When the acceleration of rod is zero, the
charge on capacitor is :
\( ^{\text {A. }} \frac{B^{2} L^{2} C Q_{0}}{M+B^{2} L^{2} C} \)
\( ^{\text {В }} \frac{B^{2} R^{4} C^{3} Q_{0}}{M+B^{2} L^{2} C^{2}} \)
c. \( \frac{B^{2} R^{4} C^{3} Q_{0}}{M+B^{2} R^{4} C^{4}} \)
D. \( \frac{B^{2} L^{2} C Q_{0}}{M+B^{2} L^{2} C^{2}} \)


Simplify:
\( \operatorname{os} \theta \cdot\left[\begin{array}{cc}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta\end{array}\right]+ \)
\( \operatorname{in} \theta \cdot\left[\begin{array}{cc}\sin \theta & -\cos \theta \\ \cos \theta & \sin \theta\end{array}\right] \)


What are the limitations of Rutherford's
model of the atom?


The charge on particles of aerosols
results due to:
A. formation and subsequent interruption of particleparticle contact
B. formation and subsequent interruption of particlesurface contact
C. adsorption of ions on the particle surface
D. either of the above


Find the term \( t_{15} \) of an A.P.:
\( 4,9,14, \dots . \)


IUPAC name of the compound is:
A. \( 1- \) Bromo -2 -chlorocyclopenta -2,4 -diene
B. \( 1- \) Chloro \( -5- \) bromocyclopenta \( -1,3- \) diene
C. \( 5- \) Bromo-1-chlorocyclopenta-1, 3 -diene
D. \( 3- \) Bromo-4-chlorocyclopenta-1,4-diene


\( \lim _{x \rightarrow \infty}\left[\frac{2+2 x+\sin 2 x}{(2 x+\sin 2 x) e^{\sin x}}\right] \) is equal to
A.
в.
\( c \cdot-1 \)
D. Does not exist


If a line makes angles \( \boldsymbol{\alpha}, \boldsymbol{\beta}, \boldsymbol{\gamma} \) with
positive directions of \( \mathrm{X}, \mathrm{Y}, \mathrm{Z} \) -axes, what is the value of \( \sin ^{2} \alpha+\sin ^{2} \beta+\sin ^{2} \gamma \)
\( ? \)


What is the number of moles of
\( K M n O_{4} \) that will be needed to react
completely with one mole of ferrous oxalate in an acidic medium?


A particle of mass \( m \) is released from
rest at point \( A \) in Figure, falling parallel to the (vertical) y-axis. Find the angular momentum of the particle at any time \( t \) with respect to the same origin \( O \)


Establish the formula for electric field
intensity at a point on the axis of an electric dipole.


The inequality \( |2 x-3|<1 \) is valid
when x lies in the interval
\( \mathbf{A} \cdot(3,4) \)
B \( \cdot(1,2) \)
\( c \cdot(-1,2) \)
D \( \cdot(-4,3) \)


An alloy which is sonorous is :
A. duralumin
B. bell metal
c. type metal
D. gun metal


If \( 9-7 x=5-3 x, \) then the value of \( x \)
is
A . 0
B. \( \frac{1}{4} \)
\( c \cdot \frac{1}{2} \)
D.


If an electron is moving with a velocity of \( 1.1 \times 10^{6} \mathrm{ms}^{-1} \) de broglie wave
length approximately is:
A \( \cdot 4.1 \times 10^{-11} \mathrm{m} \)
В . \( 4.9 \times 10^{-9} \mathrm{m} \)
c. \( 7 \times 10^{-10} m \)
D. \( 3.306 \times 10^{-8} \mathrm{m} \)


Simplify: \( (\sqrt{2} x-2 y)^{2} \)


The center of gravity of a hollow cone of height \( h \) is at distance \( x \) from its vertex
where the value of \( x \) is.


Assertion
Diatom frustules pile up at the bottom of water bodies and form big heaps of diatomite or diatomaceous earth.
Reason

Diatom frustules are resistant to
natural degradation.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A group consists of 4 couples in which
each of the 4 persons have one wife each. In how many ways could they be arranged in a straight line such that the men and women occupy alternate positions?
A . 1152
в. 1278
\( c \cdot \) 1296
D. 1176


If \( f(x), \phi(x), \varphi(x) \) are continuous
on \( [a, b] \) and differentiable on
\( (a, b) \exists c \epsilon(a, b), \) then
\( \left|\begin{array}{lll}\boldsymbol{f}(\boldsymbol{a}) & \boldsymbol{\phi}(\boldsymbol{a}) & \boldsymbol{\varphi}(\boldsymbol{a}) \\ \boldsymbol{f}(\boldsymbol{b}) & \boldsymbol{\phi}(\boldsymbol{b}) & \boldsymbol{\varphi}(\boldsymbol{b}) \\ \boldsymbol{f}^{\prime}(\boldsymbol{c}) & \boldsymbol{\phi}^{\prime}(\boldsymbol{c}) & \boldsymbol{\varphi}^{\prime}(\boldsymbol{c})\end{array}\right|= \)
\( A \cdot f^{\prime}(c) \)
B. \( \phi^{\prime}(c) \)
c. \( \varphi^{\prime}(c) \)
D.


A single slit of width \( a \) is illuminated by violet light of wave length 400 nm and
width of the diffraction pattern is measured as \( y \). Half of the slit is
covered and illuminated with 600 nm.
The width of the diffraction pattern will be
A \( \cdot \frac{y}{3} \)
B. pattern vanishes and width is zero
c. \( 3 y \)
D. none of these


If \( \boldsymbol{A}^{T}=\left[\begin{array}{cc}\mathbf{4} & \mathbf{5} \\ -\mathbf{1} & \mathbf{0} \\ \mathbf{2} & \mathbf{3}\end{array}\right] \) and \( \boldsymbol{B}= \)
\( \left[\begin{array}{ccc}2 & -1 & 1 \\ 7 & 5 & -2\end{array}\right], \) verify the following
\( \mathbf{A} \cdot(A+B)^{T}=A^{T}+B^{T}=B^{T}+A^{T} \)
В \( \cdot(A+B)^{T}=A^{T}-B^{T} \)
c. \( \left(B^{T}\right)^{T}=B \)
D. none of these


Which of the following is/ are correct
about pressure?
A. Pressure at a point acts equally in all directions
B. Liquid at rest exerts lateral pressure which decreases with depth
C. Pressure acts normally on any area whatever orientation the area may be held
D. Both
(a) and
(c) are correct


In establishing new ecosystem on rock the pioneers are
A. Lichens
B. Phytoplankton
c. Trees
D. Animals


Reactivity order of \( S_{N} 1 \) reaction for the
following compounds is:
\( \mathbf{c} \)
А. \( a>b>c>d \)
в. \( a>d>c>b \)
\( c \cdot c>d>b>a \)
\( . a>b>d>c \)
\( c \)


If the radius of a sphere doubled
without changing the charge on it, then electric flux originating form the sphere
is:
A . Double
B. Half
c. same
D. zero


Transverse waves on a string have wave
speed \( 8.00 \mathrm{m} / \mathrm{s}, \) amplitude \( 0.0700 m \)
and wavelength 0.32 m. The waves
travel in the negative \( x \) -direction and
\( t=0 \) the \( x=0 \) end of the string has its
maximum upward displacement. Write a wave function describing the wave.
A \( \cdot y(x, t)=(0.07 m) \sin 2 \pi\left(\frac{x}{0.32 m}+\frac{t}{0.04 s}\right) \)
B. \( y(x, t)=(77 m) \cos 2 \pi\left(\frac{x}{0.32 m}+\frac{t}{0.04 s}\right) \)
c. \( y(x, t)=(0.7 m) \sin 4 \pi\left(\frac{x}{0.32 m}+\frac{t}{0.04 s}\right) \)
D \( y(x, t)=(0.97 m) \sin 2 \pi\left(\frac{x}{0.32 m}+\frac{t}{0.04 s}\right) \)


If dielectric is inserted in charged capacitor (battery removed), then quantity that remains constant is.
A. Capacitance
B. Potential
c. Intensity
D. charge


Elucidate the structure of fructose.


A moving body of mass m makes a head on elastic collision with another body of
mass \( 2 \mathrm{m} \) which is initially at rest. Find
the fraction of kinetic energy lost by the colliding particle after collision.


Which of the following is the correct
statement?
A. Starch is a polymer of \( \alpha \) - glucose.
B. Amylose is not a component of starch.
C. Proteins are composed of only one type of amino acid.
D. In cyclic structure of fructose, there are five carbon and one oxygen atoms.


A body of mass \( M \) at rest explodes into
three pieces, two of which of mass \( M / 4 \)
each are thrown off in perpendicular directions with velocities of \( 3 m / s \) and \( 4 m / s \) respectively. The third piece will be thrown off with a velocity of
A. \( 1.5 \mathrm{m} / \mathrm{s} \)
в. 2.0 \( m / s \)
\( c .2 .5 \mathrm{m} / \mathrm{s} \)
D. 3.0 \( m / s \)


When a molecule of pyruvic acid is subjected to anaerobic oxidation and forms lactic acid, there is
A. Loss of 3 ATP molecules
B. Loss of 6 ATP molecules
c. Gain of 2 ATP molecules
D. Gain of 4 ATP molecules


The number of turns in the primary and
the secondary coils of a transformer are
1000 and 3000 respectively. If the primary of the coil is connected to 80
volt ac, then what is the potential difference per turn of the secondary coil
\( ? \)
A . 240
B. 24
c. \( 0.24 v \)
D. 0.08 \( v \)


The diameter of a copper wire is \( 2 \mathrm{mm} \) a steady current of 6.25 A is generated by \( 8.5 \times 10^{28} / m^{2} \) electron flowing
through it. Calculate the drift velocity of conduction electrons.


Find \( \frac{d y}{d x}, x=a\left(\cos t+\log \tan \frac{t}{2}\right), y= \)
\( a \sin t \)


State and explain Brewster's law.


A ray of light in air is incident on a glass
plate at polarising angle of incidence. It
suffers a deviation of \( 22^{\circ} \) on entering
glass. The angle of polarization is :
A . \( 90^{\circ} \)
B. 56
\( c \cdot 68 \)
D. Zero


The domain of the function \( \boldsymbol{f}(\boldsymbol{x})= \) \( \frac{1}{\sqrt{1-e^{\frac{1}{x}-1}}} \) is
B \( \cdot(-\infty, \infty) \)
C . \( (-\infty, 0] \cup[1, \infty) \)
D. none of these


n Fig 10.3 if \( \mathrm{OA}=5 \mathrm{cm}, \mathrm{AB}=8 \mathrm{cm} \) and
OD is perpendicular to AB then CD is
equal to
\( A \cdot 2 \mathrm{cm} \)
B. 3 \( \mathrm{cm} \)
\( c \cdot 4 \mathrm{cm} \)
D


What is work done in holding a body of mass \( 20 \mathrm{kg} \) at a height of \( 2 \mathrm{m} \) above the
ground? \( \left(g=10 m / s^{2}\right) \)
A . \( 40 \mathrm{J} \)
B. 400 J
c. \( 10 J \)
D. zero


Find the degree measures corresponding to the following radian measures \( \left(\boldsymbol{U s e} \boldsymbol{\pi}=\frac{\mathbf{2 2}}{\mathbf{7}}\right) \)
(i) \( \frac{11}{16} \)
(ii) -4
(iii) \( \frac{5 \pi}{3} \)
(iv) \( \frac{7 \pi}{6} \)


Two drops of small radius are falling in
air with constant velocity \( 5 \mathrm{cm} s^{-1} . \) If
they coalesce, then the terminal velocity will be
A. \( 10 \mathrm{cms}^{-1} \)
B . \( 2.5 \mathrm{cms}^{-1} \)
c. \( 5 \times \sqrt[3]{4 c m s^{-1}} \)
D. \( 5 . \sqrt{2} \mathrm{cm} \mathrm{s}^{-1} \)


Which of the following hybridization's has maximum s-character?
\( A \cdot s p^{3} \)
B \( . s p^{2} \)
\( c \cdot s p \)
D. All have same s-character


Evaluate the following definite integrals as limit of sums. \( \int_{0}^{5}(x+1) d x \)
A \( \cdot \frac{15}{2} \)
в. \( \frac{25}{2} \)
c. \( \frac{35}{2} \)
D. \( \frac{45}{2} \)


Define the phenomenon of total internal reflection.


Find the gravitational potential energy of a \( 1 k g \) mass kept at a height of \( 5 m \) above the ground if \( g=10 m s^{-2} \)
A \( .50 J \)
в. \( 5 J \)
c. \( 25 J \)
D. \( 0 . J \)


Simplify: \( (2 x+1)(1-x)\left(x^{2}+x\right) \)
A \( \cdot 2 x^{4}-x^{3}+2 x^{2}+x \)
В. \( -2 x^{4}-x^{3}+2 x^{2}+x \)
c. \( -2 x^{4}+x^{3}+2 x^{2}+x \)
D. \( -2 x^{4}-x^{3}+2 x^{2}-x \)


An equilateral triangle has lines of symmetry.
A. 0
B.
\( c \cdot 3 \)
\( D \)


Compute the energy stored in the
capacitor at \( t=2.00 m s \)
A. \( 9.5531 \mu J \)
B. \( 6.5531 \mu J \)
c. \( 3.5531 \mu J \)
D. \( 2.5531 \mu J \)


Let \( R=\left\{\left(a, a^{3}\right): a \) is a prime number \right.
less than \( 10\} \). Find range (R).


