AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A double convex lens of glass of
refraction index \( \mu \) is immersed in a
medium of refractive index \( \mu_{1} \). If a
parallel beam emerges undeviated through the lens, then:
A \( \cdot \mu=\mu_{1} \)
в. \( \mu=\frac{1}{\mu_{1}} \)
c. \( \mu>\mu_{1} \)
D . \( \mu<\mu_{1} \)
Subject: Physics
Four identical charges are placed at the points (1,0,0),(0,1,0),(-1,0,0) and
\( (0 .-1,0) \)
A. The potential at the origin is zero
B. The field at the origin is zero
c. The potential at all points on the z-axis, other than the origin, is zero
D. The potential at all points on the z-axis, other than the origin acts along the z-axis
Subject: Physics
A bullet emerge from a barrel of length \( 1.2 \mathrm{m} \) with a speed of \( 640 \mathrm{ms}^{-1} \)
Assuming constant acceleration, the approximate time that it spends in the barrel after the gun is fired is
A. \( 4 \mathrm{ms} \)
B. 40 ms
c. \( 400 \mu s \)
D. 1 s
Subject: Physics
When a glass prism of refracting angle
\( 60^{\circ} \) is immersed in a liquid its angle of
minimum deviation is \( 30^{\circ} . \) The critical
angle of glass with respect to the liquid medium is:
A \( \cdot 42^{\circ} \)
В . \( 45^{\circ} \)
\( c \cdot 50^{\circ} \)
\( D \cdot 52^{\circ} \)
Subject: Physics
The K.E of the photoelectons is E when the incident wave length is \( \frac{\lambda}{2} . \) The K.E becomes 2E when the incident wave length is \( \frac{\lambda}{3} . \) The work function of the metal is
A \( \cdot \frac{h c}{\lambda} \)
B. \( \frac{2 h c}{\lambda} \)
\( c \cdot \frac{3 h c}{\lambda} \)
D. \( \frac{h c}{3 \lambda} \)
Subject: Maths
\( \frac{\boldsymbol{d}^{2} \boldsymbol{x}}{\boldsymbol{d} \boldsymbol{y}^{2}} \) equals
\( \mathbf{A} \cdot\left(\frac{d^{2} y}{d x^{2}}\right)^{-1} \)
B \( \cdot-\left(\frac{d^{2} y}{d x^{2}}\right)^{-1}\left(\frac{d y}{d x}\right)^{-3} \)
C \( \cdot\left(\frac{d^{2} y}{d x^{2}}\right)^{-1}\left(\frac{d y}{d x}\right)^{-2} \)
D \( \cdot\left(-\frac{d^{2} y}{d x^{2}}\right)^{-1}\left(\frac{d y}{d x}\right)^{-2} \)
Subject: Maths
\( \int \frac{1-x^{7}}{x\left(1+x^{7}\right)} d x \) equals
A \( \quad \ln |x|+\frac{2}{7} \ln \left|1+x^{7}\right|+c \)
B \( \cdot \ln |x|+\frac{2}{4} \ln \left|1-x^{7}\right|+c \)
C \( \quad \ln |x|-\frac{2}{7} \ln \left|1+x^{7}\right|+c \)
D. \( -\ln |x|+\frac{2}{4} \ln \left|1-x^{7}\right|+c \)
Subject: Physics
For the velocity \( (v) \) -time \( (t) \) graphs
shown in figure, the total
distance covered by the particle in the
last two seconds of its motion is what
fraction of the total distance covered by
it in all the seven seconds?
\( A \cdot 1 / 8 \)
B. \( 1 / 6 \)
\( c \cdot 1 / 4 \)
D. \( 1 / 2 \)
Subject: Physics
Two sources of light of wavelengths \( 2500 A \) and \( 3500 A \) are used in Young's
double slit experiment simultaneously. Which orders of fringes of two wavelength patterns coincide?
