AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A rectangular carbon block has
dimensions \( 1.0 \mathrm{cm} \times 1.0 \mathrm{cm} \times 50 \mathrm{cm} \)
Resistance are measured first across
two square ends and then across two
rectangular ends, respectively. If
resistivity carbon is \( 3.5 \times 10^{-5} \Omega m \)
then value of measured resistances
respectively are
\( \mathbf{A} \cdot 17.5 \times 10^{-2} \Omega, 7 \times 10^{-5} \Omega \)
B . \( 7 \times 10^{-5} \Omega, 7.5 \times 10^{-2} \Omega \)
C. \( 17.5 \times 10^{-4} \Omega, 7 \times 10^{-7} \Omega \)
D. \( 7.5 \Omega, 7 \times 10^{-2} \Omega \)
Subject: Maths
\( |f(x)|=\left[\begin{array}{ccc}\sin x & \operatorname{cosec} x & \tan x \\ \sec x & x \sin x & x \tan x \\ x^{2}-1 & \cos x & x^{2}+1\end{array}\right] \)
then \( \ldots \int_{-a}^{a}|\boldsymbol{f}(\boldsymbol{x})| \boldsymbol{d} \) equals
\( A \)
в.
\( c \cdot 2 a \)
\( D \)
Subject: Chemistry
Consider the reaction:
\( \mathbf{C l}_{2}(\mathbf{a q})+\mathbf{H}_{2} \mathbf{S}(\mathbf{a q}) \rightarrow \mathbf{S}(\mathbf{s})+ \)
\( \mathbf{2 H}^{+}(\mathbf{a q})+\mathbf{2} \mathbf{C l}^{-}(\mathbf{a q}) \)
The rate equation for this reaction is \( = \)
\( \mathbf{k}\left[\mathbf{C l}_{2}\right]\left[\mathbf{H}_{2} \mathbf{S}\right] \)
Which of these mechanisms is/are consistent with this rate equation?
\( (\mathrm{A}) \mathrm{Cl}_{2}+\mathrm{H}_{2} S \rightarrow \mathrm{H}^{+}+\mathrm{Cl}^{-}+\mathrm{Cl}^{+}+ \)
\( \mathbf{H S}^{-}(\text {slow }) \)
\( \mathbf{C l}^{+}+\mathbf{H S}^{-} \rightarrow \mathbf{H}^{+}+\mathbf{C l}^{-}+\mathbf{S}(\text { fast }) \)
(B) \( \mathbf{H}_{2} \mathbf{S} \Leftrightarrow \mathbf{H}^{+}+\mathbf{H S}^{-} \) (fast
equilibrium) \( \mathbf{C l}_{2}+\mathbf{H S}^{-} \rightarrow \mathbf{2 C l}^{-}+\mathbf{H}^{+}+\mathbf{S}(\text { slow }) \)
A. B only
B. Both A and B
c. Neither A nor B
D. A only
Subject: Maths
Find the sixth term in the expansion of
\( \left(2 x^{2}-\frac{3}{7 x^{3}}\right)^{11} \)
A \( \cdot-^{11} C_{5} \frac{2^{6} 3^{5}}{7^{5}} x^{3} \)
В \( \cdot \quad^{11} C_{5} \frac{2^{6} 3^{5}}{7^{5}} x^{-3} \)
c. \( _{-11} C_{5} \frac{2^{6} 3^{5}}{7^{5}} x^{-3} \)
D. None of these
Subject: Maths
If \( \boldsymbol{x}-\frac{\mathbf{1}}{\boldsymbol{x}}=\sqrt{\mathbf{6}}, \) then \( \boldsymbol{x}^{2}+\frac{\mathbf{1}}{\boldsymbol{x}^{2}} \) is
\( A \cdot 2 \)
B. 4
\( c \cdot 6 \)
D.
