AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
\( \int_{1}^{2} x^{2} \log x d x_{=} \)
A. \( \frac{8}{3} \log 2-\frac{7}{9} \)
в. \( \frac{8}{3} \log 2+\frac{7}{9} \)
c. \( \frac{8}{3} \log \frac{1}{3}-\frac{7}{9} \)
D. \( \frac{8}{3} \log \frac{1}{3}+\frac{7}{9} \)
Subject: Chemistry
The equation corresponding to the wave number of spectral line in the Brackett series:
A \( \cdot R\left[\left(1 / 2^{2}\right)-\left(1 / 4^{2}\right)\right] \)
B . \( R\left[\left(1 / 4^{2}\right)-\left(1 / 5^{2}\right)\right] \)
c. \( R\left[\left(1 / 3^{2}\right)-\left(1 / 5^{2}\right)\right] \)
D. \( R\left[\left(1 / 5^{2}\right)-\left(1 / 6^{2}\right)\right. \)
Subject: Chemistry
Following are the thermochemical reactions:
\( C(\text { graphite })+\frac{1}{2} O_{2} \rightarrow C O ; \Delta H= \)
\( -110.5 \mathrm{kJ} / \mathrm{mol} \)
\( C O+\frac{1}{2} O_{2} \rightarrow C O_{2} ; \Delta H=-283.2 \)
kJ/mol
The heat of reaction (in kJ/mol) for the
following reaction is:
\( C(\text { graphite })+O_{2} \rightarrow C O_{2} \)
\( \mathbf{A} \cdot+393.7 \)
В. -393.7
c. -172.7
D. +172.7
Subject: Maths
\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}} \tan ^{-1}\left(\frac{\mathbf{1}-\boldsymbol{x}}{\mathbf{1}+\boldsymbol{x}}\right)= \)
A \( \cdot \frac{-1}{1+x^{2}} \)
B \( \cdot \frac{1}{1+x^{2}} \)
c. \( \frac{1+x}{1-x} \)
D. \( \frac{2}{1+x^{2}} \)
Subject: Chemistry
Which of the following is a non-redox
process?
This question has multiple correct options
A \( \cdot S O_{4}^{2-} \rightarrow S O_{3} \)
B. \( C r_{2} O_{7}^{2-} \rightarrow C r O_{4}^{2} \)
\( \mathbf{c} \cdot P O_{4}^{3-} \rightarrow P_{2} O_{7}^{4} \)
\( \mathrm{D} \cdot C_{2} O_{4}^{-2} \rightarrow C O_{2} \)
Subject: Maths
Given information is shown marked on
the diagrams as shown,

To prove that \( A C B \) and DFE are congruent by SAS, what additional information is
needed?
\( \mathbf{A} \cdot E F \cong B C \)
B. \( \angle D F E \cong \angle A B C \)
\( \mathbf{c} \cdot D E \cong A B \)
D. \( \angle D F E \cong \angle A C B \)
Subject: Chemistry
Substance \( \boldsymbol{X} \)
(1) reacts with \( \boldsymbol{H}_{2} \boldsymbol{S} \) to produce white
turbidity.
(II) changes light green solution of
\( F e S O_{4} \) into yellow colour.
(III) reacts with moisture to give
pungent smelling gas.
Hence \( \boldsymbol{X} \) is:
A. \( K M n O_{4} \)
в. \( K_{2} C r_{2} O_{7} \)
\( \mathrm{c} \cdot \mathrm{SO}_{2} \)
D. \( C a O C l \)
Subject: Physics
The number of photons falling per second on a completely darkened plate
to produce a force of \( 6.62 \times 10^{-5} \mathrm{N} \) is 'n'
If the wavelength of the light falling is \( 5 \times 10^{-7} m, \) then \( n=_{-1-}---\times 10^{22} \)
\( \left(h=6.62 \times 10^{-34} J-s\right) \)
A . 1
B. 5
\( c .0 .2 \)
D. 3.3
Subject: Maths
We are required to form different words with the help of the letters of the word
INTEGER. Let m1 be the number of words
in which I and \( \mathrm{N} \) are never together and \( \mathrm{m} 2 \) be the number of words which begin with I and end with \( \mathrm{R} \), then \( \mathrm{m} 1 / \mathrm{m} \) 2 is
given by:
A .42
B. 30
\( c \cdot 6 \)
D. 1/30
Subject: Chemistry
Assertion
In tetrahedral hybridization ie. in \( s p^{3} \)
hybridization all p-orbitals are involved
and no p-orbital is left for forming \( \pi \) -
bonds.
