AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
The parallel plate capacitors with different distance between the plates
are connected in parallel to voltage
source as shown in the figure. A point
positive charge is moved from a point
that is exactly in the middle between
the plates of the capacitor \( c_{1} \) to a point
2 in capacitor \( c_{2} \) that lies at the plates
of \( c_{1} \). Then the work done by the electric
force is.
A. positive
B. negative
c. zero
D. data insufficient.
Subject: Maths
A person goes to work by car, train or bus. The probabilities of person travelling by there modes are \( 3 / 10,1 / 2 \) and \( 1 / 5 \) respectively. It is found that chance of person being late for work are \( \mathbf{3} / \mathbf{7}, \mathbf{1} / \mathbf{7} \) and \( \mathbf{5} / \mathbf{7} \) by respective modes
Given that on particular day person reaches late, find the probability that on that day he had travelled by train
Subject: Chemistry
A coffee cup calorimeter initially contains
\( 125 g \) of water at a temperature of \( 24.2^{0} C \)
After (10.5gm) is added to the water at the
same temperature, the final temperature becomes \( 21.1^{0} \mathrm{C} \). The heat of solution is:
\( A \cdot 85 J / g \)
B. 110 J/g
c. 270 J/g
D. 167 J/g
Subject: Maths
If \( f(x)=a x+b \) and \( f(f(f(x)))= \)
\( 27 x+13 \) where a and b are real
numbers, then-

This question has multiple correct options
\( A \cdot a+b=3 \)
B. \( a+b=4 \)
\( c \cdot f^{\prime}(x)=3 \)
D. f'(x)=-3
Subject: Maths
Assertion (A): The principal amplitude
of complex number \( \boldsymbol{x}+\boldsymbol{i} \boldsymbol{x} \) is \( \frac{\boldsymbol{\pi}}{\boldsymbol{4}} \)
Reason (R): The principal amplitude of a
complex number \( \boldsymbol{x}+\boldsymbol{i} \boldsymbol{y} \) is \( \frac{\boldsymbol{\pi}}{\boldsymbol{4}} \) if \( \boldsymbol{y}=\boldsymbol{x} \)
A. Both A and R are true and R is the correct explanation of A
B. A is true R is false
c. A is false, R is true
D. Both A and R are false
Subject: Physics
A parallel plate capacitor is made of two
square plates of side ' \( a \) ', separated by a
distance \( d(d<<a) \). The lower
triangular portion is filled with a
dielectric of dielectric constant \( \boldsymbol{K}, \) as
shown in the figure. The capacitance of this capacitor is :
\( \mathbf{A} \cdot \frac{1}{2} \frac{k \in_{0} a^{2}}{d} \)
B. \( \frac{k \in_{0} a^{2}}{d} \ln K \)
c. \( \frac{k \in_{0} a^{2}}{d(K-1)} \ln K \)
D. \( \frac{k \in_{0} a^{2}}{2 d(K+1)} \)
Subject: Physics
The resistance of a hot tungsten filament is about 10 times the cold
resistance. What will be the resistance
of \( 100 W, 200 V \) lamp when not in use?
A . \( 20 \Omega \)
B. \( 40 \Omega \)
c. \( 200 \Omega \)
D. \( 400 \Omega \)
Subject: Physics
Two particle performed simple harmonic motion of same frequency an
about same mean position. Their
amplitude is same and is equal to \( \boldsymbol{A} \)
and their time period is \( T . \) If at \( t=0 \)
separation is maximum and is \( A \), their separation at \( t=\frac{T}{12} \) is:-
A \( \cdot \quad A \frac{\sqrt{3}}{2} \)
B. \( A \)
c. \( \frac{A}{\sqrt{2}} \)
D. \( \frac{A}{2} \)
Subject: Maths
If \( l=\lim _{n \rightarrow 3} \frac{x^{2}-9}{\sqrt{x^{2}+7}-4} \) and \( m= \)
\( \lim _{n \rightarrow-3} \frac{x^{2}-9}{\sqrt{x^{2}+7}-4}, \) then
\( \mathbf{A} \cdot l \neq m \)
B. \( l=2 m \)
c. \( l=-m \)
\( \mathbf{D} \cdot l=m \)
Subject: Maths
To find out the concentration of \( S O_{2} \) in
the air (in parts per million, i.e., ppm),
the data was collected for 30 localities
in a certain city and is presented below:
Concentration of \( S O_{2}(\text { in ppm }) \) Frequency
\( 0.00-0.04 \)
\( 0.04-0.08 \)
\( 0.08-0.12 \)
\( 0.12-0.16 \)
\( 0.16-0.20 \)
\( 0.20-0.24 \)
Find the mean concentration of \( S O_{2} \) in
the air.
