AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A rod of moment of inertia I and length
is suspended from a fixed end and
given small oscillations about the point of suspension, the restoring torque is
found to be \( -(\boldsymbol{m} \boldsymbol{g} \boldsymbol{L} / \mathbf{2}) \boldsymbol{s} \boldsymbol{i} \boldsymbol{n} \boldsymbol{\theta} . \) What will
be the angular equation of motion of the
SHM
A \( \cdot \frac{d^{2} \theta}{d t^{2}}+(m g L / I) \theta=0 \)
B \( \cdot \frac{d^{2} \theta}{d t^{2}}+(m g L / 2 I) \theta=0 \)
\( ^{\mathbf{c}} \cdot \frac{d^{2} \theta}{d t^{2}}+(2 m g L / I) \theta=0 \)
D. \( \frac{d^{2} \theta}{d t^{2}}+(m g L / 4 I) \theta=0 \)
Subject: Physics
Two circular coils each of 100 turns are
held such that one lies in the vertical
plane and the other in the horizontal plane with their centres coinciding. The radius of vertical and horizontal coils
are \( 20 \mathrm{cm} \) and \( 30 \mathrm{cm} \) respectively. If the magnetic field at their common centre is zero, find current in each coil
Horizontal component of earth's magnetic field is 27.8 Aim and angle of
dip at this place is \( 30^{\circ} \)
Subject: Chemistry
\( \begin{array}{ll}\text { List-I } & \text { List-II } \\ \text { A) } S_{8}+N a_{2} S O_{3} \rightarrow & \text { 1) } M \text { ustard gas } \\ \text { B) } 2 C_{2} H_{4}+S_{2} C l_{2} \rightarrow & \text { 2) } H_{2} S O_{3} \\ \text { C) } S+3 F_{2} \rightarrow & \text { 3) } N a_{2} S_{2} O_{3} \\ \text { D) } S C l_{4}+H_{2} O \rightarrow & \text { 4) } S F_{6}\end{array} \) The correct match is:
\( A \cdot(A)-4,(B)-2,(C)-1,(D)-3 \)
B. \( (A)-3,(B)-1,(C)-4,(D)-2 \)
C \( \cdot(A)-1,(B)-3,(C)-2,(D)-4 \)
D. \( (A)-2,(B)-4,(C)-3,(D)-1 \)
Subject: Maths
If \( \frac{a x}{\cos \theta}+\frac{b y}{\sin \theta}=a^{2}-b^{2} \) and
\( \frac{a x \sin \theta}{\cos ^{2} \theta}-\frac{b y \cos \theta}{\sin ^{2} \theta}=0 \) then \( (a x)^{2 / 3}+ \)
\( (b y)^{2 / 3}=\left(a^{2}-b^{2}\right)^{2 / 3} ? \)
A. True
B. False
Subject: Physics
One day Chetan's mother developed a severe stomach ache all of a sudden.
She was rushed to the doctor who
suggested for an immediate endoscopy test and gave an estimate of
expenditure for the same. Chetan immediately asked her class teacher and arranged the money and rushed to the hospital. On realizing that Chetan belonged to a below average income group family even the doctor offered concession for the test fee. The test was
conducted successfully. Answer the following questions based on the above information;
(a) Which principle in optics is made use of in endoscopy.?
(b) Briefly explain the values reflected in the action taken by the teacher
(c) In what way do you appreciate the response of the doctor on the given situation?
