen bonding is not possible?
A. \( N H_{3}, N H_{3} \)
в. \( N H_{3}, C H_{4} \)
с. \( H_{2} O, C H_{3} O H \)
D. \( H F, H_{2} O \)


A fly wheel of moment of inertia lis rotating at n revolutions per sec. The work needed to double the frequency would be -
\( \mathbf{A} \cdot 2 \pi^{2} I n^{2} \)
В. \( 4 \pi^{2} I n^{2} \)
\( \mathbf{c} \cdot 6 \pi^{2} I N^{2} \)
D. \( 8 \pi^{2} I n^{2} \)


How the adolescents gets safe and
nurturing environment?


Assertion
If the current in a solenoid is reversed in
direction while keeping the same magnitude, the magnetic field energy stored in the solenoid decreases.
Reason

Magnetic field energy density is proportional to square of current
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 equation of directrix and latus
rectum of a parabola are \( 3 x-4 y+ \)
\( 27=0 \) and \( 3 x-4 y+2=0 . \) Then the
length of latus rectum is
\( \mathbf{A} \cdot \mathbf{5} \)
B . 10
c. 15
D. 20


Using the principle of mathematical induction, find \( \tan \alpha+2 \tan 2 \alpha+ \)
\( 2^{2} \tan 2^{2} \alpha+\ldots . \) to \( n \) terms:
A \( \cdot \tan \alpha-2^{n} \cdot \tan \left(2^{n} \cdot \alpha\right) \)
B. \( \cot \alpha-2^{n} \cdot \cot \left(2^{n} \cdot \alpha\right) \)
c. \( \sec \alpha-2^{n} \cdot \sec \left(2^{n} \cdot \alpha\right) \)
D. None of these


Identify the equation used to determine the amount of heat required to melt
10 grams of ice:
A \( \cdot Q=m C_{s p} \Delta T \)
в. \( Q=n \triangle H \)
c. \( K E=\frac{1}{2} m v^{2} \)
D. \( P E=m g h \)
E . \( P V=n R T \)


A disc is rotated about its axis with a
certain angular velocity and lowered
gently on a rough inclined plane as
shown in figure, then
A. It will rotate at the position where it is placed and then will move downwards
B. It will go downwards just after it is lowered
c. It will go downwards first and then climb up
D. It will climb upwards and then move downwards


If the far point of a myopic person is 75 \( \mathrm{cm}, \) what should be the focal length of
the lens used to rectify this defect?


Define the magnifying power of a compound microscope when the final image is formed at infinity. Why must both the objective and the eyepiece of a compound microscope have short focal lengths? Explain.


Polymers can be classified based on
molecular forces.
(a) Classify the following polymers into elastomers and fibres:

Rubber, Nylon 6,6, Buna-S, Terylene
(b) What do you mean by thermosetting polymers? Give one example.


Which one of the following is limiting
rate of photosynthesis in nature
A. Light
в. \( C O_{2} \)
\( c \cdot O_{2} \)
D. chlorophyll


The angle made by the tangent line at (1
3) on the curve \( y=4 x-x^{2} \) with \( \overline{O X} \) is
\( A \cdot \tan ^{-1} 2 \)
B. \( \tan ^{-1}(1 / 2) \)
\( c \cdot \tan ^{-1}-2 \)
D. None of these


If no force acts on a body, then what will
happen to it?
A. It does not change its shape.
B. It continues to move but with less speed.
c. It changes its direction.
D. It can either remain at rest or continue to move in a straight line.


Point masses 1,2,3 and \( 4 k g \) are lying at the points (0,0,0),(2,0,0),(0,3,0) and (-2,-2,0) respectively. The moment of inertia of this system about x-axis will
be:
A \( \cdot 43 k g-m^{2} \)
B . \( 34 \mathrm{kg}-\mathrm{m}^{2} \)
c. \( 27 \mathrm{kg}-\mathrm{m}^{2} \)
D. \( 72 \mathrm{kg}-\mathrm{m}^{2} \)


The \( \frac{B . E}{A} \) ratio for deuteron and \( \alpha \)
particle are \( X_{1} \) and \( X_{2} \) respectively. The energy released in the fusion of
deuteron into \( \alpha \) -particle is
\( \mathbf{A} \cdot 4\left(X_{2}-X_{1}\right) \)
B \( \cdot 2\left(X_{2}-X_{1}\right) \)
\( \mathbf{c} \cdot 4\left(X_{2}+X_{1}\right) \)
D. \( \frac{X_{2}-X 1}{4} \)


A firecracker exploding on the surface of a lake is heard as two sounds a time
interval \( t \) apart by a man on a boat close
to the water surface. Sound travels by a speed \( v \) in the air. The distance from the exploding firecracker to the boat is:
A \( \cdot \frac{u v t}{u+v} \)
в. \( \frac{t(u+v)}{u v} \)
c. \( \frac{t(u-v)}{u v} \)
D. \( \frac{u v t}{u-v} \)


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


The reason for global warming is
A. Long wavelength radiation are absorbed by the atmosphere
B. Short wavelength radiation are absorbed by the atmosphere
C. Atmosphere traps radiations to increase the temperature
D. UV and infra red radiations