AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Elements A and B combine to form three
different compounds:
\( 0.3 \mathrm{g} \) of \( \mathrm{A}+0.4 \mathrm{g} \) of \( \mathrm{B} \rightarrow 0.7 \mathrm{g} \) of
compound \( x \) \( 18.0 \mathrm{g} \) of \( \mathrm{A}+48.0 \mathrm{g} \) of \( \mathrm{B} \rightarrow 66.0 \mathrm{g} \) of
compound \( Y \) \( 40.0 \mathrm{g} \) of \( \mathrm{A}+159.99 \mathrm{g} \) of \( \mathrm{B} \rightarrow 199.99 \mathrm{g} \)
of compound \( \mathbf{Z} \) State the law illustrated by these chemical combinations.
A. Law of reciprocal proportion
B. Law of multiple proportion
c. Law of constant composition
D. None of the above
Subject: Chemistry
Crystals of \( 100 \% H_{2} O_{2} \) is obtained
treating \( 90 \% \quad H_{2} O_{2} \) with:
A . solid \( C O_{2} \) and ether
B. dil. \( H_{2} S O_{4} \)
c. quick lime
D. \( N a O H+C a O \)
Subject: Physics
A wheel has a constant angular acceleration of \( 3.0 \mathrm{rad} / \mathrm{s}^{2}, \) During a
certain \( 4.0 s \) interval, it turns through an angle of 120 rad. Assuming that. \( a t=0 \)
angular speed \( \omega_{0}=3 r a d / s \) how long is
motion at the start of this 4.0 second
interval?
\( \mathbf{A} \cdot 7 s \)
B. \( 9 s \)
c. \( 4 s \)
D. \( 10 s \)
Subject: Physics
Two nucleons are at a separation of \( 1 \times \)
\( 10^{-15} \) m. The net force between them is
\( F_{1} \) if both are neutrons, \( F_{2} \) if both are
protons and \( F_{3} \) if one is a proton and
other is a neutron. In such a case
A \( \cdot F_{2}>F_{1}>F_{3} \)
в. \( F_{1}>F_{2}>F_{3} \)
C. \( F_{1}>F_{3}>F_{2} \)
D. \( F_{3}=F_{1}>F_{2} \)
Subject: Physics
A beam of unpolarised light having flux \( 10^{-3} \) watt falls normally on a polarizer
of cross sectional area \( 3 \times 10^{-4} m^{2} \)
The polarizer rotates with an angular frequency of 31.4 rad/s. The energy of light passing through the polarizer per revolution will be:
\( \mathbf{A} \cdot 10^{-4} \) joule
B . \( 10^{-3} \) joule
C \( \cdot 10^{-2} \) joule
D. \( 10^{-1} \) joule
Subject: Physics
A proton and an \( \alpha- \) particle (with their
masses in the ratio of 1: 4 and charges
in the ratio of 1: 2 ) are accelerated
from rest through a potential difference
V. If a uniform magnetic field (B) is set up perpendicular to their velocities, the
ratio of the radii \( r_{p}: r_{\alpha} \) of the circular
path described by them will be :
A. \( 1: \sqrt{2} \)
Th \( : \sqrt{2} \cdot \sqrt{2} \)
B. 1: 2
\( c \cdot 1: 3 \)
D. \( 1: \sqrt{3} \)
Subject: Chemistry
\( X e F_{6}+H_{2} O \rightleftharpoons X e O F_{4}+2 H F \)
constant \( =\boldsymbol{K}_{1}, \boldsymbol{X} \boldsymbol{e} \boldsymbol{O}_{4}+\boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{6} \rightleftharpoons \)
\( X e O F_{4}+X e O_{3} F_{2} . \) constant \( =K_{2} \)
Then equilibrium constant for the
following reaction will be: \( -\boldsymbol{X} \boldsymbol{e} \boldsymbol{O}_{\boldsymbol{4}}+ \)
\( 2 H F \rightleftharpoons X e O_{4} F_{2}+H_{2} O \)
\( ^{A} \cdot \frac{K_{2}}{K_{1}} \)
в. \( K_{1}+K_{2} \)
c. \( \frac{K_{1}}{K_{2}} \)
D. \( \frac{K_{1}}{\left(K_{2}\right)^{2}} \)
Subject: Maths
If \( \int \frac{x^{2}-x+1}{\left(x^{2}+1\right)^{\frac{3}{2}}} e^{x} d x=e^{x} f(x)+c, \) then
This question has multiple correct options
\( A . f(x) \) is an even function
B. \( f(x) \) is a bounded function
c. the range of \( f(x) \) is (0,1]
D. f(x) has two points of extrema
Subject: Maths
A class has 15 students whose ages are 14,17,15,14,21,17,19,20,16,18,20,17,16
19 and 20 years. One student is selected
in such a manner that each has the
same chance of being chosen and the
age \( X \) of the selected student is
recorded. What is the probability distribution of the random variable \( \boldsymbol{X} \) ?