Subject: Maths
Four vertices of a tetrahedron are
(0,0,0),(4,0,0),(0,-8,0) and
\( (0,0,12) . \) Its centroid has the
coordinates
A \( \cdot\left(\frac{4}{3},-\frac{8}{3}, 4\right) \)
В. (2,-4,6)
c. (1,-2,3)
a 5
D. none of these
Subject: Physics
A parallel beam of light \( \lambda=5000 A^{\circ} \)
falls normally on a single narrow slit of
width \( 0.001 m m . \) The light is focused by a convex lens on a screen placed in the focal plane. The first minimum will be
formed for the angle of diffraction are equal to:
A . \( 0^{\circ} \)
В. \( 15^{\circ} \)
\( c \cdot 30^{0} \)
D. \( 50^{\circ} \)
Subject: Chemistry
\( 500 m L \) of a glucose solution contains \( 6.02 \times 10^{22} \) molecules. The
concentration of the solution is
\( \mathbf{A} \cdot 0.1 M \)
в. \( 1.0 M \)
\( \mathbf{c} \cdot 0.2 M \)
D. \( 2.0 M \)
Subject: Chemistry
single \( N-N \) bond is weaker than the
single \( P-P \) bond. This is because of:
This question has multiple correct options
A. larger \( N-N \) bond length in comparison to \( P-P \)
bond length
B. high interelectronic repulsion of the non-bonding electrons, owing to the small \( N-N \) bond length in comparison to that in \( P-P \) single bond
c. higher electronegativity of \( N \) in comparison to \( P \)
D. smaller atomic size of \( N \) as compared to that of \( P \)
Subject: Physics
A thin circular ring of area \( A \) is held perpendicular to a uniform magnetic field of induction B. A small cut is made
in the ring and a galvanometer is
connected across the ends such that
the total resistance of the circuit is \( \mathrm{R} \).
When the ring is suddenly squeezed to
zero area, the charge flowing through
the galvanometer is
A. \( \frac{B R}{A} \)
в. \( \frac{B A}{R} \)
c. ABR
D. \( \frac{B^{2} A}{R^{2}} \)
Subject: Physics
Two particles \( A \) and \( B \) are released
from the top of incline. If \( \boldsymbol{m}_{\boldsymbol{A}}>\boldsymbol{m}_{\boldsymbol{B}} \)
then
A. Both will reach simultaneously if \( A \) released before \( B \)
B. Both will reach simultaneously if \( A \) released after \( B \)
c. Both will reach simultaneously if both are released together
D. Both will reach simultaneously if both are released together and \( A \) is given some initial velocity
Subject: Chemistry
In which of the following complexes the nickel metal is in highest oxidation
state?
\( \mathbf{A} \cdot N i(C O)_{4} \)
в. \( K_{2} N i F_{6} \)
C \( \cdot\left[N i\left(N H_{3}\right)_{6}\right]\left(B F_{4}\right) \)
D. \( K_{4}\left[N i(C N)_{6}\right] \)
Subject: Physics
A uniform metre scale balances
horizontally on a knife edge placed at \( 55 \mathrm{cm} \) mark. When a mass of \( 25 g \) is supported from one end, then the mass of the scale is:
A. \( 200 g \)
в. \( 225 g \)
c. \( 350 g \)
D. \( 275 g \)
Subject: Physics
Two beams, \( A \) and \( B \), of plane polarized light with mutually perpendicular planes of polarization are seen through a polaroid. From the position when the beam A has maximum intensity (and beam B has zero intensity), a rotation of
Polaroid through \( 30^{\circ} \) makes the two
beams appear equally bright. If the initial intensities of the two beams are
\( \boldsymbol{I}_{A} \) and \( \boldsymbol{I}_{B} \) respectively, then \( \boldsymbol{I}_{\boldsymbol{A}} / \boldsymbol{I}_{\boldsymbol{B}} \)
equals:
A . \( I \)
B. \( I / 3 \)
\( c \cdot 3 \)
D. \( 3 / 2 \)
Subject: Chemistry
Find the equilibrium constant for the reaction, \( \boldsymbol{F e}^{2+}+\boldsymbol{C e}^{4+} \rightleftharpoons \boldsymbol{F e}^{3+}+\boldsymbol{C e}^{3+} \)
\( \left[\text { Given: } \boldsymbol{E}_{C e^{4+} / C e^{3+}}^{o}=\right. \)
\( \left.\mathbf{1} . \mathbf{4 4} \boldsymbol{V} ; \boldsymbol{E}_{\boldsymbol{F e}^{3+} / \mathbf{F e}^{\mathbf{2 +}}}^{\boldsymbol{o}}=\mathbf{0 . 6 8} \boldsymbol{V}\right] \)
A . \( 7.6 \times 10^{12} \)
B . \( 5.4 \times 10^{12} \)
c. \( 3.3 \times 10^{12} \)
D. None of the above
Subject: Physics
The relative permittivity of water is \( 81 . \) If
\( \varepsilon_{0} \) and \( \varepsilon \) are permittivities of vaccum
and water respectively Then:
A \( \cdot \varepsilon_{0}=9 \varepsilon_{w} \)
В. \( \varepsilon_{0}=81 \varepsilon_{w} \)
\( \mathbf{c} \cdot \varepsilon_{w}=9 \varepsilon_{0} \)
D. \( \varepsilon_{w}=81 \varepsilon_{0} \)
Subject: Chemistry
Which of the following is the correct representation of electron dot structure of nitrogen?