Subject: Maths
A and B are two square matrices of
same order and \( A^{\prime} \) denotes the
transpose of \( A \), then
\( \mathbf{A} \cdot(A B)^{\prime}=B^{\prime} A^{\prime} \)
B. \( (A B)^{\prime}=A^{\prime} B^{\prime} \)
\( \mathbf{C} \cdot A B=0 \Rightarrow|A|=0 \) or \( |B|=0 \)
D . \( A B=0 \Rightarrow A=0 \) or \( B=0 \)
Subject: Physics
N moles of a monoatomic gas is carried
round the reversible rectangular cycle
ABCDA as shown in the diagram. The
temperature at \( \boldsymbol{A} \) is \( \boldsymbol{T}_{\mathbf{0}} . \) The
thermodynamic efficiency of the cycle
is
A. \( 15 \% \)
B. \( 50 \% \)
\( c \cdot 20 \% \)
D. \( 25 \% \)
Subject: Chemistry
Which of the following is/are autoredox
reactions?
This question has multiple correct options
A \( \cdot P_{4}+O H \longrightarrow H_{2} P O_{2}^{\ominus}+P H_{3} \)
B . \( S_{2} O_{3}^{2-} \rightarrow S O_{4}^{2-}+S \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{O}_{2} \longrightarrow \mathrm{H}_{2} \mathrm{O}+\mathrm{O}_{2} \)
D. \( _{A g C l}+N H_{3} \rightarrow\left[A g\left(N H_{3}\right)_{2}\right] C l \)
Subject: Physics
A stone is projected from the ground
with a velocity of \( 14 \mathrm{ms}^{-1} . \) One second
later it clears a wall \( 2 m \) high. The angle
of projection is \( \left(\boldsymbol{g}=\mathbf{1 0} \boldsymbol{m} \boldsymbol{s}^{-2}\right) \)
A \( \cdot 45^{\circ} \)
B. \( 30^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 15^{\circ} \)
Subject: Maths
A prisoner escapes from a jail and is equally likely to choose one of the four roads I, II, III or IV to reach away from the hands of law. If he choose I road, he is successful with probability \( 1 / 6 \) and for
I, III and IV this is \( 1 / 8,1 / 10 \) and \( 1 / 12 \). If the prisoner is successful, the probability that he chose road
Subject: Physics
(a) How does an unpolarized light incident on a Polaroid get polarized? Describe briefly, with the help of a necessary diagram, the polarization of light by reflection form a transparent medium.
(b) Two polaroids \( ^{\prime} A^{\prime} \) and \( ^{\prime} B^{\prime} \) are kept in crossed position. How should a third
Polaroid ' \( C^{\prime} \) be placed between them so that the intensity of polarized light transmitted by Polaroid \( B \) reduces to 1/8th of the intensity of unpolarized light incident of \( \boldsymbol{A} \) ?
