AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
Q Type your question.
and 142 as
shown. If an object O(a thin small rod) is placed upright on principal axis at a distance \( R \) from pole (i.e., placed at centre of curvature), then the size of image is different from size of object. STATEMENT-2: If a point object is
placed at centre of curvature of spherical surface separating two media of different refractive index, then the
image is also formed at centre of
curvature, i.e image distance is equal
to object distance.
A. Both Statement-1 and Statement-2 are True:
Statement-2 is a correct explanation for Statement-
B. Both Statement-1 and Statement-2 are True but Statement-2 is NOT a correct explanation for Statement-1
c. statement-1 is True but Statement-2 is False
Subject: Maths
The line \( 4 y-3 x+\lambda=0 \) touches the
circle \( x^{2}+y^{2}-4 x-8 y-5=0 . \) The
value of \( \lambda \) is
\( \mathbf{A} \cdot 29 \)
B . 10
c. -35
D. None of these
Subject: Maths
ff \( \boldsymbol{x}=\mathbf{3}+\mathbf{3}^{\mathbf{1} / \mathbf{3}}+\mathbf{3}^{\mathbf{2} / 3} \) then \( \boldsymbol{x}^{\mathbf{3}}-\mathbf{9} \boldsymbol{x}^{\mathbf{2}}+ \)
\( 18 x-12= \)
A . 2
B. 3
c. 0
D. 5
Subject: Physics
A solid cylinder rolls without slipping on
an inclined plane inclined at an angle \( \theta \) Find the linear acceleration of the
cylinder. Mass of the cylinder is \( M \)
A \( \cdot a=\frac{1}{3} g \sin \theta \)
B. \( a=\frac{2}{3} g \sin \theta \)
c. \( _{a=\frac{1}{3}} g \cos \theta \)
D. \( a=\frac{2}{3} g \cos \theta \)
Subject: Chemistry
Arrange the following compounds in increasing order of boiling points. Propan-1-ol, butan-1-ol, butan-2-ol, pentan-1-ol
A. Propan-1-ol, butan-2-ol, butan-1-ol, pentan-1-ol
B. Propan-1-ol, butan-1-ol,butan-2-ol, pentan-1-o
c. Pentan-1-ol, butan-2-ol, butan-1-ol, propan-1-ol
D. Pentan-1-ol, butan-1-01, butan-2-ol, propan-1-o
Subject: Maths
\( D \) and \( E \) are the mid-points of the sides
\( A B \) and \( A C \) of \( A B C \) and \( O \) is any point
on side \( B C . O \) is joined to \( A . \) If \( P \) and \( Q \)
are the mid-points of \( O B \) and \( O C \)
respectively, then \( D E Q P \) is:
A . a square
B. a rectangle
c. a rhombus
D. a parallelogram
Subject: Physics
Assertion
If infinity is taken as reference, the
gravitational potential is negative everywhere on the surface of earth.
Reason

Every body on its surface is bound to
gravitational attraction of earth.
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
Which statements are correct?