\( A \)
\( \therefore \ddot{N}: \dot{N} \)
в. \( \therefore \dot{\mathbf{N}}: \dot{\mathbf{N}} \)
\( \therefore \dot{\mathbf{N}}: \dot{\mathbf{N}} \)
D. \( \therefore \) N:
Subject: Maths
Given \( \boldsymbol{x}-\boldsymbol{y}+\mathbf{3} \boldsymbol{z}=\mathbf{5} ; \mathbf{4} \boldsymbol{x}+\mathbf{2} \boldsymbol{y}-\boldsymbol{z}=\mathbf{0} \)
\( ;-\boldsymbol{x}+\mathbf{3} \boldsymbol{y}+\boldsymbol{z}=\mathbf{5} \)
If
\( \mathbf{A}=\left[\begin{array}{ccc}\mathbf{1} & \mathbf{- 1} & \mathbf{3} \\ \mathbf{4} & \mathbf{2} & -\mathbf{1} \\ -\mathbf{1} & \mathbf{3} & \mathbf{1}\end{array}\right], \boldsymbol{X}=\left[\begin{array}{l}\boldsymbol{x} \\ \boldsymbol{y} \\ \boldsymbol{z}\end{array}\right], \boldsymbol{D}= \)
\( \left.\begin{array}{l}\mathbf{5} \\ \mathbf{0} \\ \mathbf{5}\end{array}\right\} \) such that \( \mathbf{A X}=\mathbf{D} \)
Show that \( A \) is non singular and the
cofactor elements of a matrix \( \boldsymbol{A} \) is
\( \left[\begin{array}{ccc}+(2+3) & -(4-1) & +(12+2) \\ -(-1-9) & +(1+3) & -(3-1) \\ +(1-6) & -(-1-12) & +(2+4)\end{array}\right) \)
Subject: Physics
A ball is thrown from ground at an angle
\( \theta \) with horizontal and with an initial
speed \( u_{0} . \) For the resulting projectile motion, the magnitude of average velocity of the ball up to the point when
it hits the ground for the first time is \( V_{1} \)
After hitting the ground, the ball rebounds at the same angle \( \theta \) but with
a reduced speed of \( u_{0} / \alpha . \) Its motion continues for a long time as shown in figure. If the magnitude of average velocity of the ball for entire duration of
motion is \( 0.8 V_{1}, \) the value of \( \alpha \) is
Subject: Maths
If the conjugate of \( (x+i y)(1-2 i) \) is
\( 1+i, \) then
This question has multiple correct options
A \( \cdot x-i y=\frac{1+i}{1-2 i} \)
B. \( x+i y=\frac{1-i}{1-2 i} \)
c. \( _{y}=\frac{1}{5} \)
D. \( x=-\frac{1}{5} \)
Subject: Chemistry
Free radical polymerisation requires a
free radical initiator. The most
commonly used free radical initiator is:
\( \mathbf{A} \cdot P h-C O-O-O-C O P h(\text { benzoylperoxide }) \)
B. \( \left(C H_{3}\right)_{3} C-O-O-C\left(C H_{3}\right)_{3} \) (tert-butyl peroxide)
