AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
Q Type your question
below. All point charges are of the same
magnitude.

Which table gives the best description
of the electric field at point \( P \) and the
electric potential at point P?
A. Electric Field at \( \mathrm{P} \) - Electric Potential at \( \mathrm{P} \), zero - zero
B. Electric Field at \( P \) - Electric Potential at \( P \), zero -
negative
C. Electric Field at \( P \) - Electric Potential at \( P \), downward
downward
D. Electric Field at \( P \) - Electric Potential at \( P \), downward
negative
E. Electric Field at \( \mathrm{P} \) - Electric Potential at \( \mathrm{P} \), negative -
zero
Subject: Maths
Which of the following is a quadratic
equation?
A \( \cdot x^{\frac{1}{2}}+2 x+3=0 \)
B \( \cdot(x-1)(x+4)=x^{2}+1 \)
\( \mathbf{c} \cdot x^{4}-x+5=0 \)
D. \( (2 x+1)(3 x-4)=2 x^{2}+3 \)
Subject: Chemistry
The reaction \( \boldsymbol{H}_{2} \boldsymbol{S}+\boldsymbol{H}_{2} \boldsymbol{O}_{2} \rightarrow \boldsymbol{S}+ \)
\( 2 H_{2} O \) describes:
A . acidic nature of \( H_{2} O_{2} \)
B. alkaline nature of \( H_{2} O_{2} \)
C . oxidizing nature of \( H_{2} O_{2} \)
D. reducing nature of \( H_{2} O_{2} \)
Subject: Maths
In figure the segment \( S T \) is parallel to
side \( P R \) of \( \triangle P Q R \) and it divides the
triangle into two parts of equal area.Find the ratio \( \frac{\boldsymbol{P S}}{\boldsymbol{P Q}} \)
\( \mathbf{A} \cdot 1: 2 \)
B. 1: 8
\( c \cdot 1: 4 \)
D. 1: 10
Subject: Maths
If \( \frac{1}{\sqrt{2}}<x<1 \) then \( \cos ^{-1} x+ \)
\( \cos ^{-1}\left(\frac{x+\sqrt{1-x^{2}}}{\sqrt{2}}\right) \) is equal to
A \( \cdot 2 \cos ^{-1} x-\frac{\pi}{4} \)
B. \( 2 \cos ^{-1} x \)
\( c \cdot \frac{\pi}{4} \)
\( D \)
Subject: Physics
The force of interaction between two
atoms is given by \( \boldsymbol{F}=\boldsymbol{\alpha} \boldsymbol{\beta} \exp \left(-\frac{\boldsymbol{x}^{2}}{\boldsymbol{\alpha k t}}\right) \)
where \( x \) is the distance, \( k \) is the
Boltzman constant and \( \boldsymbol{T} \) is
temperature and \( \alpha \) and \( \beta \) are two
constants. The dimension of \( \beta \) is
A \( \cdot M^{2} L^{2} T^{-2} \)
B. \( M^{2} L T^{-4} \)
c. \( M^{0} L^{2} T^{-4} \)
D. \( M L T^{-2} \)
Subject: Physics
If an electron enters with a velocity \( \bar{v}= \) \( v_{0} \hat{j} \) into a cubical region in a uniform electromagnetic field and the orbit of the electron is found to spiral down
inside the cube in plane parallel to \( x-y \) plane then the configuration of electric field and magnetic field is then
A \( \cdot \bar{E}=E_{0} \hat{j}, \bar{B}=B_{0} \hat{k} \)
B . \( \bar{E}=E_{0} \hat{i}, \bar{B}=B_{0} \hat{k} \)
c. \( \bar{E}=E_{0} \hat{i}, \bar{B}=B_{0} \hat{j} \)
D. \( \bar{E}=E_{0} \hat{j}, \bar{B}=B_{0} \hat{\jmath} \)
Subject: Biology
Assertion
Symptoms of emphysema develops when a person living on plains ascends
and stays on a mountain.