This question has multiple correct options
A. Bond energy of \( C \equiv O \) and \( N \equiv N \) are respectively
1070 and \( 946 k J \) mol\( ^{-1} \)
B. \( C O \) has resonating structure but \( N_{2} \) not
C. Bond order of both \( C O \) and \( N_{2} \) is three
D. Bond order of both \( C O^{+} \) and \( N_{2}^{+} \) are same
Subject: Maths
Assertion
\( \int_{0}^{\pi / 4} \frac{\cos x+\sin x}{\cos ^{2} x+\sin ^{4} x} d x=\frac{\pi}{4}+ \)
\( \frac{1}{2 \sqrt{3}} \log (2+\sqrt{3})=I \)
Reason
\( \boldsymbol{I}=\int_{0}^{1} \frac{\boldsymbol{d} \boldsymbol{x}}{1-\boldsymbol{x}^{2}+\boldsymbol{x}^{4}} \)
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
Let \( A \) and \( B \) be two events such that
\( \boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B})=\boldsymbol{P}(\boldsymbol{A})+\boldsymbol{P}(\boldsymbol{B})- \)
\( \boldsymbol{P}(\boldsymbol{A}) \boldsymbol{P}(\boldsymbol{B}) . \) If \( \boldsymbol{0}<\boldsymbol{P}(\boldsymbol{A})<1 \) and \( \boldsymbol{0}< \)
\( \boldsymbol{P}(\boldsymbol{B})<1, \) then \( \boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B})^{\prime} \) is equal to
A \( \cdot 1-P(A) \)
B . \( 1-P\left(A^{\prime}\right) \)
c. \( 1-P(A) P(B) \)
D \cdot \( [1-P(A)] P\left(B^{\prime}\right) \)
\( E \)
Subject: Maths
The condition that the equation \( a x+ \)
\( b y+c=0 \) represent a linear equation
in two variables is :
A \( . a \neq 0, b=0 \)
в. \( b \neq 0, a=0 \)
c. \( a=0, b=0 \)
D. \( a \neq 0, b \neq 0 \)
Subject: Physics
In Young's double slit experiment, one of
the slit is wider than other, so that
amplitude of the light from one slit
double of that from other slit. If \( \mathbf{I}_{\mathbf{m}} \) be
the maximum intensity, the resultant
intensity I. When they interfere at phase difference \( \phi \) is given by
A \( \cdot \frac{I_{m}}{9}(4+5 \cos \phi) \)
B. \( \frac{I_{m}}{3}\left(1+2 \cos ^{2} \frac{\phi}{2}\right) \)
C \( \cdot \frac{I_{m}}{5}\left(1+4 \cos ^{2} \frac{\phi}{2}\right) \)
D. \( \frac{I_{m}}{9}\left(1+8 \cos ^{2} \frac{\phi}{2}\right) \)
Subject: Maths
Function \( f(x) \) is defined as \( f(x)= \) \( \left\{\begin{array}{l}\frac{x-1}{2 x^{2}-7 x+5}, \quad x \neq 1 \\ -\frac{1}{3}, \quad x=1\end{array}\right. \)
Is \( f(x) \) differentiable at \( x=1 \) if yes find
\( \boldsymbol{f}^{\prime}(\mathbf{1}) \)
Subject: Physics
A radio active nucleus (initial mass number A and atomic number Z emits 4
\( \alpha \) - particles and 3 positrons).The ratio
of numbers of neutrons to that of
protons in the final nucleus will be
A \( \cdot \frac{A-Z-4}{Z-8} \)
B. \( \frac{A-Z-3}{Z-2} \)
c. \( \frac{A-Z-2}{Z-3} \)
D. \( \frac{A-Z-5}{Z-11} \)
Subject: Physics
n figure, \( \boldsymbol{k}=\mathbf{1 0 0} \boldsymbol{N} / \boldsymbol{m}, \boldsymbol{M}= \)
1 kgand \( F=10 N . \) A sharp blow by
some external agent imparts a speed of \( 2 m / s \) to the block towards left. Find the
sum of the potential energy of the spring and the kinetic energy of the block at this instant.