Trace of matrix \( \boldsymbol{A}^{k} \) is
\( \mathbf{A} \cdot 3^{k}+1+(-1)^{k} \)
B . \( 2^{k}+3^{k}-2 \)
c. \( 3^{k}-2^{k}+2 \)
\( \mathbf{D} \cdot 2^{k}+1 \)


Identify \( (A) \) and \( (B) \) in the following
sequence of reactions.
\( \boldsymbol{S} \boldsymbol{n} \boldsymbol{C l}_{2}+\boldsymbol{2} \boldsymbol{N} \boldsymbol{a} \boldsymbol{O} \boldsymbol{H} \rightarrow \)
\( (\boldsymbol{A})(\boldsymbol{w} \boldsymbol{h} i \boldsymbol{t} e \boldsymbol{p} \boldsymbol{p} \boldsymbol{t}) \frac{N a O \boldsymbol{H}}{(e x c e s s)}(\boldsymbol{B}) \)
A \( \cdot \operatorname{Sn}(O H)_{2}, N a_{2} \operatorname{Sn} O_{3} \)
B. \( \operatorname{Sn}(O H)_{2}, N a_{2} S n O_{2} \)
c. \( \operatorname{Sn}(O H)_{2}, N a_{2} \operatorname{Sn}(O H)_{6} \)
D. \( \operatorname{Sn}(O H)_{2} \), no effect


In a laboratory, liquid in a thermally insulated container is stirred for one
hour by a mechanical linkage to a stirrer, for this process:
A. \( W<0 ; q=0 \)
в. \( W<0 ; q>0 \)
c. \( W>0 ; q>0 \)
D. \( W>0 ; q=0 \)


A circus artist is climbing a \( 20 m \) long
rope, which is tightly stretched and tied from the top of a vertical pole of the
ground. Find the height of the pole if the angle made by the rope with the ground
level is \( 30^{\circ} \)
A . \( 12 \mathrm{m} \)
B. 10
\( c \cdot 8 m \)
\( D \cdot 6 m \)


The whole surface of a rectangular
block is \( 846 \mathrm{cm}^{3} . \) Find the volume, if
these dimensions are proportional to
\( \mathbf{5}: \mathbf{4}: \mathbf{3} \)


Maxwell's four equations are written as
(i) \( \oint \overrightarrow{\boldsymbol{E}} \cdot \overrightarrow{\boldsymbol{d}} \boldsymbol{s}=\frac{\boldsymbol{q}_{0}}{\varepsilon_{0}} \)
(ii) \( \oint \vec{B} \cdot \vec{d} s=0 \)
(iii) \( \oint \overrightarrow{\boldsymbol{E}} \cdot \overrightarrow{\boldsymbol{d}} \boldsymbol{l}=\frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{t}} \quad \boldsymbol{\oint} \overrightarrow{\boldsymbol{B}} \cdot \overrightarrow{\boldsymbol{d}} \boldsymbol{s} \)
\( (\text { iv }) \oint \vec{B} \cdot \vec{d} s=\mu_{0} \varepsilon_{0} \frac{d}{d t} \oint \vec{E} \cdot \vec{d} s \)
Which of the above Maxwell's equations
shows that electric field lines do not
form closed loops?
A. (i) only
B. (ii) only
c. (iii) only
D. (iv) only


Which of the following metals has been used for building boats because it has resistance to corrosion by sea water?
A. copper
B. Nickel
c. Fungsten
D. Titanium


The wavelength of maximum energy released during an atomic explosion was \( 2.93 \times 10^{-10} \) m. The maximum
temperature attained must be:
(Weins constant \( \left.=2.93 \times 10^{-3} m K\right) \)
\( \mathbf{A} \cdot 5.86 \times 10^{7} K \)
B \( \cdot 10^{-13} \) K
c. \( 10^{-7} K \)
\( \mathbf{D} \cdot 10^{7} K \)


The work done to split a liquid drop of radius R into N identical drops is (take
\( \sigma \) as the surface tension of the liquid):
A \( \cdot 4 \pi R^{2}\left(N^{1 / 3}-1\right) \sigma \)
B . \( 4 \pi R^{2} N \sigma \)
C \( \cdot 4 \pi R^{2}\left(N^{1 / 2}-1\right) \)
D. None of these


If \( A \) and \( B \) are two matrices of order
\( 3 \times m \) and \( 3 \times n \) respectively and \( m= \)
\( \boldsymbol{n}, \) then the order of \( \mathbf{5} \boldsymbol{A}-\mathbf{2} \boldsymbol{B} \) is
\( \mathbf{A} \cdot m \times 3 \)
B. \( 3 \times 3 \)
\( \mathrm{c} \cdot m \times n \)
D. \( 3 \times n \)


A conductance cell was calibrated by
filling it with a \( 0.02 M \) solution of
potassium chloride (specific conductance \( =0.2768 \) oh \( m^{-1} m^{-1} \)
and measuring the resistance at \( 298 K \)
which was found to be 457.3 ohm. The
cell was then filled with a calcium
chloride solution containing \( 0.555 g \) of
\( \mathrm{CaCl}_{2} \) per litre. The measure
resistance was 1050 ohm. Calculate
the molar conductivity of \( C a C l_{2} \)
solution.


Choose the correct answers from the
alternatives given:
Transcription is the transfer of genetic code from a DNA molecule to a
A. RNA molecule
B. Second DNA molecule
c. Ribosomal subunit
D. Sequence of amino acids in a protein molecule


The number of Oxygen atoms bonded to each
silicon atom in silica crystal is :
A
B. 2
\( c \cdot 3 \)
\( D \)


\( \boldsymbol{A l}+\boldsymbol{X} \stackrel{\Delta}{\rightarrow} \boldsymbol{Y} \stackrel{\boldsymbol{H}_{2} \boldsymbol{O}}{\rightarrow} \boldsymbol{Z}+\boldsymbol{N} \boldsymbol{H}_{3} \)
Here \( \boldsymbol{X}, \boldsymbol{Y} \) and \( \boldsymbol{Z} \) are respectively:
\( \mathbf{A} \cdot O_{2}, A l_{2} O_{3}, A l(O H)_{3} \)
в. \( N_{2}, \) АlN, \( A l_{2} O_{3} \)
c. \( N_{2}, \) AlN, \( A l(O H)_{3} \)
D. \( C O_{2}, A l_{4} C_{3}, C H_{4} \)


If its given :
Half-life \( \alpha \frac{1}{a}, \) what will be the order? Will it
be \( 2 ? \)


Growth of pollen tube towards embryo
sac is?
A. Chemotropic
B. Thigmotaxis
c. Geotropic
D. None of these


A microscope:
A. converges light
B. diverges light
C . reflects light
D. refracts light


Solve: \( \sqrt{\sec x-1}=\tan x \)


Find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \)
\( \mathbf{8} \boldsymbol{x}^{2}+\boldsymbol{9} \boldsymbol{y}=\boldsymbol{6} \boldsymbol{x}+\boldsymbol{2} \)


The speed of a body moving with uniform acceleration is \( u . \) This speed is
doubled while covering a distance \( S \)
When it covers an additional distance \( \boldsymbol{S} \)
its speed would become?
A \( \cdot \sqrt{3} u \)
B. \( \sqrt{5} u \)
c. \( \sqrt{11} u \)
D. \( \sqrt{7} u \)


characteristic for a semiconductor
device. Which of the following
statement is correct?
A. It is V-I characteristic for solar cell where, point represents open circuit voltage and point B short
circuit current
B. It is for a solar cell and points A and B represent open circuit voltage and current, respectively
C. It is for a photodiode and points \( A \) and \( B \) represent open circuit voltage and current respectively
D. It is for a LED and points A and B represent open circuit voltage and short circuit current, respectively


If the electron concentration is \( \left(n_{e}\right) \) and
hole concentration is \( \left(n_{h}\right) \) in a semiconductor in thermal equilibrium
then
A \( \cdot n_{e} \times n_{h}= \) constant
B . \( \frac{n_{e}=\text { constant }}{n_{h}} \) to
C \( \cdot n_{e}^{2} n_{h}= \) constant
D. \( n_{h}^{2} n_{e}= \) constant


Prove the following by using the principle of mathematical induction for
all \( \boldsymbol{n} \in \boldsymbol{N}: \mathbf{1} . \mathbf{2}+\mathbf{2} . \mathbf{3}+\mathbf{3} . \mathbf{4}+\ldots . .+ \)
\( \boldsymbol{n}(\boldsymbol{n}+1)=\left[\frac{\boldsymbol{n}(\boldsymbol{n}+1)(\boldsymbol{n}+\boldsymbol{2})}{\boldsymbol{3}}\right] \)


The work function for tungsten and
sodium are \( 4.5 e V \) and \( 2.3 e V \)
respectively. If threshold wavelength \( \lambda \) for sodium is \( 5460 A \), the value of \( \lambda \) for
tungsten is
\( \mathbf{A} .5893 \hat{A} \)
в. 10683 ,
c. 2791 ,
D. 528 月


The pollutants in the air are:
A. melting white marbles of Taj Mahal.
B. discoloring white marbles of Taj Mahal.
C. forming cracks in the marbles of Taj Mahal.
D. all of above


Assertion
Proton, electron and neutron each has its antiparticle.
Reason
Antiproton and antielectron has
opposite charge to proton and electron are called antiproton and positron
respectively. Antineutron possess only opposite spin.
A. Assertion is correct but Reason is wrong
B. Assertion is wrong but Reason is correct
C. Both Assertion and Reason are correct and Reason is correct explanation of Assertion
D. Both Assertion and Reason are correct but Reason is not correct explanation of Assertion


Reverberation time of a hall used for
speeches should be very short. Why?
A. Multiple echos will enhance the sound quality.
B. Multiple echos will interfere with the original sound
c. Both a and 6
D. None of the above


Convert each part of the ratio to
percentage.
\( \mathbf{1}: \mathbf{4} \)


Homo erectus is the zoological name of
A. Java ape man
B. Peking man
C. Neanderthal man
D. Both A and B


A man weighing \( 80 \mathrm{kg} \) is standing at the centre of a flat boat and he is \( 20 m \)
from the shore. He walks \( 8 m \) on the
boat towards the shore and then halts.
The boat weight 200 kg. How far is he
from the shore at the end of this time?
A . \( 11.2 m \)
в. \( 13.8 \mathrm{m} \)
c. 14.3 m
D. \( 15.4 \mathrm{m} \)


Which one of the following has the highest dipole moment?
\( (i) C H_{2} C l_{2}(i i) C H C l_{3} \)
\( (\boldsymbol{i} \boldsymbol{i} \boldsymbol{i}) \boldsymbol{C} \boldsymbol{C l}_{\boldsymbol{4}} \)


\( \operatorname{Let} F(x)=f(x) g(x) h(x) \) for all real \( x \)
where \( f(x), g(x) \) and \( h(x) \) are differentiable functions. At some point
\( \boldsymbol{x}_{0}, \boldsymbol{F}^{\prime}\left(\boldsymbol{x}_{0}\right)=\mathbf{2 1} \boldsymbol{F}\left(\boldsymbol{x}_{0}\right), \boldsymbol{f}^{\prime}\left(\boldsymbol{x}_{0}\right)= \)
\( 4 f\left(x_{0}\right), g^{\prime}\left(x_{0}\right)=-7 g\left(x_{0}\right) \) and
\( \boldsymbol{h}^{\prime}\left(\boldsymbol{x}_{0}\right)=\boldsymbol{k h}\left(\boldsymbol{x}_{0}\right) . \) Then \( \boldsymbol{k} \) is equal to


When metals and non-metals other
than oxygen react, what is formed?
A. water
B. A covalent compound
c. An ionic compound
D. oxygen
E. An ion


Which of the following are nonterminating numbers? This question has multiple correct options
\( A \cdot \frac{2}{3} \)
B. \( \frac{7}{15} \)
\( c \cdot \frac{2}{5} \)
\( \mathbf{D} \cdot \frac{5}{13} \)


In last step of glycolysis the
A. Protein is converted to glucose
B. Glucose is converted into glucose
c. starch is converted into glucose
D. Glucose is converted into pyruvic acid


In the following, determine the value of
\( k \) for which the given value is a solution
of the equation.
\( \mathbf{3} \boldsymbol{x}^{2}+\mathbf{2} \boldsymbol{k} \boldsymbol{x}-\mathbf{3}=\mathbf{0}, \boldsymbol{x}=-\frac{\mathbf{1}}{\mathbf{2}} \)


The value of 'a' for which the function
\( f(x)=(a+2) x^{3}-3 a x^{2}+9 a x-1 \)
decreases for all real values of \( x \) is
B \( \cdot(-\infty,-3) \)
\( c \cdot(-\infty,-2) \)
D. \( (-\infty,-3] \cup[0, \infty) \)


In a closed container at a given temperature, pressure increases from \( 100 \mathrm{mm} \) Hg to \( 160 \mathrm{mm} \) Hg in 10 sec. for
reaction.

Then the average rate of reaction in first
10 sec. will be?
A. \( 2 \mathrm{mm} / \mathrm{sec} \)
B. \( 4 \mathrm{mm} / \mathrm{sec} \)
c. \( 6 \mathrm{mm} / \mathrm{sec} \)
D. 3 mm/sec.


\( y=e^{x^{2}} \) the value of \( \frac{d y}{d x} \) is \( m x e^{x^{2}} . \) Find
\( m \)


What is immaterial for an electric fuse?
A . Its length
B. Its radius
C. Its specific resistance
D. Current flowing through it


In the circuit shown, the diodes are
ideal. \( A_{1} \) and \( A_{2} \) are ammeters of
resistance \( 5 \Omega \) each. The potentials of
the points \( A, B, C \) and \( D \) are \( V_{A}, V_{B}, V_{C} \)
and \( V_{D} \) respectively. \( \left|\boldsymbol{V}_{\boldsymbol{A}}-\boldsymbol{V}_{\boldsymbol{B}}\right|=\mathbf{1 0} \boldsymbol{V} \)
This question has multiple correct options
A. \( A_{1} \) and \( A_{2} \) will always show the same reading
B. the readings of \( A_{1} \) and \( A_{2} \) will depend on whether \( V_{A}>V_{B} \) or \( V_{A}<V_{B} \)
C. the readings of either of \( A_{1} \) or \( A_{2} \) or both will be \( 1 A \) in all cases
D. If \( V_{A}>V_{B}, A_{1} \) will show no deflection


In the soil profile, which layer is harder and more compact?
A. Bedrock
B. Subsoil
c. Surface soil
D. Parent rock


For which of the following is \( \boldsymbol{f}>\mathbf{0} \)
I. Concave mirror
II. Convex mirror
III. Converging lens
A. I only
B. II only
c. I and III only
D. II and III only
E . ।, II, and III


Give two differences between Lyophilic colloids and Lyophobic colloids.


Fill in the blanks with suitable words.
When a body changes from liquid to gas
at constant temperature, it is called


Which two orbitals are located along the
axis, and not between the axis?
\( \mathbf{A} \cdot d_{x^{2}-y^{2}}, d_{z^{2}} \)
B . \( d_{x y}, p_{z} \)
\( \mathbf{c} \cdot d_{y z}, p_{x} \)
D. \( d_{y z}, d_{x^{2}-y^{2}} \)


The binding energies per nucleon for a
deuteron and an \( \alpha \) -particle are \( x_{1} \) and
\( x_{2} \) respectively.What will be the energy Q released in the reaction \( _{1} \boldsymbol{H}^{2}+_{1} \)
\( \boldsymbol{H}^{2}+\rightarrow_{2} \boldsymbol{H} \boldsymbol{e}^{4}+\boldsymbol{Q} \)
\( \mathbf{A} \cdot 4\left(x_{1}+x_{2}\right) \)
B . \( 4\left(x_{2}-x_{1}\right) \)
c. \( 2\left(x_{1}+x_{2}\right) \)
D \( \cdot 2\left(x_{2}-x_{1}\right) \)


If \( A_{1}, A_{2} ; G_{1}, G_{2} ; H_{1}, H_{2} \) be two
A. \( M \cdot^{\prime} s, G . M .^{\prime} s \) and \( H . M .^{\prime} s \) between
two positive numbers then prove:
\( \frac{\boldsymbol{G}_{1} \boldsymbol{G}_{2}}{\boldsymbol{H}_{1} \boldsymbol{H}_{2}}=\frac{\boldsymbol{A}_{1}+\boldsymbol{A}_{2}}{\boldsymbol{H}_{1}+\boldsymbol{H}_{2}} \)


\( f\left(a_{1}, a_{2}, a_{3}, \dots, a_{n}, \dots a r e \text { in } G P \) then the \right.
determinant \( \Delta= \)
\( \left|\begin{array}{ccc}\log a_{n} & \log a_{n+1} & \log a_{n+2} \\ \log a_{n+3} & \log a_{n+4} & \log a_{n+5} \\ \log a_{n+6} & \log a_{n+7} & \log a_{n+8}\end{array}\right| \) is equal
to
A . 0
B. 1
\( c \cdot 2 \)
D.