Reason
Air pressure and partial pressure of oxygen falls with the rise in altitude.
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
Arrange the following combinations in the increasing order of focal length:
a) Two plano convex lenses of focal lengths \( 20 \mathrm{cm} \) and \( 30 \mathrm{cm} \) in contact.
b) Two convex lens of focal lengths 20 \( \mathrm{cm} \) and \( 10 \mathrm{cm} \) in contact.
c) Two convex lenses of focal length 25
\( \mathrm{cm} \) separated by \( 5 \mathrm{cm} \)
\( A \cdot a, b, c \)
B. b, a, c
\( c \cdot a, c, b \)
D. \( c, a, b \)
Subject: Maths
If \( f(x)=\int \frac{\left(x^{2}+\sin ^{2} x\right)}{1+x^{2}} \sec ^{2} x d x \) and
\( f(0)=0 \) then \( f(1) \) is equal to
A \( \cdot 1-\frac{\pi}{4} \)
B. \( \frac{\pi}{4}-1 \)
c. \( \tan 1-\frac{\pi}{4} \)
D. \( \frac{\pi}{4}-\tan 1 \)
Subject: Physics
A proton, a neutron, an electron and an
\( \alpha \) -particle have same energy. Then their de Broglie wavelengths compare as:
\( \mathbf{A} \cdot \lambda_{p}=\lambda_{n}>\lambda_{e}>\lambda_{\alpha} \)
B . \( \lambda_{\alpha}<\lambda_{p}=\lambda_{n}<\lambda_{e} \)
\( \mathbf{c} \cdot \lambda_{e}<\lambda_{p}=\lambda_{n}>\lambda_{\alpha} \)
\( \mathbf{D} \cdot \lambda_{e}=\lambda_{p}=\lambda_{n}=\lambda_{\alpha} \)
Subject: Maths
Which of the following do/does not
reduce to unity?
This question has multiple correct options
A \( \frac{\sin \left(180^{0}+A\right)}{\tan \left(180^{0}+A\right)} \frac{\cot \left(90^{0}+A\right)}{\tan \left(90^{0}+A\right)} \frac{\cos \left(360^{0}-A\right) \operatorname{cosec} A}{\sin (-A)} \)
B. \( \frac{\sin (-A)}{\sin \left(180^{0}+A\right)}-\frac{\tan \left(90^{0}+A\right)}{\cot A}+\frac{\cos A}{\sin \left(90^{0}+A\right)} \)
C. \( \frac{\sin 24^{0} \cos 6^{0}-\sin 6^{0} \cos 24^{0}}{\sin 51^{0} \cos 69^{0}-\cos 51^{0} \sin 69^{0}} \)
D. \( \frac{\cos \left(90^{0}+A\right) \sec (-A) \tan \left(180^{0}-A\right)}{\sec \left(360^{0}+A\right) \sin \left(180^{0}+A\right) \cot \left(90^{0}-A\right)} \)
Subject: Chemistry
Complete the following equations:
(a) \( 2 N a O H+C l_{2} \rightarrow N a C l+ \)
\( +H_{2} O \)
(b) \( N a_{2} S O_{3}+2 H C l \rightarrow 2 N a C l+ \)
\( \boldsymbol{H}_{2} \boldsymbol{O}+ \)
\( (c) C l_{2}+3 F_{2} \frac{573 K}{ } \)
Subject: Physics
Gold has a very low specific heat
compared to water.
Based on this fact alone, which of the
following do we know is true?
A. Gold melts at a much higher temperature than water.
B. If I add heat to a chunk of gold, its temperature will go up more than a pot of water to which I add the same amount of heat.
C. If 1 add heat to a chunk of gold, its temperature will go up less than a pot of water to which I add the same amount of heat.
D. If I add heat to a chunk of gold, its temperature will go up more than a pot of the same mass of water to which I add the same amount of heat.