Find mean, variance and standard
deviation of \( \boldsymbol{X} \)
Subject: Maths
Particular solution of differential
equation \( e^{\frac{d y}{d x}}=x ; y(1)=3 ; x>0 \) is
A \( \cdot \log y=x^{2}+4 \)
B. \( y=\ln x-x+4 \)
c. \( y^{2}=\log x+4 \)
D. \( 2 y=x^{2}+5 \)
E. \( y=x \ln x-x+4 \)
Subject: Chemistry
The EMF (in Volts) for the following electrodes are
\( \boldsymbol{P t}, \boldsymbol{H}_{2} \mid \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4}(\boldsymbol{p} \boldsymbol{H}=\mathbf{2 . 0}) \)
Subject: Maths
A swimmer can swim \( 2 \mathrm{km} \) in 15
minutes in a lake and in a river he can
swim a distance of \( 4 \mathrm{km} \) in 20 minutes
along the stream. If a paper boat is put in the river, then the distance covered by it in \( 2 \frac{1}{2} 2 \) hours will be
\( \mathbf{A} \cdot 18 \mathrm{km} \)
B. \( 12 \mathrm{km} \)
c. \( 8 \mathrm{km} \)
D. \( 10 \mathrm{km} \)
Subject: Maths
If \( \boldsymbol{A}=\left|\begin{array}{c}-\mathbf{2} \\ \mathbf{4} \\ \mathbf{5}\end{array}\right|, \boldsymbol{B}=|\mathbf{1} \quad \mathbf{3}-\mathbf{6}|, \) State
whether ist is true or false \( (A B)^{1}= \)
\( \boldsymbol{B}^{1} \boldsymbol{A}^{1} \)
A. True
B. False
Subject: Physics
In a tangent galvanometer a current of
\( 0.1 A \) produces a deflection of \( 30^{\circ} . \) The
current required to produced a
deflection of \( 60^{\circ} \) is
A . \( 0.2 A \)
в. \( 0.3 A \)
\( c .0 .4 A \)
D. \( 0.5 A \)
Subject: Chemistry
If \( \Delta \boldsymbol{H}_{\text {vaporisation}} \) of substance \( \boldsymbol{X}(l) \)
(molar mass \( : 30 g / \text { mol }) \) is \( 300 J / g \) at its boiling point \( 300 K \), then molar
entropy change for reversible condensation process is:
A. \( 30 J / \) mol. \( K \)
В \( .-300 J / \) mol. \( K \)
c. \( -30 J / \) mol. \( . \)
D. None of these
Subject: Maths
\( \int_{0}^{\infty} \frac{d x}{[x+\sqrt{x^{2}+1}]^{3}} \) is equal to
A \( \cdot \frac{3}{8} \)
B. \( \frac{1}{8} \)
\( c \cdot-\frac{3}{8} \)
D. none of these
Subject: Physics
Consider a disc rolling without slipping
on a horizontal surface at a linear speed
Vas shown in figure:
This question has multiple correct options
A. the speed of the particle A is \( 2 v \)
B. the speed of B, C and D are all equal to v.
C. the speed of \( C \) is zero
D. the speed of 0 is less than the speed of \( B \)
Subject: Biology
Choose the wrong statement in the
process of protein synthesis.