Subject: Maths
Using the Mathematical induction,
show that for any number \( n \geq 2 \)
\[
\begin{array}{c}
\frac{1}{1+2}+\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+ \\
\dots+\frac{1}{1+2+3+\ldots+n}=\frac{n-1}{n+1}
\end{array}
\]
Subject: Maths
If \( \boldsymbol{x}=\boldsymbol{y} \cos \frac{\boldsymbol{2} \boldsymbol{\pi}}{\boldsymbol{3}}=\boldsymbol{z} \cos \frac{\boldsymbol{4} \boldsymbol{\pi}}{\boldsymbol{3}}, \) then \( \boldsymbol{x} \boldsymbol{y}+ \)
\( \boldsymbol{y} \boldsymbol{z}+\boldsymbol{z} \boldsymbol{x}= \)
A . -1
B. 0
c. 1
D. 2
Subject: Maths
If \( |x|<1 \) then the coefficient of \( x^{5} \) in the expansion of \( \frac{3 x}{(x-2)(x-1)} \) is
A \( \cdot \frac{33}{32} \)
в. \( -\frac{33}{32} \)
c. \( \frac{31}{32} \)
D. \( -\frac{33}{34} \)
Subject: Maths
\( \ln \Delta A B C, \) a \( \sin (B-C)+b \sin (C- \)
\( A)+c \sin (A-B)= \)
\( A \)
B. \( a+b+c \)
c. \( a^{2}+b^{2}+c^{2} \)
D \( \cdot 2\left(a^{2}+b^{2}+c^{2}\right) \)
Subject: Physics
The resistivity of a conductor with a
current density of \( 2.5 A m^{-2} \) when an
electric field \( 5 \times 10^{-8} V m^{-1} \) is applied
to it, is
A \( \cdot 1.0 \times 10^{-8} \Omega m \)
в. \( 2.0 \times 10^{-8} \Omega \) т
\( \mathbf{c} \cdot 0.5 \times 10^{-8} \Omega m \)
D. \( 12.5 \times 10^{-8} \Omega m \)
Subject: Chemistry
According to Henry's law 'the partial pressure of the gas in vapour phase \( (p) \) is proportional to the mole fraction of
the gas in solution. The correct statement about Henry's constant is:
A . higher the value of \( K_{H} \) at a given pressure, higher is the solubility of the gas
B. higher the value of \( K_{H} \) at a given pressure, lower is the solubility of the gas
\( \mathrm{c} \cdot K_{H} \) is not a function of nature of gas
D. \( K_{H} \) value for all gases is same at a given pressure
Subject: Physics
Assertion
A Diamond sparkles more than a glass imitation cut to the same shape.
Reason
The refractive index of diamond is less
than that of glass.
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
number of runs scored by some top
batsmen of the world in one day
international cricket matches:
\begin{tabular}{ll} 
Runs scored & No. of batsman \\
\( 3000-4000 \) & 4 \\
\( 4000-5000 \) & 18 \\
\( 5000-6000 \) & 9 \\
\( 6000-7000 \) & 7 \\
\( 7000-8000 \) & 6 \\
\( 8000-9000 \) & 3 \\
\( 9000-10000 \) & 1 \\
\( 10000-11000 \) & 1 \\
\hline
\end{tabular}
Find the mode of the data
A .4608 .695652
B. 4408.695652
c. 4202.695652
D. 4882.69
Subject: Chemistry
Assertion
When the unshared pairs house in the
hybrid orbitals, its consideration
becomes accountable and it is referred
to as hybrid lone pair moment.
Reason
The hybrid orbital concentrated the electron cloud in some particular directions and the electron cloud
remains under the control of a single nucleus.

Read the above assertion and reason
and choose the correct option regarding
¡t.
A. Assertion is true, Reason is true and Reason is correct explanation for Assertion
B. Assertion is true, Reason is true and Reason is not the correct explanation for Assertion
C. Assertion is true, Reason is false
D. Assertion is false, Reason is true
Subject: Maths
Let \( f \) be a function defined for all \( \boldsymbol{x} \boldsymbol{\epsilon} \boldsymbol{R} \)
If \( f \) is differentiable and \( f\left(x^{3}\right)=x^{5} \) for
all \( \boldsymbol{x} \boldsymbol{\epsilon} \boldsymbol{R}(\boldsymbol{x} \neq \boldsymbol{0}) \) then the value of
\( \boldsymbol{f}^{\prime}(\mathbf{2 7}) \) is
A . 15
B. 45
c. 0
D. None
Subject: Physics
The length, breadth and thickness of a block are given by \( l=12 \mathrm{cm}, b=6 \mathrm{cm} \)
and \( t=2.45 \mathrm{cm} . \) The volume of the
block according to the idea of significant figure should be
A \( .2 \times 10^{2} \)
В. \( 2 \times 10^{2} c m^{3} \)
c. \( 1.763 \times 10^{2} c m \)
D. None of these
Subject: Biology
Identify the correct sequence of
taxonomical category
A. Species \( \rightarrow \) order \( \rightarrow \) phylum \( \rightarrow \) kingdom
B. Genus \( \rightarrow \) species \( \rightarrow \) order \( \rightarrow \) kingdom
C. Genus \( \rightarrow \) species \( \rightarrow \) phylum \( \rightarrow \) order
D. Genus \( \rightarrow \) species \( \rightarrow \) kingdom \( \rightarrow \) phylum
Subject: Chemistry
Which of the following statements(s)
is/are correct?