A . \( 0.25 J \)
в. 1.5
\( c \cdot 2 J \)
D. 2.5 5
Subject: Maths
If \( f(x) \) and \( g(x) \) are differentiable
functions for \( 0 \leq x \leq 1 \) such that
\( \boldsymbol{f}(\mathbf{0})=\mathbf{2}, \boldsymbol{g}(\mathbf{0})=\mathbf{0}, \boldsymbol{f}(\mathbf{1})=\mathbf{6}, \boldsymbol{g}(\mathbf{1})=\mathbf{2} \)
then in the interval \( (\mathbf{0}, \mathbf{1}) \)
\( \mathbf{A} \cdot f^{\prime}(x)=0 \) for all \( x \)
B . \( f^{\prime}(x)=2 g^{\prime}(x) \) for at least one \( x \)
C \( \cdot f^{\prime}(x)=2 g^{\prime}(x) \) for most one \( x \)
D. None of these
Subject: Maths
f \( \boldsymbol{P}(\boldsymbol{A})=\mathbf{0 . 4}, \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 8}, \boldsymbol{P}(\boldsymbol{B} / \boldsymbol{A})= \)
0.6. Find \( P(A / B) \)
Subject: Chemistry
At \( 80 C, \) the vapour pressure of pure benzene is \( 753 \mathrm{mm} \) Hg and of pure toluene \( 290 \mathrm{mm} \) Hg. Calculate the composition of a liquid in mole per cent which at \( 80 C \) is in equilibrium with the vapour containing 30 mole per cent of
benzene.
Subject: Maths
Compute the value of \( \theta \) in the first mean
value theorem \( \boldsymbol{f}(\boldsymbol{x}+\boldsymbol{h})=\boldsymbol{f}(\boldsymbol{x})+ \)
\( \boldsymbol{h} \boldsymbol{f}^{\prime}(\boldsymbol{x}+\boldsymbol{\theta h}) \) if \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{a} \boldsymbol{x}^{2}+\boldsymbol{b} \boldsymbol{x}+\boldsymbol{c} \)
A \( \cdot \frac{1}{2} \)
в. \( \frac{1}{3} \)
\( c \cdot \frac{1}{4} \)
D. \( \frac{1}{5} \)
Subject: Maths
Let two planes \( p_{1}: 2 x-y+z=2, \) and
\( \boldsymbol{p}_{2}: \boldsymbol{x}+\boldsymbol{2} \boldsymbol{y}-\boldsymbol{z}=\boldsymbol{3} \) are given. The
image of plane \( P_{1} \) in the plane mirror
\( P_{2} \) is
A. \( x+7 y-4 z+5=0 \)
B. \( 3 x+4 y-5 z+9=0 \)
c. \( 7 x-y+2 z-9=0 \)
0
D. \( 7 x+y+9 z+9=0 \)
Subject: Chemistry
When aluminium phosphide is reacted
with dil. \( \boldsymbol{H}_{2} \boldsymbol{S O}_{4}: \)
\( A \cdot S O_{2} \) is liberated
B. \( P H_{3} \) is evolved.
c. \( H_{2} S \) is evolved
D. \( H_{2} \) is evolved
Subject: Physics
Sunlight is reflected from a calm lake. The reflected light is \( 100 \% \) polarized at a certain instant. The angle between the sun light and the surface of lake is \( (\mu \) of
water is \( \frac{4}{3} \) ) \( \left(\tan ^{-1}\left(\frac{4}{3}\right)=53^{\circ} 4^{\prime}\right) \)
A .90
В. \( 53^{\circ} 4^{\prime} \)
\( \mathbf{c} \cdot 36^{\circ} 56^{\prime} \)
D. 45
Subject: Maths
The formula of standard deviation of
a grouped frequency distribution is
A \( \cdot \sqrt{\frac{\sum\left(x_{i}-\bar{x}\right)^{2}}{N}} \)
в. \( \frac{\sum\left(x_{i}-\bar{x}\right)^{2} f i}{N} \)
c. \( \sqrt{\frac{\sum\left(x_{i}-\bar{x}\right)^{2} f i}{N}} \)
D. \( \frac{\left.\sum\left(x_{i}-\bar{x}\right)^{2}\right\} i}{f i} \)
Subject: Maths
Find the area of the minor segment of a circle of radius \( 14 \mathrm{cm}, \) when its central angle is \( 60^{\circ} \). Also find the area of the
corresponding major segment. \( \left[\boldsymbol{U s e} \boldsymbol{\pi}=\frac{\mathbf{2 2}}{\mathbf{7}}\right] \)
Subject: Chemistry
\( \boldsymbol{C a}(\boldsymbol{O H})_{2}+\boldsymbol{N a}_{2} \boldsymbol{C O}_{3} \rightarrow \boldsymbol{C a} \boldsymbol{C O}_{3} \downarrow \)
\( +2 N a O H \)
This reaction made the basis of
manufacturing of NaOH in earlier days and pH of the solution was found to be greater than \( 14 . \) This indicates that
concentration of NaOH is very high. Hence, pH is greater than 14 If true enter 1 , else enter 0 .