A. 3 rd order of 1 st source and 5 th of the 2 nd
B. 7th order of 1st and 5th order of 2nd
c. 5 th order of 1 st and 3 rd order of 2 nd
D. 5 th order of 1 st and 7 th order of 2 nd
Subject: Biology
During chemiosmotic synthesis of ATP,
protons diffuse through \( C F_{0} \) channels
that activates ATPase enzyme. As a result, one molecule of ATP is formed
when \( _{\text {一一一一一一一一 }} \) passes through
ATPase.
\( \mathbf{A} \cdot 4 H^{+} \)
в. \( H^{+} \)
\( \mathbf{c} \cdot 2 H^{+} \)
D. \( 6 H^{+} \)
Subject: Maths
The ratio in which the line segment
joining the points whose position vectors are \( 2 \hat{i}-4 \hat{j}-7 \hat{k} \) and \( -3 \hat{i}+ \) \( \mathbf{5} \hat{\boldsymbol{j}}-\boldsymbol{8} \hat{\boldsymbol{k}} \) is divided by the plane whose
equation is \( \hat{r} \cdot(\hat{i}-2 \hat{j}+3 \hat{k})=13 \) is-
A. 13: 12 internally
B. 12: 25 externally
c. 13: 25 internally
D. 37: 25 internally
Subject: Physics
The potential energy function for diatomic molecule is \( U(x)=\frac{a}{x^{12}}-\frac{b}{x^{6}} \)
In a stable equilibrium, the distance between the particles is:
\( ^{A} \cdot\left(\frac{2 a}{b}\right)^{1 / 6} \)
B. \( \left(\frac{a}{b}\right)^{1 / 6} \)
\( ^{\mathrm{c}}\left(\frac{b}{2 a}\right)^{1 / 6} \)
\( \left(\frac{b}{a}\right)^{1 / 6} \)
Subject: Chemistry
Which of the following reaction is not correct during the formation of acid rain?
A. \( S+O_{2} \rightarrow S O_{2} \)
в. \( H_{2} O+S O_{2} \rightarrow H_{2} S O_{3} \)
c. \( H_{2} O+S O_{2} \rightarrow H_{2} S O_{4} \)
\( \mathrm{D} \cdot 2 \mathrm{SO}_{2}+\mathrm{O}_{2} \rightarrow 2 \mathrm{SO}_{3} \)
Subject: Maths
Solve \( \int \frac{x^{5}}{x^{2}+1} d x \)
A. \( \frac{x^{4}}{4}+\frac{x^{2}}{2}+\tan ^{-1} x+c \)
B. \( \frac{x^{4}}{4}-\frac{x^{2}}{2}+\frac{1}{2} \log \left(x^{2}+1\right)+c \)
C \( \frac{x^{4}}{4}-\frac{x^{3}}{3}+\tan ^{-1} x+c \)
D. \( \frac{x^{4}}{4}+\frac{x^{2}}{2}+\frac{1}{2} \log \left(x^{2}+1\right)+c \)
Subject: Maths
If \( a=\frac{9}{3-b}, b=\frac{9}{3-c} \) then the value of
\( c \) in terms of \( a \) is
A \( \frac{8}{3-a} \)
в. \( \frac{9}{3-a} \)
c. \( \frac{7}{3-a} \)
D. \( \frac{6}{3-a} \)
Subject: Chemistry
The Schrodinger wave equation for hydrogen atom is:
\( \mathbf{\Psi}_{2 s}=\frac{1}{4 \sqrt{2} \pi}\left(\frac{1}{a_{0}}\right)^{3 / 2}\left[2-\frac{r_{0}}{a_{0}}\right] e^{-r / a_{0}} \)
where \( a_{0} \) is Bohr radius. If the radial
node in \( 2 s \) be at \( r_{0}, \) then find \( r \) in terms
of \( a_{0} \)
A \( \cdot \frac{a_{0}}{2} \)
В. \( 2 a_{0} \)
c. \( \sqrt{2} a_{0} \)
D. \( \frac{a_{0}}{\sqrt{2}} \)
Subject: Chemistry
Which of the following lanthanoid ions is diamagnetic? (Atoms, \( C e= \)
\( \mathbf{5 8}, \boldsymbol{S m}=\mathbf{6 2}, \boldsymbol{E u}=\mathbf{6 3}, \boldsymbol{Y b}=\mathbf{7 0} \mathbf{)} \)
A \( \cdot Y b^{2} \)
в. \( C e^{2} \)
\( \mathrm{c} \cdot \mathrm{Sm}^{2+} \)
D. \( E u^{2} \)
Subject: Chemistry
Given the reaction \( \boldsymbol{A} \rightarrow \boldsymbol{B}+\boldsymbol{C}, \) when
\( \triangle \boldsymbol{H}_{\text {reaction}} \) is negative, what effect
would increase in temperature (at constant pressure) have on the system at equilibrium?