A. After uncoiling of DNA molecule, one strand acts as a template for the formation of mRNA.
B. In the presence of DNA polymerase enzyme, the mRNA is formed based on the triplet codes.
C. The mRNA that leaves nucleus reaches cytoplasm and gets attached with 30 S ribosomal subunit
D. The amino acids are transferred from the intracellular amino acid pool to the active ribosomes by the tRNA.
Subject: Chemistry
Compare the energies of two radiations
\( \boldsymbol{E}_{1} \) with wavelength \( 800 \mathrm{nm} \) and \( \boldsymbol{E}_{2} \)
with wavelength \( 400 \mathrm{nm} \)
A. \( E_{1}=2 E_{2} \)
в. \( E_{1}=E_{2} \)
\( \mathbf{c} \cdot E_{2}=2 E_{1} \)
D \( \cdot E_{2}=-\frac{1}{2} E_{1} \)
Subject: Chemistry
When carbon monoxide is passed over
solid caustic soda heated to \( 200^{\circ} \mathrm{C} \), it
forms:
A. \( N a_{2} C O_{3} \)
в. \( \mathrm{NaHCO}_{3} \)
c. \( H C O O N a \)
D. \( C H_{3} \) COONa
Subject: Biology
Assertion
Photorespiration is the respiration which occurs during the daytime.
Reason Photorespiration is biochemically different from normal respiration
involving glycolate mechanism.
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
Assertion
All the isotopes of a given element show same chemical behaviour.
Reason
Isotopes have different number of
neutrons present in the nucleus.
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: Chemistry
Which of the following is not a decomposition reaction?
\( A \cdot \operatorname{cac} 0_{3} \rightarrow \operatorname{cad}+\cos \)
В. \( 2 \mathrm{KClO}_{3} \rightarrow 2 \mathrm{KCl}+3 \mathrm{O}_{2} \)
c. Digestion of food in the body
D. NaOH+HCI \( \rightarrow \) Nacl + Hz
Subject: Chemistry
Assertion: All molecules in a gas have
same speed. Reason: Gas contains molecules of
different size and shape.
Choose the appropriate option.
A. If both assertion and reason are true and the reason is a correct explanation of the assertion.
B. If both assertion and reason are true, but reason is not a correct explanation of the assertion.
c. If the assertion is true, but reason is false.