Subject: Maths
Two forces of \( 1 N \) and \( P N \) act at a point so that the magnitude of resultant is \( \mathbf{1} N \) and it is perpendicular to \( 1 N . \) The
value of \( \boldsymbol{P} \) in newtons and the angle
between the \( 1 N \) and \( P N \) are:
A \( \cdot \sqrt{2}, 135^{\circ} \)
B . \( \sqrt{2}, 120^{0} \)
c. \( 1,45^{\circ} \)
D. \( 2,150^{\circ} \)
Subject: Chemistry
In the process of extraction of gold, Roastedgoldore \( +C N^{-}+H_{2} O \stackrel{O_{2}}{\rightarrow} \)
\( [X]+O H^{-}[X]+Z n \rightarrow[Y]+A u \)
Identify the complexes [X] and [Y]
A \( \cdot x=\left[A u(C N)_{2}^{-}\right], Y=\left[Z n(C N)_{4}\right]^{2} \)
B . \( x=\left[A u(C N)_{4}\right]^{3-}, Y=\left[Z n(C N)_{4}\right]^{2-} \)
C \( \cdot x=\left[\operatorname{Zn}(C N)_{2}\right]^{-}, \mathrm{Y}=\left[\operatorname{Zn}(C N)_{6}\right]^{4-} \)
D. \( x=\left[Z n(C N)_{4}\right]^{-}, Y=\left[Z n(C N)_{4}\right]^{2-} \)
Subject: Physics
Two coherent light sources \( S_{1} \) and \( \boldsymbol{S}_{2}(\boldsymbol{\lambda}=\mathbf{6 0 0 0} \boldsymbol{A}) \) are 1 mm apart from
each other. The screen is placed at a distance of \( 25 \mathrm{cm} \) from the sources. The width of the fringes on the screen
should be
A. \( 0.015 \mathrm{cm} \)
В. \( 0.013 \mathrm{cm} \)
c. \( 0.01 \mathrm{cm} \)
D. \( 0.10 \mathrm{cm} \)
Subject: Physics
sin the sind
uniform cross section is filled with
water and is mounted on a rotatable
shaft as shown in figure. If the tube is
rotated with a constant angular velocity
\( \omega, \) then
A. Water levels in both sections A and B go up
B. Water level in section A goes up and that in B comes down
c. water level in section A comes down and that in B it
goes up
D. Water levels remain same in both sections
Subject: Physics
A capacitor contains two square plates
with side lengths \( 5.0 \mathrm{cm} . \) The plates are separated by \( 2.0 \mathrm{mm} . \) Dry air fills the space between the plates. Dry air has a dielectric constant of 1.00 and
experiences dielectric breakdown when the electric field exceeds \( 3.010^{4} V / c m \) What is the magnitude of charge that
can be stored on each plate before the capacitor exceeds its breakdown limit and sends a spark between the plates?
\( \mathbf{A} \cdot 6.6 \times 10^{-8} C \)
В. \( 6.6 \times 10^{-5} C \)
c. \( 3.3 \times 10^{-7} C \)
D . 3.3 \( \times 10^{-8} \mathrm{C} \)
E . \( 8.1 \times 10^{-2} C \)
Subject: Chemistry
The monomer \( (G=M e \text { or } C l) \) when
treated with Zieglar - Natta catalyst undergo polymerisation as shown in the figure. The Zieglar-Natta catalyst is:
\( \mathbf{A} \cdot T i C l_{4} \)
в. \( R_{3} A l \)
c. \( R_{3} A l / T i C l_{4} \)
D. \( R_{3} B / T i C l_{4} \)
Subject: Maths
The number of solutions of the equation \( \tan ^{-1}\left(\frac{1}{2 x+1}\right)+\tan ^{-1}\left(\frac{1}{4 x+1}\right)= \)
\( \tan ^{-1}\left(\frac{2}{x^{2}}\right) \) is
\( A \)
B.