E. If I add heat to a chunk of gold, its temperature will go up less than a pot of the same mass of water to which add the same amount of heat.
Subject: Chemistry
In the following equilibrium, \( N_{2} O_{4}(g) \rightleftharpoons 2 N O_{2}(g), \) when 5 moles of
each is taken and the temperature is
kept at \( 298 K \), the total pressure was
found to be 20 bar.
(Given: \( \Delta G_{f} N_{2} O_{4}= \)
\( \left.\mathbf{1 0 0 k J}, \Delta G_{f_{N O_{2}}}^{o}=\mathbf{5 0} k J\right) \)
(a) Find \( \Delta G \) of the reaction at \( 298 K \)
(b) Find the direction of the reaction.
Subject: Maths
Find the derivative of \( \sin \left(2 \sin ^{-1} x\right) \)
A \( \cdot \frac{2 \cos \left(2 \sin ^{-1} x\right)}{\sqrt{1-x^{2}}} \)
B. \( \frac{\cos \left(2 \sin ^{-1} x\right)}{\sqrt{1-x^{2}}} \)
c. \( \frac{2 \cos \left(2 \cos ^{-1} x\right)}{\sqrt{1-x^{2}}} \)
D. \( -\frac{\cos \left(2 \cos ^{-1} x\right)}{\sqrt{1-x^{2}}} \)
Subject: Maths
The sum of \( n \) terms of \( 1^{2}+\left(1^{2}+\right. \)
\( \left.2^{2}\right)+\left(1^{2}+2^{2}+3^{2}\right)+\dots . \)
A \( \cdot \frac{n(n+a)(2 n+1)}{6} \)
в. \( \frac{n(n+1)(2 n-1)}{6} \)
c. \( \frac{1}{12} n(n+1)^{2}(n+2) \)
D. \( \frac{1}{12} n^{2}(n+1)^{2} \)
Subject: Physics
Which row describes the nature of \( \alpha \) -
particles and of \( \gamma- \) rays
A. \( \alpha \) - particles : helium nuclei ; rays - electromagnetic radiation
B. \( \alpha \) - particles : helium nuclei ; \gamma rays - electrons
c. \( \alpha \) - particles: protons; \( \gamma \) rays - electromagnetic radiation
D. \( \alpha \) - particles: protons; \( \gamma \) rays - electrons
Subject: Maths
A die is thrown 200 times and the
outcomes 1,2,3,4,5,6 have
frequencies as below:
Outcome
Frequency
\( \begin{array}{llll}10 & 38 & 43 & 29\end{array} \)
Find the probabilities of getting a number more than 1 and less than 6 in a toss
(trial)
A . 0.65
в. 0.55
c. 0.69
D. None of these
Subject: Chemistry
Assertion
Fat digestion in stomach is an emulsification process.
Reason
Emulsion of fat in water is stabilized by
the bile juice.
Read the above assertion and reason
and choose the correct option regarding
¡t.