D. If both the assertion and reason are false
Subject: Maths
Assertion
\( \sum_{r=0}^{100}\left(^{500-r} C_{3}\right)+^{400} C_{4}=^{501} C_{4} \)
Reason
\( \boldsymbol{n} \boldsymbol{C}_{\boldsymbol{r}}+^{\boldsymbol{n}} \boldsymbol{C}_{\boldsymbol{r}-\boldsymbol{1}}=\boldsymbol{n}+\boldsymbol{1} \boldsymbol{C}_{\boldsymbol{r}} \)
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 person takes 15 breathes per
minute.The volume of air inhaled in
each breath is \( 448 \mathrm{ml} \) and contains \( 21 \% \)
oxygen by volume.The exhaled air contains \( 16 \% \) of oxygen by volume.If all the oxygen is used in the combustion of sucrose, how much of the Sucrose is
burnt in the body per day\& how much
heat is evolved. \( \triangle \boldsymbol{H}_{c o m} \) of sucrose is \( = \)
\( -6000 k j m o l^{-1} \).take temperature to be \( 300 \mathrm{K} \) throughout.[Assuming
\( \left.\boldsymbol{V}_{\text {inhaledair}}=\boldsymbol{V}_{\text {exhaledair}}, \boldsymbol{P}_{\text {atm}}=\mathbf{1} \boldsymbol{a} \boldsymbol{t m}\right] \)
A. 7.822 Mj/day evolved,460 gm
B. 7.822 Mj/day evolved,560 gm
c. 9.822 Mj/day evolved,460 gm
D. 9.822 Mj/day evolved,560 gm
Subject: Physics
The amplitude of a wave disturbance propagating in the positive y-direction is given by:
\( y=\frac{1}{1+x^{2}} \) at \( t=0 s a n d y= \)
\( \frac{1}{1+(x-1)^{2}} \) at \( t=2 s, \) then wave
velocity is
A. \( 1 m / s \)
в. \( 1.5 m / s \)
c. \( 0.5 m / s \)
D. \( 2 m / s \)
Subject: Physics
A solid ball of radius \( R \) has a charge
density p given by \( \boldsymbol{p}=\boldsymbol{p}_{0}(\mathbf{1}-\boldsymbol{r} / \boldsymbol{R}) \) for
\( \mathbf{0} \leq \boldsymbol{r} \leq \boldsymbol{R} . \) The electric field outside the
ball is:
A \( \cdot \frac{p_{0} R^{3}}{\epsilon_{\sigma} r^{2}} \)
в. \( \frac{p_{0} R^{3}}{12 \epsilon_{0} r^{2}} \)
c. \( \frac{4 p_{0} R^{3}}{3 \epsilon_{0} r^{2}} \)
D. \( \cdot \frac{3 p_{0} R^{3}}{4 \epsilon_{0} r^{2}} \)
Subject: Chemistry
Assertion
Molecularity greater than three is not
observed.
Reason
The overall molecularity of a complex
reaction is equal to molecularity of the
Slowest step.
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
Match the following:
PART-A

PART-B
a)
e) All types of waves Polarisation
\( b \)
interference
f) longitudinal waves
\( c \)
diffraction
g) transverse waves
d) reflection
h) only with transverse waves
i) stationary waves produced in stretched strings
\( \mathbf{A} \cdot \mathbf{a} \rightarrow g ; \mathbf{b} \rightarrow \mathbf{e}, \mathbf{f}, \mathbf{g}, \mathbf{i} ; \mathbf{c} \rightarrow \mathbf{e}, \mathbf{f}, \mathbf{g} ; \mathbf{d} \rightarrow \mathbf{e}, \mathbf{f}, \mathbf{g} \)
\( \mathbf{B} \cdot \mathbf{a} \rightarrow \mathbf{h}, \mathbf{g} ; \mathbf{b} \rightarrow \mathbf{f}, \mathbf{g} ; \mathbf{c} \rightarrow \mathbf{g} ; \mathbf{d} \rightarrow \mathbf{h} \)
\( \mathbf{C} \cdot \mathbf{a} \rightarrow \mathbf{e}, \mathbf{f}, \mathbf{g} ; \mathbf{b} \rightarrow \mathbf{g} ; \mathbf{c} \rightarrow \mathbf{e}, \mathbf{f}, \mathbf{g} ; \mathbf{d} \rightarrow \mathbf{g} \)
\( \mathbf{D} \cdot \mathbf{a} \rightarrow \mathbf{e} ; \mathbf{b} \rightarrow \mathbf{h}, \mathbf{i} ; \mathbf{c} \rightarrow \mathbf{g}, \mathbf{h} ; \mathbf{d} \rightarrow \mathbf{e} \)
Subject: Maths
\( \operatorname{Let} g(x)=x^{5} \ln (f(x)) \) where \( f(x) \) is
adifferentiable positive function on
\( (0, \infty) \) satisfying \( f(3)=1 \) and \( f^{\prime}(3)= \)
\( 2 \operatorname{then} g^{\prime}(3) \) is equal to
A . 243
B.