\( c \cdot 2 \)
D. 3
Subject: Physics
Two spheres of the same material, but
radii \( \boldsymbol{R} \) and \( \boldsymbol{3} \boldsymbol{R} \) are allowed to fall
vertically downwards through a liquid of
uniform density. The ratio of their
terminal velocities is:
A . 1: 3
B. 1: 6
c. 1: 9
D. 1: 1
Subject: Physics
Velocity of a particle moving in \( x- \) axis is given as \( v=\alpha \sqrt{x} \) where \( \alpha \) is positive
constant. If initially particle was at
origin, the position of particle at time \( t \)
is
A \( \cdot \frac{\alpha^{2} t^{2}}{4} \)
в. \( 3 \alpha^{2} \frac{t^{2}}{4} \)
c. \( \quad \alpha^{2} \frac{t^{2}}{2} \)
D. \( 3 \alpha^{2} \frac{t^{2}}{2} \)
Subject: Chemistry
\( \mathbf{1 0 0} \mathrm{mL} \) of \( \mathbf{0 . 2} \mathrm{N} \) HCl is added to \( \mathbf{1 0 0} \mathrm{mL} \)
of \( 0.18 \mathrm{N} \). NaOH and the whole volume is
made one litre. The pH of the resulting solution is:
A . 1.2
в. 2.7
c. 3.9
D. 4
Subject: Physics
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.
Subject: Physics
Water waves in a shallow dish are \( 6 \mathrm{cm} \)
long. At one point, the water moves up and down at a rate of 4.8 oscillations/s.
What is the speed of the water waves?
A. \( 0.288 \mathrm{m} / \mathrm{s} \)
в. \( 0.3 \mathrm{m} / \mathrm{s} \)
c. \( 1.25 \mathrm{m} / \mathrm{s} \)
D. \( 1.2 \mathrm{m} / \mathrm{s} \)
Subject: Physics
Two equal point charges are fixed at \( x=-a \) and \( x=+a \) on the \( X- \) axis
Another point charge \( Q \) is placed at the
origin. The change in electrical potential energy \( Q \) when it is displaced by a smal
distance \( x \) along the \( X \) -axis, is approximately proportional to
\( A \cdot x \)
в. \( x^{2} \)
c. \( x^{3} \)
D. \( 1 / x \)
Subject: Maths
If \( \bar{E} \& \bar{F} \) are the complementary events of events E \& F respectively \& if 0 \( < \) \( \boldsymbol{P}(\boldsymbol{F})<1, \) then
This question has multiple correct options
\( \mathbf{A} \cdot P(E \mid F)+P(\bar{E} \mid F)=1 \)
B . \( P(E \mid F)+P(E \mid \bar{F})=1 \)
c. \( P(\bar{E} \mid F)+P(E \mid \bar{F})=1 \)
D. \( P(E \mid \bar{F})+P(\bar{E} \mid \bar{F})=1 \)
Subject: Chemistry
The hybridisation state of the central atom and shape of the molecules is
given below. Mark the incorrect combination.
A . \( S O_{3}-s p^{2} \) hybridisation, planar triangular
B. \( S O_{2}-s p^{2} \) hybridisation, \( V \) -shaped
c. \( H_{2} S O_{4}-s p^{2} \) hybridisation, \( v \) -shaped
D. \( O_{3}-s p^{2} \) hybridisation, angular
Subject: Physics
Assertion
The total momentum of an isolated
system of particles is conserved.
Reason
The law of conservation of momentum
follows from the second and third law of
motion.
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
One liquid contains \( 22 \frac{1}{2} \% \) of water, another \( 27 \% \). A glass is filled with 5 parts of one liquid and 7 parts off the
other. What is the percentage of water
in the glass?
A \( \cdot 22 \frac{1}{8} \% \)
B. 25.75 \%
c. \( 25.25 \% \)
D. \( 25 \frac{1}{8} \% \)
Subject: Chemistry
\( C r_{2} O_{3} \)
\( C_{7} H_{16} \frac{F e_{2} O_{3}}{773 K} A \frac{K M n O_{4} / H^{\oplus}}{ } B \)
10 atm
Then what is the incorrect statement?
