AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Bleaching powder and bleach solution
are produced on a large scale and is used in several house-hold products. The effectiveness of bleach solution is
often measured by iodometry. Bleaching powder contains a salt of an oxoacid as
one of its components. The anhydride of that oxoacid is:
A. \( C l_{2} O \)
в. \( C l_{2} O_{7} \)
\( \mathrm{c} \cdot \mathrm{ClO}_{2} \)
D. \( C l_{2} O_{6} \)
E \( . C l_{2} O_{3} \)
F. \( C l_{2} O_{5} \)
G. \( C l_{3} O_{9} \)
н. \( C l_{3} O_{5} \)
Subject: Maths
Solve the system \( : \mathbf{6} \boldsymbol{x}+\mathbf{5} \boldsymbol{y}=-\mathbf{3}, \boldsymbol{y}= \)
\( -2 x-7 \)
A. (-2,4)
()
в. (-1,2)
c \( .(-8,9) \)
D. (-7,8)
Subject: Physics
A particle of mass \( m \) is made to move
with uniform speed \( v \) along the perimeter of a regular polygon of \( 2 n \) sides. The magnitude of impulse applied at each corner of the polygon is:
A \( \cdot_{2 m v \sin } \frac{\pi}{2 n} \)
B. \( _{m v \sin } \frac{\pi}{2 n} \)
\( ^{\mathrm{c}} 2 m v \cos \left(\frac{\pi}{2 n}\right) \)
D. \( _{m v \cos } \frac{\pi}{2 n} \)
Subject: Chemistry
Vapor pressure of pure water at \( 25^{\circ} \mathrm{C} \) is
\( 20.0 \mathrm{mm} \) of \( H g \% . \) And the lowering of
vapor pressure of a sugar solution is
\( 0.070 \mathrm{mm} \) of \( H g . \) What will be the mole
fraction of water?
A . 0.9965
B. 0.0035
c. 0.0024
D. 0.7785
Subject: Maths
If \( S(n)=i^{n}+i^{-n}, \) where \( i=\sqrt{-1} \) and
\( n \) is a positive integer, then the total number of distinct values of \( \boldsymbol{S}(\boldsymbol{n}) \) is:
A . 1
B. 2
\( c .3 \)
D. 4
Subject: Chemistry
An organic compound is estimated through Dumas method and was found
to evolve 6 moles of \( C O_{2} .4 \) moles of
\( H_{2} O \) and 1 mole of nitrogen gas. The
formula of the compound is:
A \( \cdot C_{12} H_{8} N \)
в. \( C_{12} H_{8} N_{2} \)
c. \( C_{6} H_{8} N \)
D. \( C_{6} H_{8} N_{2} \)
Subject: Maths
If the S.D. of \( \boldsymbol{y}_{1}, \boldsymbol{y}_{2}, \boldsymbol{y}_{3}, \dots . . \boldsymbol{y}_{n} \) is \( \boldsymbol{6}, \) then
the variance of \( \boldsymbol{y}_{1}-\boldsymbol{3}, \boldsymbol{y}_{2}-\boldsymbol{3}, \boldsymbol{y}_{3}- \)
\( \mathbf{3}, \dots . . y_{n}-3, \) is
\( A \cdot 6 \)
B. 36
\( c .3 \)
D. 27
Subject: Maths
The range of \( f(x)=\frac{1-\tan x}{1+\tan x} \) is
\( A \cdot(-\infty, \infty) \)
в. \( (-\infty, 0) \)
c. \( (0, \infty) \)
D. \( (-\infty,-1) \cup(-1, \infty) \)
Subject: Physics
A ball is thrown vertically upward from the \( 12 \mathrm{m} \) level with an initial velocity of \( 18 \mathrm{m} / \mathrm{s} . \) At the same instant an open
platform elevator passes the \( 5 \mathrm{m} \) level, moving upward with a constant velocity of \( 2 \mathrm{m} / \mathrm{s} \). Determine \( \left(\mathrm{g}=9.8 \mathrm{m} / \mathrm{s}^{2}\right) \)
(a) when and where the ball will meet
the elevator
(b) the relative velocity of the ball with respect to the elevator when the ball
hits the elevator.