Which of the following best accounts for some of the non-ideal behavior observed
in real gases?
A. Some gaseous molecules are not spherical
B. There are intermolecular attractive forces
c. The temperature is not kept constant
D. \( R \) (gas constant) is not a true constant
E. Experimental errors are made in the measurement of the pressure and the volume


At a metro station, a girl walks up a
stationary escalator in time \( t_{1} \). If she
remains stationary on the escalator,
then the escalator take her up in time \( t_{2} \)
The time taken by her to walk up on the moving escalator will be
A \( \cdot \frac{\left(t_{1}+t_{2}\right)}{2} \)
В. \( \frac{t_{1} t_{2}}{\left(t_{2}-t_{1}\right)} \)
c. \( \frac{t_{1} t_{2}}{\left(t_{2}+t_{1}\right)} \)
D. \( t_{1}-t_{2} \)


A wheel of moment of inertia \( 5 \times \)
\( 10^{-3} k g m^{2} \) is making 20 rev \( / s . \) The
torque required to stop it in \( 10 s \) is :
A \( \cdot 2 \pi \times 10^{-2} N m \)
В . \( 2 \pi \times 10^{2} N m \)
\( \mathbf{c} \cdot 4 \pi \times 10^{-2} N m \)
D. \( 4 \pi \times 10^{2} N m \)


When a superconductor is placed in a weak external magnetic field \( \mathrm{H} \), and cooled below its transition temperature
A. the magnetic field is ejected
B. the magnetic field get magnetized
c. the magnetic field strength increased
D. none of the above


Which of the following reagents may by used to distinguish between phenol and benzoic acid?
A . Neutral \( F e C l_{3} \)
B. Aqueous \( N a O H \)
c. Tollen's reagent
D. Schiff's reagent


The ratio of the length of the parallel sides of a trapezium is 5: 3 and the
distance between them is \( 16 \mathrm{cm} \). If the
area of the trapezium is \( 960 \mathrm{cm}^{2}, \) find the length of the parallel sides


Potential Energy \( (U) \) of a body of unit mass moving in a one-dimension conservative force field is given by \( U= \)
\( \left(x^{2}-4 x+3\right) . \) All units are in S.I.
(i) Find the equilibrium position of the body
(ii) Show that oscillations of the body
about this equilibrium position is simple harmonic motion and find its time period.
(iii) Find the amplitude of oscillations if the speed of the body at equilibrium position is \( 2 \sqrt{6} m / s \)


Write any two differences between mixture and compound. Also write two examples of each.


Both \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{3} \) and \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) are dibasic
acid. But, equimolar solutions of both acids do not contain equal
concentration of \( \boldsymbol{H}^{+} \) ions. Give reason.


In which of the following reactions (I) is behaving like an electrophile?
(1)
(2) \( \mathrm{Br}_{2} \)
\[
+\mathrm{CH}_{3}-\mathrm{CH}=\mathrm{CH}_{2} \stackrel{\mathrm{CCl}_{4}}{\longrightarrow}
\]
\( (2) \mathrm{CH}_{3}-\mathrm{CH}=\mathrm{CH}_{2} \quad+\mathrm{H}-\mathrm{Br} \stackrel{\mathrm{H}_{2} \mathrm{O}}{\longrightarrow} \)
(4)
\( A \)
\( B .2 \)
\( c \cdot 3 \)
\( D \cdot 4 \)


If a body travels \( 30 m \) in an interval of
\( 2 s \) and \( 50 m \) in the next interval of \( 2 s \)
then the acceleration of the body is:
A. \( 10 \mathrm{ms}^{-2} \)
B. \( 5 m s^{-2} \)
c. \( 20 m s^{-2} \)
D. \( 25 \mathrm{ms}^{-2} \)


An iron scale is calibrated at \( 0^{\circ} C . \) The
length of a zinc rod is measured to be
\( 100 \mathrm{cm} \) by the scale when the rod and
the scale both are at \( 0^{0} C . \) What will be
the length of the rod as measured by the
scale when both are at \( 100^{\circ} \mathrm{C} \). Given :
\( \boldsymbol{\alpha}_{i r o n}=1.2 \times 10^{-5}^{\circ} \boldsymbol{C}^{-1} \) and \( \boldsymbol{\alpha}_{z i n c}= \)
\( \mathbf{2 . 6} \times \mathbf{1 0}^{-\mathbf{4} \circ} \mathbf{C}_{-\mathbf{1}} \)


A small ring of mass \( \mathrm{m} \) is connected with a particle of same mass by an ideal string and the whole system is released as shown in figure. Coefficient of friction between ring \( A \) and wire is
\( 3 / 5 . \) If ring A starts sliding when connecting string makes an angle \( \theta \) with the vertical. This angle \( \theta \) is (particle is free to move and ring can slide only):
A .30
в. 45
\( c .60 \)
D. None of these


In which of the following pairs of
carbanion, the first one is more stable
than the second?
A \( \cdot \stackrel{\ominus}{C} F_{3}, C C l_{3} \)
B. \( H C=\stackrel{\ominus}{C}, H_{2} C=\stackrel{\ominus}{C H} \)
\( c \)
D. \( \left(C H_{3}\right)_{3} \stackrel{\ominus}{C}, H_{3} C-\stackrel{\ominus}{C} H_{3} \)


Systolic pressure is higher than
diastolic pressure due to
A. Volume of blood in the heart is greater during systole
B. Arteries contract during systole
C. Blood vessels offer resistance to flowing blood during systole
D. Blood is forced into arteries during systole


What is \( Q \) -factor? Write its expression
and write the conditions for its
maximum value.


Evaluate the integral \( \int \frac{2 x+3}{\sqrt{x^{2}+4 x+1}} d x \)
A \( \cdot 2 \sqrt{x^{2}+4 x+1}-\log |x+2+\sqrt{x^{2}+4 x+1}|+C \)
B. \( \sqrt{x^{2}+4 x-1}-\log |x+2+\sqrt{x^{2}+4 x-1}|+C \)
c. \( 2 \sqrt{x^{2}+4 x+1}-\log |x-2+\sqrt{x^{2}-4 x+1}|+C \)
D. \( \sqrt{x^{2}+4 x-1}-\log |x-2+\sqrt{x^{2}+4 x-1}|+C \)


If the Gibbs free energy change when 1 mole of \( N a C l \) is dissolved in water at
\( 298 \mathrm{K} \) is \( x \mathrm{kJ}, \) then \( -1000 x \) is
Given that,
(a) Lattice energy of \( N a C l= \) \( 778 k J m o l^{-1} \)
(b) Hydration energy of \( N a C l= \) \( -774.3 k J m o l^{-1} \)
(c) Entropy change at \( 298 K= \)
43 Jmol\( ^{-1} \)
A. 9117
B. 9441
c. 9114
D. 9141


Identify which of the following is correct about the cooling process as shown above?
I. Negative work
II. An isothermal process
III. Increasing energy
A . I only
B. II only
c. I and III only
D. II and III only
E. I, II, and III


Assertion \( (A) \) If \( 0<x<\frac{\pi}{2} \) then
\( \sin ^{-1}(\cos x)+\cos ^{-1}(\sin x)=\pi-2 x \)
Reason
\( (\mathrm{R}) \cos ^{-1} x=\frac{\pi}{2}-\sin ^{-1} x \forall x \in \)
\( [\mathbf{0}, \mathbf{1}] \)
A. Both \( A \) and \( R \) are true and \( R \) is the correct explanation of \( A \)
B. Both A and R are true but R is not correct explanation of \( A \)
C. \( A \) is true but Ris false
D. A is false but \( R \) is true


What is 'Rete Pegs'?


The Sl unit of amplitude is
A. Hertz
B. Metre
c. second
D. None of these


D.E of the parabolas having x-axis as
axis and origin as focus is:
\( \mathbf{A} \cdot y\left(\frac{d y}{d x}\right)^{2}+4 x \frac{d y}{d x}=4 \)
B. \( 2 x \frac{d y}{d x}-y=0 \)
\( ^{\mathbf{C}} y\left(\frac{d y}{d x}\right)^{2}+y=2 x y \frac{d y}{d x} \)
\( y\left(\frac{d y}{d x}\right)^{2}+2 x \frac{d y}{d x}-y=0 \)


Which can be explained as applications of Le Chatelier's principle?
A. Transport of oxygen by haemoglobin in blood
B. Removal of \( C O_{2} \) from tissues by blood
c. Tooth decay due to use of sweet substances
D. All of the above


A Cell of emf \( \mathrm{E} \) is connected across a
resistance R. The potential difference between the terminals of the cell
is found to be \( V \). The internal resistance
of the cell is given as:
A \( . R(E-V) \)
в. \( \frac{E-V}{R} \)
c. \( \frac{(E-V)}{R} E \)
D. \( \frac{(E-V)}{V} R \)


A mixture of ethyl alcohol and propyl
alcohol has vapour pressure of \( 290 m m \) at \( 300 K . \) The vapour pressure of propyl alcohol is 200 mm. If mole fraction of
ethyl alcohol is 0.6 its vapour presssure at same temperature will be:-
A . 360
в. 350
\( c .300 \)
D. 700


Figure shows a potentiometer with a cell of \( 2.0 \mathrm{V} \) and internal resistance 0.40
\( \Omega \) maintaining a potential drop across
the resistor wire AB. A standard cell
which maintains a constant emf of 1.02
V gives a balance point at \( 67.3 \mathrm{cm} \)
length of the wire. The standard cell is
then replaced by a cell of unknown emf
E and the balance point, similarly turns out to be at \( 82.3 \mathrm{cm} \), length of the wire. Then the E is
\( A \cdot 1 V \)
B. 1.25 \( v \)
\( c \cdot 1.5 v \)
D. \( 1.75 \mathrm{v} \)


What are antioxidants? Give two
examples.


Assertion
An electric motor will have maximum
efficiency when back emf becomes equal to half of applied emf.
Reason
Efficiency of electric motor depends only on magnitude of back emf.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The value of houses in a particular area
are shown in the table.
Value
\[
\begin{array}{llll}
\text { per } & \mathbf{1 0}- & \mathbf{2 0}- & \mathbf{3 0}- \\
\text { house } & \mathbf{2 0} & \mathbf{3 0} & \mathbf{4 0}
\end{array}
\]
in
lakhs)
Number
of
\[
2
\]
houses
Given the mean value of the houses is
30.14 lakhs. and assumed mean is 35
\( A \cdot 7 \)
B. 8
\( c .9 \)
D. 10


\( \ln S H M \) restoring force is \( F=-k x \)
where \( k \) is force constant, \( x \) is
displacement and \( a \) is amplitude of
motion, then total energy depends upon
A. \( k, a \) and \( m \)
в. \( k, x, m \)
c. \( k, a \)
D. \( k, x \)


The graph of the function \( f(x)=x^{3}+1 \)
after translation 4 units to the right and 2 units up, resulted in a new graph \( l(x) \) What is the value of \( l(3.7) ? \)
A. 0.973
B. 1.784
c. 1.973
D. 2.027
E . 2.973


Assertion
Work done by friction force in case of pure rolling,is equal to change in rotational energy.
Reason
Ratio of kinetic energy of rotation to kinetic energy of translation is fixed for
every case.
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 degree of \( \frac{d^{2} y}{d x^{2}}+ \)
\( \left(1+\left(\frac{d y}{d x}\right)\right)^{3 / 2}=0 \)
\( A \cdot 2 \)
B.
\( c \cdot 4 \)
D. 6


Hydrogen is present in the air in traces
but in sun and stars to a maximum.
Explain.


\( \operatorname{Let} \boldsymbol{A}_{0} \boldsymbol{A}_{1} \boldsymbol{A}_{2} \boldsymbol{A}_{3} \boldsymbol{A}_{4} \boldsymbol{A}_{5} \) be a regular
hexagon inscribed in a circle of unit radius. Then the product of the length of
the line segments \( A_{0} A_{1}, A_{0} A_{2} \) and
\( \boldsymbol{A}_{0} \boldsymbol{A}_{4} \) is
A \( \cdot \frac{3}{4} \)
в. \( \frac{3}{\sqrt{3}} \)
\( c .3 \)
D. \( \frac{3 \sqrt{3}}{2} \)


Which is maximum covalent in nature?
\( \mathbf{A} \cdot B e C l_{2} \)
в. \( M g C l_{2} \)
c. \( C a C l_{2} \)
D. \( B a C l_{2} \)


If \( P=\left[\begin{array}{lll}4 & 3 & 2\end{array}\right] \) and \( Q=\left[\begin{array}{lll}-1 & 2 & 3\end{array}\right] \) then
\( P-Q= \)
\( \left.\begin{array}{lll}\text { A } \cdot[6 & -1 & -4\end{array}\right] \)
B . \( \left[\begin{array}{lll}2 & -1 & -4\end{array}\right] \)
\( \mathbf{c} \cdot\left[\begin{array}{lll}6 & 1 & 4\end{array}\right] \)
D・[-4 -1 6]


What is the basic event that takes place
during reproduction? How is it important?


Rename the following percents as decimals.
\( 62.9 \% \)
A . 6.29
B. 0.629
c. 0.0629
D. 0.00629


The process by which large molecule move out of a cell is called as
A. Plasmolysis
B. Deplasmolysis
c. Phagocytosis
D. Reverse phagocytosis


Which of the following is false?
A. Glycerol has strong hydrogen bonding
B. Alkyl halides have higher b.p. than corresponding alcohols
C. Glycol is a poisonous alcohols
D. Waxes are esters of higher alcohols with higher acids


A resistance is shown in the figure. Its
value and tolerance are given
respectively by:
\( \mathbf{A} \cdot 27 K \Omega, 20 \% \)
B \( .270 K \Omega, 5 \% \)
\( \mathbf{c} .270 K \Omega, 10 \% \)
D. \( 27 \mathrm{K} \Omega, 10 \% \)


\( H_{2} C O_{3} \) ionises as
\( \boldsymbol{H}_{2} \boldsymbol{C O}_{3} \rightleftharpoons \boldsymbol{H}^{+}+\boldsymbol{H} \boldsymbol{C O}_{3}^{-} ; \boldsymbol{K}_{1}=\mathbf{4 . 3} \times \)
\( \mathbf{1 0}^{-\mathbf{7}} \)
\( \boldsymbol{H} \boldsymbol{C O}_{3}^{-} \rightleftharpoons \boldsymbol{H}^{+}+\boldsymbol{C} \boldsymbol{O}_{3}^{2-} ; \boldsymbol{K}_{2}=\mathbf{5} . \boldsymbol{6} \times \)
\( \mathbf{1 0}^{-11} \)
Calculate the degree of hydrolysis and pH value of \( 0.12 M N a_{2} C O_{3} \) solution.


