AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
What will be the height of image when an object of 2 mm is placed at a
distance \( 20 \mathrm{cm} \) infront of the axis of a
convex mirror of radius of curvature
\( 40 \mathrm{cm} ? \)
A \( .20 \mathrm{mm} \)
B. \( 10 \mathrm{mm} \)
\( c .6 m m \)
D. \( 1 \mathrm{mm} \)
Subject: Chemistry
Which can show linkage isomerism?
\( \mathbf{A} \cdot\left[\operatorname{Cr}\left(H_{2} O\right)_{5} C l\right] C l_{2} \)
в. \( \left[C r\left(H_{2} O\right)_{6}\right] C l_{3} \)
\( \mathbf{c} \cdot\left[C o\left(N H_{3}\right)_{5}(C N)\right] C l_{2} \)
D. \( \left[\operatorname{Co}\left(N H_{3}\right)_{5} S O_{4}\right] B r \)
Subject: Physics
Q Type your questior
perpendicular to a constantmagnetic
field of magnitude \( 1 \mathrm{T} \) as shown in figure. One end of a resistanceless rod is
hinged at thecentre of ring 0 and other
end is placed on the ring. Now rod is rotated with constant angular velocity \( 4 \mathrm{rad} / \mathrm{s} \) by some external agent and circuit is connected as shown in the
figure, initially switch is open andcapacitor is uncharged. If switch S
is closed at \( t=0, \) then calculate heat
\( \operatorname{loss}(\operatorname{in} \mu \mathrm{J}) \) from the resistor \( \boldsymbol{R}_{1} \) from \( \mathrm{t} \)
\( =0 \) to the instant when voltage across the capacitor becomes half of steady state voltage. (Assume plane of ring to be horizontal and friction to be absent
at all the contacts)
Subject: Maths
The cartesian equation of plane \( \bar{r} \cdot(2,-3,4)=5 \) is
A. \( 3 y-2 x-4 z+5=0 \)
B. \( 2 x-3 y+4 z=0 \)
c. \( 2 x-3 y+4 z+5=0 \)
D. \( \frac{x-1}{2}=\frac{y-1}{-3}=\frac{z-1}{4} \)
Subject: Chemistry
Compute the molar solubility of water
that is saturated with air.
\( \left[\text { Given: } k=0.00105 \mathrm{M} / \mathrm{atm}, P_{N e} \text { in air }=\right. \)
\( 0.0341 \mathrm{atm}] \)
A \( .2 .56 \times 10^{-2} M \)
в. \( 3.58 \times 10^{-5} M \)
c. \( 4.44 \times 10^{-6} M \)
D. \( 2.78 \times 10^{-4} M \)
Subject: Physics
In the arrangement shown above, a
block of mass \( 2700 \mathrm{kg} \) is in equilibrium
on applying a force F. The value of force
\( \mathrm{F} ?\left(d_{l i q u i d}=0.75 g c m^{-3} i s\right) \)
A . \( 147 N \)
B. \( 1755.18 N \)
c. \( 153 N \)
D. \( 918 N \)
Subject: Maths
Equation of the plane through the midpoint of the line segment joining the points \( \boldsymbol{P}(\mathbf{4}, \mathbf{5},-\mathbf{1 0}), \boldsymbol{Q}(-\mathbf{1}, \mathbf{2}, \mathbf{1}) \) and
perpendicular to \( \boldsymbol{P} \boldsymbol{Q} \) is
A \( \cdot r .\left(\frac{1}{3} 2 \hat{i}+\frac{7}{2} \hat{j}-\frac{9}{2} \widehat{k}\right)=45 \)
B \( \cdot r .(-\hat{i}+2 \hat{j}+\widehat{k})=\frac{135}{2} \)
c. \( r .(5 \hat{i}+3 \hat{j}-11 \widehat{k})+\frac{135}{2}=0 \)
D. \( r .(4 \hat{i}+5 \widehat{j}-10 \widehat{k})=85 \)
E \( \cdot r_{\cdot}(5 \hat{i}+3 \hat{j}-11 \widehat{k})=\frac{135}{2} \)
Subject: Chemistry
For the reaction \( \boldsymbol{P C l}_{3}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g}) \rightleftharpoons \)
\( \boldsymbol{P C l}_{5}(\boldsymbol{g}) \) the value of \( \boldsymbol{K}_{c} \) at \( 250^{\circ} \boldsymbol{C} \) is 26