This question has multiple correct options
\( \mathbf{A} \cdot B_{2} H_{6} \) is non-planar
B. \( B_{2} H_{6} \) is polar
\( \mathbf{C} \cdot B_{2} H_{6} \) is \( e^{-} \) deficient
D. \( B_{2} H_{6} \) has two \( 3 C-2 e^{-} \) bond
Subject: Physics
The value of Faraday number in Sl unit
is:
A. 9.65 coulomb \( / \mathrm{kg} \) - equivalent
B . \( 9.65 \times 10^{7} \) coulomb \( / \mathrm{kg} \) - equivalent
c. \( 9.65 \times 10^{-7} \) coulomb / \( k g \) - equivalent
D. 9.65 coulomb \( / g \) - equivalent
Subject: Physics
\( A 20 V, 750 \mathrm{Hz} \) source is connected to a
series combination of \( \mathrm{R}=100 \Omega, \mathrm{C}=10 \)
\( \mu F \) and \( L=0.1803 H . \) Calculate the time
in which resistance will get heated by
\( 10^{\circ} \mathrm{C} . \) (If thermal capacity of the
material \( =2 \mathrm{J} /^{\circ} \mathrm{C} \)
A. 328 sec
B. 348 sec
c. \( 3.48 \mathrm{sec} \)
D. \( 4.32 \mathrm{sec} \)
Subject: Chemistry
Which of the following reaction is used to prepare colloidal sol by double decomposition?
A. \( A s_{2} O_{3}+3 H_{2} S \rightarrow A s_{2} S_{3}+3 H_{2} O \)
B . \( 2 A u C l_{3}+3 H C H O+3 H_{2} O \rightarrow 2 A u+3 H C O O H+ \)
\( 6 H C l \)
c. \( S O_{2}+2 H_{2} S \rightarrow 3 S+2 H_{2} O \)
D. \( F e C l_{3}+3 H_{2} O \rightarrow F e(O H)_{3}+3 H C l \)
Subject: Physics
\( P \) is a variable point in the square formed by the lines \( \boldsymbol{x}=\pm \mathbf{1} \) and \( \boldsymbol{y}=\pm \mathbf{1} \)
P moves such. that its distance from
the origin is loss than its distance from
any side of square. The area traced by the point \( P \) is
A \( \cdot \frac{4}{3}(4 \sqrt{2}+1) \)
B . \( \frac{4}{3}(4 \sqrt{2}-1) \)
c. \( \frac{4}{3}(4 \sqrt{2}-3) \)
D - \( \frac{4}{3}(4 \sqrt{2}-5) \)
Subject: Physics
Starting from a stationary position, Rahul paddles his bicycle to attain a velocity of \( 6 m s^{-1} \) in \( 30 s . \) Then he applies brakes such that the velocity of the bicycle cones down to \( 4 m s^{-1} \) in the
next \( 5 s . \) Calculate the acceleration of
the bicycle in both the cases.
Subject: Biology
Which of the following reactions is endergonic?