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: Maths
\( \triangle L T R \sim \triangle H Y D, \triangle H Y D \) is such
that \( \boldsymbol{H} \boldsymbol{Y}=\mathbf{7 . 2} \boldsymbol{c m}, \boldsymbol{Y} \boldsymbol{D}=\boldsymbol{6} \boldsymbol{c m}, \angle \boldsymbol{Y}= \)
\( 40^{\circ} \) and \( \frac{L R}{H D}=\frac{5}{6} \) and construct
\( \triangle \boldsymbol{L} \boldsymbol{T} \boldsymbol{R} \)
Subject: Maths
Solve the following Linear Programming problems graphically:
1. Maximize \( Z=3 x+4 y \quad \) Subject to
the constraints \( : x+y \leq 4, x \geq 0, y \geq \)
\( \mathbf{0} \)
2. Minimize \( Z=-3 x+4 y \quad \) subject
to \( x+2 y \leq 8,3 x+2 y \leq 12, x \geq \)
\( \mathbf{0}, \boldsymbol{y} \geq \mathbf{0} \)
Subject: Maths
Equation of the parabola whose vertex is (0,0) and focus is the point of intersection of the lines \( \boldsymbol{x}+\boldsymbol{y}= \)
\( 2,2 x-y=4 \) is
A \( \cdot y^{2}=2 x \)
в. \( y^{2}=4 x \)
c. \( y^{2}=8 x \)
D . \( x^{2}=8 y \)
Subject: Physics
Power of \( 10 ~ W \) is emitted by a
loudspeaker. The sound intensity
radiated by it at a distance of \( 3 m \) is
\( 2 W / m^{2} . \) If the intensity of loudspeaker
is doubled the intensity at 6 m will be
\( \mathbf{A} \cdot 1 W / m^{2} \)
в. \( 4 \mathrm{W} / \mathrm{m}^{2} \)
c. \( 0.5 W / m^{2} \)
D. \( 2 \mathrm{W} / \mathrm{m}^{2} \)
Subject: Maths
Let \( \boldsymbol{f}(\boldsymbol{x}) \) be defined in the interval [-2,2] such that \( f(x)= \)
\( \left\{\begin{array}{ll}-1, & -2 \leq x \leq 0 \\ x-1, & 0<x \leq 2\end{array} \text { and } g(x)=\right. \)
\( \boldsymbol{f}(|\boldsymbol{x}|)+|\boldsymbol{f}(\boldsymbol{x})| \) Test the differentiablity
of \( g(x) \) in (-2,2)
A. not derivable at \( x=0 \) and \( x=1 \)
B. derivable at all points
c. not derivable at \( x=0 \)
D. not derivable at \( x=1 \)
Subject: Physics
Two materials of dielectric constants
\( k_{1} \) and \( k_{2} \) are introduced to fill the
space between the two parallel plates of
a capacitor as shown in the figure. The
capacitance of the capacitor is :
A \( \cdot \frac{A \in_{0}\left(k_{1}+k_{2}\right)}{2 d} \)
в. \( \frac{2 A \in_{0}}{d}\left(\frac{k_{1} k_{2}}{k_{1}+k_{2}}\right) \)
c. \( \frac{A \in_{0}}{d}\left(\frac{k_{1} k_{2}}{k_{1}+k_{2}}\right) \)
\( \frac{A \epsilon_{0}\left(k_{1}+k_{2}\right)}{2 d k_{2} k} \)
Subject: Chemistry
\( X e F_{4} \) disproportionate in water to give:
A \( . \quad X e+H C l \)
в. \( X e \) and \( X e O_{3} \)
c. \( X e O F_{4} \) and \( H F \)
D. \( X e O_{2} F E \) and \( H F \)
Subject: Physics
An alpha particle \( \left(^{4} H e\right) \) has a mass
4.00300 amu. A proton has a mass
\( \mathbf{1 . 0 0 7 8 3} \) amu and a neutron has a mass
\( \mathbf{1 . 0 0 8 6 7} \) amu respectively. The binding
energy of alpha estimated from these data is closest to:
\( \mathbf{A} \cdot 27.9 \mathrm{MeV} \)
в. \( 22.3 \mathrm{MeV} \)
c. \( 35.0 \mathrm{MeV} \)
D. 20.4 MeV
Subject: Physics
A loaded transport truck with a mass of \( 38000 \mathrm{kg} \) is travelling at \( 1.20 \mathrm{m} / \mathrm{s} \). What will be the velocity of a \( 1400 \mathrm{kg} \) car if it has the same momentum?