A. No change
B. Cannot be determined
c. Shift to the right
D. Shift to left for \( K<1 \) and to the right for \( K>1 \)
E. Shift to the left
Subject: Maths
The ends \( A \) and \( B \) of a rod of length \( \sqrt{5} \)
are sliding along the curve \( y=2 x^{2} \). Let
\( x_{A} \) and \( x_{B} \) be the \( x \) -coordinate of the
ends. At the moment when \( A \) is at (0,0) and \( \mathrm{B} \) is at (1,2) the derivative \( \frac{d x_{B}}{d x_{A}} \) has the value equal to
\( A \cdot 1 / 3 \)
B. 1/5
\( c \cdot 1 / 8 \)
D. \( 1 / 9 \)
Subject: Physics
Two identical coils each of radius \( R \) and
each carrying a current \( I \) in the same
direction are placed along a common axis and separated by distance \( R \). At the midpoint between the two coils the
A. Magnetic field is zero
B . Magnetic field is \( 0.8 \sqrt{0.8} \mu_{0} I / R \)
C. Second derivative of magnetic field \( d^{2} B / d x^{2}=0 \)
D. First derivative of magnetic field \( d B / d x=0 \)
Subject: Maths
\( \mathbf{1 . 4}+\mathbf{2 . 5}+\ldots+\mathbf{n}(\mathbf{n}+\mathbf{3})= \)
A. \( \frac{n(n+3)(n+5)}{9} \)
в. \( \frac{n(n+1)(n+5)}{3} \)
c. \( \frac{n(n+5)(n+7)}{6} \)
D. \( \frac{n(n+3)(n+9)}{12} \)
Subject: Physics
Match list A and list B accurately:
List \( \mathbf{A} \) List B
a) spherical wave front
e) linear
source
b) plane wave front
f) point light source
c) cylindrical wave front
g) at infinite distance
\( A \cdot(a, f) ;(b, g) ;(c, e) \)
B. ( a, f); (b, e); (c, g)
\( c \cdot(a, g) ;(b, f) ;(c, e) \)
D. \( (a, e) ;(b, g) ;(c, f) \)
Subject: Maths
n given figure \( A B C D \) is a trapezium in
which \( A B \| C D \) and \( A D=B C . \) Show
that
(i) \( \angle \boldsymbol{A}=\angle \boldsymbol{B} \)
(ii) \( \angle C=\angle D \)
(iii) \( \triangle A B C \cong \triangle B A D \)
(iv) diagonal \( A C=\operatorname{diagonal~} B D \)
Subject: Maths
Find \( \mathbf{S}, \) where \( \boldsymbol{S}=\frac{[\boldsymbol{n}(\boldsymbol{n}+\mathbf{1})(\boldsymbol{2} \boldsymbol{n}+\mathbf{1})]}{\mathbf{6}} \)
and \( n=20 \)
A . 2780
в. 2870
c. 1460
D. 1870
Subject: Chemistry
Resistance of a conductivity cell filled
with 0.15 mol \( L^{-1} \) NaCl solution is \( 50 \Omega \)
If resistance of the same cell when filled
with 0.02 mol \( L^{-1} \) NaCl solution is 500
\( \Omega, \) calculate the conductivity of 0.02
mol \( L^{-1} \) NaCl solution. (The
conductivity of 0.15 mol \( L^{-1} \) NaCl solution is \( 1.5 \mathrm{s} / \mathrm{m} \) ).