Reason
Central atom can not form double bonds
in the molecules or species having \( s p^{3} \) hybridization.
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: Physics
Consider the arrangement shown in figure (17-E4). The distance \( D \) is large compared to the separation \( d \) between
the slits
(a) Find the minimum value of
\( d \) so that there is a dark fringe at \( O .(b) \)
Suppose \( d \) has this value. Find the
distance \( x \) at which the bright fringe is formed.
(c) Find the fringe-width.
Subject: Physics
Find \( C_{A B} \) in the given circuit of given
figure. Assume each capacitor is \( \mathrm{C} \)
A \( \cdot \frac{15 C}{8} \)
B. \( \frac{15 C}{7} \)
c. \( \frac{3 C}{2} \)
D. \( 2 C \)
Subject: Maths
Choose correct option which suitably
represents value of \( \boldsymbol{x} \)
\( \boldsymbol{x}<\mathbf{5}, \boldsymbol{x} \in \boldsymbol{N} \)
A \( \cdot\{0,1,2,3,4\} \)
в. \{1,2,3,4\}
c. \{1,2,3,4,5\}
D. \{0,1,2,3,4,5\}
Subject: Maths
Find the values of the following determinants
\( \left|\begin{array}{cc}\mathbf{1}+\mathbf{3} i & \boldsymbol{i}-\mathbf{2} \\ -\boldsymbol{i}-\mathbf{2} & \mathbf{1}-\mathbf{3} \boldsymbol{i}\end{array}\right| \)
where \( i=\sqrt{-1} \)
Subject: Physics
A rain drop of radius 0.3 mm has a
terminal velocity in air= \( 1 \mathrm{m} / \mathrm{s} \). The
viscocity of air is \( 8 \times 10^{-5} \) poise. The
viscous force on it is:
A \( .45 .2 \times 10^{-4} \) dyne
B . \( 101.73 \times 10^{-5} \) dyne
C. \( 16.95 \times 10^{-4} \) dyne
D. \( 16.95 \times 10^{-5} \) dyne
Subject: Chemistry
The order of pH of \( 0.200 \mathrm{M} \) solutions of
\( N H_{4} N O_{3}, N a N O_{3} \) and \( N a_{2} C O_{3} \) is :
A. \( N H_{4} N O_{3}<N a_{2} C O_{3}<N a N O_{3} \)
в. \( N H_{4} N O_{3}<N a N O_{3}<N a_{2} C O_{3} \)
c. \( N a_{2} C O_{3}<N a N O_{3}<N H_{4} N O_{3} \)
D. \( N a_{2} N O_{3}<N H_{4} N O_{3}<N a_{2} C O_{3} \)
Subject: Maths
Let \( A \) and \( B \) are two matrices of same
order \( 3 \times 3 \) given by \( \boldsymbol{A}=\left[\begin{array}{ccc}\mathbf{1} & \mathbf{3} & \boldsymbol{\lambda}+\mathbf{2} \\ \mathbf{2} & \mathbf{4} & \mathbf{6} \\ \mathbf{3} & \mathbf{5} & \mathbf{8}\end{array}\right], \boldsymbol{B}=\left[\begin{array}{ccc}\mathbf{3} & \mathbf{2} & \mathbf{4} \\ \mathbf{3} & \mathbf{2} & \mathbf{5} \\ \mathbf{2} & \mathbf{1} & \mathbf{4}\end{array}\right] \)
If \( A \) is a singular matrix, then \( t r(A+ \)
\( B \) ) is equal to
A .24
в. 11
\( c .22 \)
D. None of these
Subject: Chemistry
If the relative rates of abstraction of 2
and \( 1 \mathrm{H} \) atoms 3.8 and \( 1.0, \) respectively,
then the percentage ratios of the products 1-chloro-, 2- chloro-, and 3-
chloro- are obtained in the
photochlorination of n-hexane would be
A. 17\%, 41.5\%, 41.5\% respectively
в. 17\%, 17\%, 66\% respectively
c. 30\%, 40\%, 30\% respectively
D. 15\%, 15\%, 70\% respectively
Subject: Chemistry
\( 1.25 \mathrm{g} \) of a solid dibasic acid is completely neutralised by \( 25 \mathrm{mL} \) of 0.25 molar \( \boldsymbol{B a}(\boldsymbol{O H})_{2} \) solution. Molecular
mass of the acid is:
A. 100
B. 150
\( c \cdot 120 \)
D. 200
Subject: Physics
A body is accelerated by applying a force of 30 N. The momentum of the