A wave of frequency \( 400 H z \) has a
velocity of \( 320 m s^{-1} . \) The distance between the particles differing in phase
by \( 90^{\circ} \) is
\( \mathbf{A} \cdot 80 \mathrm{cm} \)
B. \( 60 \mathrm{cm} \)
c. \( 40 \mathrm{cm} \)
D. \( 20 \mathrm{cm} \)


Assertion: Thin films such a soap
bubble or a thin layer of oil on water show beautiful colours when
illuminated by white light. Reason: It happens due to the interference of light reflected from the upper surface of the thin film.
A. If both assertion and reason are true but the reason is the correct explanation of assertion
B. If both assertion and reason are true but the reason is not the correct explanation ofassertion
c. If assertion is true but reason is false
D. If both the assertion and reason are false
E. If reason is true but assertion is false


A force is applied to box of mass \( 4 \mathrm{kg} \) and it changes the velocity from \( 3 \mathrm{m} / \mathrm{s} \) to \( 6 \mathrm{m} / \mathrm{s} \) in \( 8 \mathrm{s} \). Determine the work done
by force during the this process.
A . 27 J
B. 54 J
c. 72 J
D. 96 J
E. cannot be determined from the information given


The value of \( \Delta H_{O-H} \) is \( 109 k c a l m o l^{-1} \) The formation of one mole of water in
gaseous state from \( H(g) \) and \( O(g) \) is accompanied by:
A \( .218 \mathrm{kcal} \)
B . -109 kcal
c. -218 kcal
D. Unpredictable


Which part of alimentary canal receives
bile from the liver?
A. Stomach
B. Small intestine
c. Large intestine
D. Oesophagus


The smog is essentially caused by the
presence of
\( A \cdot O_{2} \) and \( O_{3} \)
B. \( O_{2} \) and \( N_{2} \)
c. \( O_{3} \) and \( N_{2} \)
D. oxides of sulphur and Nitrogen


\( \operatorname{Let} \boldsymbol{A}(\mathbf{1}, \mathbf{3}), \boldsymbol{B}(\mathbf{0}, \mathbf{0}) \) and \( \boldsymbol{C}(\boldsymbol{k}, \boldsymbol{0}) \) be
vertices of a triangle \( A B C \) such that
area of \( \triangle A B C \) is \( 3 . \) Find the value of \( k \)
\( A \cdot \pm 2 \)
B. ±3
\( c .\pm 4 \)
D. ±1


When a steady current passes through a cylindrical conductor, is there an electric
field inside the conductor?


(i) Write the two side effects of aspirin.
(ii) Explain the following term and give one example in each case.
(a) Cationic detergents
(b) Anionic detergents


Spin on magnetic moment of the
compound \( \boldsymbol{H} \boldsymbol{g}\left[\boldsymbol{C} \boldsymbol{o}(\boldsymbol{S} \boldsymbol{C} \boldsymbol{N})_{4}\right] \) is:
A \( \cdot \sqrt{3} \)
B. \( \sqrt{15} \)
c. \( \sqrt{24} \)
D. \( \sqrt{8} \)


Let \( f=50 \mathrm{Hz}, \) and \( \mathrm{C}=100 \mu \mathrm{F} \) in an \( \mathrm{AC} \)
circuit containing a capacitor only. If the peak value of the current in the circuit is \( 1.57 \mathrm{A} \) at \( \mathrm{t}=0 . \) The expression for the instantaneous voltage across the capacitor will be:
A \( . E=50 \sin (100 \pi t-\pi / 2) \)
В. \( E=100 \sin (50 \pi t) \)
c. \( E=50 \sin \pi t \)
D. \( E=50 \sin (100 \pi t+\pi / 2) \)


Four concentric spherical shell is \( A, B, C \) AND \( D \) has radius \( a, 2 a, 3 a \) and
\( 4 a \) shell \( B \) and \( D \) has charge \( +q \) and \( -q \)
The shell \( ^{\prime} C^{\prime} \) is earthed. Find \( V_{A}-V_{C} \)
A \( \cdot \frac{k q}{2 a} \)
в. \( \frac{k q}{3 a} \)
\( c \cdot \frac{k q}{4 a} \)
D. \( \frac{k q}{6 a} \)


\( \underbrace{r}_{i \atop j \atop j \atop j} \)


A transformer steps up an ac supply from 220 to 2200 V. If the secondary coi of the transformer has 2000 turns, Then
find the number of turns in its primary coil.


Express the following in the form of \( a+ \)
\( \boldsymbol{b} \boldsymbol{i} \)
(i) \( (-i)(2 i)\left(-\frac{1}{8} i\right)^{3} \)


When the electron of a hydrogen atom jumps from \( n=4 \) to \( n=1 \) state, the
number of spectral lines emitted will
be:
A . 15
B. 6
\( c .3 \)
\( D \)


A block of mass \( 2 \mathrm{kg} \) is pushed against a
rough vertical wall with a force of \( 40 N \) coefficient of static friction being 0.5
Another horizontal force of \( 15 N \), is
applied on the block in a direction parallel to the wall. Will the frictional force exerted by the wall on the block?


For \( n=3 \) energy level, the number of possible orbitals is:
A . 1
B. 3
\( c \cdot 4 \)
D.


Find the value of \( x \) in each of the
following diagrams
\( (\mathbf{i}) \)
(ii)


The reaction, \( 2 H_{2} O(l) \rightarrow 4 H^{+}(a q .)+ \)
\( O_{2}(g)+4 e^{-} \) is?
A. A oxidation reaction
B. A hydrolysis reaction
C. A solvolysis reaction
D. An oscillatory reaction
E. An acid catalyst reaction


Assertion
Al obtained only by electrolytic reduction of Alumina (pure)
Reason
Aluminium metal has a strong affinity
for oxygen and the oxide of \( \mathrm{Al} \) is \( A l_{2} O_{3} \)
which is a very stable oxide. Hence ordinary chemically reducing agents
are not sufficient to reduce \( A l_{2} O_{3} \) to \( A l \)
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


Resolve a weight of \( 10 N \) in two
directions which are parallel and
perpendicular to a slope inclined at \( 30^{\circ} \)
to the horizontal.


If soap bubbles of different radii are in
communication with each other
A. Air flows from the larger bubble into the smaller one until the two bubbles are of equal size
B. The sizes of the bubbles remain unchanged
c. Air flows from the smaller into the larger one and larger bubble grows at the expense of the smaller one
D. None of these


In a binomial distribution \( \boldsymbol{A} \boldsymbol{M}=\mathbf{3} \)
variance \( =4 . \) The statement is
A. True
B. False
c. we cannot say
D. None


Complete the following reaction:
\( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{6}+\boldsymbol{2} \boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \)


Parkinsonia and Australian Acacia are
example of
A. Phylloclade
B. Winged fruit
c. Parachute mechanism
D. Phyllode


The amplitude of the magnetic field of a harmonic electromagnetic wave in
vacuum is \( B_{0}=510 \) nT. The amplitude of
the electric field part of the wave is
\( \mathbf{A} \cdot 120 \mathrm{N} C^{-1} \)
B . \( 163 \mathrm{N} C^{-1} \)
c. \( 510 \mathrm{N} C^{-1} \)
D. 153 N \( C^{-1} \)


The solubility of all solids in water increase with increase in temperature.
A. True
B. False


Solve
\( \left|\boldsymbol{x}+\frac{1}{3}\right|>\frac{8}{3} \)


If \( \cos ^{-1} x-\cos ^{-1} \frac{y}{2}=\alpha \) where -1
\( 1 \leq x \leq 1,-2 \leq y \leq 2, x \leq \frac{y}{2} \) then for
all \( 4 x^{2}-4 x y \cos \alpha+y^{2} \) is equal to
A \( \cdot 4 \sin ^{2} \alpha-2 x^{2} y^{2} \)
B. \( 4 \cos ^{2} \alpha+2 x^{2} y^{2} \)
\( \mathbf{c} \cdot 4 \sin ^{2} \alpha \)
\( D \cdot 2 \sin ^{2} \alpha \)


What is the slope of a line whose inclination with the positive direction of
\( x \) axis is \( 120^{\circ} ? \)


Find the value of \( q \)
\( A \cdot 3 \sqrt{5} \)
B. \( 3 \sqrt{10} \)
\( c \cdot 2 \sqrt{10} \)
D. \( 8 \sqrt{10} \)


In the given circuit initially the charge
on capacitor is \( Q_{0} \) At \( t=0 \) the switch \( S \)
is closed Which of the following statement(s) is/are correct?
This question has multiple correct options
A . Maximum current through the inductor is \( \frac{Q_{0}}{\sqrt{L C}} \)
B. charge on the capacitor is zero at \( t=\frac{\pi}{2} \sqrt{L C} \)
C. Current through the inductor is maximum at \( t= \)
\( \frac{\pi}{2} \sqrt{L C} \)
D. Maximum magnetic energy can be stored in the inductor is \( \frac{Q_{0}^{2}}{2 C C} \)


The length of seconds hand of watch is
\( 1.5 \mathrm{cm} \) and its mass is \( 7 \times 10^{-3} \mathrm{g} \). Its
angular momentum is,
A \( \cdot 1.1 \times 10^{-11} \mathrm{kgm}^{2} \mathrm{s}^{-1} \)
B . \( 5.5 \times 10^{-11} \mathrm{kgm}^{2} \mathrm{s}^{-1} \)
C. \( 1.1 \times 10^{-12} \mathrm{kgm}^{2} \mathrm{s}^{-1} \)
D. \( 5.5 \times 10^{-13} k g m^{2} s^{-1} \)


The experimental value of dis found to
be smaller than the estimate obtained
using Graham's law. This is due to:
A. larger mean free path for \( x \) as compared to that of \( Y \)
B. larger mean free path for Y as compared to that of \( x \)
C. increased collision frequency of Y with the inert gas as compared to that \( X \) with the inert gas
D. increased collision frequency of \( X \) with the inert gas as compared to that of Y with inert gas


Part of a simple harmonic motion is
graphed in the figure, where \( y \) is the
displacement from the mean position. The correct equation describing this
S.H.M. is


The area of the triangle formed by \( (0,0),\left(a^{x^{2}}, 0\right),\left(0, a^{6 x}\right) \) is \( \frac{1}{2 a^{5}} s q \) unit
then \( x \) is equal to
\( \mathbf{A} \cdot 1 \) or 5
B. -1 or 5
c. 1 or -5
D. -1 or -5


The variation of lengths of two metal
rods \( A \) and \( B \) with change in
temperature are shown in figure.
The coefficients of linear expansion \( \boldsymbol{\alpha}_{\boldsymbol{A}} \)
for the metal \( A \) and the temperature \( T \)
will be :
(Given \( \left.\alpha_{B}=9 \times 10^{-6} /^{\circ} \mathrm{C}\right) \)
\( \mathbf{A} \cdot \alpha_{A}=3 \times 10^{-6} /^{\circ} \mathrm{C}, 500^{\circ} \mathrm{C} \)
B . \( \alpha_{A}=3 \times 10^{-6} /^{\circ} \mathrm{C}, 222.22^{\circ} \mathrm{C} \)
C \( \cdot \alpha_{A}=27 \times 10^{-6} /^{\circ} \mathrm{C}, 500^{\circ} \mathrm{C} \)
D. \( \alpha_{A}=27 \times 10^{-6} /^{\circ} \mathrm{C}, 222.22^{\circ} \mathrm{C} \)


The barometric pressure and height on the earth are \( 10^{5} \) Pa and \( 760 \mathrm{mm} \). If it is
taken to moon, then barometric height will be :-
A. 76 mm
B. \( 126.6 \mathrm{mm} \)
c. zero
D. 760 \( \mathrm{mm} \)


An aqueous solution of a substance molar mass 240 has osmotic pressure
\( 0.2 \mathrm{atm} \) at \( 300 \mathrm{K} \). The density of solution \( \operatorname{in} g \cdot d m^{3} \) is: \( (R= \)
\( \left.0.08 \text { litre atm } K^{-1} m o l^{-1}\right) \)


What is a catalyst? give one example.


The prefix used for denoting an order of
magnitude of \( 10^{6} \) is
A . Giga
B. Kilo
c. Mega
D. Micro


The development of a sporophyte from mass of gametophytic tissue without sexual reproduction it is
A. Parthenogenesis
B. Apogamy
c. Apospory
D. Amphimixis


The phase difference between the displacement and acceleration of particle executing S.H.M. in radian
A . \( \pi / 4 \)
В. \( \pi / 2 \)
\( c . \pi \)
D. \( 2 \pi \)


If \( \left|z_{1}\right|=\left|z_{2}\right|=\left|z_{3}\right|=\ldots \ldots . .=\left|z_{n}\right|=1 \)
then \( \left|z_{1}+z_{2}+z_{3}+\ldots \ldots .+z_{n}\right|= \)
A \( \cdot\left|\frac{1}{z_{1}}+\frac{1}{z_{2}}+\frac{1}{z_{3}}+\ldots . .+\frac{1}{z_{n}}\right| \)
в. \( \left|\frac{1}{z_{1}}-\frac{1}{z_{2}}-\frac{1}{z_{3}}-\ldots . .+\frac{1}{z_{n}}\right| \)
с \( \cdot\left|\frac{1}{z_{1}^{2}}+\frac{1}{z_{2}^{2}}+\frac{1}{z_{3}^{2}}+\ldots . .+\frac{1}{z_{n}^{2}}\right| \)
D \( \cdot\left|\frac{1}{z_{1}^{2}}-\frac{1}{z_{2}^{2}}-\frac{1}{z_{3}^{2}}-\ldots . .+\frac{1}{z_{n}^{2}}\right| \)


The resistance of \( 10 \mathrm{m} \) long
potentiometer wire is \( 20 \Omega \). It is connected in series with a 3 V battery
and \( 10 \Omega \) resistor. The potential
difference between two points
separated by distance \( 30 \mathrm{cm} \) is equal to
A . \( 0.02 \mathrm{V} \)
B. \( 0.06 \mathrm{V} \)
c. \( 0.1 \mathrm{v} \)
D. 1.2v


Factors of \( 8 x^{2}-18 x+9 \) are :
A. \( (4 x-3) \) and \( (2 x+3) \)
B. \( (8 x-1) \) and \( (x-9) \)
c. \( (8 x-3) \) and \( (x-3) \)
D. \( (2 x-3) \) and \( (4 x-3) \)


A and B play a game in which \( \mathbf{A}^{\prime} \) s chance of winning is \( \frac{1}{5} \) in a series of 6
games, the probability that A will win
all the 6 games is
\( ^{\mathrm{A}} \cdot_{\frac{6}{2} C}\left(\frac{1}{5}\right)^{6} \)
\( ^{\mathrm{B}} \cdot_{6}^{6} C\left(\frac{1}{5}\right)^{6}\left(\frac{4}{5}\right)^{0} \)
\( ^{\mathbf{C}} \cdot\left(\frac{4}{5}\right)^{6} \)
\( ^{\mathrm{D} \cdot}_{^{6}} C\left(\frac{1}{5}\right)^{5}\left(\frac{4}{5}\right) \)


The molality of \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) solution is \( \boldsymbol{9} \). The
weight of the solute in \( 1 \mathrm{kg} H_{2} S O_{4} \) solution is:
A . \( 900.0 \mathrm{g} \)
в. \( 469 \mathrm{g} \)
c. \( 882.0 \mathrm{g} \)
D. \( 9.0 \mathrm{g} \)


Complete the following reactions
(a) \( \boldsymbol{I}_{2}+\boldsymbol{I F}_{3} \longrightarrow \)
(b) \( C l_{2}+H_{2} O \longrightarrow \)
(c) \( C l_{2}+H_{2} S \longrightarrow \)
\( \mathbf{A} \ldots \underset{\rightarrow}{B I F} \)
\( \rightarrow H C l+H O C l \)
\( \rightarrow 2 H C l+S \)


A tube is attached as shown in closed
vessel containing water. The velocity of
water coming out from a small hole is
\( \mathbf{A} \cdot \sqrt{2} m / s \)
B. \( 2 m / s \)
C. Depends on pressure of air inside vessel
D. None of these


Which colour deviate minimum during the dispersion of light through a prism?