Subject: Chemistry
Assertion
Assertion: \( \mathrm{pH} \) of a buffer solution is not
affected by dilution.
Reason
Reason : \( p H=p K_{a}+ \)
\( \log \frac{\text {Conjugate acid, } \boldsymbol{B H}^{+}}{\text {Base}, \boldsymbol{B}} \)
A. If both the assertion and reason are true and reason is
the correct explanation of assertion.
B. If both the assertion and reason are true but reason is not the correct explanation of assertion.
C. If assertion is true but reason is false
D. If both assertion and reason are false.
Subject: Chemistry
Find out A from the given flowchart.
\( \mathbf{A} \cdot C u_{2} S \)
B. \( C u F e S_{2} \)
\( \mathbf{c} \cdot \operatorname{Fe} S_{2} \)
\( \mathrm{D} \cdot \mathrm{Fe}_{3} \mathrm{O}_{4} \)
Subject: Physics
A radiation is incident on a metal
surface of work function \( 2.3 e V \). The
wavelength of incident radiation is
600 nm. If the total energy of incident
radiation is \( 23 J \), then the number of
photoelectrons is
A. zero
B \( \cdot>10^{4} \)
\( \mathbf{c} \cdot=10^{4} \)
D. None of these
Subject: Physics
Two particles of masses \( m \) and \( 2 m \) are kept at a distance a. Find their relative
velocity of approach when separation becomes \( a / 2 \)
\( \mathbf{1} \)
2
A \( \cdot 2 \sqrt{\frac{3 a}{2 G M}} \)
B. \( \sqrt{\frac{a}{2 G M}} \)
\( ^{\mathbf{C}} \cdot 2 \sqrt{\frac{2 G M}{3 a}} \)
D. \( \sqrt{\frac{6 G M}{a}} \)
Subject: Maths
Given \( f^{2}(x)+g^{2}(x)+h^{2}(x) \leq 9 \) and
\( \boldsymbol{U}(\boldsymbol{x})=\boldsymbol{3} \boldsymbol{f}(\boldsymbol{x})+\mathbf{4} \boldsymbol{g}(\boldsymbol{x})+\mathbf{1 0 h}(\boldsymbol{x}), \) where
\( f(x) \cdot g(x) \) and \( h(x) \) are continuous \( \forall x \in \)
R. If maximum value of \( U(x) \) is \( \sqrt{N} \)
Then find \( N \)
Subject: Chemistry
Assertion
In free expansion of a gas inside an adiabatic chamber \( Q, W \) and \( \Delta U \) all
are zero.
Reason In such an expansion \( \boldsymbol{P} \boldsymbol{\alpha} \frac{\mathbf{1}}{\boldsymbol{V}} \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Maths
A survey shows that \( 63 \% \) of the Americans like cheese where as \( 76 \% \)
like apples. If \( x \% \) of the Americans like
both cheese and apples, then
A \( . x=39 \)
B. \( x=63 \)
c. \( 39 \leq x \leq 63 \)
D. None of these
Subject: Physics
The linear momentum of a ball of mass
\( 50 g \) is \( 0.5 k g m s^{-1} . \) Find its velocity.
\( \mathbf{A} \cdot 0.01 \mathrm{ms}^{-1} \)
B. \( 1 \mathrm{ms}^{-1} \)
\( \mathrm{c} \cdot 5 \mathrm{ms}^{-1} \)
D. \( 10 \mathrm{ms}^{-1} \)
Subject: Physics
An electric motor operating on \( 50 V \) D.C.