body after 2 sec:
A. \( 7.5 \mathrm{kg}-\mathrm{m} / \mathrm{s} \)
B. 40 kg-m/s
c. \( 120 \mathrm{kg}-\mathrm{m} / \mathrm{s} \)
D. \( 60 \mathrm{kg}-\mathrm{m} / \mathrm{s} \)
Subject: Physics
A car accelerates from rest at a
constant rate \( \alpha \) for some time after
which it decelerates at a constant rate
\( \beta \) to come to rest. If the total time
elapsed is \( t, \) the maximum velocity
acquired by the car is given by
\( ^{\mathrm{A}} \cdot\left(\frac{\alpha^{2}+\beta^{2}}{\alpha \beta}\right) t \)
\( ^{\text {В }} \cdot\left(\frac{\alpha^{2}-\beta^{2}}{\alpha \beta}\right) \)
\( ^{c \cdot}\left(\frac{\alpha+\beta}{\alpha \beta}\right) t \)
\( ^{D \cdot}\left(\frac{\alpha \beta}{\alpha+\beta}\right) t \)
Subject: Maths
\( \boldsymbol{A}=\left[\begin{array}{ccc}\mathbf{1} & \mathbf{- 1} & \mathbf{1} \\ \mathbf{2} & \mathbf{1} & -\mathbf{3} \\ \mathbf{1} & \mathbf{1} & \mathbf{1}\end{array}\right] \) and \( \boldsymbol{B}= \)
\( \left[\begin{array}{ccc}4 & 2 & 2 \\ -5 & 0 & \alpha \\ 1 & -2 & 3\end{array}\right] \) If \( B \) is the adjoint of \( A \)
then \( \alpha \) equals
A .2
в.
\( c \cdot-2 \)
D.
Subject: Maths
Find the sum of the following vectors:
\( \overrightarrow{\boldsymbol{a}}=\hat{\boldsymbol{i}}-\mathbf{2} \hat{\boldsymbol{j}}, \overrightarrow{\boldsymbol{b}}=\mathbf{2} \hat{\boldsymbol{i}}-\boldsymbol{3} \hat{\boldsymbol{j}}, \overrightarrow{\boldsymbol{c}}=\mathbf{2} \hat{\boldsymbol{i}}+\boldsymbol{3} \hat{\boldsymbol{k}} \)
Subject: Physics
A body dropped from the top of a tower reaches the ground in 4 s. Height of the tower is (Take \( \boldsymbol{g}=\mathbf{9 . 8} \boldsymbol{m} / \boldsymbol{s}^{2} \) ):
A . \( 39.2 m \)
в. \( 44.1 \mathrm{m} \)
c. \( 58.8 m \)
D. \( 78.4 \mathrm{m} \)
Subject: Biology
One molecule of an enzyme is able to catalyse conversion of two molecules of substrate into products in 5 minutes.
Ten molecules of enzyme and 25 molecules of substrate are mixed in a
test tube. At the end of 10 minutes the
test tube will have
A. Products only
B. Products and enzymes molecules
c. Products and 5 unreacted substrate molecules
D. Products, enzyme molecules and 5 molecules of substrate
Subject: Chemistry
Statement - I : Every collision of
reactant molecule is not successful
Statement - II: Every collision of reactant molecule with proper
orientation is successful one.
A. Both statements are true Statement- - II is correct explanation of Statement- -
B. Both statements are true but statement- -II is not correct explanation of Statement- -
c. statement-lis true but statement- - II is false
D. Statement- - lis false but Statement - || is true
Subject: Maths
The equation of ellipse whose major axis is along the direction of \( x \) -axis, eccentricity is \( e=2 / 3 \)
A \( \cdot 36 x^{2}+20 y^{2}=405 \)
B . \( 20 x^{2}+36 y^{2}=405 \)
c. \( 30 x^{2}+22 y^{2}=411 \)
D. \( 22 x^{2}+32 y^{2}=409 \)
Subject: Physics
One end of a slack wire (Youngs
modulus \( Y, \) length \( L \) and cross
sectional area \( A \) ) is clamped to a rigid wall and the other end to a block (mass
m) which rests on a smooth horizontal
plane. The block is set in motion with a speed v. What is the maximum
distance the block will travel after the
wire becomes taut?