Subject: Maths
The percentage of marks obtained by the students in a class of 50 are given
below. Find the mean for the following
data.
Marks \( \begin{array}{lll}\mathbf{4 0}- & \mathbf{5 0}- & \mathbf{6 0}- \\ \mathbf{5 0} & \mathbf{6 0} & \mathbf{7 0}\end{array} \)
\( (\%) \)
Number
of
12
14
students
A . \( 64.6 \% \)
B . \( 65.6 \% \)
c. \( 66.6 \% \)
D. \( 67.6 \% \)
Subject: Physics
Assertion
The various energy bands in a solid may or may not overlap depending on the structure of the solid.
Reason
If they do not overlap then the intervals between them represent energies which the electrons in the solid cannot have.
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
Find \( p, q, r \) and \( s, \) if \( \left[\begin{array}{cc}\boldsymbol{p}+\boldsymbol{4} & \boldsymbol{2} \boldsymbol{q}-\boldsymbol{7} \\ \boldsymbol{s}-\boldsymbol{3} & \boldsymbol{r}+\boldsymbol{2} \boldsymbol{s}\end{array}\right]=\left[\begin{array}{cc}\boldsymbol{6} & -\boldsymbol{3} \\ \boldsymbol{2} & \boldsymbol{1} \boldsymbol{4}\end{array}\right] \)
Subject: Maths
\( f(\vec{a}, \vec{b}, \vec{c} \) are unit vectors such that \( \vec{a}+\vec{b}+\vec{c}=0, \) find the value of \( \vec{a} \cdot \vec{b}+\vec{b} \cdot \vec{c}+\vec{c} \cdot \vec{a} \)
Subject: Physics
If an alternating current \( \boldsymbol{i}=\boldsymbol{i}_{m} \sin \omega \boldsymbol{t} \) is
flowing through a capacitor then
voltage drop \( \Delta V_{C} \) across capacitor \( C \)
will be?
A \( \cdot-\frac{i_{m}}{\omega C} \sin \omega t \)
в. \( -\frac{i_{m}}{\omega C} \cos \omega t \)
c. \( -\frac{i_{m}}{\omega C}\left(\sin \omega t+\frac{\pi}{4}\right) \)
D. \( \frac{i_{m}}{\omega C}\left(\sin \omega t-\frac{\pi}{4}\right) \)
Subject: Maths
If \( \bar{u}, \bar{v}, \bar{w} \) are non-coplanar vectors and p, \( q \) are real numbers, then the equality \( [\mathbf{3} \overline{\boldsymbol{u}} \boldsymbol{p} \overline{\boldsymbol{v}} \boldsymbol{p} \overline{\boldsymbol{w}}]-[\boldsymbol{p} \overline{\boldsymbol{v}} \overline{\boldsymbol{w}} \boldsymbol{q} \overline{\boldsymbol{u}}]-[\mathbf{2} \overline{\boldsymbol{w}} \boldsymbol{q} \overline{\boldsymbol{v}} \boldsymbol{q} \overline{\boldsymbol{u}}]= \)
0 hold for
A. Exactly one value of \( (p, q) \)
B. Exactly two value of \( (p, q) \)
c. More than two but not all values of \( (p, q) \)
D. All value of \( (p, q) \)
Subject: Chemistry
The redox reaction among the following
is :
\( \mathbf{A} \cdot \) reaction of \( \left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right] \mathrm{Cl}_{3} \) with \( \mathrm{AgNO}_{3} \)
B. formation of ozone from atmospheric oxygen in the presence of sunlight
C. combination of dinitrogen with dioxygen at \( 2000 K \)
D. reaction of \( H_{2} S O_{4} \) with \( N a O H \)
Subject: Physics
The co-ordinates of a particle restricted to move in a plane is given by \( \boldsymbol{X}=\boldsymbol{6} \cos \pi \boldsymbol{t} \)
\( \boldsymbol{y}=1-4 \cos 2 \pi t \)
The magnitude of acceleration of particle at \( t=1.5 s \) is (where \( x \) and \( y \)
are in meter and \( t \) is in seconds)
A. Zero
В. \( 6 \pi^{2} m / s^{2} \)
c. \( 16 \pi^{2} \mathrm{m} / \mathrm{s}^{2} \)
D. \( 8 \pi^{2} m / s^{2} \)
Subject: Chemistry
A gas is expanded from volume \( V_{0} \) to
\( 2 V_{0} \) under three different processes.