\( \mathbf{c} \cdot P h-N-(N O)-P h(\text { azoxybenzene }) \)
D. \( C H_{2} N_{2} \) (diazomethane)
Subject: Maths
Let \( \lim _{x \rightarrow a} f(x) \) exists but it is not equal to
\( f(a) . \) Then \( f(x) \) is discontinuous at \( x=a \)
and a is called a removable
discontinuity. If \( \lim _{x \rightarrow a^{-}} f(x)= \)
land \( \lim _{x \rightarrow a^{+}} f(x)=m \) exist but \( l \neq \)
\( m . \) Then a is called a jump
discontinuity. If one of the limits (left
hand limit or right hand limit ) does not
exist, then a is called an infinite
discontinuity. \( \operatorname{Let} f(x)=\left\{\begin{array}{cl}x^{2}+|x|, & x<-5 \\ 25 & x=-5 \\ \frac{3 x^{2}}{5}+15 & x>-5\end{array} . \) Then \right.
\( \boldsymbol{x}=-\mathbf{5} \) is
A. a point of discontinuity
B. a jump discontinuity
c. a removable discontinuity
D. an infinite discontinuity
Subject: Chemistry
The oxidation number of \( S \) in \( N a_{2} S_{4} O_{6} \)
is :
A . +2.5
B. +2 and +3 (two \( S \) have +2 and other two have +3 )
\( \mathrm{c} \cdot+2 \) and +3 (three \( S \) have +2 and one \( S \) has +3
D. +5 and 0 (two S have +5 and the other two \( S \) have 0 )
Subject: Maths
Calculate the values of the
determinants:
\( \left|\begin{array}{cccc}\mathbf{1} & \mathbf{1} & \mathbf{1} & \mathbf{1} \\ \mathbf{1} & \mathbf{2} & \mathbf{3} & \mathbf{4} \\ \mathbf{1} & \mathbf{3} & \mathbf{6} & \mathbf{1 0} \\ \mathbf{1} & \mathbf{4} & \mathbf{1 0} & \mathbf{2 0}\end{array}\right| \)
Subject: Physics
Three identical bars \( A, B \) and \( C \) are
made of different magnetic materials. When kept in a uniform magnetic field, the field lines around them look as
given in the figure. Make the
correspondence of these bars with their material being diamagnetic (D), ferromagnetic (F) and paramagnetic (P)
A. \( A \leftrightarrow F, B \leftrightarrow D, C \leftrightarrow P \)
в. \( A \leftrightarrow D, B \leftrightarrow P, C \leftrightarrow F \)
c. \( A \leftrightarrow F, B \leftrightarrow P, C \leftrightarrow D \)
D. \( A \leftrightarrow P, B \leftrightarrow F, C \leftrightarrow D \)
Subject: Chemistry
Which one of the following paires of elements is most likely to form an ionic
compount?