A \( \cdot v \sqrt{\frac{m L}{A Y}} \)
B. \( v \sqrt{\frac{2 m L}{A Y}} \)
c. \( v \sqrt{\frac{m L}{2 A Y}} \)
D \( \cdot L \sqrt{\frac{m v}{A Y}} \)
Subject: Physics
How can we change a camera from \( \boldsymbol{F} / \mathbf{4} \)
\( \operatorname{to} F / 5.6 ? \)
A. Increase the aperture to 2 time keeping the focal distance constant
B. Increase the aperture to \( \sqrt{2} \) time keeping the focal distance constant
C . Increase the aperture to \( \frac{1}{2} \) time keeping the focal
distance constant
D. Increase the aperture to \( \frac{1}{\sqrt{2}} \) time keeping the focal
distance constant
Subject: Physics
A battery of \( 9 V \) is connected in series
with resistors of \( 0.5,0.3,0.4,0.2, \) and 12
How much current would now through the 0.4 resistors?
\( \mathbf{A} \cdot 22.5 A \)
B . \( 2.25 A \)
c. \( 0.67 A \)
D. \( 6.7 A \)
Subject: Maths
Let \( f(x) \) be a real valued function not identically zero, such that
\( \boldsymbol{f}\left(\boldsymbol{x}+\boldsymbol{y}^{n}\right)=\boldsymbol{f}(\boldsymbol{x})+(\boldsymbol{f}(\boldsymbol{y}))^{n} \quad \forall \boldsymbol{x}, \boldsymbol{y} \in \)
\( \boldsymbol{R} \)
where \( n \in N(n \neq 1) \) and \( f^{\prime}(0) \geq 0 . \) We
may get an explicit form of the function \( \boldsymbol{f}(\boldsymbol{x}) \)
\( \int_{0}^{1} f(x) d x \) is equal to
A \( \cdot \frac{1}{2 n} \)
B. \( 2 n \)
\( c \cdot \frac{1}{2} \)
D. 2
Subject: Physics
Assertion
Magnetic force on a moving charge is always perpendicular to the magnetic field.
Reason
Electric force on a charge is along the direction of electric field.
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: Physics
A moving-coil galvanometer has its coil of 24 turns and \( 12 \Omega \) resistance. By how much the number of turns should be
increased so that the current sensitivity of the galvanometer increases by \( 25 \% ? \)
If, in doing so, the resistance of the coil
increases to \( 20 \Omega \), what will be the effect on the voltage-sensitivity of the galvanometer?
Subject: Physics
Figure shows two coherent sources \( S_{1} \)
and \( S_{2} \) emitting wavelength \( \lambda \). The
separation \( S_{1} S_{2}=1.5 \lambda \) and \( S_{1} \) is
ahead in phase by \( \pi / 2 \) relative \( S_{2} \). Then the maxima occur in direction \( \theta \) given
by \( \sin ^{-1} \) of
\( (i) 0 ;(i i) 1 / 2 ;(i i i)-1 / 6 ;(i v)-5 / 6 \)
Correct options are:
A. \( (i i),(i i i),(i v) \)
B. (i),( \( (i i),(i i i) \)
c. \( (i),(i i i),(i v) \)
D. all of the above
Subject: Maths
If \( \boldsymbol{A}_{\boldsymbol{i}}=\frac{\boldsymbol{x}-\boldsymbol{a}_{\boldsymbol{i}}}{\left|\boldsymbol{x}-\boldsymbol{a}_{\boldsymbol{i}}\right|} \) where \( \boldsymbol{i}=\mathbf{1}, \boldsymbol{2}, \boldsymbol{3} \) and
\( \boldsymbol{a}_{1}<\boldsymbol{a}_{2}<\boldsymbol{a}_{3} \) then \( \lim _{\boldsymbol{x} \rightarrow \boldsymbol{a}_{2}} \boldsymbol{A}_{1} \boldsymbol{A}_{2} \boldsymbol{A}_{3}= \)
A . -1
B.
\( c \cdot 0 \)
D. does not exist
Subject: Chemistry
Select the correct IUPAC name for
\( N a_{2}\left[F e(C N)_{5} N O\right] \) complex.