A. \( 32.57 \mathrm{m} / \mathrm{s} \)
B. 30 \( \mathrm{m} / \mathrm{s} \)
\( c \cdot 15 m / s \)
D. 32.67 \( \mathrm{m} / \mathrm{s} \)
Subject: Physics
What is the distance travelled by a point during the time t. if it moves in \( x \) Y plane according to relation.
\[
\begin{array}{l}
\boldsymbol{X}=\boldsymbol{a} \boldsymbol{s} \boldsymbol{i} \boldsymbol{n} \boldsymbol{\omega} \boldsymbol{t} \\
\boldsymbol{Y}=\boldsymbol{a}(1-\boldsymbol{c o s} \boldsymbol{\omega} \boldsymbol{t})
\end{array}
\]
Subject: Maths
If there is an error of \( 0.01 \mathrm{cm} \) in the
diameter of a sphere then percentage error in surface area when the radius \( = \)
\( 5 c m, \) is
A . \( 0.005 \% \)
B. \( 0.05 \% \)
\( c \cdot 0.1 \% \)
D. \( 0.2 \% \)
Subject: Physics
In the arrangement shown in figure
when the switch \( S_{2} \) is open, the
galvanometer shows no deflection for
\( l=L / 2 . \) When the switch \( S_{2} \) is closed,
the galvanometer shows no deflection
for \( l=5 L / 12 . \) The internal resistance
\( (r) \) of \( 6 \mathrm{V} \) cell, and the emf \( E \) of the other
battery are respectively
\( A \cdot 3 \Omega, 8 V \)
B. \( 2 \Omega, 12 V \)
c. \( 2 \Omega, 24 V \)
D. \( 3 \Omega, 12 V \)
Subject: Chemistry
An atom with an electron configuration of \( 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{4} \) will probably exhibit an oxidation state of:
\( A \cdot+2 \)
в. -2
\( c \cdot+3 \)
D. -
\( E \cdot+5 \)
Subject: Maths
If \( \boldsymbol{y}=\sec \left(\tan ^{-1} x\right), \) then \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \) at \( \boldsymbol{x}=\mathbf{1} \) is
equal to.
A \( \cdot \frac{1}{\sqrt{2}} \)
B. \( \frac{1}{2} \)
\( c \cdot 1 \)
D. \( \sqrt{2} \)
Subject: Physics
The given graph shows variation with
time in the source voltage and steady
state current drawn by a series RLC
circuit.

Which of the following statements
is/are correct?
This question has multiple correct options
A. Current lags the voltage
B. Resistance in the circuit is \( 250 \sqrt{3} \Omega \)
C. Reactance in the circuit is \( 250 \Omega \)
D. Average power dissipation in the circuit is \( 20 \sqrt{3} \mathrm{w} \)
Subject: Physics
A coil of self inductance \( 10 m H \) and
resistance \( 0.1 \Omega \) is connected through a switch to a battery of internal resistance \( 0.9 \Omega \) After the switch is closed, the time taken for the current to attain \( 80 \% \) of the saturation value is :
(Take \( l n 5=1.6) \)
A . \( 0.103 s \)
B. \( 0.016 s \)
c. \( 0.002 s \)
D. \( 0.324 s \)
Subject: Maths
Which of the following binomial expressions has a least term
independent of \( x ? \)
\( ^{\mathrm{A}} \cdot\left(\sqrt{x}-\frac{3}{x^{2}}\right)^{1} \)
B. \( \left(x+\frac{1}{x}\right)^{6} \)
c. \( (1+x)^{32} \)
\( ^{\mathrm{D}}\left(\frac{3}{2} x^{2}-\frac{1}{3 x}\right)^{9} \)
Subject: Physics
Light traveling through three transparent substances follows the
path shown in Fig. Arrange the indices
of refraction in order from smallest to
largest. Note that total internal
reflection does occur on the bottom
surface of medium 2
\( \mathbf{A} \cdot n_{1}<n_{2}<n_{3} \)
B \( . n_{2}<n_{1}<n_{3} \)
\( \mathbf{c} \cdot n_{1}<n_{3}<n_{2} \)
\( \mathrm{D} \cdot n_{3}<n_{1}<n_{2} \)
Subject: Biology
Match column I with column II and
select the correct option from the given codes.