c. 1
D. 486
Subject: Maths
Find the value \( c \) in mean value theorem
for the function \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}+\frac{\mathbf{1}}{\boldsymbol{x}}, \boldsymbol{x} \boldsymbol{\epsilon}[\mathbf{1}, \boldsymbol{3}] \)
Subject: Chemistry
The standard reduction potentials of
\( Z n^{2+} \mid Z n \) and \( C u^{2+} \mid C u \) are \( -0.76 V \) and
\( +0.34 \mathrm{V} \) respectively. What is the cell EMF of the following cell?
\( Z n\left|Z n^{2+}(0.05 M)\right|\left|C u^{2+}(0.005 M)\right| C u \)
\( \left[\frac{R T}{F}=0.059\right] \)
A . 1.1295
в. 1.0705 V
c. 1.1000
D. 1.0412 v
Subject: Biology
Gases referred to as 'green house gases'
are
\( \mathbf{A} \cdot \mathrm{CO}_{2}, \mathrm{O}_{2}, \mathrm{NO}_{2}, \mathrm{NH}_{3} \)
B. Chlorofluoro carbon, \( \mathrm{CO}_{2}, \mathrm{NH}_{3}, \mathrm{N}_{2} \)
\( \mathbf{C} \cdot \mathrm{CH}_{4}, \mathrm{N}_{2}, \mathrm{CO}_{2}, \mathrm{NH}_{3} \)
D. Chlorofluoro carbon, \( \mathrm{CO}_{2}, \mathrm{CH}_{4}, \mathrm{NO}_{2} \)
Subject: Chemistry
For mercury at \( 0^{\circ} \mathrm{C} \) specific
conductance,
\( \boldsymbol{K}=\mathbf{1 . 0 6 2 9 6 3} \times \mathbf{1 0}^{\mathbf{6}} \boldsymbol{S} / \boldsymbol{m} \)
(a) If the resistance of a cell containing mercury is 0.243166 ohm, What is the
cell constant of the cell?
(b) If the same cell is fixed with \( K C l \)
solution at \( 0^{\circ}, \) the resistance of the cell
is \( 3.966 \times 10^{4} \) ohm. What is the
conductivity of \( K C l \) solution?
(c) If the average cross-sectional area of
the cell is \( 0.9643 m m^{2}, \) what is the
effective distance between the
electrodes?
Subject: Physics
A force \( F \) is related to the position of \( a \)
particle by the relation \( \boldsymbol{F}=\left(\mathbf{1 0} \boldsymbol{x}^{2}\right) \boldsymbol{N} \)
The work done by the force when the particle moves from \( x=2 m \) to \( x=4 \) m is
A \( \cdot \frac{56}{3} J \)
в. \( 560 J \)
c. \( \frac{560}{3} J \)
D. \( \frac{3}{560} J \)
Subject: Chemistry
The rate of the zero order reaction; \( \boldsymbol{A}+ \)
\( B \rightarrow C \) follows the rate equation:
Rate \( =\boldsymbol{k}[\boldsymbol{A}]^{0}[\boldsymbol{B}]^{0} \)
Then the rate of the reaction is:
A. dependent on the concentration of reactant
B. dependent on the concentration of product
c. independent of concentrations of both reactant and product
D. none of these
Subject: Chemistry
This species has \( s p^{2} \) hybrid orbitals
A. \( B e F_{2} \)
в. \( N H_{3} \)
\( \mathrm{c} \cdot \mathrm{CH}_{4} \)
D. \( C H_{2} C H_{2} \)
E \( \cdot C C l_{4} \)
Subject: Physics
A mirror faces the negative x-axis. (Normal to its reflecting surface is \( -\hat{\mathbf{i}} \) )
While a particle starts moving such that its image is formed in the mirror.
At a certain instant the velocity of the particles is \( 3 \hat{i}+4 \hat{j}+5 \hat{k} \) and that of the mirror is \( \hat{\mathbf{1}}-\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} \) Choose the correct
options.