Process 1 is isobaric process, process 2
is isothermal and process 3 is
adiabasic. Let \( \triangle \boldsymbol{U}_{1}, \triangle \boldsymbol{U}_{2} \) and \( \triangle \boldsymbol{U}_{3} \) be
the change in internal energy of the gas
in these three processes. Then
A. \( \triangle U_{1}>\triangle U_{2}>\triangle U_{3} \)
В. \( \triangle U_{1}<\Delta U_{2}<\triangle U_{3} \)
c. \( \triangle U_{2}<\triangle U_{1}<\Delta U_{3} \)
D. \( \triangle U_{2}<\Delta U_{3}<\triangle U_{1} \)
Subject: Chemistry
What is the frequency of light emitted
when an electron in a hydrogen atom jumps from \( 2^{n d} \) orbit to \( 1^{s t} \) orbit?
A \( .24 .63 \times 10^{-34} \mathrm{Hz} \)
В. \( 13.6 \times 10^{-34} \mathrm{Hz} \)
c. \( 3.4 \times 10^{-34} \mathrm{Hz} \)
D. \( 1.6 \times 10^{-24} \mathrm{Hz} \)
Subject: Physics
A particle of mass \( M \) is placed at the centre of a uniform spherical shell of mass \( 2 M \) and radius The gravitational potential on the surface of the shell is:
A. \( -\frac{G M}{R} \)
в. \( -\frac{3 G M}{R} \)
c. \( -\frac{2 G M}{R} \)
D. zero
Subject: Chemistry
Which of the following half-reactions is correctly balanced?
A \( \cdot M n O_{4}^{-} \rightarrow M n^{2+}+4 H_{2} O \)
B. \( C u+2 A g^{+} \rightarrow 2 A g+C u^{2+} \)
\( \mathbf{c} \cdot H_{2}+O H^{-} \rightarrow 2 H_{2} O \)
\( \mathbf{D} \cdot P b^{2+}+2 e^{-} \rightarrow P b \)
E \( \cdot 2 F^{-}+2 e^{-} \rightarrow F_{2} \)
Subject: Chemistry
The EMF of a cell corresponding to the reaction:
\( \boldsymbol{Z} \boldsymbol{n}(\boldsymbol{s})+\boldsymbol{2} \boldsymbol{H}^{\oplus}(\boldsymbol{a} \boldsymbol{q}) \rightarrow \)
\( Z n^{2+}(0.1 M)+H_{2}(g, 1 a t m) \) is \( 0.82 V \)
\( \operatorname{at} 25^{\circ} C \)
The pH of the solution at the hydrogen electrode is:
\( \boldsymbol{E}_{Z n^{2+} \mid \boldsymbol{Z n}}^{\ominus}=-\mathbf{0 . 7 6} \boldsymbol{V} \)
\( \boldsymbol{E}_{\boldsymbol{H}^{\ominus} \mid \boldsymbol{H}_{2}}^{\Theta}=\mathbf{0} \)
If the value is \( 63 \times 10-x \), then what is
the value of \( x ? \)
Subject: Maths
In triangle \( A B C, M \) is mid-point of \( A B \)
and a straight line through \( \boldsymbol{M} \)
and parallel to \( B C \) cuts \( A C \) in \( N \). Find
the lenghts of \( A N \) and \( M N \) if \( B C=7 \)
\( \mathrm{cm} \) and \( \boldsymbol{A C}=\mathbf{5} \mathrm{cm} \)
A. \( A N=2.5 \mathrm{cm} \) and \( M N=3.5 \mathrm{cm} \)
B. \( A N=1.5 \mathrm{cm} \) and \( M N=3.5 \mathrm{cm} \)
c. \( A N=2.5 \mathrm{cm} \) and \( M N=4.5 \mathrm{cm} \)
D. none of the above
Subject: Chemistry
Which of the following statements given
about emulsions is incorrect?