supply draws a current of \( 10 A \). If the efficiency of the motor is \( 40 \% \), then the resistance of the winding of the motor is:
A. \( 1.5 \Omega \)
B. 3\Omega
c. \( 4.5 \Omega \)
D. \( 6 \Omega \)
Subject: Maths
Evaluate \( \sum_{n=1}^{N} U_{n} \) if
\[
\boldsymbol{U}_{\boldsymbol{n}}=\mid \begin{array}{ccc}\boldsymbol{n} & \mathbf{1} & \mathbf{5} \\ \boldsymbol{n}^{2} & \boldsymbol{2} \boldsymbol{N}+\mathbf{1} & \boldsymbol{2} \boldsymbol{N}+\mathbf{1} \\ \boldsymbol{n}^{\boldsymbol{3}} & \boldsymbol{3} \boldsymbol{N}^{2} & \boldsymbol{3} \boldsymbol{N}\end{array}
\]
Subject: Chemistry
For the gas phase exothermic reaction,
\( A_{2}+B_{2} \rightleftharpoons C_{2}, \) carried out in a closed
vessel, the equilibrium moles of \( A_{2}, \) can be increased by:
A. increasing the temperature
B. decreasing the pressure
c. adding inert gas at constant pressure
D. removing some \( C_{2} \)
Subject: Physics
Energy levels I, II, Ill of a certain atom correspond to increasing values of
energy i.e., \( \boldsymbol{E}_{\boldsymbol{I}}<\boldsymbol{E}_{\boldsymbol{I I}}<\boldsymbol{E}_{\boldsymbol{I I I}} . \) If \( \boldsymbol{\lambda}_{1}, \boldsymbol{\lambda}_{2}, \boldsymbol{\lambda}_{3} \)
be the wavelengths of radiations corresponding to the transitions III to II
II to I and III to I respectively, which of the following relations is correct?
A. \( \lambda_{1}=\lambda_{2}+\lambda_{3} \)
B. \( \lambda_{3}=\frac{\lambda \lambda_{2}}{\lambda_{1}+2_{2}} \)
c. \( \lambda_{1}+\lambda_{2}+\lambda_{3}=0 \)
D \( \cdot \lambda \frac{2}{3}=\lambda_{1}^{2}+\lambda \frac{2}{2} \)
Subject: Chemistry
Do you observe anything happening
around the zinc granules?
Is there any change in its temperature?
Why is glass tube not dipped in di
\( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} ? \)
How is \( H_{2} \) gas collected by downward
displacement or upward displacement
of water?

Is \( H_{2} \) gas soluble or insoluble in water?
s \( H_{2} \) gas heavier or lighter than air?
Subject: Physics
The set of values of \( x \) for which the angle between the vectors \( \vec{a}=x \hat{i}-3 \hat{j}-\hat{k} \) and \( \vec{b}=2 x \hat{i}+x \hat{j}-\hat{k} \) is acute and the
angle between the vector \( \vec{b} \) and the axis of ordinates is obtuse, is:
A. \( 1<x<2 \)
B. \( x>2 \)
c. \( x<1 \)
D. \( x<0 \)
Subject: Chemistry
\( F e^{3+} \) compounds are more stable than
\( F e^{2+} \) compounds because:
A. \( F e^{3+} \) has smaller size than \( F e^{2+} \)
B. \( F e^{3+} \) has \( 3 d^{5} \) configuration (half-filled)
C. \( F e^{3+} \) has higher oxidation state
D. \( F e^{3+} \) is paramagnetic in nature
Subject: Physics
A leakage begins in water tank at
position \( P \) as shown in the figure. The
initial gauge pressure pressure above
that of the atmosphere) at \( P \) was \( 5 x \)
\( 10^{5} N / m^{2} \). If the density of water is
1000kg/ \( m^{3} \) the initial velocity with
which water gushes out is:
A \( .3 .2 m s^{-1} \)
B. \( 32 m s^{-1} \)
\( \mathbf{c} \cdot 28 m s^{-1} \)
D. \( 2.8 m s^{-1} \)
Subject: Physics
A block of sided \( 0.5 m \) is \( 30 \% \)
submerged in a liquid of density 1 gm / cc. Then find mass of an object
placed on block for complete submergence.