Subject: Physics
A particle that carries a charge \( -q \) is placed at rest in uniform electric field
\( 10 N / C . \) It experiences a force and moves in a certain time \( t, \) it is observed to acquire a velocity \( 10 \vec{i}-10 \vec{j} \mathrm{m} / \mathrm{s} \). The
given electric field intersects a surface of area \( A m^{2} \) in the \( X \) -Z plane. Electric flux
through surface is:
в. \( 5 A N m^{2} / C \)
c. \( \sqrt{2} A N m^{2} / C \)
\( \mathbf{D} \cdot 2 \sqrt{5} A N m^{2} / C \)
Subject: Physics
The direction cosines of \( \hat{i}+\hat{j}+\hat{k} \) are
\( \mathbf{A} \cdot 1,1,1 \)
B. 2,2,2
c. \( 1 / \sqrt{2}, 1 / \sqrt{2}, 1 / \sqrt{2} \)
D. \( 1 / \sqrt{3}, 1 / \sqrt{3}, 1 / \sqrt{3} \)
Subject: Chemistry
Assertion
Following reaction fail to produce benzoic acid
Reason
Aryl halides do not usually undergo \( S_{N} 2 \)
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. Assertion is incorrect but Reason is correct
Subject: Physics
In free space, a particle A of charge \( 1 \mu C \) is held fixed at a point P. Another particle B of the same charge and mass \( 4 \mu g \) is kept at a distance of 1 mm from
P. if \( \mathrm{B} \) is released, then its velocity at a distance of \( 9 \mathrm{mm} \) from \( \mathrm{P} \) is :
\( \left[\text { Take } \frac{1}{4 \pi \varepsilon_{0}}=9 \times 10^{9} N m^{2} C^{-2}\right] \)
A \( .2 .0 \times 10^{3} \mathrm{m} / \mathrm{s} \)
в. \( 3.0 \times 10^{4} \mathrm{m} / \mathrm{s} \)
c. \( 1.5 \times 10^{2} m / s \)
D. \( 1.0 m / s \)
Subject: Chemistry
For the reaction, \( S O_{2}(g)+\frac{1}{2} O_{2}(g) \rightleftharpoons \)
\( \boldsymbol{S} \boldsymbol{O}_{3}(\boldsymbol{g}), \) the value of \( \boldsymbol{K}_{c} \) is \( 1.7 \times 10^{12} \) at
\( 300 K . \) Calculate the equilibrium
constants for the following reactions at
\( \mathbf{3 0 0 K}: \)
(।) \( 2 S O_{2}(g)+O_{2}(g) \rightleftharpoons 2 S O_{3}(g) \)
\( (\mathrm{II}) \boldsymbol{S} \boldsymbol{O}_{3}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{S} \boldsymbol{O}_{2}(\boldsymbol{g})+\frac{1}{2} \boldsymbol{O}_{2}(\boldsymbol{g}) \)
Subject: Physics
An electron of mass m with an initial velocity \( \vec{V}=V_{0} \hat{i}\left(V_{0}>0\right) \) enters an electric field \( \overrightarrow{\boldsymbol{E}}=-\boldsymbol{E}_{0} \hat{\boldsymbol{i}}\left(\boldsymbol{E}_{0}= \) constant \right.
\( >0) \) at \( t=0 . \) If \( \lambda_{0} \) is its de-Broglie
wavelength initially, then its de-Broglie wavelength at time t is?