A. \( B \) will give effervescence with \( N a H C O_{3} \)
B. \( A \) has degree of unsaturation equal to 4
c. \( B \) with slaked lime gives a symmetrical ketone
D. None of these
Subject: Physics
Dimensions of Gyromagnetic ratio are?
A \( \cdot\left[L^{1} M^{0} T^{1} I^{1}\right] \)
B . \( \left[L^{0} M^{-1} T^{1} I\right] \)
C \( \cdot\left[L^{1} M^{0} T^{0} I^{-1}\right] \)
D \cdot \( \left[L^{-1} M^{0} T^{1} I^{1}\right] \)
Subject: Physics
Time period of oscillation for given combination will be
A \( \cdot 2 \pi \sqrt{\frac{m\left(K_{1}+K_{2}\right)}{K_{1} K_{2}}} \)
в. \( 2 \pi \sqrt{\frac{m}{K_{1}+K_{2}}} \)
c. \( 2 \pi \sqrt{\frac{m K_{1} K_{2}}{K_{1}+K_{2}}} \)
D. \( 2 \pi \sqrt{\frac{m K_{1}}{K_{2}}} \)
Subject: Maths
f \( |\vec{a}|=7,|\vec{b}|=11,|\vec{a}+\vec{b}|=10 \sqrt{3} \)
then \( |\vec{a}-\vec{b}|= \)
A . 10
B. \( \sqrt{10} \)
c. \( 2 \sqrt{10} \)
D. 20
Subject: Physics
In Young's double-slit experiment, the \( y- \) coordinates of central maxima and 10 th
maxima are \( 2 c m \) and \( 5 c m \), respectively
When the YDSE apparatus is immersed
in a liquid of refractive index \( 1.5, \) the corresponding y-coordinates will be
\( \mathbf{A} \cdot 2 c m, 7.5 c m \)
B. \( 3 \mathrm{cm}, 6 \mathrm{cm} \)
\( \mathbf{c} .2 \mathrm{cm}, 4 \mathrm{cm} \)
D. \( 4 / 3 c m, 10 / 3 c m \)
Subject: Physics
A silver atom in a solid oscillates in
simple harmonic motion in some
direction with a frequency of \( 10^{12} / \) sec.
What is the force constant of the bonds
connecting one atom with the other? (Mole wt. of silver \( =108 \) and Avagadro
number \( =\mathbf{6 . 0 2} \times \mathbf{1 0}^{\mathbf{2 3}} \mathbf{g} \mathbf{m} \mathbf{m o l}^{-\mathbf{1}} \) ).
A. \( 2.2 \mathrm{N} / \mathrm{m} \)
в. \( 5.5 \mathrm{N} / \mathrm{m} \)
c. \( 6.4 \mathrm{N} . \mathrm{m} \)
D. \( 7.1 \mathrm{N} / \mathrm{m} \)
Subject: Chemistry
Which selection applies to the process shown below?