A. The droplets in emulsions are often negatively charged and can be precipitated by electrolytes.
B. Emulsion can be diluted with any amount of the dispersed liquid. On the other hand, the dispersion medium when mixed, forms a separate layer.
C. Emulsions can be broken into constituent liquids by heating, freezing, centrifuging, etc.
D. Emulsions also show Brownian movement and
Tyndall effect.
Subject: Chemistry
How many moles of electrons weighs
one kilogram? [Mass of electron \( =\mathbf{9 . 1 0 8} \times \mathbf{1 0}^{-\mathbf{3 1}} \mathbf{k g} \)
Avogadro's number \( =6.023 \times 10^{23} \)
A. \( 6.023 \times 10^{23} \)
в. \( \frac{1}{9.108} \times 10^{31} \)
c. \( \frac{6.023}{9.108} \times 10^{54} \)
D. \( \frac{1}{9.108 \times 6.023} \times 10^{8} \)
Subject: Physics
Consider a 'beam expander' which
consists of two converging lenses of focal lengths \( 40 \mathrm{cm} \) and \( 100 \mathrm{cm} \) having a common optical axis. A laser beam of diameter \( 2 \mathrm{mm} \) is incident on the \( 40 \mathrm{cm} \)
focal length lens. Then what is the
diameter (in mm) of the final beam (see
figure)?
Subject: Chemistry
Consider the statements about
cellulose.
I. It is the principle structural component of vegetable matter.
II. Wood has \( 40-50 \% \) cellulose.
III. Cotton has \( 90 \% \) cellulose.
IV. Cellulose is formed in the
photosynthesis process. The incorrect statements is/are:
A. only I
B. only II and III
c. only I, Il and IV
D. none of the above
Subject: Physics
Find the time dependence of the velocity
\( \overrightarrow{\boldsymbol{v}} \) vector.
A \( . \vec{v}=2 a \vec{i}-b t \vec{j} \)
B . \( \vec{v}=-2 a \vec{i}-2 b t \vec{j} \)
C \( . \vec{v}=-2 a \vec{i}-b t \vec{j} \)
D. \( \vec{v}=a \vec{i}-2 b t \vec{j} \)
Subject: Maths
\( \int_{1}^{2}\left(x+\frac{1}{x}\right)^{3 / 2} \frac{x^{2}-1}{x^{2}} d x \)
\( \mathbf{A} \cdot \frac{5}{2} \sqrt{\left(\frac{5}{2}\right)}+\frac{8}{5} \sqrt{2} \)
B \( \cdot \frac{5}{2} \sqrt{\left(\frac{5}{2}\right)}-\frac{8}{5} \sqrt{2} \)
\( \mathrm{C} \cdot \sqrt{\left(\frac{5}{2}\right)}-\frac{8}{5} \sqrt{2} \)
D \( \frac{3}{2} \sqrt{\left(\frac{3}{2}\right)}-\frac{8}{5} \sqrt{2} \)
Subject: Maths
Find the degree measure of the angle
subtended at the centre of a circle of
radius \( 10 \mathrm{cm} \) by an arc of length \( 22 \mathrm{cm} \) \( \left(\boldsymbol{U} \boldsymbol{s e} \boldsymbol{\pi}=\frac{\boldsymbol{2} \boldsymbol{2}}{\mathbf{7}}\right) \)
Subject: Physics
The terminal velocity of a rain drop is \( 30 c m / s, \) If the viscosity of air is \( 1.8 \times \) \( 10^{-5} N s m^{-2}, \) The radius of rain drop is:
A. \( 0.01 m m \)
B. \( 0.5 m m \)
c. \( 0.05 \mathrm{mm} \)
D. \( 1 \mathrm{mm} \)
Subject: Physics
Surface are of \( _{13} A l^{27} \) is \( S_{0}, \) then surface
area of \( Z n^{64} \) is then
A \( \cdot \frac{16}{9} S_{0} \)
в. \( \frac{4}{3} S_{0} \)
c. \( \frac{64}{27} S_{0} \)
D. \( \frac{3}{2} S_{0} \)
Subject: Maths
In the given figure, \( A B C \) is an equilatera
triangle whose side is \( 2 \sqrt{3} \mathrm{cm} . \) A circle
is drawn which passes through the
midpoints \( D, E \) and \( F \) of its sides. The area of the shaded region is:
\( A \)
B \( \cdot \frac{1}{4}(2 \pi-\sqrt{3}) c m^{2} \)
c. \( \frac{1}{4}(\pi-3 \sqrt{3}) c m^{2} \)
D.