This question has multiple correct options
A. Magnitude of relative velocity of the image w.r.t mirrror is \( \sqrt{45} \)
B. Magnitude of relative velocity of image w.r.t object is 4
C. Magnitude of relative velocity of image w.r.t mirrror is \( \sqrt{45} \)
D. Absolute velocity of the image w.r.t ground is \( \sqrt{42} \)
Subject: Physics
The ratio of the radii of planets \( A \) and \( B \)
is \( K_{1} \) and ratio of accelerations due to
gravity on them is \( K_{2} \) The ratio of escape velocities from them will be:
A. \( K_{1} K_{2} \)
B. \( \sqrt{K_{1} K_{2}} \)
c. \( \sqrt{\frac{K_{1}}{K_{2}}} \)
D. \( \sqrt{\frac{K_{2}}{K_{1}}} \)
Subject: Chemistry
I. Rutherford's gold foil experiment
directed a beam of alpha particles at a thin sheet of gold foil and helped to prove the existence of positively charged particles.
II. Most of the positively charged alpha
particles were able to pass directly through the gold foil.
A. Statement \( I \) is true, Statement \( I I \) is true
B. Statement I is true, Statement II is false
c. Statement \( I \) is false, statement \( I I \) is true
D. Statement I is false, Statement \( I I \) is false
Subject: Maths
If the perimeter of rectangular base
\( A B C D \) of a semi-right circular cylinder
is \( 36 \mathrm{m}, \) then the maximum volume of
this semi-cylinder is
\( \mathbf{A} \cdot 36 \pi m^{3} \)
B. \( 96 \pi m^{3} \)
C. \( 108 \pi m^{3} \)
D. \( 54 \pi m^{3} \)
Subject: Physics
Two equal charges \( q \) are placed at a
distance \( 2 a \) and a third charge \( -2 q \) is
placed at the midpoint. The potential energy of the system is
A \( \cdot \frac{9 q^{2}}{8 \pi \epsilon_{0} a} \)
В. \( \frac{q^{2}}{8 \pi \epsilon_{0} a} \)
c. \( \frac{-7 q^{2}}{8 \pi \epsilon_{0} a} \)
D. \( \frac{6 q^{2}}{8 \pi \epsilon_{0} a} \)
Subject: Chemistry
Which of the following is Loschmidt
number?
A \( \cdot 6 \times 10^{23} \)
3 \( ^{3} 100-10^{0} \)
B . \( 2.69 \times 10^{25} \)
\( \mathrm{c} \cdot 3 \times 10^{23} \)
D. None of these
Subject: Chemistry
\( \boldsymbol{O H} \quad \boldsymbol{H}-\underset{\boldsymbol{H}}{\boldsymbol{C}}-\underset{\boldsymbol{H}}{\boldsymbol{C}}-\boldsymbol{H} \quad \boldsymbol{C}_{\boldsymbol{H}}=\underset{\boldsymbol{H}}{\boldsymbol{C}} \)
(1)
\( (\mathbf{3}) \)
The structures of four molecules are
shown.

Which molecules belong to the same homologous series?
A. 1 and 2
B. 1 and 3
\( c \cdot 2 \) and 4
D. 3 and 4
Subject: Physics
A charge \( 10 n C \) is situated in a medium
of relative permittivity 10. The potential due to this charge at a distance of \( 0.1 m \)
is :
\( \mathbf{A} \cdot 900 V \)
в. \( 90 V \)
\( c .9 V \)
D. \( 0.09 V \)
Subject: Maths
\( \int_{0}^{1 / 2} e^{x}\left[\sin ^{-1} x+\frac{1}{\sqrt{1-x^{2}}}\right] d x= \)
\( ^{A} \cdot \frac{e^{4}}{4} \)
B. \( \frac{\pi \sqrt{6}}{6} \)
\( c \cdot \frac{\sqrt{\pi}}{_{1}} \)
D. \( \frac{\pi \sqrt{6}}{2} \)
Subject: Chemistry
Which one of the following statements
is false?