A thin circular ring of mass \( M \) and
radius \( r \) is rotating about its axis with
a constant angular velocity \( \omega . \) Two
objects, each of mass \( \boldsymbol{m}, \) are attached gently to the opposite ends of the
diameter of the ring. The wheel now rotates with an angular velocity
\( \mathbf{A} \cdot \frac{\omega M}{(M+m)} \)
B. \( \frac{\omega(M-2 m)}{(M+2 m)} \)
\( ^{\mathbf{c}} \cdot \frac{\omega M}{(M+2 m)} \)
D. \( \frac{\omega(M+2 m)}{M} \)


Number of lobes present in \( d_{z^{2}} \) orbital is
A . 10
B. 5
\( c \cdot 4 \)
D. 2


The distances covered by a particle thrown in a vertical plane, in horizontal and vertical directions at any instant of
time 't' are \( x=3 t \) and \( y=4 t-5 t^{2} \)
.The acceleration due to gravity is
A \( .8 m / s^{2} \)
B . \( 9 m / s^{2} \)
\( \mathrm{c} \cdot 10 \mathrm{m} / \mathrm{s}^{2} \)
D. \( 16 m / s^{2} \)


For \( |z-1|=1, \) find \( \tan \left[\arg \frac{((z-1)}{\left.\left.\left(2-2 \frac{i}{z}\right)\right)\right]}\right. \)
\( \mathbf{A} \cdot i \)
B.
\( c \cdot-i \)
D. -


The e/m value for cathode rays:
A. varies with the nature of the gas
B. does not vary with the nature of gas
C. was not determined by J. J. Thomson
D. both
(b) and
(c) are correct


A body at rest is falling freely under gravity. The distance travelled by the body in the first 3 s is equal to the distance traveled by the same body in the same body in the nth second. What
is the value of n?
\( A \cdot 3 \)
B. 4
\( c \cdot 5 \)
\( D \)


Which of the following is true of
ecological pyramids
A. Pyramids built upon biomass of organisms at each level eliminate size as a factor in the organisms
B. Energy gains between trophic levels occur based upon biomass conversion
C. limited number of trophic levels man ecological pyramid are due to increasing complexity and size of organisms at each greater trophic level
D. None of the above


Identify disproportionation reaction.
\( \mathbf{A} \cdot C H_{4}+2 O_{2} \rightarrow C O_{2}+2 H_{2} O \)
\( \mathbf{B} \cdot C H_{4}+4 C l_{2} \rightarrow C C l_{4}+4 H C l \)
\( \mathbf{c} \cdot 2 F_{2}+2 O H^{-} \rightarrow 2 F^{-}+O F_{2}+H_{2} O \)
D. \( 2 N O_{2}+2 O H^{-} \rightarrow N O_{2}^{-}+N O_{3}^{-}+H_{2} O \)


If the temperature of a hot body is increased by \( 50 \% \) then the increase in the quantity of emitted heat radiation will be
A. \( 125 \% \)
B . 200\%
c. 300\%
D. 400\%


Find the value of \( k \) if line PQ is parallel to line RS where \( \boldsymbol{P}(\mathbf{2}, \boldsymbol{4}), \boldsymbol{Q}(\boldsymbol{3}, \boldsymbol{6}), \boldsymbol{R}(\boldsymbol{8}, \boldsymbol{1}) \)
and \( S(10, k) \)


Two short electric dipoles are placed as
shown ( \( r \) is distance between their
centres). The energy of electric interaction between these dipoles will
be:
\( \left(C \text { is centre of dipole of moment } \boldsymbol{P}_{2}\right) \)
\( A \)
B. \( -\frac{2 k P_{1} P_{2} \cos \theta}{r^{3}} \)
c. \( \frac{-2 k P_{1} P_{2} \sin \theta}{r^{3}} \)
D.


General solution of \( \sin ^{3} x+\cos ^{3} x+ \)
\( \frac{3}{2} \sin 2 x=1 \)
A. \( x=n \pi \) when \( n \) is even integer
B. \( x=2 n \pi \) when \( n \) is odd integer
C \( \cdot x=n \pi+\frac{\pi}{2} \) when \( n \) is odd integer
D・ \( x=n \pi-\frac{\pi}{2} \)


The dimensions of Planck's constant
are
\( \mathbf{A} \cdot\left[M L^{-3} T^{-1}\right] \)
в. \( \left[M L^{-2} T^{-1}\right] \)
\( \mathbf{c} \cdot\left[M^{0} L^{-1} T^{-3}\right. \)
D・ \( \left[M L^{2} T^{-1}\right] \)


ff \( y=\left(\tan ^{-1} x\right)^{2} \) then show
\( \left(x^{2}+1\right)^{2} y_{2}+2 x\left(x^{2}+1\right) y_{1}=2 \)


Verify Rolle's theorem for \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}(\boldsymbol{x}+ \)
\( \mathbf{3}) e^{-\boldsymbol{x} / 2} \) in \( (-\mathbf{3}, \mathbf{0}) \)
A. Yes Rolle's theorem is applicable and the stationary point is \( x=-2 \)
B. Yes Rolle's theorem is applicable and the stationary point is \( x=-1 \)
C. No Rolle's theorem is not applicable in the given interval
D. Both A and B


The radius of the sun is \( 7 \times 10^{8} \mathrm{m} \) and
its mass is \( 2 \times 10^{30} k g . \) What is the
order of magnitude of density of the sun?


Factorization is the \( \ldots \). process of
multiplication.
A. equal
B. same
c. inverse
D. common


Assertion \( \operatorname{Let} \boldsymbol{A}=\left[\begin{array}{ll}\boldsymbol{a}_{11} & \boldsymbol{a}_{12} \\ \boldsymbol{a}_{21} & \boldsymbol{a}_{22}\end{array}\right], \boldsymbol{X}=\left[\begin{array}{l}\boldsymbol{x}_{1} \\ \boldsymbol{x}_{2}\end{array}\right], \boldsymbol{y}= \)
\( \left[\begin{array}{l}\boldsymbol{y}_{1} \\ \boldsymbol{y}_{2}\end{array}\right. \)
If \( A \) is symmetric, then \( X^{\prime} A Y=Y^{\prime} A X \)
for each pair of \( X \) and \( Y \)
Reason
If \( \boldsymbol{X}^{\prime} \boldsymbol{A} \boldsymbol{Y}=\boldsymbol{Y}^{\prime} \boldsymbol{A} \boldsymbol{X} \) for each pair of \( \boldsymbol{X} \)
and \( Y, \) then \( A \) is symmetric.
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


A body moving with uniform acceleration travels a distance \( s_{n}= \)
\( (0.4 n+9.8) m \) in \( n^{t h} \) second. Initial
velocity of the body is \( \left(\operatorname{in} m s^{-1}\right) \)
A. 0.4
B. 10
\( c .3 .5 \)
D. 4


If the series resistance decreases in an
unloaded zener regulator, the zener
current
A . Decreases
B. Stays the same
c. Increases
D. Equals the voltage divided by the resistance


Two cards are drawn from a single deck of 52 cards one after the other. Find the
probability of selecting a king from the first card and queen from the second card.
A \( \cdot \frac{1}{26} \)
в. \( \frac{4}{52} \)
c. \( \frac{16}{663} \)
D. \( \frac{4}{663} \)


Rohanpreet obtained 548 marks out of 800 and Rahman obtained 460 marks
out of 600 in Mathematics.Whose
performance is better?


If a cyclist takes a turn of radius \( 10 m \) going at a speed of \( 10 \mathrm{m} / \mathrm{s} \) then find the
angle through which he must bend in
order to avoid overturning. [asume \( \boldsymbol{g}= \)
\( \left.10 m / s^{2}\right] \)
A \( .90^{\circ} \)
B. \( 0^{\circ} \)
\( c \cdot 45^{\circ} \)
D. 30


Adsorption played an important role in:
A. heterogeneous catalysis
B. homogeneous catalysis
c. positive catalysis
D. negative catalysis


Vertical displacement of a plank with a body of mass \( m \) on it is varying according to law \( y=\sin \omega t+\sqrt{3} \cos \omega t \)
The minimum value of \( \omega \) for which the
mass just breaks off the plank and the moment it occurs first after \( t=0, \) are
given by
A. \( \sqrt{g / 2}, \frac{\sqrt{2}}{6} \frac{\pi}{\sqrt{g}} \)
в. \( \frac{g}{\sqrt{2}}, \frac{2}{3} \sqrt{\pi / g} \)
c. \( \sqrt{g / 2}, \frac{\pi}{3} \sqrt{2 / g} \)
D. \( \sqrt{2 g}, \sqrt{2 \pi / 3 g} \)


Check wheather the equality of the equation in maintained or not, by putting the value of the given variable written next to the equation below. \( 4 y-3=17 \) if \( y=2 \)
A. True
B. False


A disc rolling down the incline has lesser acceleration as compared to the same disc sliding down the incline
A. True
B. False


\( f^{20} P_{r}=13 \times^{20} P_{r-1}, \) then the value of
is


In which of the following, Anti Markovnikov addition of \( H B r \) is not
observed?
A. propene
B. but-1-ene
c. but-2-ene
D. pent-2-ene


Which of the following values corresponds to the value of energy required to remove the second electron
from the ground state of helium atom?
\( \mathbf{A} \cdot-27.2 e V \)
B. \( -13.6 e V \)
c. \( -6.8 e V \)
D. \( -54.4 e V \)


The mass of a wire of resistance 20 ohm
is 50 gram. The resistance of the same
wire of mass 10 gram is
A . \( 4 \Omega \)
B. 5\Omega
\( c \cdot 100 \Omega \)
D. 80\Omega


Which of the following rational number lies between \( \frac{4}{9} \) and \( \frac{4}{5} ? \)
A. -1
в. \( \frac{28}{45} \)
c. 0
\( D \)


Match ligule with one of the followings
A. Root
B . Leaf
c. stem
D. Rhizome


Obtain the formula for the capacitance
of a parallel plate capacitor.


Temperature at which liquid changes to
gaseous state
A. Freezing point
B. Boiling point
c. Neutral state
D. None


What is the current drawn from the
source in the given circuit?
\( A \cdot 2 A \)
B. 1.5
\( c \cdot 4 A \)
D. 3 A


\( \mathrm{E}^{o} \) for a cell having 2 electrons involved
in redox change is 0.2655 V. The equilibrium constant for the redox
change is \( 10^{a} \). The value of a is :


Solve: \( 2 x^{2}+3=5 \)


Find determinant \( \boldsymbol{D} \boldsymbol{c}=\left|\begin{array}{ccc}\mathbf{1} & \mathbf{1} & -\mathbf{2} \\ \mathbf{1} & -\mathbf{2} & \mathbf{3} \\ \mathbf{2} & -\mathbf{1} & -\mathbf{1}\end{array}\right| \)


Let \( \alpha \) be the distance between the lines
\( -x+y=2 \) and \( x-y=2, \) and \( \beta \) be the distance between the lines \( 4 x-3 y=5 \) and \( 6 y-8 x=1, \) then find \( \alpha \) and \( \beta \)


Why does a lump of cotton wool shrink
in water?


An ice block at \( 0^{0} C \) is dropped from
height h above the ground. What should be the value of \( h \) so that it just melts completely by the time it reaches the bottom assuming the loss of whole gravitational potential energy is used
as heat by the ice ? [Given : \( L_{f}=80 \) cal/gm]
A. 33.6 \( m \)
B. 33.6 km
\( c \cdot 8 m \)
\( D .8 \mathrm{km} \)


Which of the following physical quantity is different from others?
A. Displacement
B. Velocity
c. Force
D. Kinetic energy


The random variable takes the values \( 1,2,3, \dots \dots \dots, m . \) If \( P(X=n)=\frac{1}{m} \) to each \( n \)
then the variance of \( X \) is
A \( \cdot \frac{(m+1)(2 m+1)}{6} \)
в. \( \frac{m^{2}-1}{12} \)
c. \( \frac{m+1}{2} \)
D. \( \frac{m^{2}+1}{12} \)


Evaluate the integral \( \int_{0}^{1 / 2} \frac{x \sin ^{-1} x}{\sqrt{1-x^{2}}} d x \)


Show that the height of a closed right
circular cylinder of given volume and least surface area is equal to its
diameter.


The diagram given shows the
reproduction processes of 3 organisms \( P, Q \) and \( R . \) Which of the above shows the
process of sexual reproduction being taking place?
A. Only P
B. Only P and Q
c. Only
D. Only P and


Add the followign:
\( 13 x^{2},-31 x^{2}, 25 x^{2} \)


Using elementary transformation, find the inverse of the matrix \( \left[\begin{array}{ccc}2 & -3 & 3 \\ 2 & 2 & 3 \\ 3 & -2 & 2\end{array}\right] \)


General electronic configuration of
inner transition element is


According to international convention of colour coding in a wire
A. Live is red, neutral is yellow and earth is green
B. Live is red, neutral is green and earth is black
c. Live is brown, neutral is blue and earth is black
D. Live is red, neutral is black and earth is green


Doubly ionised Helium atoms and
Hydrogen ions are accelerated from rest through the same potential drop. The ratio of the final velocities of the Helium
and the Hydrogen ions is
\( A \cdot 2 \)
B. \( \sqrt{2} \)
\( c \cdot 1 / 2 \)
D. \( 1 / \sqrt{2} \)


The correct order of basic strength of
the compounds?
\( \mathbf{A} \cdot I>I I>I I I \)
В . \( I I>I>I I I \)
c. \( I I I>I I>I \)
D. \( I I>I I I>I \)


What is the \( p H \) of \( 0.001 \mathrm{M} \) aniline
solution ? The ionization constant of
aniline can be taken from Table 7.7
Calculate the degree of ionization of
aniline in the solution. Also calculate
the ionization constant of the conjugate acid of aniline.


Which of the following is commonly present in fresh water?
(A)- Ulothrix
(B)- Spirogyra
(C)- Ectocarpus
(D)- Batrachospermum
A. A and B
B. A,B and D
c. \( A, B, C \) and \( D \)
D. A,B and C


Why does the dental system in animals has different types of teeth?