\( \mathbf{A} \cdot \mathbf{B} \) and \( C I_{2} \)
B. \( \mathrm{K} \) and \( \mathrm{O}_{2} \)
c. \( O_{2} \) and \( C I_{2} \)
D. Al and \( I_{2} \)
Subject: Physics
The mass ' \( M^{\prime} \) of a stone that can be
moved by water current depends upon velocity ' \( V^{\prime} \) of the stream, density of
water ' \( d \) and acceleration due to gravity
'g'. The relation between the mass and velocity is:
\( \mathbf{A} \cdot M \propto V^{6} \)
B. \( M \propto V^{2} \)
c. \( M \propto d^{2} \)
D. \( M \propto V \)
Subject: Physics
A force \( (10 \hat{i}-3 \hat{j}+6 \hat{k}) \) newton acts on a body of mass \( 100 g \) and displaces it from \( (6 \hat{i}-5 \hat{j}-3 \hat{k}) \) metre to \( (10 \hat{i}-2 \hat{j}+7 \hat{k}) m \)
The work done is
\( \mathbf{A} \cdot 21 J \)
в. \( 361 J \)
c. \( 121 J \)
D. \( 1000 J \)
Subject: Chemistry
One mole of an ideal diatomic gas
undergoes a transition from \( A \) to \( B \)
along a path \( A B \) as shown in the figure
The change in internal energy of the gas during the transition is:
A. 20 .
B. \( -12 k J \)
\( c \cdot 20 k J \)
D. \( -20 k J \)
Subject: Maths
For construction of a quadrilateral \( A B C D, \) where \( A B=4.2 \mathrm{cm}, B C=3.8 \)
\( \mathrm{cm}, C D=4.9 \mathrm{cm}, A D=5.4 \mathrm{cm} \) and
\( \angle B=72, \) its steps for construction is given injumbled form. Identify the third step from the following
1) From \( B \), set off \( B C=3.8 \mathrm{cm} \)
2) Draw \( A B=4.2 \mathrm{cm} \) and : Make
\( \angle A B X=72 \)
3) With \( A \) as center and radius equal to
\( 5.4 \mathrm{cm} \) draw an arc.
4) With \( C \) as center and radius equal to
\( 4.9 \mathrm{cm}, \) draw another arc, cutting the previous arc at \( D \). Join \( A D \) and \( C D \)
A. 3
в.
\( c \)
D.
Subject: Maths
If \( \mathbf{f}(\mathbf{x}) \) is minimum at \( \mathbf{x}=\mathbf{a} \) then
A. There exists \( \delta>0 \) such that \( a-\delta<x<a \Rightarrow f(x)<f(a) \)
B. There exists \( \delta>0 \) such that \( a<x<a+\delta \Rightarrow f(x)>f(a) \)
C. There exists \( \delta>0 \) such that \( a-\delta<x<a+\delta \Rightarrow \)
\( f(x) \geq f(a) \)
D. There exists \( \delta>0 \) such that \( a-\delta<x<a+\delta \Rightarrow \)
\( f(x) \leq f(a) \)
Subject: Chemistry
List-I
A) Polystyrene
\( \mathbf{p}) \boldsymbol{C}_{6} \boldsymbol{H}_{\mathbf{5}}- \)
\( \boldsymbol{C H}=\boldsymbol{C H}_{2} \)
B) Buna-S
q) \( C H_{2}=C H- \)
\( \boldsymbol{C H}=\boldsymbol{C H}_{2} \)
C) Buna - N
r) \( C H_{2} O H- \)
\( C H_{2} O H \)
D) Terylene
s) Condensation polymer This question has multiple correct options
A \( \cdot a-p \)
B. b-p.q
\( c \cdot c- \)
D. d-r.s
Subject: Maths
State whether the following statement is true or false.
\( \frac{\cos A-\sin A+1}{\cos A+\sin A-1}=\operatorname{cosec} A+\cot A \)
(by using the identity \( \operatorname{cosec}^{2} \boldsymbol{A}=1+ \)
\( \left.\cot ^{2} A .\right) \)
A . True
B. False
Subject: Biology
Assertion
Systematics is the branch of biology
that deals with classification of living organisms.
Reason
The aim of classification is to group the
organisms in an orderly manner
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
If \( f:\left(-\frac{\pi}{2}, \frac{\pi}{2}\right) \rightarrow(-\infty, \infty) \) is defined
by \( f(x)=\tan x, \) then \( f^{-1}(2+\sqrt{3})= \)
\( A \cdot \frac{\pi}{12} \)
в.
c. \( \frac{5 \pi}{12} \)
D.