A . \( 87.3 k g \)
B. \( 85.3 k g \)
c. \( 82.3 k g \)
D. \( 80.3 k g \)
Subject: Chemistry
Nitrogen reacts with a metal \( M \) to
produce a compound \( X . \) This compound
\( X, \) when dissolved in water forms
pungent gas \( Y \) which can be identified easily by the formation of white fumes in the presence of \( \boldsymbol{H} \boldsymbol{C l} \)
Identify the compound \( \boldsymbol{X} \)
A. Iron nitride
B. Calcium nitride
c. Nitrolim
D. Sodium nitride
Subject: Maths
For polynomial \( \boldsymbol{P}(\boldsymbol{x})=\mathbf{6} \boldsymbol{x}^{\mathbf{3}}+\mathbf{2} \mathbf{9} \boldsymbol{x}^{\mathbf{2}}+ \)
\( \mathbf{4 4} \boldsymbol{x}+\mathbf{2 1}, \) find \( \mathbf{P}(-\mathbf{2}) \)
Subject: Physics
of the rod is \( M \) ad mass of bead is \( m \)
and \( M>m . \) The bead slides with some
friction. The mass of the pulley and friction in its axle are negligible. At the
initial moment the bead was located
opposite the lower end. If set free both the bodies move with constant
accelerations. The frictional force
between the bead and the thread so that
\( t \) second after release ball reaches the
upper end of the rod is given as \( \boldsymbol{F}_{\boldsymbol{f}}= \) \( \frac{\boldsymbol{x} \boldsymbol{m} \boldsymbol{M} \boldsymbol{l}}{(\boldsymbol{M}-\boldsymbol{m}) \boldsymbol{t}^{2}} . \) Find \( \boldsymbol{x}, \) Length of the rod is
\( l \)
Subject: Physics
Assertion: A beam of white light gives a spectrum on passing through a hollow prism. Reason: Speed of light outside the prism is different from the speed of light inside the glass prism.
A. Both assertion and reason are correct and reason is the correct explanation of the assertion
B. Both assertion and reason are correct, but reason is not the correct explanation of the assertion
c. Assertion is correct, but reason is incorrect
D. Assertion is incorrect, but reason is correct
E. Both assertion and reason are incorrect.
Subject: Maths
Using the method of successive subtraction of numbers
\( \mathbf{1}, \mathbf{7}, \mathbf{1 9}, \mathbf{3 7}, \mathbf{6 1}, \mathbf{9 1}, \mathbf{1 2 7}, \mathbf{1 6 9}, \mathbf{2 1 7}, \mathbf{2 7 1}, \mathbf{3 3} \)
Examine if the following number is a perfect cube or not 792
Subject: Physics
Two loudspeakers are emitting sound
waves of wavelength \( \mu \) with an initial
phase difference of \( \frac{\pi}{2} . \) At what minimum distance from 0 on line AB
will one hear a maxima?