\( \boldsymbol{C H}_{3} \boldsymbol{O H}(l) \rightarrow \boldsymbol{C H}_{3} \boldsymbol{O H}(\boldsymbol{g}) \)
A. \( \Delta H_{f u s} \)
в. \( \Delta H_{c} \)
c. \( \Delta H_{s o l n} \)
D. \( \Delta H_{v a p} \)
Subject: Physics
Two bodies of masses \( 10 \mathrm{kg} \) and \( 2 \mathrm{kg} \) are moving with velocities \( 2 \hat{i}-7 \hat{k}+ \) \( 3 \hat{j} m s^{-1} \) and \( -10 \hat{i}+35 \hat{k}-3 \hat{j} m s^{-1} \)
respectively. The velocity of their centre of mass is
A \( \cdot 2 \hat{i} m s^{-1} \)
в. \( 2 \hat{j} \) ms\( ^{-1} \)
\( \mathbf{c} \cdot(2 \hat{j}+2 \hat{k}) m s^{-1} \)
D. \( (2 \hat{i}+2 \hat{j}+2 \hat{k}) m s^{-1} \)
Subject: Physics
A longer conducting cylinder carrying a
charge \( +q \) is surrounded by a
conducting cylindrical shell having
charge \( -2 q . \) The charge on the inner
and outer side of conducting shell is:
\( \mathbf{A} \cdot q,-q \)
B. \( -q,-3 q \)
\( \mathbf{c} .-q,+3 q \)
\( \mathbf{D} \cdot-q,-q \)
Subject: Maths
If a sphere and a cube have the same
surface area, then the ratio of the
diameter of sphere to edge of the cube is
A. \( \sqrt{6}: \sqrt{\pi} \)
(年) \( \sqrt{\pi} \). \( \pi \)
B. \( \sqrt{\pi}: \sqrt{6} \)
c. 2: 1
D. 1: 2
Subject: Physics
When n small drops of a conducting
liquid, each of surface charge density \( \sigma \)
and radius \( r \) are made to combine to
form a big drop of radius \( R \), then:
A \( . \) potential becomes \( n^{1 / 3} \) times original potential and charge density decreases to \( n^{1 / 3} \) times original charge density
B. potential becomes \( n^{2 / 3} \) times and charge density increases to \( n^{1 / 3} \) times original charge density
C . potential and charge density decrease to \( n^{4 / 3} \) times original values
D. potential and charge density increase to n times original values
Subject: Physics
In a potention meter of one metre length an unknown emf voltage source is balanced at \( 60 \mathrm{cm} \) length of potention meter wire, while a \( 3 v \) battery is balanced at \( 45 \mathrm{cm} \) length. Then, the emf of the unknown voltage source is :
\( A \cdot 3 v \)
B. 2.25
\( c \cdot 4 v \)
D. \( 4.5 \mathrm{v} \)
Subject: Chemistry
Assertion
Chlorine reacts with freshly prepared calcium hydroxide to produce bleaching powder.
Reason
Chlorine has a great affinity for
hydrogen.
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
Evaluate: \( \left|\begin{array}{ccc}\mathbf{1} & \boldsymbol{b} \boldsymbol{c} & \boldsymbol{a}(\boldsymbol{b}+\boldsymbol{c}) \\ \mathbf{1} & \boldsymbol{c} \boldsymbol{a} & \boldsymbol{b}(\boldsymbol{c}+\boldsymbol{a}) \\ \boldsymbol{1} & \boldsymbol{a} \boldsymbol{b} & \boldsymbol{c}(\boldsymbol{a}+\boldsymbol{b})\end{array}\right| \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c . a b c \)
D. \( a^{2}+b^{2}+c^{2} \)
Subject: Maths
If \( P(x, y, x) \) is a point on the line
segment joining \( Q(2,2,4) \) and \( R(3,5,6) \) such that the projection of \( O P \) on the axis are \( \frac{13}{5}, \frac{19}{5}, \frac{26}{5} \)
respectively, then \( P \) divides \( Q R \) in the
ratio
A . 1: 2
B. 3: 2
\( c \cdot 2: 3 \)
D. 1: 3
Subject: Physics
The position of centre of mass of a system consisting of two particles of
masses \( m_{1} \) and \( m_{2} \) separated by a
distance \( L \) apart, from \( m_{1} \) will be
A \( \cdot \frac{m_{1} L}{m_{1}+m_{2}} \)
В. \( \frac{m_{2} L}{m_{1}+m_{2}} \)
c. \( \frac{m_{2}}{m_{1}} L \)
D. \( \frac{L}{2} \)
Subject: Physics
(2) Explaıri clearly, wırn ex \( \mathbf{S}, \) Ine
distinction between:
(a) magnitude of displacement over an interval of time and the total length of
path covered by a particle over the same interval;
(b) magnitude of average velocity over an interval of time, and the average
speed over the same interval.
Show in both (a) and (b) that the second
quantity is either greater than or equal
to the first. When is the equality sign
true?