Coefficient of \( x^{5} \) in \( \left(1+x^{2}\right)^{5}(1+x)^{4} \) is
A . 60
B. 80
\( c \cdot 90 \)
D. 100


A helicopter rises vertically with a speed of \( 100 \mathrm{m} / \mathrm{s} \). If helicopter has length \( 10 \mathrm{m} \) and horizontal component
of earth's magnetic field is \( 5 \times \)
\( 10^{-3} W b / m^{2}, \) then the induced emf
between the tip of nose and tail of helicopter is:
A. \( 50 v \)
B. 0.5 \( v \)
\( c \cdot 5 v \)
D. 25 V


Which configuration has no stereogenic
center?
4
3
\( c \)
\( D \)


Observe the given figure and identify
the correct statements.
(i) Poles 1,3 and 5 are unlike poles
(ii) Poles 2,4 and 6 are like poles
(iii) Pole 1 will attract pole 3 and 5
(iv) Pole 4 will be attracted by pole 1
\begin{tabular}{|l|l|l|}
\hline 1 & 2 & 3 & 4 & 5 \\
\hline Magnet & Magnet & Magnet
\end{tabular}
A. Only (i) and (iii)
B. Only (ii) and (iv)
c. Only (i) and (ii)
D. Only (iii) and (iv)


Which polymer is used in controlled drugs capsules?
\( \mathbf{A} \cdot S B R \)
в. \( P T F E \)
с. \( P H B V \)
D. \( P A N \)


In the magnet and coil experiment, the magnet and the coil are moved in the same direction with same speed, the
emf induced in the coil is
A. Maximum
B. Minimum
c. Either (1) or (2)
D. zero


In an inelastic collision,
This question has multiple correct options
A. the velocity of both the particles may be the same after the collision
B. the kinetic energy is not conserved
C. the linear momentum of the system is conserved
D. the velocity of separation will be less than velocity of approach


Differentiate the given function w.r.t. \( x \) \( \boldsymbol{y}=\sqrt{e^{\sqrt{x}}}, \boldsymbol{x}>0 \)


For the reaction, \( A \rightleftharpoons n B \) the
concentration of A decreases from 0.06
to 0.03 mol \( L^{-1} \) and that of \( \mathrm{B} \) rises from
0 to 0.06 mol \( L^{-1} \) at equilibrium. The
values of \( n \) and the equilibrium constant for the reaction, respectively,
are:
\( A \cdot 2 \) and 0.12
B. 2 and 1.2
c. 3 and 0.12
D. 3 and 1.2


n figure the sides \( A B \) and \( A C \) of \( \Delta A B C \)
are produced to point \( \mathrm{E} \) and \( \mathrm{D} \) repectively. If bisector BO and CO of
\( \angle C B E \) and \( \angle B C D \) respectively meet a point \( 0, \) then \( \angle B O C=90^{\circ}-\frac{1}{2} \angle B A C \)


Most favourite and ideal material for
researches in genetics is
A. Housefly
B. Mosquito
c. Frog
D. Fruitfly


Which of the statements is incorrect
about the simple microscope?
A. Biology students use to see the slides
B. It is not used for magnification of an object at far away from the observer
C. Magnification of microscope is inversely proportional to the least distance of distinct vision
D. A convex lens of microscope with shorter focal length yields higher magnification


The two components of an ecosystem
are
A. Organism and plants
B. Weeds an trees
c. Frog and man
D. Biotic and abiotic


De-Broglie wavelength of electron in \( n \) th orbit of \( \boldsymbol{H}- \) atom is \( (\mathbf{3 . 1 8} \boldsymbol{\pi}) \boldsymbol{A} . \) The value
of \( n \) is:
\( A \cdot 1 \)
B . 2
\( c \cdot 3 \)
D. 4


Assertion: Radio waves can'be
polarised.

Reason: Sound waves in air are
longitudinal in nature.
A. If both assertion and reason are true but the reason is the correct explanation of assertion
B. If both assertion and reason are true but the reason is not the correct explanation of assertion
c. If assertion is true but reason is false
D. If both the assertion and reason are false
E. If reason is true but assertion is false


A root swollen in the form of closely arranged rings is called
A. Annulated
B. Moniliform
c. Fasciculated
D. Beaded


Silicon is an important constituent of:
A. chlorophyll
B. haemoglobin
c. rocks
D. amalgams


Which of the following expressions is
correct?
\( \boldsymbol{A} \cdot \ldots_{p}=K_{c}\left(\frac{R T}{\sum n}\right)^{\Delta n} \)
\( \mathrm{B} \cdot \quad K_{p}=K_{x}\left(\frac{P}{\sum n}\right)^{\Delta n} \)
\( \mathrm{C} \cdot_{p}=K_{n}\left(\frac{P}{\sum n}\right)^{\Delta n-1} \)
\( \mathrm{D} \cdot_{p}=K_{c}\left(\frac{P}{\sum n}\right)^{-\Delta n+1} \)


Five years later, the father's age will be
three times the age of his son. Five years ago, father was seven times as old
as his son. Find their present ages.


From the given \( v-t \) graph, it can be
inferred that the object is:
This question has multiple correct options
A. in uniform motion
B. at rest
c. in non - uniform motion
D. moving with uniform acceleration


The mass in grams of a single chlorine
atom and of a single molecule of \( \boldsymbol{O}_{2} \) is :
A \( \cdot 5.89 \times 10^{-23} g / \) atom \( , 5.31 \times 10^{-23} g / \) molecule
в. \( 8.81 \times 10^{-23} g / \) atom \( , 4.31 \times 10^{-23} g / \) molecule
C. \( 5.81 \times 10^{-25} g / \) atom, \( 5.31 \times 10^{-25} g / \) molecule
D. None of the above


A small piece of wire bent into an \( \boldsymbol{L} \)
shape, with upright and horizontal portions of equal lengths, is placed with the horizontal portion along the axis of
the concave mirror whose radius of
curvature is \( 10 \mathrm{cm} \). If the bend is \( 20 \mathrm{cm} \)
from the pole of the mirror,then the ratio
of the lengths of the images of the upright and horizontal portions of the wire is
A. 1: 2
B. 3: 1
c. 1: 3
D. 2: 1


What are carbohydrates? Write the reaction for the preparation of Nylon- 6


Convert the given mixed fractions into improper \( 6 \frac{1}{10} \)


Bernoulli's principle is based on the law of conservation of
A. Angular momentum
B. Linear momentum
c. Mass
D. Energy


An antiforest measure is
A. Afforestation
B. Selective grazing
c. Clearing forest
D. Selective felling


If \( \frac{\boldsymbol{I}_{1}}{\boldsymbol{I}_{2}}=\frac{\boldsymbol{9}}{\mathbf{1}} \) then \( \frac{\boldsymbol{I}_{\boldsymbol{m a x}}}{\boldsymbol{I}_{\boldsymbol{m i n}}}=? \)
A. 100: 64
в. 64: 100
c. 4: 1
D. 1: 4


Find \( x: \)
\( 12 \frac{1}{2} \% \) of \( x \) is 64
\( 150 \% \) of 50 is \( x \)
\( 1 \% \) of \( x \) is 8


In the elastic collision of heavy vehicle
moving with a velocity \( 10 \mathrm{ms}^{-1} \) and a small stone at rest, the stone will fly away with a velocity equal to:
A. \( 40 \mathrm{ms}^{-1} \)
B. 20 \( \mathrm{ms}^{-1} \)
\( c \cdot 10 \mathrm{ms}^{-1} \)
\( D \cdot 5 \mathrm{ms}^{-1} \)


On treatment of \( 100 \mathrm{mL} \) of \( 0.1 \mathrm{M} \) solution
of \( C o C l_{3} .6 H_{2} O \) with excess
\( A g N O_{3}, 1.2 \times 10^{22} \) ions are
precipitated. The complex is :
A \( \cdot\left[C o\left(H_{2} O\right)_{4} C l_{2}\right] C l .2 H_{2} O \)
в. \( \left[C o\left(H_{2} O\right)_{3} C l_{3}\right] .3 H_{2} O \)
\( \mathbf{c} \cdot\left[\operatorname{Co}\left(H_{2} O\right)_{6}\right] C l_{3} \)
D. \( \left[\operatorname{Co}\left(H_{2} O\right)_{5} C l\right] C l_{2} . H_{2} O \)


Assertion
The fraction of molecules having speed
in the range \( u \) and \( (u+d u) \) of a gas of
molar mass \( M \) at temperature \( T \) is the
same as that of gas of molar mass of
\( 2 M \) and temperature \( 2 T \)
Reason
The fraction of molecules having their speed within the range \( u \) to \( (u+d u) \propto \)
\( \frac{M}{T} \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


According to Maxwell's hypothesis,
changing of electric filed give rise to
A. magnetic field
B. pressure gradient
c. charge
D. voltage


\( A \) borrowed Rs. 2,500 from \( B \) at \( 12 \% \)
per annum compound interest. After 2 years, \( A \) gave Rs. 2,936 and a watch to
\( B \) to clear the account. Find the cost of
the watch.


Give IUPAC name of the following compounds:
(a) \( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{O H} \)
(b) \( \boldsymbol{H} \boldsymbol{C O O H} \)
(c) \( \boldsymbol{C H}_{3}-\boldsymbol{C H}=\boldsymbol{C H}-\boldsymbol{C H}_{3} \)


What is the chemical composition of
Nicol prism?
A. \( A l_{2} O_{3} \)
в. \( \mathrm{CaSO}_{4} \)
\( \mathrm{c} \cdot \mathrm{CaCO}_{3} \)
D. \( N a_{3} A l F_{6} \)


25 \( \$ \$ \mathrm{cm}^{\wedge 3} \$ \$ \) of oxalic acid completely neutralise 0.064 g of sodium hydroxide. Molarity of the oxalic acid solution is
A . 0.032
B. 0.064
\( c \cdot 0.0004 \)
\( D \cdot+4 \)


64 spherical rain drops of equal size are falling vertically through air with a terminal velocity \( 1.5 m s^{-1} . \) If these
drops coalesce to form a big spherical drop, then terminal velocity of big drop is:
\( \mathbf{A} \cdot 8 m s^{-1} \)
В. \( 16 \mathrm{ms}^{-1} \)
c. \( 24 m s^{-1} \)
D. \( 32 \mathrm{ms}^{-1} \)


For given G.P. \( 1, \frac{1}{10}, \frac{1}{100}, \frac{1}{1000}, \frac{1}{10000}, . . \) find the
common ratio.
A \( \cdot \frac{1}{10} \)
B. \( \frac{1}{100} \)
c. \( \frac{1}{50} \)
D. \( \frac{3}{10} \)


\( \int \frac{x^{2}+x-6}{(x-2)(x-1)} d x= \)


If \( f(x) \) and \( g(x) \) are differentiable
functions for \( 0 \leq x \leq 1 \) such that
\( \boldsymbol{f}(\mathbf{0})=\mathbf{2}, \boldsymbol{g}(\mathbf{0})=\mathbf{0}, \boldsymbol{f}(\mathbf{1})=\mathbf{6}, \boldsymbol{g}(\mathbf{1})=\mathbf{2} \)
then in the interval \( (\mathbf{0}, \mathbf{1}) \)
\( \mathbf{A} \cdot f^{\prime}(x)=0 \) for all \( x \)
B . \( f^{\prime}(x)=2 g^{\prime}(x) \) for at least one \( x \)
C \( \cdot f^{\prime}(x)=2 g^{\prime}(x) \) for most one \( x \)
D. None of these


Let \( L \) denote the set of all straight lines
in a plane, Let a relation \( R \) be defined by
\( l R m, \) iff \( l \) is perpendicular to \( m \) for all
\( l \in L . \) Then, \( R \) is
A . reflexive
B. symmetric
c. transitive
D. none of these


consists of a large number of
gases.
A. Hydrosphere
B. Lithosphere
c. Atmosphere
D. Biosphere


When \( C a(O H)_{2} \) attains solubility equilibrium, the:
A. solution is saturated
B. \( p H \) will be less than 7
C . trial \( K_{s p} \) is less than the \( K_{s p} \)
D. concentrations of the ions are equal


Which of the following can form a super oxide very easily?
A. Sodium
B. Potassium
c. caesium
D. Lithium


List five rational numbers between:
¡) -1 and 0
ii) -2 and -1


A charge particle having mass \( \mathrm{m} \) and charge \( +\boldsymbol{q}, \) given a velocity \( \overrightarrow{\boldsymbol{V}}_{0}=\mathbf{2} \overline{\boldsymbol{i}}+ \)
\( 4 j m / s \) in a region where electric field
and magnetic field exists. Magnetic field in the region is \( \vec{B}=6 \bar{i}-8 \bar{j} \) (Tesla). It is observed of charged particle remains constant. Electric field in the region is:
A. \( 50 N / C \)
в. \( 40 N / C \)
c. \( 30 N / C \)
D. \( 60 N / C \)


Which of the following belongs to the actinoids series of elements?
A. \( Y \)
в. \( T a \)
\( c \cdot U \)
D. \( P \)


The amplitude of oscillation of a particle is 0.05 m.lf its period is 1.57 s. Then the velocity at the mean position
is
\( A \cdot 0.1 \mathrm{m} / \mathrm{s} \)
B. \( 0.2 \mathrm{m} / \mathrm{s} \)
\( c \cdot 0.3 \mathrm{m} / \mathrm{s} \)
D. \( 0.5 \mathrm{m} / \mathrm{s} \)


The principal value of \( \sin ^{-1}\left\{\cos \left(\sin ^{-1} \frac{\sqrt{3}}{2}\right)\right\} \)
A. \( \frac{\pi}{6} \)
в. \( \frac{\pi}{3} \)
\( c \cdot-\frac{\pi}{3} \)
D. none of these


The two observations \( A \& B \) are given
by \( 100,101, \ldots \ldots .149 \) and
\( 200,201, \ldots \ldots, 249 \) with \( V_{A} \) and \( V_{B} \) are
variances of \( A \) and \( B \) than \( V_{A} \) is equal
to:
A. \( V_{B} \)
в. \( 100 V_{B} \)
\( \mathbf{c} \cdot 50 V_{B} \)
D. \( 200 V_{B} \)


Identify the disadvantages of RNA over DNA as a genetic material and explain ¡t.


Ventilators are provided at the top of a
room:
A. To bring oxygen for breathing.
B. So that sunlight may enter the room.
C. To maintain convectional currents to keep the air fresh in the room.
D. To provide an outlet for carbon dioxide.


Under the effect of mutual internal
attractions-
A. The linear momentum of a system increases
B. The linear momentum of a system decreases
c. The linear momentum of a system is conserved
D. The angular momentum increases


Suppose once again that the minute hand of a clock is a vector of magnitude 4 and the hour hand is a vector
of magnitude \( 2 . \) If, at 5 o'clock, one were
to take the cross product of the minute
hand the hour hand, what would the
magnitude of resultant vector be?


Area of the quadrilateral formed by the
ends of major axis and minor axis of an ellipse is \( 8 \sqrt{3} \). The distance between the foci is \( 4 \sqrt{2}, \) then the eccentricity of the ellipse is:
A \( \cdot \frac{1}{\sqrt{3}} \)
B. \( \frac{1}{3} \)
c. \( \sqrt{\frac{2}{3}} \)
D. 4


If \( z=\frac{\sqrt{3}+i}{\sqrt{3}-i} \) then the fundamental
amplitude of z is
A. \( -\frac{\pi}{3} \)
в. \( \frac{\pi}{3} \)
c. \( \frac{\pi}{6} \)
D. None of these


A square of side \( 4 \mathrm{cm} \) and uniform
thickness is divided into four squares.
The square portion \( \boldsymbol{A}^{\prime} \boldsymbol{A} \boldsymbol{B}^{\prime} \boldsymbol{D} \) is removed
and the removed portion is placed over
the square \( \boldsymbol{B}^{\prime} \boldsymbol{B C}^{\prime} \) D. The new position
of centre of mass is
\( A \cdot(2 \mathrm{cm}, 2 \mathrm{cm} \)
B. \( (2 \mathrm{cm}, 3 \mathrm{cm}) \)
c. \( (2 \mathrm{cm}, 2.5 \mathrm{cm}) \)
\( \mathrm{D} \cdot(3 \mathrm{cm}, 3 \mathrm{cm}) \)


For the reaction \( N_{2} O_{4}(g) \rightleftharpoons 2 N O_{2}(g) \)
if percentage dissociation of \( N_{2} O_{4} \) and
\( 20 \%, 45 \%, 65 \% \) and \( 80 \% \) then the
sequence of observed vapour densities
will be:
A \( \cdot d_{20}>d_{45}>d_{65}>d_{80} \)
В. \( d_{80}>d_{65}>d_{45}>d_{20} \)
C \( . d_{20}=d_{45}=d_{65}=d_{80} \)
D \( \cdot\left(d_{20}=d_{45}\right)>\left(d_{65}=d_{80}\right) \)


Distinguish between Vital capacity and Total Iung capacity.