A. Raoult's law states that the vapour pressure of a component over a solution is proportional to its mole fraction
B. The osmotic pressure ( \( \pi \) ) of a solution is given by the equation \( \pi=M R T \), where, \( M \) is the molarity of the
solution
C. The correct order of osmotic pressure for \( 0.01 \mathrm{M} \)
aqueous solution of each compound is \( B a C l_{2}> \) \( K C l>C H_{3} C O O H> \)sucrose
D. Two sucrose solutions of same molality prepared in different solvents will have the same freezing point depression
Subject: Physics
In the circuit shown in the figure the
heat produced in the 5 ohm resistor due
to the current flowing through it is 10
calories per second. The heat generated
in the 4 ohm resistor is
A. 1 calorie \( / \)per
B. 2 calorie/sec
c. 3 calorie \( / \)per
D. 4 calorie / per
Subject: Maths
Suppose \( M=\int_{0}^{\pi / 2} \frac{\cos x}{x+2} d x, N= \)
\( \int_{0}^{\pi / 4} \frac{\sin x \cos x}{(x+1)^{2}} d x . \) Then, the value of
\( (M-N) \) equals
A \( \frac{3}{\pi+2} \)
в. \( \frac{2}{\pi-4} \)
c. \( \frac{4}{\pi-2} \)
D. \( \frac{2}{\pi+4} \)
Subject: Chemistry
Assertion
Transperent soaps are made by
dissolving soaps in ethanol
Reason
Ethanol makes things invisible.
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
A sealed bottle containing some water
is made up of two cylinders \( A \) and \( B \) of
radius \( 1.5 \mathrm{cm} \) and \( 3 \mathrm{cm} \) respectively, as
shown in the figure. When the bottle is
placed right up on a table, the height of
water in it is \( 15 \mathrm{cm}, \) but when placed
upside down, the height of water is \( 24 \mathrm{cm} . \) The height of the bottle is
A \( .25 \mathrm{cm} \)
B. \( 26 \mathrm{cm} \)
c. \( 27 \mathrm{cm} \)
D. 28 cm
Subject: Physics
In a coil of resistance \( 100 \Omega \), a current is
induced by changing the magnetic flux through it as shown in the figure. The
magnitude of change in flux through
the coil is :
A. \( 275 \mathrm{Wb} \)
в. \( 200 \mathrm{Wb} \)
\( c \cdot 225 W b \)
D. \( 250 \mathrm{Wb} \)
Subject: Chemistry
The 0 - 0 bond length in ozone is
A . \( 1.54 \mathrm{A}^{\circ} \)
B . \( 1.27 \mathrm{A}^{\circ} \)
c. \( 1.34 \mathrm{A}^{\circ} \)
D. \( 1.10 \mathrm{A}^{\circ} \)
Subject: Physics
In an RLC series circuit shown in figure,
the readings of voltmeters \( V_{1} \) and \( V_{2} \)
are \( 100 \mathrm{V} \) and \( 120 \mathrm{V}, \) respectively. The
same voltage is \( 130 \mathrm{V} \). For this situation, mark out the incorrect statement.