\( \mathbf{A} \cdot A T P \rightarrow A D P+P_{i} \)
B \( \cdot N A D H \rightarrow N A D^{+}+H^{+} \)
\( \mathbf{c} \cdot\left(C H_{2} O\right)_{n}+O_{2} \rightarrow C O_{2}+H_{2} O \)
D. None of the above
Subject: Physics
A NOR gate and a NAND gate are
connected as shown in the figure. Two different sets of inputs are given to this set up. In the first case, the input to the
gates are \( A=0, B=0, C=0 . \) In the second
case, the inputs are \( A=1, B=0, C=1 . \) The output D in the first case and second case respectively are
A. 0 and 0
B. O and 1
c. 1 and 0
D. 1 and 1
Subject: Physics
The cycle is shown in figure is made of
one mole of perfect gas in a cylinder
with a piston. The processes \( A \) to \( B \) and \( \mathrm{C} \) to \( \mathrm{D} \) are isochoric whereas process \( \mathrm{B} \)
to \( C \) and \( D \) to \( A \) are adiabatic, the work
done in one cycle is \( \left(V_{A}=V_{B}=V, V_{C}=\right. \)
\( \left.V_{D}=2 V \text { and } \Upsilon=5 / 3\right) \)
A \( \cdot\left[1-4^{3 / 2}\right]\left(P_{B}-P_{A}\right) V \)
B \( \cdot \frac{3}{2}\left[1-3^{2 / 3}\right]\left(P_{B}-P_{A}\right) V \)
c. \( \frac{3}{2}\left[1-2^{-2 / 3}\right]\left(P_{B}-P_{A}\right) V \)
D. \( \frac{5}{2}\left[1-2^{-2 / 3}\right]\left(P_{B}-P_{A}\right) V \)
Subject: Maths
The curve \( y=a x^{2}+b x+c \) passes
through the point (1,2) and its tangent
at origin is the line \( y=x \). The area
bounded by the curve, the ordinate of the curve at minima an the tangent line
is
A \( \cdot \frac{1}{24} \)
B. \( \frac{1}{12} \)
\( c \cdot \frac{1}{8} \)
D. \( \frac{1}{6} \)
Subject: Chemistry
How do we differentiate between \( \boldsymbol{F} \boldsymbol{e}^{\boldsymbol{3}+} \)
and \( C r^{3+} \) in group III?
A . By taking excess of \( N H_{4} O H \)
B. By increasing \( N H_{4}^{+} \) ion cocentration
C. By decreasing \( O H^{-} \) ion concentration
D. Both (b) and (c)
Subject: Chemistry
Assertion
Benzene \( \left(C_{6} H_{6}\right) \) can be drawn as a
series of resonance structures.
Reason
Its bonds are a hybrids of single and double bond character.
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
According to Joule's law, if the potential difference across a conductor of
resistivity \( \rho \) remains constant, then the
heat produced in the conductor is
proprotional to
\( A \cdot \frac{1}{\rho} \)
в. \( \frac{1}{\sqrt{\rho}} \)
\( \mathbf{c} \cdot \rho^{2} \)
D.
Subject: Maths
If \( \boldsymbol{A}=\{\boldsymbol{x}:-\mathbf{1} \leq \boldsymbol{x} \leq \mathbf{1}\}=\boldsymbol{B} . \) Discuss
the following function w.r.t one-one onto bijective and write their characteristics \( \boldsymbol{f}(\boldsymbol{x})=\frac{\boldsymbol{x}}{\boldsymbol{2}} \)
A. one one, into
B. one one, onto
c. many one, into
D. many one, onto
Subject: Chemistry
Compare the concentrations of each of the species \( N a^{+}, H^{+} \) and \( C N \) in the
solution.
A \( \cdot N a^{+}>O H^{-}>C N^{-} \)
В. \( C N^{-}>O H^{-}>N a^{+} \)
c. \( N a^{+}>C N^{-}>O H^{-} \)
D. \( O H^{-}>C N^{-}>N a^{+} \)
Subject: Physics
Which of the following gives off a purple vapour when sublimes?
A. Sodium hydroxide, NaOH(s)
B. Graphite, c(s)
c. Iron(III) chloride, \( F e C l_{3}(s) \)
D. sucrose, \( C_{12} H_{22} O_{11} \) (s)
E . lodine, \( I_{2} \) (s)
Subject: Chemistry
The vapours of \( H g \) absorb some electrons accelerated by a potential diff of 4.5 volt as a result of which light is emitted. If the full energy of single
incident \( e^{-} \) is supposed to be converted
into light emitted by single \( \boldsymbol{H} \boldsymbol{g} \) atom
find the wave no. \( \left(\operatorname{in} m^{-1}\right) \) of the light.