This question has multiple correct options
A. Sodiumpentacyanidonitrosoniumferrate(II)
B. Sodiumpentacyanidonitrosyliumferrate(II)
c. sodiumpentacyanidonitrosyl ferrate(II)
D. sodiumpentacyanidonitrosyliron(II)
Subject: Physics
A point charge \( +Q \) is placed just
outside an imaginary hemispherical
surface of radius \( R \) as shown in the
figure. Which of the following statements
is/are correct?
This question has multiple correct options
A. The electric flux passing through the curved surface of the hemisphere is \( -\frac{Q}{2_{\varepsilon_{0}}}\left(1-\frac{1}{\sqrt{2}}\right) \)
B. Total flux through the curved and the flat surface is \( \underline{Q} \)
C. The component of the electric field normal to the flat surface is constant over the surface
D. The circumference of the flat surface is an
equipotential
Subject: Chemistry
Match the column I with column II with respect to applications of properties of colloids in different fields and mark the
appropriate choice.
Column I Column I
(A) Coagulation
(i) Colloidal medicines
(B) Adsorption
(ii) Photographic films
(C) Electrophoresis
(iii) Sewage disposal
(D) Emulsions
(iv) Smoke precipitator
B. (A) \( \rightarrow \) (ii), (B) \( \rightarrow \) (iii), \( (c) \rightarrow(i),(D) \rightarrow( \) iv )
c. \( (A) \rightarrow(\text { iii) },(B) \rightarrow(i),(C) \rightarrow(i v),(D) \rightarrow( \text { ii) } \)
D. \( (A) \rightarrow(\text { i) },(B) \rightarrow(\text { iv) },(C) \rightarrow(\text { iii) },(D) \rightarrow( \text { ii) } \)
Subject: Physics
One milliwatt of light of wavelength \( \lambda=4560 A \) is incident on a cesium
metal surface. Calculate the electron
current liberated. Assume a quantum efficiency of \( \boldsymbol{\eta}=\mathbf{0 . 5 \%} \). [Work function
for cesium \( =1.89 e V] \) take \( h c= \)
\( 12400 e V-A \)
Subject: Physics
Out of the following functions representing motion of a particle which
represents \( \boldsymbol{S H} \boldsymbol{M} \) ?
(A) \( y=\sin \omega t-\cos \omega t \)
(B) \( y=\sin ^{3} \omega t \)
(C) \( y=5 \cos \left(\frac{3 \pi}{4}-3 \omega t\right) \)
(D) \( \boldsymbol{y}=\mathbf{1}+\boldsymbol{\omega} \boldsymbol{t}+\boldsymbol{\omega}^{2} \boldsymbol{t}^{2} \)
A. Only \( (A) \) and \( (B) \)
B. only \( (A) \)
c. only \( (D) \) does not represent \( S H M \)
D. only \( (A) \) and \( (C) \)
Subject: Physics
around a conducting wire connected to
a battery and a switch. As the switch is
closed, the free electrons in the wire
start moving along the wire. In any time interval, the number of electrons
entering the closed surface \( S \) is equal
to the number of electrons leaving it. On
closing the switch, the flux of the
electric field through the closed surface
(more than one option may be correct)
This question has multiple correct options
A. is increased
B. is decreased
C. remains unchanged
D. remains zerç
Subject: Physics
Infinite charges of magnitude \( q \) each
are lying at \( \boldsymbol{x}=\mathbf{1}, \mathbf{2}, \mathbf{4}, \mathbf{8}, \dots \dots \dots \) metre on
X-axis. The value of intensity of electric
field at point \( x=0 \) due to these
charges will be
A \( \cdot 12 \times 10^{9} q N / C \)
в. zero
c. \( 6 \times 10^{9} q N / C \)
D. \( 4 \times 10^{9} q N / C \)
Subject: Physics
An object (O) is placed in a medium M
of refractive index \( 5 / 3 \). A convex lens of
focal length \( 15 \mathrm{cm} \) is placed in front of the object as shown in the figure. Determine the position of the image
formed by the lens.