Column I Column
A. Royal Botanical Garden, Kew
B. Indian Botanical Garden
(ii) England
C. National Botanical Research Institute
(iii) Howrah
(iv)
D. Llyod Botanical Garden
A. A-(ii), B-(iii), C-(i), D-(iv)
B. A-(i), B-(iii), C-(ii), D-(iv)
C . A-(iv), B-(ii), C-(i), D-(iii)
D. A-(iv), B-(iii), C-(ii), D-(i)
Subject: Chemistry
The homogeneous catalysts is shown
by:
A \( . \) Haber's process, \( N_{2}+3 H_{2} \stackrel{F e}{\longrightarrow} 2 \mathrm{NH}_{3} \)
B. Ostwald process, \( 4 N H_{3}+5 O_{2} \stackrel{P t}{\longrightarrow} 4 N O+6 H_{2} O \)
C. Contact process, \( 2 S O_{2}+O_{2} \frac{V_{2} O_{5}}{\longrightarrow} 2 S O_{3} \)
\( \mathbf{D} \cdot 2 C_{2} H_{5} O H \frac{H_{2} S O_{4}}{\longrightarrow} C_{2} H_{5}-O-C_{2} H_{5}+H_{2} O \)
Subject: Chemistry
Cleansing action of soap occurs
because:
A. oil and grease can be absorbed into the hydrophobic centres of soap micelles and washed away
B. oil and grease can be absorbed into hydrophilic centres of soap micelles and washed away
C. oil and grease can be absorbed into both hydrophilic and hydrophobic centres but cannot be washed away
D. cleansing action is not related to micelles
Subject: Chemistry
A solution of \( N a_{2} S_{2} O_{3} \) is saturated iodometrically against 0.334 g of pure \( K B r O_{3}\left(\text { converted to } B r^{-}\right) \) requiring 40
\( \mathrm{ml} . \mathrm{Na}_{2} \mathrm{S}_{2} \mathrm{O}_{3} \) solution. What is the
molarity of \( N a S_{2} O_{3} \) solution? (Molar
mass of \( \boldsymbol{K} \boldsymbol{B} \boldsymbol{r} \boldsymbol{O}_{3}=\mathbf{1 6 7} \) g \( \boldsymbol{m o l}^{-1} \) )
Subject: Chemistry
Which of the following statements is
not correct?
A. The velocity of an electron in the first orbit of hydrogen atom is the same as that of an electron in the second
orbit of helium positive ion.
B. The radius of the first orbit in hydrogen atom is the same as that of the second orbit in beryllium tripositive ion.
C. The energy of an electron in the first orbit of hydrogen atom is the same as that of an electron in the second orbit of helium positive ion.
D. The potential energy of an electron in the first orbit of hydrogen atom is the same as that of an electron in the fourth orbit of helium positive ion.
Subject: Physics
A rigid container has a hole in its wall. When the container is evacuated, its weight is 100 gm. When someair is filled in it at \( 27 C \), its weight becomes 200 gm. Now the temperature of air inside is
increased by \( \Delta \mathrm{T} \), the weight becomes 150 gm. \( \Delta \) T should be :
A .27
в. \( \frac{27^{\circ}}{4} \) с
\( c .300 \)
D. 327
Subject: Physics
Assertion
When a charge is brought near a
conductor then a very small value
current is established in the conductor
Reason
since electric field inside the conductor
has to be zero so to overcome the
electric field of the external charge,
internal charge of conductor is
collected all accross the surface.