The value of \( \boldsymbol{K}_{\boldsymbol{p}} \) at this temperature will
be:
A . 0.61
B. 0.57
c. 0.83
D. 0.46
Subject: Maths
Multiply: \( (x-2)\left(x^{2}+3 x+7\right) \)
A \( \cdot x^{3}+2 x^{2}+6 x-14 \)
B. \( x^{3}+x^{2}+6 x-14 \)
c. \( x^{3}+x^{2}+x-14 \)
D. \( x^{3}+2 x^{2}+3 x-14 \)
Subject: Chemistry
There is \( S-S \) linkage in:
This question has multiple correct options
\( \mathbf{A} \cdot S_{2} O_{3}^{2-} \)
B. \( S_{2} O_{4}^{2-} \)
\( \mathbf{c} \cdot S_{2} O_{5}^{2-} \)
\( \mathrm{D} \cdot S_{2} O_{7}^{2-} \)
Subject: Physics
The magnetic flux through a circuit of resistance 'R' changes by an amount
\( \Delta \Phi \) at a time \( \Delta t . \) Then the total
quantity of electric charge \( Q \) that passes any point in the circuit during the time \( \Delta t \) is represented by
\( ^{\mathbf{A}} \cdot Q=\frac{\Delta \Phi}{R} \)
в. \( Q=\frac{\Delta \Phi}{\Delta t} \)
c. \( Q=R \cdot \frac{\Delta \Phi}{\Delta t} \)
D. \( Q=1 R \cdot \frac{\Delta \Phi}{\Delta t} \)
Subject: Maths
5 cards are drawn at random from a well
shuffled pack of 52 playing cards. If it is known that there will be at least 3
hearts, the probability that all the 5 are hearts is
A \( \cdot \frac{13}{^{52} C_{5}} \)
в.
c.
D. \( \frac{^{13} C_{5}}{^{13} C_{3} \times^{13} C_{4} \times^{13} C_{5}} \)
Subject: Maths
Fill in the blanks with the help of options, given in the box.
I. In
(P) sketch of the solid, the measurements are kept proportional.
Il. \( \mathbf{A} \)
(Q) polygon has as many lines of symmetry as it has sides. III. \( \mathbf{A} \)
(R) is a skeleton-outline of
a solid that can be folded to make the
solid.
IV. While rectangle is a 2 -D figure,
(S) is a 3 -D figure.
A. P- Oblique, Q- Regular, R- Net, S- Cuboid
B. P- Isometric, Q- - Irregular, R- Net, S- Cuboid
c. P- oblique, Q- - Irregular, R- Net, S- Cuboid
D. P- Isometric, Q- Regular, R- Net, S- Cuboid
Subject: Chemistry
IUPAC name of the following compound:
\( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\underset{\boldsymbol{C H}_{2} C \boldsymbol{H}_{3}}{\boldsymbol{C} \boldsymbol{H}-\boldsymbol{C H}_{2}}-\underset{\boldsymbol{C H}_{3}}{\boldsymbol{C H}}- \)
\( \boldsymbol{C H}_{2}-\boldsymbol{C H}_{3} \)
A. 3-Ethyl-5-methylheptane
B. 5-Ethyl-3-methylheptane
c. 1,1-Diethyl-3-methylpentane
D. 3-Methyl-5,5-diethylpentane
Subject: Maths
Range of \( f(x)=\frac{\sec x+\tan x-1}{\tan x-\sec x+1} \)
\( \boldsymbol{x} \epsilon\left(\mathbf{0}, \frac{\pi}{2}\right) \) is
A \( .(0,1) \)
B. \( (0, \infty) \)
c. (-1,0)
D. \( (-\infty,-1) \)
Subject: Physics
A charged oil drop falls with terminal
velocity \( V_{0} \) in the absence of electric
field. An electric field 'E' keeps it stationary. The drop acquires additional charge \( q \) and starts moving
upwards with velocity \( V_{0} . \) The initia
charge on the drop was
\( A \cdot 49 \)
B. 29
\( c \cdot q \)
D. \( 9 / 2 \)
Subject: Physics
The input signal given to a a CE
amplifier having a voltage gain of 150 is \( V_{i}=2 \cos \left(15 t+\frac{\pi}{3}\right) . \) The
corresponding output signal will be
A \( \cdot 300 \cos \left(15 t+\frac{4 \pi}{3}\right) \)
B. \( 300 \cos \left(15 t+\frac{\pi}{3}\right) \)
c.