\( A \cdot 15 \mathrm{cm} \)
B. 20 cm
c. 30 \( \mathrm{cm} \)
D. \( 60 \mathrm{cm} \)
Subject: Physics
We have two electric dipoles. Each dipole consists of two equal and opposite point charges at the ends of an insulating rod of length d. The dipoles sit along the \( x \) -axis a distance \( r \) apart, oriented as shown in figure. Their separation \( r>>d \). The dipole on the left:
This question has multiple correct options
A. wil feel a force to the left
B. will feel a force to the right
c. will feel a torque trying to make it rotate counterclockwis
D. will feel no torque
Subject: Maths
A hall has dimensions \( 24 \mathrm{m} \times 8 \mathrm{m} \times 6 \)
m The length of the longest pole which can be accommodated in the hall is
A. \( 26 \mathrm{m} \)
B. 28 m
\( c \cdot 30 m \)
D. 36 m
Subject: Maths
When will the quadratic equation
\( \boldsymbol{a} \boldsymbol{x}^{2}+\boldsymbol{b} \boldsymbol{x}+\boldsymbol{c}=\boldsymbol{0} \) NOT have Real Roots?
A. \( b^{2}-4 a c \geq 0 \)
B . \( b^{2}-4 a c>0 \)
c. \( b^{2}-4 a c<0 \)
D. None of these
Subject: Maths
Evaluate \( \int\left(\frac{1}{7}-\frac{1}{y^{5 / 4}}\right) d y \)
A \( \cdot_{I}=\frac{y}{7}+\frac{4}{y^{1 / 4}}+c \)
B. \( I=-\frac{y}{7}+\frac{4}{y^{1 / 4}}+c \)
\( ^{\mathrm{C}} \cdot_{I}=\frac{y}{7}-\frac{4}{y^{1 / 4}}+c \)
D. None of these
Subject: Physics
A thin circular loop of radius R rotates about its vertical diameter with an angular frequency \( \omega . \) Show that a small bead on the wire loop remains at its lower most point for \( \omega \leq \sqrt{g / R} \). What
is the angle made by the radius vector joining the centre to the bead with the vertical downward direction for \( \omega= \)
\( \sqrt{2 g / R} ? \) Neglect friction.
Subject: Physics
Consider \( \boldsymbol{\alpha}- \) particles \( , \boldsymbol{\beta}- \) particles
and \( \gamma- \) rays, each having an energy of
\( 0.5 \mathrm{MeV} . \) In increasing order of penetrating powers, the radiations are
A. \( \alpha, \beta, \gamma \)
в. \( \alpha, \gamma, \beta \)
c. \( \beta, \gamma, \alpha \)
D. \( \gamma, \beta, \alpha \)
Subject: Chemistry
During the cycle
A. work done by the gas is about \( 55 J \) and heat absorbed by the gas is also about \( 55 J \)
B. work done by the gas is about \( 42 J \) and heat rejected by the gas is \( 60 J \)
C. work done on the gas is \( 60 J \) and heat rejected by the \( \operatorname{gas} \) is also \( 60 J \)
D. work done on the gas is \( 60 J \) and heat absorbed by the gas is also about \( 60 J \)
Subject: Physics
At temperatures close to \( 0 \mathrm{K} \), the specific heat capacity c of a particular solid is given by \( c=b T^{3}, \) where \( T \) is the
temperature and b is a constant, characteristic of the solid.
The Sl unit of specific heat capacity is \( \boldsymbol{k} \boldsymbol{g}^{-1} \boldsymbol{K}^{-1} \)
What is the unit of constant b,
expressed in SI base units?
B. \( m^{2} s^{-2} K^{-4} \)
c. \( \operatorname{kgm}^{2} s^{-2} K^{-3} \)
D. \( k g m^{2} s^{-2} K^{-4} \)
Subject: Chemistry
Find the number of acid(s) from the
following in which \( X-H \) bond is/are
present Given \( X \) is central atom:
\( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{2}, \boldsymbol{H}_{4} \boldsymbol{P}_{2} \boldsymbol{O}_{7}, \boldsymbol{H}_{4} \boldsymbol{P}_{2} \boldsymbol{O}_{5}, \boldsymbol{H}_{2} \boldsymbol{S}_{2} \boldsymbol{O}_{6}, \boldsymbol{H} \)
Subject: Physics
Which of the following are fissile isotopes?