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
If the refractive indices of crown glass
for red, yellow and violet colours are
respectively \( \mu_{r}, \mu_{y} \) and \( \mu_{v}, \) then the dispersive power of this glass would be:
A \( \cdot \frac{\mu_{v}-\mu_{r}}{\mu_{y}-1} \)
в. \( \frac{\mu_{v}-\mu_{y}}{\mu_{r}-1} \)
c. \( \frac{\mu_{v}-\mu_{y}}{\mu_{y}-\mu_{r}} \)
D. \( \frac{\mu_{v}-\mu_{r}}{\mu_{y}}-1 \)
Subject: Maths
Point \( D \) has coordinates as (3,4,5)
Referring to the given figure, find the
coordinates of point \( \boldsymbol{B} \)
A \( \cdot(3,0,4) \)
\( \mathbf{B} \cdot(4,3,0) \)
C. (4,0,3)
D. (3,4,0)
Subject: Physics
A charge of \( +4 \mu C \) is kept at a distance
of \( 50 \mathrm{cm} \) from a charge of \( -6 \mu C \). Find the two points where the potential is
zero
A. Internal point lies at a distance of \( 20 \mathrm{cm} \) from \( 4 \mu \mathrm{C} \) charge and external point lies at a distance of \( 100 \mathrm{cm} \) from \( 4 \mu C \) charge
B. Internal point lies at a distance of \( 30 \mathrm{cm} \) from \( 4 \mu C C \) charge and external point lies at a distance of \( 100 \mathrm{cm} \) from \( 4 \mu C \) charge
c. Potential is zero only at \( 20 \mathrm{cm} \) from \( 4 \mu \mathrm{C} \) charge between the two charges
D. Potential is zero only at \( 20 \mathrm{cm} \) from \( -6 \mu \mathrm{C} \) charge between the two charges
Subject: Chemistry
Formic acid is considered as a
resonance hybrid of the four structures
Which of the above order is correct for
the stability of the four contributing
structures:
\( \boldsymbol{O} \)
\( \boldsymbol{H}-\stackrel{\|}{\boldsymbol{C}}-\boldsymbol{O} \boldsymbol{H} \leftrightarrow \boldsymbol{H}-\dot{\boldsymbol{C}}=\boldsymbol{O} \boldsymbol{H} \leftrightarrow \boldsymbol{H} \)
\( o \)
\( \stackrel{1+}{C}-O-H \leftrightarrow H-C-O-H \)
\( \boldsymbol{I} \quad \boldsymbol{I I} \)
\( \boldsymbol{I} \boldsymbol{V} \)
A \( . I>I I>I I I>I V \)
В . \( I>I I>I V>I I I \)
c. \( I>I I I>I I>I V \)
D. \( I>I V>I I I>I I \)
1
Subject: Maths
If \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left(\frac{\sin ^{m} x}{\sin ^{n} x}\right)^{m+n} \cdot\left(\frac{\sin ^{n} x}{\sin ^{p} x}\right)^{n+p} \cdot\left(\frac{\sin ^{p} x}{\sin ^{m} x}\right) \)
then \( f^{\prime}(x) \) is equal to
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( \mathbf{c} \cdot \cos ^{m+n+p} x \)
D. None of these
Subject: Maths
The foot of the perpendicular from the
point \( \boldsymbol{A}(\mathbf{7}, \mathbf{1 4}, \mathbf{5}) \) to the plane \( \mathbf{2} \boldsymbol{x}+\mathbf{4} \boldsymbol{y}- \)
\( z=2 \) is?
A. (3,1,8)
в. (1,2,8)
c. (3,-3,5)
D. (5,-3,-4)
Subject: Chemistry
HCOOH\( \frac{\operatorname{conc} \boldsymbol{H}_{2} \boldsymbol{S O}_{4}}{\mathbf{3 7 3 K}} \boldsymbol{A}+\boldsymbol{B}, \) then
identify the incorrect statement
regarding \( B ? \)
A. It act as a \( \pi \) -acceptor ligand in coordinates compounds
B. It acts as a reducing agent
\( \mathrm{C} \). It is almost water insoluble gas
D. It is failed to reduce an aqueous \( P d C I_{2} \) solution to metallic \( P d \)
Subject: Chemistry
Assertion
Helium shows only positive deviation from ideal behaviour at room
temperature.
Reason
Helium is an inert gas.