\( 75 \cos \left(15 t+\frac{2 \pi}{3}\right) \)
D. \( 2 \cos \left(15 t+\frac{5 \pi}{6}\right) \)
Subject: Physics
In case of theory of light nature of light
match the following:
List - I List - II
a) Light is a collection of
e) Newton's theory photons
b) Light is a form of
f) Huygen's theory electromagnetic wave
g) Maxwell's
c) Light is a wave
d) Light is a stream of
h) Max planck's corpuscles theory
\( \mathbf{A} \cdot \mathrm{a}-\mathrm{h} ; \mathrm{b}-\mathrm{g} ; \mathrm{c}-\mathrm{f} ; \mathrm{d}-\mathrm{e} \)
B. \( a-e ; b-f ; c-g ; d-h \)
C. \( a-g ; b-h ; c-g ; d-f \)
D. \( a-h ; b-g ; c-e ; d-f \)
Subject: Chemistry
A boy of mass \( 50 \mathrm{kg} \) runs up a staircase of 45 steps in 9 s. If the height of each step of the staircase is \( 15 \mathrm{cm} \), find the
power of the boy.
\( \mathbf{A} \cdot 375 W \)
в. \( 480 \mathrm{W} \)
c. \( 550 W \)
D. \( 5390 W \)
Subject: Maths
Lightning quickly heats the air causing it to expand, which produces the sound
of thunder.

Sound travels approximately 1 mile in 5 seconds. Knowing \( \boldsymbol{X}=\boldsymbol{r} \cdot \boldsymbol{t} \) (where \( \boldsymbol{D}= \)
distance, \( r=\text { rate and } t=\text { time }), \) how
far away is a thunderstrom when you
notice a 3 -second delay between the
flash of lightning and the sound of
thunder?