This question has multiple correct options
A \( \cdot \frac{238}{92} U \)
В \( \cdot \frac{233}{92} U \)
\( \mathbf{c} \cdot_{94}^{239} \mathrm{Pu} \)
D \( \cdot \frac{203}{90} \mathrm{Th} \)
Subject: Physics
A sphere of mass \( m \) moving with a
constant velocity \( \boldsymbol{v} \) hits another
stationary sphere of the same mass. If \( e \)
is the coefficient of restitution, then the
ratio of the velocities of the first sphere
to the second spheres after the collision
will be :
A \( \cdot\left(\frac{1+e}{1-e}\right) \)
B \( \cdot\left(\frac{e-1}{e+1}\right) \)
c. \( \left(\frac{1-e}{e+1}\right) \)
D. \( \left(\frac{1+e}{e-1}\right) \)
Subject: Maths
Given two independent events \( A \) and \( B \) such that \( \boldsymbol{P}(\boldsymbol{A})=\mathbf{0 . 3} \) and \( \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 6 .} \)
Find \( \boldsymbol{P}\left(\boldsymbol{A}^{\prime} \cap \boldsymbol{B}^{\prime}\right) \)
Subject: Physics
A man pushes a \( 10 k g \) box at a constant
velocity over a distance of \( 4 m \) on a
rough horizontal surface. The coefficient of kinetic friction between
the box and the floor is \( 0.3 . \) Calculate
the work done by the person on the box?
A . \( 12 J \)
B. \( 40 J \)
c. \( 75 J \)
D. \( 120 J \)
E . \( 400 J \)
Subject: Physics
A small piece of wire bent into an \( \boldsymbol{L} \)
shape, with upright and horizontal portions of equal lengths, is placed with the horizontal portion along the axis of
the concave mirror whose radius of
curvature is \( 10 \mathrm{cm} \). If the bend is \( 20 \mathrm{cm} \)
from the pole of the mirror,then the ratio
of the lengths of the images of the upright and horizontal portions of the wire is
A. 1: 2
B. 3: 1
c. 1: 3
D. 2: 1
Subject: Physics
A train travels from one station \( X \) to
another station \( Y \) at a rate of \( 20 \mathrm{km} / \mathrm{hr} \)
and returns at the rate of \( 30 \mathrm{km} / \mathrm{hr} \). The
average speed of the total journey is
\( \mathbf{A} \cdot 25 \mathrm{km} / \mathrm{hr} \)
B. \( 24 \mathrm{km} / \mathrm{hr} \)
\( \mathbf{c} .35 \mathrm{km} / \mathrm{hr} \)
D. \( 40 \mathrm{km} / \mathrm{hr} \)
Subject: Physics
Two capacitors connected in parallel
having the capacities \( C_{1} \) and \( C_{2} \) are
given ' \( q^{\prime} \) charge, which is distributed among them. The ratio of the charge on
\( C_{1} \) and \( C_{2} \) will be :
A \( \cdot \frac{C_{1}}{C_{2}} \)
в. \( \frac{C_{2}}{C_{1}} \)
\( \mathbf{c} \cdot C_{1} C_{2} \)
D. \( \frac{1}{C_{1} C_{2}} \)
Subject: Maths
The difference between the length \( 2 a \) of the transverse axis of a hyperbola of
eccentricity \( e \) and the length of its latus
rectum is :
A \( \cdot 2 a\left|3-e^{2}\right| \)
В \( \cdot 2 a\left|2-e^{2}\right| \)
c. \( 2 a\left(e^{2}-1\right) \)
D. \( a\left(2 e^{2}-1\right) \)
Subject: Physics
During an adiabatic change the density
becomes \( \frac{1}{16} t h \) of the initial value, then \( \frac{\boldsymbol{P}_{1}}{\boldsymbol{P}_{2}} \) is \( :(\gamma=\mathbf{1 . 5}) \)
A . 16
B. 4
c. 32
D. 64
Subject: Physics
Amperes circuital law is given by
A \( \cdot \oint \bar{H} \cdot \overline{d l}=\mu_{0} I_{e n c} \)
B . \( \oint \bar{B} . \overline{d l}=\mu_{0} I \)
C \( . \oint \bar{B} . \overline{d l}=\mu_{0} J \)
D \( \cdot \oint \bar{H} \cdot \bar{d} l=\mu_{0} J \)
Subject: Chemistry
Alcohol \( +H C l \leftrightharpoons \) Alkyl halide \( +H_{2} O \)
Fo this above reaction, which is needed
to make the reaction reversible.
A. Anhydrous \( Z n C l_{2} \)
в. conc. \( H_{2} S O_{4} \)
c. \( C a C l_{2} \)
D. Excess of water
Subject: Chemistry
Observe the following chemical reaction
\( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{4}+\boldsymbol{O}_{2} \boldsymbol{F}_{2} \rightarrow \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{\mathbf{6}}+\boldsymbol{O}_{2} \)
Enter 1 if true else 0