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
What are the average distance and the most probable distance of an electron from the nucleus in the 1 s orbital of a
hydrogen atom? \( \left(a_{0}= \) the radius of the \right. first Bohr orbit)
A \( .1 .5 a_{0} \) and \( a_{0} \)
B. \( a_{0} \) and \( 5 a_{0} \)
c. \( 1.5 a_{0} \) and \( 0.5 a_{0} \)
\( \mathbf{D} \cdot a_{0} \) and \( 0.5 a_{0} \)
Subject: Physics
Assume that the nuclear binding energy
per nuclear \( (B / A) \) versus mass
number \( (A) \) as shown in the figure. Use
this plot to choose the correct choice \( (s) \)
given below.
A. Fusion of two nuclei with mass number lying in the range of \( 51<A<100 \) will release energy
B. Fission of a nucleus lying in the mass range of \( 200< \) \( A<260 \) will release energy when broken into two
equal fragments
c. Both (a) and (b)
D. None of the above
Subject: Maths
For \( \frac{\boldsymbol{x}^{\mathbf{3}}+\mathbf{2} \boldsymbol{x}+\mathbf{1}}{\mathbf{5}}-\frac{\mathbf{7}}{\mathbf{2}} \boldsymbol{x}^{2}-\boldsymbol{x}^{\mathbf{6}}, \) write
i) the degree of the polynomial
ii) the coefficient of \( x^{3} \)
iii) the coefficient of \( x^{6} \)
iv) the constant term
Subject: Chemistry
In an estimation of sulphur by Carius method, 0.234 g of an organic sulphur compound afforded 0.334 g of \( B a S O_{4} \) Find the percentage of Sulphur in the compound.
A . \( 12.28 \% \)
B. 19.60\%
c. \( 15.96 \% \)
D . 23.67\%
Subject: Maths
ff \( f(x+y)=f(x y) \) for all \( x, y, \in R, \) and
\( \boldsymbol{f}(\mathbf{2 0 0 3})=\mathbf{2 0 0 3}, \) then \( \boldsymbol{f}(\mathbf{2 0 0 0}) \) equals
A . 2003
B.
c. -2003
D. none of these
Subject: Maths
Two parallel chords \( A B \) and \( C D \) are 3.9
cm apart and lie on opposite sides of the centre of a circle. If \( A B=1.4 \mathrm{cm} \)
and \( C D=4 \mathrm{cm}, \) find the radius of the
circle.
A. \( 3 \mathrm{cm} \)
B. \( 3.2 \mathrm{cm} \)
\( c .2 .3 \mathrm{cm} \)
D. \( 2 \mathrm{cm} \)
Subject: Maths
For an ellipse with axes are coordinate axes, \( A \) and \( L \) are the ends of major axis and latusrectum respectively. Area of \( \triangle O A L=8 s q . \) units and, \( e=\frac{1}{\sqrt{2}}, \) then
equation of the ellipse is:
\( ^{\text {A }} \cdot \frac{x^{2}}{16}+\frac{y^{2}}{8}=1 \)
B. \( \frac{x^{2}}{32}+\frac{y^{2}}{16}=1 \)
c. \( \frac{x^{2}}{64}+\frac{y^{2}}{32}=1 \)
D. \( \frac{x^{2}}{8}+\frac{y^{2}}{4}=1 \)
Subject: Physics
In an a.c. circuit, the instantaneous
e.m.f. and current are given by \( e= \) \( \mathbf{1 0 0} \sin \mathbf{3 0} t, \boldsymbol{i}=\mathbf{2 0} \sin \left(\mathbf{3 0} \boldsymbol{t}-\frac{\boldsymbol{\pi}}{\mathbf{4}}\right) . \) In one
cycle of a.c., the average power consumed by the circuit and the wattles current are, respectively.
A \( \cdot \frac{50}{\sqrt{2}}, 0 \)
в. 50,0
c. 50,10
D. \( \frac{1000}{\sqrt{2}}, 10 \)