\( \mathbf{A} \cdot 1 \) mile away
B. \( 3 / 5 \) mile away
c. \( 1 / 2 \) mile away
D. \( 1 / 5 \) mile away
Subject: Maths
Find the sum the infinite G.P.:
\( 1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\dots \dots \)
A \( \cdot \frac{3}{5} \)
B. \( \frac{3}{2} \)
c. \( \frac{49}{27} \)
D. 8
Subject: Maths
The sum of the first three terms of an
A.P. is 9 and the sum of their square is
35. The sum to first \( n \) terms of the
series can be

This question has multiple correct options
A. \( n(n+1) \)
B \( \cdot n^{2} \)
c. \( n(4-n) \)
D. \( n(6-n) \)
Subject: Physics
The mass of a lead ball is \( M \). It falls
down in a viscous liquid with terminal velocity \( V \). The terminal velocity of
another lead ball of mass \( 8 M \) in the
same liquid will be:
A . \( 64 . V \)
B. \( 4 V \)
\( c \cdot 8 V \)
D. \( V \)
Subject: Physics
A photon of wavelength 300 nm interacts with a stationary hydrogen atom in ground state. During the interaction, whole energy of the photon is transferred to the electron of the
atom. State which possibility is correct. (consider, Planck's constant \( =4.1 \times \)
\( 10^{-15} e V s, \) velocity of light \( =3 x \)
\( 10^{8} m / s, \) ionisation energy of hydrogen
\( =13.6 \mathrm{eV} \)
A. Electron will be knocked out of the atom
B. Electron will go to any excited state of the atom
C. Electron will go only to first excited state of the atom
D. Electron will keep orbiting on the ground state of the atom
Subject: Maths
The point \( P(3,4) \) is reflected to \( P^{\prime} \) in the
\( x \) -axis and \( O^{\prime} \) is the image of 0 (the
origin) when reflected in the line \( P P^{\prime} \) Using Graph paper give :
1) The coordinates of \( P^{\prime} \) and \( O^{\prime} \)
2) The length of segments \( P P^{\prime} \) and \( O O^{\prime} \)
3) The perimeter of the quadrilateral POP' \( O^{\prime} \)
4) Geometrical name of the figure POP' \( \boldsymbol{O}^{\prime} \)
Subject: Physics
A battery and a variable resistor are in
series with a small fan. A switch is
closed, and the fan runs. When the variable resistor is moved slightly to the left, the fan slows down a little. When
the variable resistor is moved slightly to the right, the fan speeds up a little. If the variable resistor in the circuit is set
all the way to the right, what happens in the circuit?
I. The fan runs faster
II. The voltage decreases.
III. The current increases.
A . I only
B. Il only
c. I and III only
D. I I and III only
E . I, II, and III
Subject: Chemistry
The statements given below represent
the characteristics of nitrates of
different metals
(a) Nitrate of sodium liberates brown
coloured gas on strong heating.
(b) Nitrate of calcium liberates a pair of colourless gases on strong heating.
(c) Metallic silver can be obtained from
its nitrate on strong heating.
(d) Nitrate of potassium gives a solid product and a colourless gas on strong heating.
Which of the following options is
correct?
A. a and
B. c and d
c. only d
D. only b
Subject: Chemistry
\[
\begin{array}{l}
\boldsymbol{C H}_{3}-\underset{\Gamma H_{2} C H_{3}}{C H}-\stackrel{C H_{3}}{\boldsymbol{C}} \boldsymbol{H}-\boldsymbol{C} \boldsymbol{H}_{2}- \\
\frac{C H_{2} C H_{3}}{\boldsymbol{C} \boldsymbol{H}}-\boldsymbol{C H}_{3}
\end{array}
\]
What will be the IUPAC name of given
compount?
A. 2, 5-diethyl-4-methylhexane
B. 3, 4, 5-trimethyloctane
c. \( 2,5, \) 6-trimethyloctane
D. 3, 5-dimethyl-6-ethylheptane
Subject: Maths
\( \operatorname{Let} \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{1} & \frac{\mathbf{3}}{2} \\ \mathbf{1} & \mathbf{2}\end{array}\right], \boldsymbol{B}= \)
\( \left[\begin{array}{cc}\mathbf{4} & -\mathbf{3} \\ -\mathbf{2} & \mathbf{2}\end{array}\right] \) and \( \boldsymbol{C}_{\boldsymbol{r}}= \)
\( \left[\begin{array}{cc}r .3^{r} & 2^{r} \\ 0 & (r-1) 3^{r}\end{array}\right] \) be 3 given matrices.
Compute the value of
\( \sum_{r=1}^{50} t r \cdot\left((A B)^{r} C_{r}\right) .(\text { where } t r .(A) \)
denotes trace of matrix \( \mathbf{A} \) )
\( \mathbf{A} \cdot 3\left(49.3^{50}+1\right) \)
B \( \cdot 3\left(49.3^{49}+1\right) \)
C \( .3\left(49.3^{48}+1\right) \)
D. None of these
Subject: Chemistry
An athlete is given \( 100 g \) of glucose
\( C_{6} H_{12} O_{6} \) of energy equivalent to
\( 1560 k J . \) He utilizes \( 50 \% \) of this gained energy in an event. In order to avoid
storage of energy in the body what is the weight of water, he would need to perspire? The enthalpy of evaporation of water is \( 44 k J / \) mol.