A \( \cdot \lambda_{0}\left(1+\frac{e E_{0}}{m V_{0}} t\right) \)
в. \( \lambda_{0} \)
\( ^{c} \cdot \frac{\lambda_{0}}{\left(1+\frac{e E_{0}}{m V_{0}} t\right)} \)
D. \( \lambda_{0} \)
Subject: Maths
Let \( \boldsymbol{f}: \mathbb{R} \rightarrow \mathbb{R} \) be twice continuously
differentiable. Let \( \boldsymbol{f}(\mathbf{0})=\boldsymbol{f}(\mathbf{1})= \)
\( \boldsymbol{f}^{\prime}(\mathbf{0})=\mathbf{0} . \) Then
A \( . f^{\prime \prime}(x) \neq 0 \) for all \( x \)
B. \( f^{\prime \prime}(c)=0 \) for some \( c \epsilon \mathbb{R} \)
c. \( f^{\prime \prime}(x) \neq 0 \) if \( x \neq 0 \)
D. \( f^{\prime}(x)>0 \) for all \( x \)
Subject: Chemistry
The first IE of lithium is \( 5.4 \mathrm{eV} \) and first
electron affinity of \( C l \) is \( 3.6 \mathrm{eV} \). The value
\( \Delta \boldsymbol{H} \) for the reaction \( \boldsymbol{L} \boldsymbol{i}_{(\boldsymbol{g})}+\boldsymbol{C l}(\boldsymbol{g}) \rightarrow \)
\( \boldsymbol{L} \boldsymbol{i}_{\boldsymbol{g})}^{+}+\boldsymbol{C l}_{(\boldsymbol{g})}^{-}, \) is \( (\text {in } \mathrm{eV}) \)
A . +1.8
в. +2.8
c. -2.8
\( D \ldots+9 \)
Subject: Chemistry
Q Type your ques
\( 20^{\circ} \mathrm{C}:(1) 1 \) mole of solid
\( \left(C O O N H_{4}\right)_{2} H_{2} O \) is burned in oxygen
(2) 1 mole of solid \( (C O O H)_{2}\left(H_{2} O\right)_{2} \) is
burned in oxygen,
(3) 1 mole of solid
\( \left(C O O N H_{4}\right)_{2} H_{2} O \) is dissolved in a large excess of water, (4) 1 mole of solid
\( (C O O H)_{2}\left(H_{2} O\right)_{2} \) is dissolved in a
large excess of water, (5) 1 mole of oxalic acid in dilute solution is
neutralized with gaseous ammonia.
They found
(1) \( 189.86 k c a l,(2) \)
53.10kcal, (3) - 11.47kcal, (4)
\( -8.62 k c a l \)
(5) \( 43.13 k c a l ;(1) \) and were measured at constant volume, the
others at constant pressure. The end products of (1) and (2) were nitrogen, carbon-di-oxide and water. The heat of
formation for 1 mole of water from the
elements had previously been
determined as \( 68.35 k \) cal at constant
pressure and \( 20^{\circ} \mathrm{C} \). Find the change in
enthalpy when 1 mole of \( N H_{3} \) is formed
from the elements at \( 20^{\circ} \mathrm{C} \) (only
magnitude in nearest integer in kcal)
Subject: Physics
The figure shows the position time \( (x- \)
t) graph of one-dimensional motion of a
body of mass 0.4 kg. The magnitude of each impulse is
A. \( 0.4 \mathrm{Ns} \)
B. 0.8 Ns
c. \( 1.6 \mathrm{Ns} \)
D. \( 0.2 \mathrm{Ns} \)
Subject: Physics