Subject: Maths
If the polynomial \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left(6 x^{4}+8 x^{2}+17 x^{2}+21 x+7\right) \) is
divided by another polynomial \( g(x)= \)
\( 3 x^{2}+4 x+1 \) the remainder is \( (a x+b) \)
Find \( a \) and \( b \)
Subject: Biology
Match the items given in Column I with
those in Column II and select the correct
option given below:
Column I
\( a \)
Tricuspid \( \quad 1 \quad \) Between left atrium valve
\( b \)
Bicuspid
valve 2 Between right ventricle and pulmonary artery
Semilunar
valve Between right
\( \mathrm{C} \)
3 atrium an
ventricle een right
m and right
icle
\( \mathbf{A} \cdot A-1, B-2, C-3 \)
B \( . A-3, B-1, C-2 \)
c. \( A-2, B-1, C-3 \)
D. \( A-1, B-3, C-2 \)
Subject: Chemistry
Satpal organized a 'health camp' for the poor farmers living in a nearby village.
After check-up, he was shocked to see
that most of the farmers suffered from
cancer due to regular exposure to pesticides and many were diabetic. They distributed free medicines to
them. Dr. Satpal immediately reported
the matter to the National Human
Rights Commission (NHRC). On the
suggestions of NHRC, the government decided to provide medical care,
financial assistance, setting up of super-speciality hospitals for treatment and prevention of the deadly disease in the affected villages all over India.
(i) Write the values shown by
(a) Dr.
Satpal
(b) NHRC?
(ii) What type of analgesics are chiefly used for the relief of pains of terminal
cancer?
(iii) Give an example of artificial
sweetener that could have been
recommended to diabetic patients.
Subject: Maths
Assertion
\( \int_{-1}^{1} \frac{\sin x-x^{4}}{4-|x|} d x \) is same as
\( \int_{0}^{1} \frac{-2 x^{4}}{4-|x|} d x \)
Reason \( \int_{-1}^{1}(f(x)+g(x)) d x=2 \int_{0}^{1} f(x) d x \) if \( g(x) \)
is an odd function and \( f(x) \) is an even
function.
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
A boy begins to walk eastward along a
street in front of his house and the
graph of his position from home is
shown in the following figure. His
average speed for the whole time interval is equal to?
\( A .8 \mathrm{m} / \mathrm{min} \)
B. \( 6 \mathrm{m} / \mathrm{min} \)
c. \( \frac{8}{3} \mathrm{m} / \mathrm{min} \)
\( \mathrm{D} \cdot 2 \mathrm{m} / \mathrm{min} \)
Subject: Chemistry
Select the correct statement.
A. The charge to mass ratio of the particles in anode rays depend on the gas present in the tube
B. Behavior of cathode rays particle and anode rays particle are same in presence of magnetic field (in terms of extent of deviations)
C. Cathode and anode rays start from cathode and anode respectively
D. The charge to mass ratio of the particle in cathode rays depends on the voltage applied across the terminal
Subject: Maths
f \( \mathbf{y}=\boldsymbol{a} \cos (\log \mathbf{x})+\mathbf{b} \sin (\log \mathbf{x}), \) then
\( \boldsymbol{x}^{2} \boldsymbol{y}^{\prime \prime}+\boldsymbol{x} \boldsymbol{y}^{\prime}= \)
A. \( -y \)
B.