A. \( 319 g \)
в. \( 638 g \)
c. \( 14040 g \)
D. 35.45 g
Subject: Chemistry
Assertion
The first ionization energy of Be is
greater than that B.
Reason
2p orbital is lower in energy than 2 s.
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
Subject: Maths
Find the equation of the plane which contains the line \( \boldsymbol{x}=\mathbf{2}, \boldsymbol{y}-\boldsymbol{z}=\mathbf{0} \) and
is perpendicular to the plane \( \boldsymbol{x}+\boldsymbol{z}=\mathbf{3} \)
Find the point where this plane meets the line \( \frac{x}{2} \equiv \frac{y}{3}=\frac{z}{1} \)
Subject: Maths
A swimming pool is \( 100 \mathrm{m} \) long and \( 15 \mathrm{m} \) wide its deep and \( 24 \mathrm{m} \) height
respectively. Find the capacity of the
pool
A. \( 36,000 \mathrm{m} \)
в. \( 36,000 m^{3} \)
c. \( 36,000 m^{2} \)
D. 36,000 \( c m \)
Subject: Maths
If \( A \) is non-singular and \( (A-2 I)(A- \) \( 4 I)=0 \) then \( \frac{1}{6} \mathbf{A}+\frac{4}{3} \mathbf{A}^{-1}= \)
\( A \cdot I \)
B.
c. \( 2 I \)
D. \( 6 I \)
Subject: Chemistry
Assertion
The sum of mole fractions of all the
components of a solution is unity.
Reason
Mole fraction is a temperature
dependent mode of concentration.
Choose the correct option.
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
Subject: Chemistry
A man writes his biodata with carbon
pencil on the plane paper having mass 150 mg. After writing his biodata, he weighs the written paper and find its mass \( 152 \mathrm{mg} \). What is the number of carbon atoms present in the paper?
A \( .1 .0036 \times 10^{20} \)
B . \( 5.02 \times 10^{20} \)
\begin{tabular}{l}
\( c .1 .0036 \times 10^{23} \) \\
\hline
\end{tabular}
D. \( 0.502 \times 10^{20} \)
Subject: Physics
At what maximum width \( \delta_{\max }, \) of the
slit are the interference fringes on the
screen observed still sharp?
\( \mathbf{A} \cdot 42 \mu m \)
B. \( 36 \mu m \)
\( \mathrm{c} .64 \mu \mathrm{m} \)
D. none of these
Subject: Maths
The expression \( \frac{3-4 i}{5+3 i} \) is equivalent to
A \( \cdot \frac{27-29 i}{34} \)
в. \( \frac{27-29 i}{16} \)
c. \( \frac{3-29 i}{34} \)
D. \( \frac{1}{8} \)
E . \( 15-8 i \)
Subject: Maths
If three unit vector \( \hat{a}, \hat{b}, \hat{c} \) satisfy \( \hat{a}+ \) \( \hat{\boldsymbol{b}}+\hat{\boldsymbol{c}}=\hat{\mathbf{0}}, \) then the angle between \( \hat{\boldsymbol{a}} \) and
\( \hat{b} \) is
A \( \cdot \frac{\pi}{3} \)
в. \( \frac{2 \pi}{3} \)
c. \( \frac{\pi}{6} \)
D. \( \frac{5 \pi}{6} \)
Subject: Physics
A stone drop from height 'h' reaches at earth surface in 1 sec. If the same stone
is taken to moon and dropped freely from height \( h, \) then it will reach the surface of moon in \( \ldots \ldots \) sec
A \( \cdot \sqrt{6} \sec \)