A. Voltage across resistor, inductor and capacitor are 50 \( \vee, 50 \sqrt{3} \mathrm{V} \) and \( 120+50 \sqrt{3} \mathrm{V}, \) respectively
B. Voltage across resistor. inductor and capacitor are 50 V, \( 50 \sqrt{3} \) V and \( 120-50 \sqrt{3} \) V, respectively
c. Power factor of the circuit is \( 5 / 13 \)
D. The circuit is capacitance in nature
Subject: Maths
A chord of a circle of radius \( 6 \mathrm{cm} \)
subtends an angle of \( 60^{\circ} \) at the centre
of the circle. The area of the minor
segment is (use \( \pi=3.14) \)
A \( \cdot 6.54 \mathrm{cm}^{2} \)
в. \( 0.327 \mathrm{cm}^{2} \)
c. \( 7.25 \mathrm{cm}^{2} \)
D. 3.27 \( c m^{2} \)
Subject: Maths
The value of \( \lim _{n \rightarrow \infty} \Sigma_{1}^{n} \cos \left(\frac{\pi}{2}+\frac{\pi i}{2 n}\right) \frac{\pi}{2 n}=? \)
A \( \cdot \int_{\frac{\pi}{2}}^{\pi} \cos x \)
B. \( \int_{\frac{\pi}{2}}^{\pi} \cos x \)
\( ^{\mathrm{c}} \cdot \int_{\frac{\pi}{2}}^{2 \pi} \cos x \)
D. \( \int_{\frac{\pi}{2}}^{5 \pi} \cos x \)
Subject: Physics
A particle with total mechanical energy, which is small and negative, is under the influence of a one dimensional
potential \( U(x)=x^{4} / 4-x^{2} / 2 \) Jwhere \( x \)
is in meters. At time \( t=0 \) s, it is at \( x= \)
\( -0.5 \mathrm{m} . \) Then at a later time it can be
found.
A. anywhere on the x axis.
B. between \( x=-1.0 \mathrm{m} \) to \( x=1.0 \mathrm{m} \)
c. between \( x=-1.0 \mathrm{m} \) to \( x=0.0 \mathrm{m} \)
D. between \( x=0.0 \mathrm{m} \) to \( x=1.0 \mathrm{m} \)
Subject: Maths
If \( x=a t^{2}, y=2 a t, \) then \( \frac{d^{2} y}{d x^{2}}= \)
A. \( -\frac{1}{t^{2}} \)
в. \( \frac{1}{2 a t^{3}} \)
c. \( -\frac{1}{t^{3}} \)
D. \( -\frac{1}{2 a t^{3}} \)
Subject: Maths
Find the locus of a point which moves so that the difference of its distances from
the points, (5,0) and (-5,0) is 2 is:
A \( \cdot \frac{x^{2}}{1}+\frac{y^{2}}{24}=1 \)
B. \( \frac{x^{2}}{24}+\frac{y^{2}}{1}=1 \)
c. \( \frac{x^{2}}{24}-\frac{y^{2}}{2}=1 \)
D. \( \frac{x^{2}}{1}-\frac{y^{2}}{24}=1 \)
Subject: Chemistry
At \( 25^{\circ} C, \) the standard oxidation
potential of \( Z n \) and \( A g \) in water are:
\( Z n(s) \rightarrow Z n^{+2}(a q)+2 e^{-}, E^{0}= \)
\( 0.76 V \)
and \( A g(s) \rightarrow A g^{+}(a q)+e^{-}, E^{0}= \)
\( -0.80 V \)
Which of the following reaction actually takes place?
A \( \cdot Z n^{2+}(a q)+2 A g(s) \rightarrow 2 A g^{+}(a q)+Z n(s) \)
B. \( Z n(s)+2 A g^{+}(a q) \rightarrow Z n^{2+}(a q)+2 A g(s) \)
C. \( Z n^{2+}(a q)+2 A g^{+}(a q) \rightarrow Z n(s)+2 A g(s) \)
D. \( Z n(s)+A g(s) \rightarrow Z n^{2+}(a q)+A g^{+}(a q) \)
Subject: Physics
Two point charges \( +q \) and \( +q \) are fixed \( \operatorname{at}(a, 0,0) \) and \( (-a, 0,0) . \) A third point
charge \( -q \) is at origin. State whether its equilibrium is stable, unstable or neutral if it is slightly displaced along
\( y- \) axis.
A . Stable
B. Unstable
c. Neutral
D. Data insufficient