Subject: Maths
\( f\left(1, \frac{\pi}{6}\right),\left(2, \frac{\pi}{3}\right) \) and \( \left(3, \frac{\pi}{2}\right) \) be the
angular points of a triangle.Then the
area of the triangle is
\( \left(\frac{13-3 \sqrt{3}}{4}\right) \) sq.unit
\( ^{\mathbf{B}} \cdot\left(\frac{11-3 \sqrt{3}}{4}\right) \) sq.unit
\( ^{c} \cdot\left(\frac{10-3 \sqrt{3}}{4}\right) \) sq.unit
\( D \)
Subject: Physics
Two uniform rods of equal length \( \left(l_{n}\right) \) and equal mass have the coefficient of linear expansion \( \alpha \) and \( 2 \alpha \) are placed in
contact on a smooth horizontal surface
as shown in the figure. The temperature
of the system is \( \theta^{0} C . \) Now the
temperature is increased by \( \Delta \theta^{0} C \).The junction of the rods will shift its initial
position by:
A \( \cdot \frac{l_{0} \alpha \Delta \theta}{2} \)
B. \( \frac{l_{0} \alpha \Delta \theta}{3} \)
c. \( \frac{l_{0} \alpha \Delta \theta}{4} \)
D
Subject: Chemistry
Assertion
Red phosphorous on heating changes its colour to black.
Reason
Black phosphorus contain \( P_{4} \) units.
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
Two identical particles of mass \( m \) carry
charge \( Q \) each. Initially one is at rest on a smooth horizontal plane and the other is projected along the plane directly towards first particle from a large
distance with speed \( v \). The closest
distance of approach will be
A \( \cdot \frac{1}{4 \pi \varepsilon_{0}} \frac{Q^{2}}{m v} \)
B. \( \frac{1}{4 \pi \varepsilon_{0}} \frac{4 Q^{2}}{m v} \)
\( ^{\mathbf{C}} \frac{1}{4 \pi \varepsilon_{0}} \frac{4 Q^{2}}{m v^{2}} \)
\( ^{\mathrm{D}} \frac{1}{4 \pi \varepsilon_{0}} \frac{2 Q^{2}}{m v^{2}} \)
Subject: Physics
The \( x-y \) plane is the boundary
between two transparent media. Medium-1 with \( z>0 \) has refractive
index \( \sqrt{2} \) and medium- 2 with \( z<0 \) has a refractive index \( \sqrt{3} . \) A ray of light in medium-1 given by the vector \( \overrightarrow{\boldsymbol{A}}= \) \( 6 \sqrt{3} \hat{i}+8 \sqrt{3} \hat{j}-10 \hat{k} \) is incident on the
plane of separation. Find the unit vector
in the direction of refracted ray in medium-2.