\( c \cdot y \)
D. \( y^{2} \)
Subject: Physics
A charged particle having a charge of
\( -2 \times 10^{-6} C \) is placed close to a non
conducting plate having a surface charge density as \( 4 \times 10^{-6} \mathrm{Cm}^{-2} . \) What
will be the force of attraction between
them:
A . \( 0.5 N \)
B. \( 0.45 N \)
c. \( 0.25 N \)
\( D \ldots .0 .75 N \)
Subject: Physics
For electrolytes, Ohm's Law may be written as:
A \( \cdot \frac{V}{I}=R \)
B. \( \frac{V+V_{b a c k}}{I}=R \)
c. \( \frac{V-V_{b a c k}}{I}=R \)
D. \( \frac{V_{b a c k-V}}{I}=R \)
Subject: Chemistry
On introducing a catalyst at \( 500 K \), the rate of a first order reaction increases
by 1.718 times. The activation energy in
the presence of a catalyst is \( 6.05 k J \) \( m o l^{-1} . \) The slope of the plot of
\( \ln k\left(\sec ^{-1}\right) \) against \( 1 / T \) in the absence
of catalyst is:
A . +1
B. - 1
c. +1000
D. -1000
Subject: Physics
A particle starts from a point \( \boldsymbol{P} \) at a
distance of \( A / 2 \) from the mean position
O \& travels towards left as shown in the
figure. If the time period of \( \mathrm{SHM} \)
executed about \( O \) is \( T \) and amplitude \( A \)
then the equation of motion of particle
is :
\( \mathbf{A} \cdot_{x}=A \sin \left(\frac{2 \pi}{T} t+\frac{\pi}{6}\right) \)
В. \( x=A \sin \left(\frac{2 \pi}{T} t+\frac{5 \pi}{6}\right) \)
\( ^{\mathbf{C}} \cdot_{x}=A \cos \left(\frac{2 \pi}{T} t+\frac{\pi}{6}\right) \)
D. \( x=A \cos \left(\frac{2 \pi}{T} t+\frac{\pi}{3}\right) \)
Subject: Chemistry
heated on the flame directly. It crumbled to give white powder of calcium oxide. After cooling, when water is added to it a hissing sound is heard and water started boiling. If it is allowed to stay over night, a clear solution (top layer) is taken and for this experiment
below as lime water.

When carbon dioxide is bubbled into
testtube a clear solution of lime water,
turbidity appears first and later a white precipitate of calcium carbonate is formed. Carbon dioxide is continued to
passed into the same solution and the solution again became clear because of formation of calcium bicarbonate. On
heating the contents of the tube, white precipitate of calcium carbonate
reappears.
On heating limestone, the following are formed.
A. Calcium hydroxide, carbon dioxide
B. Calcium bicarbonate
c. calcium oxide and carbon dioxide
D. Calcium oxide and water
Subject: Maths
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
Subject: Maths
Let \( S \) be a set containing \( n \) elements. Then the total number of binary
operations on \( \boldsymbol{S} \) is
\( \mathbf{A} \cdot n^{n} \)
B \( .2^{n} \)
c. \( n^{n^{2}} \)
D. \( n^{2} \)
Subject: Chemistry
If the density of a solution is
\( 3.12 g m / m l^{-1}, \) the mass of \( 1.5 m l \) solution in significant figures is:
A. \( 4.7 g \)
В. \( 4680 \times 10^{-3} g \)
c. \( 4.680 g \)
D. \( 46.80 g \)
Subject: Maths
\( f\left(\begin{array}{cc}x+y & x-y \\ 2 x+z & x+z\end{array}\right)=\left(\begin{array}{cc}0 & 0 \\ 1 & 1\end{array}\right), \) then
the values of \( x, y \) and \( z \) are respectively
\( \mathbf{A} \cdot 0,0,1 \)
в. 1,1,0
\( \mathrm{c} \cdot-1,0,0 \)
\( \mathbf{D} \cdot 0,0,0 \)
Subject: Physics
A heavy uniform chain lies on a
horizontal table top. If the coefficient of friction between the chain and the table
surface is \( 0.25, \) then find the maximum
\( \% \) of the length of the chain that can hang over one edge of the table.
A . \( 20 \% \)
B. 25\%
\( c .35 \% \)
D. \( 15 \% \)
Subject: Maths
If \( \boldsymbol{y}=\boldsymbol{a}+\frac{\boldsymbol{b}}{\boldsymbol{x}}, \) where \( \boldsymbol{a} \) and \( \boldsymbol{b} \) are
constants and if \( \boldsymbol{y}=\mathbf{1} \) when \( \boldsymbol{x}=-\mathbf{1} \)
and \( y=5 \) when \( x=-5, \) what is the
value of \( a+b ? \)
A. -1
B. 0
\( c \cdot 1 \)
D. 11
Subject: Chemistry
The correct descending order of the priority of the following atoms or group is:
\( -\boldsymbol{C H O},-\boldsymbol{C H}_{2} \boldsymbol{O H},-\boldsymbol{C H}_{3},-\boldsymbol{O H} \)
A .2,4,1,3
B. 1,2,3,4
c. \( 4,3,2, \)
D. 1,4,2,3