Subject: Physics
A charged oil drop is moving downward
with a velocity \( V_{1} . \) As it acquires an
additional charge it moves up with the velocity \( V_{2} \) in the same electric field. It
fall freely with a velocity \( V \) in the absence of electric field. The ratio of the
charges before and after acquiring additional charge is
A. \( \frac{V_{1}+V}{V_{2}-V_{1}} \)
B. \( \frac{V_{1}+V_{2}}{2 V} \)
c. \( \frac{V-V_{1}}{V+V_{2}} \)
D. \( \frac{V_{2}-2 V_{1}}{2 V_{1}+V} \)
Subject: Maths
Let \( A \) be a \( 3 \times 3 \) matrix such that
\[
\boldsymbol{A} \times\left[\begin{array}{lll}
\mathbf{1} & \mathbf{2} & \mathbf{3} \\
\mathbf{0} & \mathbf{2} & \mathbf{3} \\
\mathbf{0} & \mathbf{1} & \mathbf{1}
\end{array}\right]=\left[\begin{array}{lll}
\mathbf{0} & \mathbf{0} & \mathbf{1} \\
\mathbf{1} & \mathbf{0} & \mathbf{0} \\
\mathbf{0} & \mathbf{1} & \mathbf{0}
\end{array}\right]
\]
Then \( \boldsymbol{A}^{-1} \) is :
A.
\[
\left[\begin{array}{lll}
3 & 2 & 1 \\
3 & 2 & 0 \\
1 & 1 & 0
\end{array}\right]
\]
B.
\[
\left[\begin{array}{lll}
0 & 1 & 3 \\
0 & 2 & 3 \\
1 & 1 & 1
\end{array}\right]
\]
c.
\[
\left[\begin{array}{lll}
3 & 1 & 2 \\
3 & 0 & 2 \\
1 & 0 & 1
\end{array}\right]
\]
D.
\[
\left[\begin{array}{lll}
1 & 2 & 3 \\
0 & 1 & 1 \\
0 & 2 & 3
\end{array}\right]
\]
Subject: Physics
In a region of uniform magnetic
induction \( B=10^{-2} \) tesla, a circular coil
of radius \( 30 \mathrm{cm} \) and resistance \( \pi^{2} \) ohm is rotated about an axis, which is perpendicular to the direction of B and which forms a diameter of coil. If the
coil rotates at 200 r.p.m., the amplitude of alternating current induced in the coil is :-
A \( \cdot 4 \pi^{2} \mathrm{m} \)
B. 30 mA
\( c \cdot 6 m \)
D. 200 mA
Subject: Physics
Two lenses of focal length \( f_{1}=10 \mathrm{cm} \)
and \( f_{2}=20 c m \) are kept as shown. The
resultant power of combination will be:
A. \( -10 D \)
B. \( 5 D \)
\( c .-5 D \)
D. \( 10 D \)
Subject: Physics
The potential difference across a \( 150 m H \) inductor as a function of time
is shown in figure. Assume that the initial value of the current in the
inductor is zero. What is the current
when \( t=4.0 m s ? \)
A \( \cdot 2.67 \times 10^{-4} \mathrm{A} \)
B \( \cdot 3.67 \times 10^{-2} \mathrm{A} \)
\( c \cdot 6.67 \times 10^{-2} \mathrm{A} \)
D. \( 9.67 \times 10^{-4} \mathrm{A} \)
Subject: Biology
A large quantity of fluid is filtered every day by the nephrons in the kidneys, only about \( 1 \% \) of it is excreted as urine. The
remaining \( 99 \% \) of the filtrate
A. Gets collected in the renal pelvis
B. Is lost as sweat.
c. Is stored in the urinary bladder.