Parathormone causes
A. Increased level of serum calcium
B. Increased level of blood sugar
C. Decreased level of serum calcium
D. Decreased level of blood sugar


Find that points at which continuity and differentiability should be checked.
A. 1 and 2
B. 0,1,2 and 3
c. 1,2 and 3
D. 0,1 and 2


A small cube of mass 'm' slides down a
circular path of radius 'R' formed from a arge block of mass 'M' as shown in
figure 'M' rests on a table and both blocks move without friction. The blocks
are initially at rest and 'm' starts from
the top of the path. Find the velocity 'v' of the cube as it leaves the block. Initially
the line joining \( \mathrm{m} \) and the centre is horizontal.


Assertion (A): Nitrogen cannot form pentahalides. Reason (R): Nitrogen cannot expand its octet configuration
A. Both (A) and (R) are true and (R) is the correct explanation of (A)
B. Both (A) and (R) are true and (R) is not the correct explanation of (A)
c. (A) is true and (R) is false
D. (A) is false but (R) is true


Which of the following does not define
solubility?
A. The concentration of solute in a saturated solution
B. The moles of solute dissolved in a given volume of solution
C. The maximum mass of solute that can dissolve in a given volume of solution
D. The minimum moles of solute needed to produce one litre of a saturated solution


The given reaction is called:
\[
\mathbf{R}-\mathbf{C}^{-} \mathbf{R} \frac{\mathbf{N}_{3} \mathbf{H}}{\mathbf{U}}-\mathbf{R} \mathbf{C O N H R}+\mathbf{N}_{\mathbf{2} \mathbf{S O}_{\mathbf{4}}}^{\mathbf{J}}
\]
A. Claisen-Schmidt reaction
B. Kolbe-Schmidt reaction
C. Schmidt reaction
D. Kolbe's reaction


Which element has the symbol \( S b ? \)
A. Arsenic
B. Antimony
c. Lead
D. Seaborgium
E. Silver


The triplet UUU codes for
A. Leucine
B. Methionine
C. Phenyl alanine
D. Glycine


If the vectors \( a \) and \( b \) are linearly independent satisfying \( (\sqrt{3} \tan \theta+ \)
1) \( \vec{a}+(\sqrt{3} \sec \theta-2) \vec{b}=0, \) then the
most general values of \( \theta \) are
A \( \cdot n \pi-\frac{\pi}{6}, n \in Z \)
B. \( 2 n \pi \pm \frac{11 \pi}{6}, n \in Z \)
c. \( n \pi \pm \frac{\pi}{6}, n \in Z \)
D. \( 2 n \pi+\frac{11 \pi}{6}, n \in Z \)


Which one is correct about a
hypothetical electrochemical cell shown
below?
\( \underset{A}{\Theta}\left|\boldsymbol{A}^{+}(\boldsymbol{X} \boldsymbol{M}) \| \boldsymbol{B}^{+}(\boldsymbol{Y} \boldsymbol{M})\right| \underset{\boldsymbol{B}}{\oplus} \boldsymbol{E}_{c e l l}= \)
\( +0.20 V \)
A. The cell reaction cannot be predicted
B . \( A+B^{+} \rightarrow A^{+}+B \)
\( \mathbf{c} \cdot A^{+}+B \rightarrow A+B^{+} \)
D. \( A^{+}+e \rightarrow A ; B^{+}+e \rightarrow B \)


Match the following:
Name of the sugar Hydrolysis
products
A) Sucrose
i) Glucose + Fructose Galactose
B) Lactose
ii) Glucose + Fructose
c) Maltose
iii) Glucose + Galactose
D) Raffinose
iv) Glucose + Glucose
A. A-iii, B- ii, C-i, D-iv.
B. A-ii, B- iii, C-i, D-iv
c. A- ii, B- iii, C- iv, D-i
D. A- ii, B- iv, C- iii, D-i


State the laws of reflection. Draw a
diagram to show incident and reflected
rays.


Assertion (A): Fragments produced in
the fission of \( U^{235} \) are radioactive
Reason (R) : The fragments have abnormally high proton to neutron ratio
A. Both A and R are true and R is correct explanation of A
B. Both A and R are true and R is not correct explanation of
c. \( A \) is true but \( R \) is false
D. A is false but R is true


Define the term metallurgy


\( P C l_{5} \) is formed but \( N C l_{5} \) is not.
A . True
B. False


Isotopes of same element exists in
nature.How they differ from each other
\( ? \)
A. They will have different locations on the periodic table
B. They will have different numbers of electrons
c. They will have undergo different chemical reactions.
D. They have different numbers of protons
E. They have different numbers of neutrons


A charged particle moving in a magnetic field experiences a resultant force ?
A. In the direction opposite to the field
B. In the direction of field
c. In the direction perpendicular to both the field and its velocity
D. None of the above


A high jumper can jump \( 2.0 \mathrm{m} \) on earth,
With the same effort how high will he be
able to jump on a planet whose density is one-third and radius one-fourth those
of the earth?
\( A \cdot 4 m \)
B. 8 m
\( c \cdot 18 m \)
D. 24 m


The mean of the numbers \( a, b, 8,5,10 \) is
6 and the variance is \( 6.80, \) then which of
the following gives possible values of \( a \) and \( b \)
A \( . a=0, b=7 \)
В. \( a=5, b=2 \)
c. \( a=1, b=6 \)
D. \( a=3, b=4 \)


The equation of circle with its centre at
the origin is \( \boldsymbol{x}^{2}+\boldsymbol{y}^{2}=\boldsymbol{r}^{2} \)
A. True
B. False
c. Neither
D. Either


Write the name of radioactive halogen?


Find \( a_{1}+a_{6}+a_{11}+a_{16} \) if it is known
that \( a_{1}, a_{2} \dots \) is an A.P. and \( a_{1}+a_{4}+ \)
\( \boldsymbol{a}_{\boldsymbol{7}}+\ldots+\boldsymbol{a}_{\mathbf{1 6}}=\mathbf{1 4 7} \)


If
\( \left(\begin{array}{cc}1 & -\tan \theta \\ \tan \theta & 1\end{array}\right)\left(\begin{array}{cc}1 & \tan \theta \\ -\tan \theta & 1\end{array}\right)^{-1}= \)
\( \left[\begin{array}{cc}\boldsymbol{a} & -\boldsymbol{b} \\ \boldsymbol{b} & \boldsymbol{a}\end{array}\right], \) then
This question has multiple correct options
\( \mathbf{A} \cdot a=\cos 2 \theta \)
В . \( a=1 \)
c. \( b=\sin 2 \theta \)
D. \( b=-1 \)


Amphoteric behaviour is shown by the
oxides of :
\( \mathbf{A} \cdot A l \) and \( C a \)
B. \( P b \) and \( B a \)
c. \( C r \) and \( M g \)
D. \( S n \) and \( Z n \)


\( \lim _{n \rightarrow \infty} \frac{\left(1^{2}+2^{2}+3^{2}+\ldots+n^{2}\right)\left(1^{3}+2^{3}+\right.}{\left(1^{6}+2^{6}+3^{6}+\ldots+n^{6}\right)} \)
\( ? \)
A \( \cdot \frac{1}{6} \)
B. \( \frac{1}{12} \)
c. \( \frac{7}{12} \)
D. \( \frac{1}{7} \)


Sulphur colloid prepared by:
A. mechanical dispersion
B. oxidation
c. electrical dispersion
D. reduction


Which device uses slip rings?
A. A d.c electric motor
B. A relay
C. A transformer
D. An a.c. generator


The angle between reflected ray and the
is called angle of reflection
A. normal
B. incident ray
c. reflecting surface
D. none of the above


The element whose II (I.P.) is less than
its \( |(\mid . P .) \)
A. \( L \)
B. Be
c. не
D. None


Calculate the work done (in Joules)
when 0.2 mole of an ideal gas at 300 K expands isothermally and reversibly
from an initial volume of 2.5 liters to the
final volume of 25 liters.
A .996
B. -1148
c. 11.48
D. 897


Evaluate \( \int_{0}^{\pi / 2} \frac{\cos ^{2} x}{1+3 \sin ^{2} x} d x \)
\( A \cdot \frac{\pi}{4} \)
в.
c.
D.


State Raoult's Law. Calculate the mole
fraction of \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) in a solution
containing \( 98 \% \) of \( H_{2} S O_{4} \) by mass.


If \( x=\frac{1}{5-x} \) and \( x \neq 5, \) find the value of \( x^{3}+\frac{1}{x^{3}} \)
A . 80
в. 240
c. 110
D. 530


Image of point \( \mathrm{P}(1,2,3) \) with respect to plane \( \boldsymbol{x}+\boldsymbol{y}+\boldsymbol{z}=\mathbf{1 2}, \) is
A. (5,4,3)
)
B. (9,6,3)
c. (5,6,7)
D. (3,4,5)


A car A moving at \( 10 m s^{-1} \) on a straight
road, is ahead of car B moving in the
same direction at \( 6 m s^{-1} . \) Find the
velocity of A relative to B and vice versa.


Draw \( \overline{P Q}, \) where \( P Q=10 c m . \) Draw
\( \operatorname{circle} \odot(P, 4) \) and \( \odot(Q, 3) . \) Draw
tangents to each circle from the centre
of the other circle. Write points of construction.


The current passing through a choke coil of \( 5 H \) is decreasing at the rate of \( 2 A / s . \) The e.m.f. developed across the coil is
A . \( 10 V \)
в. \( -10 V \)
\( \mathrm{c} .2 .5 \mathrm{V} \)
D. \( -2.5 V \)


Cell growth occurs dining
A. Interphase
B. Mitotic phase
c. Postmitotic phase
D. Interphase and postmitotic phase


Let
\( [x] \) denotes the greatest integer less than or equal to \( x \). Then, the value of \( \alpha \)
for which the function \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{ll}\frac{\sin \left[-\boldsymbol{x}^{2}\right]}{\left[-\boldsymbol{x}^{2}\right]} & \boldsymbol{x} \neq \mathbf{0} \\ \boldsymbol{\alpha} & \boldsymbol{x}=\mathbf{0}\end{array} \) is continuous at \right.
\( \boldsymbol{x}=\mathbf{0}, \) is
\( \mathbf{A} \cdot \alpha=0 \)
B. \( \alpha=\sin (-1) \)
c. \( \alpha=\sin (1) \)
\( \mathbf{D} \cdot \alpha=1 \)


The value of \( m \) for which one of the roots
of \( x^{2}-3 x+2 m=0 \) is double of one of
the roots of \( x^{2}-x+m=0 \) is
A . -2
B.
\( c \cdot 2 \)
D. None of the above


What is breathing?


Find domain of the function \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \frac{1}{\log _{10}(1-x)}+\sqrt{x+2} \)


The value of a for which the function \( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{cc}\tan ^{-1} \boldsymbol{a}-\mathbf{3} \boldsymbol{x}^{2}, & \boldsymbol{0}<\boldsymbol{x}<\mathbf{1} \\ -\boldsymbol{6} \boldsymbol{x}, & \boldsymbol{x} \geq \mathbf{1}\end{array}\right. \)
has a maximum at \( \boldsymbol{x}=\mathbf{1} \), is?
\( A \cdot 0 \)
B.
\( c \cdot 2 \)
D. None of these


Enter 1 if true else 0 \( \frac{1}{\sqrt{3}}(\hat{i}+\hat{j}+\hat{k}) \) is the unit vector in the
direction of vector \( \overrightarrow{P Q} \)
where \( P \) and \( Q \) are the point (1,2,3)
and (4,5,6)


A box contains \( L, C \) and \( R \). When \( 250 V \) dc
is applied to the terminals of the box, a
current of \( 1.0 A \) flows in the circuit.
When ac source of \( 250 \mathrm{V} \) rms at
\( 2250 r a d / s \) connected, a current of
\( 1.25 A \mathrm{rms} \) flows. It is observed that the
current rises with frequency and becomes maximum at 4500 rad/s. Find
the values of \( L, C \) and \( R . \) Draw the circuit
diagram.


A chemical reaction \( A+2 B \rightarrow A B_{2} \)
follows in two steps:
\( A+B \rightarrow A B(\text { slow }) \)
\( A B+B \rightarrow A B_{2}(\text { fast }) \)
Then the order of the reaction is:
\( A \cdot 3 \)
B. 2
\( c \cdot 1 \)
D.


The value of
\( \cos \left[\frac{1}{2} \cos ^{-1}\left[\cos \left[-\frac{14 \pi}{5}\right]\right]\right] \) is/are -
This question has multiple correct options
\( ^{A} \cdot \cos \left[-\frac{7 \pi}{5}\right] \)
B. \( \sin \left[\frac{\pi}{10}\right. \)
\( ^{\mathbf{c}} \cdot \cos \left[\frac{2 \pi}{5}\right] \)
D. \( -\cos \left[\frac{3 \pi}{5}\right] \)


Which of the above is reactive non
metal?
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot 3 \)
\( D \)


Assertion
Oxidation number of chromium in
\( \boldsymbol{C r} \boldsymbol{O}_{5} \) is \( +\boldsymbol{6} \)
Reason
Oxidation number of each oxygen atom
in \( C r O_{5} \) is -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 freshwater stored in the ground is
much more than that present in the rivers and lakes of the world.
A. True
B. False


A solenoid of 10 henry inductance and 2 ohm resistance, is connected to a 10
volt battery. In how much the magnetic
energy will be increases to \( 1 / 4 \) th of the maximum value?
A \( .3 .5 \mathrm{sec} \)
B. 2.5 sec
\( c .5 .5 \mathrm{sec} \)
D. 7.5 sec


A motorcycle travelling on the highway at a speed of \( 120 k m / h \) passes a car travelling at a speed of \( 90 \mathrm{km} / \mathrm{h} \). From the point of view of a passenger on the car, what is the velocity of the motorcycle?
A. \( 43 k m / h \)
в. \( 23 k m / h \)
c. \( 30 k m / h \)
D. \( 29 k m / h \)


Which of the following is most soluble in water?
A. \( C_{2} H_{5} O C_{2} H_{5} \)
в. \( C_{2} H_{5} O H \)
c. \( C_{2} H_{5} C O O C_{2} H_{5} \)
D. \( C_{6} H_{6} \)


Two particles \( A \) and \( B \) are moving as shown in the figure. Their total angular
momentum about the point 0 is.
A. \( 9.8 k g m^{2} / s \)
B. Zero
c. \( 52.7 k g m^{2} / s \)
D. \( 37.9 k g m^{2} / s \)


An object shaped as 'L' is placed between two parallel plane mirrors as
shown. In the first seven closest images, how many laterally inverted images are formed?
\( A \)
B. 2
\( c \cdot 3 \)
\( D \)


The gravitational force is a
A. contact force
B. action at a distance force
C. non contact force
D. both (B) and (C)


A particle starts with velocity \( u \) and moves with constant acceleration \( a \)
What is the nature of graph between the displacement \( (x) \) vs. time \( (t) ? \)
A. Straight line
B. Part of an ellipse
c. Parabola
D. Rectangular hyperbola


\( \frac{\sin (B-C)}{\cos B \cos C}+\frac{\sin (C-A)}{\cos C \cos A}+ \)
\( \frac{\sin (A-B)}{\cos A \cos B}= \)


In the following figure; \( A B \) is the largest
side and \( B C \) is the smallest side of
triangle \( A B C . \) Write the angles \( x^{0}, y^{0} \)
and \( z^{0} \) in ascending order of their
values.
A \( \cdot y^{0}<z^{0}<x^{0} \)
В . \( z^{0}<y^{0}<x^{0} \)
c. \( z^{0}>y^{0}>x^{0} \)
D. \( z^{0}>x^{0}>y^{0} \)


Three forces of magnitudes 30,60 and
\( P \) Newton acting at a point are in
equilibrium. If the angle between the
first two is \( 60^{\circ} \), the value of \( P \) is:
A \( \cdot 25 \sqrt{2} \)
в. \( 30 \sqrt{3} \)
c. \( 30 \sqrt{6} \)
D. \( 30 \sqrt{7} \)


Two identical rods of a mental are
welded in series then 20 cal of heat
flows through them in 4 minute. If the rods are welded in parallel then same amount of heat will flow in
A. 1 minute
B. 2 minute
c. 4 minute
D. 15 minute


Answer the following as true or false.
(i) \( \vec{a} \) and \( -\vec{a} \) are collinear
(ii) Two collinear vectors are always equal in magnitude.
(iii) Two vectors having same magnitude are collinear
(iv) Two collinear vectors having the
same magnitude are equal.