B. \( 9 s e c \)
\( c .3 s e c \)
D. 6 sec
Subject: Physics
In a Wheatstones's bridge, three resistances \( P, Q \) and \( R \) are connected in the three arms and the fourth arm is
informed by two resistances \( S_{1} \) and \( S_{2} \) connected in parallel. The condition for the bridge to be balanced will be
\( ^{\mathrm{A}} \cdot \frac{P}{Q}=\frac{2 R}{S_{1}+S_{2}} \)
B. \( \frac{P}{Q}=\frac{R\left(S_{1}+S_{2}\right)}{S_{1} S_{2}} \)
c. \( \frac{P}{\bar{Q}}=\frac{R\left(S_{1}+S_{2}\right)}{2 S_{1} S_{2}} \)
D. \( \frac{P}{Q}=\frac{R}{S_{1}+S_{2}} \)
Subject: Maths
\( a^{-1}+b^{-1}+c^{-1}=0 \) such that
\( \left|\begin{array}{ccc}1+a & 1 & 1 \\ 1 & 1+b & 1 \\ 1 & 1 & 1+c\end{array}\right|=\triangle \) then the
value of \( \triangle \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B. abco
\( \mathrm{c} .-a b c \)
D. None of these
Subject: Physics
Observe the given situation and answer
the following questions. Rahul and Ravi
are playing in a ground. They start running from the same point \( x \) simultaneously in the ground and reach
point \( Y \) at the same time by following
paths marked 1 and 2 respectively, as shown in the figure.

Which of the following path does show the displacement?
A. \( x y \)
в. хоу
c. xorx
D. xyo
Subject: Physics
\( 32 g \) of \( O_{2} \) is contained in a cubical
container of side \( 1 m \) and maintained
at a temperature of \( 127^{0} C . \) The isothermal bulk modulus of elasticity of
the gas in terms of universal gas constant \( \boldsymbol{R} \) is
\( \mathbf{A} \cdot 127 R \)
B. \( 400 R \)
\( c \cdot 200 R \)
D. \( 560 R \)
Subject: Physics
A rope of length \( L \) and mass \( M \) is being
pulled on a rough horizontal floor by a
constant horizontal force \( \boldsymbol{F}=\boldsymbol{m} \boldsymbol{g} \). The
force is acting at one end of the rope in the same direction as the length of the rope. The coefficient of kinetic friction between rope and floor is \( 0.5 . \) Then, tension at the midway of the rope is:
A. \( \frac{M g}{4} \)
в. \( \frac{3 M g}{4} \)
c. \( \frac{M g}{8} \)
D. \( \frac{M g}{2} \)
Subject: Physics
To produce a minimum reflection of wavelengths near the middle of visible spectrum (550nm), how thick should a
coating of \( M g F_{2}(\mu=1.38) \) be
vacuum-coated on a glass surface?
A \( \cdot 10^{-7} \)
B \( \cdot 10^{-10} \)
\( \mathbf{c} \cdot 10^{-9} m \)
D. \( 10^{-8} m \)
Subject: Chemistry
The complexes
\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{6}\right]\left[\boldsymbol{C r}(\boldsymbol{C} \boldsymbol{N})_{6}\right] \boldsymbol{a} \boldsymbol{n} \boldsymbol{d}\left[\boldsymbol{C r}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{6}\right. \)
are the examples of which type of isomerism?