A bar Magnet of Magnetic Moment 3.0 amp.m \( ^{2} \) is placed in a uniform Magnetic
induction field \( 2 \times 10^{-5} \) T. If each pole of
the magnet experience a force of \( 6 \times 10^{-4} \)
N, the length of the magnet is
\( A \cdot 05 \mathrm{m} \)
B. \( 0.3 \mathrm{m} \)
c. \( 0.2 \mathrm{m} \)
D. \( 0.1 \mathrm{m} \)
Subject: Maths
Assertion
STATEMENT 1: Domain of \( \tan ^{-1} x \) and
\( \cot ^{-1} x \) is \( R \)
Reason
STATEMENT 2: \( \boldsymbol{f}(\boldsymbol{x})=\tan \boldsymbol{x} \) and \( \boldsymbol{g}(\boldsymbol{x})= \)
\( \cot x \) are unbounded function
A. Both the statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT1
B. Both the statements are TRUE and STATEMENT 2 is NOT the correct explanation of STATEMENT1
C. STATEMENT1 is TRUE and STATEMENT 2 is FALSE
D. STATEMENT1 is FALSE and STATEMENT 2 is TRUE
Subject: Maths
Find vector equation of line passing through (1,4,1),(1,2,2)
A \( . \bar{r}=\bar{i}+(4-2 \lambda) \bar{j}+(1+\lambda) \bar{k} \)
B . \( \bar{r}=\bar{i}+(4+2 \lambda) \bar{j}+(1+\lambda) \bar{k} \)
c. \( \bar{r}=\bar{i}-(4-2 \lambda) \bar{j}+(1+\lambda) \bar{k} \)
D. \( \bar{r}=\bar{i}+(4-2 \lambda) \bar{j}+(1-\lambda) \bar{k} \)
Subject: Chemistry
Assertion
Small quantity of soap is used to
prepare a stable emulsion.
Reason
Soap lowers the interfacial tension
between oil and water.
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
Two particles undergo SHM along same line with same time period (T) and same amplitude
(A) At particular instant one particle is \( x=-A \) and the other is at \( x=0 \) If they move in same
direction then they will meet each other
at
A \( \cdot x=\frac{A}{2} \)
в. \( x=\frac{A}{\sqrt{2}} \)
c. \( x=\frac{A}{4} \)
D. \( x=\frac{4}{8} \)
Subject: Chemistry
MATCH THE COLUMN
\( (C) \)
\( (D) \)
\( (A) \rightarrow p, s(B) \rightarrow p, s(C) \rightarrow q, r(D) \rightarrow r, s \)
\( \mathbf{A} \cdot 1 \)
B. \( 1 .(\mathrm{A}) \rightarrow \mathrm{q}, \mathrm{s}(\mathrm{B}) \rightarrow \mathrm{p}, \mathrm{s}(\mathrm{C}) \rightarrow \mathrm{q}, \mathrm{r}(\mathrm{D}) \rightarrow \mathrm{r}, \mathrm{s} \)
C \( . \) 1. \( (A) \rightarrow p, s(B) \rightarrow q, s(C) \rightarrow p, r(D) \rightarrow r, s \)
D. \( 1 .(A) \rightarrow q, s(B) \rightarrow p, s(C) \rightarrow p, r(D) \rightarrow r, s \)
Subject: Physics
A dip circle, lying initially in the magnetic meridian is rotated through an angle \( \theta \) in the horizontal plane, then the tangent of the angle of dip is increased in the ratio
of :
A. \( 1: \cos \theta \)