(ii) A man walks on a straight road
from his home to a market \( 2.5 k m \) away
with a speed of \( 5 k m h^{-1} \). Finding the
market closed, he instantly turns and walks back home with a speed of
\( 7.5 k m h^{-1} . \) What is the:
(a) magnitude of average velocity, and
(b) average speed of the man over the interval of time (i) 0 to 30 min, (ii) 0 to
\( \mathbf{5 0 m i n},(\text { iii) } 0 \text { to } 40 m i n ? \)
Subject: Maths
Four angles of a quadrilateral are in the ratio \( 3: 5: 7: 9 . \) The greatest angle is
A . \( 125^{\circ} \)
B . \( 75^{\circ} \)
\( \mathbf{c} \cdot 135^{\circ} \)
D. \( 120^{\circ} \)
Subject: Maths
\( \lim _{x \rightarrow \frac{n}{2}} \frac{1-(\sin x)^{\frac{-1}{3}}}{1-(\sin x)^{\frac{-2}{3}}} \) is?
\( A \)
B. \( \frac{3}{2} \)
\( c \cdot 1 \)
2
\( D \)
Subject: Physics
Assertion
Work done by friction on a body sliding
down an inclined plane is negative
Reason
Work done is greater than zero, if angle between force and displacement is
acute or both are in same direction
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: Physics
Prove theoretically the relation between
e.m.f. induced in a coil and rate of
change of magnetic flux in
electromagnetic induction. A paralle plate air condenser has a capacity of 20
\( \mu F . \) What will be the new capacity if
(a) the distance between the two plates is doubled?
(b) a marble slab of dielectric constant
8 is introduced between the two plates?
Subject: Maths
Let \( \boldsymbol{f}:[\mathbf{1}, \mathbf{3}] \rightarrow \mathbf{R} \) be a continuous
function that is differentiable in \( (\mathbf{1}, \mathbf{3}) \)
and \( f^{\prime}(x)=|f(x)|^{2}+4 \) for all \( x \in(1,3) \)
Then?
This question has multiple correct options
A \( . f(3)-f(1)=5 \) is true
B. \( f(3)-f(1)=5 \) is false
c. \( f(3)-f(1)=7 \) is false
D. \( f(3)-f(1)<0 \) only at one point of (1,3)
Subject: Chemistry
Determine the osmotic pressure of a solution prepared by dissolving \( 2.5 \times \) \( 10^{-2} g \) of \( K_{2} S O_{4} \) in \( 2 L \) of water at 25
assuming that it is completely dissociated
\( \left(R=0.0821 L \operatorname{atm} K^{-1} m o l^{-1}, \) Molar \right.
\( \operatorname{mass} \) of \( K_{2} S O_{4}=174 \mathrm{g} m o l^{-1} \) ).
Subject: Physics
In the arrangement, shown in figure, pulleys are massless and frictionless and threads are inextensible block of
\( \operatorname{mass} \boldsymbol{m}_{2} \) will remain at rest if.
\( ^{\mathrm{A}} \cdot \frac{1}{m_{1}}=\frac{1}{m_{2}}+\frac{1}{m_{3}} \)
в. \( \frac{4}{m_{1}}=\frac{1}{m_{2}}+\frac{1}{m_{3}} \)
\( \mathbf{c} \cdot m_{1}=m_{2}+m_{3} \)
D. \( \frac{1}{m_{3}}=\frac{2}{m_{2}}+\frac{3}{m_{1}} \)
Subject: Chemistry
In the following electronic configuration
\( n s^{2}(n-1) d^{0-1}(n-2) f^{1-14} . \) If value
of \( (\boldsymbol{n}-\mathbf{1})=\mathbf{6} \) the configuration will be
of:
A. lanthanides
B. d- block
c. actinides
D. s - block
Subject: Chemistry
\( \boldsymbol{A}+\boldsymbol{B} \longrightarrow \boldsymbol{C} ; \boldsymbol{\Delta} \boldsymbol{H}=+\boldsymbol{6} \boldsymbol{0} \boldsymbol{K} \boldsymbol{J} / \boldsymbol{m o l} \)
\( \boldsymbol{E}_{\boldsymbol{a} t} \) is \( 150 \mathrm{kj} . \) What is the activation energy for the backward reation?