\( f \sin \theta=0.0958, \) find the angle \( \theta \)


According to Bohr's theory of hydrogen atom, the product of the binding energy of the electron in \( n^{t h} \) orbit and the
radius of the \( n^{t h} \) orbit :
A . is proportional to \( n^{2} \)
B . is inversely proportional to \( n^{3} \)
c. has a constant value of \( 10.2 e V A^{0} \)
D. has a constant value of \( 7.2 e V A^{0} \)


\( \boldsymbol{A u}(s) \rightleftharpoons \boldsymbol{A} \boldsymbol{u}(l) \)
Above equilibrium is favoured at
A. High pressure low temperature
B. High pressure high temperature
c. Low pressure, high temperature
D. Low pressure, low temperature


Will a parachute work in vacuum?
A. Yes
B. No
c. Sometimes
D. Yes, if made with a lighter cloth


The ion \( A^{n+} \) is oxidised to \( A O_{3}^{-} \) by
\( M n O_{4}^{-} \) changing to \( M n^{2+} \) in acid
medium. Given that \( 2.68 \times 10^{-3} \) mole of
\( A^{n+} \) required \( 1.61 \times 10^{-3} \) mole \( M n O^{-} \)
What is the value of n?


Describe the construction of a
laboratory thermometer


Which of the following is NOT an antiseptic compound?
A. Boric acid
B. lodoform
c. Hydrogen peroxide
D. Potassium sulphite


If \( v \) is the variance and \( \sigma \) is the
standard deviation, then
A \( \cdot v^{2}=\sigma \)
B . \( v^{2}=\sigma^{3} \)
c. \( v^{2}=\frac{1}{\sigma} \)
D. \( v^{2}=\frac{1}{\sigma^{2}} \)


Smaller area enclosed by the circle \( x^{2}+y^{2}=4 \) and the line \( x+y=2 \) is
A. \( 2(\pi-2) \)
B. \( \pi-2 \)
c. \( 2 \pi-1 \)
D. \( 2(\pi+2) \)


In froth floatation process in the concentration of sulphide ore froth adsorbs ore particles.
If true enter 1 else enter 0


Construct a triangle \( A B C \) in which
\( B C=6 c m, \angle A=45^{\circ} \) and median
\( A D=5 \mathrm{cm} \)


I. Nitrogen \( \left(N_{2}\right) \) reacts with oxygen \( \left(O_{2}\right. \)
, the compound \( N O_{2} \) can be formed as
a product.
II. Nitrogen atoms donate four
electrons to form \( N^{4+} \) ions and oxygen
atoms gain two electrons to form \( O^{2-} \)
ions when nitrogen and oxygen form an ionic bond.
A. Statement \( I \) is true, Statement \( I I \) is true
B. Statement I is true, Statement \( I I \) is false
c. statement \( I \) is false, statement \( I I \) is true
D. Statement I is false, Statement II is false


What is the frequency in Hz from B as heard by the listener?


\( f(x)=\frac{1+e^{1 / x}}{1-e^{1 / x}}(x \neq 0), f(0)=1, \) then
\( f(x) \) is
A. left coninuous at \( x=0 \)
B. right continuous at \( x=0 \)
c. continuous at \( x=0 \)
D. none


Salts which are important Ammonium
Bromide.


A tightrope walker in a circus holds a
long flexible pole to help stay balanced
on the rope. Holding the pole
horizontally and perpendicular to the
rope helps the performer.
This question has multiple correct options
A. by lowering the overall centre-of-gravity.
B. by increasing the rotation inertia.
C. in the ability to adjust the centre-of-gravity to be over the rope
D. in achieving the centre of gravity to be under the rope


Cyclohexene is treated with cold dilute,
alkaline \( K M n O_{4} . \) The spatial
arrangement of two hydroxyl groups in the products would be
A . trans
B. equatorial-equatorial
c. cis-planer
D. equatorial-axial


Three resistances are joined together to
form a letter \( Y \) as shown in the figure.If
the potentials of the terminals \( \mathbf{A}, \mathbf{B} \) and
\( \mathrm{C} \) are \( \mathrm{V}_{1}, \mathrm{V}_{2} \) and \( \mathrm{V}_{3} \) respectively, then
determine the potential of the node \( \boldsymbol{O} \)
\( ^{\mathbf{A}} \cdot\left[\frac{V_{1}}{R_{1}^{\frac{1}{1}}}+\frac{V_{2}}{R_{2}^{2}}+\frac{V_{3}}{R_{3}^{3}}\right]\left[\frac{1}{R_{1}}+\frac{1}{R_{2}}+\frac{1}{R_{3}}\right]^{-2} \)
\( ^{\mathbf{B}} \cdot\left[\frac{V_{1}}{R_{1}}+\frac{V_{2}}{R_{2}}+\frac{V_{3}}{R_{3}}\right]\left[\frac{1}{R_{1}}+\frac{1}{R_{2}}+\frac{1}{R_{3}}\right]^{-1} \)
\( \mathbf{C} \cdot\left[\frac{V_{1}}{R_{1}}+\frac{V_{2}}{R_{2}}+\frac{V_{3}}{R_{3}}\right]\left[R_{1}+R_{2}+R_{3}\right] \)
D. \( \left[\frac{V_{1}}{R_{2}^{2}}+\frac{V_{2}}{R_{2}^{2}}+\frac{V_{3}}{R_{2}}\right]\left[R_{1}^{2}+R_{2}^{2}+R_{3}^{2}\right] \)


Two particles of masses \( m \) and \( 2 m \) are kept at a distance a. Find their relative
velocity of approach when separation becomes \( a / 2 \)
\( \mathbf{1} \)
2
A \( \cdot 2 \sqrt{\frac{3 a}{2 G M}} \)
B. \( \sqrt{\frac{a}{2 G M}} \)
\( ^{\mathbf{C}} \cdot 2 \sqrt{\frac{2 G M}{3 a}} \)
D. \( \sqrt{\frac{6 G M}{a}} \)


Select the correct option:
A cell's division time is 1 minute In 20
minutes, a culture tube (culture medium) is \( 1 / 8^{t h} \) filled with cells, When the tube will be fully filled?
A . 21 minutes
B. 23 minutes
c. 60 minutes
D. 160 minutes


Which of the following is not an essential part of an emulsion?
A. Dissolved salt
B. water
c. oil
D. Emulsifier


If a vector \( 2 \hat{i}+3 \hat{j}+8 \hat{k} \) is perpendicular to the vector \( 4 \hat{j}-4 \hat{i}+\alpha \hat{k} . \) Then, the
value of \( \alpha \) is :
A \( \cdot \frac{-1}{2} \)
B. - -
\( c \cdot \frac{1}{2} \)
D. 1


The work done in rotating a body from
angle \( \theta_{1} \) to angle \( \theta_{2} \) by a constant
torque \( \boldsymbol{\tau} \) will be :
A \( \cdot \frac{\tau}{\left(\theta_{1}-\theta_{2}\right)} \)
В \( \cdot \tau\left(\theta_{2}-\theta_{1}\right) \)
c. 0
D. \( \frac{\left(\theta_{1}-\theta_{2}\right)}{\tau} \)


Which of the following is represented by perfect identity?
\( \mathbf{A} \cdot \mathbf{1} \)
B.
\( c \cdot-1 \)
D. None of the above


When 3 -methylbutan-2-ol is treated with HBr, the following reaction takes
place. What are the correct steps for formation of the above product?
\[
\begin{array}{c}
\mathbf{C H}_{3}-\underset{\mathbf{C}}{\mathbf{C}} \mathbf{H}-\mathbf{C H}-\mathbf{C H}_{3} \frac{\mathbf{H B r}}{\mathbf{I}} \\
\mathbf{U}_{3} \mathbf{O H} \\
\mathbf{B H}_{3}-\mathbf{C}-\mathbf{C H}_{2}-\mathbf{C H}_{3} \\
\mathbf{C H}_{3}
\end{array}
\]
A. Formation of carbocation \( \rightarrow \) Nucleophilic attack by \( B r^{c} \)
B. Formation of carbocation \( \rightarrow 1,2 \) hydride shift Nucleophilic attack by \( B r^{\circ} \)
c. Formation of carbocation \( \rightarrow 1,2 \) methyl shift Nucleophilic attack by \( B r^{\ominus} \)
D. None of these


Draw a circle of radius \( 5 \mathrm{cm} \). From a
point \( 13 \mathrm{cm} \) away from its centre,
construct the pair of tangents to the circle and measure their length. Also verify the measurement by actual calculation.


The suffix used for naming an aldehyde
is:
A . -ol
B. -al
c. - -one
D. -ene


A car moving on a road when overtaken by a bus:
A. is pulled towards the bus
B. is pulled away from the bus
c. is not affected by the bus
D. information is insufficient


is defined as a process
where materials, usually metals, deteriorate as a result of a chemical
reaction with air, moisture, chemical
etc. For example, iron, in the presence of
moisture, reacts with oxygen to form hydrated iron oxide.


Which acid produces sugar charcoal from sugar?


Find the value of \( x \) and \( y \) in \( 3 x+2 y=4 \)
and \( 2 x-3 y=7 \)


0.2175 g of the substance gave 0.5825 g
of \( B a S O_{4} \) by Carius method.Calculate
the percentage of Sulphar.
A. 36.78\%
B. 39.52\%
c. 32.86\%
D. 41.85\%


Eight dipoles of charges of magnitude \( e \)
are placed inside a cube. The total
electric flux coming out of the cube will
be
\( A \cdot \frac{8 e}{\varepsilon_{0}} \)
В. \( \frac{16 e}{\varepsilon_{0}} \)
\( c \cdot \frac{e}{\varepsilon_{0}} \)
D. zero


f \( \boldsymbol{f}:[\mathbf{0}, \boldsymbol{\pi}] \rightarrow \boldsymbol{R}, \boldsymbol{f}(\boldsymbol{x})=\cos \boldsymbol{x}, \) then \( \boldsymbol{f} \) is
A. one-one onto
B. one-one into
c. many-one onto
D. many-one into


\( f(1+x)\left(1+x^{2}\right)\left(1+x^{4}\right) \dots .(1+ \)
\( \left.x^{128}\right)=\sum_{r=0}^{n} x^{r} \) then findthe value of \( n \)


An uniform circular motion is an
uniform velocity motion
A. True
B. False


If at \( t=0, \) a travelling wave pulse on a string is described by the function. \( y=\frac{6}{x^{2}+3} . \) What will be the wave
function representing the pulse at
time \( t, \) if the pulse is propagating along positive \( x \) -axis with speed \( 4 \mathrm{m} / \mathrm{s} ? \)
A \( \cdot y=\frac{6}{(x+4 t)^{2}+3} \)
B. \( y=\frac{6}{(x-4 t)^{2}+3} \)
c. \( y=\frac{6}{(x-t)^{2}} \)
D. \( y=\frac{6}{(x-t)^{2}+12} \)


In a parallelgoram \( A B C D, P \) and \( Q \) are midpoints of \( B C \) and \( C D, a r(A P Q) \) will be \( _{\text {- }-\text { - }-\text { - of parallelogram }} \)
A. Equal
B. \( \frac{1}{8} \)
\( c \cdot \frac{1}{4} \)
D. \( \frac{3}{8} \)


The \( \pi \) acid ligands donate their lone pairs to the metal to form a normal
bond with the latter in addition to it, the
vacant orbitals accept e- from the filled metal orbitals to form a type of \( \pi \) -bond which supplements the \( \sigma \) bond.

Which of the following has lowest C-O bond length?
A \( \cdot\left[N i(C O)_{4}\right] \)
в. \( \left[\operatorname{Co}(C O)_{4}\right]^{-} \)
c. \( \left[F e(C O)_{4}\right]^{2} \)
D. \( \left[M n(C O)_{6}\right]^{+} \)


Explain briefly the extraction of aluminium from bauxite.


The gravitational P.E. of a rocket of mass \( 100 \mathrm{kg} \) at a distance of \( 10^{7} \mathrm{m} \) from the earths centre is \( -4 \times 10^{9} \) J.
The weight of the rocket at a distance of \( 10^{9} \mathrm{m} \) from the centre of the earth is :
A \( \cdot 4 \times 10^{-2} \mathrm{N} \)
В. \( 4 \times 10^{-9} \mathrm{N} \)
c. \( 4 \times 10^{-6} \mathrm{N} \)
D. \( 4 \times 10^{-3} \mathrm{N} \)


f \( 3 x+y+z=0 \) show that \( 27 x^{3}+ \)
\( \boldsymbol{y}^{3}+\boldsymbol{z}^{3}=\mathbf{9} \boldsymbol{x} \boldsymbol{y} \boldsymbol{z} \)


In \( \triangle A B C, D \) is a point on \( B C \) such that \( A B=A D=B D=D C, \) then:
\( \angle A D C: \angle C=3: 1 \)
A. True
B. False


In Mendeleev's periodic table, gaps were left for the element to be discovered
later on, which of the following elements found a place on the periodic table later
on:
A. germanium
B. chlorine
c. silicon
D. oxygen


ff \( y=\log \left(\sqrt{x}+\frac{1}{\sqrt{x}}\right), \) prove that
\( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\frac{\boldsymbol{x}-\mathbf{1}}{\boldsymbol{2} \boldsymbol{x}(\boldsymbol{x}+\mathbf{1})} \)


For any two sets \( A \) and \( B, A=B \) is
equivalent to
This question has multiple correct options
\( \mathbf{A} \cdot A-B=B-A \)
\( \mathbf{B} \cdot A \cup B=A \cap B \)
\( \mathbf{c} . A \cup C=B \cup C \) and \( A \cap C=B \cap C \) for any set \( C \)
\( \mathbf{D} \cdot A \cap B=\phi \)


A display garden that concentrates on herbs and lianas is often referred to as
an arboretum.
A. True
B. False


The standard deviation of the data
6,5,9,13,12,8,10 is
A \( \cdot \sqrt{\frac{52}{7}} \)
в. \( \frac{52}{7} \)
\( c \cdot \sqrt{6} \)
D. 6


Blood clot inside a blood vessel is
known as
A. Thrombosis
B. Agglutinin
c. clot
D. Thrombus