B. \( 1: \tan \theta \)
c. \( 1: \cot \theta \)
D. \( 1: \sin \theta \)
Subject: Chemistry
If the intermolecular forces vanish
away, the volume occupied by the molecules of \( 4.5 k g \) water at \( S T P \) will
be:
\( \mathbf{A} \cdot 5.6 m^{3} \)
B. \( 5.6 L \)
c. \( 11.2 L \)
D. \( 11.2 m^{3} \)
Subject: Maths
\( A B \) is a chord of a circle with center 0
The tangent at B cuts AO produced at T
if \( \angle B A T=25^{\circ} \) Then the value of
\( \angle B T A \) is
A . \( 30^{\circ} \)
B. \( 60^{\circ} \)
\( c \cdot 25 \)
D. \( 40^{\circ} \)
Subject: Physics
Three charges, each \( +q \), are placed at
the corners of an isosceles triangle
\( A B C \) of sides \( B C \) and \( A C, 2 a . D \) and \( E \)
are the mid points of \( B C \) and \( C A \). The
work done in taking a charge \( Q \) from \( D \)
to \( \boldsymbol{E} \) is :
A \( \cdot \frac{e q Q}{8 \pi \epsilon_{0} a} \)
в. \( \frac{q Q}{4 \pi \epsilon_{0} a} \)
c. zero
D. \( \frac{3 q Q}{4 \pi \epsilon_{n} a} \)
Subject: Chemistry
The energy of an electron in the \( 3 s \)
orbital (excited state) of H-atom is:
A . \( -1.5 e V \)
B . \( -13.6 e V \)
c. \( -3.4 e V \)
D. \( -4.53 e V \)
E. \( 4.53 e V \)
Subject: Chemistry
For the reaction given below the values of standard Gibbs free energy of formation at \( 298 \mathrm{K} \) are given. What is the nature of the reaction?
\( \boldsymbol{I}_{2}+\boldsymbol{H}_{2} \boldsymbol{S} \rightarrow \mathbf{2} \boldsymbol{H} \boldsymbol{I}+\boldsymbol{S} \)
\( \boldsymbol{\Delta} \boldsymbol{G}_{f}^{0}(\boldsymbol{H} \boldsymbol{I})=\mathbf{1 . 8} \boldsymbol{k} \boldsymbol{J} \boldsymbol{m o l}^{-1} \)
\( \Delta G_{f}^{0}\left(H_{2} S\right)=33.8 k J m o l^{-1} \)
A. Non-spontaneous in forward direction
B. Spontaneous in forward direction
c. Spontaneous in backward direction
D. Non-spontaneous in both forward and backwardd directions
Subject: Physics
In the given circuit \( R \) in pure resistance
and \( X \) is unknown circuit element. An
AC voltage source is applied across \( \boldsymbol{A} \)
and \( C . \) If \( V_{A B}=V_{A C}, \) then \( X \) is
A. Pure resistance
B. Pure inductance
C. Combination of inductance and capacitance at
resonance
D. None of the above
Subject: Maths
25 students can do a job in 12 days, but on the starting day, five of them informed thet they are not coming. By what fraction will the number of days
required for doing the whole work get increased?
A \( \cdot \frac{3}{5} \)
B. \( \frac{3}{7} \)
\( c \cdot \frac{3}{4} \)
D.