D. Is reabsorbed into the blood
Subject: Chemistry
The specific conductivity of a saturated
solution of silver chloride is \( 2.30 \times \)
\( 10^{-6} \) mho \( c m^{-1} \) at \( 25^{\circ} C . \) Calculate the
solubility of silver chloride at \( 25^{\circ} \mathrm{C} \) if
\( \lambda_{A g^{+}}=61.9 m h o c m^{2} m o l^{-1} \) and
\( \boldsymbol{\lambda}_{C l^{-}}=\mathbf{7 6 . 3} \boldsymbol{m h o c m}^{2} \boldsymbol{m o l}^{-1} \)
Subject: Physics
A body of mass \( m \) is dropped freely from
a height \( h \). The de-Broglie wavelength of the body as it reaches the ground is:
A \( \cdot \frac{h}{\sqrt{g H}} \)
в. \( \frac{h}{m \sqrt{g H}} \)
c. \( \frac{h}{2 \sqrt{g H}} \)
D. \( \frac{h}{m \sqrt{2 g H}} \)
Subject: Maths
If \( p \) and \( q \) are the lengths of
perpendiculars from the origin to the \( \operatorname{lines} x \cos \theta-y \sin \theta=k \cos 2 \theta \) and
\( x \sec \theta+y \csc \theta=k, \) respectively prove
that \( p^{2}+4 q^{2}=k^{2} \)
Subject: Maths
If \( \boldsymbol{A}(\overrightarrow{\boldsymbol{a}}), \boldsymbol{B}(\overrightarrow{\boldsymbol{b}}), \boldsymbol{C}(\overrightarrow{\boldsymbol{c}}) \) be the vertices
of a triangle whose circumcentre is the origin, then orthocenter is given by
\( \frac{\vec{a}+\vec{b}+\vec{c}}{3} \)
\( ^{\mathrm{B}} \frac{\vec{a}+\vec{b}+\vec{c}}{2} \)
c. \( \vec{a}+\vec{b}+\vec{c} \)
D. None of these
Subject: Chemistry
Consider the three statements about
reaction energy diagrams and the relative magnitudes of the activation
energy, \( E_{a}, \) and the enthalpy of reaction,
\( \Delta \boldsymbol{H} \)
One or more of the statements is true.
Identify the correct statement or
combination of statements from the
four choices below.
Statement
For an endothermic reaction, the magnitude
of \( E_{a} \) is always greater than \( \triangle H \)

For an exothermic reaction, the magnitude of
| \( E_{a} \) is always greater than \( \triangle H \)
For an exothermic reaction, adding a catalyst
III \( \quad \) will decrease the magnitude of \( \triangle H \)
A. Statement I only is true.
B. Statement II only is true.
C. Both statements I and II are true.
D. Both statements I and III are true.
Subject: Physics
Dimensional formula for the universal
gravitational constant \( G \) is
A \( \cdot M^{-1} L^{2} T^{-2} \)
B . \( M^{0} L^{0} T^{0} \)
c. \( M^{-1} L^{3} T^{-2} \)
D. \( M^{-1} L^{3} T^{-1} \)
Subject: Maths
Evaluate \( \cos ^{-1} x+ \)
\( \cos ^{-1}\left\{\frac{x}{2}+\frac{1}{2} \sqrt{3-3 x^{2}}\right\}, x \epsilon\left[\frac{1}{2}, 1\right] \)
A \( \cdot-\frac{\pi}{6} \)
B. \( +\frac{\pi}{6} \)
\( c \cdot-\frac{\pi}{3} \)
D. \( +\frac{\pi}{3} \)
Subject: Physics
A coil having an area \( A_{0} \) is placed in a
magnetic field which changes from \( \boldsymbol{B}_{\mathbf{0}} \)
to \( 4 B_{0} \) in time interval t. The e.m.f.