A. Linkage isomerism
B. lonization isomerism
c. coordination isomerism
D. Geometrical isomerism
Subject: Maths
Prove that
\[
\left|\begin{array}{ccc}
\boldsymbol{x}+\boldsymbol{y}+\mathbf{2} \boldsymbol{z} & \boldsymbol{x} & \boldsymbol{y} \\
\boldsymbol{z} & \boldsymbol{y}+\boldsymbol{z}+\mathbf{2} \boldsymbol{x} & \boldsymbol{y} \\
\boldsymbol{z} & \boldsymbol{x} & \boldsymbol{z}+\boldsymbol{x}+\boldsymbol{2} \boldsymbol{y}
\end{array}\right|
\]
\( 2(x+y+z)^{3} \)
Subject: Maths
\( \boldsymbol{A B}=\mathbf{0} \) where
\( \boldsymbol{A}=\left[\begin{array}{cc}\cos ^{2} \boldsymbol{\theta} & \cos \boldsymbol{\theta} \sin \boldsymbol{\theta} \\ \cos \boldsymbol{\theta} \sin \boldsymbol{\theta} & \sin ^{2} \boldsymbol{\theta}\end{array}\right] \)
\( \boldsymbol{B}=\left[\begin{array}{cc}\cos ^{2} \boldsymbol{\phi} & \cos \phi \sin \phi \\ \cos \phi \sin \phi & \sin ^{2} \phi\end{array}\right] \)
then find \( |\boldsymbol{\theta}-\boldsymbol{\phi}|=? \)
Subject: Physics
particle moves uniform in a circle of
radius \( 10 \mathrm{cm}, \) converting a linear distance of \( \mathrm{cm} \) in a time 2.5 sec. Find
the time taken for 10 revolutions,
A \( .0 .2 s e c \)
B. 18.34 sec
c. 79.12 sec
D. 50 sec
Subject: Physics
connected by a string going over
clamped light smooth pulley as shown
in figure. The system is released from
rest. The larger mass is stropped for a
moment \( 1.0 s \) after the system is set in
motion. Find the time elapsed before the
string is tight again.
\( \mathbf{A} \cdot \frac{1}{3} s \)
B . \( 1 s \)
c. \( 2 s \)
D. \( 3 s \)
Subject: Physics
A motorcyclist executes a horizontal loop at a speed of \( 65 k m / h \) while
himself making an angle of \( 12^{\circ} \) with the
horizontal. What is the radius of the
\( \operatorname{loop} ?(\operatorname{in} m) \)
\( \mathbf{A} \cdot 123.6 \)
B. 156.6
c. 156.3
D. 174.3
Subject: Chemistry
Assertion
For liquid dishwashing, non-ionic type
of detergent are used.
Reason
Remove grease and oil by micelle formation.
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
Subject: Maths
For any two rational numbers \( x \) and \( y \) which of the following properties are correct?
\( (i) x<y(i i) x=y(\text { iii }) x>y \)
A. Only (i) and (ii) are correct
B. Only (ii) and (iii) are correct
c. only (ii) is correct
D. All (i), (ii) and (iii) are correct
Subject: Physics
A long dielectric cylinder of radius \( \boldsymbol{R} \) is
statically polarized so that at all its points the polarization is equal to \( \vec{P}= \) \( \alpha \vec{r}, \) where \( \alpha \) is a positive constant, and
\( \vec{r} \) is the distance from the axis.

The cylinder is set into rotation about
its axis with an angular velocity \( \omega . \) Find
the magnetic induction \( B \) at the centre
of the cylinder
Subject: Physics
Two parallel plates have equal and opposite charge. When the space between them is evacuated. the electric
field between the plates \( 2 \times 10^{5} V / m \)
When the space is filed with dielectric
the electric field becomes \( 10^{5} V / m \) The
dielectric constant of he dielectric
material is
A . 2
B. 4
c. 5
D. 9
Subject: Maths
\( \frac{\boldsymbol{x}^{2}+\mathbf{2} \boldsymbol{x}+\mathbf{3}}{\boldsymbol{x}^{3}}=\frac{\boldsymbol{A}}{\boldsymbol{x}}+\frac{\boldsymbol{B}}{\boldsymbol{x}^{2}}+\frac{\boldsymbol{C}}{\boldsymbol{x}^{3}} \Rightarrow \boldsymbol{A}+ \)
\( \boldsymbol{B}-\boldsymbol{C}= \)
\( A \cdot 6 \)
B. 3
\( c \)
\( D \)
Subject: Physics
An electron is moving round the nucleus of a hydrogen atom in a circular orbit of radius r. The coulomb
force \( \vec{F} \) between the two is -
\( ^{A} \cdot_{K} \frac{e^{2}}{r^{2}} \)
в. \( -K \frac{e^{2}}{r^{3}} \)
c. \( _{K} \frac{e^{2}}{r^{3}} \vec{r} \)
D. \( -K \frac{e^{2}}{r^{2}} \)
Subject: Maths
\( P \) and \( Q \) are mid point of sides RS \( \& R T \)
respectively of \( \triangle \) RST.