A . 210 k.
B. 105kJ
c. 90 k
D. 145kJ
Subject: Chemistry
Which one of the following orders is
correct regarding the \( -I \) effect of the
substituents?
A. \( -N R_{2}<-O R>-F \)
B . \( -N R_{2}>-O R>-F \)
c. \( -N R_{2}<-O R<-F \)
D. \( -N R_{2}>-O R<-F \)
Subject: Maths
\( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{lll}{[\boldsymbol{x}]+[-\boldsymbol{x}],} & \boldsymbol{w} \boldsymbol{h} e \boldsymbol{n} & \boldsymbol{x} \neq \boldsymbol{2} \\ \boldsymbol{\lambda} & , & \boldsymbol{w} \boldsymbol{h} \boldsymbol{e} \boldsymbol{n} & \boldsymbol{x}=\boldsymbol{2}\end{array}\right. \)
If \( f(x) \) is continuous at \( x=2 \) then, the
value of \( \lambda \) will be
A . -1
B.
c.
\( D \)
Subject: Physics
One point electric charge \( Q \) is placed at
the point \( P . A \) closed surface is placed
near the point \( P . \) The electrical flux
passing through a closed surface will be
\( \mathbf{A} \cdot Q \epsilon_{0} \)
В . \( \epsilon_{0} / Q \)
\( c \cdot Q / \epsilon_{0} \)
D. zero
Subject: Maths
Let \( A \) and \( B \) be two finite sets having \( m \)
and \( n \) elements respectively. Then the
total number of mapping from \( \boldsymbol{A} \) to \( \boldsymbol{B} \) is:
A . \( m n \)
B. \( 2^{\text {mn }} \)
\( \mathrm{c} \cdot m^{n} \)
D. \( n^{\text {m }} \)
Subject: Maths
If \( \boldsymbol{f}:\left[\mathbf{0}, \frac{\boldsymbol{\pi}}{\mathbf{2}}\right] \rightarrow[\mathbf{0}, \infty] \) be a function
defined by \( y=\sin \left(\frac{x}{2}\right), \) then \( f \) is
A . Injective
B. Surjective
c. Bijective
D. None of these
Subject: Chemistry
The solution of a salt of a weak acid and
weak base will have \( \mathrm{pH}:\left(K_{b}=1 \times 10^{-6}\right. \)
and \( \boldsymbol{K}_{\boldsymbol{a}}=\mathbf{1} \times \mathbf{1 0}^{-\mathbf{4}} \mathbf{)} \)
A . 7.0
B. 8.0
\( c \cdot 6 \)
D. 4.0
Subject: Physics
The extension produced in a wire by the application of a load is \( 3.0 \mathrm{mm} \). The
extension produced in a wire of the same material and length but half the radius by the same load is:
\( \mathbf{A} \cdot 5 \mathrm{mm} \)
B. \( 9 \mathrm{mm} \)
\( c .12 \mathrm{mm} \)
D. \( 13 \mathrm{mm} \)
Subject: Physics
Two coils \( A \) and \( B \) having turns 300 and 600 respectively are placed near each other, on passing a current of 3.0 ampere in \( A \), the flux linked with \( A \) is 1.2
\( x 10^{-4} \) weber and with \( B \) it is \( 9.0 \times 10^{-5} \)
weber. The mutual induction of the
system is:
Subject: Chemistry
\( E_{1}, E_{2}, E_{3} \) are the emf values of the
three galvanic cells respectively.
(i) \( Z n\left|Z n_{1 M}^{2+}\right|\left|C u_{0.1 M}^{2+}\right| C u \)
\( (\text { ii }) Z n\left|Z n_{1 M}^{2+}\right|\left|C u_{1 M}^{2+}\right| C u \)
(iii) \( Z n\left|Z n_{0.1 M}^{2+} \| C u_{1 M}^{2+}\right| C u \)
Which one of the following is true?