induced in the coil will be
A \( \cdot 3 A_{0} B_{0} / t \)
в. \( 4 A_{0} B_{0} / t \)
c. \( 3 B_{0} / A_{0} t \)
D \( \cdot 4 A_{0} / B_{0} t \)
Subject: Maths
If \( f(x) \) be such that \( f(x)=\max \)
\( \left\{|2-x|, 2-x^{3}\right\}, \) then
This question has multiple correct options
A continuous \( \forall x \in R \)
\[
f(x) \text { is continuous } x \in R
\]
B. \( f(x) \) is differentiable \( \forall x \in R \)
c. \( f(x) \) is non-differentiable at one point only
D. \( f(x) \) is non-differentiable at 4 points only
Subject: Physics
Two plano-convex lenses each of focal
3
length \( 10 c m \) s refractive index \( \frac{-a r e}{2} \) are
placed as shown in the figure in the
space left, water \( \left(\boldsymbol{R} \boldsymbol{I}-\frac{\boldsymbol{4}}{\mathbf{3}}\right) \) is filled.The
whole arrangement is in air. The optical power of the system is (in dioptre):
A . 6.67
B . -6.67
\( c \cdot 33.3 \)
D. 20
Subject: Chemistry
Assertion
lodination of alkanes is carried out in
the presence of oxidising agents like
\( H I O_{3} \) or \( H N O_{3} \)
Reason
lodination of alkanes is an irreversible
reaction.
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
Assertion
Conc. \( H_{2} S O_{4} \) can not be used to
prepare pure HBr from NaBr.
Reason
It reacts slowly with NaBr
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
The pH of an aqueous solution of
\( \boldsymbol{C H}_{3} \boldsymbol{C O O N} \boldsymbol{a} \) of concentration \( \boldsymbol{C}(\boldsymbol{M}) \) if
given by
A \( \cdot \quad 7-\frac{1}{2} p K_{a}-\frac{1}{2} \log C \)
B. \( \frac{1}{2}^{p K_{w}}+\frac{1}{2} p K_{b}+\frac{1}{2} \log C \)
\( ^{\mathrm{c}} \cdot \frac{1}{2}^{p} K_{w}-\frac{1}{2} p K_{b}-\frac{1}{2} \log C \)
\( ^{\mathrm{D} \cdot \frac{1}{2} p K_{w}+\frac{1}{2} p K_{a}+\frac{1}{2} \log C} \)
Subject: Physics
Two equal negative charges are fixed at the points \( (0, \pm a) \) on the \( y \) -axis. \( A \) positive charge \( Q \) is released from rest at the points \( (2 a, 0) \) on the \( x \) -axis. The
charge \( Q \) will :
A. execute simple harmonic motion about the origin
B. move to the origin ad remain at rest
c. move to infinity
D. execute oscillatory but not simple harmonic motion
Subject: Maths
\( \operatorname{Given} \boldsymbol{A}(\mathbf{1},-\mathbf{1}, \mathbf{0}) ; \boldsymbol{B}(\mathbf{3}, \mathbf{1}, \mathbf{2}) \)
\( C(2,-2,4) \) and \( D(-1,1,-1) \) which of
the following points neither lie on \( \boldsymbol{A B} \)
nor on \( C D ? \)
A \( .(2,2,4) \)
В. (2,-2,4)
c. (2,0,1)
D. (0,-2,-1)
Subject: Maths
Find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \) for the following
i) \( y=\tan ^{-1}\left(\frac{3 x-x^{3}}{1-3 x^{2}}\right),-\frac{1}{\sqrt{3}}<x< \)
\( \frac{1}{\sqrt{3}} \)
ii) \( y=\sin ^{-1}\left(\frac{1-x}{1+x}\right), 0<x<1 \)
Subject: Maths
Consider the following statements:
\( f(x)=\ln x \) is an increasing function
on \( (0, \infty) \)
2. \( f(x)=e^{x}-x(\ln x) \) is an increasing
function on \( (1, \infty) \) Which of the above statements is lare
correct?
A. 1 only
B. 2 only
c. Both 1 and 2
D. Neither 1 nor 2