\( \mathrm{PQ}=5 \mathrm{cm}, \mathrm{RS}=\mathrm{RT}=10 \mathrm{cm}, \) then
perimeter of \( \triangle \mathrm{RST} \) is:
A . \( 27.5 \mathrm{cm} \)
B. \( 20 \mathrm{cm} \)
\( c .25 \mathrm{cm} \)
D. \( 30 \mathrm{cm} \)
Subject: Maths
If \( \boldsymbol{A}=\{\boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c}\}, \boldsymbol{B}=\{\boldsymbol{c}, \boldsymbol{d}, \boldsymbol{e}\}, \boldsymbol{C}= \)
\( \{a, d, f\}, \) then \( A \times(B \cup C) \) is
A \( \cdot\{(a, d),(a, e),(a, c)\} \)
в. \( \{(a, d),(b, d),(c, d)\} \)
c. \( \{(d, a),(d, b),(d, c)\} \)
D. none of these
Subject: Biology
Study the statements about chordates
and identify correct ones:
(a) Columella auris present in the middle year of amphibians is modified hyomandibula of fishes.
(b) Reptiles lay cleidoic eggs.
(c) Sphenodon is connecting link between amphibians and reptiles.
(d) Panthera tigris is an extinct animal of India.
\( A \cdot(a),(c) \)
B. \( (b),(d) \)
\( c \cdot(a),(b) \) and \( (c) \)
D. (b), (c) aand (d)
Subject: Maths
Arrange the fractions \( \frac{4}{5}, \frac{9}{11}, \frac{3}{5}, \frac{7}{12} \) in descending order.
A \( \cdot \frac{7}{12}, \frac{9}{11}, \frac{4}{5}, \frac{3}{5} \)
В. \( \frac{7}{12}, \frac{4}{5}, \frac{3}{5}, \frac{9}{11} \)
c. \( \frac{9}{11}, \frac{4}{5}, \frac{3}{5}, \frac{7}{12} \)
D. None of these
Subject: Maths
A coin is tossed \( (\mathbf{m}+\mathbf{n}) \) times \( (\mathbf{m}<\mathbf{n}) \) The probability for getting atleast 'n consecutive heads is
A \( \cdot \frac{m+2}{2^{n+1}} \)
в. \( \frac{n+2}{2^{m+1}} \)
c. \( \frac{m}{2^{n+1}} \)
D. \( \frac{(m+1) \times(m+2)}{2^{(m+n+1)}} \)
Subject: Maths
Compute \( \boldsymbol{P}(\boldsymbol{A} \mid \boldsymbol{B}) \) if \( \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 5} \) and
\( \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B})=\mathbf{0 . 3 2} \)
Subject: Maths
\( \left|\begin{array}{ccc}\boldsymbol{x} & \boldsymbol{y} & \boldsymbol{z} \\ \boldsymbol{x}^{2} & \boldsymbol{y}^{2} & \boldsymbol{z}^{2} \\ \boldsymbol{x}^{\boldsymbol{3}} & \boldsymbol{y}^{\boldsymbol{3}} & \boldsymbol{z}^{\boldsymbol{3}}\end{array}\right|=\boldsymbol{x} \boldsymbol{y} \boldsymbol{z}(\boldsymbol{x}-\boldsymbol{y})(\boldsymbol{y}-\boldsymbol{z})(\boldsymbol{z} \)
\( \boldsymbol{x}) \)
A. True
B. Falss