A \( .25 \lambda \)
B. \( \frac{100 \lambda}{\sqrt{15}} \)
\( c \cdot \frac{25 \lambda}{3} \)
D. \( 50 \lambda \)
Subject: Chemistry
The molar heat of vaporization of
toluene is \( \Delta H_{v} . \) If its vapour pressure at \( 315 \mathrm{K} \) is 60 torr \( \& \) that at \( 355 \mathrm{K} \) is 300
torr then \( \Delta H_{v}=?(\log 2=0.3) \)
A . 37.4 kJ/mole
B. 3.74 kJ/mole
c. 37.4 J/mol
D. 3.74 J/mole
Subject: Physics
An alternating voltage of 260 volt and \( \omega \) \( =100 \) radian/second, is applied in an
LCR
series circuit where \( \mathrm{L}=0.01 \mathrm{H}, \mathrm{C}=4 \times \)
\( 10^{-4} F \) and \( R=10 \Omega . \) the power supplied
by the source is:
A. 1000 w
в. 6760 w
\( c . \) 3380 \( w \)
D. 3000
Subject: Chemistry
List- List-II
\( (\mathrm{A}) \mathrm{O}_{3} \)
(1) Turns benzidine paper to brown
(B) Hypo
(2) Turns anhydrous \( C u S O_{4} \) to blue
(C) \( H_{2} O \)
(3) Violet colour with \( \mathrm{FeCl}_{3} \)
(D) \( H_{2} S \)
(4) Rotten egg smel
The correct match is :
A. A-2, B-3, C-1, D-4
B. A-4, B-2, C-3, D-1
C. \( A-1, B-3, C-2, D-4 \)
D. A-3, B-4, C-2, D-1
Subject: Physics
If a fully charged capacitor \( C \) with
initial charge \( q_{0} \) is connected to a coil of
self inductance \( L \) at \( t=0 . \) The time at
which the energy is stored equally between the electric field and magnetic
field is :
A \( . \pi \sqrt{L C} \)
в. \( \frac{\pi}{4} \sqrt{L C} \)
c. \( \frac{\pi}{2} \sqrt{L C} \)
D. \( \frac{\pi}{6} \sqrt{L C} \)
Subject: Physics
Four spheres \( A, B, C \) and \( D \) of different metals but of same radius are
kept at same temperature.The ratios of their densities and specific heats are 2: 3: 5: 1 and \( 3: 6: 2: 4 . \) Which
sphere will show the fastest rate of
cooling (initially)?
A. \( A \)
в. \( B \)
\( c . c \)
D. \( D \)
Subject: Maths
A horse is tied to a vertex of a field
having the shape of an equilatera triangle with a rope, the length of which is half of the length of a side of the triangle. The percentage of the total area of the field over which the horse can graze is approximately
A . 20 to 22\%
B. 25 to 27\%
c. 30 to 32\%
D. 48 to 50\%
Subject: Maths
The value of \( x \) in the equation \( 3 x^{x+1} \)
\( C_{2}=2 \times^{x+2} C_{2}, x \in N \) is
\( \mathbf{A} \cdot x=4 \)
B. \( x=5 \)
c. \( x=6 \)
D. \( x=7 \)
Subject: Chemistry
A solution is
\( \mathbf{1 0}^{-4} \mathbf{M} \) in \( \boldsymbol{C l}^{-}, \mathbf{1 0}^{-\mathbf{5}} \boldsymbol{M} \) in \( \boldsymbol{B r}^{-}, \mathbf{1 0}^{-\mathbf{3}} \boldsymbol{M} \)
is added slowly to the solution. The
minimum concentration of \( \boldsymbol{A} \boldsymbol{g}^{+} \) required to start precipitation of all
three ions is \( 10^{-x} \) then the value of \( x \) is:
\( \left[\text { Given }, \boldsymbol{K}_{s p(A g C l)}=\mathbf{1 0}^{-10}, \boldsymbol{K}_{s p(A g B r)}=\right. \)
\( \left.\mathbf{1 0}^{-\mathbf{1 3}}, \boldsymbol{K}_{s p(\boldsymbol{A g I})}=\mathbf{1 0}^{-\mathbf{1 7}}\right] \)
\( A \cdot 8 \)
B. 14
\( c \cdot 5 \)
D.
Subject: Maths
Find a and
b, if \( 2\left[\begin{array}{ll}5 & a \\ 3 & 4\end{array}\right]+\left[\begin{array}{ll}0 & 1 \\ 1 & b\end{array}\right]= \)
\( \left[\begin{array}{cc}10 & 5 \\ 7 & 0\end{array}\right] \)
Subject: Chemistry
Assertion \( (\mathrm{A}): H_{2} S \) acts only as
reducing agent.
Reason \( (\mathrm{R}): \boldsymbol{H}_{2} \boldsymbol{S} \) is a dibasic acid.
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true and Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
Subject: Chemistry
Assertion
Equivalent mass of \( K M n O_{4} \) is equal to
one-third of its molecular mass when it
acts as an oxidising agent in an alkaline medium.