\( \mathbf{A} \cdot 45^{\circ} \)
B. \( 60^{\circ} \)
\( \mathbf{c} \cdot 75^{\circ} \)
D. 30 \( ^{\circ} \)
Subject: Chemistry
The number of positively and negatively charged ions present in \( 1 L \) of \( 0.1 M \) aluminium sulphate solution are:
A \( \cdot 1.2 \times 10^{22}+v e \) ions and \( 1.8 \times 10^{22}-v e \) ions
B . \( 1.2 \times 10^{23}+ \) ve ions and \( 1.8 \times 10^{22}- \) ve ions
c. \( 1.2 \times 10^{23}+ \) ve ions and \( 1.8 \times 10^{23}- \) ve ions
D. \( 1.2 \times 10^{21}+v e \) ions and \( 1.8 \times 10^{21}- \) ve ions
Subject: Maths
The differential equation of all circles passing through the origin and having their centres on the X-axis, is
A \( x^{2}=x^{2}+2 x y \frac{d y}{d x} \)
B. \( _{y^{2}}=x^{2}-2 x y \frac{d y}{d x} \)
c. \( _{y^{2}=x^{2}+x y \frac{d y}{d x}} \)
D. \( y^{2}=x^{2}+3 x y \frac{d y}{d x} \)
Subject: Chemistry
Some properties of sulphuric acid are listed below. Choose the role played by
sulphuric acid as \( A, B, C \) or \( D \) which is
responsible for the reaction
(i) to (v).
Some role/s may be repeated:
\( M g O+H_{2} S O_{4} \rightarrow M g S O_{4}+H_{2} O \)
A . Dilute acid
B. Dehydrating agent
c. Non-volatile acid
D. oxidising agent
Subject: Physics
In a zener-regulated power supply a
zener diode with \( V_{z}=6 \) volt is used for
regulation. The load current is to be \( 4 m A \) and the unregulated input is 10
volt. What should be the value of series
resistor \( \boldsymbol{R}_{s} \) if the current through diode
is five times the load current?
Subject: Physics
A barometer is faulty. When the true barometer reading are 73 and \( 75 \mathrm{cm} \) of \( \mathrm{Hg}, \) the faulty barometer reads \( 69 \mathrm{cm} \) and \( 70 \mathrm{cm} \) respectively. What is the true reading when the faulty barometer reads \( 69.5 \mathrm{cm} ? \)
Subject: Physics
Q Type your question-
length \( 4.9 \mathrm{m} \). The other end of the spring (see the figure) is fixed. The system lies on a horizontal frictionless surface. The
block is stretched by \( 0.2 \mathrm{m} \) and released from rest at \( t=0 . \) It then executes simple
harmonic motion with angular
frequency \( \omega=\frac{\pi}{3} r a d / s \)
Simultaneously at \( t=0, \) a small pebble is projected with speed v from point \( \mathrm{P} \) at an angle of 45 as shown in the figure. Point \( P \) is at a horizontal distance of 10
\( \mathrm{m} \) from \( 0 . \) If the pebble hits the block at \( t=1 \mathrm{s}, \) the value of \( \mathrm{v} \) is
\( \left(\operatorname{take} g=10 m / s^{2}\right) \)
\( \mathbf{A} \cdot \sqrt{50} m / s \)
B. \( \sqrt{51} \mathrm{m} / \mathrm{s} \)
c. \( \sqrt{52} \mathrm{m} / \mathrm{s} \)
D. \( \sqrt{53} \mathrm{m} / \mathrm{s} \)
Subject: Biology
Study the graph which shows results of
three different experiments \( P, Q \) and \( R \)
Now compare curves \( Q \) and \( R \) and
answer the following question:
Which factor has been altered to
produce the differences you can see
between two curves?
\( A \cdot C O_{2} \) concentration
B. Temperature
\( c . \) Both \( A \) and \( B \)
D. None of the above
Subject: Maths
if \( ^{2017} c_{0}+^{2017} c_{1}+^{2017} c_{2}+ \)
\( \ldots+^{2017} c_{1008}=\lambda^{2}(\lambda>0), \) then
remainder when \( \lambda \) is divided by 33 is
\( A \cdot 8 \)
B. 13
\( c \cdot 17 \)
D. 25
Subject: Maths
Find a vector in the direction of vector \( \vec{a}=\hat{i}-2 \hat{j} \) that has magnitude 7 units.