Subject: Maths
The contrapositive of "if \( x \) has courage
then \( x \) will win", is
A. If \( x \) will in, then \( x \) has courage
B. If \( x \) has no courage, then \( x \) will not win.
c. If \( x \) will not win, then \( x \) has no courage
D. If \( x \) will not win, then \( x \) has courage
Subject: Physics
In the cube of side ' \( a^{\prime} \) shown in the
figure, the vector from the central point
of the face \( A B O D \) to the central point
of the face \( B E F O \) will be
A \( \cdot \frac{1}{2} a(\hat{i}-\hat{k}) \)
B \( \cdot \frac{1}{2} a(\hat{j}-\hat{i}) \)
c. \( \frac{1}{2} a(\hat{k}-\hat{i}) \)
D. \( \frac{1}{2} a(\hat{j}-\hat{k}) \)
Subject: Chemistry
The number of moles of \( C r_{2} O_{7}^{2-} \) needed
to oxidize 0.136 equivalent of \( N_{2} H_{5}^{+} \)
through the reaction \( N_{2} H_{5}^{+}+ \) \( \boldsymbol{C r}_{2} \boldsymbol{O}_{\mathbf{7}}^{2-} \rightarrow \boldsymbol{N}_{2}+\boldsymbol{C r}^{3+}+\boldsymbol{H}_{2} \boldsymbol{O}, \) is :
A . 0.236
B. 0.087
c. 0.136
D. 0.488
Subject: Maths
A man has 7 relatives, 4 of them are
ladies and 3 gentlemen; his wife has 7 relatives and 3 of them are ladies and 4
gentlemen. The number of ways they can invite a dinner party of 3 ladies and 3 gentlemen so that there are 3 of men's relatives and 3 of wife's relative is
A . 455
B. 565
c. 485
D. None of these
Subject: Physics
The resistance of hot tungesten filament is about 10 times the cold resistance. The resistance of \( 100 \mathrm{W} \) and
\( 200 \mathrm{V} \) lamp, when not in use is
A . \( 40 \Omega \)
B. 20\Omega
c. \( 400 \Omega \)
D. 200\Omega
Subject: Chemistry
\( Z n O(S)+A \rightarrow Z n(s)+B: \)
A \( \cdot a=H_{2}, b=O_{2} \)
В \( . a=C, b=C O \)
\( \mathbf{c} \cdot a=S, b=S O_{2} \)
D. \( a=N, b=N O \)
Subject: Physics
A square loop of side length \( a \) having \( n \)
turns is kept in a horizontal plane. \( \mathbf{A} \) uniform magnetic field \( B \) exists in vertical direction as shown in figure. Now, the loop is rotated with constant angular speed \( \omega \) as shown below. Which of the following statement is correct?
\( \begin{array}{llllll}\mathbf{X} & \mathbf{X} & \mathbf{X} & \mathbf{X} & \mathbf{X} & \mathbf{X}\end{array} \)
\( \mathbf{x} \quad \mathbf{x} \quad \mathbf{x} \quad \mathbf{x} \quad \mathbf{x} \quad \mathbf{x} \quad \mathbf{x} \)
A. Same emf is induced in both cases (i) and (ii)
B. Maximum emf is induced in case (i)
c. Emf induced in case
(ii) is more than (i)
D. No emf induced in case (ii)
Subject: Chemistry
A closed system receives \( 200 k J \) of
constant volume. It then rejects \( 100 k J \) of heat while it has \( 50 k J \) of work done
on it at constant pressure. If an adiabatic process can be found which can be found which will restore the
system to its initial state, the work done by the system during this process is
A. \( 100 k J \)
J \( J \)
B. \( 50 k J \)
c. \( 150 k J \)
D. 200 k
Subject: Chemistry
Assertion
Silver metal does not show any change
when it is placed in HCl solution.
Reason
Silver metal does not react with dilute
HCI
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
Which of the following is the negation of the statement, For all odd primes \( \boldsymbol{p}<\boldsymbol{q} \)
there exists positive non-primes \( r<s \)
such that \( p^{2}+q^{2}=r^{2}+s^{2} \)
A. For all odd primes \( p<q \) there exists positive nonprimes \( r<s \) such that \( p^{2}+q^{2}=r^{2}+s^{2} \)
B. There exists odd primes \( p<q \) such that for all positive non-primes \( r<s, p^{2}+q^{2}=r^{2}+s^{2} \)
C. There exists odd primes \( p<q \) such that for all positive non-primes \( r<s, p^{2}+q^{2} \neq r^{2}+s^{2} \)
D. For all odd primes \( p<q \) and for all positive nonprimes \( r<s, p^{2}+q^{2} \neq r^{2}+s^{2} \)
Subject: Maths
Choose the correct options for the figure
This question has multiple correct options
A. Point A is substitute into the equation for line \( l_{2} \)
B. Point A is substitute into the equation for line \( l_{1} \)
C. Point \( C \) is substitute into the equation for line \( l_{1} \)
D. Point \( C \) is substitute into the equation for line \( l_{2} \).