Reason
Oxidation number of \( M n \) is +7 in
\( \boldsymbol{K} \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{4} \)
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
In the given figure, \( O \) is the centre of the
circle and \( \angle Q P R=x^{\circ} ; \angle O R Q=y^{\circ} \)
Which statement is true about \( x^{\circ} \) and
\( \boldsymbol{y}^{\circ} ? \)
A \( \cdot x^{\circ}+y^{\circ}=120^{\circ} \)
В . \( x^{\circ}+y^{\circ}=180^{\circ} \)
c. \( x^{\circ}+y^{\circ}=90^{\circ} \)
D. \( x^{\circ}+y^{\circ}=150^{\circ} \)
Subject: Physics
Q Type your question
placed near a long straight current-
carrying wire. The dimensions are
shown in the figure. The lone wire lies in
the plane of the loop. The current in the
long wire varies as \( \boldsymbol{I}=\boldsymbol{I}_{\mathbf{0}}(\boldsymbol{t}) . \) The
mutual inductance of the pair is
A \( \cdot \frac{\mu_{0} a}{2 \pi} \ln \left(\frac{2 a+l}{l}\right) \)
B. \( \frac{\mu_{0} a}{2 \pi} \ln \left(\frac{2 a-l}{l}\right) \)
c. \( \frac{2 \mu_{0} a}{2 \pi} \ln \left(\frac{a+l}{l}\right) \)
D. \( \frac{\mu_{0} a}{2 \pi} \ln \left(\frac{a+l}{l}\right) \)
Subject: Maths
Simplify \( \cot ^{-1} \frac{1}{\sqrt{x^{2}-1}} \) for \( x<-1 \)
\( A \cdot \cos ^{-1} x \)
\( \mathbf{B} \cdot \sec ^{-1} x \)
\( \mathbf{c} \cdot \operatorname{cosec}^{-1} x \)
D. \( \tan ^{-1} x \)
Subject: Chemistry
Assertion: 1 mole \( O_{3}(\text { ozone })=N \)
molecule of \( O_{3}(\text { ozone })=3 N \) atoms of
\( \boldsymbol{O}(\boldsymbol{o} \boldsymbol{x} \boldsymbol{y} \boldsymbol{g} \boldsymbol{e} \boldsymbol{n})=\boldsymbol{4} \boldsymbol{8} \boldsymbol{g} \)
Reason: A mole is the amount of matter
that contains as many as objects as the number of atoms exactly in 12 g C-12 \( (N \)
Avogadro number)
A. Assertion is correct but Reason is incorrect
B. Assertion is incorrect but Reason is correct
c. Both Assertion and Reason are correct and Reason is correct explanation of Assertion
D. Both Assertion and Reason are correct but Reason is not correct explanation of Assertion
Subject: Physics
Assertion
First law of thermodynamics can be applied for ideal gases only.
Reason
First law is simply, law of conservation of energy.
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 incorrect but Reason is correct
D. Both Assertion and Reason are incorrect
Subject: Chemistry
Which of the following statements is incorrect for \( \sigma \) and \( \pi \) -bonds formed
between two carbon atoms?
A. \( \sigma \) -bond is stronger than a \( \pi \) -bond
B. Bond energies of \( \sigma \) and \( \pi \) -bonds are of the order of \( 264 k J / m o l \) and \( 347 k J / m o l \)
C. Free rotation of surrounding atoms about a \( \sigma \) -bond is allowed but not in case of a \( \pi \) -bond
D. \( \sigma \) -bond determines the direction between carbon atoms but a \( \pi \) -bond has no primary effect in this regardd
Subject: Maths
Given, \( \boldsymbol{A}=\{\text { Quadrilaterals }\}, \boldsymbol{B}=\{ \)
Rectangles \( \}, C=\{\text { Squares }\}, D=\{ \) Rhombuses \( \} . \) State whether the
following statement is correct or
incorrect. Give reasons.
\( \boldsymbol{D} \subset \boldsymbol{A} \)