A \( \cdot \frac{7}{\sqrt{5}}(\hat{i}-2 \hat{j}) \)
B. \( \frac{7}{\sqrt{5}}(\hat{i}+2 \hat{j}) \)
c. \( \frac{7}{\sqrt{5}}(-\hat{i}-2 \hat{j}) \)
D. None of these
Subject: Physics
A short linear object of length \( L \) lies on the axis of a spherical mirror of focal length \( f \) at a distance \( u \) from the mirror.
Its image has an axial length \( L \) equal to
\( ^{\mathrm{A}} \cdot\left[\frac{f}{(u-f)}\right]^{1 / 2} \)
\( ^{\mathrm{B}} \cdot\left[\frac{u+f}{(f)}\right]^{1 / 2} \)
\( ^{\mathbf{c}} \cdot\left[\frac{u+f}{(f)}\right]^{2} \)
\( ^{\mathrm{D}} \cdot\left[\frac{f}{(u-f)}\right]^{2} \)
Subject: Chemistry
From application of thermodynamics on
chemical reaction,
we get \( \Delta G=\Delta G^{0}+R T \ln Q \)
Also \( \Delta G=\Delta H-T \Delta S \)
If \( \Delta G=0, \) reaction is at equilibrium.
If \( \Delta G>0 \) reaction is non-spontaneous
under given condition. \( I f \Delta G<0 \)
reaction is spontaneous under given condition.
Consider the reaction given below. \( \boldsymbol{A}(s) \rightleftharpoons 2 \boldsymbol{B}(\boldsymbol{g}) \quad \boldsymbol{\Delta} \boldsymbol{H}^{0}=\mathbf{1 6 0} \mathrm{KJ} / \mathrm{mol} \)
\( \Delta S^{0}=400 \mathrm{J} / \mathrm{mol}-\mathrm{K} \) at \( 400 \mathrm{K} \)
Which of the following is correct at 400
K?
A. On adding more \( A(s) \), more \( B(g) \) is produced, when \( A(s) \) and \( B(g) \) were in equilibrium
B. The equilibrium constant at \( 400 \mathrm{K} \) can't be found
c. The reaction is at equilibrium at \( 400 \mathrm{K} \) and standard condition
D. The \( \Delta G \) of the reaction is greater than zero, at 400 k and standard condition
Subject: Physics
Two particles are in SHM in parallel straight lines close to each other. Amplitude \( A \) and time period \( T \) of both
the particles are equal. At \( t=0, \) one
particle is at displacement \( \boldsymbol{x}_{\mathbf{1}}=+\boldsymbol{A} \) and other at \( x_{2}=-\frac{A}{2} \) an they are
approaching towards each other, after what time they will cross each other?
A. \( T / 3 \)
в. \( T / 4 \)
\( \mathrm{c} \cdot 5 T / 6 \)
D. \( T / 6 \)
Subject: Chemistry
Which of the following ions having following electronic structure would have maximum magnetic moment?
A \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 3 d^{3} \)
B . \( 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 3 d^{5} \)
\( \mathbf{c} \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 3 d^{7} \)
D \cdot \( 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 3 d^{9} \)
Subject: Chemistry
Suppose elements \( X \) and \( Y \) combine to
form two compounds \( X Y_{2} \) and \( X_{3} Y_{2} \)
when 0.1 mole of former weight \( 10 g \)
while 0.05 mole of the latter weighs \( 9 g \)
What are the atomic weights of \( X \) and
\( Y ? \)
A. 40,30
B. 60,40
c. 20,30
D. 30,20
Subject: Physics
A ray of light is incident on the left vertical face of glass cube of refractive
index \( n_{2}, \) as shown in figure. The plane
of incidence is the plane of the page, and the cube is surrounded by liquid (refractive index \( =\{n\}_{-}\{1\} \) ). What is the
largest angle of incidence \( \theta_{1} \) for which
total internal reflection occurs at the
top surface?