A \( . E_{2}>E_{3}>E_{1} \)
в. \( E_{3}>E_{2}>E_{1} \)
c. \( E_{1}>E_{2}>E_{3} \)
D. \( E_{1}>E_{3}>E_{2} \)
Subject: Physics
A steel bolt is inserted into a copper
tube as shown in figure. Find the forces induced in the bolt and in the tube when
the nut is turned through one revolution. Assume that the length of the tube is \( l \), the pitch of the bolt thread
is \( h \) and the cross-sectional areas of the
steel bolt and the copper tube are \( \boldsymbol{A}_{s} \)
and \( A_{c}, \) respectively
Subject: Chemistry
Metals are usually hard. Hence metals are strong and can with stand heavy loads over them. Due to this property they are difficult to cut and can be used in the construction of heavy machines, buildings etc. On the other hand, non-
metals are usually brittle. On hammering them they break into small pieces converting themselves into the fine powder

In the following elements identify the element that is relatively brittle. This question has multiple correct options
A. sulphur
B. Diamond
c. Iron
D. Magnesium
Subject: Physics
The figure represents two bodies of masses \( 10 \mathrm{kg} \) and \( 20 \mathrm{kg} \) and moving with an initial velocity of \( 10 m s^{-1} \) and
\( 5 m s^{-1}, \) respectively. They are colliding with each other, After collision, they are
moving with velocities \( 12 m s^{-1}, 4 m s^{-1} \) respectively. The time of collision is 2 s.
Then calculate \( F_{1} \) and \( F_{2} \)
Subject: Physics
In a certain gas, the ratio of the speed of sound and root mean square speed is \( \frac{\mathbf{5}}{\mathbf{g}} \) The molar heat capacity of the gas in a process given by \( \mathrm{PT}= \) constant is (Take \( R=2 \) cal/mole \( K \) ). Treat the gas as ¡deal.
\( A \cdot \frac{f+2}{f} \)
в. \( \frac{3 R}{2} \)
c. \( \frac{5 R}{2} \)
D. \( \frac{7 R}{2} \)
Subject: Maths
The value of \( \tan \left(2 \tan ^{-1} 1 / 5-\pi / 4\right) \) is?
A. \( -7 / 17 \)
в. \( +7 / 17 \)
c. \( -12 / 17 \)
D. \( -+2 / 17 \)
Subject: Maths
Find determinant of \( \left|\begin{array}{lll}\mathbf{1} & \mathbf{0} & \mathbf{2} \\ \mathbf{2} & \mathbf{1} & \mathbf{0} \\ \mathbf{3} & \mathbf{2} & \mathbf{1}\end{array}\right| \)
Subject: Chemistry
A sample of a hydrate of barium chloride weighing \( 61 \mathrm{g} \) was heated until all the water of hydration is removed. The dried sample weighed 52 g. The formula of the hydrated salt is : (atomic mass, \( \mathrm{Ba}=137 \mathrm{amu}, \mathrm{Cl}=35.5 \text { amu }) \)
A. BaCl \( _{2} .4 \mathrm{H}_{2} \mathrm{O} \)
B. BaCl_.2H_O
c. ваСг_на 0
D. BaCl \( _{2} .3 \mathrm{H}_{2} \mathrm{O} \)
Subject: Maths
Which of the following equations shows
the shaded region in the above figure?
A \( \cdot x\left(y-\frac{2}{3} x\right) \geq 0 \)
B. \( x\left(y-\frac{3}{2} x\right) \geq 0 \)
c. \( x\left(y+\frac{3}{2} x\right) \geq 0 \)
D \( \cdot x\left(y+\frac{2}{3} x\right) \geq 0 \)
E \( \cdot x\left(y+\frac{3}{2} x\right) \leq 0 \)