Subject: Physics
The \( x \) location and mass of two masses
are given as \( (1 m, 3 k g) \) and \( (-2 m, 2 k g) \)
A third mass weighs \( 1 k g \)
Given that the center of mass of the
system lies at \( x=-1 m, \) what must be
the \( x \) position of the third mass?
A \( . x=-5 m \)
B . \( x=-3 m \)
c. \( x=-2.5 m \)
D. \( x=-2 m \)
E . \( x=2 m \)
Subject: Chemistry
When water is added to \( H_{2} S O_{4} \), the
reaction is exothermic. It is because of
formation of:
A. viscous nature of \( H_{2} S O_{4} \)
B. hydrates of \( H_{2} S O_{4} \)
c. corrosive nature of \( H_{2} S O_{4} \)
D. none of these
Subject: Physics
In a long straight solenoid with cross-
sectional radius \( a \) and number of turns
per unit length, \( n \), the current varies
with the rate \( \boldsymbol{I} \boldsymbol{A} / \boldsymbol{s} \). The magnitude of
the induced current field strength as a function of distance \( r \) from the solenoid
axis is
A \( \cdot \frac{1}{2} \frac{n I a^{2}}{\mu_{0} r} \)
В \( \cdot \frac{1 I a^{2}}{2 \mu_{0} r} \)
С \( \cdot \frac{n I a^{2}}{\mu_{0} r} \)
D. \( \frac{1}{2} \frac{\mu_{0} n I a^{2}}{r} \)
Subject: Maths
Find the value of the determinant \( \left|\begin{array}{ccc}1 & 0 & 0 \\ 2 & \cos x & \sin x \\ 3 & \sin x & \cos x\end{array}\right| \)
\( \mathbf{A} \cdot \cos 2 x \)
B.
\( c \cdot 0 \)
D. \( \sin 2 x \)
Subject: Chemistry
The density of water and ethanol at room temperature is \( 1.0 \mathrm{g} / \mathrm{mL} \) and \( 0.789 g / \) mL respectively. What volume
of ethanol contains the same number of
molecules as are present in \( 100 \mathrm{mL} \) of
water?
A. \( 307.8 \mathrm{mL} \)
B . \( 168.7 \mathrm{mL} \)
c. \( 323.9 \mathrm{mL} \)
D. \( 253.3 \mathrm{mL} \)
Subject: Maths
Solve:
\( \int x^{2 / 3}\left(1+x^{5 / 3}\right)^{\frac{-13}{3}} d x \)
\( \mathbf{A} \cdot-\frac{9}{25\left(1+x^{5 / 3}\right)^{\frac{10}{3}}}+C \)
B. \( -\frac{9}{15\left(1+x^{5 / 3}\right)^{\frac{10}{3}}}+C \)
c. \( -\frac{9}{50\left(1+x^{5 / 3}\right)^{\frac{10}{3}}}+C \)
D. None of these
Subject: Chemistry
Barium hydroxide is an alkali. It reacts with hydrochloric acid. How does the pH of the hydrochloric acid change as an excess of aqueous barium hydroxide is added?
A. The pH decrease from \( p H \) 14 and becomes constant at \( p H \)
B. The pH decreases from \( p H \) 14 to about \( p H \)
c. The pHincreases from \( p H \) 1 and becomes constant at \( p H \)
D. The pH increases from \( p H \) 1 to about \( p H \) 14
Subject: Maths
For \( \boldsymbol{x}>\boldsymbol{o}, \) if \( (\boldsymbol{2} \boldsymbol{x})^{2 \boldsymbol{y}}=\boldsymbol{4} \boldsymbol{e}^{2 \boldsymbol{x}-\boldsymbol{2} \boldsymbol{y}}, \) then
\( \left(1+\log _{e} 2 x\right)^{2} \frac{d y}{d x} \) is equal to
\( \mathbf{A} \cdot \log _{e} 2 x \)
в. \( \frac{x \log _{e} 2 x-\log _{e} 2}{x} \)
c. \( x \log _{e} 2 x \)
D. \( \frac{x \log _{e} 2 x+\log _{e} 2}{x} \)